TOWARDS DAMAGE-FREE MICRO-FABRICATION OF SILICON SUBSTRATES USING A HYBRID LASER-WATERJET TECHNOLOGY
by
VIBOON TANGWARODOMNUKUN B.Eng.(1st Hons), M.Eng.
A thesis submitted to the University of New South Wales in fulfillment of the requirements for the degree of Doctor of Philosophy
School of Mechanical and Manufacturing Engineering The University of New South Wales
February 2012 PLEASE TYPE THE UNIVERSITY OF NEW SOUTH WALES Thesis/Dissertation Sheet
Surname or Family name: Tangwarodomnukun
First name: Viboon Other name/s:
Abbreviation for degree as given in the University calendar: PhD
School: Mechanical and Manufacturing Engineering Faculty: Engineering
Title: Towards Damage-Free Micro-Fabrication of Silicon Substrates Using a Hybrid Laser-Waterjet Technology
Abstract 350 words maximum: (PLEASE TYPE)
A novel hybrid laser-waterjet machining technology is developed in this thesis using a new material removal concept to achieve near damage-free micromachining. Using this concept, a laser is used to heat and soften the material while a waterjet is used to expel and remove the laser-softened material in a layer by layer manner, so that material is removed in its solid-state below its melting temperature. Water also takes a cooling action. An experimental rig has been built to realize this novel concept and an extensive experimental investigation has been carried out to understand the process and the effect of various parameters on the process using a single-crystalline silicon as the specimen material. It has been found that near free of heat-affected zone and high material removal rate can be achieved when using this hybrid laser-waterjet technology, as compared to the dry laser micromachining process. Specifically, a laser Raman spectroscopy study has found that a much thinner amorphous layer within 40 nm was formed than that found in the dry laser machining process.
In order to understand the coupled effect of laser and waterjet on the material removal process and to predict and control the process on a mathematical and quantitative basis, a temperature-field model has been developed whereby a model for the dry laser machining process is developed first before it is extended to the hybrid laser- waterjet process incorporating the waterjet cooling and expelling effects. The parabolic heat conduction associated with enthalpy method is numerically solved by using an explicit finite difference scheme for predicting the two- dimensional temperature field. The thermal model has been verified by comparing the predicted temperatures with the temperatures measured by an infrared camera. The simulated groove depths are also compared with the experimental data under the corresponding conditions and it is found that they are in good agreement. A simulation study of the hybrid laser-waterjet process is finally reported which provides an in-depth understanding of the material removal process and mechanisms and the interaction between laser, waterjet and material under the coupled effect of laser heating and waterjet cooling and expelling.
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I hereby grant the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation.
I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstract International (this is applicable to doctoral theses only).
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iv Abstract
A comprehensive literature review on laser physics, the underlying science and models in laser machining as well as other novel machining technologies using lasers has been carried out. It is shown that while laser micomachining is the preferred technology in industry, damage-free micromachining of difficult-to-cut materials is still one of the most challenging technologies for processing micro-structures accurately with little or no damage induced by the process. A novel hybrid laser-waterjet micromachining technology is developed in this thesis using a new material removal concept to minimize the thermal damage that normally occurs in traditional laser machining processes. Using this concept, a laser is used to heat and soften the material while a waterjet is used to expel and remove the laser- softened material in an element to element (or layer by layer) manner. Water also takes a cooling action. In this way, the material is removed in its solid-state below its melting temperature. As a result, less laser-work interaction time may be required which gives the potential to increase the material removal rate. An experimental rig has been built to realize this novel concept and an extensive experimental investigation has been carried out to understand the process and the effect of various parameters on the process using a single-crystalline silicon as the specimen material. It has been found that near free of heat-affected zone (HAZ) and high material removal rate can be achieved when using this hybrid laser-waterjet technology, as compared to the dry laser micromachining process. However, the overlap of laser beam with the waterjet has been found to markedly decrease the laser fluence and the cut quality, so that it is recommended to place the laser beam just outside the intersection of the waterjet with the work surface. Plausible trends of the machining performance with respect to the process parameters have been found. It is shown that groove width, depth and HAZ size increase with an increase in laser pulse energy and pulse overlap, while
v ABSTRACT
focal plane position and waterjet offset distance have to be properly selected for a high ablation performance. Moreover, the groove width and depth increase with an increase in water pressure and waterjet impact angle, while the effect of these parameters on HAZ is not significant. Surface and subsurface damage of silicon in terms of material micro-structural changes has been investigated by using a laser Raman spectroscopy analysis to determine the crystallinity of silicon and the amorphous layer thickness formed after the ablation. When silicon was ablated by the new process, a much thinner amorphous layer within 40 nm was formed than that found in the dry laser machining process. The effects of laser pulse energy, pulse overlap and water pressure on the amorphous layer thickness and the material crystallinity on the cut surfaces and subsurfaces have been analyzed and discussed. It is found that low laser pulse energy, low pulse overlap and high water pressure can significantly reduce the damaged layer thickness. In order to understand the coupled effect of laser and waterjet on the material removal process and to predict and control the process on a mathematical and quantitative basis, a temperature-field model is developed whereby a model for the dry laser machining process is developed first before it is extended to the hybrid laser- waterjet process incorporating the waterjet cooling and expelling effects. The parabolic heat conduction associated with the enthalpy method is numerically solved by using an explicit finite difference scheme for predicting the two-dimensional temperature field. The thermal model has been verified by comparing the predicted temperatures with the temperatures measured by an infrared camera. The simulated groove depths are also compared with the experimental data under corresponding conditions and it is found that they are in good agreement. A simulation study of the hybrid laser-waterjet process is finally reported which provides an in-depth understanding of the material removal process and mechanisms and the interaction between laser, waterjet and material under the coupled effect of laser heating and waterjet cooling and expelling.
Keywords: Hybrid laser-waterjet process; Laser; Waterjet; Micromachining; Silicon wafer; Heat transfer; Finite difference method; Damage-free machining
vi Acknowledgements
I would like to thank many people who provided great support and had an important role in this project. First of all, I wish to express my gratitude to my supervisor, Professor Jun Wang, for his continuous support and valuable guidance throughout this project. I am deeply thankful to my co-supervisor, Associate Professor Philip Mathew, for his constructive advice. My thanks also go to Dr Yasser Ali for his useful suggestions in the early stage of the project.
I gratefully acknowledge receiving helpful assistance from Associate Professor Gary Rosengarten and Mr Alexander Litvak. My appreciation is also expressed to Mr John Barron, Mr Seetha Mahadevan and Mr Ian Cassapi for their technical support.
Special acknowledgements are extended to the University of New South Wales for a full-scholarship through the University International Postgraduate Award, and to the Australian Research Council (ARC) for financial support under the Discovery-Projects scheme.
Last but not least, I wish to profoundly thank my mother for her unconditional love and limitless support. Without her encouragement, I would not have been able to overcome many challenges and eventually complete this thesis.
I would also like to take this opportunity to dedicate this thesis to my late father who cherished a fervent hope for my future.
vii Contents
Originality Statement ii Copyright Statement and Authenticity Statement iii Abstract v Acknowledgements vii Contents viii List of Figures xiii List of Tables xxi Nomenclature xxii
1 INTRODUCTION 1 1.1 Statement of Problems 1 1.2 Objectives of the Research 3 1.3 Thesis Outline 3
2 LITERATURE REVIEW 5 2.1 Introduction 5 2.2 Fundamentals of Laser Technology 6 2.2.1 Laser Generation Mechanism 6 2.2.2 Types of Lasers 7 2.2.3 Laser Beam Properties 8 2.3 Laser Micromachining and Damage Mechanisms 11 2.3.1 Laser Micro-Drilling 12 2.3.2 Laser Micro-Cutting and Grooving 16 2.4 Novel Laser Micromachining Processes 18
viii CONTENTS
2.4.1 Short Pulsed Laser Machining 19 2.4.2 Liquid-Assisted Laser Machining 20 2.4.2.1 Underwater Laser Machining 21 2.4.2.2 Waterjet-Guided Laser Machining 26 2.4.2.3 Liquid-Assisted Front Side Laser Machining 29 2.5 Modeling of Laser Machining Process 33 2.5.1 Empirical Approach 34 2.5.2 Analytical Approach 35 2.5.3 Numerical Approach 39 2.6 Waterjet Impinging Mechanisms and Models 43 2.6.1 Effects of Waterjet Cooling on the Flat Surface 44 2.6.2 Effects of Waterjet Impact on the Flat Surface 49 2.7 Concluding Remarks 54
3 EXPERIMENTAL STUDY OF HYBRID LASER-WATERJET MICROMACHINING OF SILICON 57 3.1 Introduction 57 3.2 The Technology and Its Experimental Apparatus 58 3.3 Experimental Design and Setup 61 3.4 Interactions of Laser Beam and Waterjet 65 3.5 Comparison with the Conventional Dry Laser Machining 68 3.6 Effects of Process Parameters on the Groove Width 70 3.6.1 Statistical Analysis 70 3.6.2 The Effect of Laser Pulse Energy 71 3.6.3 The Effect of Focal Plane Position 72 3.6.4 The Effect of Laser Pulse Overlap 74 3.6.5 The Effect of Waterjet Offset Distance 75 3.6.6 The Effect of Water Pressure 78 3.6.7 The Effect of Waterjet Impact Angle 78 3.7 Effects of Process Parameters on the Groove Depth 80 3.7.1 Statistical Analysis 80 3.7.2 The Effect of Laser Pulse Energy 81 3.7.3 The Effect of Focal Plane Position 82
ix CONTENTS
3.7.4 The Effect of Laser Pulse Overlap 83 3.7.5 The Effect of Waterjet Offset Distance 84 3.7.6 The Effect of Water Pressure 85 3.7.7 The Effect of Waterjet Impact Angle 86 3.8 Effects of Process Parameters on the HAZ Width 87 3.8.1 Statistical Analysis 87 3.8.2 The Effect of Laser Pulse Energy 88 3.8.3 The Effect of Focal Plane Position 89 3.8.4 The Effect of Laser Pulse Overlap 90 3.8.5 The Effect of Waterjet Offset Distance 91 3.8.6 The Effect of Water Pressure 93 3.8.7 The Effect of Waterjet Impact Angle 94 3.9 Concluding Remarks 95
4 SUBSURFACE DAMAGES IN SILICON CAUSED BY THE HYBRID LASER-WATERJET PROCESS 97 4.1 Introduction 97 4.2 Experiment 99 4.3 Evaluation of Experimental Data 100 4.4 Results and Discussion 104 4.4.1 Comparison of Subsurface Damages Caused by Dry and Hybrid Processes 105 4.4.2 Effect of Laser Pulse Energy 107 4.4.3 Effect of Laser Pulse Overlap 109 4.4.4 Effect of Water Pressure 111 4.5 Concluding Remarks 113
5 DEVELOPMENT OF TEMPERATURE FIELD MODEL FOR CONVENTIONAL DRY LASER MACHINING 115 5.1 Introduction 115 5.2 Temperature Field Model Formulation 116 5.2.1 Governing Equations 116 5.2.2 Assumptions and Boundary Conditions 117
x CONTENTS
5.2.3 Discretization Using Finite Difference Method 119 5.2.4 Laser Heating and Pulse Shape Functions 123 5.2.5 Silicon Properties 127 5.3 Assessment of the Temperature Field Model 130 5.3.1 Setup for Temperature Measurement 130 5.3.2 Comparison of Measured and Simulated Temperature Profiles 132 5.3.3 Comparison of Experimental and Simulated Groove Characteristics 139 5.3.4 Laser Heating and Ablation Process 143 5.4 Concluding Remarks 146
6 MODELING OF TEMPERATURE FIELD AND GROOVE CHARACTERISTICS IN HYBRID LASER-WATERJET MICROGROOVING OF SILICON 147 6.1 Introduction 147 6.2 Temperature Field Model Formulation 148 6.2.1 Finite Difference Model for Laser Heating 148 6.2.2 Waterjet Cooling Effect and Heat Losses 150 6.2.3 Waterjet Impingement and the Maximum Shear Stress 153 6.3 Model Assessment 160 6.3.1 Setup for Temperature Measurement 161 6.3.2 Comparison of Measured and Simulated Temperature Profiles 162 6.4 Simulation of Groove Characteristics 165 6.4.1 Simulation Conditions 165 6.4.2 Comparison of Experimental and Simulated Results 167 6.5 Heating and Ablation Process in Hybrid Laser-Waterjet Machining 170 6.6 Concluding Remarks 176
7 FINAL CONCLUSIONS AND FUTURE WORK 178 7.1 Final Conclusions 178 7.2 Proposed Future Work 181
REFERENCES 183
xi CONTENTS
APPENDIXES Appendix A Technical Data of Nanosecond Fiber Laser A-1 Appendix B Experimental Results of Hybrid Laser-Waterjet Machining of Silicon B-1 Appendix C Temperature Measurement Data Obtained from an Infrared Camera C-1 Appendix D Experimental Results of Dry Laser Machining of Silicon D-1 Appendix E MATLAB Codes for Simulation Using Finite Difference Method E-1
xii List of Figures
Figure 2.1. Laser beam generation 7 Figure 2.2. Schematic of Gaussian beam profile and beam diameters 10 Figure 2.3. Absorption coefficient for silicon at 300K 12 Figure 2.4. Laser ablation mechanisms 14 Figure 2.5. Ablation mechanism for laser grooving 16 Figure 2.6. Laser-induced damages along the cut surface 17 Figure 2.7. Absorption length of pure water at 298 K against the different wavelengths of light 22 Figure 2.8. Different types of underwater laser machining: (a) top-opened liquid container type, (b) gas-assisted underwater type and (c) closed chamber type 25 Figure 2.9. Waterjet-guided laser process 26 Figure 2.10. Water-laser machine tool of Kuykendal’s design 28 Figure 2.11. Liquid-assisted front side method: (a) vertical thin film method and (b) liquid or vapor spray-induced thin film method 29 Figure 2.12. Off-axial waterjet-assisted laser machining 31 Figure 2.13. Waterjet-assisted laser machining (Klingel’s design) 32 Figure 2.14. Waterjet-assisted front side laser cutting (Gangemi’s designs) 33 Figure 2.15. Schematic of a free-surface liquid jet impingement 46 Figure 2.16. Inclination angles in oblique liquid jet impingement 47 Figure 2.17. Maximum heat transfer position shifted to the upstream side 47 Figure 2.18. Structure of a waterjet beam 49 Figure 2.19. A long rod impacts against a solid target 50 Figure 2.20. Process of a single droplet impact 53
xiii LIST OF FIGURES
Figure 3.1. The laser machine structures 60 Figure 3.2. The hybrid laser-waterjet cutting head 61 Figure 3.3. Setting parameters in the hybrid laser-waterjet micromachining process 61 Figure 3.4. The experimental setup of the hybrid laser-waterjet micromachining 64 Figure 3.5. The measurement of groove geometries 64 Figure 3.6. Idealized relationship between waterjet and laser beam under different waterjet offset distances: (a) non-overlap, and (b) overlap 65 Figure 3.7. The water layer thickness formed in the hybrid process 66
Figure 3.8. (a) Waterjet impact angle versus water layer thickness (hw) at different waterjet offset distances, and (b) major diameter of
waterjet impact area (dimp,major) 67 Figure 3.9. The laser-waterjet overlap inside the groove 67 Figure 3.10. The surface characteristics of silicon after dry and hybrid machining when the laser pulse energies of 0.3 mJ to 0.6 mJ and the pulse overlaps of 99.3% to 99.9% were used (focal plane position=0 mm, waterjet offset distance=0.4 mm, water pressure=10 MPa and waterjet impact angle=40°) 68 Figure 3.11. The surface characteristics of silicon after machining (focal plane position=0 mm, pulse overlap=99.9%, waterjet offset distance=0.6 mm, and waterjet impact angle=40o) 70 Figure 3.12. Residual plots for groove width 71 Figure 3.13. The effect of laser pulse energy on groove width 72 Figure 3.14. The effect of focal plane position on groove width 72 Figure 3.15. The effects of focal plane position on: (a) laser beam diameter at the top workpiece surface and (b) the laser energy density under different laser pulse energies 73 Figure 3.16. The effect of laser energy density on groove width 74
xiv LIST OF FIGURES
Figure 3.17. The surface characteristics of silicon after hybrid laser-waterjet machining when laser pulse energies of 0.3 mJ to 0.6 mJ and focal plane positions of 0 mm and -0.6 mm were used (pulse overlap=99.9%, waterjet offset distance=0.6 mm, water pressure=10 MPa and waterjet impact angle=40°) 74 Figure 3.18. The effects of laser pulse overlap on groove width 75 Figure 3.19. The effects of waterjet offset distance on groove width 76 Figure 3.20. The surface characteristics of silicon after hybrid machining when laser pulse overlaps of 99.3% to 99.9% and waterjet offset distances of 0 mm to 0.6 mm were used (laser pulse energy=0.3 mJ, focal plane position=0 mm, water pressure=10 MPa and waterjet impact angle=40°) 77 Figure 3.21. The effect of water pressure on groove width 78 Figure 3.22. The effects of waterjet impact angle on groove width 79 Figure 3.23. The surface characteristics of silicon after hybrid machining when water pressures of 5 MPa to 20 MPa and waterjet impact angles of 30° to 60° were used (laser pulse energy=0.6 mJ, focal plane position=0 mm, pulse overlap=99.9% and waterjet offset distance=0.4 mm) 79 Figure 3.24. Residual plots for groove depth 81 Figure 3.25. The effect of laser pulse energy on groove depth 82 Figure 3.26. The effects of focal plane position on groove depth 83 Figure 3.27. The effects of laser pulse overlap on groove depth 84 Figure 3.28. The effects of waterjet offset distance on groove depth 85 Figure 3.29. The effect of water pressure on groove depth 85 Figure 3.30. Characteristics of water after the impact under different pressures 86 Figure 3.31. The effects of waterjet impact angle on groove depth 87 Figure 3.32. Residual plots for HAZ width 88 Figure 3.33. The effect of laser pulse energy on HAZ width 89 Figure 3.34. The effects of focal plane position on HAZ width 90 Figure 3.35. The effects of laser pulse overlap on HAZ width 91 Figure 3.36. The effects of waterjet offset distance on HAZ width 92
xv LIST OF FIGURES
Figure 3.37. The surface characteristics of silicon after hybrid machining when waterjet offset distances of 0 mm to 0.6 mm and focal plane positions of 0 to -0.6 mm were used (laser pulse energy=0.6 mJ, pulse overlap=99.9%, water pressure=10 MPa and waterjet impact angle=40°) 92 Figure 3.38. The effects of water pressure on: (a) HAZ width and (b) the ratio of HAZ to groove width 94 Figure 3.39. The effects of waterjet impact angle on HAZ width 95 Figure 4.1. Pressure-temperature phase diagram of silicon 98 Figure 4.2. The measured positions for the laser Raman testing 100 Figure 4.3. The typical Raman spectrum of silicon after machining 101 Figure 4.4. Schematic of Raman scattering in amorphous and crystalline layers 101 Figure 4.5. The heights and the half-power bandwidths of the amorphous and the crystalline peaks 103 Figure 4.6. The Raman spectrum of c-Si wafer before machining 105 Figure 4.7. The Raman spectra of samples from the dry, hybrid processes and an unmachined c-Si sample 106 Figure 4.8. Comparisons of Raman intensity ration (r) and amorphous layer
thickness (da) for samples machined by dry laser and hybrid laser-waterjet processes, and unmachined c-Si samples (showing
zero r and da) 107 Figure 4.9. The comparison of Raman crystallinity factor for samples machined by dry laser and hybrid laser-waterjet processes and an unmachined c-Si sample 107 Figure 4.10. The Raman spectra for different laser pulse energies: (a) 0.3 mJ, (b) 0.4 mJ, (c) 0.5 mJ and (c) 0.6 mJ (focal plane position=0 mm, pulse overlap=99.9%, waterjet offset distance=0.4 mm, water pressure=10 MPa and waterjet impact angle=40°) 108 Figure 4.11. The effect of laser pulse energy on: (a) the calculated amorphous layer thickness and (b) the Raman crystallinity factor 109
xvi LIST OF FIGURES
Figure 4.12. The Raman spectra for different laser pulse overlaps: (a) 99.3%, (b) 99.5%, (c) 99.7% and (d) 99.9%. (laser pulse energy=0.6 mJ, focal plane position=0 mm, waterjet offset distance=0.4 mm, water pressure=10 MPa and waterjet impact angle=40°) 110 Figure 4.13. The relationships between laser pulse overlap and: (a) the calculated amorphous layer thickness and (b) the Raman crystallinity factor 111 Figure 4.14. The Raman spectra for different water pressures: (a) 5 MPa, (b) 10 MPa, (c) 15 MPa and (d) 20 MPa (laser pulse energy=0.6 mJ, focal plane position=0 mm, pulse overlap=99.9%, waterjet offset distance=0.4 mm and waterjet impact angle=40°) 112 Figure 4.15. The relationships between water pressure and: (a) the calculated amorphous layer thickness and (b) the Raman crystallinity factor 113 Figure 5.1. Boundary conditions for a 2-D semi-infinite heat transfer model 119 Figure 5.2. Grid points on x and z axis 120 Figure 5.3. Laser pulse shape in the space and time domains 124
Figure 5.4. Moving laser heat source at a cross-section at position yp 125 Figure 5.5. The change of laser-irradiated position in the dry laser ablation 127 Figure 5.6. Temperature-dependent silicon properties 129 Figure 5.7. Laser beam moving across the workpiece edge for temperature measurement at the cross-sectional surface: (a) start, (b) measured and (c) stop positions 131 Figure 5.8. Micrograph of silicon wafer captured by the infrared camera 131 Figure 5.9. Temperature profiles measured by an infrared camera under different laser pulse energies (laser pulse frequency=20 kHz, focal plane position=0 mm and traverse speed=10 mm/s) 132 Figure 5.10. Temperature profiles measured by an infrared camera under different laser focal plane positions (laser pulse energy=0.8 mJ, pulse frequency=20 kHz and traverse speed=10 mm/s) 133 Figure 5.11. Temperature profiles measured by an infrared camera under different laser traverse speeds (laser pulse energy=0.8 mJ, pulse frequency=20 kHz and focal plane position=0 mm) 133
xvii LIST OF FIGURES
Figure 5.12. Temperature profiles measured by an infrared camera at 30 ȝm from the laser axis under different laser pulse energies, focal plane positions and traverse speeds 134 Figure 5.13. The simulated temperature profiles for constant and temperature- dependent silicon properties at the cutting front (laser pulse energy=0.6 mJ, pulse frequency=20 kHz, focal plane position=0 mm and traverse speed=10 mm/s) 136 Figure 5.14. The simulated temperature profiles for constant and temperature- dependent properties at the laser axis (laser pulse energy=0.6 mJ, pulse frequency=20 kHz, focal plane position=0 mm and traverse speed=10 mm/s) 137 Figure 5.15. The comparison of simulated and measured temperature profiles at 30 ȝm from the laser axis under different laser pulse energies (laser pulse frequency=20 kHz, focal plane position=0 mm and traverse speed=10 mm/s) 137 Figure 5.16. The comparison of simulated and measured temperature profiles at 30 ȝm from the laser axis under different laser focal plane positions (laser pulse energy=0.8 mJ, pulse frequency=20 kHz and traverse speed=10 mm/s) 138 Figure 5.17. The comparison of simulated and measured temperature profiles at 30 ȝm from the laser axis under different laser traverse speeds (laser pulse energy=0.8 mJ, pulse frequency=20 kHz and focal plane position=0 mm) 139 Figure 5.18. The experimental and the simulated groove depths of dry laser grooving at different laser pulse energies, focal plane positions and traverse speeds (pulse frequency=20 kHz) 140 Figure 5.19. The simulated groove profiles of dry laser grooving at different laser pulse energies (laser pulse frequency=20 kHz, focal plane position=0 mm and traverse speed=10 mm/s) 141 Figure 5.20. The simulated groove profiles of dry laser grooving at different laser focal plane positions (laser pulse energy=0.8 mJ, pulse frequency=20 kHz and traverse speed=10 mm/s) 142
xviii LIST OF FIGURES
Figure 5.21. The simulated groove profiles of dry laser grooving at different laser traverse speeds (laser pulse energy=0.8 mJ, pulse frequency=20 kHz and focal plane position=0 mm) 143 Figure 5.22. The simulated temperature fields and ablation depths for the first three pulses of dry laser drilling when the temperature-dependent silicon properties are used (laser pulse energy=0.8 mJ, focal plane position=0 mm, laser pulse frequency=20 kHz, laser pulse duration=42 ns) 144 Figure 5.23. Work temperature variation with time and laser pulses under different laser pulse energies 145
Figure 6.1. Boundary conditions for a 2-D symmetric semi-infinite model at yp 150 Figure 6.2. Schematic of a waterjet impact on a target surface for cooling 151 Figure 6.3. The effect of water pressure on heat transfer coefficient 153 Figure 6.4. Schematic of waterjet impingement in the hybrid process 154 Figure 6.5. Cross-sectional and elliptic impact areas of waterjet 156 Figure 6.6. Mohr’s circle and free-body diagrams for a waterjet impacted work element 157 Figure 6.7. The effect of waterjet impact angle on the maximum shear stress factor according to Equation 6.28 158 Figure 6.8. Mechanical strengths of silicon 158 Figure 6.9. Flow diagram for simulation of the hybrid laser-waterjet machining process 160 Figure 6.10. Setup for measuring the back surface temperature of silicon 161 Figure 6.11. Thermal images of silicon back surface under different laser pulse energies and water pressures (focal plane position=0 mm, pulse overlap=99.3%, waterjet offset distance=0.4 mm and waterjet impact angle=40°) 162 Figure 6.12. Simulated temperature profiles at the cutting front under different laser pulse energies and water pressures (focal plane position=0 mm, pulse overlap=99.3%, waterjet offset distance=0.4 mm and waterjet impact angle=40°) 163
xix LIST OF FIGURES
Figure 6.13. Comparison of measured and simulated temperatures at silicon back surface under different laser pulse energies, pulse overlaps and water pressures (focal plane position=0 mm, waterjet offset distance=0.4 mm and waterjet impact angle=40°) 164 Figure 6.14. The relationship between time step, water pressure and work temperature 166 Figure 6.15. The simulated and experimental groove depths under different laser pulse energies 167 Figure 6.16. The simulated and experimental groove depths under different laser pulse overlaps 168 Figure 6.17. The simulated and experimental groove depths under different water pressures 169 Figure 6.18. The comparison of simulated and experimental groove profiles under: (a) 5 MPa, (b) 10 MPa, (c) 15 MPa and (d) 20 MPa water pressures 170 Figure 6.19. Temperatures and groove profiles at different times (laser pulse energy=0.3 mJ, focal plane position=0 mm, pulse overlap=99.9%, waterjet offset distance=0.4 mm, water pressure=20 MPa and waterjet impact angle=40°) 171 Figure 6.20. Temperatures and groove profiles at different times (laser pulse energy=0.6 mJ, focal plane position=0 mm, pulse overlap=99.9%, waterjet offset distance=0.4 mm, water pressure=20 MPa and waterjet impact angle=40°) 173 Figure 6.21. Temperature threshold for silicon removal in the hybrid process 174 Figure 6.22. The maximum workpiece temperature versus time under different laser pulse energies and water pressures: (a) 5 MPa and (b) 20 MPa (focal plane position=0 mm, pulse overlap=99.9%, waterjet offset distance=0.4 mm and waterjet impact angle=40°) 176
xx List of Tables
Table 2.1. The coefficients used in Equation 2.25 45 Table 2.2. The coefficients for each nozzle diameter in Equation 2.30 48 Table 3.1. Silicon material properties 62 Table 3.2. Parameters used in the first set of experiments 63 Table 3.3. Parameters used in the second set of experiments 63 Table 3.4. Analysis of variance for groove width 71 Table 3.5. Analysis of variance for groove depth 81 Table 3.6. Analysis of variance for HAZ width 88 Table 4.1. Conditions examined in the subsurface damage investigation 99 Table 5.1. Constant thermal and optical properties of silicon 128 Table 5.2. Temperature-dependent properties of silicon 128 Table 5.3. Parameters used in the temperature measurement 130 Table 6.1. Thermal and optical properties of water 152 Table 6.2. Parameters used for measuring the silicon temperature in the hybrid process 161 Table 6.3. Parameters used for the hybrid laser-waterjet grooving simulation 166
xxi Nomenclature
Ab Absorption coefficient
Abw Absorption coefficient of water
Ah Heat source area
Aimp Waterjet impacted area
Aj Cross-sectional area of waterjet beam
Al Projected area of laser beam cp Heat capacity at constant pressure cpw Heat capacity of water
Css Shock wave velocity in solid material
Csw Shock wave velocity in water
Cw Sound velocity in water da Amorphous layer thickness da-limit Maximum sensing depth of amorphous phase df Focused laser beam diameter dimp Impact diameter on target surface dj Waterjet diameter dn Nozzle diameter dz Gaussian beam diameter at z distance from the focused position D Maximum sensing depth of Raman measurement
Dg Groove depth
Di Laser beam diameter projecting on a focusing lens E Energy
Edth Damage threshold
Ek Kinetic energy
xxii NOMENCLATURE
Ep Laser pulse energy
Ev Threshold energy for vaporization f Frequency
Fimp Impact force
Fl Focal length of lens fpp Focal plane position
Gh Heat generation h Heat transfer coefficient h0 Heat transfer coefficient on stagnation region hb Heat transfer coefficient at boiling point hw Water layer thickness H Specific enthalpy
Hl Laser heat source
HR Radiation heat loss I Laser beam intensity
I0 Laser beam intensity at center position
I0w Light intensity above water layer
Ihw Light intensity after distance hw
Isa Raman scattered light intensity induced by amorphous phase
Isc Raman scattered light intensity induced by crystalline phase k Thermal conductivity kf Thermal conductivity of fluid kp Laser pulse shape coefficient kw Thermal conductivity of water la Light absorption length
Lc Characteristic length
Lm Latent heat of melting
Ln Nozzle length
Lv Latent heat of vaporization mr Amount of material removed M2 Laser beam quality factor Nu Nusselt number
Nu0 Nusselt number at stagnation point
xxiii NOMENCLATURE
Nuavg Averaged Nusselt number
Nuloc Local Nusselt number P Laser power
Ph Water hammer pressure
Pimp Impact pressure
Pwj Waterjet pressure Pe Peclet number Pr Prandtl number PO Laser pulse overlap r Raman intensity ratio
Rf Reflectivity
Rfw Reflectivity of water Ra Arithmetic mean roughness Re Reynolds number s0 Distance from stagnation point t Time T Temperature
T0 Initial temperature
Tm Melting temperature
Ts Surface temperature
Tsur Surrounding temperature
Tv Boiling temperature v Velocity vcrit Critical velocity vd Liquid-drop impact velocity vj Liquid jet velocity vjavg Average liquid jet velocity vt Traverse speed vw Wave propagation speed V Volume wk Kerf width x Cartesian system coordinate xwl Waterjet offset distance
xxiv NOMENCLATURE
Xc Crystalline volume fraction y Cartesian system coordinate z Cartesian system coordinate zi Non-intersectional depth znt Nozzle-to-target distance or stand-off distance zR Rayleigh length
Į Thermal diffusivity
Įa Absorption coefficient of amorphous phase
Įc Absorption coefficient of crystalline phase
Įj Waterjet beam divergence angle ȕ Coefficient for correcting boundary nodes Ȗ Stability of explicit finite difference method į Boundary layer thickness of HAZ İ Emissivity Ș Coefficient for correcting fictitious nodes ș Inclination angle
șd Waterjet beam divergence
șj Waterjet impact angle
șls Turning angle of lead screw for changing waterjet offset distance Ȝ Light wavelength ȝ Dynamic viscosity Ȟ Kinematic viscosity
ȞR Raman shift ȟ Maximum shear stress factor ȡ Density
ȡs Solid density
ȡw Water density
ısa Scattering coefficient of amorphous phase
ısb Stefan-Boltzmann’s constant
ısc Scattering coefficient of crystalline phase
ız Normal tensile stress IJ Laser pulse duration
xxv NOMENCLATURE
IJm Shear strength of work material
IJtotal Total pulse width
IJxz Shear stress ij Inclination angle
ijj Azimuthal angle of liquid jet impingement
ijn Waterjet nozzle coefficient
c Raman crystallinity factor
Ȥwj Geometrical characteristic factor of waterjet Ȧ Laser pulse shape function
Ȧkp Laser pulsing factor ∇ Gradient
Abbreviations
ADE Alternating direction explicit ADI Alternating direction implicit DOF Depth of focus FDM Finite difference method FEM Finite element method FVM Finite volume method FTCS Forward-time central space FWHM Full width at half maximum HAZ Heat-affected zone TEM Transverse electromagnetic mode
xxvi Chapter 1
Introduction
With the fast growth of the semiconductor and electronic industries, the need for smaller devices with higher effectiveness drives the electronic technologies to another level to manufacture miniature components. An example of this development can be seen in the evolution of central processing units or CPUs of personal computers, where millions of transistors are deposited on a tiny integrated-circuit chip and the number of transistors continues to increase greatly. From a manufacturing point of view, the smaller the transistors can be fabricated, the more number of transistors can be added into a substrate wafer in an attempt to introduce higher computing performance. Moreover, micro-component fabrication can be seen in many other fields such as micro- electro-mechanical system (MEMS), photovoltaic and biomedical devices. These areas require micro-components with high precision and accuracy to gain the greatest functionality of the devices in their specific applications. Due to the miniature and high- complex structures of the micro-components, traditional manufacturing processes can no longer satisfy the needs for high accuracy and free of damage on the micro and sub- micro structures of the components. The development of damage-free (or near damage free) micro-fabrication processes has thus become more important than ever before.
1.1 Statement of Problems
Even though micro-fabrication has been utilized in many fields of industry with plenty of fabrication methods, its main endeavor is to make small components of high
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quality within a short processing time. Regarding the making of semiconductor and related electronic devices, materials that can provide suitable electrical properties have to be utilized as base materials for micro-fabrication. In the past, germanium (Ge) was mainly used to make the semiconductor components before being replaced by gallium arsenide (GeAs) and silicon (Si). Though the electron mobility of gallium arsenide is better than silicon, it provides lower thermal stability and higher defect density in the bulk material [1]. Silicon has become a famous semi-conductor material widely employed in electronic and other high-density systems. Gower in 2008 [2] stated that semiconductor lithography, flat panel displays and photovoltaic solar cells are currently the three main sectors of micro-fabrication, and the demand of these sectors, particularly solar cells, increases continually and significantly. Grohe et al. in 2006 [3] noticed that the solar cell industry increased by 30-40% from 2001 to 2006. More than 90% of mono- and poly-crystalline silicon has been used in solar cells and other high- density systems where micro-fabrication plays a vital role in their production. The need to develop an appropriate micro-fabrication technology for silicon substrates is thus apparent. Due to the many steps involved in processing conventional photolithography and the slow speed of wet and dry etching processes which can achieve only 1 to 2 μm per minute [1], other faster micro-removal processes, such as mechanical and thermal processes, have become the alternative ways to fabricate the micro-components. However, the mechanical processes, such as grinding, micro-drilling and micro-milling, require a higher cutting force and a stronger cutting tool to remove material in micro scale. Taniguchi [4] and Shaw [5] noted that a decrease in chip thickness increases the resisting shear stress of material significantly. The rapid increase in tool wear rate, residual stress and micro-cracks on cut material surface are the main effects that are hard to avoid, particularly in brittle materials such as silicon. A number of noticeable micro-subtractive processes, such as mechanical sawing, grinding, abrasive jet, chemical etching, electrochemical and laser micromachining, have been used for wafer scribing, dicing, drilling and grooving. Among these processes, laser micromachining as a non-contact material-removal process appears to be more accepted by industry due to its high processing efficiency, and many other advantages such as no tool wear and high accuracy over the other micromachining processes [6-8]. However, traditional laser ablation processes still cause considerable or
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significant damages to the micro-components, such as cracking, heat-affected zone (HAZ), dross, spatter, striation, distortion and phase transformations. Among these damages, the HAZ is an important cause of many subsequent damages and is typically found on the cut and the vicinity area. Such damages become more significant when processing micro-parts where the thermal damages can affect the entire parts. Hence, a new technology using a hybrid laser-waterjet action will be developed in this study to reduce or eliminate this thermal damage in laser ablation.
1.2 Objectives of the Research
This research attempts to minimize the thermal damage while maximizing the material removal rate of laser micromachining. Due to its wide applications, silicon is used as the specimen in this study. Specifically, this project aims to achieve the following objectives: - To develop a hybrid laser-waterjet cutting system incorporating a laser and a waterjet components to robustly perform the hybrid micromachining process. - To understand the effects of process parameters on the groove characteristics, including the interactions of laser, waterjet and silicon, introduced by the hybrid laser-waterjet process. - To investigate the effect of process parameters on the subsurface damage of silicon. - To develop a numerical model by using finite difference method for predicting the temperature-field and the cut profile of silicon in the hybrid laser-waterjet micromachining process.
1.3 Thesis Outline
This thesis is organized into seven chapters. Following this introductory chapter, Chapter 2 provides a detailed review of the conventional and advanced laser micromachining processes and their relevant removal mechanisms with a particular focus on the recent research and developments. The experimental study of the hybrid laser-waterjet micro-grooving process is presented in Chapter 3. Chapter 4 reports a laser Raman spectroscopy study of the surface and subsurface damage of silicon in
3 CHAPTER 1
terms of phase transformations after the hybrid laser-waterjet machining process. The temperature-field model of laser heating is reported in Chapter 5, where the transient heat transfer model associated with the finite difference scheme is taken into consideration in order to numerically predict the temperature and the cut profiles. In Chapter 6, the model for the hybrid laser-waterjet micromachining of silicon is presented by including the effects of waterjet cooling and expelling into the thermal model developed in Chapter 5. The model assessment is also performed by comparing the simulated temperature profiles with the measured data from an experiment using an infrared camera. The comparison of the experimental and the simulated cut profiles is also presented in this chapter. Finally, the main research findings and contributions are concluded in Chapter 7 where recommendations for future research are also given.
4 Chapter 2
Literature Review
2.1 Introduction
Micro- and submicro-fabrication has become a main stream of making electronic components and high density systems. Silicon has been employed as the most commonly used base material for electronic component fabrications. This is because of the properties of silicon that are found to be very useful not only for the semiconductor applications, but also for the functional devices such as silicon solar cells. Though the commercial silicon solar cells made of mono or polycrystalline silicon can produce the energy conversion efficiency of only 17% with a cost of $1.50/watt, the solar cells comprising silicon-based materials still share almost 90% of photovoltaic devices over glass panel and multilevel junctions of composite materials. This is due to the acceptable quality and the relatively low manufacturing costs [2]. In order to fabricate solar cells and many other silicon-based semiconductor components, laser micromachining is a promising subtractive process for drilling, cutting and grooving of silicon in micro and submicro scales. In this chapter, basic laser technology and laser micromachining processes will be reviewed in both theories and applications to provide an essential understanding of laser processing and ablation mechanisms of silicon and other functional materials. Laser- induced damage and substantial thermal effects on work materials will also be discussed. The advanced laser micromachining processes including those using short- pulsed lasers and liquid-assisted lasers will be presented and evaluated to reveal their
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concepts and ability to reduce thermal damage on the work materials. Empirical, analytical and numerical-based models for laser machining processes will be reviewed, and the temperature fields and the heat-affected zone induced by laser will be demonstrated through the heat transfer theories. Lastly, the effects of waterjet impingement will be addressed considering its thermal convection and mechanical impact actions.
2.2 Fundamentals of Laser Technology
Laser standing for Light Amplification by Stimulated Emission of Radiation was invented in the mid-1960s by Theodore Maiman who successfully produced a pulsed laser from quartz flash lamp and ruby rod. At the end of the 1960s, the first continuous wave laser was developed by a group of physicists at Bell Laboratories, and lasers subsequently became a well-known system by the late 1980s. Currently, there are many kinds of lasers being used as a tool for communications, measurements, cleaning, cutting, welding and heat treatment in which those different applications require different laser characteristics.
2.2.1 Laser Generation Mechanism In order to create a laser beam, a medium substance is firstly stimulated by a flashlight or electrical discharge, until the energy level of atoms or molecules of the medium is shifted from ground state to excited state. This amount of energy has to be higher than the band gap energy in order to excite electrons to a higher level. Once atoms or molecules are in the excited state, where they are not stable enough to maintain their energy in this level, they try to release their energy in terms of photons or light to revert to the ground state. Practically, the emitted light energy is not always 100% efficient. Non-radiative energy will be lost in the form of heat in the initial state of transition before releasing the remaining energy as photons or light to the ground state. Photons emitted by the excited atoms create a population inversion in which light will be reflected back and forth in the cavity resonator. A fully reflective mirror is placed at the end of the resonator while a partially transparent mirror is on the other end. A focused beam will subsequently be generated, due to the same directional reflection of photons,
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and will then pass through the partial transparent mirror to become a laser beam as shown in Figure 2.1.
Figure 2.1. Laser beam generation [9].
2.2.2 Types of Lasers Lasers can be classified according to many aspects such as active medium, wavelength, power and mode of operation [9], but the categorization by means of active medium, i.e. gas, liquid and solid states, is widely recognized. In gas lasers, the medium that can be either inert or active gas is stimulated by an electrical discharge in the cavity. The advantages of gas laser, i.e. homogeneity of medium and inexpensive equipment, are the main reasons of using this type of laser in
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material processing. The different types of gas used provide different characteristics of laser, such as CO2 gas provides an infrared laser for general cutting purposes, while the ion of argon or krypton gas produces UV laser for fine-scale material processing [9-11]. Liquid laser generally known as dye laser has been used in a few applications. A specific solution of fluorescent organic dye is employed as a liquid-state medium for emitting a particular light wavelength. The laser wavelength and the medium lifetime are dependent on the type of dye used. An advantage of liquid laser is that the medium can be prepared easily as compared to gas and solid-state lasers [9]. Solid-state lasers are popularly employed since their system is simpler and smaller than gas and liquid lasers. Solid-state lasers can offer laser wavelengths from 300 nm to 3,000 nm depending on the type of element used. A single-crystalline medium with low thermal expansion coefficient is used to produce a high laser beam quality [12]. Nd:YAG laser being a well-known solid-state laser is widely used in many applications, particularly in manufacturing processes. The ions of neodymium (Nd3+) doping in yttrium aluminum garnet (Y3Al5O12) are excited by flashlight rather than the electrical discharge as used in the gas lasers. Another solid-state laser is fiber laser. A rare-earth element, such as Erbium (for producing 1550 nm laser) or Ytterbium (for 1080 nm laser), is doped in the silica glass fiber optic cable in order to absorb and emit a high- stable light energy as a cavity resonator. A simple diode pump producing a light wavelength falling within 690 nm to 980 nm is normally used to excite the doped silica glass at the end of the cable. The change of energy level in the doped fiber glass cable produces the photons with a specific wavelength regarding the doped element used. The emitted light is recollimated on the other end of the cable to introduce a focused laser beam. However, the limited output of laser power and the low efficiency are the major drawbacks of solid-state lasers.
2.2.3 Laser Beam Properties The important characteristics of laser are coherent and monochromatic (single wavelength) properties where the divergence is low or where the beam diameter very slightly changes with an increase in projected length. Different transverse electromagnetic modes (TEM) indicate different shapes of a laser beam spot in a spatial domain, for examples TEM00 provides a circular beam spot, TEM10 provides a ring shape with a smaller circular spot inside, while TEM01 presents two elliptical shapes.
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These modes are influenced by cavity geometry, cavity alignment, active medium and apertures in the resonator. Typically, a laser intensity profile of TEM00 mode is distributed as the Gaussian determined by [9]
§ − 2d 2 · 4P = II exp¨ z ¸ = (2.1) 0 ¨ 2 ¸ π 2 © d f ¹ d z
where I0, dz and P are laser intensity, Gaussian beam diameter at z distance from the focused spot (df) and laser power, respectively. The Gaussian beam diameter (dz) at z distance from the focused spot (df) can be calculated by using [9]
2 2/1 ª § z · º dd «1+= ¨ ¸ » (2.2) fz ¨ z ¸ ¬« © R ¹ ¼» πd 2 z = f (2.3) R 4λ
where zR is Rayleigh length. The focused laser beam diameter (df) written in a function 2 of focal length (Fl), laser wavelength (Ȝ), beam quality (M ) and the entering beam diameter (Di) is given by [9]
4 λMF 2 d = l (2.4) f π Di πθ d M 2 = fd (2.5) 4λ
2 The beam quality (M ) indicates a degree of beam diffraction from the TEM00 mode 2 where șd is beam divergence. A perfect beam quality has M value of 1.0 where the waist diameter is equal to the beam diameter of TEM00 mode. Figure 2.2 presents a schematic of Gaussian beam characteristics. The depth of focus (DOF) is the distance between waist planes in which the beam 1/2 diameter is 2 times the focused diameter (df). It can be calculated by [9]
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πd 2 DOF 2z == f (2.6) R 2λ
Figure 2.2. Schematic of Gaussian beam profile and beam diameters.
Another important laser property is temporal mode. This refers to continuous and pulsed operations in time domain. Many gas and solid-state lasers can be operated in the continuous wave mode where the laser beam is emitted uninterruptedly [8]. This continuous wave laser is normally used for general cutting with high material removal rate as it can facilitate the continuous mass removal in the cutting process. In the pulsed operation, a high power laser beam will be released from the cavity when energy reaches the threshold, and the beam is periodically fired in a certain period of time. The simple rectangular pulse shape is normally obtained. However, Gaussian, Soliton (sech2), Lorentz and Asymmetric-sech2 could be provided in other shorter pulsed laser systems [13]. The above review on the fundamental laser technologies and the optics theories enables the basic understanding and applicable concepts for laser material processing in order to select a suitable laser for a particular application and to determine the beam properties in spatial and time domains. Due to the outstanding laser beam characteristics, laser technologies have been used in many high-precision applications such as medical surgery [14], rapid prototyping [15-16] and micromachining [2, 7, 10,
10 CHAPTER 2
17-19]. Laser micromachining is one of the micro-fabrication processes where laser plays an important role for removing material at micro- and submicro-scales with high precision and fast operation [20]. The micromachining of silicon and other difficult-to- cut materials, in terms of drilling, cutting and grooving processes, will be reviewed and discussed in the following sections.
2.3 Laser Micromachining and Damage Mechanisms
In many applications, lasers have been employed to replace the conventional subtractive methods, particularly in micro-component fabrications. Dunsky [20] stated that lasers can provide higher cutting speed, lower chipping and smaller kerf width for silicon wafer dicing than the conventional sawing process when wafer thickness is less than 100 μm. Whether using pulsed lasers or continuous wave lasers, the ablation process relies on the same basis whereby photons of laser are absorbed by electrons of material and if the provided energy is high enough to break down the lattice, material will start to melt and even vaporize for the high laser energy [21-22]. By projecting laser on a material, heat from laser radiation will be absorbed, transmitted and reflected in different amounts depending on the optical, physical and thermal properties of material. This indicates that the type of laser has to correspond well with the type of work material for high ablating performance. When a pulsed or continuous wave laser is used, the high power density of laser mainly causes heating and melting processes. The irradiated area is heated and a molten layer is formed when the temperature goes beyond the melting temperature of the work material. The material expulsion creates a deeper depth of cut due to the hydrodynamics of a vigorous molten layer. Jackson and Robinson [21] noted that the heat conduction and the formation of plasma significantly affects the sidewall ablation rate by introducing a deeper and larger cut area. In addition, an assisted gas can be supplied coaxially with the laser beam to blow out the molten material from the eroded front in order to increase the ablation rate. For laser micro-drilling and micro-cutting processes, pulsed lasers with shorter wavelength are often employed due to their higher resolution beams than those of longer wavelength lasers. With the use of short wavelength lasers, the laser beam spot size of slightly over 1 μm can be accomplished for micro- and submicro-fabrications [20].
11 CHAPTER 2
In laser micromachining of silicon and other difficult-to-cut materials, three main issues need to be taken into consideration, i.e. their low temperature threshold for surface damages, critical requirements of surface integrity, and their sensitivity to high laser intensity and long pulse duration which cause substantial surface and subsurface damages. The thermal absorptivity of silicon decreases with an increase in laser wavelength as shown in Figure 2.3. This indicates that the use of a longer wavelength laser produces a poorer ablation quality and lower material removal rate. This is why some types of lasers enhance ablation rate, while others require more energy input to yield the same outcome. In the laser micromachining of silicon, it is suggested that the laser wavelength should be less than 1.1 μm in order to yield a remarkable ablation [23- 24].
Figure 2.3. Absorption coefficient for silicon at 300K [24].
2.3.1 Laser Micro-Drilling Laser micro-drilling was firstly introduced in the early 1980s in the printed circuit board industry using CO2 and Nd:YAG lasers [11]. Lim and Mai [18] noted that CO2,
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Nd:YAG and 3rd Nd:YAG lasers were normally used to perform the micro-drilling to achieve hole diameters of less than 50 μm. Excimer lasers are also used to produce micro-holes, but it usually needs to be projected through a mask due to their poor focusing property. High-aspect ratio hole drilling is the main purpose of laser micro-drilling processes where the hole depth created is many times the hole diameter. A small wall taper, less cutting material blockage and less plasma formation are the main requirements for producing the high-aspect ratio hole [18]. Jiang et al. [25] reported that the use of multiple pulse drilling can produce a deeper hole, but it is limited to a certain depth since weaker laser intensity at the bottom of the hole and lower assisted gas pressure cannot provide further melting to blow out the molten material from the hole. Thus, they recommended that the focused laser spot should be positioned below the workpiece surface to increase the hole depth. This effect of focal position on the drilling depth was also studied by Jiao et al. [26]. The maximum drill depth prediction was proposed by Salonitis et al. [27]. Though their model can predict the drill depth close to the experiment, a correction factor is required since some effects, such as material vaporization and plasma formation, were not included in the model. In addition, they also found that the maximum drill depth is not proportional to the laser pulse frequency when low to medium laser power densities are operated. As shown in Figure 2.4, the plasma is a group of loosely bound electrons and ions which can absorb and reflect laser energy over the molten layer, so that the plasma can be considered as the second heat source for enhancing the ablation rate. However, an important drawback of having another uncontrolled heat source in the process is that the amount of thermal energy over the irradiated area is not stable as the plasma size can dynamically be changed during the irradiation. In order to control the size of the plasma, laser intensity, pulse duration, laser wavelength and ambient condition have to be properly selected corresponding with the type of work material ablated. The plasma expansion and ejection of vaporized material across the Knudsen layer, which represents a region of a few microns of gasdynamic discontinuity [28], can cause shock waves over and underneath the ablated area. The shock waves and hydrodynamic mechanism in the molten pool are responsible for molten material expulsion. In addition, the combination of shock wave and thermal stress in bulk material can result in fractures on and under the ablated surface. Though a large number of experimental
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and theoretical studies have been reported and discussed on the plasma formation, a clear understanding of this effect in laser micromachining is still needed for yielding an effective ablation with less damage caused by the plasma.
Figure 2.4. Laser ablation mechanisms.
Heat-affected zone (HAZ) is a substantial problem in laser micromachining processes, particularly to thermal-sensitive materials since it can cause serious fractures on and underneath the ablated surface and its vicinity. For laser micro-fabrications, the HAZ can occur on the entire micro-part structure. It also causes the changes to the material micro-structural and properties. This is considered as a critical problem especially for semiconductor and other functional materials whose properties are not allowed to be changed. Pompe et al. [29] reported that compression and expansion of ceramics in the laser heating process lead to crack generation due to the residual tensile stress on the workpiece surface. This is similar to the crack formation of silicon studied by Gross et al. [30]. They found that the tensile stress occurred in the deformed zone and the compressive stress in the outer zone where the micro-cracks presented near the transition zone. The influence of laser power, focal length and pulse duration on the
14 CHAPTER 2
surface integrity of silicon carbide in laser micro-drilling was studied by Sciti and Bellosi [31], showing that the HAZ and the micro-cracks could be minimized by using low laser intensity and short pulse duration. Other damages or defects introduced by lasers, such as spatter deposition, have to be minimized; otherwise an additional process, such as surface finishing or cleaning, has to be applied, resulting in higher manufacturing time and cost. Low et al. [32] recommended that the use of shorter pulse duration, higher pulse frequency and lower peak power can reduce spatter deposition area and spatter thickness in the laser drilling process. In another study of Low et al. [33], the linearly increasing sequential pulse delivery pattern was recommended rather than the uniform pulse pattern for percussion drilling since a smoother hole profile can be produced and the deposition of spatter area can be reduced by up to 60%. By using an appropriate assist gas in the laser drilling process, it not only increases the material removal rate, but also reduces damages or defects on the work material.
Low et al. [34-35] compared the use of O2, N2, Ar and normal compressed air to assist the 400-W Nd:YAG pulsed laser for percussion drilling of Nimonic 263 alloy sheets. Spatter thickness, bonding strength and recast layer were observed, and the results showed that the O2 gas could reduce the spatter thickness and the bonding strength between the deposited spatter droplet and the workpiece surface. This is due to a higher expelling rate of an exothermic reaction and the brittle porous structure of spatter that are caused by the O2 gas. However, the exothermic reaction is limited to the steel ablation only since the melting point of ferrous oxide is lower than the base material. The combination of other advanced techniques can also improve drilling quality as presented by Yue et al. [36] who studied the use of an ultrasonic-aided laser drilling method. This study showed that a deeper hole with a thinner recast layer could be achieved by using the assistance of ultrasonic vibration. According to the above review, it can be noted that the laser micro-drilling parameters, such as laser wavelength, laser power, pulse duration, pulse frequency and focal plane position, should be selected well and correspond with the properties of the work material for effective drilling with fewer damages. In addition, the coaxial assist gas can be applied to improve the hole qualities as the pressurized gas can provide the chemical reaction, the molten material expulsion and the cooling effect to the cutting area. However, the HAZ and the micro-cracks induced by lasers could take place on and
15 CHAPTER 2
underneath the cut and the vicinity areas due to the heat accumulation, the plasma formation and the shock wave propagation during the process.
2.3.2 Laser Micro-Cutting and Grooving Once a motion mechanism is used, the laser beam and workpiece can be moved relatively and a more complex removal profile can be produced. A depth of a few microns can be achieved in the laser marking process using a very low laser power [20], while the use of a higher laser power increases the amount of material removed. The laser ablation mechanisms for the laser grooving process shown in Figure 2.5 are generally similar to the laser drilling process, but an additional consideration on the traverse of laser beam has to be taken into account. This is due to thermal and physical damages that can occur along the cut as shown in Figure 2.6.
Figure 2.5. Ablation mechanism for laser grooving.
Kancharla et al. [37] compared the ceramic cut results under different short- wavelength lasers, i.e. ArF (193 nm), 3rd Nd:YAG (266 nm) and UV excimer laser (308 nm), and found that the shortest wavelength produced the best cut quality on Al2O3, poly-vinyl alcohol, poly-styrene and Pyrex glass. This again indicates that the laser wavelength plays an important role on the cut surface quality as the absorption coefficient of material depends on the light wavelength. The relationship between laser power, traverse speed, kerf width, HAZ, surface roughness and striation were
16 CHAPTER 2
investigated by Rajaram et al. [38]. They reported that a decrease in laser power decreases the size of HAZ and kerf width dramatically, while surface roughness and striation are strongly dependent on traverse speed. The effect of traverse speed on the groove depth in multi-crystalline silicon ablation was studied by Dobrzanski and Drygala [39]. According to their results, the use of higher traverse speeds introduces a shallower groove depth while the kerf width remains about the same under different traverse speeds. This is evident in that the traverse speed has a profound effect on the groove depth rather than the width.
Figure 2.6. Laser-induced damages along the cut surface.
Other important laser parameters, such as pulse number, pulse rate and laser fluence, also affect the depth of cut and surface morphology. Eyett et al. [40] showed that the increasing pulse numbers of XeCl excimer laser in a range of 250 to 10,000 pulses at tested traverse speeds increases the depth of cut on a ceramic (PZT) significantly. This is similar to the study of Tseng et al. [41] who used ArF excimer laser for glass grooving and found that depth of cut increases with an increase in pulse number. Moreover, a higher laser fluence tends to form a wider groove with a U-shaped profile rather than the typical V-shaped. In the laser cutting process, dross can be formed on the backside of the workpiece. This is due to the use of improper traverse speed and insufficient assist gas pressure that cannot effectively expel the molten material away from the cut area. Yan [42]
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concluded that there were three kinds of cut profile obtained in the laser cutting process; they were a non-straight cutting edge with dross on the backside, a straight cutting edge with dross, and a straight cutting edge without dross. In order to minimize the dross formation, Chen [43] and Gross [44] noted that a higher assist gas pressure is required to produce a better cut surface profile with less dross appearance. Furthermore, the high traverse speed of a laser beam can create an obvious pattern of waviness on the cut surface. The causes of this wavy or striation pattern come from the fluctuation of the molten layer and the dynamic nature of laser. Ivarson et al. [45] observed the striation cycle based on the oxidation reaction when cutting a mild steel, and concluded that the striation cycle consisted of four main stages which were ignition, burning, extinction and reignition. The predictions of kerf width, striation width and striation frequency were reported by Yilbas [46], showing that a decrease in traverse speed obviously increased the striation width due to the sideways burning. However, the understanding of striation formation on other non-ferrous materials is still not clear and needs more fundamental research to be carried out. According to this review, it can be noted that the use of shorter wavelength lasers can provide a better surface finish in the micro-cutting and grooving processes due to their high focusing beam property and high absorption coefficient for many materials. In addition, dross and striation are the major consequences of the laser cutting process that could be minimized by using a proper laser power, traverse speed and assist gas pressure. The HAZ can appear along the cut when too high laser power and slow traverse speed are employed. However, by utilizing the ultra-short pulsed laser, material can be ablated with less thermal effect. In addition, liquid can be applied into the laser ablation processes to cool the workpiece temperature in an attempt to reduce the thermal damage for damage-free micro-fabrications. In the next section, these novel laser processes and their material removal mechanisms will be addressed.
2.4 Novel Laser Micromachining Processes
There are two main approaches to reducing the damage in laser micro-fabrication. Firstly, the process has to be improved by modifying or optimizing process parameters to enhance the cut surface quality such as using a shorter wavelength laser or shorter pulse duration; secondly, the process is combined with another process to accomplish a
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better cut quality, such as multi-wavelength excitation [47], ultrasonic-aided laser machining [36] or liquid-assisted laser ablation. In the following review, the two main approaches of using short pulsed laser and liquid-assisted laser in micromachining will be discussed.
2.4.1 Short Pulsed Laser Machining The first short pulsed laser was developed by Fork et al. in 1981 [48], where the pulse duration of less than 0.1 picoseconds can be generated. The femtosecond laser was later introduced in 1985 by Knox et al. [49-50]. Currently, short pulsed lasers have been widely used in micro- and submicro-fabrications and thermal-sensitive material ablation processes. Jackson and Robinson [21] reported that with the use of a short pulse laser, material is ablated without heat flow, plasma and melt pool formations during the process, so that HAZ is very small or even non-existent. The short pulsed laser ablation is sometimes called athermal laser ablation process since material is not removed by the thermodynamic equilibrium of electrons and lattice as occurred in the typical pulsed lasers whose pulse duration is longer than some several picoseconds causing work material heating and melting. The electrons and lattice on the excitation with the ultra- short pulsed laser are considered as the non-equilibrium, where the disordering of the atomic lattice takes place due to the excitation of a large fraction of the valence electrons to the conduction band [51]. A very small amount of elemental material is evaporated immediately after being irradiated by the short pulsed laser without the need of assist gas [52]. This is due to the laser pulse energy that is much higher than the typical pulsed lasers. Moreover, a better side wall surface quality can be achieved by using femtosecond pulsed laser associated with a higher repetition rate [53]. This can produce a high aspect ratio groove with very small HAZ. A comparison of machining using nanosecond, picosecond and femtosecond pulsed lasers were performed by Chichkov et al. [54], demonstrating that a shorter pulse duration produces a better hole surface quality. Hirayama and Obara [55] reported that HAZ is small when femtosecond laser is applied. However, an amorphous structure with the thickness of about 1 μm could be formed on the ablated surface after being irradiated by a femtosecond laser. This is due to the excessive heat energy that introduces a thin molten layer which then cools down rapidly, resulting in the
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amorphous phase. In addition, mechanical stress and amorphization of single-crystalline silicon wafers were studied by Amer et al. [56] and Rogers et al. [57], showing that femtosecond lasers could introduce less stress and amorphization on silicon wafers than nanosecond lasers. However, femtosecond lasers can result in ripples with the size of 0.5 to 2 μm, amorphous and polymorph structures around the ablated area on the single- crystalline silicon due to their high power density and high pulse numbers [58-59]. Ren [60] investigated and compared the characteristics of surfaces produced by three different intensities of nanosecond and femtosecond lasers on silicon, and found that a good surface morphology with minimum thermal damage could be achieved when lower laser intensity and shorter pulse duration were used, while higher beam intensity and longer pulse duration were favored for increasing the ablation rate. However, the relatively low removal rate was found when too high laser intensity was used. This is due to the formation of plasma shielding and the insufficiency of photon energy that limits the molten silicon expulsion. Furthermore, low beam stability, low reliability, low ablation rate and the high photon cost of short pulsed lasers are the drawbacks of this technology [19, 61]. Hence, it can be said that achieving damage-free results with high machining rates still remains the big issue in laser micromachining process.
2.4.2 Liquid-Assisted Laser Machining Liquid-assisted laser processes have been used since the 1970s for cutting, shock processing and surface cleaning [62-63]. Liquid is applied into the laser micromachining processes in an attempt to reduce thermal effects and also achieve high cutting quality. The liquid can be water or any chemical solution which is able to produce no damage on work material in the laser ablation process. However, pure water is commonly used to assist lasers since it is cheap, safe, and recyclable, and has high cooling capability. Though various water applying methods have been proposed by many researchers, three main methods have been used, i.e. underwater, waterjet-guided laser and liquid assisted front side. These methods have been applied in macro- to submicro-fabrications of silicon substrates and other thermal-sensitive materials. Their machining mechanisms, applications and the associated interaction between laser, water or waterjet and workpiece material in terms of physical, thermal, mechanical and cut surface characteristics after machining will be discussed in the following sections.
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2.4.2.1 Underwater Laser Machining Underwater laser machining is a water-assisted laser ablation process where the specimen is submerged in water, and a laser beam passes through a water layer and strikes on the specimen surface to cause material removal. Though the process varies depending on laser type, water layer thickness and equipment setup, it involves the same phenomena during the process; i.e. light absorption by water, vaporization of water, plasma formation, shockwave formation and bubble formation [64]. As the workpiece is submerged in water, the optical effect of the laser beam is an important issue to be considered. The absorption length of water over various light wavelengths reported by Kruusing [62] is shown in Figure 2.7. It demonstrates that green light wavelength (500 nm) provides the longest absorption length in water. In the case of Nd:YAG laser whose wavelength is 1064 nm, the laser beam can go into water of 30 mm depth before about 63.2% of laser energy is absorbed by water. This feature can be determined by the Beer-Lambert law as
§ h · ¨−= w ¸ hw II 0w exp¨ ¸ (2.7) © la ¹
where Ihw, I0w, hw and la are light intensity at hw depth, light intensity above water layer, water layer thickness and light absorption length, respectively. The absorption length drastically decreases with an increase in light wavelength, and the decreasing rate decreases after the wavelength of 7 μm in which the absorption length varies between 5 to 25 μm. Kruusing also [63] mentioned that water layer thickness of 1 mm is normally applied in underwater laser ablation process. Sano et al. [65] found that the shockwave pressure generated under water is greater than in air due to the plasma formation. Such high shockwave pressure is known as shock processing or shock peening. This is similar to the study of Zhu et al. [66] in which silicon ablation rate in water was higher than in ambient air since the formation of plasma in a confined volume introduced more heat and pressure to enhance the ablation. Fabbro et al. [67] stated that the impact pressure in the confined water was 4 to 10 times greater than in air, and the maximum temperature of plasma could be more than 10000 K as reported by Barnes and Rieckhoff [68]. According to the study of Park et al. [69], the compressive pressure of 1 MPa produced by the shock wave could be
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generated in the confined water when KrF excimer nanosecond-pulsed laser was applied at the laser fluence of 0.1 J/cm2.
Figure 2.7. Absorption length of pure water at 298 K against the different wavelengths of light [62].
In addition, the effects of the shockwave and collapse of bubbles over the ablated area produce a non-thermal material removal process. Chen et al. [70] and Lu et al. [71] noted that four main mechanisms were involved in the underwater laser ablation process; i.e. high impact pressure in confined water, weak plasma shielding, collapse of bubbles and high heat conductivity of water. It is observed that the material removal mechanism of underwater laser ablation relies not only on the thermal ablation, but also the high mechanical impact of cavitation (collapse of bubbles) on the specimen surface. The plasma expansion causes a shock wave where kinetic energy is changed to potential energy, creating and expanding air bubbles in the cavitation. Due to the multiple collapses of bubbles in microseconds, the surrounding water is compressed and subsequently creates a high impact pressure of small liquid jets over the workpiece
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surface. The magnitude of this liquid jet impact was reported to be about 10 times greater than laser ablation in ambient air. This effect has also been found in laser shock processing where a laser power of lower than the ablation threshold is employed for surface treatment and work hardening [65]. However, in the underwater laser ablation process, bubbles and debris created in water can reduce the material removal rate due to light scattering and laser energy absorption [63, 72]. Morita et al. [73] performed a study on underwater laser ablation of silicon nitride
(Si3N4) using the Q-switch Nd:YAG laser and found that no recast layer formed on the cut surfaces. This is due to the ablated material that is rapidly solidified and flushed away by water. Kerf width, crack and cut quality of ceramics in air and in water were compared by Zhu et al. [74], showing that a smoother edge and fewer cracks could be achieved by the underwater approach. Different water layer thicknesses were also investigated and it was found that a thicker water layer produced a narrower cut. This is because of the laser energy absorption of water that increases with the water layer thickness, hence decreasing the amount of material removed. The applications of underwater laser drilling were presented by Tsai and Li [75] who investigated the use of a CO2 laser for drilling, percussion drilling and trepanning LCD plates in water with a water layer thickness of 1 mm. They found that a keyhole and air bubbles were formed during the process due to the rapid vaporization of water around the laser beam. They also found that the diameter and the length of the keyhole were proportional to the focused beam diameter and the laser power, respectively. In addition, more bubbles occurred around the keyhole when a higher laser pulse frequency was applied. These findings are similar to that in the study of Mueller et al. [76] which showed that an increase in laser power increased the keyhole length and decreased the bubble size. They also noted that the hole diameter created was slightly larger than the keyhole diameter, so that water can flow into the drilled hole for cooling the hole surface. As a result, micro-cracks, HAZ and redeposition could be reduced. Zhu et al. [66], Ren et al. [77] and Das et al. [78] compared the surface geometry of silicon formed in air and underwater and found that a U-shape profile could be produced by the underwater method while a V-shape was found in the dry laser machining approach. Ren et al. [77] indicated that the underwater method associated with femto- and nanosecond pulsed lasers could increase the material removal rate and surface quality of silicon. This finding is similar to that in the work of Daminelli et al.
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[72] which studied the interaction between Ti:sapphire femtosecond laser and silicon in water. They found that smaller ripples and a cleaner cut surface could be obtained when the underwater method was used. The underwater laser micromachining of magnetic materials and silicon was studied by Kruusing et al. [79-80]. A cleaner ablated surface and a narrower kerf width than in laser cutting in air could be produced. Redeposition and taper angle caused by laser drilling of silicon in air and in water were studied and compared by Wee et al. [81]. They found that the underwater method can significantly reduce the redeposition size and the hole taper angle. They also noted that though a greater amount of silicon was removed in the underwater process than in air, a poorer cut surface was formed due to the interference of air-bubbles (and possibly laser distortion by the water), causing a ripple-rich cut surface. Furthermore, Karimzadeh et al. [82] compared the cut surface morphologies and hole diameters of silicon when the 532 nm nanosecond laser was applied under pure water and dimethyl sulfoxide (DMSO) solution. Their results showed that a slightly better surface quality with smaller hole diameter could be achieved when silicon was ablated under DMSO than in water. By considering costs and recyclability, water is still considered as an effective fluid for the liquid-assisted laser ablation process. Gas-assisted underwater laser ablation could be performed for gaining a chemical reaction over the ablated surface. Alfille et al. [83] increased the cutting performance of stainless steel by utilizing oxygen gas coaxially with the laser beam in the underwater process for introducing the exothermic reaction and increasing the cutting speed. Ceramics cutting with the gas-assisted underwater laser method was carried out by
Black et al. [84-85]. A CO2 laser assisted by argon, nitrogen, oxygen and air was employed for ceramic tile cutting, and the results showed that the rapid solidification of molten ceramic with less burnt region could be achieved. In their study, only oxygen gas could not produce cracks on ceramic tile. In addition, by using a continuous wave laser, high cutting speed could be achieved, while a smoother cut surface and fewer number of cracks were obtained in the pulse mode. Besides the top-opened water container, a closed chamber can be employed in the underwater laser ablation method. A principal difference between the top-opened container and the closed chamber is that the debris carrying mechanism in the top- opened container is mainly caused by the bubble formation, while a directional fluid
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flow can be provided in the closed chamber system [63]. The top side of the closed chamber is made of a quartz window allowing the laser beam to pass through for ablating purposes. This method can also prevent damage to the laser equipment due to vapor and water bouncing during the ablation process. According to the above reviews, it can be concluded that underwater laser machining can be classified into three main methods as shown in Figure 2.8. The top- opened water container type shown in Figure 2.8(a) can be performed by submerging the whole workpiece in water, with the laser directly projected on the material surface through a layer of water. The assist gas type shown in Figure 2.8(b) can be applied to create a chemical reaction and enhance material removal for a specific material, e.g. the exothermic reaction for steel cutting. Figure 2.8(c) shows the closed-chamber type where a quartz window is placed between the laser and water in order to prevent the bouncing of water during the process and also to control the water layer thickness. Moreover, the debris, bubbles and hot fluid are forced to flow away from the cut area by using this closed-chamber type.
(a) (b) (c) Figure 2.8. Different types of underwater laser machining: (a) top-opened liquid container type, (b) gas-assisted underwater type and (c) closed chamber type.
In this section, the advantages of the underwater laser machining process have been reviewed. With the underwater laser machining process, a clearer cut surface, smaller taper angle and fewer cracks can be obtained, with minimum oxidation, HAZ, and plasma size. Furthermore, the high plasma pressure produced in the confined liquid volume enhances the material removal rate due to the bubble formation and collapse over the cut surface. Although the underwater method can reduce thermal damage by cooling the whole workpiece in water, the bubbles and debris appeared in the process can reduce the laser beam intensity due to the light scattering and absorption. This
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feature directly affects the material removal rate and the cut surface quality as discussed earlier. In addition, too thick a water layer applied can cause a significant loss of laser energy according to the Beer-Lambert law, while too thin a layer reduces the cooling effect, so that an appropriate water layer thickness needs to be used for the efficient use of this technique.
2.4.2.2 Waterjet-Guided Laser Machining Waterjet-guided laser or laser microjet was invented in 1993 by scientists at Swiss Federal Institute of Technology of Lausanne with its initial purpose being to accommodate the uneven target surfaces and large cutting depths such as those used for medical surgeries/incisions. This technology was patented by Richerzhagen in 1995 [86]. In this technology, a laser beam is guided by a stream of water where laser light is fully reflected inside the boundary of water-air interface as shown in Figure 2.9 [87].
Figure 2.9. Waterjet-guided laser process [87].
Generally, pulsed laser is recommended since it allows waterjet cooling on the cut surface between pulses. The laser beam is projected through a quartz window into a pressurized water chamber with a pressure ranging from 5 to 50 MPa. The pressurized water with a focused laser beam is passed through an orifice to form a jet of water-laser at the nozzle exit with a diameter ranging from 50 to 200 μm. It is claimed that the jet can travel up to 50 to 100 mm without significant disintegration under a proper water pressure. An important concern is the positioning of the laser focal point at the center of the orifice. Contact between the laser beam and the orifice body may lead to severe damage to the orifice and the change of laser intensity profiles [88-89]. It is understood
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that laser can heat and vaporize water rapidly. However, this phenomenon can be avoided by selecting a proper laser wavelength that is not significantly absorbed by water. The laser wavelength used in this method is in the range of 250 to 1100 nm [90]. The orifice geometry used in this system is in a conic style where the nozzle diameter is divergent at the nozzle exit, as shown in Figure 2.9. The waterjet beam diameter is about 83% of the orifice diameter due to the geometry of the cone down nozzle [90-92]. The waterjet breakup was investigated by Vago et al. [93] and Couty et al. [94], which indicated that the jet breakup length (i.e. the jet length before disintegration) was proportional to the mean jet velocity. As the mean jet velocity increased above a critical value, the continuous smooth jet was no longer provided, resulting in a decreased jet breakup length. Thus it can be stated that the allowable distance for the waterjet-guided laser method is subject to the jet breakup length. In the waterjet-guided laser machining process, the focal depth of the laser can be disregarded since the stream of water acts as an optical fiber, so that the spot size of the laser is controlled by the water beam diameter. It means that the change of distance in the z-axis has no influence on the laser beam diameter, so that thick material can be cut through with almost zero-degree taper angle. It is observed that the process simultaneously provides laser ablation, water cooling and impact force to expel the debris away from the cut area. More reliable cut quality, lower mechanical stresses and better cut surface roughness could be achieved in silicon wafer dicing by using the waterjet-guided laser machining technology [87, 95-98]. Richerzhagen [96] claimed that the arithmetic mean roughness (Ra) of 3 μm could be obtained on the cut surface in the 660 μm thick silicon wafer dicing. Instead of using water, other chemical solutions, such as potassium hydroxide (KOH), can be applied to form a jet in laser chemical processing (LCP) [99-100]. The LCP is a combination of the waterjet-guided laser and the chemical wet etching processes to reduce the damage after machining. According to the study of Kray [99], a smoother ablated surface and a smaller dislocation density in silicon could be produced using LCP. However, the use of such a chemical solution did not significantly increase the ablation rate, nor did it prevent the redeposition of molten silicon on the material surface. Another type of waterjet-guided laser was documented in a patent of Kuykendal in 1998 [101]. Pressurized water is fed into a chamber which has a diffuser to spread the
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flow of water uniformly before entering to a knife edge orifice as shown in Figure 2.10 [102]. Kuykendal noted that this equipment was also suitable for machining, shaping and cutting applications.
Figure 2.10. Water-laser machine tool of Kuykendal’s design [101].
According to the above review, it can be concluded that the advantages of the waterjet-guided laser over the conventional laser cutting processes are the parallel sidewall cutting, low stress, low thermal effect and high cut surface quality. Since the waterjet is coaxially applied with a laser beam, it provides both the workpiece cooling the material and expelling debris from the work surface. However, a waterjet beam may be disturbed due to the expulsion of material during the process. This then requires a short moment to allow the beam of the waterjet to be settled down to a straight flow again. In addition, a non-horizontal flat surface and other beam orientation may make it difficult to be operated due to the deflection of the water beam in a particular impact angle and the gravity force [103]. Moreover, this technology is limited to some lasers whose wavelength fits the water transmission spectrum [104]. This may limit the optimum selection of lasers for a work material. The waterjet is also required to have specific flow characteristics in order to act as a liquid optical fiber for total laser beam reflections and delivery; for instance, waterjet disintegration and water atomization that can occur in high pressure water are not allowed. In addition, the diameter of the waterjet-guided laser beam is controlled by the waterjet diameter and the required beam sizes may not be achievable. In order to robustly apply a waterjet to the laser ablation process and overcome some limitations of the waterjet-guided laser method, the waterjet should be applied
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independently with the laser beam. In the next section, liquid-assisted front side laser machining will be discussed as an alternative method for damage-free laser ablation.
2.4.2.3 Liquid-Assisted Front Side Laser Machining Liquid-assisted front side laser machining is a method for reducing the damage in the laser ablation process where liquid is applied only to the top work surface. Though there are several techniques for applying water to the sample, three main approaches have been used; i.e. thin film layer, liquid spraying and water jetting. The thin water film is the most basic technique among the three approaches. The low pressure water is applied either horizontally or vertically. However, the vertical setup is preferred to enable a unidirectional liquid flow and an effective thermal convection due to the gravity force as shown in Figure 2.11(a). Dupont et al. [105] used the thin water film technique for improving the ablation performance and the cut surface quality of stainless steel 304. They found that the material removal rate was 15 times higher than the dry laser ablation with no oxide deposition on the material. The ablation performance is subject to the plasma formation in the thin water layer that causes the mechanical ablation effects as occurred in the underwater method. However, the thin water film method using a much thinner water layer produces a smaller plasma size than the underwater method. As the water layer thickness formed in this method is very thin, the laser energy absorption of water is relatively low compared to the underwater approach.
(a) (b) Figure 2.11. Liquid-assisted front side method: (a) vertical thin film method and (b) liquid or vapor spray-induced thin film method.
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The thin water film method may not be able to deliver a water layer thin enough to minimize the light absorption of water, particularly for long wavelength lasers. The water spraying method proposed by Geiger et al. [106-107] is another technique to form a very thin water film on work material as shown in Figure 2.11(b). The workpiece is positioned vertically to provide a self-flow fluid layer due to the gravity force, and water is sprayed on the work sample to form a very thin water film. This method results in not only a clean ablated surface with less redeposition, but also a smaller plasma formation than dry laser machining. As the size of the plasma is small, the impact force caused by the shock wave decreases and hence results in fewer cracks in the work material. Ethyl and methyl alcohols were also used in this spraying method to improve the wetting property as reported by Roth and Geiger [108], and the results showed that though the wetting angle of the solution droplet increased with an increase in alcohol concentration, surface integrity and ablation rate were not significantly improved. Furthermore, steam can be used instead of the water spray. This method proposed by Hong et al. [109] and Koh et al. [110] showed that the steam spraying technique could provide a higher ablation rate than the typical thin water film method and about twice the rate of the air-assisted laser ablations on copper and silicon due to the plasma shielding effect. A deep hole, clean surface and edge protrusion reduction could be obtained by using this technique. According to their investigations, plasma size and plasma lifetime in water film generated by this steam spraying technique were much lower than in air and in the thin water film methods. To enhance the material removal rate and the cooling action, a high pressure waterjet should be used instead of using the thin water film or the water spraying method. Due to the limitations of the waterjet-guided laser technique as discussed earlier, an off-axial waterjet would be applied along with the laser beam for cooling and removing the work material. Chryssolouris et al. [111-112] proposed an off-axial waterjet to assist laser grooving on composite material as shown in Figure 2.12. The laser beam was placed perpendicularly to the work surface, while a waterjet was supplied with a small forward angle to the laser beam for cooling and debris removal. It was reported that though this technology reduced HAZ by up to 70%, water can absorb some laser energy and caused 45% groove depth reduction as compared to the conventional dry laser grooving.
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Figure 2.12. Off-axial waterjet-assisted laser machining.
With this off-axial laser-waterjet setup, Molian et al. [113] and Kalyanasundaram et al. [114-115] attempted to remove work material through a thermal shocking process to initiate a controllable crack on aluminum nitride. The CO2 laser with O2 assist gas was used to heat the work material, while a low pressure waterjet was positioned after the laser beam about 4 mm for rapid quenching. After the laser heating and the rapid cooling, thermal shock occurred due to the change of compressive stress to tensile stress and then resulted in cracks on the workpiece surface. It was observed that this thermal shocking method could cut through the hard-to-cut brittle materials with very small kerf width, low HAZ and low striation due to the controllable crack propagation. It was also found that the cutting mechanisms of this shocking method could be divided into three stages, these were scribe-cut, crack-cut and slag-cut. In the scribe-cut stage, the process caused small melting and cracking on the material surface due to the low laser intensity, resulting in a thin recast layer, fine cracks and shallow mark. As a higher laser intensity was applied, the effect of thermal stress-induced cracking became more dominant in the crack-cut stage providing very small kerf width and good cut surface. However, the surface integrity was poor in the slag-cut stage where the melting and the evaporation processes played the important role, so that slag formation, redeposition, striation, burr and poor surface integrity were apparent. Hence, it can be stated that this thermal shocking-cutting process has to be maintained in the crack-cut stage to produce a good cut result. Though the thermal shocking process proposed by Molian et al. could produce a cut with almost zero kerf width, the residual stress and the micro-cracks in work material structure are a major concern, particularly in the micro-component fabrications. In addition, the properties of work material should be able to promote a local controllable crack in the thermal shocking process, so that Molian’s method is limited to some brittle
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materials with specific material properties. By contrast, the Chryssolouris’ method uses a shorter distance between laser beam and waterjet for cooling and removing material and debris, so that material could be removed directly by the waterjet with less restriction on material properties and crack formation. Hence, the off-axial laser- waterjet method proposed by Chryssolouris et al. seems to be more applicable for producing the damage-free micro-fabrication of various materials than the Molian’s method. However, there is very little knowledge of the underlying mechanisms of this cutting process, so that more research is needed in order to improve this technique as a near damage-free micro-fabrication process. Other waterjet-assisted laser machining methods were patented by Klingel in 1983 [116] and Gangemi in 1991 [117] as shown in Figures 2.13 and 2.14, respectively. In Klingel’s design, the waterjet nozzle can be rotated around the laser beam for two- dimensional contouring. As the target material cannot be cooled effectively from the top side, another waterjet beam may be applied at the bottom side to cool the material and also reduce burr and dross formations. Two designs of Gangemi were documented for web slitting in paper cutting application in order to minimize the thermal effect of laser and the amount of fiber dust in the paper cutting process. It can be observed that these methods are fundamentally the same as that of Chryssolouris et al. discussed earlier, except that the waterjet and the laser beams are applied in different ways with the primary aim of minimizing HAZ and other thermal damages.
Figure 2.13. Waterjet-assisted laser machining (Klingel’s design) [116].
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Figure 2.14. Waterjet-assisted front side laser cutting (Gangemi’s designs) [117].
According to the review on liquid-assisted front side methods, three main water applying techniques have been drawn; i.e. thin water film, water spraying and waterjet approaches. These methods can provide a cooling action on the workpiece surface where some thermal defects, such as HAZ and redeposition, can be reduced. Regarding the thin water film and the water spraying methods, the plasma size, the plasma lifetime and the HAZ can be kept to a minimum. However, the redeposition may be apparent as the quick evaporation of thin water film results in a lack of water protection on the work surface. By using the off-axial waterjet method, it offers not only a high cooling rate, but also an increased ablation rate due to the action of the waterjet. Thus this method would be possible for reducing thermal damage in the laser micromachining. It should be noted that when the waterjet pressure applied is high enough to yield the failure threshold of the work material, it would be able to remove the solid-state material softened by laser. Thus this could not only remove the work material at below its melting temperature, but also reduce the thermal damage due to the strong waterjet cooling. This can be seen as a research gap and a new avenue for further research. In the next sections, the modeling of laser ablation and liquid-assisted laser machining processes will be reviewed, which is hoped to also provide an understanding of the process mechanisms.
2.5 Modeling of Laser Machining Process
As the laser ablation process uses thermal energy for heating and removing materials, process modeling has been mostly based on a heat transfer model associated with the conservations of energy, mass and momentum. Three main modeling approaches, i.e.
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empirical, analytical and numerical, have been used and will be reviewed together with the resultant models in the following sections.
2.5.1 Empirical Approach Empirical modeling is an experimental-based method, where the model is formulated from a set of experimental data by using the regression method to determine the fitting coefficients for a predefined algebraic equation. As it is easy to create a model directly from the experiment, this method has been employed in very broad applications. The accuracy of the model is dependent on the experimental data and the mathematical function selected for modeling. For laser ablation, some researchers proposed empirical models along with their research findings for process prediction and optimization. Black [118] established an empirical model to predict a suitable laser traverse speed for yielding a good cut quality in ceramic tile cutting. Ghoreishi et al. [119] developed a model for predicting hole diameter, taper angle and circularity in laser percussion drilling where laser power, pulse duration, pulse repetition, numbers of pulses, assisted gas pressure and focal plane position were varied. With similar laser drilling parameters, David and Botis [120] proposed an empirical model for predicting hole circularity and surface integrity. Other empirical models for predicting HAZ, surface roughness, striation frequency and kerf width were reported by Kuar et al. [121], Rajaram et al. [38], Sundar et al. [122] and Wee et al. [123]. In addition, Martan et al. [124] used a dimensional analysis approach to create models for predicting the maximum surface temperature, melting threshold, melting duration and plasma formation threshold for various metallic materials heated by a nanosecond-pulsed laser. Hence, it can be said that any parameter effect can be modeled by using the regression method associated with a suitable amount of experimental data as long as the parameter can be included in the test. However, empirical models developed are only applicable within the conditions covered by the specific experiment from which the model is developed. The optimization of the laser machining process can be achieved by determining the derivatives of the model. However, heuristic optimization techniques, such as artificial- neural network (ANN) and genetics algorithm (GA), can be applied to find the optimal condition based on a set of experimental data. Dhupal et al. [125-127] used a multilayer feed-forward ANN and response surface method to determine the optimal laser power,
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pulse frequency, pulse duration, assisted gas pressure and laser traverse speed for laser- grooving of ceramics. Back-propagation ANN with multiple regression analysis and GA were used by Tsai et al. [128] in order to find the optimal ceramic cutting condition for minimizing the HAZ. The general regression neural network and GA were studied by Ghoreishi and Nakhjavani [129] to optimize the geometrical characteristic of the hole formed by the laser percussion drilling process. It can be noted that though laser ablation processes can be modeled and optimized by using the regression method and some optimization techniques, the model created cannot provide a correct prediction when the parameter is not in the range covered by the experiment. Furthermore, regression models are unable to give an insight into the physics of the problem, but form an equation for “best fitting” the experimental data. Thus, theoretical models using analytical and numerical approaches are preferred to represent the process.
2.5.2 Analytical Approach Analytical models can be formed either in dimension or dimensionless terms to satisfy the conservations of energy, mass and momentum. As the laser machining process uses heat energy for melting and vaporizing material, many analytical models have been developed from the energy balance equation of heat conduction. The models have been formed as elliptic, parabolic or hyperbolic functions for solving steady-state, time- dependent or thermal shock problems as follow:
2T =∇ 0 (2.8) 1 § ∂T · 2T =∇ ¨ ¸ (2.9) α © ∂t ¹
1 § ∂ 2T · 1 § ∂T · 2T =∇ ¨ ¸ + ¨ ¸ (2.10) 2 ¨ ∂ 2 ¸ α ∂ vw © t ¹ © t ¹
where Į and vw are thermal diffusivity and wave propagation speed, respectively. However, parabolic equation is mostly employed since it can show the growth of temperature not only in the space domain as the elliptic equation, but also in the time domain. For the hyperbolic model, it is normally used for solving the laser-material interaction in very high rates of change of temperature and very small interaction times
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such as short-pulsed lasers and submicro heat transfer problems. An 1-D analytical model derived from the parabolic heat equation for temperature gradient prediction is given by [130]
()− 18 RP f ° 2/1 ª z º°½ T = ()αt ierfc (2.11) ,tz π 2 ® « ()α 2/1 »¾ dk f ¯° ¬2 t ¼¿°
where Rf, P and df are reflectivity, laser power and the focused laser beam diameter, respectively. In the case of pulsed lasers, the temperature model can be written as [130]
()− 18 RP f ° 2/12/1 ª z º T = ()α ()t ierfc ,tz π 2 ® « ()α 2/1 » dk f ¯° ¬2 t ¼ (2.12) ª º½ ()−− 2/1 z ° tt 0 ierfc« » ()α()− 2/1 ¾ ¬«2 tt 0 ¼»¿°
where t0 is non-irradiating time. From the last two equations presented above, an error function term (ierfc) is included in the model to represent the Gaussian beam profile. The ierfc is an integral of the complementary error function which can be determined by
exp()− u 2 ierfc u)( = u[]−− erf u)(1 (2.13) π 2/1
In addition, Rosenthal [131] proposed an analytic temperature model for a moving heat source, where workpiece temperature is calculated by
()− ª 1 RP f § vx · 2 § vd f ·º TT += exp − exp¨− ¸ (2.14) 0 « π ¨ α ¸ ¨ α ¸» ¬« 2 k © 2 ¹ d f © 4 ¹¼»
This model was later modified and implemented by many researchers for modeling the laser-material interactions. Cline and Anthony [132] proposed an analytical model consisting of temperature field, cooling rate and depth of melting with a moving heat source on a semi-infinite
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scheme, where Green’s function was applied to solve the non-homogenous differential equation of laser heating. The effects on material thickness with quasi-steady state heat transfer were studied by Mazumder and Steen [133], where a moving heat source of Gaussian beam, temperature-independent material properties and phase change of solid- vapor were taken into account along with a convection effect of gas jet to assist the ablation process. Their model could demonstrate the temperature gradient, HAZ, thermal cycle and effect of material thickness. Moody and Hendel [134] proposed an accurate temperature prediction model for a moving laser heat source on silicon where the temperature-dependent silicon properties and the eccentricity of the Gaussian beam were taken into consideration. Liarokapis and Raptis [135] formulated an analytical model to predict the laser-material interactions in the laser melting process. They also noted that the temperature-dependent reflectivity and absorption coefficient of silicon should be considered for enhancing the accuracy of prediction. An analytical model written in the enthalpy form for temperature field prediction of melting and recrystallization of a thin silicon film was proposed by Grigoropoulos et al. [136]. The partial phase change of solid-liquid or mushy state was considered along with the temperature-dependent silicon properties. An analytical model for pulsed laser processing was developed by Yilbas [137-140], where an exponential pulse shape function was applied with different pulse duration and pulse intensity. Laplace and invert-Laplace transforms were applied to facilitate the modeling process for temperature field prediction. Furthermore, hole geometry of laser drilling has been modeled by using the analytical approach [141]. The cutting front geometry of laser grooving was also modeled as a function of traverse speed, molten layer thickness, assisted gas parameters and temperature by applying the conservations of mass, momentum and energy [142]. For the waterjet-assisted laser machining process, Chryssolouris et al. [112] proposed analytical models for predicting groove depth and HAZ in off-axial laser- waterjet grooving of a composite material. Their models were formed as a function of laser power, traverse speed, beam diameter, material density, absorptivity, heat capacity, boiling temperature and latent heat of the composite material. The material was considered to be removed by the waterjet (similar to the use of an assist gas) once the vaporization temperature was reached. Laser power, heat conduction and phase change are balanced such that
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−= § dT · + θρ Ab Idxdy k¨ ¸dA v vL tan dxdy (2.15) © dn ¹
dA 1 2 ++= tantan 2 ϕθ dxdy (2.16) where dA, ș and ij are cutting front area, and two inclination angles at the cutting front with respect to x and y axis respectively. By adding the heat convection term into the above model for waterjet cooling, the model is given by
−= § dT · + θρ ()−+ Ab Idxdy k¨ ¸dA v vL tan dxdy TTh vvb water )( dA (2.17) © dn ¹
where hb is the heat transfer coefficient at boiling temperature. To yield the material expulsion, the momentum of the waterjet has to be greater than the surface tension and vapor pressure of the material at its vaporization temperature. As the momentum loss due to side wall friction along the groove surface was not significant compared to the waterjet pressure applied, the momentum loss was disregarded. The thermal resistance of superheated vapor was also added into the model when water above the cutting front was changed to vapor. Their groove depth models for gas-assisted and waterjet-assisted laser processes are given by
2 PA D = b (2.18) g gas)( 2/1 ρπ []()+− vpf ∞ LTTcvd v
2 PA D = b (2.19) g waterjet )( 2/1 []ρπ ()ρ ()−++− d vc vpf TT ∞ vL TTh vvbv water )(
where Dg and Lv are groove depth and latent heat of vaporization. In addition, HAZ model for dry grooving is calculated by
1 2 ++ tantan 2 ϕθα § −TT · HAZ width = ln¨ v sur ¸ (2.20) gas)( θ ¨ − ¸ v tan © c TT sur ¹
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where Tc and Tsur are characteristic temperature and surrounding temperature, respectively. For the waterjet-assisted laser process, Chryssolouris et al. noted that HAZ was reduced by up to 70%. According to the review, it can be noted that though the analytical approach can very well represent the laser machining processes, the model is not easy to be formulated when many terms of dynamic parameters are applied such as temperature- dependent and time-dependent parameters. Araya and Gutierrez [143] indicated that the computing time of analytical approach was longer than the numerical approach when a complex laser ablation with highly non-linear functions was considered. Hence, the numerical approach may be more relevant for solving such complicated boundary-value problems by using approximation techniques such as finite difference, finite element and finite volume methods. Numerical methods for laser and liquid-assisted laser ablation processes will be reviewed and discussed in the next section.
2.5.3 Numerical Approach Numerical method is a mathematical tool for solving complicated problems that an analytical approach cannot handle due to the difficulties of applying non-linear functions and complex boundary conditions [144]. In the early stages of development, numerical methods were used in very limited applications due to the limitation of calculating performance for large-scale and complex problems. After the development of computer technologies to a more comprehensive level in the 1990s, numerical methods become more effective than the traditional analytical methods. The complicated boundary-value problems of heat transfer, fluid dynamics and other partial differential equations can be solved by using numerical approximation techniques. Three well-known numerical methods, i.e. finite difference, finite element and finite volume methods, have been used for solving both simple and complex sciences and engineering problems. Finite difference method (FDM) is the oldest method among the three finite approximations. It was firstly developed by Richardson in 1910 [145] for stress analysis in structural problems. This method approximates the differential equation to be a simple form of finite difference which provides a faster computation. The FDM can also be applied in various problems, such as computational fluid dynamics, heat transfer and other mathematical physics, which are not easily solved by using the closed-form
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analytical approach. In laser material processing, FDM has been utilized for laser heating [146-148], welding [149-150] and machining processes [151-155]. However, an important drawback of FDM is the truncation error in Taylor’s series expansion [156]. This issue is not relevant to the finite element method (FEM) since Taylor’s series is not involved in the FEM approach. FEM was firstly used by Courant in 1943 [157] to solve a mechanical torsion problem, and it was later modified in the 60s and 70s for structural analyses and mechanical problems. FEM can offer a more realistic irregular shape of model than the FDM. Hence, the geometric-dependent problems, such as stress analysis, thermal expansion and vibration, normally use FEM as a solving technique. FEM has also been employed in laser material processing, but it is mostly found in solving the thermo- mechanical related problems. Akarapu et al. [158] and Chen et al. [159] applied FEM to analyze the thermal stress and damage mechanism on ceramics and silicon in the laser cutting process. The temperature field and the cut profile predictions of laser drilling and cutting processes using the FEM were investigated by Polak et al. [160] and Kim [161]. From these studies, it can be seen that FEM can be used for solving both thermal and geometrical-related problems. However, the required computing time of FEM is much higher than FDM [156]. This is why FDM is often used in a wide range of applications. Another numerical approach is finite volume method (FVM). This method plays a major role in fluid flow problems where the conservations of mass, momentum and energy can be yielded even when very coarse control volume grids are applied. For the laser ablation process, Ganesh et al. [162-164] used FVM to simulate the effects of fluid flow and recoil pressure in the molten layer. According to their studies, FVM is an effective method for solving thermo-fluid problems. However, the false thermal diffusion can be obtained when the simple or improper interpolation scheme is employed. Among these three finite approximation approaches, FDM has been widely used for solving temperature and heat flow problems. This is due to the ease of implementation, simplicity and fast computing time that make the FDM more effective than the other numerical approaches. In order to determine the temperature field using the FDM, the calculation can be performed by using explicit, implicit or combined methods [156]. The explicit method is the easiest approach where the number of unknown variables is
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less than the known variables, so that a straight-forward calculation can be made. The well-known explicit methods are forward Euler, forward-time central-space (FTCS) and alternating direction explicit (ADE) methods. Though differential equations can be solved by using this method, a proper time step has to be yielded to avoid the divergence of computations. This can be noted that if the simulation has to be performed over a large period of time, the number of calculations will be extremely large in the explicit method. To overcome this time-step constraint, the implicit methods, such as backward Euler and alternating direction implicit (ADI), may be applied instead [165]. As the number of unknown variables is more than the known variables in the implicit method, many calculations have to be iteratively solved to reveal the unknown variables. Thus this may require a long computing time for yielding a converged result. The explicit and the implicit approaches can be combined together becoming the Crank-Nicolson method. This method is unconditionally stable without restriction on the size of time step. It also provides the second-order computation in both the space and time domains. The general finite difference equation for explicit, implicit and combined methods are given in [156] as
n+1 − TT n ª n+1 2 n+1 +− TTT n+1 n 2 n +− TTT n º i i = ςα i+1 i i−1 ()1−+ ς i+1 i i−1 (2.21) Δ « 2 2 » t ¬ ()Δx ()Δx ¼ where ȗ=0 for the explicit method, ȗ=1 for the implicit method and ȗ=0.5 for the Crank- Nicolson method [156]. Since the traditional laser ablation process removes the irradiated material by melting and vaporization, material phase changes have to be taken into account in the finite difference model. Ozisik [156] stated that there were five methods for solving a phase change problem, i.e. fixed grid, variable grid, front-fixing, adaptive grid generation and enthalpy methods. As the dual phases of solid-liquid at the melting point and the liquid-vapor at the boiling point take place during phase transformations, the enthalpy method is normally used to handle these phase change problems [156, 166- 167]. The enthalpy method could be applied with the explicit FDM [168], implicit iterative FDM [169] or implicit direct FDM [170] for solving heat transfer and phase change problems.
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The fundamental concept of the enthalpy method relies on the change of enthalpy and the conservation of energy rather than the change of temperature, such that
ρ § ∂H · 2T =∇ ¨ ¸ (2.22) k © ∂t ¹
T = TcTH )()( dT (2.23) ³ p T0 where H is enthalpy. Furthermore, the change of enthalpy could be replaced by the change of volumetric heat energy as proposed by Qiu et al. [151]. Phase change of material could be calculated by considering the total heat energy and the latent heat of melting or vaporization using the following equation
Δ=Δ ρ ()Δ+− ρ mps LVTTcVQ ml (2.24)
where Q, Vs, Vl and Lm are heat energy, solid phase volume, liquid phase volume and latent heat of melting, respectively. The hydrodynamics of liquid flow, the collapse of the keyhole and the material removal mechanism in the molten pool in laser material processing were investigated by implementing the explicit FDM for solving the temperature field and the cut surface morphology [171]. The explicit central space FDM was utilized by Atanasov et al. [172] for predicting the drill depth and the growth rate of the surface temperature where the solid-vapor phase change and plasma absorption effects were included in the model. The 3-D temperature field and the kerf width of the laser cutting process were investigated by using the Crank-Nicolson and the adaptive grid size schemes to reduce the computing time [152]. The 3-D explicit FDM for cut geometry prediction was also studied by Fell et al. [144, 173], in which the enthalpy-based FDM was applied to handle the phase changes of silicon in the laser grooving process. The effects of assisted gas, fluid dynamics, super heating and plasma were omitted to simplify the model, while the temperature-dependent material properties were considered. The adaptive grid size technique was applied to provide a more accurate prediction at the irradiated zone. Fell et al. [144, 173] also found that there was no substantial difference between the explicit and the implicit methods in terms of computing time due to the high
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nonlinearity of the phase changes. Another explicit FDM developed by Shin and Chung [174] was claimed to be able to predict melting and evaporating depths by using a sharp interface method rather than a general front tracking method. This method was applied for solving the problem where the melting and evaporating interfaces were very close to each other. Shin and Chung also noted that by using the sharp interface approach, a more accurate temperature prediction could be achieved. By applying a thermal convection and a constraint for material removal into the energy balance model, the temperature field and the cut profile of the liquid-assisted laser process have been predicted by using numerical modeling. However, there is very limited reported work in this area. A substantial implementation of the FDM on the liquid-assisted laser process was proposed by Li et al. [154-155]. They developed a temperature field model for the waterjet-guided laser drilling and grooving of silicon. The explicit central space FDM was applied along with the temperature-dependent material properties and the solid-liquid phase change condition. Another similar modeling work for the waterjet-guided laser machining of silicon using the finite element method (FEM) was reported by Yang et al. [175]. According to their model, the material was removed by the waterjet when the silicon completely changed to the liquid phase. However, their model has not included the waterjet impinging effect as this effect is not considered to be relevant to material removal in the waterjet-guided laser machining process. For other laser-waterjet ablation processes, there is currently no significant numerical modeling for predicting the temperature field, cut surface characteristic and material removal rate. In the next section, the effects of waterjet impingement will be reviewed. This knowledge is essential for modeling the hybrid laser-waterjet process that will be developed in this study.
2.6 Waterjet Impinging Mechanisms and Models
In the liquid-assisted laser machining processes, a pure waterjet can be applied along with a laser beam to decrease the HAZ. By properly controlling the process as in the technology to be developed in this thesis, the waterjet can increase the material removal rate. The effects of waterjet impingement on the target surface can thus be considered to take both thermal and mechanical effects. In the following sections, the effects of
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waterjet cooling and waterjet impact on the flat target surface will be presented and discussed.
2.6.1 Effects of Waterjet Cooling on the Flat Surface Liquid jet impingement has been employed in various applications such as metal and glass industries for cooling and tempering. Furthermore, it is also used in heat exchangers for cooling both large structures and micro-components [176]. Fluid mechanics and heat transfer in liquid jet impingement were studied by Watson [177], Chaudhury [178]. The in-depth investigations of jet impingement on heat transfer and fluid flow were further studied by Cadek [179] and Obot [180]. An analytical solution for a laminar jet cooling against a flat plate was firstly reported by Miyazaki and Silberman [181]. Currently, there are numerous studies both using theoretical and experimental approaches on the liquid jet impingement for cooling applications. The liquid jet can impinge on the target surface by submerging the jet under a medium, i.e. submerge jet in water, or as a free liquid jet in ambient air [182]. Garimella et al. [183-184] reported the effects of nozzle diameter (dn), Reynolds number (Re) and nozzle stand-off distance (znt) on the heat transfer coefficient in the submerged jet condition. They found that an increase in nozzle stand-off distance decreased the heat transfer coefficient, particularly when znt/dn was greater than 5 due to the reduction of jet velocity and the increasing turbulent level. The comparison of the submerged jet and the free-surface jet was reported by Stevens et al. [185] and Elison and Webb [186]. They stated that the jet velocity was affected by the jet broadening in the free-surface jet condition, while the jet destabilization occurred in the submerged jet impingement. The Nusselt number (Nu) for the laminar to turbulent flow at the stagnation point under the free-surface and the submerged jet conditions can be determined by [186]
9/1 = []()()α β 9 + α β −9 Nu0 lar eReR tur (2.25)
where Nu0, Į and ȕ are Nusselt number at the stagnation point and empirical coefficients. Table 2.1 shows the empirical coefficients in the above equation from Elison and Webb’s study [186].
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Table 2.1. The coefficients used in Equation 2.25 [186]. Nozzle diameter (mm)0.32 0.58 0.25 0.32 0.58 Type Free-surface Free-surface Submerged Submerged Submerged
znt/dn < 50 < 50 < 50 < 8 < 8
Įlar 0.0473 0.109 0.0449 0.0955 0.345
ȕlar 0.852 0.847 0.834 0.781 0.697
Įtur 1.08 1.175 0.123 0.963 1.50
ȕtur 0.444 0.465 0.682 0.473 0.491
A schematic of the free-surface liquid jet impingement is presented in Figure 2.15. The liquid jet may be divided into three main regions, i.e. free jet, stagnation and wall- jet regions [179-180, 183]. In addition, Gardon and Akfirat [187] noted that the stagnation or impinging region was about 1.2 times the jet diameter. Furthermore, Zhao et al. [188] and Shu [176] mentioned that the radial flow velocity in the wall-jet region was initially constant, and then gradually decreased due to the viscous effects at the outer region. A study of free-surface waterjet impingement under different Prandtl numbers (Pr) was presented by Vader et al. [189]. According to their study, the approximated Nusselt number at the stagnation region (Nu0) can be approximated by
= .05.0 376 Nu0 .0 569 rPeR (2.26)
Webb and Ma [190] also noted that the Nusselt number at the stagnation region (Nu0) can be separately considered as
= 4.05.0 << Nu0 .0 715 rPeR for .0 15 rP 0.3 (2.27) = .05.0 333 > Nu0 .0 797 rPeR for rP 0.3 (2.28)
Generally, the Prandtl number (Pr) for 0°C to 100°C water is varied within a range of 1.7 to 13.0 [190].
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Figure 2.15. Schematic of a free-surface liquid jet impingement [179-180].
The heat transfer coefficient was introduced by Stevens and Webb as a function of nozzle stand-off distance and nozzle diameter [182]. They found that the Nu for the r/dn of less than 0.75 (stagnation region) could be considered as a constant, and the Nu sharply dropped when the r/dn increased over 0.75. In addition, an increase in nozzle diameter and Re increased the heat transfer coefficient significantly [186, 191-192]. However, the heat transfer coefficient in the wall-jet region was found to be insensitive to the change of nozzle diameter [193]. As the Reynolds number is in a range of 4,000 to 52,000, the Nu at the stagnation region could be calculated by [182]
− .0 0336 − .0 237 § z · § v · = .0 567 ¨ nt ¸ 4.0 ¨ j ¸ Nu0 .2 67 eR ¨ ¸ rP ¨ ¸ (2.29) © d n ¹ © d n ¹
where vj is jet velocity. This equation can estimate the heat transfer coefficient with an error of 5 to 14%. Oblique waterjet impingement was investigated by Stevens and Webb [194]. Two different angles were considered as shown in Figure 2.16, i.e. șj and ijj that are inclination angle and azimuthal angle, respectively. The inclination and the azimuthal angles were varied from 40 to 90 degrees and 0 to 90 degrees. The 1-D temperature profile was measured along the x axis, and the results showed that the change of the
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angles affected the temperature profile significantly. Moreover, they also found that the maximum heat transfer position was shifted to the upstream side by s0 from the stagnation point as shown in Figure 2.17. A decrease in inclination angle (from 90 to 70 degrees) increased s0/dn on the upstream side, and the shift distance was 0.25dn at the inclination angle of 70 degrees. However, the shift could be reached to 0.5dn in some experimental cases [194]. It was also observed that when the inclination angle was greater than 80 degrees, the maximum heat transfer position was shifted to the downstream side with a reduction of cooling ability by 15-20%. In addition, a decrease in the inclination angle strongly decreased the heat transfer coefficient, while the change of azimuthal angle was reported to have a very small effect on the temperature profile.
Figure 2.16. Inclination angles in oblique liquid jet impingement [194].
Figure 2.17. Maximum heat transfer position shifted to the upstream side [194].
The local Nusselt number (Nuloc) for the upstream (r/dn < 0) and the downstream
(r/dn > 0) sides can be determined by
= α β [(χθ 2 γθ ++ δ )()] Nuloc eR exp jj / dr n (2.30)
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where Į, ȕ, Ȥ, Ȗ and į are empirical coefficients for each nozzle diameter given in Table 2.2.
Table 2.2. The coefficients for each nozzle diameter in Equation 2.30 [194]. Nozzle diameter (mm) 4.6 4.6 9.3 9.3
r/dn > 0 < 0 > 0 < 0 Į 1.330 0.831 4.40 3.92 ȕ 0.534 0.586 0.448 0.468 Ȥ 0.0968 0.0696 0.0972 0.232 Ȗ -0.272 -0.225 -0.243 -0.658 į 0.0339 0.389 0.0978 0.788
The effect of nozzle configuration on the heat transfer coefficient was studied by Stevens et al. [185] and Pan et al. [195]. By comparing the average jet exit velocity of different nozzle types, the cone-down with sharp-edge nozzle provided the maximum jet velocity followed by the sharp-edge with screen nozzle, the fully developed pipe type and the contoured edge nozzle. It was observed that the faster the jet velocity, the higher the heat transfer coefficient obtained. The average Nu at the stagnation point for all nozzle shapes is given by
.0 58 ª ()/ vvd º Nu = .0 50 eR .0 53 j javg rP 4.0 (2.31) 0 « ()» ¬ / drd n ¼
where vjavg is the average jet velocity at the nozzle exit. It has been shown that the flow profile of the liquid jet could also affect the heat transfer coefficient. Lee et al. [196] and Tong [191] investigated different flow profiles and found that the Nu was proportional to the Re0.5 for parabolic (fully developed) and uniform jet profiles. In addition, the parabolic profile provided the highest heat transfer coefficient in the stagnation region over the 1/7th power law and the uniform profiles. However, the heat transfer coefficient of these three profiles was not so different at the outer region. They also found that an increase in the impinging time significantly increased the heat transfer coefficient. In addition, the maximum cooling effect was located at the stagnation zone and gradually decreased along the radial distance [192].
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2.6.2 Effects of Waterjet Impact on the Flat Surface The main applications of pure waterjet impingement are waterjet cutting, peening, cleaning [197-203] and other surface preparations [204-205]. As presented in Figure 2.18, the waterjet structure can be separated into three main regions, i.e. initial, main and final regions [200, 202]. A continuous flow with a very small effect of air entrainment occurs in the initial region whose jet velocity has almost the same velocity at the nozzle exit. The initial-to-main region is applied for cutting applications, while the main region is generally used for cleaning and surface preparation applications due to water droplet impact and large projecting area. The waterjet totally breaks up into small droplets in the final region where the jet momentum is very low. In the waterjet cutting process, a high pressure continuous jet is preferred in order to obtain a high kinetic energy for material removal. By contrast, waterjet cleaning and peening processes do not allow the work material to be removed, so that a lower pressure or a longer stand-off distance has to be employed for producing the water droplet impact. Hence, the mechanical interaction of waterjet and work material can be considered by two main approaches, i.e. the continuous jet impact and the droplet impact.
Figure 2.18. Structure of a waterjet beam [202].
In continuous jet impact, the energy balance models can be applied in terms of jet kinetic energy and mechanical strength of the target material. When the impact pressure is higher than the failure strength of the target material, the material is deformed and
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removed. However, there is as yet no comprehensive analytical model for solving and predicting the waterjet cutting process, although many studies have been carried out to establish the process parameter relationships since the 1960s for cutting and cleaning processes. This is due to the complex mechanisms of the liquid jet impact that take place in less than a microsecond which have not been understood well enough to be able to formulate a universal model. A few process modelings for the parameter relationships were studied through numerical simulation using FEM and smoothed-particle hydrodynamics (SPH) as reported by Adler in 1995 [206], Mabrouki et al. in 2000 [207], Maniadaki et al. in 2007 [208], Ma et al. in 2008 [209] and Li et al. in 2011 [210]. However, many assumptions and some experimental data have to be applied with the simulation in order to yield an accurate prediction. The continuous waterjet impingement against a solid flat surface can also be considered as an impact between two solid materials, as shown in Figure 2.19. In the study of Tate [211-213], the impacts of a long rod were theoretically and experimentally investigated. Tate proposed that once a rigid rod impacted on a solid target surface, the rod and the target could behave like a fluid at a certain impact pressure due to the hydrodynamic effect and the elastic-plastic motion.
Figure 2.19. A long rod impacts against a solid target [211].
Tate modified Bernoulli’s equation by adding the effective dynamic strengths of rod and target into the model in order to predict the crater depth on the target and the deformation of rod, so that
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1 1 ρ 2 Pv =+ ρ ()2 +− Pvv (2.32) 2 target impact target 2 rodrod impact rod
where Ptarget and Prod are effective dynamic strengths for the target and the rod, respectively. The difference between such dynamic strengths was approximated to be 4.5 times the tensile strength of the target material. Tate noted that the shock waves were generated instantly after the impact and then propagated into the target and the rod where the rod-target interface moved in a subsonic speed with regard to the elastic wave speed [211]. Once the shock wave decayed, the deformation at the crater surface was obtained. The crater was deepened at a constant speed of penetration, and the hydrodynamic analogy was applied when the impact pressure was greater than the yield strength of materials. In the Tate studies, three impact cases of Ptarget > Prod, Ptarget < Prod and Ptarget = Prod were considered. The material was deformed when a critical velocity was reached. The critical velocity in terms of dynamic strengths and rod density is calculated by
(2 − PP ) v = at rget rod ሺ2.33) crit ρ rod
and the penetration depth (Df) is given by
2 § ρ 2 Lv ·§ r · D = ¨ rodrodrod ¸¨ rod ¸ (2.34) f ¨ ¸¨ ¸ © Ptarget ¹© rcrater ¹
where Lrod, rrod and rcrater are rod length, rod radius and crater radius, respectively. In addition, Tate noted that the square of crater radius is approximately twice the square of rod radius, i.e.
2 = 2 crater 2rr rod (2.35)
For the water droplet impact, there are more reported studies of the continuous jet impact. The fundamental concept of the droplet impact is the same as the abrasive
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particle impact in the abrasive jet or abrasive waterjet machining processes, but the hydrodynamic effect of the droplet has to be included. The mechanisms of liquid-drop impact on a dry solid surface were initially studied in 1945 to understand the rain erosion of the high speed air-craft or missiles flying in rain and mist vapors [203, 214]. The main mechanism of droplet impact is called water hammer whose impact pressure can be calculated by
ρρ vCC P = w sw s ss d (2.36) h + ρρ w sw sCC ss
where Ph, ȡw, Csw, ȡs, Css and vd are droplet impact pressure, water density, shock wave speed in water, density of target material, shock wave speed in the target material and impact velocity, respectively. For the rigid target, the equation can be simplified as
= ρ wh swvCP d (2.37)
The shock wave speed (Csw) could be approximated as the sound velocity in water (Cw) when the impact velocity is low. For a high impact velocity, the shock wave speed could be calculated by [214]
2 C § v · § v · sw += d − d ¨ ¸ 1.021 ¨ ¸ (2.38) Cw © Cw ¹ © Cw ¹
Field et al. [215] found that the pressure generated on the edge of droplets during the impact was about 3 times higher than the center. They also observed that the impact could be divided into four main stages as shown in Figure 2.20. When a liquid droplet impacts on a target surface at a high velocity, the liquid is compressed and results in a shock wave at the liquid-solid interface as shown in Figure 2.20(b). At this stage, the impact-induced force is introduced and causes macro and micro cracks on the material due to the tensile stress waves. As the pressure on the droplet edge is higher than the center, a ring profile erosion is produced [203]. Within the next few nanoseconds, the shock wave envelope moves upward against the impact direction to the free surface of
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the droplet as shown in Figure 2.20(c). An incompressible flow is developed which results in a lower pressure that can be found from
ρ v 2 P = dw (2.39) h 2
In this third stage, the lateral jetting begins to flow away radically. In the final stage shown in Figure 2.20(d), cavitation takes place inside the droplet producing a high mechanical impact on the target surface for further eroding of the material.
(a) (b) (c) (d) Figure 2.20. Process of a single droplet impact [215].
The failure of brittle materials is caused by the high tensile stress around the contact area [216], while the high compressive force causing a significant shear stress results in the plastic deformation in ductile materials [215]. Kennedy and Field [216] reported that the damage threshold velocities for liquid-drop impact on silicon were 225 m/s, 196 m/s and 170 m/s for 0.6 mm, 0.8 mm and 1.2 mm nozzle diameters, respectively. Kunaporn et al. [199] proposed a mathematical model for waterjet peening of aluminum alloys. Their model was formulated from the conversation law of momentum in control volume. The droplet distribution and diameter were assumed to be uniform and identical, respectively. The water hammer pressure of the impact is given by
3 ª º « » P d = 3CP wj « j » (2.40) imp sw v « §α ·» t « + () ¨ j ¸» j 2 zd nt tan¨ ¸ ¬« © 2 ¹¼»
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where Įj and znt are waterjet beam divergence angle and nozzle stand-off distance, respectively. Another approach was done by considering only the kinetic energy where the waterjet exit velocity is calculated by [205]
2P v = ϕ wj (2.41) nj ρ w
where ijn is waterjet nozzle coefficient. Due to the difficulties of modeling the pure waterjet impingement, there is very little theoretical knowledge reported in the literature. Many models developed were purely based on experiments, and some were formulated by combining the experimental data with some basic fluid mechanic models [217]. According to this review, it can be stated that the process model for the continuous jet and droplet impingements may be developed using the Bernoulli’s equation and the conservations of mass, momentum and energy.
2.7 Concluding Remarks
In this literature review, the fundamentals of laser technology were presented to provide a basic understanding of the optics in laser material processing. The effects of the relevant process parameters on the surface and subsurface integrity in laser micro- drilling, cutting and grooving processes were discussed. It has been known that high laser energy, high pulse frequency and low traverse speed can yield good material removal rates. However, the HAZ and other damages caused by the process could increase when these conditions are utilized. The ultra-short pulsed lasers and the liquid-assisted lasers are considered as an approach towards damage-free laser ablation processes. Due to the expensive photon cost of the short-pulsed lasers and the relatively low power available for ultrashort pulsed lasers, the liquid-assisted laser approach seems to be an effective method to reduce the damage while giving high material removal rates. Three main groups of liquid-assisted laser processes, i.e. underwater laser, waterjet-guided laser and liquid- assisted front side laser, were reviewed to reveal their fundamentals and theoretical aspects. Pure water has been normally used in the liquid-assisted laser processes due to
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its safety, cheapness and recyclability. Though other liquid media, such as alcohol and dimethyl sulfoxide, have been tested to assist the process, the advantage that these liquids brought about was found to be inadequate compared to pure water. In the underwater laser method, the work material is ablated in water where the excessive heat and the cut debris are carried away by the water, resulting in a reduction of thermal damage on the cut surface and vicinity. Since the laser beam has to pass through a layer of water, the loss of laser energy is inevitable, particularly for long laser wavelengths. The laser and the waterjet are emitted from the same nozzle in the waterjet-guided laser method. This approach can simultaneously remove and cool work material at the same time to reduce thermal damages. However, the laser wavelength has to fit within the water transmission spectrum to maintain the full reflection of laser beam inside the waterjet beam. This means that only some laser wavelengths can be employed to yield the effective use of this method. In addition, the waterjet pressure is limited to a certain level to produce a continuous flow without water atomization or jet break up, such that the use of higher water pressure for gaining more material removal rate is not possible. Furthermore, the diameter of the waterjet-guided laser is controlled by the waterjet nozzle or the waterjet diameter, so that a small jet diameter is difficult to achieve. The liquid-assisted front side method has been used in laser micromachining processes to reduce the heat-affected zone and the debris redeposition on work materials. This approach can be divided into three sub-categories, i.e. thin water film, water spraying and off-axial waterjet methods. The thin water film method is similar to the underwater approach in that there is a layer of water covering the work material for cooling and preventing the redeposition. However, the whole workpiece is not submerged in water, but only one side of the workpiece (ablated side) is shielded by a thin water layer. To produce a thinner water film, the water spraying technique may be used. As this technique can produce a water film much thinner than the thin water film method, the loss of laser energy by the water layer can be minimized. However, the thin water film and the water spraying methods are not able to gain a higher ablation rate. As a result, a waterjet has been applied off-axially with the laser beam to increase the material removal rate and decrease the thermal induced damage to the workpiece. From the literature, such an approach was tested for laser grooving.
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The finite difference approach has been found to be a powerful method for calculating complex thermal problems. In addition, the effects of liquid jet parameters on the heat transfer coefficient were reviewed; it has been found that an increase in Reynolds number, Prandtl number and waterjet nozzle diameter increases the thermal convection effect. The pure waterjet impingement was also reviewed in both the continuous jet impact and droplet impact. It has been shown that the waterjet impact model is essentially based on Bernoulli’s equation and the momentum balance where an increased water pressure increases the amount of material removed. From this literature review, the waterjet-guided laser appears to be a substantial innovation in laser machining technology. If the waterjet and laser can be applied separately as in the case of liquid-assisted front side laser machining where a waterjet is applied off-axially, any lasers may be used in the system. Further, the pressure of the waterjet can be independently controlled according to the process needs since the waterjet is no longer used as a liquid optical fiber to conduct the laser beam. As a result, the waterjet may be used to remove material with its impacting energy, such that the material can be removed in its solid state after softening by laser heating. On this ground, the laser is in fact used to heat and soften the material while the waterjet is simultaneously used to remove the softened material element by element (or layer by layer) at below its melting temperature. This combined with the cooling action of the waterjet can be expected to vastly reduce thermal-induced damage, while a shorter interaction between the laser and work material required to soften, but not to melt or vaporize, the material will have the potential to increase the material removal rate. This idea will be implemented and tested in the next chapter through an experimental investigation, where a single crystalline silicon is used as the specimen.
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Experimental Study of Hybrid Laser- Waterjet Micromachining of Silicon
3.1 Introduction
Damage occurring during laser machining has become an important issue since laser was first employed in the manufacturing industries. Thermal and physical damage occurring at the cut surface and subsurface are significant when work material is removed at a micro-scale. This is because small damages may lead to critical failures of the entire micro-structural components. According to the comprehensive review in Chapter 2, thermal damage, namely heat-affected zone (HAZ), and the redeposition of removed material unavoidably take place in laser machining due to the excessive heat, the dynamics of the melt pool and the rapid resolidification of molten material. In order to remove or recover the laser-damaged region, some secondary processes, such as ultrasonic cleaning, chemical etching and surface/subsurface treatments, are required to yield the acceptable quality and integrity of the ablated area. However, the secondary processes are considered as non-value added processes, and the associated costs are significant, particularly in highly competitive manufacturing industries where processing time and costs need to be minimized. Thus, a hybrid laser-waterjet micromachining technology has been proposed in this study as a damage-free (or nearly free) micro-fabrication process.
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The fundamental of this hybrid micromachining technology is that, rather than achieving material removal through melting and vaporizing the material by lasers, elemental material is heated and softened by laser heating and subsequently removed by the expulsion of a high pressure waterjet. This will not only reduce the temperature for material removal so as to reduce thermal damage, but also requires less thermal energy input that allows the laser traverse speed to be increased for a high cutting rate. Further, the cooling action by the waterjet reduces the thermal effect on the workpiece. It is believed that the pulsed laser heating and waterjet expelling process also involves thermal shock effect on the work material which may result in micro-cracks on the material and a subsequent material removal [115]. However, it is anticipated that with a suitable pressure setting of the waterjet, the contribution of this thermal shock to material removal should be minimal. In this chapter, micro-grooving of silicon using the proposed hybrid laser-waterjet machining technology is performed under different process parameters. Plausible trends of the groove characteristics with respect to the considered process parameters are analyzed to examine the effects of the parameters on groove width, depth and the HAZ width. The findings of this study will form the essential knowledge for selecting the appropriate process parameters to maximize the material removal rate while minimizing the HAZ for the hybrid laser-waterjet micro-grooving process. In the following sections, the hybrid laser-waterjet technology, experimental work, and a study of the micro- grooving performance using the hybrid technology will be discussed.
3.2 The Technology and Its Experimental Apparatus
A Yb:Glass nanosecond-pulsed fiber laser (Manlight ML20-PL-R-OEM) with a wavelength of 1080 nm providing a Gaussian beam with random polarization was used in this study. The maximum average power and the laser pulse duration (FWHM) are 19.4 W and 42 ns, respectively, at 20 kHz pulse frequency. The laser pulse frequency can be varied from 20 kHz to 100 kHz with a minimum step of 1 kHz. More details on technical specifications of the laser system can be found in Appendix A. The laser beam diameter exiting from the fiber is approximately 0.5 mm at 1/e2 of the Gaussian profile. The laser beam was expanded by an 8X beam expander (Linos
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bm.x 8x) before being focused by a focusing lens of 50 mm focal length (Precitec
FS50Z). The laser beam diameter at the focal position (df) can be calculated by [9]
4 λMF 2 d = l (3.1) f π Di
2 where Fl, Ȝ, Di and M are the focal length of the focusing lens, laser wavelength, entering beam diameter and beam quality factor, respectively. The beam quality (M2) for the laser used in this study is less than 1.5. Thus, the focal beam diameter (df) could be varied within the following boundaries:
4 λMF 2 × −3 × −9 = l = (4 1050 )( 101080 )( )0.1 = μ d 2 17.19 m (3.2) Mf )0.1(, π π × −3 Di 4( 10 ) 4 λMF 2 × −3 × −9 = l = (4 1050 )( 101080 )( )5.1 = μ d 2 25.78 m (3.3) Mf )5.1(, π π × −3 Di 4( 10 )
Further, the depths of focus (DOF) for M2 of 1.0 and 1.5 are [9]:
πd 2 π × − 26 f == (17. 1019 ) = DOF 2 .0 43 mm (3.4) M )0.1( 2λ (2 ×101080 −9 )
πd 2 π × − 26 f == (25. 1078 ) = DOF 2 .0 97 mm (3.5) M )5.1( 2λ (2 ×101080 −9 )
The depth of focus indicates a distance over the focal position that does not provide a significant change in the focused beam diameter as the target (such as a workpiece) is moved from the original focal position [9]. With respect to the Rayleigh range, the laser beam diameter is increased by up to 21/2 times the focused beam diameter within the DOF. According to the calculated DOF, the distances from the focal position for M2=1.0 and M2=1.5 are ±0.215 mm and ±0.485 mm, respectively. The optical components of the apparatus were mounted on a CNC x-y stage, where the laser cutting head can be moved 300x300 mm with the accuracy of ±1 ȝm along x and y directions. The movement of the cutting head in the z-axis is adjusted manually
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by a Newport precision stage with the accuracy of ±1 ȝm. The laser machine layout design is shown in Figure 3.1. The laser and the motion of the worktable are controlled by a computer.
x-axis Beam expander y-axis z-axis (max. 300 mm) (max. 300 mm) (max. 100 mm)
Workpiece Laser cutting head support
Machine table
Figure 3.1. The laser machine structures.
To enable the waterjet to expel and remove the laser-softened elemental material, the waterjet and laser beam have to be moved simultaneously during the traverse motion. For this purpose, a hybrid laser-waterjet cutting head has been developed as shown in Figure 3.2. A waterjet nozzle is incorporated into the laser cutting head by placing the waterjet unit side-by-side with the laser head. There are three required functions for the cutting head. Firstly, the waterjet nozzle has to be able to move up and down along its axis in order to provide different stand-off distances; secondly, the waterjet nozzle has to be able to move horizontally in order to change the impact position on the workpiece surface in relation to the laser-material interaction location; and thirdly, the waterjet impact angle has to be adjustable with respect to the laser beam. If for commercial applications, more functions would be required for the hybrid cutting head to perform. In addition, the nozzle tube can be bent to obtain a small angle with the laser beam that the typical setup cannot achieve due to constraints from the equipment.
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Figure 3.2. The hybrid laser-waterjet cutting head.
3.3 Experimental Design and Setup
In this hybrid technology, laser is used for heating and softening work material, while a waterjet is used for expelling the heated and softened material. Thus, the waterjet nozzle has to be placed over or after the laser beam to achieve such an action. The process parameters relevant to the hybrid laser-waterjet process are shown in Figure 3.3. A nozzle diameter of 0.57 mm is used to form the waterjet. The high pressure water is generated by a pressurized air driven pump able to yield water pressure of up to 67 MPa with an accumulator to stabilize the water pressure.
Figure 3.3. Setting parameters in the hybrid laser-waterjet micromachining process.
The experiment was conducted on a single crystalline silicon wafer of 700 ȝm thickness, whose major properties are given in Table 3.1. This hybrid laser-waterjet machining process involves a number of process parameters such as laser pulse energy,
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pulse frequency, focal plane position, water pressure, waterjet offset distance, waterjet impact angle, waterjet standoff distance and cutting head traverse speed.
Table 3.1. Silicon material properties [218]. Density [kg/m3] 2329 Thermal conductivity [W/mK] 130 Heat capacity [J/kgK] 700 Thermal diffusivity [m2/s] 7.974x10-5 Melting temperature [K] 1687
Since laser pulse frequency (f) and traverse speed (vt) may be combined as a non- dimensional term to represent the effect of the two parameters, a term of pulse overlap (PO) is introduced such that [219-220]
ª § v ·º PO 1−= ¨ t ¸ ⋅100% (3.6) « ¨ ⋅ ¸» ¬ © df b ¹¼
2 § 4λ ⋅ fpp · dd 1+= ¨ ¸ (3.7) fb ¨ π 2 ¸ © d f ¹
where db, df, Ȝ and fpp are the laser beam diameter at the workpiece surface, the focused laser beam diameter, the laser wavelength and the focal plane position, respectively. The fpp could be either above, on or below the workpiece surface, where a negative value is used for fpp when the focal plane is below the work surface and vice versa. However, a positive fpp will focus the laser beam outside the work material and is not recommended for machining applications. It is believed that a large variation of the laser pulse frequency may contribute to a large variation of the accumulated heat and hence affects the material removal process [219]. It is anticipated that this effect is small, particularly when a single level of laser frequency was considered in this study, as will be stated later. In order to facilitate the experimental design, some trial tests were carried out first with the relevant parameters selected to span a wide range within the system limitation. To accommodate the number of variables involved and to control the number of tests in a manageable size, a single level of laser pulse frequency (20 kHz) and a single
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level of waterjet standoff distance (2 mm) are considered. To consider the other parameters, two sets of experiments using the full-factorial design scheme were conducted. In the first set, multiple levels of the laser pulse energy, pulse overlap, laser focal plane position and waterjet offset distance were tested under a single level of water pressure (10 MPa) and waterjet impact angle (40 degrees), as given in Table 3.2.
Table 3.2. Parameters used in the first set of experiments. Level Process parameters 1 2 3 4
Laser pulse energy (Ep) [mJ] 0.3 0.4 0.5 0.6 Laser pulse overlap (PO) [%] 99.3 99.5 99.7 99.9 Laser focal plane position (fpp) [mm] 0 -0.2 -0.4 -0.6
Waterjet offset distance (xwl) [mm] 0 0.2 0.4 0.6
Water pressure (Pwj) [MPa] 10
Waterjet impact angle (θj) [deg] 40
The second set of experiments focuses on the effect of water pressure and waterjet impact angle. The variables and their levels selected are given in Table 3.3. Specifically, four levels of water pressure and four levels of waterjet impact angle were considered with two levels of laser pulse energy and pulse overlap that were taken from the maximum and minimum values in the first set of experiments. The other parameters were kept constant, including focal plane position (0 mm), and waterjet offset distance (0.4 mm).
Table 3.3. Parameters used in the second set of experiments. Level Process parameters 1 2 3 4
Laser pulse energy (Ep) [mJ] 0.3 0.6 Pulse overlap (PO) [%] 99.3 99.9 Focal plane position (fpp) [mm] 0
Waterjet offset distance (xwl) [mm] 0.4
Water pressure (Pwj) [MPa] 5 10 15 20
Waterjet impact angle (șj) [deg] 30 40 50 60
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The experimental setup is depicted in Figure 3.4, where the waterjet is positioned after the laser beam with a waterjet offset distance.
Laser Waterjet nozzle
Waterjet impact angle
Traverse direction Workpiece
Waterjet offset distance
Figure 3.4. The experimental setup of the hybrid laser-waterjet micromachining.
Surface finish is not a major concern in silicon grooving or dicing and not a concern in this study, and, for the extremely small kerf geometry, it is very difficult to measure and get correct values for a sensible analysis. The surface characteristics and cut geometries in terms of groove width, depth and HAZ width were observed and measured by using a 3D digital microscope (Keyence Model VHX-100) with the maximum magnification of 5000 times. Figure 3.5 shows the measured groove geometrical features. The HAZ size in this study is identified on the top work surface where color transition and deformation of laser-softened material are seen under the microscope on non-removed material as shown in Figure 3.5. All experimental data are given in Appendix B.
Figure 3.5. The measurement of groove geometries.
According to a statistical study of the tests data, the sample size of three for each cutting condition is enough to yield the power of the test of 80% for 95% confidence
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interval and, as such, three measurements were performed for each test, while the average was taken as the final reading.
3.4 Interactions of Laser Beam and Waterjet
The relative position of the laser beam and waterjet is adjusted by the waterjet offset distance. The laser beam can strike on the workpiece surface within or outside the perimeter of the waterjet at its intersection with the target surface. This intersection is in fact an elliptic profile whose major and minor diameters are given by
d d = j (3.8) imp,major θ cos j = imp,minor dd j (3.9)
where dimp,major, dimp,minor and șj are major and minor diameters of the waterjet impact profile and waterjet impact angle, respectively. When the laser beam is set outside the elliptic profile of the waterjet on the target surface, the laser has to go through a thin water layer on the target surface as shown in Figure 3.6(a). If ignoring the water bouncing effect, the water layer thickness at outside the waterjet impact area, but before the hydraulic jump, can be approximated to be 10% of the waterjet diameter [191]. However, when the waterjet offset distance is small, the laser beam will overlap with the waterjet and has to go through a thick layer of water (Figure 3.6(b)) before striking on the target.
(a) (b) Figure 3.6. Idealized relationship between waterjet and laser beam under different waterjet offset distances: (a) non-overlap, and (b) overlap.
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According to Equation 3.8, an increase in the waterjet impact angle increases the waterjet impact area on the work surface. It will also result in a thick water layer to be formed and hence increase the interference of water to the laser beam. The thickness of water layer can be determined with the known waterjet diameter (dj), waterjet impact angle (șj) and waterjet offset distance (xwl), by taking an idealized jet impact without considering the jet spreading and bouncing. The resulting equation for the water layer thickness (hw) is given by
ª d j º d j d j °« − x » tan(90 −θ ;) x −≤≤− 1.0 d tanθ 2cosθ wl j 2cosθ wl 2cosθ jj = °¬« j ¼» j j hw ® (3.10) d ° 1.0 d ; x j −> 1.0 d tanθ ° j wl θ jj ¯ 2cos j
The geometrical dimensions of the idealized jet, water layer and waterjet offset distance are shown in Figure 3.7.
Figure 3.7. The water layer thickness formed in the hybrid process.
According to the waterjet nozzle diameter used in this study, the waterjet offset distance of equal or greater than 0.4 mm will theoretically separate the laser beam from the waterjet when the impact angle is 40 degrees. When the jet impact angle increases or the waterjet offset distance decreases, the waterjet and the laser beam will overlap each other at the work surface and water layer thickness will increase monotonically. Figures 3.8(a) and (b) show the relationship between the water layer thickness and the waterjet impact angle under different waterjet offset distances, and how the major diameter of the elliptic impact profile changes with the waterjet impact angle.
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1.8 3.5 Waterjet nozzle diameter: 0.57 mm Waterjet nozzle diameter: 0.57 mm 1.6 Offset distance 3 1.4 0 mm 2.5 1.2 0.2 mm
1 0.4 mm (mm) 2
(mm) 0.6 mm
w 0.8 1.5 h imp,major
0.6 d 1 0.4 0.5 0.2 0 0 0 102030405060708090 0 102030405060708090 Waterjet impact angle (deg) (a) Waterjet impact angle (deg) (b)
Figure 3.8. (a) Waterjet impact angle versus water layer thickness (hw) at different
waterjet offset distances, and (b) major diameter of waterjet impact area (dimp,major).
Though the non-overlap condition can take place at the top workpiece surface with a proper waterjet offset distance, the laser beam and the waterjet are eventually overlapped again when a certain groove depth is created as shown in Figure 3.9. Such overlap and a longer travel distance of the laser beam in water could lead to a reduction of ablation rate.
Figure 3.9. The laser-waterjet overlap inside the groove.
In order to minimize the laser-waterjet overlap inside the groove created, a small waterjet impact angle with a proper offset distance should be applied to extend the non- intersection depth (zi), which can be approximated by
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2 x cosθ −⋅ d d z = wl jj ; x j −> 1.0 d tanθ (3.11) i θθ wl θ jj 2cos tan jj 2cos j
The above analysis indicates that the laser beam has to go through a water layer in the hybrid process. As a result, some laser energy could be lost by the laser reflection, distortion and energy absorption of water. Moreover, the waterjet cooling effect causes a high heat transfer coefficient on the work surface. These optical and thermal effects may require a higher laser energy input to soften the material, than otherwise needed, and the disturbance and the reflection of the laser beam by the water layer result in a larger, yet low quality, beam size at the work surface. This presumably increases the heated area, and hence increases the groove width, but reduces the groove depth.
3.5 Comparison with the Conventional Dry Laser Machining
Dry laser ablation of silicon was performed with the corresponding laser parameter settings used in this study for a comparison purpose. Dry laser machining and hybrid laser-waterjet machining results were comparatively investigated in order to reveal cut quality and advantages of the hybrid process for near damage-free micromachining. The samples of the machined grooves and the surrounding area are shown in Figure 3.10.
Laser pulse overlap 99.3% 99.5% 99.7% 99.9% Laser pulse energy = 0.3 mJ
Dry
Hybrid
Figure 3.10. The surface characteristics of silicon after dry and hybrid machining when the laser pulse energies of 0.3 mJ to 0.6 mJ and the pulse overlaps of 99.3% to 99.9% were used (focal plane position=0 mm, waterjet offset distance=0.4 mm, water pressure=10 MPa and waterjet impact angle=40°).
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Laser pulse overlap 99.3% 99.5% 99.7% 99.9% Laser pulse energy = 0.4 mJ
Dry
Hybrid
Laser pulse energy = 0.5 mJ
Dry
Hybrid
Laser pulse energy = 0.6 mJ
Dry
Hybrid
Figure 3.10. (cont.) The surface characteristics of silicon after dry and hybrid machining when the laser pulse energies of 0.3 mJ to 0.6 mJ and the pulse overlaps of 99.3% to 99.9% were used (focal plane position=0 mm, waterjet offset distance=0.4 mm, water pressure=10 MPa and waterjet impact angle=40°).
It can be seen that the dry laser machining process could not yield proper grooves on the silicon, but generated a large HAZ with a remarkable redeposition whose size increases with an increase in laser pulse energy and pulse overlap. This is in contrast to the hybrid laser-waterjet cutting process that has produced a clear cut without
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discernible HAZ and the redeposition of removed material. It may be explained that the heat transfer coefficient of dry laser ablation is only about 10 W/m2K [221-222], while 2 to 20 MW/m2K is accounted at the work surface when a 10 MPa waterjet is used for cooling [154-155, 182, 186, 189-190, 194], such that the workpiece temperature resulted in the hybrid laser-waterjet process is low, hence decreasing the HAZ. In the laser-waterjet micromachining process, the waterjet has removed the laser- softened material to form a groove on the workpiece. Figure 3.11 shows that the groove width increases with an increase in water pressure, indicating that a higher pressure waterjet can remove the material at a lower temperature. Further, the cut surface and the surrounding areas were protected by a layer of water, flowing radially from the waterjet impact area on the work surface, to prevent the deposition of removed material and other debris. These factors together with the water cooling action have significantly reduced the formation of a thermal damaged area in the hybrid process. It can thus be stated that free or near-free thermal-damage and an improved material removal rate can be achieved by using this hybrid laser-waterjet micromachining technology.
Laser dry ablation 5 MPa water pressure 10 MPa water pressure
Pulse energy Ep = 0.3 mJ
Pulse energy Ep = 0.6 mJ
Figure 3.11. The surface characteristics of silicon after machining (focal plane position=0 mm, pulse overlap=99.9%, waterjet offset distance=0.6 mm, and waterjet impact angle=40o).
3.6 Effects of Process Parameters on the Groove Width
3.6.1 Statistical Analysis The residual plots for groove width shown in Figure 3.12 demonstrate the normal distribution of the data from the two sets of experiments given in Tables 3.2 and 3.3.
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The graph of residual versus observation order presents a random pattern, indicating that the experiments and the measurements were randomly conducted to minimize the hysteresis and other related errors during the operations. By using the ANOVA, all process parameters shown in Table 3.4 have a p-value of less than 0.05, such that all parameters significantly affect the groove width at the 95% confidence interval. It is observed that the highest F-value is on the focal plane position (fpp), implying that the groove width is mostly affected by the change of focal position.
5HVLGXDO )UHTXHQF\ 5HVLGXDO 2EVHUYDWLRQ2UGHU
Figure 3.12. Residual plots for groove width.
Table 3.4. Analysis of variance for groove width. Sources DoF Seq SS Adj SS Adj MS F p-value fpp 3 693731 631275 210425 121.01 0 xwl 3 193548 189373 63124 36.3 0
Ep 3 126116 126374 42125 24.22 0 PO 3 296576 296576 98859 56.85 0
șj 3 214190 74172 24724 14.22 0
Pwj 3 30157 55788 18596 10.69 0 Error 941 1636337 1636337 1739 Total 959 3190656
3.6.2 The Effect of Laser Pulse Energy The effect of laser pulse energy on groove width is shown in Figure 3.13. It indicates that an increase in laser pulse energy increases groove width. This is attributed to the size of the laser-heated region that expands with the laser heat input into the work
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material, so that the waterjet can remove the softened material to open a wider groove when a higher pulse energy is used.
280 PO: 99.9 % fpp xwl: 0.4 mm 0 mm 240 P : 10 MPa wj -0.2 mm ș : 40 j -0.4 mm
m) 200
ȝ -0.6 mm 160
120
80 Groove width ( width Groove
40
0 0.2 0.3 0.4 0.5 0.6 0.7 Laser pulse energy (mJ) Figure 3.13. The effect of laser pulse energy on groove width.
3.6.3 The Effect of Focal Plane Position The effect of laser focal plane position (fpp) on the top groove width shown in Figure 3.14 indicates that the fpp has a marginal effect on the groove width. It can be seen that the zero fpp yielded a narrower groove than the negative fpp. It follows that the laser is focused and has the minimum spot size on the work surface when zero fpp is used, so that it produces a small top groove width.
280 PO: 99.9 % Pulse energy xwl: 0.4 mm 0.3 mJ 240 P : 10 MPa wj 0.4 mJ ș : 40 j 0.5 mJ
m) 200
ȝ 0.6 mJ 160
120
80 Groove width ( width Groove
40
0 -0.8 -0.6 -0.4 -0.2 0 0.2 Focal plane position (mm) Figure 3.14. The effect of focal plane position on groove width.
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The groove width is, however, found to increase when a small fpp is used and then slightly decrease with a further decrease in fpp. This can be explained in that a small negative fpp, i.e. within the depth of focus (0.215 ȝm), results in a relatively large laser- irradiated area where laser energy density is still high enough to yield a wider groove under waterjet cooling. However, as the laser-irradiated area increases with a further decrease in fpp, the laser energy density drastically decreases as shown in Figures 3.15(a) and (b), such that a wide groove cannot be produced due to the insufficient laser energy density for softening the silicon.
90 300 Pulse energy
80 ) 0.3 mJ 2 250 0.4 mJ 70 0.5 mJ 60 200 0.6 mJ 50 Ȝ : 1080 nm
m) 150 df : 17.2 ȝm ȝ ( 40 Depth of focus: 0.215 ȝm 30 100 20 Ȝ : 1080 nm df : 17.2 ȝm 50 10 (J/cm density energy Laser Depth of focus: 0.215 ȝm Laser beam diameter at top surface top at diameter beam Laser 0 0 -1 -0.8 -0.6 -0.4 -0.2 0 -1 -0.8 -0.6 -0.4 -0.2 0 Focal plane position (mm) Focal plane position (mm) (a) (b) Figure 3.15. The effects of focal plane position on: (a) laser beam diameter at the top workpiece surface and (b) the laser energy density under different laser pulse energies.
The plot of laser energy density against groove width is shown in Figure 3.16. This demonstrates that the laser energy density caused by the small fpp can produce a narrower groove than the large fpp at a similar energy density level. Thus it can be noted that the laser-irradiated area caused by fpp significantly affects the groove width in the hybrid laser-waterjet machining process. Some selected samples are shown in Figure 3.17 to demonstrate the cut surface characteristics under different laser pulse energies and fpp’s tested as discussed above.
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280 PO: 99.9 % fpp xwl: 0.4 mm 0 mm 240 P : 10 MPa wj -0.2 mm ș : 40 j -0.4 mm
m) 200
ȝ -0.6 mm 160
120
80 Groove width ( width Groove
40
0 0 50 100 150 200 250 300 Laser energy density (J/cm2) Figure 3.16. The effect of laser energy density on groove width.
Laser pulse energy 0.3 mJ 0.4 mJ 0.5 mJ 0.6 mJ Focal plane position = 0 mm
Focal plane position = -0.6 mm
Figure 3.17. The surface characteristics of silicon after hybrid laser-waterjet machining when laser pulse energies of 0.3 mJ to 0.6 mJ and focal plane positions of 0 mm and - 0.6 mm were used (pulse overlap=99.9%, waterjet offset distance=0.6 mm, water pressure=10 MPa and waterjet impact angle=40°).
3.6.4 The Effect of Laser Pulse Overlap As shown in Figures 3.18(a) and (b), an increase in laser pulse overlap increases the groove width. A possible explanation is that a high pulse overlap allows more laser energy to be transferred to a given volume (or area) of the work material than the low pulse overlap, so that the laser-heated region becomes larger and more softened material can be removed by the waterjet impingement.
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280 280 Pulse energy fpp: 0 mm fpp Ep: 0.6 mJ 0.3 mJ xwl: 0.4 mm 0 mm x : 0.4 mm 240 240 wl 0.4 mJ Pwj: 10 MPa -0.2 mm Pwj: 10 MPa 0.5 mJ șj: 40 -0.4 mm șj: 40
m) 200 0.6 mJ m) 200 -0.6 mm ȝ ȝ 160 160
120 120
80 80 Groove width ( width Groove Groove width ( width Groove
40 40
0 0 99.1 99.3 99.5 99.7 99.9 99.1 99.3 99.5 99.7 99.9 Pulse overlap (%) Pulse overlap (%) (a) (b) Figure 3.18. The effects of laser pulse overlap on groove width.
The plot in Figure 3.18(a) also indicates that a wider groove can be produced when a higher laser pulse overlap or a higher laser pulse energy is used. In general, the effects of laser pulse overlap and pulse energy on the groove width are similar in that they affect the size of laser-heated region. This means that the use of a high laser pulse overlap with a low laser energy can produce an equivalent groove width when a low pulse overlap but a high pulse energy is used. However, from a manufacturing point of view, high laser energy with low pulse overlap is preferred to enhance the material removal rate. Figure 3.18(b) shows the effect of laser pulse overlap on groove width under different focal plane positions. This indicates that a narrower top groove width is produced when a smaller fpp or a lower laser pulse overlap is applied.
3.6.5 The Effect of Waterjet Offset Distance The effect of waterjet offset distance can be seen in Figures 3.19(a) to (c) which shows that a decrease in the waterjet offset distance increases the groove width. This is due to the fact that as the offset distance decreases, more laser beam interference occurs and the laser has to go through a thicker layer of water. Such interference can increase the laser spot size due to the laser beam defocusing after passing through the water layer, so that the groove width increases. According to the plot shown in Figure 3.8(a), the water layer thickness increases when the offset distance decreases. This is associated with a significant increase in
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groove width from the transition of non-overlap (0.4 mm) to overlap (0.2 mm) where a considerably thick water layer is formed and hence a wide groove is created. In addition, as the offset distance further increases, the laser-heated material is found to be hardly removed by a high waterjet impingement due to the rapid cooling at the work surface, so that a narrow groove is obtained. Thus, it can be pointed out that the waterjet offset distance should be kept to a minimum within the non-overlap condition, i.e. at the transition of the overlap to the non-overlap approximated by the major radius of the elliptic waterjet impact profile, to gain more material removed in the hybrid laser- waterjet machining process.
280 280 Pulse energy Pulse overlap 0.3 mJ 240 240 99.30% 0.4 mJ 99.50% 0.5 mJ 99.70%
m) 200
m) 200
ȝ 0.6 mJ ȝ 99.90% 160 160
120 120
80 Groove width ( width Groove 80 Groove width ( Groove width fpp: 0 mm Ep: 0.6 mJ PO: 99.9 % fpp: 0 mm 40 40 Pwj: 10 MPa Pwj: 10 MPa șj: 40 șj: 40 0 0 -0.2 0 0.2 0.4 0.6 0.8 -0.2 0 0.2 0.4 0.6 0.8 Waterjet offset distance (mm) Waterjet offset distance (mm) (a) (b)
280 fpp 240 0 mm -0.2 mm -0.4 mm
m) 200
ȝ -0.6 mm 160
120
80 Groove width ( width Groove Ep: 0.6 mJ PO: 99.9 % 40 Pwj: 10 MPa șj: 40 0 -0.2 0 0.2 0.4 0.6 0.8 Waterjet offset distance (mm) (c) Figure 3.19. The effects of waterjet offset distance on groove width.
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When examining the combined effect of waterjet offset distance and laser pulse energy on the groove width, an increase in waterjet offset distance decreases the top groove width for all laser energies used as shown in Figure 3.19(a), where a lower energy input to the work material gives a narrower groove. A similar decreasing trend can also be seen in Figure 3.19(b) since the laser pulse energy and the pulse overlap affect the laser-material interaction in a similar way. The effect of waterjet offset distance on the top groove width under different fpp shown in Figure 3.19(c) demonstrates that some large negative fpp cannot produce a cut due to a significant reduction of laser energy density at small waterjet offset distances. Some grooves produced under different waterjet offset distances are shown in Figure 3.20.
Laser pulse overlap 99.3% 99.5% 99.7% 99.9% Waterjet offset distance = 0 mm
Waterjet offset distance = 0.2 mm
Waterjet offset distance = 0.4 mm
Waterjet offset distance = 0.6 mm
Figure 3.20. The surface characteristics of silicon after hybrid machining when laser pulse overlaps of 99.3% to 99.9% and waterjet offset distances of 0 mm to 0.6 mm were used (laser pulse energy=0.3 mJ, focal plane position=0 mm, water pressure=10 MPa and waterjet impact angle=40°).
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In most cases where the waterjet overlaps with the laser at the work surface (e.g. xwl=0 mm), the quality of cuts is relatively poor and the groove width is large. When a laser beam is optically disturbed by the waterjet in the overlap conditions, the laser may be defocused and distorted. This optical disturbance results in a larger (and maybe uneven) heated area on the work surface, yielding a wider groove of lower quality.
3.6.6 The Effect of Water Pressure The effect of water pressure on the groove width is shown in Figure 3.21. It can be seen that an increase in water pressure increases the groove width. This is due to the high water pressure that can remove more material at relatively low temperature (or in less soft status), and thus increases the groove width. It can also be noticed that an increase in laser pulse energy or pulse overlap also increases the groove width as discussed earlier.
280 Ep=0.3 mJ, PO=99.3% fpp: 0 mm Ep=0.6 mJ, PO=99.3% x : 0.4 mm 240 wl Ep=0.3 mJ, PO=99.9% șj: 40 Ep=0.6 mJ, PO=99.9% 200 m) ȝ 160
120
80 Groove width ( width Groove
40
0 0 5 10 15 20 25 Water pressure (MPa) Figure 3.21. The effect of water pressure on groove width.
3.6.7 The Effect of Waterjet Impact Angle Figure 3.22(a) shows the effect of waterjet impact angle on the groove width. It is apparent that an increase in this parameter increases the groove width. This may be attributed to the fact that the oblique waterjet impact force acts with a horizontal component and a vertical component. As the impact angle increases, the horizontal force component increases, which increases the shear force in the direction parallel to the work surface and hence opens a wider groove.
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280 Ep=0.3 mJ, PO=99.3% fpp: 0 mm 280 Ep: 0.6 mJ Ep=0.6 mJ, PO=99.3% x : 0.4 mm 240 wl fpp: 0 mm Ep=0.3 mJ, PO=99.9% Pwj: 10 MPa 240 PO: 99.9 % Ep=0.6 mJ, PO=99.9% xwl: 0.4 mm 200 m)
m) 200 ȝ ȝ 160 160
120 120
80 Water pressure
Groove width ( width Groove 80 Groove width ( width Groove 5 MPa 10 MPa 40 40 15 MPa 20 MPa 0 0 20 30 40 50 60 70 20 30 40 50 60 70 Waterjet impact angle (deg) Waterjet impact angle (deg) (a) (b) Figure 3.22. The effects of waterjet impact angle on groove width.
The effect of waterjet impact angles on the groove width under different water pressures is shown in Figure 3.22(b). It can be noticed that a higher water pressure can produce a wider groove for all waterjet impact angles considered in this study. It can also be observed that a significant increase in groove width can be achieved at the waterjet impact angles of greater than 40°. This is attributed to the laser-waterjet overlap effect that occurs when the impact angle is greater than 40° (xwl=0.4 mm) as shown in Figure 3.8(a). The grooves formed on silicon under different waterjet pressures and impact angles are shown in Figure 3.23, which clearly demonstrates that an increase in the water pressure and the waterjet impact angle increases the groove width.
Water pressure 5 MPa 10 MPa 15 MPa 20 MPa Waterjet impact angle = 30 degrees
Figure 3.23. The surface characteristics of silicon after hybrid machining when water pressures of 5 MPa to 20 MPa and waterjet impact angles of 30° to 60° were used (laser pulse energy=0.6 mJ, focal plane position=0 mm, pulse overlap=99.9% and waterjet offset distance=0.4 mm).
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Water pressure 5 MPa 10 MPa 15 MPa 20 MPa Waterjet impact angle = 40 degrees
Waterjet impact angle = 50 degrees
Waterjet impact angle = 60 degrees
Figure 3.23. (cont.) The surface characteristics of silicon after hybrid machining when water pressures of 5 MPa to 20 MPa and waterjet impact angles of 30° to 60° were used (laser pulse energy=0.6 mJ, focal plane position=0 mm, pulse overlap=99.9% and waterjet offset distance=0.4 mm).
3.7 Effects of Process Parameters on the Groove Depth
3.7.1 Statistical Analysis The residual plots for groove depth shown in Figure 3.24 demonstrate that the residual data distribute about zero as a normal shape. The plot of residual versus observation order shows a random pattern, indicating that the experiments and the measurements were conducted in a random sequence to minimize the uncontrolled effects during the operations. All process parameters obtained from the ANOVA are shown in Table 3.5. It can be seen that all p-values are less than 0.05, indicating that all parameters significantly affect the groove depth under a 95% confidence interval. It is also observed that the F-value of focal plane position (fpp) is the highest, implying that the change of focal plane position strongly affects the groove depth.
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5HVLGXDO )UHTXHQF\ 5HVLGXDO 2EVHUYDWLRQ2UGHU
Figure 3.24. Residual plots for groove depth.
Table 3.5. Analysis of variance for groove depth. Sources DoF Seq SS Adj SS Adj MS F p-value fpp 3 740859 671405 223802 243.31 0 xwl 3 505839 499237 166412 180.92 0
Ep 3 132557 132717 44239 48.1 0 PO 3 389659 389659 129886 141.21 0
șj 3 323060 52209 17403 18.92 0
Pwj 3 126771 37216 12405 13.49 0 Error 941 865548 865548 920 Total 959 3084292
3.7.2 The Effect of Laser Pulse Energy The effect of laser pulse energy on groove depth is shown in Figure 3.25. It can be noticed that the groove depth increases with an increase in laser pulse energy. It follows that the laser-heated region expands in all directions from the irradiated spot under high laser energy inputs, so that it does not only increase the groove width, but also the depth. In addition, the formation of plasma on the work material in water could occur at higher radiant exposure regimes, i.e. 1 to 10 GW/cm2 [66, 81]. The strong plasma expansion and vaporization of water can result in a compressive driving force for debris expulsion leading to an increase in material removal rate [82, 223-224], and the depth of cut.
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280 fpp PO: 99.9 % 240 0 mm xwl: 0.4 mm -0.2 mm Pwj: 10 MPa -0.4 mm șj: 40
m) 200
ȝ -0.6 mm 160
120
80 Groove depth ( depth Groove
40
0 0.2 0.3 0.4 0.5 0.6 0.7 Laser pulse energy (mJ) Figure 3.25. The effect of laser pulse energy on groove depth.
3.7.3 The Effect of Focal Plane Position The effect of laser focal plane position on the groove depth is plotted in Figure 3.26(a). It shows that a decrease in the focal plane position decreases the groove depth. This could be explained that a higher laser energy density at or close to the work surface under a smaller or less negative fpp provides a larger heated and softened region. As a result, a deeper groove can be made by the waterjet impingement (Figure 3.26(b)). By contrast, a larger negative fpp (where the laser focuses at below the work surface) may cause more laser energy loss when it travels through the water layer in a non-focused and low energy density status, thus decreasing the groove depth. In addition, the laser energy losses become more obvious as the depth of the groove increases since the laser beam needs to travel even further to reach a transient bottom surface of a groove, while the focal position is not moved with the depth created. This also results in a lower ablation rate.
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280 280 PO: 99.9 % PO: 99.9 % x : 0.4 mm xwl: 0.4 mm 240 wl 240 Pwj: 10 MPa Pwj: 10 MPa șj: 40 șj: 40
m) 200 m) 200 ȝ ȝ 160 160
120 120 Pulse energy fpp 80 80 Groove depth ( depth Groove Groove depth ( depth Groove 0.3 mJ 0 mm 0.4 mJ -0.2 mm 40 0.5 mJ 40 -0.4 mm 0.6 mJ -0.6 mm 0 0 -0.8 -0.6 -0.4 -0.2 0 0.2 0 50 100 150 200 250 300 Focal plane position (mm) Laser energy density (J/cm2) (a) (b) Figure 3.26. The effects of focal plane position on groove depth.
3.7.4 The Effect of Laser Pulse Overlap The influence of laser pulse overlap on groove depth is shown in Figures 3.27(a) and (b), where an increase in laser pulse overlap increases the groove depth. This is similar to the effect of laser pulse energy in that a high heat input from a higher percentage of laser overlap provides a larger and deeper laser-heated region and results in a deeper groove. According to the relationships between pulse overlap, laser pulse energy and focal plane position shown in Figures 3.27(a) and (b), it can be noted that low pulse overlap, high laser pulse energy and small fpp should be applied to form a remarkable groove for increasing the material removal rate. Regarding the Wee’s study [81], an intense hydrodynamic motion of the bulk water could be activated, which generates an upward flow including a bulk-water ejection in underwater laser ablation. Such vigorous flow behavior of water and jet rebounding due to the irregular profile of groove could possibly cause a significant laser beam interference under low pulse overlap in the hybrid laser-waterjet machining process as well. This may result in a substantial disturbance of the laser beam by water and hence decreases the laser intensity and the groove depth accordingly.
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280 280 Pulse energy fpp Ep: 0.6 mJ 0.3 mJ 0 mm x : 0.4 mm 240 240 wl 0.4 mJ -0.2 mm Pwj: 10 MPa 0.5 mJ -0.4 mm șj: 40
m) 200 0.6 mJ 200 -0.6 mm ȝ m) ȝ 160 160
120 120
80 80 Groove depth ( depth Groove fpp: 0 mm ( depth Groove x : 0.4 mm 40 wl 40 Pwj: 10 MPa șj: 40 0 0 99.1 99.3 99.5 99.7 99.9 99.1 99.3 99.5 99.7 99.9 Pulse overlap (%) Pulse overlap (%) (a) (b) Figure 3.27. The effects of laser pulse overlap on groove depth.
3.7.5 The Effect of Waterjet Offset Distance The effect of waterjet offset distance on the groove depth is shown in Figures 3.28(a) and (b). It can be seen that an increase in the waterjet offset distance causes an increase in groove depth initially, but as the offset distance further increases to beyond 0.4 mm, there is a decreasing trend for groove depth. This is because the laser-waterjet overlap condition takes place at 0 and 0.2 mm offset distances where an increase in the offset distance reduces the water layer thickness for the laser to go through, so that there is a reduced water layer effect on the laser beam and hence the groove depth increases. When the offset distance is equal to or greater than 0.4 mm in the current setup, there is no overlap between the laser beam and waterjet at the work surface, as discussed earlier in the chapter. In such a case, the removal of softened material is mainly based on the weak horizontal shear force imposed by the water flow on the work surface. As a result, the decrease in the effect of water layer on the groove depth is traded off by the decreased effectiveness of the waterjet expelling effect, hence the groove depth starts to decrease as the waterjet offset distance further increases.
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280 280 fpp: 0 mm Pulse energy Pulse overlap PO: 99.9 % 0.3 mJ 99.30% 240 P : 10 MPa 240 wj 0.4 mJ 99.50% ș : 40 j 0.5 mJ 99.70%
m) 200 m) 200
ȝ 99.90%
0.6 mJ ȝ 160 160
120 120
80 80 Groove depth ( depth Groove Groove depth ( depth Groove Ep: 0.6 mJ fpp: 0 mm 40 40 Pwj: 10 MPa șj: 40 0 0 -0.2 0 0.2 0.4 0.6 0.8 -0.2 0 0.2 0.4 0.6 0.8 Waterjet offset distance (mm) Waterjet offset distance (mm) (a) (b) Figure 3.28. The effects of waterjet offset distance on groove depth.
3.7.6 The Effect of Water Pressure Figure 3.29 shows that, in general, an increase in water pressure increases the groove depth. This is attributed to the fact that a high water pressure can expel more softened material, so that when the other conditions remain unchanged, an increase in water pressure removes more laser-heated material, and hence increases the groove depth. In addition, with a high pressure waterjet, the ablated material and debris particles are removed and flushed away from the irradiated zone. This leads to a greater absorption of incident laser reaching the work material surface and results in a deeper groove.
320 Ep=0.3 mJ, PO=99.3% 280 Ep=0.6 mJ, PO=99.3% Ep=0.3 mJ, PO=99.9% 240 Ep=0.6 mJ, PO=99.9% m) ȝ 200
160
120
Groove depth ( depth Groove 80 fpp: 0 mm 40 xwl: 0.4 mm șj: 40 0 0 5 10 15 20 25 Water pressure (MPa) Figure 3.29. The effect of water pressure on groove depth.
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However, this effect is very marginal at low laser pulse energy and/or low laser pulse overlap. An increase in water pressure increases the Reynolds number of the water flow, which causes an increase in the heat transfer coefficient. As a result, the material becomes less softened and requires a higher water pressure to reach its failure strength. This is why the effect of water pressure on the groove depth is small when low laser pulse energies and/or low pulse overlap conditions are used. Furthermore, air entrainment, waterjet rebounding and mist formation above the water layer can occur during the process, particularly at high water pressure as shown in Figure 3.30. These phenomena could optically cause the reflection and the deflection of the laser beam, which in turn cause a poor laser beam quality and consequently decrease the material removal rate. Hence, when a higher water pressure is used, a relatively higher laser energy or pulse overlap should be applied to overcome such energy losses.
Hydraulic Waterjet Air entrainment jump nozzle
Silicon wafer Water pressure: 5 MPa Water pressure: 10 MPa
Mist
Water pressure: 15 MPa Water pressure: 20 MPa Figure 3.30. Characteristics of water after the impact under different pressures.
3.7.7 The Effect of Waterjet Impact Angle Figure 3.31(a) shows that an increase in waterjet impact angle causes a decrease in groove depth. This may be due to the decreased penetration force along the depth direction and the increased shear force along the work surface by the waterjet at an increased impact angle. The former reduces the depth of cut formed, while the latter
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facilitates the expelling of softened material from the groove and increases the groove width. Furthermore, a large waterjet impact angle increases the likelihood of the overlap between laser beam and waterjet, as shown in Figure 3.8(a), so that it causes an increase in the water layer thickness for the laser to penetrate before striking the material. As a result, the laser energy loss when going through the thick water layer causes a decrease in groove depth. In addition, the interaction of the waterjet impact angle and water pressure plotted in Figure 3.31(b) demonstrates that as the waterjet impact angle decreases, the laser beam has an increased opportunity to interact with the work material, which enhances the laser coupling with the material and hence increases the ablation efficiency.
320 Ep=0.3 mJ, PO=99.3% 320 fpp: 0 mm Ep: 0.6 mJ Ep=0.6 mJ, PO=99.3% x : 0.4 mm 280 wl 280 fpp: 0 mm Ep=0.3 mJ, PO=99.9% Pwj: 10 MPa PO: 99.9 % Ep=0.6 mJ, PO=99.9% 240 240 xwl: 0.4 mm m) m) ȝ 200 ȝ 200 160 160
120 120 Water pressure Groove ( depth 80 ( depth Groove 80 5 MPa 10 MPa 40 40 15 MPa 20 MPa 0 0 20 30 40 50 60 70 20 30 40 50 60 70 Waterjet impact angle (deg) Waterjet impact angle (deg) (a) (b) Figure 3.31. The effects of waterjet impact angle on groove depth.
3.8 Effects of Process Parameters on the HAZ Width
3.8.1 Statistical Analysis The residual plots for HAZ width are shown in Figure 3.32. It is observed that the residual data distribute as a normal shape. The plot of residual versus observation order shows a random pattern, implying that the experiments and the measurements were randomly conducted to avoid the hysteresis and other related errors induced by a specific sequence of operations. Based on the ANOVA results shown in Table 3.6, the p-value of laser pulse overlap (PO), water pressure (Pwj) and waterjet impact angle (șj)
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is greater than the significant level of 0.05, such that the change of these parameters is statistically insignificant to the HAZ width. In addition, the waterjet offset distance (xwl) has the highest F-value, indicating that the change of xwl affects the HAZ width more than other parameters.
5HVLGXDO )UHTXHQF\ 5HVLGXDO 2EVHUYDWLRQ2UGHU
Figure 3.32. Residual plots for HAZ width.
Table 3.6. Analysis of variance for HAZ width. Sources DoF Seq SS Adj SS Adj MS F p-value fpp 3 122406 106058 35353 57.45 0 xwl 3 324155 322027 107342 174.44 0
Ep 3 26169 26053 8684 14.11 0 PO 3 2857 2857 952 1.55 0.201
șj 3 120356 13 4 0.01 0.999
Pwj 3 22150 343 114 0.19 0.906 Error 941 579042 579042 615 Total 959 1197135
3.8.2 The Effect of Laser Pulse Energy Figure 3.33 exhibits the influence of laser pulse energy on the HAZ width. It is observed that the HAZ width slightly increases with an increase in laser pulse energy. As discussed earlier, the laser pulse energy is actually associated with the laser-heated region whose size increases with an increase in laser pulse energy. It is noted that when high laser pulse energy is used, material is softened enough to be removed by the waterjet. However, the heat energy at the outer irradiated area is still below the
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threshold for removal where the material is too strong for the waterjet to remove, thus causing an increased HAZ. As a result, a high laser pulse energy not only causes a larger groove width, but at the same time produces a larger HAZ.
200 PO: 99.9 % fpp xwl: 0.4 mm 0 mm P : 10 MPa wj -0.2 mm 160 ș : 40 j -0.4 mm -0.6 mm m) ȝ 120
80 HAZ width ( HAZ width 40
0 0.20.30.40.50.60.7 Laser pulse energy (mJ) Figure 3.33. The effect of laser pulse energy on HAZ width.
3.8.3 The Effect of Focal Plane Position The effect of laser focal plane position on the HAZ width is shown in Figure 3.34(a), where the HAZ width decreases as the fpp increases from negative to zero. This is due to an intense laser energy of the small fpp at the work surface that introduces a significant material softening and removal over the heated area, so that only the small HAZ is left. By contrast, a decrease in fpp increases the laser irradiated area at the work surface. As a result, the HAZ width is large. In addition, Figure 3.34(b) exhibits that the HAZ width increases with a decrease in laser energy density. This is attributed to the fact that the material is heated by an insufficient energy density caused by the large fpp, so that the heated material cannot be removed by waterjet, but instead results in an increased HAZ width.
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200 200 PO: 99.9 % Pulse energy PO: 99.9 % fpp x : 0.4 mm wl 0.3 mJ xwl: 0.4 mm 0 mm P : 10 MPa P : 10 MPa 160 wj 0.4 mJ 160 wj -0.2 mm șj: 40 ș : 40 0.5 mJ j -0.4 mm 0.6 mJ
m) -0.6 mm m) ȝ 120 ȝ 120
80 80 HAZ width ( HAZ width HAZ width ( HAZ width 40 40
0 0 -0.8 -0.6 -0.4 -0.2 0 0.2 0 50 100 150 200 250 300 Focal plane position (mm) Laser energy density (J/cm2) (a) (b) Figure 3.34. The effects of focal plane position on HAZ width.
3.8.4 The Effect of Laser Pulse Overlap Figures 3.35(a) and (b) show the effect of laser pulse overlap on the HAZ size. It reveals that in general, pulse overlap does not affect the HAZ significantly. While an increase in this parameter may increase the laser-heated area on material, the waterjet is able to remove the softened area to increase the groove width, but not significantly increase the HAZ. Although the interaction of laser pulse energy and pulse overlap shown in Figure 3.35(a) is insignificant to the HAZ width, the effect of fpp and pulse overlap depicted in Figure 3.35(b) shows that a larger negative fpp produces a wider HAZ, especially at a higher pulse overlap. This is because of the large laser-heated area and long laser-material interaction time that cause a high heat conduction towards the work material, hence increasing the HAZ.
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200 200 Pulse energy fpp: 0 mm fpp Ep: 0.6 mJ 0.3 mJ xwl: 0.4 mm 0 mm xwl: 0.4 mm P : 10 MPa P : 10 MPa 160 0.4 mJ wj 160 -0.2 mm wj 0.5 mJ șj: 40 -0.4 mm șj: 40 0.6 mJ -0.6 mm m) m) ȝ 120 ȝ 120
80 80 HAZ width ( HAZ width ( HAZ width 40 40
0 0 99.1 99.3 99.5 99.7 99.9 99.1 99.3 99.5 99.7 99.9 Pulse overlap (%) Pulse overlap (%) (a) (b) Figure 3.35. The effects of laser pulse overlap on HAZ width.
3.8.5 The Effect of Waterjet Offset Distance Figures 3.36(a) to (c) show that a decrease in waterjet offset distance increases the HAZ width. This may be attributed to the fact that a decrease in the offset distance increases the waterjet-laser interference and the water layer thickness which in turn decreases the laser beam quality. As a result, an increased, but unevenly, heated area is generated on the material surface, resulting in an increased HAZ. This can be seen in the plots shown in Figures 3.36(a) and (b). Figure 3.36(c), however, exhibits a large HAZ at small waterjet offset distances, particularly under large negative fpp’s. It indicates that low laser intensity and the insufficient energy input into the material take place at the laser-waterjet overlap condition (xwl<0.4 mm for this setting). As a result, a larger irradiated area is produced leading to a larger HAZ. In addition, Figure 3.37 demonstrates the cut surface characteristics of silicon under different waterjet offset distances and focal plane positions. This shows that a small fpp and a proper waterjet offset distance should be employed to obtain a clear trench groove with less damage.
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200 200 fpp: 0 mm Pulse energy Ep: 0.6 mJ Pulse overlap fpp: 0 mm PO: 99.9 % 0.3 mJ 99.30% P : 10 MPa P : 10 MPa 160 wj 0.4 mJ 160 wj 99.50% ș : 40 șj: 40 j 0.5 mJ 99.70% 99.90% m) m) 0.6 mJ ȝ ȝ 120 120
80 80 HAZ width ( HAZ width HAZ width ( HAZ width 40 40
0 0 -0.2 0 0.2 0.4 0.6 0.8 -0.2 0 0.2 0.4 0.6 0.8 Waterjet offset distance (mm) Waterjet offset distance (mm) (a) (b)
200 fpp 0 mm 160 -0.2 mm -0.4 mm
m) -0.6 mm ȝ 120
Ep: 0.6 mJ PO: 99.9 % 80 Pwj: 10 MPa
HAZ width ( HAZ width șj: 40 40
0 -0.2 0 0.2 0.4 0.6 0.8 Waterjet offset distance (mm) (c) Figure 3.36. The effects of waterjet offset distance on HAZ width.
Waterjet offset distance 0 mm 0.2 mm 0.4 mm 0.6 mm Focal plane position = 0 mm
Figure 3.37. The surface characteristics of silicon after hybrid machining when waterjet offset distances of 0 mm to 0.6 mm and focal plane positions of 0 to -0.6 mm were used (laser pulse energy=0.6 mJ, pulse overlap=99.9%, water pressure=10 MPa and waterjet impact angle=40°).
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Waterjet offset distance 0 mm 0.2 mm 0.4 mm 0.6 mm Focal plane position = -0.2 mm
Focal plane position = -0.4 mm
Focal plane position = -0.6 mm
Figure 3.37. (cont.) The surface characteristics of silicon after hybrid machining when waterjet offset distances of 0 mm to 0.6 mm and focal plane positions of 0 to -0.6 mm were used (laser pulse energy=0.6 mJ, pulse overlap=99.9%, water pressure=10 MPa and waterjet impact angle=40°).
3.8.6 The Effect of Water Pressure As shown in Figure 3.38(a), a slight decrease in the HAZ is seen as the water pressure increases. This is due to the fact that the water pressure applied in this hybrid laser- waterjet machining process is able to effectively remove the softened material as well as simultaneously provide a high thermal convection effect and hence results in a small HAZ along the groove. The ratio of HAZ to the groove width under the different water pressures is shown in Figure 3.38(b). It exhibits that the HAZ width decreases with an increase in water pressure as compared to the groove width created. This demonstrates that a smaller HAZ groove can be produced when a higher water pressure is used.
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200 0.5 Ep=0.3 mJ, PO=99.3% fpp: 0 mm Ep=0.3 mJ, PO=99.3% fpp: 0 mm Ep=0.6 mJ, PO=99.3% xwl: 0.4 mm Ep=0.6 mJ, PO=99.3% xwl: 0.4 mm ș : 40 Ep=0.3 mJ, PO=99.9% ș : 40 160 Ep=0.3 mJ, PO=99.9% j 0.4 j Ep=0.6 mJ, PO=99.9% Ep=0.6 mJ, PO=99.9% m) ȝ 120 0.3
80 0.2 HAZ width ( HAZ width HAZ/Groove width HAZ/Groove 40 0.1
0 0 0 5 10 15 20 25 0 5 10 15 20 25 Water pressure (MPa) Water pressure (MPa) (a) (b) Figure 3.38. The effects of water pressure on: (a) HAZ width and (b) the ratio of HAZ to groove width.
3.8.7 The Effect of Waterjet Impact Angle The effect of waterjet impact angle on the HAZ is shown in Figures 3.39(a) and (b). It can be noticed that the waterjet impact angle does not have a profound effect on the HAZ size. It may be anticipated that an increase in the waterjet impact angle increases the likelihood or amount of overlap between the laser beam and the waterjet, which in turn increases the interference of water to the laser beam, causing the disturbance to and reducing the quality of the laser beam. As a result, the laser-heated area on the top work surface is expected to increase, as is the HAZ. However, an increase in the waterjet impact angle also facilitates the removal of material by its impact force along the work surface, so that material may be removed at a less softened status. This trades off the effect of water interference to the laser beam and, as a result, its effect on HAZ is minimal.
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200 Ep=0.3 mJ, PO=99.3% fpp: 0 mm 200 Ep: 0.6 mJ Water pressure Ep=0.6 mJ, PO=99.3% x : 0.4 mm wl fpp: 0 mm 5 MPa Ep=0.3 mJ, PO=99.9% Pwj: 10 MPa PO: 99.9 % 160 10 MPa Ep=0.6 mJ, PO=99.9% 160 x : 0.4 mm wl 15 MPa
m) 20 MPa m) ȝ 120 ȝ 120
80 80 HAZ width ( HAZ width ( width HAZ 40 40
0 0 20 30 40 50 60 70 20 30 40 50 60 70 Waterjet impact angle (deg) Waterjet impact angle (deg) (a) (b) Figure 3.39. The effects of waterjet impact angle on HAZ width.
3.9 Concluding Remarks
A hybrid laser-waterjet micromachining technology has been presented with an attempt to cut materials with minimal thermal damage. A nanosecond pulsed laser was used to locally soften the material, while a high pressure waterjet was used to remove the softened material and reduce the thermal effect by its cooling action. Single-crystalline silicon was used as the specimen material to assess the technology. It has been found that this technology is able to realize material removal using the setting parameters with which the conventional laser machining process is unable to form a groove, although some energy losses are expected by the water used in this hybrid technology. It leaves very small HAZ within about 20 ȝm on the specimen when a proper condition is applied to achieve near damage-free micromachining. The debris and redeposition typically formed in the conventional dry laser ablation can effectively be flushed away by the high velocity water flow in this hybrid process, producing a clean surface around the cut. It has been found that the applied waterjet causes an interference to the laser beam and affects the material removal, so that a proper selection of the waterjet offset distance is crucial to minimize this interference while allowing the waterjet to remove the softened material. Plausible trends between the process parameters and kerf
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characteristics, e.g. top groove width, groove depth and HAZ size, have been discussed to understand the effect of these parameters. The analysis of the effect of process parameters on the cut characteristics was statistically performed by using the analysis of variance (ANOVA) to identify the parameters that have a significant effect on the cut. It has been found that the laser pulse energy and pulse overlap affect the groove width and depth in a similar way. At high laser pulse energy or high pulse overlap, the heat generation is high to soften the work material to be removed by the waterjet, resulting in a wide and deep groove, while the effect of these parameters on HAZ has been found to be indiscernible. From a manufacturing point of view, high laser pulse energy and low pulse overlap (fast traverse speed) conditions have been found to yield a high material removal rate. Small focal plane position with a proper waterjet offset distance should be applied to gain more material removal with less HAZ since their settings directly affect the optical disturbance to laser beam under the laser-waterjet overlap. By passing the laser beam through an intense waterjet in the overlap conditions, it could significantly result in strong laser energy absorption and reflection leading to a large laser beam diameter with poor beam intensity. The waterjet offset distance of about the major radius of the waterjet impact profile has been recommended to reduce such strong overlap effect. The influences of water pressure and waterjet impact angle on the groove characteristics showed that a large groove width can be obtained under a high water pressure or a large impact angle, while a small impact angle produces a deeper groove than a large angle. It has also been found that the water pressure and the waterjet impact angle have less effect on the HAZ size under the parameter ranges considered. According to this experimental study, it can be concluded that the hybrid laser- waterjet technology is a promising near damage-free micromachining technology for silicon with higher material removal rate and smaller HAZ than the traditional dry laser machining process. It can also yield better surface quality. This work has formed the essential knowledge base for the studies to understand the material removal mechanisms under the coupled effect of laser heating and waterjet expelling and cooling. The investigation of surface and subsurface damage caused by the process and the temperature and groove geometry models for this hybrid micromachining process will be presented in the following chapters.
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Subsurface Damages in Silicon Caused by the Hybrid Laser-Waterjet Process
4.1 Introduction
When a single-crystalline silicon is melted and ablated by a high power laser, the temperature effect and shock waves could cause defects in the crystalline structure in the form of phase transformations, thermo-mechanical stresses and dislocations [57, 65- 67, 70-71, 225]. The micro-structural changes and the residual stresses which appear at the machined surface and subsurface are considered as damages that influence the mechanical, optical and electrical performances of silicon components. In laser micromachining processes, the formation of an amorphous layer is hardly avoided. Rogers et al. [57] reported that an amorphous layer with the thickness of up to 1 ȝm on silicon substrate can be formed after being irradiated by a nanosecond pulsed laser. In general, there are two major phases of silicon which occur after being processed by lasers, they are crystalline and amorphous. The crystalline silicon (c-Si) is a diamond cubic structure with each of the atoms tetrahedrally coordinated, while the amorphous phase (a-Si) arranges as a continuous random network structure. The phase transformations between crystalline and amorphous can take place by annealing silicon above the recrystallization temperature of about 600°C with a proper cooling rate [226]. Thompson et al. [227] and Cullis et al. [228] reported that a melting layer thickness of 100 nm is normally formed and subsequently cooled with a rate of 1010 K/s after silicon
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is irradiated by a laser pulse of less than 30 ns in duration. The result of such a cooling rate can lead to the growth of epitaxial crystals on the substrate. Conversely, amorphous silicon can be transformed back to a perfect single-crystalline structure by applying a sufficient laser fluence over the amorphous structure [229]. However, if a higher cooling rate is applied to induce the crystal regrowth velocity of above 15 m/s, the crystal regrows defectively and may result in the amorphous structure. Hence, it can be noted that the rate of cooling significantly influences the phase transformations of silicon involved in a laser machining process. Besides the thermal effect, phase transformations can occur under a high pressure as shown in Figure 4.1. This is due to residual stresses and dislocations that present near the loaded surface. The subsurface damages due to the high processing pressure normally occurs in mechanical cutting, grinding and polishing processes where an extremely high contact pressure between the cutting tool and work material can cause the phase transformations even at room temperature [230].
Figure 4.1. Pressure-temperature phase diagram of silicon [231].
In this chapter, surface and subsurface damages in silicon are investigated in terms of silicon crystallinity and amorphous layer thickness under different hybrid laser-
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waterjet machining conditions. As the mechanical effect by the hybrid machining process is expected to be small, this chapter is limited to the study of thermal effect that causes damages to the surface and subsurface of the machined silicon.
4.2 Experiment
According to the experimental work in Chapter 3, the hybrid laser-waterjet machining process removed silicon by laser heating and waterjet expelling actions. Focal plane position and waterjet offset distance were found to significantly affect the HAZ size in the hybrid laser-waterjet machining process due to the interference of water to the laser beam. However, these two parameters are not the actual cause of damages but only magnify the size of the damage. Laser pulse energy, pulse overlap and water pressure are instead the main parameters, relating to the thermal interaction and damage in the process. The laser pulse energy and pulse overlap are responsible for the amount of heat input transferring to the work material, while the water pressure influences the cooling and removing actions in the hybrid process. To examine the subsurface damages caused by the hybrid laser-waterjet machining process, four levels of laser pulse energy, pulse overlap and water pressure corresponding with the conditions used in Chapter 3 were considered with a single level of focal plane position (0 mm), waterjet offset distance (0.4 mm) and waterjet impact angle (40 degrees). The investigation of these three main parameters was separately conducted to accommodate the number of tests as given in Table 4.1.
Table 4.1. Conditions examined in the subsurface damage investigation.
Effect of Ep Effect of PO Effect of Pwj
Ep [mJ] 0.3, 0.4, 0.5 and 0.6 0.6 0.6 PO [%] 99.9 99.3, 99.5, 99.7 and 99.9 99.9 fpp [mm] 0 0 0 xwl [mm] 0.4 0.4 0.4
Pwj [MPa] 10 10 5, 10, 15 and 20
θj [deg] 40 40 40
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In this study, Renishaw inVia Raman Microscope equipped with a 514 nm Argon- ion excitation laser of 1.5 ȝm focused diameter at 50x magnification and the output power of 25 mW was used to examine the subsurface damage in terms of silicon crystallinity and damage layer thickness. The measurements were made at different positions along the groove profile. However, it was found that the Raman spectra at different positions were not significantly different. Thus, the Raman measurements were only conducted at the center groove surface as shown in Figure 4.2. All measurements were performed under the same controlled conditions to diminish any error that may be involved in the tests. An unmachined single-crystalline silicon and a dry laser ablation sample (Ep=0.6 mJ, PO=99.9 % and fpp=0 mm) were also examined for comparison purposes.
Raman spectrometer Ar laser Scattered light Workpiece
Groove
Figure 4.2. The measured positions for the laser Raman testing.
4.3 Evaluation of Experimental Data
In laser Raman spectroscopy, the light scattered off the target surface is detected by a Raman spectrometer to classify the scattered light spectrums with different Raman shifts indicating the material micro-structures, impurities and residual strains. Typically, three main peaks of Raman shift are considered for silicon [232] as shown in Figure 4.3, they are the Raman shift centered at 520 cm-1 that indicates the crystalline phase of silicon (c-Si); the 510 cm-1 peak that represents the defective crystalline phase (p-Si) in either the poly-crystalline diameter of less than 10 nm [233] or the twinning defects in silicon Wurtzite phase [234]; and a broad band peak centered at 480 cm-1 that represents the amorphous phase (a-Si). However, as is usual, only the crystalline (c-Si) and amorphous (a-Si) phases are normally considered in subsurface damage investigation for determining the amorphous layer formation in this study.
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Figure 4.3. The typical Raman spectrum of silicon after machining.
As the material micro-structures can be classified by the different scattered light vibration frequencies or Raman shifts, the phase density is indicated by the scattered light intensity or Raman intensity as shown in Figure 4.4. The Raman scattered light intensity for amorphous phase (Isa) can be calculated by [235]
γσ = sa II []1 exp()−− 2α d (4.1) sa α 0 aa 2 a
where I0, Ȗ, ısa, Įa and da are the applied laser intensity, intensity losses, scattering coefficient of amorphous, absorption coefficient of amorphous (1.5x105 cm-1) and amorphous layer thickness, respectively.
Figure 4.4. Schematic of Raman scattering in amorphous and crystalline layers.
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Another scattered light intensity is subject to the crystalline phase denoted by Isc. However, this scattered ray has to pass through both crystalline and amorphous layers. The scattered light intensity for crystalline, hence, consists of two Beer-Lambert absorption terms, so that
γσ = sc II exp()α d {}12 exp[]2α ()−−−− dD (4.2) sc α 0 aa c a 2 c where
§ α · α D ¨1−= a ¸ + a dd (4.3) ¨ α ¸ a α a−limit © c ¹ c
ısc, Įc, D and da-limit are scattering coefficient of crystalline, absorption coefficient of crystalline (1.0x104 cm-1), maximum sensing depth and maximum sensing depth of amorphous phase, respectively. With regard to the amorphous and crystalline scattered light intensities expressed in Equations 4.1 and 4.2, the Raman intensity ratio (r) can be determined by [235]
I ασ exp()α d −12 ½ r sa == sa c aa (4.4) ασ ® []α ()−−− ¾ I sc sc a ¯1 exp 2 c dD a ¿
According to the study of Yan et al. [235], the ratio of ısa to ısc for silicon and the da-limit are approximately 8.84 and 150 nm, respectively. By substituting Equation 4.3 into 4.4 and transforming it to an explicit function of r, the amorphous layer thickness (da) can be calculated by [235]
+ ×= § .8 1584 r · da 33 3. ln¨ ¸ (4.5) © .8 84 + .0 167r ¹ where the Raman intensity ratio (r) is determined by
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1 bh r ⋅= aa (4.6) π bh cc
ha, hc, ba and bc are respectively the height of a-Si peak, the height of c-Si peak, the half-power band width of a-Si peak and the half-power band width of c-Si peak regarding the full-width at half-maximum (FWHM) in the Raman spectrum as shown in
Figure 4.5. The Raman intensity ratio (r) and the amorphous layer thickness (da) can be used as the quantitative parameters for comparison purposes.
Figure 4.5. The heights and the half-power bandwidths of the amorphous and the crystalline peaks.
In addition, crystalline volume fraction (Xc) is another quantitative parameter for determining the amount of crystalline phase at the examined work surface. According to the study of Tsu et al. [236] and Bustarret et al. [237], the crystalline volume fraction can be calculated by
I X = sc (4.7) c + I sc yI sa
where y is the ratio of c-Si to a-Si Raman diffusion cross-section. In general, the Isc and
Isa are directly obtained from the Raman spectrum while the y value is empirically defined subject to the size of crystallites and laser excitation wavelength [236-238]. In order to avoid the complexity in determining the y value, Droz et al. [232] proposed
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Raman crystallinity factor (c) by setting y=1, thus the ratio of Raman intensities is given by
I φ = sc (4.8) c + II sasc
,(This c can be considered as a lower limit for the actual crystalline volume fraction (Xc where the crystallinity factor of 1 means 100% crystalline phase and 0 for 100% amorphous phase within the sensing depth of Raman measurement [239]. Hence, the
crystallinity factor (c) can also be used to indicate the amount of crystalline structure in samples.
4.4 Results and Discussion
The Raman spectrum of the unmachined c-Si sample shown in Figure 4.6 reveals that there is only a sharp peak centered at 520 cm-1 in the spectrum, while the responses at other Raman shifts have completely disappeared. This indicates that the micro-structure of the unmachined sample at the top sample surface has only the single-crystalline silicon phase (c-Si). By using Equation 4.6, the Raman intensity ratio (r) can be calculated and the result shows that the value approaches zero. This is due to the scattered ray intensity of the amorphous phase that cannot significantly be detected from the measurement. It thus demonstrates that there is no amorphous structure formed at the examined sample surface. In addition, by using Equation 4.8, the Raman crystallinity factor of the unmachined c-Si sample is close to 1.0 which represents the perfect single-crystalline silicon. As the calculated crystallinity factor for this sample is 0.99, a small variation of 0.01 is subject to background noises in the Raman spectrum. This value has been used as a reference of damage-free single-crystalline silicon for a comparison study. With reference to the c-Si spectrum, the subsurface damage caused by dry and hybrid laser-waterjet processes will be compared. The effects of laser pulse energy, pulse overlap and water pressure on the Raman results will subsequently be discussed in the following sections.
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7 c = 0.99כ
6 c-Si
counts) 5 3 4
3
2
1 Raman intensity (10 intensity Raman
0 400 450 500 550 600 Raman shift (cm-1) Figure 4.6. The Raman spectrum of c-Si wafer before machining.
4.4.1 Comparison of Subsurface Damages Caused by Dry and Hybrid Processes A major difference of thermal effects in the conventional dry laser and the hybrid laser- waterjet machining processes is that the latter provides a high cooling effect on the work material to minimize HAZ. As the heat conduction is effectively reduced in the hybrid process, the silicon recrystallization is also minimized. Figure 4.7 shows that the Raman spectrum of silicon after being machined by the hybrid process has a sharp peak centered at 520 cm-1 (c-Si) and a small amplitude of a broad peak centered at 480 cm-1 (a-Si), while the dry ablation yields significant Raman intensities of both c-Si and a-Si peaks. This implies the following two points. Firstly, an amorphous layer thickness formed in the dry ablation is thicker than that formed by the hybrid approach, and secondly, the c-Si peak can be seen in both Raman spectra, indicating that the bulk silicon structure beneath the amorphous layer is still in the crystalline phase. In the dry laser ablation process, a thin liquid silicon layer is formed at the irradiated surface. This liquid layer is basically metallic whose absorption rate is very high, and becomes thicker as the irradiating time increases. Due to the rapid resolidification of the molten silicon layer, the silicon atoms have no time to reconstruct and regrow as an epitaxial crystal structure, but to form the amorphous phase. Since the absorption coefficient and the melting temperature of amorphous silicon are, respectively, 15-times higher and about 200 K lower than those of the stable crystalline silicon [235, 240], there will be sufficient absorption of laser near the target surface to form a thick layer of transformed phase in the dry laser process.
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7 Dry Ep: 0.6 mJ Hybrid fpp: 0 mm 6 c-Si sample c-Si PO: 99.9 % xwl: 0.4 mm
counts) 5 Pwj: 10 MPa 3 a-Si șj: 40 4
3
2
1 Raman intensity (10 intensity Raman
0 400 450 500 550 600 Raman shift (cm-1) Figure 4.7. The Raman spectra of samples from the dry, hybrid processes and an unmachined c-Si sample.
In the hybrid laser-waterjet machining process, the softened solid silicon whose strength is lower than the waterjet impact pressure can be removed by the waterjet, so that the liquid silicon and the thick layer of phase transformation may not be formed as in the case of dry laser ablation. This may be explained in that the heated silicon, whose temperature is above the recrystallization but below the removal threshold, is rapidly cooled by the waterjet and subsequently results in amorphization within a submicron layer at the machined surface. By using Equations 4.5 and 4.6, the Raman intensity ratio
(r) and the amorphous layer thickness (da) of the sample machined by the dry process are 10.23 and 91.03 nm, respectively, while the corresponding values for the sample from the hybrid process are 1.31 and 38.16 nm. By contrast, the r and da for the unmachined c-Si sample are both zero as shown in Figure 4.8. According to these results, the amorphous layer thickness obtained from the hybrid process is about 58% thinner than the dry approach; this confirms that less subsurface damage in silicon can be expected in the hybrid laser-waterjet process.
The Raman crystallinity factors (c) for samples machined by conventional dry laser and the hybrid laser-waterjet processes and an unmachined c-Si sample are compared in Figure 4.9. It shows that the crystallinity factor obtained from the hybrid process is 0.801 which is higher than 0.5001 for the dry laser ablation process, while the factor for the unmachined c-Si sample is close to 1.0. It exhibits that the crystallinity of silicon increases when the hybrid laser-waterjet process is used. Thus it is again evident that the
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subsurface damage due to phase transformation in silicon after machining can be minimized in the hybrid process.
14 140 Dry Dry 12 Hybrid laser-waterjet 120 Hybrid laser-waterjet c-Si sample c-Si sample 10 100
8 80
6 60
4 Ep: 0.6 mJ 40 Ep: 0.6 mJ Raman intensity ratio intensity Raman fpp: 0 mm fpp: 0 mm PO: 99.9 % PO: 99.9 % x : 0.4 mm x : 0.4 mm 2 wl Amorphous layerthickness (nm) 20 wl Pwj: 10 MPa Pwj: 10 MPa șj: 40 șj: 40 0 0
(a) (b) Figure 4.8. Comparisons of Raman intensity ration (r) and amorphous layer thickness
(da) for samples machined by dry laser and hybrid laser-waterjet processes, and
unmachined c-Si samples (showing zero r and da).
1 Dry 0.9 Hybrid laser-waterjet 0.8 c-Si sample 0.7 0.6 0.5 0.4
0.3 Ep: 0.6 mJ fpp: 0 mm Raman crystallinity factor crystallinity Raman 0.2 PO: 99.9 % xwl: 0.4 mm 0.1 Pwj: 10 MPa șj: 40 0
Figure 4.9. The comparison of Raman crystallinity factor for samples machined by dry laser and hybrid laser-waterjet processes and an unmachined c-Si sample.
4.4.2 Effect of Laser Pulse Energy The Raman spectra of silicon under different laser pulse energies are shown in Figure 4.10. It can be noticed that there is a sharp peak centered at 520 cm-1 and a broad peak
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centered at 480 cm-1 for crystalline and amorphous phases, respectively. This is actually the typical Raman spectrum for silicon processed by high laser energy where a thin layer of silicon is transformed to the amorphous phase (a-Si) at the irradiated surface, while the bulk region underneath still remains in crystalline state (c-Si). According to the Raman spectra, the Raman intensity of a-Si peak is found to increase with an increase in laser pulse energy. This is due to the laser-heated region that enlarges with the laser pulse energy and results in a large random network structure of amorphous phase at the top of the machined surface due to the rapid cooling of the heated region.
7 7 Ep: 0.3 mJ Ep: 0.4 mJ 6 6
counts) 5 counts) 5 3 c-Si 3 c-Si 4 4
3 3
2 2 a-Si 1 1 Raman intensity (10 intensity Raman a-Si (10 intensity Raman 0 0 400 450 500 550 600 400 450 500 550 600 Raman shift (cm-1) Raman shift (cm-1) (a) (b)
7 7 Ep: 0.5 mJ Ep: 0.6 mJ 6 6 c-Si c-Si counts) counts) 5 5 3 3 4 4
3 3
2 2 a-Si a-Si 1 1 Raman intensity (10 intensity Raman Raman intensity (10 intensity Raman
0 0 400 450 500 550 600 400 450 500 550 600 Raman shift (cm-1) Raman shift (cm-1) (c) (d) Figure 4.10. The Raman spectra for different laser pulse energies: (a) 0.3 mJ, (b) 0.4 mJ, (c) 0.5 mJ and (c) 0.6 mJ (focal plane position=0 mm, pulse overlap=99.9%, waterjet offset distance=0.4 mm, water pressure=10 MPa and waterjet impact angle=40°).
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For the purpose of a quantitative comparison, the Raman intensity ratio (r) and the
Raman crystallinity factor (c) were determined from the Raman spectra by using
Equations 4.6 and 4.8, respectively. Since the amorphous layer thickness (da) is proportional to the Raman intensity ratio as expressed in Equation 4.5, only the da and
c are calculated and plotted as shown in Figure 4.11. It is observed that the amorphous layer thickness increases with an increase in laser pulse energy, while a reverse trend is found for the Raman crystallinity factor. The amorphous layer thickness of the samples machined under 0.3, 0.4, 0.5 and 0.6 mJ laser pulse energies is 22.74, 29.57, 33.64 and 38.16 nm, respectively. As a result, the high crystallinity with a thin amorphous layer at the cut surface can be obtained when low laser pulse energy is used. However, less material removed becomes a major drawback when low laser energy is applied. Hence, the high laser pulse energy with fast traverse speed would be employed to gain a high material removal rate while minimizing the damage layer thickness.
50 1 c = 0.99כ fpp: 0 mm PO: 99.9 % 0.95 x : 0.4 mm 40 wl Pwj: 10 MPa 0.9 șj: 40 0.85 30 0.8
20 0.75 fpp: 0 mm 0.7 PO: 99.9 % 10 Raman crystallinity factor crystallinity Raman xwl: 0.4 mm 0.65 Pwj: 10 MPa Amorphous layer thickness (nm) thickness layer Amorphous șj: 40 0 0.6 0.20.30.40.50.60.7 0.2 0.3 0.4 0.5 0.6 0.7 Laser pulse energy (mJ) Laser pulse energy (mJ) (a) (b) Figure 4.11. The effect of laser pulse energy on: (a) the calculated amorphous layer thickness and (b) the Raman crystallinity factor.
4.4.3 Effect of Laser Pulse Overlap The influence of laser pulse overlap on the Raman spectrum is shown in Figure 4.12. It can be seen that an increase in laser pulse overlap increases the Raman intensity of a-Si peak centered at 480 cm-1, while a sharp peak at 520 cm-1 (c-Si) is not significantly affected by the change in laser pulse overlap. These Raman spectra indicate that a greater amount of the amorphous phase is formed at the tested sample surface when a
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higher laser pulse overlap is used. This is attributed to the fact that a higher pulse overlap provides more pulses of irradiation over a given sample area and hence introduces a larger recrystallizable region which is subsequently cooled and transferred to the amorphous phase.
7 7 PO: 99.3 % PO: 99.5 % 6 6 counts) counts) 5 c-Si 5
3 c-Si 3 4 4
3 3
2 2
1 a-Si 1 a-Si Raman intensity (10 intensity Raman Raman intensity (10 intensity Raman
0 0 400 450 500 550 600 400 450 500 550 600 Raman shift (cm-1) Raman shift (cm-1) (a) (b)
7 7 PO: 99.7 % PO: 99.9 % 6 6 c-Si counts) counts) 5 c-Si 5 3 3 4 4
3 3
2 2 a-Si 1 a-Si 1 Raman intensity (10 intensity Raman Raman intensity (10 intensity Raman
0 0 400 450 500 550 600 400 450 500 550 600 Raman shift (cm-1) Raman shift (cm-1) (c) (d) Figure 4.12. The Raman spectra for different laser pulse overlaps: (a) 99.3%, (b) 99.5%, (c) 99.7% and (d) 99.9%. (laser pulse energy=0.6 mJ, focal plane position=0 mm, waterjet offset distance=0.4 mm, water pressure=10 MPa and waterjet impact angle=40°).
The amorphous layer thickness and the Raman crystallinity factor have been calculated from Equations 4.5 and 4.8, respectively, and plotted against the laser pulse
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overlap as shown in Figure 4.13. It demonstrates that the amorphous layer thickness increases, while the Raman crystallinity factor decreases with an increase in laser pulse overlap. The amorphous layer thickness of the samples machined under 99.3, 99.5, 99.7 and 99.9% pulse overlaps is 11.53, 25.74, 28.66 and 38.16 nm, respectively. According to these results, low laser pulse overlap should be applied to minimize the amorphous layer thickness and to gain the high crystallinity at the machined surface.
50 1 c = 0.99כ Ep: 0.6 mJ fpp: 0 mm 0.95 x : 0.4 mm 40 wl Pwj: 10 MPa 0.9 șj: 40 0.85 30 0.8
20 0.75
Ep: 0.6 mJ 0.7 fpp: 0 mm 10 Raman crystallinity factor crystallinity Raman xwl: 0.4 mm 0.65 Pwj: 10 MPa
Amorphous layer thickness (nm) thickness layer Amorphous șj: 40 0 0.6 99.1 99.3 99.5 99.7 99.9 99.1 99.3 99.5 99.7 99.9 Pulse overlap (%) Pulse overlap (%) (a) (b) Figure 4.13. The relationships between laser pulse overlap and: (a) the calculated amorphous layer thickness and (b) the Raman crystallinity factor.
4.4.4 Effect of Water Pressure The Raman spectra of silicon under different water pressures are shown in Figure 4.14, where an increase in water pressure significantly decreases the amplitude of the broad peak centered at 480 cm-1 (a-Si). This indicates that a high water pressure can remove more heated material in a less softened state, leaving the less heated layer to transfer into the amorphous phase. It may be noted that the amorphous layer can be reheated faster than the c-Si after each laser pulse since the absorption coefficient of a-Si is higher than the c-Si, so that the amorphous layer formed in the preceding pulse irradiation is quickly resoftened by a subsequent laser pulse and removed by the waterjet. Therefore, the amorphous layer becomes thinner as the water pressure increases.
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7 7 P : 10 MPa Pwj: 5 MPa wj 6 6 c-Si
c-Si counts) 5 counts) 5 3 3 4 4
3 3
2 2 a-Si a-Si 1 1 Raman intensity (10 Raman intensity (10 intensity Raman
0 0 400 450 500 550 600 400 450 500 550 600 Raman shift (cm-1) Raman shift (cm-1) (a) (b)
7 7 Pwj: 15 MPa Pwj: 20 MPa 6 6
c-Si c-Si
counts) 5 counts) 5 3 3 4 4
3 3
2 2
1 a-Si 1
Raman intensity (10 intensity Raman (10 intensity Raman a-Si
0 0 400 450 500 550 600 400 450 500 550 600 Raman shift (cm-1) Raman shift (cm-1) (c) (d) Figure 4.14. The Raman spectra for different water pressures: (a) 5 MPa, (b) 10 MPa, (c) 15 MPa and (d) 20 MPa (laser pulse energy=0.6 mJ, focal plane position=0 mm, pulse overlap=99.9%, waterjet offset distance=0.4 mm and waterjet impact angle=40°).
For a quantitative comparison, the amorphous layer thickness and the Raman crystallinity factor have been calculated by using Equations 4.5 and 4.8, respectively. Figure 4.15 shows that the a-Si layer thickness decreases with an increase in water pressure, while the Raman crystallinity factor increases with the water pressure. The amorphous layer thickness of the samples machined under 5, 10, 15 and 20 MPa water pressures is 39.35, 38.16, 25.27 and 21.59 nm, respectively. According to these findings, it can be noted that the subsurface damage due to the phase transformation in
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silicon after the hybrid machining can be minimized when a high water pressure is applied.
50 Ep: 0.6 mJ 1 c = 0.99כ fpp: 0 mm PO: 99.9 % 0.95 40 xwl: 0.4 mm șj: 40 0.9 30 0.85 0.8 20 0.75
Ep: 0.6 mJ 0.7 10 fpp: 0 mm
Raman crystallinity factor crystallinity Raman PO: 99.9 % 0.65 xwl: 0.4 mm Amorphous layer thickness (nm) șj: 40 0 0.6 0 5 10 15 20 25 0 5 10 15 20 25 Water pressure (MPa) Water pressure (MPa) (a) (b) Figure 4.15. The relationships between water pressure and: (a) the calculated amorphous layer thickness and (b) the Raman crystallinity factor.
4.5 Concluding Remarks
The surface and subsurface damage in silicon after the hybrid laser-waterjet micromachining has been investigated in this chapter by using a laser Raman spectroscopy. Some cut samples from the experiments presented in Chapter 3 were selected for the laser Raman spectroscopy investigation. The comparison between Raman spectra for the samples produced by dry laser machining and hybrid laser- waterjet machining showed that the amorphous Raman intensity of the samples from hybrid machining is much lower than those from the dry laser ablation. This indicates that the amorphous layer thickness on the cut by the hybrid process is thinner than that obtained from the sample by dry laser machining. This is due to the high pressure waterjet that is able to expel the heated material in its softened status, leaving a thinner layer of heated material that is transferred to amorphous silicon than that in dry laser machining. In addition, the Raman crystallinity factors have been determined from the Raman spectrum for a comparison. It has been found that the crystallinity factor for the cuts by the hybrid process is much higher than that from the dry laser process. This
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finding amply demonstrates the reduction of subsurface damage in silicon when using this hybrid laser-waterjet process. The effects of three major process parameters in the hybrid laser-waterjet machining on the crystalline-to-amorphous phase transformation on the machined surface have been investigated. An increased intensity of a-Si peak in the Raman spectra demonstrates the amount of amorphous phase within the Raman sensing depth. It has been found that the a-Si peak increases with an increase in laser pulse energy and pulse overlap. However, an increase in water pressure significantly decreases the amorphous layer thickness. Based on these findings, the subsurface damage can be minimized when low laser pulse energy, low pulse overlap and high water pressure are applied. However, less material is removed when low laser pulse energy is used. From a practical point of view, a relatively high laser pulse energy with a low pulse overlap and a high water pressure should be applied to yield a high material removal rate while keeping the subsurface damage to a minimum. This study has clearly shown that the damage layer thickness on the single- crystalline silicon can be markedly reduced by using the hybrid laser-waterjet machining process. As a result, a secondary process to remove the damaged layer which may be required in conventional laser machining can be eliminated to reduce production time and costs. To gain a better understanding of the effect of process parameters on the hybrid laser-waterjet machining process, a temperature field model will be developed. For this purpose, the model for dry laser machining is developed first in the next chapter.
114 Chapter 5
Development of Temperature Field Model for Conventional Dry Laser Machining
5.1 Introduction
The modeling of laser machining processes can be made by using three main approaches, i.e. empirical, analytical and numerical methods. The empirical model is formulated from a set of experimental data by using the least-square or regression method to determine the proper coefficients for providing a good fitting of an algebraic equation. However, the empirical model can only provide the parameter relationships with less theoretical consideration towards the process, and the model prediction is only applicable for the conditions covered in the experiment. In order to express the parameter relationships and to understand the fundamentals behind the process, the model needs to be developed by considering the conservation of energy. The analytical modeling approach has been widely employed in many theoretical analyses of laser machining processes to determine the temperature field and material removal mechanisms through heat transfer and laser-material interactions [133-135, 137, 139, 241-242]. The analytical model is normally formed from many derivative and integral terms to represent the thermal gradient in the space and time domains with respect to laser parameters and material properties. However, this modeling method is very
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complex and may need some advanced mathematical techniques to formulate a closed- form equation for solving a specific laser ablation process. In order to solve the complicated boundary-value problem with highly non-linear functions, the numerical method is found to be a more practical method than the analytical approach to calculate the complex problems with fewer predefined mathematical functions. In this chapter, a transient heat transfer model associated with a numerical method, namely finite difference (FD) method, is applied to develop a temperature field model for the laser ablation process. Both constant and temperature-dependent material properties will be considered in the modeling process to investigate the effect of material properties. The numerical model will be verified by comparing the simulated temperatures with the temperatures obtained from the experiment. The model for the conventional dry laser machining is considered first in this chapter, and the model will then be extended in the next chapter for the hybrid laser-waterjet machining process.
5.2 Temperature Field Model Formulation
5.2.1 Governing Equations In this study, a two-dimensional (2-D) thermal model based on the Cartesian coordinate system is applied to calculate the thermal gradient of workpiece surface and subsurface in the laser machining process. A partial differential equation of a transient heat conduction model is given by
∂Tc § ∂ 2Tk ∂ 2T · p = ¨ + ¸ + H (5.1) ¨ 2 2 ¸ l ∂t ρ © ∂x ∂z ¹
where ȡ, cp, k, T, Hl, t, x and z are material density, heat capacity of material, thermal conductivity of material, temperature, laser heat source, time, position along the workpiece surface and position along the workpiece thickness, respectively. Enthalpy method is employed in this study to enable the calculation in energy, rather than temperature, for accommodating the phase change of material in the laser ablation process, so that the transient thermal equation can be rewritten as [156]
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∂H § ∂ 2Tk ∂ 2T · = ¨ + ¸ + H (5.2) ¨ 2 2 ¸ l ∂t ρ © ∂x ∂z ¹ where H is the specific enthalpy (J/kg). This model is capable of solving the phase change problem by including the latent heats of melting (Lm) and vaporization (Lv) of material into the calculation, such that
= cH dT ; < TT (5.3) ³ p m
c dT cH dT +≤≤ L ; = TT (5.4) p ³³ p m m
cH dT += L ; << TTT (5.5) ³ p m m v
c dT cHL dT ++≤≤+ LL ; = TT (5.6) ³ p m ³ p vm v
cH dT ++= LL ; > TT (5.7) ³ p vm v
where Tm and Tv are melting and vaporization temperatures of target material.
5.2.2 Assumptions and Boundary Conditions Since the main material removal mechanism of nanosecond pulsed laser is an evaporation process [138-140, 242-245], other effects, i.e. plasma formation, superheat vaporization, hydrodynamics of melt pool and gasdynamics of vaporization, are neglected in this study. A semi-infinite model as shown in Figure 5.1 is applied by utilizing the Dirichlet boundary condition at the bottom, left and right boundaries. The temperature of the Dirichlet boundaries is always kept constant at the surrounding temperature (Tsur), while the top boundary equals the surrounding temperature only at the beginning of the calculation. The Dirichlet boundary conditions can be written as
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= = Ts bottom left,, right Tsur ; it (5.8)
= = s top TT sur t 0; (5.9)
The Neumann boundary condition is applied to all but the top boundary, where the boundaries are considered as a thermally insulated condition without the flow of heat into and out of the surfaces or satisfying the adiabatic condition as denoted by
∂ 2T = 0 (5.10) ∂ 2 n bottom left,, right
The heat convection and radiation losses for the semi-infinite model are considered at the top work surface according to the Robin boundary condition [156]. In the dry laser machining process, the heat transfer coefficient (h) is considered as the natural convection in which the h is approximately 10 W/m2K [221-222]. According to Fourier’s law of heat, Newton’s law of cooling and radiation loss, the heat transfer balance across the top surface can be determined by
∂T − k ()TTh εσ ()−+−= TT 44 (5.11) ∂ sur sb sur z top
-8 where İ and ısb are emissivity of material and Stefan-Boltzmann’s constant (5.67x10 W/m2K4) [218], respectively. By considering the heat transfer balance at the top boundary, the equation can be written as
∂Tc k ∂ p 2 HT −+∇= []()TTh εσ ()−+− TT 44 (5.12) ∂t ρ l ρ∂z 0 sur sb sur where the left-hand side of the equation shows the rate of enthalpy change, while the right-hand side presents the heat conduction, laser heat source, heat convection and radiation losses, respectively. Figure 5.1 depicts the semi-infinite condition for the 2-D heat transfer model, where the gain and loss of heat are only applied at the top boundary.
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Figure 5.1. Boundary conditions for a 2-D semi-infinite heat transfer model.
5.2.3 Discretization Using Finite Difference Method Since the FD method is easy to implement and needs relatively short computing time, the explicit forward-time central-space (FTCS) FD approach has been employed in this study. With the aid of Taylor series, the partial differential equations given in Equation 5.2 can be approximated and discretized in the FD terms for the time domain, and the first and second derivatives of space domains, respectively, i.e.
i+1 − i § ∂H · § ,nm HH ,nm · ≈ ¨ ¸ (5.13) ¨ ∂ ¸ ¨ Δ ¸ © t ¹i+ 2/1 © t ¹ i − i § ∂T · § + nm TT ,,1 nm · ≈ ¨ ¸ (5.14) ¨ ∂ ¸ ¨ Δ ¸ © x ¹ + ,2/1 nm © x ¹
i − i § ∂T · § nm + TT ,1, nm · ≈ ¨ ¸ (5.15) ¨ ∂ ¸ ¨ Δ ¸ © z ¹ nm + 2/1, © z ¹
ª§ ∂T · § ∂T · º «¨ ¸ − ¨ ¸ » 2 ∂ ∂ ()i i +− i ∂ T «© x ¹ + ,2/1 nm © x ¹ − ,2/1 nm » + 2 TTT − ≈ ¬ ¼ ≈ ,1 nm ,nm ,1 nm (5.16) ∂x 2 Δx Δx 2
ª§ ∂T · § ∂T · º «¨ ¸ − ¨ ¸ » 2 ∂ ∂ ()i i +− i ∂ T «© z ¹ nm + 2/1, © z ¹ nm − 2/1, » + 2 TTT − ≈ ¬ ¼ ≈ nm 1, nm nm 1,, (5.17) ∂z 2 Δz Δz 2
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The notations of i, m and n represent time, and positions in x and z directions as shown in Figure 5.2. By substituting Equations 5.13 to 5.17 into Equation 5.2, a 2-D FD heat transfer equation is given by
i+1 − i ()i i +− i ()i i +− i § HH · k ª + 2 TTT − + 2 TTT − º ¨ ,nm ,nm ¸ = ,1 nm ,nm ,1 nm + nm 1, nm nm 1,, + H (5.18) ¨ Δ ¸ ρ « Δ 2 Δ 2 » l © t ¹ ¬« x z ¼»
Figure 5.2. Grid points on x and z axis.
The fictitious nodes on each side of the boundaries cannot be applied into the model; for instance, the enthalpy and temperature at nodes -1 and M+1 in the x direction are the imaginary nodes which do not actually exist in the considered space, where M is the right-most node in the x direction. Thus, the boundary nodes have to be modified to overcome such imaginary terms. Based on the work of Ozisik [156], the correction equations for the 2-D model can be given as follows:
For bottom-left corner node (0,0):
+1 ii i i § − HH · k ª()+− 222 ηβ − TTT ¨ 0,0 0,0 ¸ = 0,00,00,1 0,1 sur ¨ Δ ¸ ρ « Δ 2 © t ¹ ¬ x (5.19) ()i i +− 222 ηβ TTT º + −1,00,00,01,0 sur Δ 2 » z ¼
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For top-left corner node (0,N):
i+1 i i i § − HH · k ª()T − 22 β T + 2η− T ¨ ,0 N ,0 N ¸ = ,1 N ,0,0 NN ,1 N sur ¨ Δ ¸ ρ « Δ 2 © t ¹ ¬ x (5.20) ()2η − 2β i + 2TTT i º + N +1,0 sur ,0,0 NN N −1,0 Δ 2 » z ¼
For bottom-right corner node (M,0):
i+1 i i i § − HH · k ª()2η + T − 2β + 2TT − ¨ M 0, M 0, ¸ = M 0,1 sur MM 0,0, M 0,1 ¨ Δ ¸ ρ « Δ 2 © t ¹ ¬ x (5.21) ()T i − 22 β T i + 2η T º + M 1, MM 0,0, M −1, sur Δ 2 » z ¼
For top-right corner node (M,N):
i+1 i i i § − HH · k ª()2η + T − 2β + 2TT − ¨ ,NM ,NM ¸ = ,1 NM sur ,, NMNM ,1 NM ¨ Δ ¸ ρ « Δ 2 © t ¹ ¬ x (5.22) ()2η T − 2β i + 2TT i º + NM +1, sur ,, NMNM NM −1, Δ 2 » z ¼
For left node (0,n) where n is varied from 1 to N-1:
i+1 i i i § − HH · k ª()+− 222 ηβ − TTT ¨ ,0 n ,0 n ¸ = n ,0,0,1 nn ,1 n sur ¨ Δ ¸ ρ « Δ 2 © t ¹ ¬ x (5.23) ()T i 2β i +− TT i º + n+ nn n−1,0,0,01,0 Δ 2 » z ¼
For right node (M,n) where n is varied from 1 to N-1:
i+1 i i i § − HH · k ª()2η + T − 2β + 2TT − ¨ ,nM ,nM ¸ = ,1 nM sur ,, nMnM ,1 nM ¨ Δ ¸ ρ « Δ 2 © t ¹ ¬ x (5.24) ()T i − 2β i + TT i º + nM +1, nMnM nM −1,,, Δ 2 » z ¼
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For top node (m,N) where m is varied from 1 to M-1:
i+1 i i i i § − HH · k ª()T + − 2β + TT − ¨ ,Nm ,Nm ¸ = ,1 Nm ,, NmNm ,1 Nm ¨ Δ ¸ ρ « Δ 2 © t ¹ ¬ x (5.25) ()2η T − 2β i + 2TT i º + Nm +1, sur ,, NmNm Nm −1, Δ 2 » z ¼
For bottom node (m,0) where m is varied from 1 to M-1:
i+1 i i i i § − HH · k ª()T + 2β +− TT − ¨ m 0, m 0, ¸ = m 0,1 mm m 0,10,0, ¨ Δ ¸ ρ « Δ 2 © t ¹ ¬ x (5.26) ()i TT i +− 222 ηβ T º + m 1, mm 0,0, m −1, sur Δ 2 » z ¼
The ȕ and Biot number (Ș) can be calculated by using the following equations:
η β += § · 1¨ ¸ (5.27) © ξ ¹ Δnh η = (5.28) k where ȟ=1 for corner nodes, otherwise ȟ=2. ǻn and h are grid size and heat transfer coefficient. The accuracy of explicit numerical computation depends upon the size of time step applied which can be expressed as
Δn2 t ≤Δ γ ; min( ΔΔ=Δ zxn ), (5.29) § Δnh · α¨1+ ¸ © k ¹ where Ȗ is the stability of computation. In order to avoid the calculation divergence, the stability is recommended to be equal to or less than 0.25 [156]. In addition, Fell et al. [144] recommended that the stability value of 0.4 may be applied to avoid the divergence of FD computation. It can be seen from the equation that the time step size (ǻt) decreases with an increase in heat transfer coefficient (h). This relationship will be
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discussed further in the next chapter where the waterjet cooling effect is considered in modeling the hybrid laser-waterjet machining process.
5.2.4 Laser Heating and Pulse Shape Functions A nanosecond pulsed laser is used in this study, so that the laser intensity is periodically changed with time by means of laser pulse frequency and pulse duration. The laser heat source which is a function of the space and time can be determined by
),,( AtzxP tzxH ),,( = b (5.30) l ρ Al
where P, Ab and Al are laser power, absorption coefficient of material and laser irradiated area, respectively. According to the Beer-Lambert law, the laser heat source can be written in terms of laser pulse energy (Ep), pulse duration (IJ), reflectivity of material (Rf) and absorption coefficient (Ab) in the form of
(1− ) exp()− ψ ω txzAARE )()( tzxH ),,( = bfp b (5.31) l τρ Al
The space (ȥ) and the time (Ȧ) functions of the laser heating are distributed as the Gaussian and the polynomial-exponential functions, respectively, so that [242]
§ 4x 2 · ψ x)( exp¨−= ¸ (5.32) ¨ 2 ¸ © db ¹
i ª n § t · º § − βt · t)( = « αω ¨ ¸ » exp¨ ¸ (5.33) ¦ i ¨τ ¸ ¨τ ¸ ¬« i=1 © total ¹ ¼» © total ¹
A curve fitting is employed to determine the coefficients of the polynomial-exponential pulse shape function with regard to the pulse shape data supplied by the laser machine manufacturer as presented in Appendix A. The fitted pulse shape function with an R- square of 0.995 is approximated by
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2 ª § t · § t · ω t −= .0)( 223 .1 ×+ 10365 2 ®« ¨ −7 ¸ ¨ −7 ¸ ¯¬ © .3 ×10125 ¹ © .3 ×10125 ¹ 3 4 ×− 3 § t · ×+ 4 § t · .4 10166 ¨ − ¸ .5 10961 ¨ − ¸ © .3 ×10125 7 ¹ © .3 ×10125 7 ¹ 5 6 ×− 5 § t · ×+ 5 § t · .3 10304 ¨ − ¸ .9 10359 ¨ − ¸ © .3 ×10125 7 ¹ © .3 ×10125 7 ¹ 7 8 (5.34) ×− 6 § t · ×+ 6 § t · .1 10487 ¨ − ¸ .1 10338 ¨ − ¸ © .3 ×10125 7 ¹ © .3 ×10125 7 ¹ 9 10 § t · § t · º .6 ×− 10311 5 ¨ ¸ .1 ×+ 10198 5 ¨ ¸ » × −7 × −7 © .3 10125 ¹ © .3 10125 ¹ ¼» § − .9 01t ·½ exp¨ −7 ¸¾ © .3 ×10125 ¹¿
The plot of pulse shape in the space and time domains is shown in Figure 5.3.
1
0.75
0.5
0.5
Normalized intensity Normalized 0 80 60 80 40 60 40 20 20 0 Space 0 Time
Figure 5.3. Laser pulse shape in the space and time domains.
Due to the complexity and highly non-linear equation of the pulse shape function in the time domain, a simplified function may be made by considering the polynomial- exponential pulse as the equivalent uniform pulse. By integrating Equation 5.34 with respect to the time within the laser pulse duration of 42 ns at the full-width at half- maximum (FWHM), the integral of the pulse shape function is given by
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= ω tk dt ≈ .0)( 914 (5.35) p ³ FWHM
where kp is a pulse shape coefficient. The simplified laser heat source is thus given by
(1− ) exp()− ψ ω txzAAREk )()( tzxH ),,( = bfpp b kp (5.36) l τρ Al where
1 ; pulsing ω = kp t)( ® (5.37) ¯ 0 ;otherwise
Furthermore, the moving laser heat source along the traverse direction (y axis) in laser cutting can be calculated by varying the laser energy according to the Gaussian profile with the time and distance moved. An imaginary cross-sectional plane located at yp from the origin is assigned to exhibit temperature field and cut profile at that position with the traverse speed of vt, as shown in Figure 5.4.
Figure 5.4. Moving laser heat source at a cross-section at position yp.
This 2-D temperature field model associated with the moving heat source term can be achieved by applying the following equation as the laser heat source into the FD model:
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(1− ) exp()− ω tzAARE )( tzyxH ),,,( = bfp b l τρ Al (5.38) 22 ª ()− 2 º ª 4()+ yx º § 4 tp tvy · exp«− »«exp¨− ¸» d 2 ¨ d 2 ¸ ¬ b ¼¬« © b ¹¼»
The absorption coefficient of silicon greatly increases with an increase in temperature [136, 246]. In implementing the model, the volumetric laser heat source is not used when silicon reaches its melting temperature (1687 K); instead, a surface heat flux is applied using the following equation:
()− ω tRE )(1 ª ()+ 22 ºª § 4()− tvy 2 ·º = fp − 4 yx ¨− tp ¸ l tzyxH ),,,( exp« »«exp » (5.39) τρ ΔzA d 2 ¨ d 2 ¸ l ¬ b ¼¬« © b ¹¼»
In addition, the laser-heated position (or the laser-material initial interaction position) moves along the laser beam axis after the irradiated elemental layer of material reaches the threshold energy for removal. At the initial state, the laser projects at the top work surface to heat the material. As the enthalpy of the elemental material reaches the removal threshold, the element is removed and the laser-heated position is moved downwards to project on the next non-removed element consecutively. The laser heating and removing processes repeat until the final time step is reached. Such a moving boundary condition (or repositioning of laser heating along the laser beam axis) enables the simulation model to demonstrate the real laser-material interactions and the groove formation during the laser material removal process. For this study, the threshold energy for material removal is determined by
() ()+−++−= mpv sur LTTcLTTcE vmvpm (5.40)
where Ev is specific energy of vaporization. A schematic of dry laser ablation including the phase changes is shown in Figure 5.5.
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Figure 5.5. The change of laser-irradiated position in the dry laser ablation.
Since the focal plane position remains unchanged while the laser-material interaction position is relocated after each elemental material is removed, the laser beam intensity at the irradiated positions inside the cut needs to be recalculated with time. The laser irradiated area (Al) at the workpiece surface can be determined by [9]
π 2 22 d f 4 fpp λ A += (5.41) l π 2 4 d f
where df, Ȝ and fpp are the focused laser beam diameter, laser wavelength and laser focal plane position from the top work surface, respectively.
5.2.5 Silicon Properties In general, more accurate temperature prediction is obtained when the temperature- dependent material properties are applied. However, a drawback of using the temperature-dependent material properties is the long computing time due to the complexity of highly non-linear functions for the material properties, so that in many cases, some properties are assumed to be constant and some may be ignored due to their insignificant effect on the problem considered. The constant silicon properties are given in Table 5.1. According to the studies of Ohsaka et al. [247], Touloukian [248-249], Grigoropoulos et al. [136], and Moody and Hendel [134], the temperature-dependent silicon properties are expressed in Table 5.2. The plots of these temperature-dependent properties are shown in Figures 5.6(a) to (e).
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Table 5.1. Constant thermal and optical properties of silicon. Constant properties Ref. Density (ȡ) [kg/m3] 2329 [218] Thermal conductivity (k) [W/mK] 130 [218]
Heat capacity at constant pressure (cp) [J/kgK] 700 [218] Thermal diffusivity (Į) [m2/s] 7.974x10-5 [218]
Melting temperature (Tm) [K] 1687 [218]
Vaporization temperature (Tv) [K] 3538 [218] 6 Latent heat of melting (Lm) [J/kg] 1.79x10 [218] 7 Latent heat of vaporization (Lv) [J/kg] 1.28x10 [218]
Reflectivity (Rf) 0.33 [155]
Absorption coefficient of solid silicon (Ab) [1/m] 2792.79 [24, 155] 7 Absorption coefficient of liquid silicon (Ab) [1/m] 8.6x10 [246] Emissivity of solid silicon (İ) 0.66 [250] Emissivity of liquid silicon (İ) 0.27 [250]
Table 5.2. Temperature-dependent properties of silicon. Temperature-dependent properties Ref. .2 10311 3 .2 1063 −2 ()−×−× TT ; ≤ TT ρ T )( = m m [247] ® 3 ()−4 ()−×−−−× 2 > ¯ .2 10580 .0 171 TT m .1 1061 m ; TTTT m 29900 Tk )( = [248-249] ()T − 99
§ 106 ·§ .0 17066T · ¨ ¸ + ≤ °¨ ¸¨ .1 4743 ¸ ; TT m ° ρ T )( © 300 ¹ Tc )( = © ¹ [136] p ® × 6 ° .2 10432 > ; TT m ¯° ρ T)( 128 α T )( = [248-249] 4 ()T −15910
()()−5 ×+×+ −15 4 ≤ = .0 367 .4 1029 T .2 10691 T ; 3019KT f TR )( ® [134] ¯ .0 72 ; > 3019KT
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2600 200
2400 150 ) 3 2200 100 2000 Density (kg/m Density 50 1800 Thermal conductivity (W/mK) conductivity Thermal
1600 0 0 1000 2000 3000 4000 0 500 1000 1500 2000 (a) Temperature (K) (b) Temperature (K)
1200 2E-04
1100 /s) 2 1000 1E-04
900
800 5E-05 Heat capacity (J/kgK) capacity Heat
700 (m diffusivity Thermal
600 0E+00 0 1000 2000 3000 4000 0 500 1000 1500 2000 (c) Temperature (K) (d) Temperature (K)
0.8
0.7
0.6
0.5 Reflectivity
0.4
0.3 0 1000 2000 3000 4000 (e) Temperature (K) Figure 5.6. Temperature-dependent silicon properties [134, 136, 247-249].
In order to assess the thermal model using the constant and the temperature- dependent material properties, the simulated temperature profile will be compared with the measurement observed by an infrared camera. The details of measurement equipment and setup will be presented in the next section.
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5.3 Assessment of the Temperature Field Model
In the following sections, the temperature field model developed above will be assessed by comparing with the measured temperatures using an infrared camera under a set of dry laser grooving experiments. The calculated or simulated temperatures from the model will consider both constant and temperature-dependent material properties discussed earlier.
5.3.1 Setup for Temperature Measurement An infrared camera (Titanium 560M) was used to measure the workpiece temperature for assessing the thermal model. A microscope extension lens and a high-temperature filter were incorporated with the camera to provide micro-scale thermal gradient measurements. The camera was calibrated by a black body with the temperatures varied from 873 K to 1773 K. Since the emissivity of silicon is 0.66 [250], the measurable range for silicon is approximately 1173 K to 2073 K [251]. The infrared camera was positioned as shown in Figure 5.7. A single crystalline silicon wafer of 700 ȝm thickness was used as the specimen material. The side-view micrograph of silicon is shown in Figure 5.8. Four levels of laser pulse energy, four levels of traverse speed and four levels of focal plane position were considered with a single level of laser pulse frequency (20 kHz), as given in Table 5.3, which gives 64 test conditions using the full-factorial experimental design. The laser beam moved from inside to outside the sample along the camera axis. When the laser beam reached the wafer edge (Figure 5.7(b)), a thermal image indicating the surface and subsurface temperatures of sample at the laser cutting front was captured by the infrared camera.
Table 5.3. Parameters used in the temperature measurement. Level Process parameters 1 2 3 4
Laser pulse energy (Ep) [mJ] 0.5 0.6 0.7 0.8 Laser pulse frequency (f) [kHz] 20
Laser traverse speed (vt) [mm/s] 10 30 50 70 Laser focal plane position (fpp) [mm] 0 -0.2 -0.4 -0.6
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(a) (b)
(c) Figure 5.7. Laser beam moving across the workpiece edge for temperature measurement at the cross-sectional surface: (a) start, (b) measured and (c) stop positions.
Workpiece surface
Figure 5.8. Micrograph of silicon wafer captured by the infrared camera.
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5.3.2 Comparison of Measured and Simulated Temperature Profiles Some samples of thermal images obtained from the infrared camera are shown in Figures 5.9 to 5.11 for different laser pulse energies, focal plane positions and traverse speeds, respectively. Since the measurement was made through a high-pass filter, the temperature that is out of the calibrated range has not been taken into account. The experimental results show that the laser-heated region (temperature above 1173 K) is large when high laser pulse energy, zero focal plane position and slow traverse speed are employed.
K K
Top work Laser axis Top work 2000 Laser axis 2000 m) surface m) surface μ -100 μ -100
1800 1800 0 0
100 1600 100 1600
200 Ep : 0.5 mJ 1400 200 Ep : 0.6 mJ 1400 f : 20 kHz f : 20 kHz fpp : 0 mm fpp : 0 mm 300 vt : 10 mm/s 300 vt : 10 mm/s
Distance from the top surface ( surface top the from Distance 1200 ( surface top the from Distance 1200
-300 -200 -100 0 100 200 300 -300 -200 -100 0 100 200 300 (a) Distance from the laser axis (μm) (b) Distance from the laser axis (μm)
K K Top work Laser axis Top work Laser axis 2000 2000 m) m) surface surface μ μ -100 -100
1800 1800 0 0
100 1600 100 1600
1400 1400 200 Ep : 0.7 mJ 200 Ep : 0.8 mJ f : 20 kHz f : 20 kHz fpp : 0 mm fpp : 0 mm 300 300 v : 10 mm/s
1200 ( surface top the from Distance 1200 Distance from the top surface ( surface top the from Distance vt : 10 mm/s t
-300 -200 -100 0 100 200 300 -300 -200 -100 0 100 200 300 (c) Distance from the laser axis (μm) (d) Distance from the laser axis (μm) Figure 5.9. Temperature profiles measured by an infrared camera under different laser pulse energies (laser pulse frequency=20 kHz, focal plane position=0 mm and traverse speed=10 mm/s).
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K K Top work Laser axis 2000 Top work Laser axis 2000 m) surface m) μ -100 μ -100 surface
1800 1800 0 0
100 1600 100 1600
200 Ep : 0.8 mJ 1400 200 Ep : 0.8 mJ 1400 f : 20 kHz f : 20 kHz fpp : 0 mm fpp : -0.2 mm 300 v : 10 mm/s 300 v : 10 mm/s Distance from the top surface ( surface top the from Distance t 1200 ( surface top the from Distance t 1200
-300 -200 -100 0 100 200 300 -300 -200 -100 0 100 200 300 (a) Distance from the laser axis (μm) (b) Distance from the laser axis (μm)
K K Top work Laser axis Top work Laser axis 2000 2000 m) surface m) surface μ -100 μ -100
1800 1800 0 0
100 1600 100 1600
1400 1400 200 Ep : 0.8 mJ 200 Ep : 0.8 mJ f : 20 kHz f : 20 kHz fpp : -0.4 mm fpp : -0.6 mm 300 300 Distance from the top surface ( surface top the from Distance vt : 10 mm/s 1200 ( surface top the from Distance vt : 10 mm/s 1200
-300 -200 -100 0 100 200 300 -300 -200 -100 0 100 200 300 (c) Distance from the laser axis (μm) (d) Distance from the laser axis (μm) Figure 5.10. Temperature profiles measured by an infrared camera under different laser focal plane positions (laser pulse energy=0.8 mJ, pulse frequency=20 kHz and traverse speed=10 mm/s).
K K Top work Laser axis Top work 2000 Laser axis 2000 m) m) surface
μ surface μ -100 -100
1800 1800 0 0
100 1600 100 1600
200 Ep : 0.8 mJ 1400 200 Ep : 0.8 mJ 1400 f : 20 kHz f : 20 kHz fpp : 0 mm fpp : 0 mm 300 v : 10 mm/s 300 v : 30 mm/s
Distance from the top surface ( surface top the from Distance t 1200 ( surface top the from Distance t 1200
-300 -200 -100 0 100 200 300 -300 -200 -100 0 100 200 300 (a) Distance from the laser axis (μm) (b) Distance from the laser axis (μm) Figure 5.11. Temperature profiles measured by an infrared camera under different laser traverse speeds (laser pulse energy=0.8 mJ, pulse frequency=20 kHz and focal plane position=0 mm).
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K K Top work Laser axis Top work Laser axis 2000 2000 m) surface m) surface
μ -100 μ -100
1800 1800 0 0
100 1600 100 1600
200 Ep : 0.8 mJ 1400 200 Ep : 0.8 mJ 1400 f : 20 kHz f : 20 kHz fpp : 0 mm fpp : 0 mm 300 v : 50 mm/s 300 Distance from the top surface ( surface top the from Distance t 1200 ( surface top the from Distance vt : 70 mm/s 1200
-300 -200 -100 0 100 200 300 -300 -200 -100 0 100 200 300 (c) Distance from the laser axis (μm) (d) Distance from the laser axis (μm) Figure 5.11. (cont.) Temperature profiles measured by an infrared camera under different laser traverse speeds (laser pulse energy=0.8 mJ, pulse frequency=20 kHz and focal plane position=0 mm).
Since the interference of radiation scattering to the measurement and the material temperatures above the calibrated range occurred at the laser-irradiated area, the temperature profile was considered at 30 ȝm from the laser beam axis for comparison. The temperature measurement data are given in Appendix C. The effects of laser pulse energy, focal plane position and traverse speed on the temperature at different distances from the top work surface are shown in Figures 5.12(a) to (c). It indicates that the maximum temperature is located at the top work surface (0 mm from the top surface) and gradually decreases from the top work surface to inside the workpiece.
3000 3000 f : 20 kHz Pulse energy Ep : 0.8 mJ fpp fpp : 0 mm 0.5 mJ f : 20 kHz 0 mm 2600 vt : 10 mm/s 2600 vt : 10 mm/s 0.6 mJ -0.2 mm 0.7 mJ -0.4 mm 2200 2200 0.8 mJ -0.6 mm
1800 1800
1400 1400 Temperature (K) Temperature Temperature (K) Temperature
1000 1000
600 600 0 102030405060708090100 0 102030405060708090100 (a) Distance from the top surface (ȝm) (b) Distance from the top surface (ȝm) Figure 5.12. Temperature profiles measured by an infrared camera at 30 ȝm from the laser axis under different laser pulse energies, focal plane positions and traverse speeds.
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3000 Ep : 0.8 mJ Traverse speed f : 20 kHz 10 mm/s 2600 fpp : 0 mm 30 mm/s 50 mm/s 2200 70 mm/s
1800
1400 Temperature (K) Temperature
1000
600 0 102030405060708090100 (c) Distance from the top surface (ȝm) Figure 5.12. (cont.) Temperature profiles measured by an infrared camera at 30 ȝm from the laser axis under different laser pulse energies, focal plane positions and traverse speeds.
The results also demonstrate that an increase in laser pulse energy increases the surface and subsurface temperatures, while the temperatures decrease with an increase in laser traverse speed and focal position from the target surface (more negative fpp value). This is due to the high laser energy density and long laser-material interaction time that cause more heat input to the target material and hence increase the work temperature. A symmetric semi-infinite model was used in order to reduce the computing time, where a half of laser beam was considered at the top-left position of the model. The Neumann boundary condition was applied at the right and bottom nodes as the adiabatic condition. The convection and radiation heat losses were given at the model top surface where a heat transfer coefficient of 10 W/m2K was utilized as the natural convection. The initial and the surrounding temperatures were kept at 300 K. A uniform grid size of 2 ȝm and a constant time step of 5 ns were employed. Since the modulus of the time step and the laser pulse duration was not zero, a fraction of the laser energy (EHl) occupied during 40 to 42 ns has been computed and included into the calculation by using
dt PA dE = b dt (5.42) Hl ³ ρ 0 Al
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For a comparison purpose, the simulation was performed under the constant and the temperature-dependent silicon properties. The simulated temperature fields are shown in Figures 5.13(a) to (d). It exhibits that the laser-heated region associated with the constant material properties increases during the pulse irradiation and rapidly decreases at the end of pulse cycle. By contrast, the rapid change of temperature gradient does not occur in the simulation with the temperature-dependent silicon properties. This is attributed to the high thermal conductivity and low heat capacity of silicon given in the constant properties that cause the overestimated heating and cooling actions for on- and off-pulse periods, respectively. Figures 5.14(a) and (b) show the temperature profiles of work material along the laser beam axis. It exhibits that the simulation with the constant material properties causes a higher predicted temperature and a lesser heat accumulation than using the temperature-dependent properties.
Radial width (μm) Radial width (μm) 100 200 300 400 500 K 100 200 300 400 500 K 3500 3500 0 Pulse irradiating period 0 End of pulse cycle (Heating) (Cooling) 3000 3000 100 100 2500 2500 m) m)
μ 200 μ 200 2000 2000
Depth ( Depth 1500 ( Depth 1500 300 Ep : 0.6 mJ 300 Ep : 0.6 mJ f : 20 kHz f : 20 kHz fpp : 0 mm 1000 fpp : 0 mm 1000 400 vt : 10 mm/s 400 vt : 10 mm/s Constant material properties 500 Constant material properties 500 (a) (b)
Radial width (μm) Radial width (μm) 100 200 300 400 500 K 100 200 300 400 500 K 0 3500 0 3500 Pulse irradiating period End of pulse cycle (Heating) (Cooling) 3000 3000 100 100 2500 2500
m) 200 m) 200 μ 2000 μ 2000
Depth ( Depth 300 1500 ( Depth 300 1500 Ep : 0.6 mJ Ep : 0.6 mJ f : 20 kHz f : 20 kHz fpp : 0 mm 1000 fpp : 0 mm 1000 400 400 vt : 10 mm/s vt : 10 mm/s Temperature-dependent properties 500 Temperature-dependent properties 500 (c) (d)
Figure 5.13. The simulated temperature profiles for constant and temperature-dependent silicon properties at the cutting front (laser pulse energy=0.6 mJ, pulse frequency=20 kHz, focal plane position=0 mm and traverse speed=10 mm/s).
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5000 5000 Simulation (Temperature-dependent) Simulation (Temperature-dependent) 4500 4500 Simulation (Constant) Simulation (Constant) 4000 4000 Tv = 3538 K Tv = 3538 K 3500 3500 Ep : 0.6 mJ Ep : 0.6 mJ 3000 f : 20 kHz 3000 f : 20 kHz fpp : 0 mm fpp : 0 mm 2500 vt : 10 mm/s 2500 vt : 10 mm/s Pulse irradiating period End of pulse cycle 2000 2000 T = 1687 K Temperature (K) Temperature Tm = 1687 K (Heating) (K) Temperature m (Cooling) 1500 1500 1000 1000 500 500 0 100 200 300 400 0 100 200 300 400 (a) Distance from the top surface (ȝm) (b) Distance from the top surface (ȝm) Figure 5.14. The simulated temperature profiles for constant and temperature-dependent properties at the laser axis (laser pulse energy=0.6 mJ, pulse frequency=20 kHz, focal plane position=0 mm and traverse speed=10 mm/s).
For the comparison with the measured results, the simulated temperature profiles at 30 ȝm from the laser axis were plotted and compared as shown in Figures 5.15 to 5.17. It indicates that the simulation with the temperature-dependent silicon properties provides a good agreement with the measurements, while the use of constant material properties results in much lower temperatures predicted. It is thus apparent that the prediction is accurate when the temperature-dependent material properties are applied.
3200 3200 Measurement Measurement 2800 Simulation (Temperature-dependent) 2800 Simulation (Temperature-dependent) Simulation (Constant) Simulation (Constant)
Ep : 0.5 mJ Ep : 0.6 mJ 2400 f : 20 kHz 2400 f : 20 kHz fpp : 0 mm fpp : 0 mm 2000 vt : 10 mm/s 2000 vt : 10 mm/s
1600 1600
Temperature (K) Temperature 1200 (K) Temperature 1200
800 800
400 400 0 102030405060708090100 0 102030405060708090100 (a) Distance from the top surface (ȝm) (b) Distance from the top surface (ȝm) Figure 5.15. The comparison of simulated and measured temperature profiles at 30 ȝm from the laser axis under different laser pulse energies (laser pulse frequency=20 kHz, focal plane position=0 mm and traverse speed=10 mm/s).
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3200 3200 Measurement Measurement 2800 Simulation (Temperature-dependent) 2800 Simulation (Temperature-dependent) Simulation (Constant) Simulation (Constant)
Ep : 0.7 mJ Ep : 0.8 mJ 2400 f : 20 kHz 2400 f : 20 kHz fpp : 0 mm fpp : 0 mm 2000 vt : 10 mm/s 2000 vt : 10 mm/s
1600 1600
Temperature (K) Temperature 1200 (K) Temperature 1200
800 800
400 400 0 102030405060708090100 0 102030405060708090100 (c) Distance from the top surface (ȝm) (d) Distance from the top surface (ȝm) Figure 5.15. (cont.) The comparison of simulated and measured temperature profiles at 30 ȝm from the laser axis under different laser pulse energies (laser pulse frequency=20 kHz, focal plane position=0 mm and traverse speed=10 mm/s).
3200 3200 Measurement Measurement 2800 Simulation (Temperature-dependent) 2800 Simulation (Temperature-dependent) Simulation (Constant) Simulation (Constant)
Ep : 0.8 mJ Ep : 0.8 mJ 2400 f : 20 kHz 2400 f : 20 kHz fpp : 0 mm fpp : -0.2 mm 2000 vt : 10 mm/s 2000 vt : 10 mm/s
1600 1600
Temperature (K) Temperature 1200 (K) Temperature 1200
800 800
400 400 0 102030405060708090100 0 102030405060708090100 (a) Distance from the top surface (ȝm) (b) Distance from the top surface (ȝm)
3200 3200 Measurement Measurement 2800 Simulation (Temperature-dependent) 2800 Simulation (Temperature-dependent) Simulation (Constant) Simulation (Constant)
Ep : 0.8 mJ Ep : 0.8 mJ 2400 f : 20 kHz 2400 f : 20 kHz fpp : -0.4 mm fpp : -0.6 mm 2000 vt : 10 mm/s 2000 vt : 10 mm/s
1600 1600
Temperature (K) Temperature 1200 (K) Temperature 1200
800 800
400 400 0 102030405060708090100 0 102030405060708090100 (c) Distance from the top surface (ȝm) (d) Distance from the top surface (ȝm) Figure 5.16. The comparison of simulated and measured temperature profiles at 30 ȝm from the laser axis under different laser focal plane positions (laser pulse energy=0.8 mJ, pulse frequency=20 kHz and traverse speed=10 mm/s).
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3200 3200 Measurement Measurement 2800 Simulation (Temperature-dependent) 2800 Simulation (Temperature-dependent) Simulation (Constant) Simulation (Constant)
Ep : 0.8 mJ Ep : 0.8 mJ 2400 f : 20 kHz 2400 f : 20 kHz fpp : 0 mm fpp : 0 mm 2000 vt : 10 mm/s 2000 vt : 30 mm/s
1600 1600
Temperature (K) Temperature 1200 (K) Temperature 1200
800 800
400 400 0 102030405060708090100 0 102030405060708090100 (a) Distance from the top surface (ȝm) (b) Distance from the top surface (ȝm)
3200 3200 Measurement Measurement 2800 Simulation (Temperature-dependent) 2800 Simulation (Temperature-dependent) Simulation (Constant) Simulation (Constant)
Ep : 0.8 mJ Ep : 0.8 mJ 2400 f : 20 kHz 2400 f : 20 kHz fpp : 0 mm fpp : 0 mm 2000 vt : 50 mm/s 2000 vt : 70 mm/s
1600 1600
Temperature (K) Temperature 1200 (K) Temperature 1200
800 800
400 400 0 102030405060708090100 0 102030405060708090100 (c) Distance from the top surface (ȝm) (d) Distance from the top surface (ȝm) Figure 5.17. The comparison of simulated and measured temperature profiles at 30 ȝm from the laser axis under different laser traverse speeds (laser pulse energy=0.8 mJ, pulse frequency=20 kHz and focal plane position=0 mm).
5.3.3 Comparison of Experimental and Simulated Groove Characteristics A comparison of the experimental and simulated groove characteristics in dry laser grooving was performed under the same conditions given in Table 5.3. The groove depths obtained from the experiments were measured and compared with those from the simulation. The experimental data for the laser grooving of silicon are given in Appendix D. The constant and temperature-dependent silicon properties were also considered for a comparison purpose. The boundary conditions applied were the same as the previous simulation, where the symmetric semi-infinite model was employed with the Neumann condition and the natural convection at the right, bottom and top boundaries, respectively. A uniform FD grid size of 2 ȝm and a time step of 5 ns were applied for explicit-numerical computations.
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The plots of experimental and simulated groove depths are shown in Figures 5.18(a) to (c). It indicates that an increase in laser pulse energy increases the groove depth, whereas the groove depth decreases with an increase in laser traverse speed and focal position from the work surface. It also demonstrates that the simulated groove depth under the temperature-dependent silicon properties provides an excellent agreement with the experiment, while the use of constant material properties results in an over prediction. This is due to the rapid heating in the simulation using the constant material properties that causes a deeper groove predicted so as a deeper heated region during the pulse period, as discussed earlier. According to this comparison, it is evident that the temperature field model associated with the temperature-dependent silicon properties not only results in more accurate temperature prediction, but also provides more accurate groove depth prediction than the use of constant material properties.
200 200 Experiment Experiment Simulation (Temperature-dependent) Simulation (Temperature-dependent) 160 Simulation (Constant) 160 Simulation (Constant) m) m) ȝ ȝ 120 120
80 80 Groove depth ( depth Groove ( depth Groove 40 f : 20 kHz 40 Ep : 0.8 mJ fpp : 0 mm f: 20 kHz vt : 10 mm/s vt : 10 mm/s 0 0 0.4 0.5 0.6 0.7 0.8 0.9 -0.8 -0.6 -0.4 -0.2 0 0.2 (a) Laser pulse energy (mJ) (b) Focal plane position (mm)
200 Experiment Simulation (Temperature-dependent) 160 Simulation (Constant) m)
ȝ Ep : 0.8 mJ 120 f: 20 kHz fpp : 0 mm
80 Groove depth ( depth Groove 40
0 0 20406080 (c) Traverse speed (mm/s) Figure 5.18. The experimental and the simulated groove depths of dry laser grooving at different laser pulse energies, focal plane positions and traverse speeds (pulse frequency=20 kHz).
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The simulated groove profiles for the constant and temperature-dependent material properties under different laser pulse energies, focal plane positions and traverse speeds are shown in Figures 5.19 to 5.21. It indicates that the simulation using the temperature- dependent properties results in a good correlation with the experiment. The groove depth is found to increase with an increase in laser pulse energy as show in Figures 5.19(a) to (d), while the groove width is not significantly changed with the laser pulse energy. The effect of focal plane position on the groove profile is shown in Figures 5.20(a) to (d). It indicates that zero focal plane position results in the deepest groove among the focal plane positions tested in this study. This is due to the laser energy density that is highest at the zero fpp. In addition, an increase in focal position from the target surface (more negative fpp value) slightly increases the groove width in the experiment. However, the effect on the groove width is relatively small compared to the groove depth, so that the change cannot be detected by the simulation.
Radial width (ȝm) Radial width (ȝm) 0 1020304050 0 1020304050 0 0 Ep : 0.5 mJ Ep : 0.6 mJ f : 20 kHz f : 20 kHz fpp : 0 mm fpp : 0 mm 40 vt : 10 mm/s 40 vt : 10 mm/s m) m) ȝ ȝ
80 80
Groove ( depth 120 Groove ( depth 120 Experiment Experiment Simulation (Temperature-dependent) Simulation (Temperature-dependent) Simulation (Constant) Simulation (Constant) (a) 160 (b) 160 Radial width (ȝm) Radial width (ȝm) 0 1020304050 0 1020304050 0 0 Ep : 0.7 mJ Ep : 0.8 mJ f : 20 kHz f : 20 kHz fpp : 0 mm fpp : 0 mm 40 vt : 10 mm/s 40 vt : 10 mm/s m) m) ȝ ȝ
80 80
Groove ( depth 120 Groove ( depth 120 Experiment Experiment Simulation (Temperature-dependent) Simulation (Temperature-dependent) Simulation (Constant) Simulation (Constant) (c) 160 (d) 160 Figure 5.19. The simulated groove profiles of dry laser grooving at different laser pulse energies (laser pulse frequency=20 kHz, focal plane position=0 mm and traverse speed=10 mm/s).
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Radial width (ȝm) Radial width (ȝm) 0 1020304050 0 1020304050 0 0 Ep : 0.8 mJ Ep : 0.8 mJ f : 20 kHz f : 20 kHz fpp : 0 mm fpp : -0.2 mm 40 vt : 10 mm/s 40 vt : 10 mm/s m) m) ȝ ȝ
80 80
Groove ( depth 120 Groove ( depth 120 Experiment Experiment Simulation (Temperature-dependent) Simulation (Temperature-dependent) Simulation (Constant) Simulation (Constant) (a) 160 (b) 160
Radial width (ȝm) Radial width (ȝm) 0 1020304050 0 1020304050 0 0 Ep : 0.8 mJ Ep : 0.8 mJ f : 20 kHz f : 20 kHz fpp : -0.4 mm fpp : -0.6 mm 40 vt : 10 mm/s 40 vt : 10 mm/s m) m) ȝ ȝ
80 80
Groove ( depth 120 Groove ( depth 120 Experiment Experiment Simulation (Temperature-dependent) Simulation (Temperature-dependent) Simulation (Constant) Simulation (Constant) (c) 160 (d) 160 Figure 5.20. The simulated groove profiles of dry laser grooving at different laser focal plane positions (laser pulse energy=0.8 mJ, pulse frequency=20 kHz and traverse speed=10 mm/s).
The effect of laser traverse speed on the groove profile is shown in Figures 5.21(a) to (d). It demonstrates that a decrease in laser traverse speed increases the groove depth, while the groove width is not significantly affected by the traverse speed considered in this study. Even though the predicted depths when using the constant and temperature- dependent material properties have not been found to be significantly different, the use of temperature-dependent properties is recommended for accurate predictions as discussed above.
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Radial width (ȝm) Radial width (ȝm) 0 1020304050 0 1020304050 0 0 Ep : 0.8 mJ Ep : 0.8 mJ f : 20 kHz f : 20 kHz fpp : 0 mm fpp : 0 mm 40 vt : 10 mm/s 40 vt : 30 mm/s m) m) ȝ ȝ
80 80
Groove ( depth 120 Groove ( depth 120 Experiment Experiment Simulation (Temperature-dependent) Simulation (Temperature-dependent) Simulation (Constant) Simulation (Constant) (a) 160 (b) 160
Radial width (ȝm) Radial width (ȝm) 0 1020304050 0 1020304050 0 0 Ep : 0.8 mJ Ep : 0.8 mJ f : 20 kHz f : 20 kHz fpp : 0 mm fpp : 0 mm 40 vt : 50 mm/s 40 vt : 70 mm/s m) m) ȝ ȝ
80 80
Groove ( depth 120 Groove ( depth 120 Experiment Experiment Simulation (Temperature-dependent) Simulation (Temperature-dependent) Simulation (Constant) Simulation (Constant) (c) 160 (d) 160 Figure 5.21. The simulated groove profiles of dry laser grooving at different laser traverse speeds (laser pulse energy=0.8 mJ, pulse frequency=20 kHz and focal plane position=0 mm).
5.3.4 Laser Heating and Ablation Process It has been shown in previous sections that the temperature field model developed for dry laser ablation of silicon can accurately predict the temperature profile and the cut depth when the temperature-dependent silicon properties are used. In this section, the simulation was performed in the first three pulses in a drilling process to examine the laser-material interaction leading to the heating and ablation process. The process parameters applied were the same as given in Table 5.3, except for the traverse speed and focal plane position which were zero. The initial and the boundary conditions were set up based on the previous investigation, where the symmetric semi-infinite model associated with the Neumann condition and the natural convection was employed. Figures 5.22(a) to (i) show the simulated temperature fields and the cut profiles of silicon under the laser pulse energy of 0.8 mJ. It is observed that the silicon temperature
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is heated up to about 900 K within the first 10 ns and increases with time until the end of the first pulse (42 ns).
Radial width (μm) Radial width (μm) Radial width (μm) 10 20 30 K 10 20 30 K 10 20 30 K 0 0 0 1600
800 1200 1400 10 10 10 1200 700 1000 m) m) m) 20 20 20 μ μ μ 1000 600 800 30 30 30
Depth ( Depth ( 800 Depth ( Depth 500 600 40 40 40 600 400 t : 10 ns t : 20 ns 400 t : 30 ns 400 50 300 50 50 (a) (b) (c) Radial width (μm) Radial width (μm) Radial width (μm) 10 20 30 K 10 20 30 K 10 20 30 K 0 0 0 900 3000 3000 800 10 10 10 2500 2500 700
m) 20 2000 m) 20 2000 m) 20 μ μ μ 600 1500 1500 30 30 30 Depth ( Depth ( Depth ( 500 1000 End of 1000 40 40 1st pulse 40 500 500 400 t : 40 ns t : 42 ns t : 50000 ns 50 50 50 300 (d) (e) (f)
Radial width (μm) Radial width (μm) Radial width (μm) 10 20 30 K 10 20 30 K 10 20 30 K 0 0 0 1200 3000 3000 10 10 10 2500 2500 1000
m) 20 m) 20 m) 20 2000 μ μ μ 2000 800 1500 30 30 30
1500 ( Depth ( Depth Depth ( End of 600 End of 1000 nd rd 40 2 pulse 1000 40 40 3 pulse 500 t : 50042 ns 400 t : 100042 ns 500 t : 100000 ns 50 50 50 (g) (h) (i) Figure 5.22. The simulated temperature fields and ablation depths for the first three pulses of dry laser drilling when the temperature-dependent silicon properties are used (laser pulse energy=0.8 mJ, focal plane position=0 mm, laser pulse frequency=20 kHz, laser pulse duration=42 ns).
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The elemental material at the top surface starts to be vaporized at somewhere between 30 and 40 ns, and it reaches to a cut depth of about 8 ȝm at the end of the pulse. At this stage, the liquid-vapor phase (3538 K) may take place at the cut surface, while the melting and the solid-liquid transition phases (1687 K) are located below the cut surface. At the end of the first pulse period (50000 ns), the maximum residual work temperature decreases to be about 900 K. The work temperature rapidly increases again for the second pulse heating. The ablation depth further increases to 24 ȝm and 42 ȝm after the second and the third pulses, respectively. It can be noticed that the maximum residual temperature after each pulse has increased (e.g. from 900 K after the first pulse to 1300 K after the second pulse), as shown in Figure 5.23. In addition, the figure also demonstrates that an increase in laser pulse energy increases the residual temperature with time. This is attributed to the fact that an increase in absorption coefficient and a decrease in thermal conductivity of silicon at high temperatures cause a significant heat accumulation inside the bulk silicon, particularly at high laser pulse energy.
f: 20 kHz Pulse energy 5500 fpp : 0 mm 0.5 mJ 0.6 mJ 4500 0.7 mJ 0.8 mJ 3500
2500
1500 Maximum temperature (K) Maximum temperature
500 0 50000 100000 150000 Time (ns) Figure 5.23. Work temperature variation with time and laser pulses under different laser pulse energies.
From the above analysis, it can be noted that a relatively high laser energy is needed to increase the silicon temperature to its vaporization temperature for removal. In addition, the cooling rate during the off-pulse period is too low to carry away the residual heat from the cut surface before the next pulse starts. Such high temperature
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and the lack of cooling action are anticipated to cause a large HAZ and a large micro- structural change in silicon.
5.4 Concluding Remarks
In this chapter, a heat transfer model with the explicit forward-time central-space (FTCS) finite difference method has been developed for predicting the 2-D thermal gradient in a pulsed laser heating/ablation process. The enthalpy method has been utilized for calculating the energy balance and phase changes in the thermal model. The laser heat source was formed as a nonlinear function representing the laser pulse shape and the beam intensity profile. The convection and radiation heat losses according to Newton’s law of cooling and Stefan-Boltzmann law have been applied to the top boundary of the semi-infinite model, while other boundaries have been considered as the adiabatic condition. The thermal model for dry laser heating has been assessed to ensure that accurate temperature predictions can be made before it is extended in the next chapter for the hybrid laser-waterjet machining process. The model assessment was carried out by comparing the simulated temperatures with the measured temperatures using an infrared camera under the corresponding conditions. In addition, the simulated groove depth under different laser pulse energies, focal plane positions and traverse speeds was compared with the dry laser grooving experiment. The investigation showed that the simulation provided a good agreement with the measured temperatures when the temperature-dependent material properties were used. The laser heating and removing process of silicon were examined and it has been found that the liquid-vapor phase occurs at the cut surface during the heating and removing actions, while the melting and solid-liquid transition phases are located below the cut surface. In addition, an increase in the number of pulses increases the cut depth and the heat energy accumulated in the bulk material, causing a large HAZ after machining. This indicates a pressing need for a technology to reduce such thermal damage in the laser machining process. In the next chapter, the temperature field model will be extended and further developed for the hybrid laser-waterjet machining process by introducing the waterjet cooling and expelling effects into the model.
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Modeling of Temperature Field and Groove Characteristics in Hybrid Laser- Waterjet Microgrooving of Silicon
6.1 Introduction
As presented in Chapter 5, a transient heat transfer model has been developed using a forward-time central-space (FTCS) finite difference method to numerically find the temperature gradient in dry laser machining processes. An experimental assessment has shown that the model can accurately predict the temperature field and the cut profile of silicon when the temperature-dependent material properties are used. To further develop the model for the hybrid laser-waterjet process, two additional effects have to be taken into consideration. Firstly, the waterjet cooling effect needs to be applied as a forced convection rather than the natural convection used in the dry laser ablation; secondly, the waterjet expelling effect has to be investigated for removal with respect to the thermo-mechanical strength of silicon. The model will also be assessed by an experiment using an infrared camera. A numerical simulation of the hybrid laser- waterjet grooving process for silicon will be carried out using the developed model, and a comparison will be made with the kerf characteristics found from the experiment work in Chapter 3. The laser heating and the waterjet removing processes in the hybrid laser-
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waterjet machining process will also be studied by examining the interactions between laser, waterjet and work material.
6.2 Temperature Field Model Formulation
6.2.1 Finite Difference Model for Laser Heating The 2-D explicit forward-time central-space FD model using the enthalpy method has been used in this study to numerically solve the transient laser ablation problem. The parabolic heat balance equation is given by
∂Tc k p 2 +∇= HT (6.1) ∂t ρ l
where cp, k, ȡ and Hl are heat capacity of material, thermal conductivity of material, material density and laser heat source, respectively. The moving laser heat source formed as a function of the space and time domains is determined by
(1− ) exp()− ω tzAARE )( tzyxH ),,,( = bfp b l τρ Al (6.2) ()+ 22 ª § 4()− tvy 2 ·º ª− 4 yx º ¨− tp ¸ exp« 2 »«exp 2 » d ¨ d ¸ ¬ b ¼¬« © b ¹¼»
where Ep, Rf, Ab, Ȧ(t), IJ and Al are laser pulse energy, reflectivity of material, absorption coefficient of material, laser pulse function in time domain, laser pulse duration and laser-irradiated area, respectively. Since the absorption coefficient of silicon is very high at the melting temperature [136, 246], the laser heat source can be considered as the surface heat flux instead by using
()− ω tRE )(1 ª ()+ 22 ºª § 4()− tvy 2 ·º = fp − 4 yx ¨− tp ¸ l tzyxH ),,,( exp« »«exp » (6.3) τρ ΔzA d 2 ¨ d 2 ¸ l ¬ b ¼¬« © b ¹¼»
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The two exponential terms on the right-hand side of the equation are, respectively, the
Gaussian beam profile with the laser beam diameter of db, and the coefficient term for moving heat source with the traverse speed of vt at the imaginary plane yp. As the laser- irradiated area is changed after an elemental layer of material is removed; the irradiated area is determined by
π 2 22 d f 4 fpp λ A += (6.4) l π 2 4 d f
where Ȝ, df and fpp are laser wavelength, the focused laser beam diameter and laser focal plane position, respectively. By utilizing a symmetric semi-infinite scheme to reduce the computing time, only a half of laser beam is considered where the laser beam projects at the top-left node as shown in Figure 6.1. The Dirichlet boundary conditions are given by
= = Ts bottom,right Tsur ; it (6.5)
= = s left,top TT sur t 0; (6.6)
where Tsur is surrounding temperature. The Neumann condition at the bottom and right surface boundaries is given by
∂ 2T = 0 (6.7) ∂ 2 n bottom,right
The convection and radiation heat losses are only applied at the top boundary whose energy balance equation is given by
∂T − k ()TTh εσ ()−+−= TT 44 (6.8) ∂ sur sb sur z top
where h, İ and ısb are heat transfer coefficient, emissivity of material and Stefan- Boltzmann’s constant (5.67x10-8 W/m2K4) [218], respectively.
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Convective and radiative boundary
vt Starting point
Symmetric boundary
Semi-infinite boundary
Figure 6.1. Boundary conditions for a 2-D symmetric semi-infinite model at yp.
Since the explicit FD method is used in this study, the time step for yielding the numerical stability has to satisfy the following condition [2]
Δn2 t ≤Δ .0 25 ; min( ΔΔ=Δ zxn ), (6.9) § Δnh · α¨1+ 0 ¸ © k ¹ where ǻn and Į are the FD grid size and the thermal diffusivity of work material.
6.2.2 Waterjet Cooling Effect and Heat Losses The waterjet cooling effect has to be applied to the developed thermal model to enable the temperature field prediction in the hybrid laser-waterjet machining process. According to the comprehensive review in Chapter 2, the Elison and Webb’s model for waterjet cooling of a heated flat plate [186] is employed in this study. This is due to the fact that the waterjet cooling condition used in this study is almost the same as that used in their study. Since the waterjet diameter (Dn=570 ȝm) is more than 30 times the focused laser beam diameter (df=17.2 ȝm), the effect of radial convection is disregarded. The heat transfer coefficient on the stagnation zone (h0), shown in Figure 6.2, is given by [186]
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§ k · 9 −9 9/1 = ¨ f ¸[]()()0.847 + 0.465 h0 ¨ ¸ 0.109 eR 1.175 eR (6.10) © Lc ¹
where kf, Lc and Re are thermal conductivity of fluid, characteristic length of water flow and Reynolds number of waterjet, respectively. According to the study of Tong [191], a water layer thickness radially formed after a jet impact is approximately 10% of the waterjet nozzle diameter. Hence, the characteristic length (Lc) of the water layer is set to be equal to 0.1Dn.
Figure 6.2. Schematic of a waterjet impact on a target surface for cooling.
With reference to the studies of Hale and Querry [252], Palmer and Williams [253] and Kruusing [62], the absorption coefficient of water (Abw) at 1080 nm light -1 wavelength is approximately 158.6 m , while the reflectivity of water (Rfw) can be calculated by using the Fresnel equation for a normal-incidence spectral reflectance as [253]
()2 +− 2 = 1 kn R fw (6.11) ()1 2 ++ kn 2 where n and k are real and imaginary terms which are 1.327 and 1.366x10-6, respectively, for the 1080 nm light wavelength. Thus the reflectivity of water is approximately 0.01975. By applying these two water properties into the thermal model, the enthalpy of laser heat source can be modified as
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( )(11 −− ) exp()− exp (− )ω thAAzAARRE )( tzyxH ),,,( = fp fw b b bw bw w l τρ Al (6.12) ()+ 22 ª § 4()− tvy 2 ·º ª 4 yx º ¨ tp ¸ exp«− »«exp − » d 2 ¨ d 2 ¸ ¬ b ¼¬« © b ¹¼»
where hw is water layer thickness. Other thermal and optical properties of water are given in Table 6.1.
Table 6.1. Thermal and optical properties of water. Water properties Ref. 3 Density (ȡw) [kg/m ] 1000 [218] 2 -7 Kinematic viscosity (Ȟw) [m /s] 8.9 x 10 [218] -4 Dynamic viscosity (ȝw) [Pa.s] 8.9 x 10 [218]
Thermal conductivity (kw) [W/mK] 0.674 [218] 3 Heat capacity at constant pressure (cpw) [J/kgK] 4.2 x 10 [218]
Reflectivity (Rfw) 0.0198 [253]
Absorption coefficient (Abw) [1/m] 158.6 [62, 252-253]
In addition to the traverse motion, the initial interaction between the laser and material surface in the laser beam axis direction moves downwards after a heated layer of material is removed. Since the silicon is removed at below the melting temperature in the hybrid laser-waterjet machining process, this condition has to be included into the model and will be addressed in the next section. According to Equation 6.10 and Bernoulli’s equation, the heat transfer coefficient can be written as a function of water pressure. The relationship between the heat transfer coefficient and the water pressure is shown in Figure 6.3. It indicates that an increase in water pressure increases the heat transfer coefficient. This is due to an increase in flow velocity that produces a higher thermal convection effect for carrying heat away from the work surface.
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35 K) 2 30
25
20
15
10
5 Heat transfer coefficient (MW/m coefficient transfer Heat 0 0 5 10 15 20 25 30 35 Water pressure (MPa) Figure 6.3. The effect of water pressure on heat transfer coefficient.
When using a laser to soften the work material for removal by a waterjet in the hybrid laser-waterjet machining process, the workpiece temperature is much higher than the boiling temperature of water. This results in the vaporization of water on the work surface, where the generation and collapse of water bubbles in the boiling water causes a natural convection on the workpiece surface [218]. However, this convection effect is very low as compared to the waterjet cooling, so that zero heat convection is applied during the pulse heating period to simplify the model.
6.2.3 Waterjet Impingement and the Maximum Shear Stress The fundamental concept of waterjet impingement in this hybrid process is the same as that of the pure waterjet cutting process, where a high pressure waterjet has to reach the failure strength of material to result in a large plastic deformation and/or fractures for material removal. As a waterjet is employed in this hybrid process for removing silicon in a soft solid status at a relatively high temperature, it is not unreasonable to assume that the impinging mechanism is a purely elastic scheme. Figure 6.4 shows a schematic of an oblique waterjet impingement in the hybrid laser-waterjet machining process. With the aid of a momentum balance equation, the impact pressure caused by the waterjet impingement can be determined by
∂u ∂u 1 ∂P μ ∂2u + u −= wj g ++ w (6.13) ∂ ∂ ρ ∂ x ρ ∂ 2 t x w x w x
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where ȡw, ȝw, gx, Pwj, u, x and t are water density, dynamic viscosity of water, gravitation, water pressure, jet velocity, position on the waterjet axis and time, respectively.
Figure 6.4. Schematic of waterjet impingement in the hybrid process.
When a steady-state inviscid flow is applied without considering the gravity effect, the momentum equation is reduced to be the Bernoulli’s equation as given by
∂u 1 ∂P u −= wj (6.14) ∂ ρ ∂ x w x
The impact force resulted by the waterjet impingement can vary with the jet dynamic pressure distribution along the jet radius (or cross-section) and the jet travel distance from the nozzle exit. By integrating Equation 6.14, the waterjet pressure may be determined by [254]
2 A3 A4 ½ ρ ª z § z · § z · ºª§ r · 22 rA º w °ϕ « +⋅= ¨ ¸ ¨ ++ ¸ »«¨ − ¸ + 5 »° wj zrP ),( ® jn Av 1 A2 11 ¾ (6.15) 2 « d ¨ d ¸ ¨ d ¸ »«¨ d ¸ d » ¯° ¬ j © j ¹ © j ¹ ¼¬© j ¹ j ¼¿°
where ijn, vj, r and z are waterjet nozzle coefficient, average jet velocity, the radial distance from the jet axis and the distance from the nozzle exit, respectively, while A1,
A2, A3, A4 and A5 are empirical coefficients.
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Since a small (a few millimeters) nozzle stand-off distance is used in this hybrid process, the waterjet diameter is assumed to be equal to the nozzle diameter and the dynamic pressure variation along the jet flow direction is ignored. In addition, a uniform pressure distribution on the jet cross-section is applied to simplify the analysis. It is expected that this assumption should cause a small error in numerical calculations and its viability will be assessed in model verification. To further simplify the model, water bouncing and spreading after an impact are neglected in this study. By considering the waterjet impingement as a static problem, the equations for the horizontal (Fimp,x) and vertical (Fimp,z) components of impact force of an oblique waterjet impact can be given by
= θ imp,x wj APF sin jj (6.16) = θ imp,z wj APF cos jj (6.17)
where Pwj, Aj and șj are water pressure, cross-sectional area of waterjet beam and waterjet impact angle, respectively. According to Equations 6.16 and 6.17, normal and shear stresses can be determined by using the following equations:
F σ = imp,z z (6.18) Aimp F τ = imp,x xz (6.19) Aimp
Since the waterjet strikes on the workpiece surface with an angle, the impact profile becomes an ellipse as shown in Figure 6.5. The waterjet impact area (Aimp) is calculated by
πd 2 A = j (6.20) imp θ 4cos j
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Figure 6.5. Cross-sectional and elliptic impact areas of waterjet.
By substituting Equations 6.16, 6.17 and 6.20 into 6.18 and 6.19, the normal and the shear stresses acting on the waterjet impact area are respectively given by
σ = 2 θ z Pwj cos j (6.21) τ = θθ xz Pwj sin cos jj (6.22)
The maximum shear stress or the Tresca criterion is used to determine the yielding threshold of the impingement. The maximum shear stress as a function of principal stresses is expressed by [255]
§ − σσ −− σσσσ · τ = ¨ 21 1332 ¸ max max¨ , , ¸ (6.23) © 2 2 2 ¹
With the plane strain, all stress flows are only located in the x-z plane, indicating that the strain in y direction is zero. By considering Mohr’s circle and free-body diagrams shown in Figure 6.6, the principal and the maximum shear stresses on the impacted work surface can be calculated as follows:
σ σ z −= τ (6.24) 1 2 max σ σ z += τ (6.25) 2 2 max
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σ 2 τ = § z · +τ 2 max ¨ ¸ xz (6.26) © 2 ¹
In addition, it can be noticed that the average stress (ıavg) behaves as a hydrostatic stress in the maximum shear condition. This is due to the uniaxial compressive stress caused by the waterjet impingement.
Figure 6.6. Mohr’s circle and free-body diagrams for a waterjet impacted work element.
By substituting Equations 6.21 and 6.22 into 6.26, the maximum shear stress can be given as
cos4 θ τ = P j + sin 2 cos2 θθ (6.27) max wj 4 j j
From the above equation, it can be observed that the waterjet impact angle affects the maximum shear stress. As shown in Figure 6.7, the waterjet impact angle of about 35 degrees can produce the highest shear factor (ȟ), resulting in the highest shear stress in the target material. Equation 6.27 may be rewritten as
= ξτ max Pwj (6.28)
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1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
Maximum shear stress factor, ȟ factor, stress shear Maximum 0.1 0 0 102030405060708090 Waterjet impact angle (deg) Figure 6.7. The effect of waterjet impact angle on the maximum shear stress factor according to Equation 6.28.
The temperature-dependent mechanical strength of silicon is also taken into consideration when determining the stress threshold for material removal. The mechanical properties of silicon were taken from Wijaranakula [256], Ruoff [257] and Mathews and Gross [258]. It is found that the silicon strength decreases with an increase in temperature as shown in Figure 6.8. It is evident therefore that silicon is soft at high temperature and can be removed when a sufficient pressure is applied through a waterjet impact.
1E+07 Compressive strength (dynamic) Compressive strength (static) 1E+06 Te n s i l e s t r e n g t h Shear strength 1E+05 Predicted shear strength
1E+04
1E+03
1E+02 Strength (MPa) Strength
1E+01
1E+00 0 400 800 1200 1600 Temperature (K) Figure 6.8. Mechanical strengths of silicon [256-258].
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The shear strength value for silicon is approximately one-half of the tensile strength [259]. It can also be noticed that the strengthening effect takes place at the temperature of above 1473 K [258], where oxygen diffuses into the silicon and results in the dislocation locking [260]. However, the strengthening effect at the high temperature is negligible since the effect is low as compared to the waterjet impact pressure used in this study. A regression model of the temperature-dependent silicon shear strength plotted in Figure 6.8 is given by
τ 6 9 ()−3 ⋅×−×+×= m T 4)( 10 .7 10296 exp .5 10929 T (6.29)
According to the temperature field model developed earlier, the elemental material impacted by the waterjet is removed when the shear stress of that element (IJmax) exceeds the material shear strength (IJm) under a certain temperature. The material removal constraint can be written as
> ττ max m (T ) (6.30)
With the use of the parabolic thermal model with forced convection, the temperature field of silicon can be numerically predicted by using the FD method in which the laser is used for heating and the waterjet is used for cooling and expelling. The maximum shear stress of an oblique waterjet impingement and the temperature-dependent shear strength of silicon have also been considered for material removal. By combining the mechanical stress with the thermal model developed earlier, the simulation model for the hybrid laser-waterjet machining of silicon is applicable for both temperature gradient and cut profile predictions. A flow diagram for the hybrid laser-waterjet simulation is shown in Figure 6.9. The diagram can be divided into three main parts. The first part is subject to the pulsed laser heating, where the laser will periodically emit according to the pulse period (f-1) and the pulse duration (IJ) given. The waterjet impingement associated with the maximum shear criterion takes place in the second section where material will be removed when the maximum shear stress (IJmax) is greater than the material strength (IJm). The third section is to update the laser heating position according to the laser traverse speed (vt). The boundary conditions will be updated after every time step throughout the simulation,
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and the simulation will be terminated when the final time step is reached. The core codes of the program are given in Appendix E.
Start A Apply initial values and boundary conditions += tt pp dt += 1 tt vv dt No > −1 p ft 3 > No Yes tv dx / vt t = 0 p Yes = tv 0 No ≤ τ t p Change the laser heating Yes position to x+dx Laser provides heat to the workpiece Update the boundary conditions No τ > τ max m zxTzx ),,(),(
Yes No Reach to the Material at (x,z) is removed by waterjet end position?
Laser and waterjet project Yes at (x,z+dz) 2 End
A Figure 6.9. Flow diagram for simulation of the hybrid laser-waterjet machining process.
6.3 Model Assessment
Similar to the assessment of the dry laser machining model reported in Chapter 5, in this section the model for the temperature field in the hybrid laser-waterjet machining of silicon will be assessed by comparing the calculated or simulated temperature profile with the measured data under the corresponding conditions.
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6.3.1 Setup for Temperature Measurement An infrared camera (Titanium 560M) was employed to measure the workpiece temperature for assessing the model. Since water is not an infrared-transparent fluid, the measurement of the workpiece surface covered by a layer of water cannot be achieved by using the infrared camera. In order to measure the sample temperature without the disturbance of water, the temperatures on the back side of silicon wafer were measured rather than the side under the direct laser radiation. The experimental setup is shown in Figure 6.10; a workpiece support with a through hole was utilized to allow the infrared camera to reach the back surface of the sample for measurement. In addition, the support can also prevent the interference of water on the back surface during the measurement. A set of experiments was conducted under four levels of laser pulse energy, four levels of pulse overlap and four levels of water pressure with a single level of focal plane position (0 mm), waterjet offset distance (0.4 mm) and waterjet impact angle (40 degrees), as given in Table 6.2. This results in 64 tests using a full-factorial experimental design.
Figure 6.10. Setup for measuring the back surface temperature of silicon.
Table 6.2. Parameters used for measuring the silicon temperature in the hybrid process. Level Process parameters 1 2 3 4
Laser pulse energy (Ep) [mJ] 0.3 0.4 0.5 0.6 Focal plane position (fpp) [mm] 0 Laser pulse overlap (PO) [%] 99.3 99.5 99.7 99.9
Waterjet offset distance (xwl) [mm] 0.4
Water pressure (Pwj) [MPa] 5 10 15 20
Waterjet impact angle (șj) [deg] 40
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6.3.2 Comparison of Measured and Simulated Temperature Profiles Figure 6.11 shows the temperature profiles measured by the infrared camera under different conditions. In general, it has been found that temperatures increase with an increase in laser pulse energy and pulse overlap. By contrast, an increase in water pressure causes a reduced temperature gradient due to an increased waterjet cooling effect. The temperature measurement data are given in Appendix C. More discussion of the effect of process parameters on the temperature profiles will be given later in this section.
Pulse energy: 0.3 mJ Pulse energy: 0.3 mJ Water pressure: 5 MPa Water pressure: 20 MPa Focal plane position: 0 mm Focal plane position: 0 mm Pulse overlap: 99.3% Pulse overlap: 99.3% Waterjet offset distance: 0.4 mm Waterjet offset distance: 0.4 mm Waterjet impact angle: 40° Waterjet impact angle: 40°
(a) (b)
Pulse energy: 0.6 mJ Pulse energy: 0.6 mJ Water pressure: 5 MPa Water pressure: 20 MPa Focal plane position: 0 mm Focal plane position: 0 mm Pulse overlap: 99.3% Pulse overlap: 99.3% Waterjet offset distance: 0.4 mm Waterjet offset distance: 0.4 mm Waterjet impact angle: 40° Waterjet impact angle: 40°
(c) (d) Figure 6.11. Thermal images of silicon back surface under different laser pulse energies and water pressures (focal plane position=0 mm, pulse overlap=99.3%, waterjet offset distance=0.4 mm and waterjet impact angle=40°).
The simulation was performed using the same conditions as those in the temperature measurements given in Table 6.2. The symmetric semi-infinite model and the temperature-dependent silicon properties were employed to predict the temperature field. The Neumann boundary condition was applied at the right and bottom boundaries, while the convection and radiation heat losses were applied at the top boundary. The initial and the surrounding temperatures were set at 300 K. A uniform grid size of 2 ȝm
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and a constant time step of 5 ns were utilized. The simulated temperature profiles at the cutting front are shown in Figure 6.12. It demonstrates that the temperature gradient is large at high laser pulse energy and/or low water pressure.
Radial width (μm) Radial width (μm) 10 20 30 40 50 10 20 30 40 50 0 1100 0 1100
100 Ep: 0.3 mJ 1000 100 Ep: 0.3 mJ 1000 P : 5 MPa Pwj: 20 MPa wj 900 900 200 200 fpp: 0 mm
m) fpp: 0 mm m) μ PO: 99.3% 800 μ PO: 99.3% 800 300 300 xwl: 0.4 mm xwl: 0.4 mm 700 ș : 40° 700 400 șj : 40° 400 j 600 600 500 500 Groove depth ( depth Groove 500 ( depth Groove 500
600 400 600 400
700 300 700 300 (a) (b)
Radial width (μm) Radial width (μm) 10 20 30 40 50 10 20 30 40 50 0 1600 0 1600 E : 0.6 mJ 100 p 1400 100 Ep: 0.6 mJ 1400 Pwj: 5 MPa Pwj: 20 MPa 200 fpp: 0 mm 200 m) 1200 m) fpp: 0 mm 1200 μ PO: 99.3% μ PO: 99.3% 300 300 xwl: 0.4 mm 1000 xwl: 0.4 mm 1000 ș : 40° 400 j 400 șj : 40° 800 800 500 500 Groove depth ( depth Groove 600 ( depth Groove 600 600 600 400 400 700 700 (c) (d) Figure 6.12. Simulated temperature profiles at the cutting front under different laser pulse energies and water pressures (focal plane position=0 mm, pulse overlap=99.3%, waterjet offset distance=0.4 mm and waterjet impact angle=40°).
According to the resolution of thermal images obtained from the measurements, the simulated back surface temperatures locating within 50 ȝm from the laser axis were averaged to be compared with the measured temperatures. A comparison of the measured and calculated temperatures under different laser pulse energies, pulse overlaps and water pressures is shown in Figures 6.13(a) to (c). The results exhibit that the simulated temperatures show a good agreement with the measured data under different heating and cooling conditions tested in this study. It is also observed that an increase in laser pulse energy and pulse overlap increases the maximum back surface temperature. This is attributed to the laser-heated region that expands with these two parameters and hence results in increased back surface temperatures. In addition, an
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increase in water pressure decreases the workpiece temperature. This is due to the heat transfer coefficient that increases with the water pressure and thus causes a reduction of thermal gradient.
Water pressure fpp: 0 mm 490 Water pressure Ep: 0.6 mJ 390 5 MPa (Measurement) PO: 99.3% 5 MPa (Measurement) fpp: 0 mm 10 MPa (Measurement) xwl: 0.4 mm 10 MPa (Measurement) xwl: 0.4 mm șj: 40 450 15 MPa (Measurement) șj: 40 370 15 MPa (Measurement) 20 MPa (Measurement) 20 MPa (Measurement) 5 MPa (Simulation) 5 MPa (Simulation) 350 10 MPa (Simulation) 410 10 MPa (Simulation) 15 MPa (Simulation) 15 MPa (Simulation) 20 MPa (Simulation) 20 MPa (Simulation) 330 370
310 330 Bottom surface temperature (K) Bottom surface temperature (K) temperature surface Bottom 290 290 0.2 0.3 0.4 0.5 0.6 0.7 99.1 99.3 99.5 99.7 99.9 (a) Pulse energy (mJ) (b) Pulse overlap (%)
fpp:0 mm 0.3 mJ (Measurement) 390 PO: 99.3% 0.4 mJ (Measurement) xwl: 0.4 mm 0.5 mJ (Measurement) șj: 40 0.6 mJ (Measurement) 370 0.3 mJ (Simulation) 0.4 mJ (Simulation) 350 0.5 mJ (Simulation) 0.6 mJ (Simulation)
330
310 Bottom surface temperature (K) temperature surface Bottom 290 0 5 10 15 20 25 (c) Waterjet pressure (MPa) Figure 6.13. Comparison of measured and simulated temperatures at silicon back surface under different laser pulse energies, pulse overlaps and water pressures (focal plane position=0 mm, waterjet offset distance=0.4 mm and waterjet impact angle=40°).
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6.4 Simulation of Groove Characteristics
6.4.1 Simulation Conditions According to the experimental findings and the laser-waterjet interactions discussed in Chapter 3, the waterjet offset distance of 0.4 mm and the waterjet impact angles of 30 and 40 degrees are considered in this simulation. This is to ensure less water disturbance to the laser beam, i.e. the waterjet does not overlap with the laser beam. The complex optical, thermal and physical phenomena involved in the process, such as laser beam defocusing, multi-reflection, plasma formation, Leidenfrost separation, fluid dynamics of water and dynamic behaviors of silicon, are not considered in this study as their effects are considered to be minimal when the waterjet and laser beam are not overlapped. A water layer formed after the jet impacts on the top work surface is assumed to have a constant thickness of 0.1Dn [191] without air entrainment, bubble formation and cut debris, such that only water absorption and reflection effects are considered. The idealized and uniform waterjet beam without water bouncing, spreading and loss of jet kinetic energy is considered in this work, so that the waterjet impact force is uniform along jet length and jet cross-section. The waterjet impact is considered as the 2-D plane strain condition shown in Figure 6.4. The work material is assumed to be isotropic, where the constraint for material removal is subject to the Tresca criterion in a purely elastic scheme. The 2-D symmetric semi-infinite model with the temperature-dependent material properties is applied for predicting the temperature field and the cut profile of silicon. The Neumann boundary condition is assigned at the right and bottom nodes as the adiabatic condition. The convection and radiation heat losses are given at the top work surface where the heat transfer coefficient can be calculated by using Equation 6.10. The process parameters used for this simulation are given in Table 6.3. This results in 128 conditions using the full-factorial experimental design. According to Figure 6.3 and Equation 6.9, an increase in water pressure increases the heat transfer coefficient which in turn decreases the time step size of the FD computation. As the FD grid size of 2 ȝm and the temperature-dependent silicon properties were used in this simulation, the recommended time step under different water pressures and temperatures is shown in Figure 6.14. It is observed that 10 ns step size is small enough to yield the numerical stability for the parameters considered.
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Figure 6.14. The relationship between time step, water pressure and work temperature.
Table 6.3. Parameters used for the hybrid laser-waterjet grooving simulation. Level Process parameters 1 2 3 4
Laser pulse energy (Ep) [mJ] 0.3 0.4 0.5 0.6 Focal plane position (fpp) [mm] 0 Laser pulse overlap (PO) [%] 99.3 99.5 99.7 99.9
Waterjet offset distance (xwl) [mm] 0.4
Water pressure (Pwj) [MPa] 5 10 15 20
Waterjet impact angle (șj) [deg] 30 40 Workpiece thickness [ȝm] 700 Grid size [ȝm] 2 Time step (dt) [ns] 10 Pulse duration (IJ) [ns] 42
Laser beam diameter (df) [ȝm] 18
Waterjet diameter (dj) [ȝm] 570
Initial temperature (T0) [K] 300
Surrounding temperature (Tsur) [K] 300
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6.4.2 Comparison of Experimental and Simulated Results A comparison of the experimental and the simulated groove depth is shown in Figures 6.15 to 6.17, where the simulation shows a good agreement with the experiment. The effect of laser pulse energy is shown in Figure 6.15. It can be seen that an increase in laser pulse energy increases the groove depth. This is attributed to the fact that the laser- heated region is larger at a higher laser pulse energy, resulting in a greater amount of softened material to be removed.
600 600 fpp: 0 mm Water pressure fpp: 0 mm Water pressure 500 xwl : 0.4 mm 5 MPa (Experiment) 500 xwl : 0.4 mm 5 MPa (Experiment) PO : 99.3% 5 MPa (Simulation) PO : 99.3% 5 MPa (Simulation)
m) șj : 30 deg 20 MPa (Experiment) m) șj : 40 deg 20 MPa (Experiment) ȝ 400 ȝ 400 20 MPa (Simulation) 20 MPa (Simulation) 300 300
200 200 Groove depth ( depth Groove ( depth Groove 100 100
0 0 0.20.30.40.50.60.7 0.20.30.40.50.60.7 (a) Pulse energy (mJ) (b) Pulse energy (mJ)
600 600 fpp: 0 mm Water pressure fpp: 0 mm Water pressure 500 xwl : 0.4 mm 5 MPa (Experiment) 500 xwl : 0.4 mm 5 MPa (Experiment) PO : 99.9% 5 MPa (Simulation) PO : 99.9% 5 MPa (Simulation)
m) șj : 30 deg 20 MPa (Experiment) m) șj : 40 deg 20 MPa (Experiment) ȝ 400 ȝ 400 20 MPa (Simulation) 20 MPa (Simulation) 300 300
200 200 Groove depth ( depth Groove ( depth Groove 100 100
0 0 0.2 0.3 0.4 0.5 0.6 0.7 0.2 0.3 0.4 0.5 0.6 0.7 (c) Pulse energy (mJ) (d) Pulse energy (mJ) Figure 6.15. The simulated and experimental groove depths under different laser pulse energies.
The effect of laser pulse overlap on the groove depth is shown in Figure 6.16. It indicates that an increase in laser pulse overlap increases the groove depth. This is due to the work material that is reheated more frequently at a higher pulse overlap, so that a larger material region is softened causing an increased groove depth.
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600 600 fpp: 0 mm Pulse energy fpp: 0 mm Pulse energy 500 xwl : 0.4 mm 0.3 mJ (Experiment) 500 xwl : 0.4 mm 0.3 mJ (Experiment) Pwj : 5 MPa 0.3 mJ (Simulation) Pwj : 5 MPa 0.3 mJ (Simulation)
m) șj : 30 deg 0.6 mJ (Experiment) m) șj : 40 deg 0.6 mJ (Experiment) ȝ 400 ȝ 400 0.6 mJ (Simulation) 0.6 mJ (Simulation) 300 300
200 200 Groove depth ( depth Groove ( depth Groove 100 100
0 0 99.1 99.3 99.5 99.7 99.9 99.1 99.3 99.5 99.7 99.9 (a) Pulse overlap (%) (b) Pulse overlap (%)
600 600 fpp: 0 mm Pulse energy fpp: 0 mm Pulse energy 500 xwl : 0.4 mm 0.3 mJ (Experiment) 500 xwl : 0.4 mm 0.3 mJ (Experiment) Pwj : 20 MPa 0.3 mJ (Simulation) Pwj : 20 MPa 0.3 mJ (Simulation)
m) șj : 30 deg 0.6 mJ (Experiment) m) șj : 40 deg 0.6 mJ (Experiment) ȝ 400 ȝ 400 0.6 mJ (Simulation) 0.6 mJ (Simulation) 300 300
200 200 Groove depth ( depth Groove ( depth Groove 100 100
0 0 99.1 99.3 99.5 99.7 99.9 99.1 99.3 99.5 99.7 99.9 (c) Pulse overlap (%) (d) Pulse overlap (%) Figure 6.16. The simulated and experimental groove depths under different laser pulse overlaps.
The effect of water pressure on the groove depth is shown in Figure 6.17, demonstrating that an increase in water pressure increases the groove depth. This can be explained that the internal stress of impacted material increases with the water pressure, so that a deeper groove is formed. However, the increasing rate of groove depth tends to decrease at water pressures of above 15 MPa. This might be attributed to the influence of waterjet cooling that becomes more significant than the removal effect. This feature is also found at a lower pulse overlap where the laser beam coupling with the work material is less. In addition, the waterjet impact angle considered in this test is found to have no significant effect on the groove depth. This is because the shear factors (ȟ) for 30 and 40 degree impact angles are almost the same as shown in Figure 6.7, so that the difference of groove depths obtained is not apparent.
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600 600 fpp: 0 mm Pulse energy fpp: 0 mm Pulse energy 500 xwl : 0.4 mm 0.3 mJ (Experiment) 500 xwl : 0.4 mm 0.3 mJ (Experiment) PO : 99.3% 0.3 mJ (Simulation) PO : 99.3% 0.3 mJ (Simulation)
m) șj : 30 deg 0.6 mJ (Experiment) m) șj : 40 deg 0.6 mJ (Experiment) ȝ 400 ȝ 400 0.6 mJ (Simulation) 0.6 mJ (Simulation) 300 300
200 200 Groove depth ( depth Groove ( depth Groove 100 100
0 0 0 5 10 15 20 25 0 5 10 15 20 25 (a) Water pressure (MPa) (b) Water pressure (MPa)
600 600 fpp: 0 mm Pulse energy fpp: 0 mm Pulse energy 500 xwl : 0.4 mm 0.3 mJ (Experiment) 500 xwl : 0.4 mm 0.3 mJ (Experiment) PO : 99.9% 0.3 mJ (Simulation) PO : 99.9% 0.3 mJ (Simulation)
m) șj : 30 deg 0.6 mJ (Experiment) m) șj : 40 deg 0.6 mJ (Experiment) ȝ 400 ȝ 400 0.6 mJ (Simulation) 0.6 mJ (Simulation) 300 300
200 200 Groove depth ( depth Groove ( depth Groove 100 100
0 0 0 5 10 15 20 25 0 5 10 15 20 25 (c) Water pressure (MPa) (d) Water pressure (MPa) Figure 6.17. The simulated and experimental groove depths under different water pressures.
A comparison of the calculated and experimental groove profiles is shown in Figure 6.18. Although the groove widths obtained from the experiment are found to be wider than the simulated data, in general, the model calculations are reasonable and in good agreement with the experimental data. The small deviation may be attributed to the simplifications considered in the model, as well as the optical deflection and scattering of the laser beam.
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K K
Ep : 0.6 mJ Ep : 0.6 mJ fpp : 0 mm fpp : 0 mm PO : 99.9% PO : 99.9% xwl : 0.4 mm xwl : 0.4 mm Pwj : 5 MPa Pwj : 10 MPa șj : 40° șj : 40°
Simulation Experiment Simulation Experiment (a) (b)
K K
Ep : 0.6 mJ Ep : 0.6 mJ fpp : 0 mm fpp : 0 mm PO : 99.9% PO : 99.9% xwl : 0.4 mm xwl : 0.4 mm Pwj : 15 MPa Pwj : 20 MPa șj : 40° șj : 40°
Simulation Experiment Simulation Experiment (c) (d) Figure 6.18. The comparison of simulated and experimental groove profiles under: (a) 5 MPa, (b) 10 MPa, (c) 15 MPa and (d) 20 MPa water pressures.
According to the model assessment and the above comparison, it is evident that the models developed for the temperature fields and groove characteristics in the hybrid laser-waterjet machining process can provide accurate predictions of these quantities when the major effects of laser heating, waterjet cooling and expelling have been included in the model. By using the developed models, the laser heating under the waterjet cooling condition as well as the silicon ablation process is discussed next.
6.5 Heating and Ablation Process in Hybrid Laser-Waterjet Machining
From the previous section, a hybrid laser-waterjet ablation model has successfully been developed. It has been shown that the model can accurately predict the temperature profiles and the groove profile of silicon. In order to examine the heating and removing process, a simulation was performed to investigate the laser-material and the waterjet- material interactions including the temperature gradient and cut formation within a
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pulse period. The process parameters applied were the same as those given in Table 6.3, except the laser pulse overlap which was kept constant at 99.9%. The effect of laser pulse energy is shown in Figures 6.19 and 6.20 for the laser pulse energies of 0.3 mJ and 0.6 mJ, respectively. It can be observed that the laser-material interaction is similar to that in the dry laser heating process discussed in Chapter 5 in that the workpiece temperature increases with the laser pulse energy and the time during the heating period. According to these setups, material is heated to the threshold for removal within the first 40 ns for both 0.3 mJ and 0.6 mJ pulse energies. However, the amount of material removed for the 0.6 mJ pulse energy is larger than the 0.3 mJ due to a larger heated and softened region. The heating and removing actions are found to continue until the end of the pulse (42 ns). At this stage, it can be noted that silicon is removed in the soft-solid status whose temperature is below the melting temperature of silicon (1687 K). The removal action occurs when the shear strength of elemental material is lower than the impact stress induced by the waterjet.
Radial width (μm) Radial width (μm) 10 20 30 40 50 K 10 20 30 40 50 K 0 0 700 Ep: 0.3 mJ Ep: 0.3 mJ 100 100 Pwj: 20 MPa 450 Pwj: 20 MPa 650 200 fpp: 0 mm 200 fpp: 0 mm 600 m) m) μ PO: 99.9% μ PO: 99.9% 550 300 xwl: 0.4 mm 400 300 xwl: 0.4 mm șj : 40° șj : 40° 500 400 400 450 500
Groove depth ( depth Groove 500 350 ( depth Groove 400 600 t : 10 ns t : 20 ns 600 350
700 300 700 300 (a) (b)
Radial width (μm) Radial width (μm) 10 20 30 40 50 K 10 20 30 40 50 K 0 0 700 1200 E : 0.3 mJ 100 Ep: 0.3 mJ 100 p 650 Pwj: 20 MPa Pwj: 20 MPa 200 fpp: 0 mm 600 200 fpp: 0 mm 1000 m) m) μ PO: 99.9% μ PO: 99.9% 300 550 300 x : 0.4 mm xwl: 0.4 mm wl 800 ș : 40° 500 șj : 40° 400 j 400 450 500 600
Groove depth ( depth Groove 500 400 ( depth Groove 600 t : 30 ns 600 t : 40 ns 350 400 700 300 700 (c) (d) Figure 6.19. Temperatures and groove profiles at different times (laser pulse energy=0.3 mJ, focal plane position=0 mm, pulse overlap=99.9%, waterjet offset distance=0.4 mm, water pressure=20 MPa and waterjet impact angle=40°).
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Radial width (μm) Radial width (μm) 10 20 30 40 50 K 10 20 30 40 50 K 0 0 1200 1200 100 Ep: 0.3 mJ 100 Ep: 0.3 mJ Pwj: 20 MPa Pwj: 20 MPa 1000 200 fpp: 0 mm 1000 200 fpp: 0 mm m) m) μ PO: 99.9% μ PO: 99.9% 300 300 xwl: 0.4 mm 800 xwl: 0.4 mm 800 ș : 40° ș : 40° 400 j 400 j 600 500 600 500 Groove depth ( depth Groove ( depth Groove
600 600 t : 42 ns 400 t : 100 ns 400 700 700 (e) (f)
Radial width (μm) Radial width (μm) 10 20 30 40 50 10 20 30 40 50 0 K 0 K 800 650 100 Ep: 0.3 mJ 100 Ep: 0.3 mJ Pwj: 20 MPa Pwj: 20 MPa 600 200 fpp: 0 mm 700 200 fpp: 0 mm m) m) μ PO: 99.9% μ PO: 99.9% 550 300 300 xwl: 0.4 mm 600 xwl: 0.4 mm 500 șj : 40° ș : 40° 400 400 j 500 450 500 500 Groove depth ( depth Groove ( depth Groove 400 400 600 t : 500 ns 600 t : 1000 ns 350
700 300 700 300 (g) (h)
Radial width (μm) Radial width (μm) 10 20 30 40 50 10 20 30 40 50 0 K 0 K 400 325 100 Ep: 0.3 mJ 100 Ep: 0.3 mJ Pwj: 20 MPa 380 Pwj: 20 MPa 320 200 fpp: 0 mm 200 fpp: 0 mm m) m) μ PO: 99.9% μ PO: 99.9% 300 360 300 315 xwl: 0.4 mm xwl: 0.4 mm ș : 40° ș : 40° 400 j 400 j 340 310 500 500 Groove depth ( depth Groove ( depth Groove 320 305 600 t : 5000 ns 600 t : 10000 ns
700 300 700 300 (i) (j) Figure 6.19. (cont.) Temperatures and groove profiles at different times (laser pulse energy=0.3 mJ, focal plane position=0 mm, pulse overlap=99.9%, waterjet offset distance=0.4 mm, water pressure=20 MPa and waterjet impact angle=40°).
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Radial width (μm) Radial width (μm) 10 20 30 40 50 K 10 20 30 40 50 K 0 0 650 100 Ep: 0.6 mJ 100 Ep: 0.6 mJ 1000 Pwj: 20 MPa 600 Pwj: 20 MPa 900 200 fpp: 0 mm 200 fpp: 0 mm m) 550 m) μ PO: 99.9% μ PO: 99.9% 800 300 300 xwl: 0.4 mm 500 xwl: 0.4 mm 700 șj : 40° șj : 40° 400 450 400 600 500
Groove depth ( depth Groove 500 400 ( Groove depth 500
600 t : 10 ns 350 600 t : 20 ns 400
700 300 700 300 (a) (b)
Radial width (μm) Radial width (μm) 10 20 30 40 50 K 10 20 30 40 50 K 0 0 E : 0.6 mJ 1200 100 p 1000 100 Ep: 0.6 mJ Pwj: 20 MPa Pwj: 20 MPa 900 200 fpp: 0 mm 200 fpp: 0 mm m) m) 1000 μ PO: 99.9% 800 μ PO: 99.9% 300 xwl: 0.4 mm 300 xwl: 0.4 mm 700 800 șj : 40° șj : 40° 400 400 600 500 500 600 Groove depth ( Groove depth 500 ( Groove depth 600 t : 30 ns 600 t : 40 ns 400 400 700 300 700 (c) (d)
Radial width (μm) Radial width (μm) 10 20 30 40 50 K 10 20 30 40 50 K 0 0 1100 1200 100 Ep: 0.6 mJ 100 Ep: 0.6 mJ 1000 Pwj: 20 MPa Pwj: 20 MPa 200 1000 200 fpp: 0 mm 900 fpp: 0 mm m) m) μ μ PO: 99.9% PO: 99.9% 800 300 300 xwl: 0.4 mm xwl: 0.4 mm 800 700 ș : 40° șj : 40° 400 j 400 600 600 500 500 ( depth Groove Groove depth ( depth Groove 500
600 t : 42 ns 600 t : 100 ns 400 400 700 700 300 (e) (f)
Radial width (μm) Radial width (μm) 10 20 30 40 50 K 10 20 30 40 50 K 0 0 1000 900 100 Ep: 0.6 mJ 100 Ep: 0.6 mJ Pwj: 20 MPa 900 Pwj: 20 MPa 800 200 fpp: 0 mm 200 fpp: 0 mm m) m) μ PO: 99.9% 800 μ PO: 99.9% 700 300 300 xwl: 0.4 mm 700 xwl: 0.4 mm șj : 40° șj : 40° 600 400 600 400
500 500 500 Groove depth ( depth Groove 500 ( depth Groove
600 t : 500 ns 400 600 t : 1000 ns 400
700 300 700 300 (g) (h) Figure 6.20. Temperatures and groove profiles at different times (laser pulse energy=0.6 mJ, focal plane position=0 mm, pulse overlap=99.9%, waterjet offset distance=0.4 mm, water pressure=20 MPa and waterjet impact angle=40°).
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Radial width (μm) Radial width (μm) 10 20 30 40 50 K 10 20 30 40 50 K 0 0 650 Ep: 0.6 mJ Ep: 0.6 mJ 100 100 500 Pwj: 20 MPa 600 Pwj: 20 MPa 200 fpp: 0 mm 200 fpp: 0 mm m) m)
μ 550 μ PO: 99.9% PO: 99.9% 450 300 300 xwl: 0.4 mm 500 xwl: 0.4 mm șj : 40° șj : 40° 400 400 450 400 500 500 Groove depth ( depth Groove 400 ( depth Groove 350 600 t : 5000 ns 350 600 t : 10000 ns
700 300 700 300 (i) (j) Figure 6.20. (cont.) Temperatures and groove profiles at different times (laser pulse energy=0.6 mJ, focal plane position=0 mm, pulse overlap=99.9%, waterjet offset distance=0.4 mm, water pressure=20 MPa and waterjet impact angle=40°).
The threshold temperature for material removal with respect to water pressure is plotted in Figure 6.21 under different waterjet impact angles. It demonstrates that an increase in water pressure decreases the threshold temperature for material removal in the hybrid laser-waterjet machining of silicon. This is due to the waterjet impact force that increases with the water pressure, so that a less soft status of silicon can be removed. Based on the shear factors (ȟ) plotted in Figure 6.7, the maximum shear stress factor has its peak value at the waterjet impact angle of about 35 degrees, so that the temperature for material removal tends to increase at the impact angles of above and below 35 degrees.
1600 Impact angle 1500 20 30 40 1400 50 60 1300 70
1200
1100 Temperature for removal (K) removal for Temperature
1000 5 1015202530 Water pressure (MPa)
Figure 6.21. Temperature threshold for silicon removal in the hybrid process.
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The waterjet cooling effect takes place during laser heating and after the laser pulse, and in the latter case, it results in a rapid temperature decrease with time during the off- pulse period (t>42 ns). It can be observed that the cut formation is no longer developed due to the cooling action on the cut surface. It is also found that while the work temperature decreases with the time, an amount of heat below the cut surface still conducts towards the bulk material. However, under the waterjet cooling effect, the heat inside the bulk material gradually decreases, as does the work temperature. In the dry laser grooving process, a greater amount of accumulated heat in the work material can be obtained even when a lower pulse frequency, at the same pulse overlap, is used as reported by Gilbert et al. [219]. As a result, a deeper groove is produced so as the thermal damage. However, this hybrid laser-waterjet machining process provides a greater cooling effect to reduce the workpiece temperature than the dry laser ablation approach, so that the heat accumulation is anticipated to be minimized. The maximum workpiece temperature is plotted against time as shown in Figure 6.22, where the laser pulse energies of 0.3 mJ and 0.6 mJ are compared. It is observed that the temperature decreases with the increasing time during the off-pulse period as discussed earlier. In addition, it is noticed that the use of only 5 MPa water pressure can effectively cool the workpiece to the room temperature (300 K) within 40000 ns before the next pulse cycle starts at 50000 ns for the pulse frequency of 20 kHz. Hence, the heat accumulation does not occur in this hybrid laser-waterjet machining process, leading to an effective reduction of HAZ. By comparing the cooling rate of 5 MPa and 20 MPa water pressures as shown in Figures 6.22(a) and 6.22(b), it can be seen that the use of a higher water pressure can decrease the workpiece temperature faster than a lower water pressure. This is attributed to the fact that a higher water pressure causes a higher jet velocity, hence producing a higher heat transfer coefficient. However, when the laser pulse energy of 0.3 mJ is used, the cooling rate for the 20 MPa water pressure is lower than the 5 MPa. A reason for this feature is that a shallower groove depth is created when the 5 MPa water pressure is used, so that the heated region is limited to near the workpiece surface only, and the water can cool more effectively for decreasing the temperature during the off-pulse period. This implies that cooling rate can also be affected by groove depth or the position of the laser-material interactive zone (or laser-irradiated zone).
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1800 1800 Ep 0.3 mJ Ep 0.3 mJ 1600 Ep 0.6 mJ 1600 Ep 0.6 mJ 1400 fpp: 0 mm 1400 fpp: 0 mm PO: 99.9 % PO: 99.9 % 1200 1200 xwl: 0.4 mm xwl: 0.4 mm P : 5 MPa P : 20 MPa 1000 wj 1000 wj șj: 40 șj: 40 800 800
600 600
400 400
Maximum workpiece temperature (K) temperature Maximum workpiece 200 (K) temperature Maximum workpiece 200 0 1020304050 0 1020304050 (a) Time (ȝs) (b) Time (ȝs) Figure 6.22. The maximum workpiece temperature versus time under different laser pulse energies and water pressures: (a) 5 MPa and (b) 20 MPa (focal plane position=0 mm, pulse overlap=99.9%, waterjet offset distance=0.4 mm and waterjet impact angle=40°).
6.6 Concluding Remarks
A model for the temperature profiles for hybrid laser-waterjet micromachining of silicon has been developed in this chapter by using the explicit 2-D FD method associated with the parabolic heat conduction model. The model can also be used to predict the groove profile generated by the process. The thermal effects of waterjet have been applied into the model as a forced convection, while its mechanical or impact effect has been determined by using the maximum shear stress under the plane strain condition. The idealized waterjet with uniform pressure distribution along and across the jet and without water bouncing, spreading and loss of jet kinetic energy has been considered in order to simplify the model development. In addition, some dynamic effects, e.g. plasma formation, shock wave, cavitation, gasdynamics and hydrodynamics, have been neglected. The temperature-dependent silicon properties have been utilized in this model to provide the accurate predictions based on the study in Chapter 5. The mechanical behavior of the softened silicon is assumed to be purely elastic throughout this study regardless of the plastic deformation and other dynamic effects of silicon under various mechanical loads and temperatures, so that silicon is assumed to be removed when the maximum shear stress exceeds its temperature- dependent shear strength.
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The model has then been verified by comparing the predicted temperatures with those measured by an infrared camera under corresponding conditions. Since water is not an infrared-transparent fluid, the measurement was performed at the back side of the specimen rather than the surface under the direct laser radiation. The results showed that the model predictions are in a good agreement with the experimental results. This indicates that the developed thermal model can be applied for predicting the temperature field of silicon in the hybrid laser-waterjet machining process. A simulation study of the hybrid laser-waterjet grooving process using the developed model has been carried out with the conditions used in the experimental work in Chapter 3. The laser-waterjet non-overlap setup was considered, so that the waterjet offset distance of 0.4 mm and the waterjet impact angles of 30 and 40 degrees were applied. According to the simulated results, the groove depth was found to increase with an increase in laser pulse energy, laser pulse overlap and water pressure. In addition, the increasing rate of groove depth was found to decrease as the water pressure increased to above 15 MPa. This may be attributed to the waterjet cooling action that becomes more significant at high water pressures. By comparing the groove profile, the simulation results also showed a good agreement with those of the experiment. However, the predicted groove width has been found to be smaller than the corresponding experimental data. The reasons for this would be the effects of some unconsidered variables and the optical reflection of the laser beam by the waterjet, resulting in a wider groove in the experiment. However, the overall predicted results have shown that the developed thermal model for the hybrid process can predict the temperature field and the groove profile of silicon with a reasonable and acceptable accuracy. The laser heating, waterjet cooling and material removing process associated with this new machining process have also been investigated. It has been found that the workpiece temperature rapidly increases during the heating (or pulses) period and subsequently decreases with time in the off-pulse period due to the waterjet cooling action. The silicon temperature can be reduced to the room (or initial) temperature (300 K) within 40000 ns for the “worst-case” condition of the high laser pulse energy and the low water pressure considered in this work. This indicates that the heat accumulation in the work material does not occur, so that the damage is anticipated to be very small in the hybrid laser-waterjet machining process, as has been found in Chapter 4.
177 Chapter 7
Final Conclusions and Future Work
7.1 Final Conclusions
An extensive literature review of conventional and novel laser micromachining processes has been carried out to understand the laser physics, material removal processes and mechanisms associated with these processes, and the development of advanced uses of these technologies for minimizing damages in the laser ablation processes. Though ultra-short pulsed lasers can produce cuts with very small thermal damages, their high photon cost and process capability make them unsuitable for high material removal rate or fast processing. Liquid-assisted laser ablation technique has been found to be a more economical method than the short-pulsed lasers to remove material with less damage due to the high cooling effect and the prevention of debris redeposition by the water used. Pure water is normally used to assist the laser ablation process as it is cheap, safe and recyclable. Water can be used in the laser ablation process by three main approaches, i.e. underwater laser, waterjet-guided laser and liquid-assisted front side laser. Among these processes, the off-axial waterjet assisted laser technique has been selected in this study for further development using a totally new material removal mechanism, i.e. by using laser to heat and soften the material and waterjet to remove the softened material; water also performs a cooling action. In this process, the laser beam and the waterjet parameters can be adjusted independently to optimize the process, regardless of whether or not the properties of the laser and the waterjet are optically unmatchable. As a result, a hybrid laser-waterjet micromachining
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technology has been developed in this study in an attempt to minimize the thermal damage while maximizing the material removal rate. A hybrid laser-waterjet cutting system has been developed by placing a waterjet after a laser beam. A nanosecond pulsed laser was used for heating and softening the work material, while a waterjet was used for cooling and expelling the heated and softened material. Thus, the material removal could be performed at a relatively low temperature due to the high waterjet impingement. In order to assess this hybrid laser- waterjet machining technology, a single-crystalline silicon wafer was used as the work material in this study. A study of the cut geometries and HAZ size with respect to the major process parameters has shown that laser pulse energy and pulse overlap have a profound effect on the cut geometries, where an increase in these two parameters increases the groove width and depth. However, the effect of these parameters on the HAZ width was found to be indiscernible. In addition, small focal plane positions located within the laser depth of focus have been recommended to produce a narrow and deep groove with less HAZ. The effect of laser-waterjet overlap in the hybrid process can be minimized by placing the laser beam slightly ahead of the waterjet impact region, such that a greater material removal with less HAZ can be produced. A waterjet offset distance of about the major radius of the waterjet impact profile on the work surface has been suggested to reduce the laser energy absorption and the optical interference to the laser by the waterjet. The effect of water pressure and waterjet impact angle on the groove width has been studied. It has been found that a large groove width can be produced under a high water pressure and a large waterjet impact angle. Further, a deep groove can be achieved by using a high water pressure and a small waterjet impact angle as this condition increases the vertical jet impact force for increasing the depth. The study also found that the HAZ size was marginally affected by the water pressure and waterjet impact angle under the tested conditions. According to a comparison with dry laser ablation, the hybrid laser-waterjet technology has demonstrated its viability and advantages to achieve near damage-free micromachining of silicon. Plausible trends of the groove geometries and HAZ size with respect to the process parameters have been revealed to provide an in-depth understanding of the hybrid process.
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An investigation of surface and subsurface damages in terms of the micro-structural changes in the single-crystalline silicon has been performed on selected cut samples. The laser Raman spectroscopy study has shown that the thickness of the amorphous layer was less than 40 ȝm when silicon was ablated by the hybrid process. In addition, when low laser pulse energy, low pulse overlap and high water pressure were applied, the amorphous layer thickness formed on the cut surface was even thinner. Thus, it may be claimed that the hybrid laser-waterjet technology developed can provide near damage-free micromachining of silicon. A temperature field model for the conventional dry laser machining process has been developed first. The explicit forward-time central-space finite difference method has been applied to numerically solve the 2-D transient heat conduction model for the convectional dry laser machining process, and the associated model has been assessed by comparing the simulated results with the measurement data by an infrared camera in a dry laser grooving experiment. It has been shown that the simulated results were in good agreement with the experimental data when the temperature-dependent silicon properties were used. The model for dry laser machining has then been extended to the case of the hybrid laser-waterjet machining process. The waterjet cooling and expelling effects have been applied to the thermal model through Newton’s law of cooling and Tresca criterion of failure, respectively. The heat transfer coefficient has been found to increase with an increase in water pressure according to the Reynolds number and Bernoulli’s equation. An idealized waterjet has been considered without considering water bouncing, spreading and loss of jet kinetic energy in order to simplify the simulation model. The mechanical behavior of silicon has been assumed to be purely static in this study, such that the silicon is removed when the maximum shear stress exceeds the temperature- dependent shear strength of silicon. The thermal model for the hybrid process has been assessed by an experiment using an infrared camera, and the simulated temperature profiles showed a good agreement with the measured data. A simulation study of the grooving or material removing process for silicon using the hybrid laser-waterjet machining technology has been carried out. The simulated results showed that the workpiece temperature rapidly increased during the pulsed heating and subsequently decreased with time due to the waterjet cooling in the non- pulse period. The simulation also indicated that the groove depth increases with an
180 CHAPTER 7
increase in laser pulse energy, laser pulse overlap and water pressure. An excellent agreement between the simulated groove depths and those obtained from the experiments has been presented. Although the predicted groove width did not match well with the experiments, mainly due to effects of the unconsidered optical reflection of the laser beam that resulted in a wider groove in the experiments, the overall predictions are still reasonable. In summary, the work reported in this thesis has made a notable contribution to the following aspects. It has proposed and developed a novel hybrid laser-waterjet micromachining process using a new concept of material removal which has been proven to be able to conduct near damage-free micromachining while using the available high laser power for high machining rates. The experimental study has provided an essential understanding of the effect of process parameters on the various micromachining performance measures and the fundamental base for implementing the technology in practice. The work has for the first time developed a model for predicting the temperature field as well as the machined groove profile for the hybrid laser- waterjet machining process, with which the simulation study conducted has provided a fundamental understanding of the interaction between laser, waterjet and silicon in this new engineering phenomenon under the coupled effect of laser heating and softening and waterjet expelling and cooling. It has also revealed, for the first time, the material removal mechanism under a pulsed laser heating and softening of material and waterjet cooling and removal of the softened material still in its solid state. The models developed can be used in practice for the planning, optimization and control of the micromachining process using this technology.
7.2 Proposed Future Work
From the investigations carried out in this thesis, a few possible future avenues of research derived immediately from this work can be suggested. As the current hybrid laser-waterjet cutting head is limited to straight cutting only, the development of an automated-rotating hybrid cutting head system is recommended to facilitate profile cutting. In addition, an intelligent control system may be applied to automatically change the waterjet offset distance and impact angle.
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Material removal mechanism of the hybrid laser-waterjet machining process should be further studied to enable a deeper understanding of the complex interaction between waterjet and laser-softened material under different temperatures and pressures. It is anticipated that the study will provide an insight into the cut formation mechanisms under the coupled effects of laser, waterjet and work material. The dynamic behaviors of work material as well as the effect of waterjet or water layer on the laser beam property should be taken into consideration to refine the current simulation model for improved prediction accuracy, particularly for kerf width. This may involve plastic deformation and fractures of material at high temperature. Such theoretical investigations and modeling should result in greater knowledge of thermal and mechanical coupling with the work material in the hybrid laser-waterjet process. Since near damage-free micromachining of silicon has been demonstrated in this study by using the hybrid laser-waterjet machining process, the implementation of the technology on other materials, particularly thermal-sensitive and functional materials, should be undertaken to explore the advantages of this technology and the knowledge needed to effectively use the technology. Such studies should include meso- and micro- scale machining.
182 References
1. Jackson, M.J. (2006). Micro- and nanofabrication. In M.J. Jackson (Editor), Microfabrication and Nanomanufacturing. New York: CRC Taylor & Francis. 1-32. 2. Gower, M. (2008). Laser microfabrication in industry - Perspectives from the past, present and future. In Proceedings of SPIE - The International Society for Optical Engineering, San Jose, CA, 6879021-68790215. 3. Grohe, A., Preu, R., Glunz, S.W. and Willeke, G. (2006). Laser applications in crystalline silicon solar cell production. In Proceedings of SPIE - The International Society for Optical Engineering, Strasbourg, 6197171-6197177. 4. Taniguchi, N. (1994). The state of the art of nanotechnology for processing of ultraprecision and ultrafine products. Precision Engineering, 16, 5-24. 5. Shaw, M.C. (2003). The size effect in metal cutting. Sadhana – Academy Proceedings in Engineering Sciences, 28(5), 875-896. 6. Zheng, H.Y., Han, Z.Z., Chen, Z.D., Chen, W.L. and Yeo, S. (1996). Quality and cost comparisons between laser and waterjet cutting. Journal of Materials Processing Technology, 62(4), 294-298. 7. Naeem, M. and Collins, P. (2005). Micro- Machining for industrial applications. In Proceedings of SPIE - The International Society for Optical Engineering, Dublin, 274-284. 8. Dahotre, N.B. and Harimkar, S.P. (2008). Laser Fabrication and Machining of Materials. New York: Springer. 9. Ion, J.C. (2005). Laser Processing of Engineering Materials. Great Britain: Elsevier Butterworth-Heinemann.
183 REFERENCES
10. Meijer, J. (2004). Laser beam machining (LBM), state of the art and new opportunities. Journal of Materials Processing Technology, 149(1-3), 2-17. 11. Gower, M. (2000). Excimer laser microfabrication and micromachining. In Proceedings of SPIE - The International Society for Optical Engineering, Omiya, Jpn: Society of Photo-Optical Instrumentation Engineers, 124-131. 12. Fornasiero, L., Mix, E., Peters, V., Petermann, K. and Huber, G. (2000). 3+ Czochralski growth and laser parameters of RE -doped Y2O3 and Sc2O3. Ceramics International, 26, 589-592. 13. Diels, J.-C. (2006). Ultrashort Laser Pulse Phenomena. USA: Elsevier. 14. Sander, M., Muller, M. and Tetz, M.R. (2008). Possible retina damage potential of the femtosecond laser in situ keratomileusis (fs-LASIK) refractive surgery. Medical Laser Application, 23, 39-45. 15. Pham, D.T. and Gault, R.S. (1998). A comparison of rapid prototyping technologies. International Journal of Machine Tools & Manufacture, 38, 1257- 1287. 16. Li, X., Choi, H. and Yang, Y. (2002). Micro rapid prototyping system for micro components. Thin Solid Films, 420-421, 515-523. 17. Gillner, A., Holtkamp, J., Hartmann, C., Olowinsky, A., Gedicke, J., Klages, K., Bosse, L. and Bayer, A. (2005). Laser applications in microtechnology. Journal of Materials Processing Technology, 167(2-3), 494-498. 18. Lim, G.C. and Mai, T.A. (2002). Laser micro-fabrications: Present to future applications. In Proceedings of SPIE - The International Society for Optical Engineering, Singapore, 170-176. 19. Sugioka, K. (2001). Overview of novel approaches for laser microfabrication of advanced materials. In Proceedings of SPIE - The International Society for Optical Engineering, St. Petersburg-Pushkin, 149-157. 20. Dunsky, C.M. (2005). Laser material processing in microelectronics manufacturing: Status and near-term opportunities. In Proceedings of SPIE - The International Society for Optical Engineering, San Jose, CA, 200-214. 21. Jackson, M.J. and Robinson, G.M. (2006). Laser-based micro- and nanofabrication. In M.J. Jackson (Editor), Microfabrication and Nanomanufacturing. New York: CRC Taylor & Francis. 221-248.
184 REFERENCES
22. Dabby, F.W. and Paek, U.C. (1972). High- intensity laser- induced vaporization and explosion of solid material. IEEE Journal of Quantum Electronics, QE-8(2), 106-111. 23. Fonash, S.J. (1981). Solar Cell Device Physics. New York: Academic Press. 24. Green, M.A. (1995). Silicon Solar Cells Advanced Principles & Practice. Sydney: The University of New South Wales. 25. Jiang, C.Y., Lau, W.S., Yue, T.M. and Chiang, L. (1993). On the maximum depth and profile of cut in pulsed Nd:YAG laser machining. CIRP Annals - Manufacturing Technology, 42(1), 223-226. 26. Jiao, L., Ng, E.Y.K., Wee, L.M. and Zheng, H. (2009). Parametric study of femtosecond pulses laser hole drilling of silicon wafer. Advanced Materials Research, 74, 273-277. 27. Salonitis, K., Stournaras, A., Tsoukantas, G., Stavropoulos, P. and Chryssolouris, G. (2007). A theoretical and experimental investigation on limitations of pulsed laser drilling. Journal of Materials Processing Technology, 183(1), 96-103. 28. Knight, C.J. (1979). Theoretical modeling of rapid surface vaporization with back pressure. AIAA Journal, 17(5), 519-523. 29. Pompe, W., Bahr, H.A., Pflugbeil, I., Kirchhoff, G., Langmeier, P. and Weiss, H.J. (1997). Laser induced creep and fracture in ceramics. Materials Science and Engineering A, 233(1-2), 167-175. 30. Gross, T.S., Hening, S.D. and Watt, D.W. (1991). Crack formation during laser cutting of silicon. Journal of Applied Physics, 69(2), 983-989. 31. Sciti, D. and Bellosi, A. (2001). Laser-induced surface drilling of silicon carbide. Applied Surface Science, 180(1-2), 92-101. 32. Low, D.K.Y., Lia, L. and Corfe, A.G. (2001). Characteristics of spatter formation under the effects of different laser parameters during laser drilling. Journal of Materials Processing Technology, 118(1-3), 179-186. 33. Low, D.K.Y., Li, L. and Byrd, P.J. (2001). The influence of temporal pulse train modulation during laser percussion drilling. Optics and Lasers in Engineering, 35(3), 149-164. 34. Low, D.K.Y., Li, L. and Corfe, A.G. (2000). The influence of assist gas on the mechanism of material ejection and removal during laser percussion drilling.
185 REFERENCES
Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 214(7), 521-527. 35. Low, D.K.Y., Li, L. and Corfe, A.G. (2000). Effects of assist gas on the physical characteristics of spatter during laser percussion drilling of NIMONIC 263 alloy. Applied Surface Science, 154, 689-695. 36. Yue, T.M., Chan, T.W., Man, H.C. and Lau, W.S. (1996). Analysis of ultrasonic-aided laser drilling using finite element method. CIRP Annals - Manufacturing Technology, 45(1), 169-172. 37. Kancharla, V.V., Hendricks, K.K. and Chen, S. (2001). Micromachining of packaging materials for MEMS using lasers. In Proceedings of SPIE - The International Society for Optical Engineering, San Francisco, CA, 220-224.
38. Rajaram, N., Sheikh-Ahmad, J. and Cheraghi, S.H. (2003). CO2 laser cut quality of 4130 steel. International Journal of Machine Tools and Manufacture, 43(4), 351-358. 39. Dobrzanski, L.A. and Drygala, A. (2007). Laser processing of multicrystalline silicon for texturization of solar cells. Journal of Materials Processing Technology, 191(1-3), 228-231. 40. Eyett, M., Bauerle, D., Wersing, W. and Thomann, H. (1987). Excimer-laser- induced etching of ceramic PbTi1-xZr xO3. Journal of Applied Physics, 62(4), 1511-1514. 41. Tseng, A.A., Chen, Y.T. and Ma, K.J. (2004). Fabrication of high-aspect-ratio microstructures using excimer laser. Optics and Lasers in Engineering, 41(6), 827-847. 42. Yan, Q. (2005). Influence of the element silicon on laser processing. In Proceedings of SPIE - The International Society for Optical Engineering, Beijing, 392-399. 43. Chen, S.L. (1999). Effects of high-pressure assistant-gas flow on high-power
CO2 laser cutting. Journal of Materials Processing Technology, 88(1), 57-66. 44. Gross, M.S. (2006). On gas dynamic effects in the modelling of laser cutting processes. Applied Mathematical Modelling, 30(4), 307-318. 45. Ivarson, A., Powell, J., Kamalu, J. and Magnusson, C. (1994). The oxidation dynamics of laser cutting of mild steel and the generation of striations on the cut edge. Journal of Materials Processing Tech., 40(3-4), 359-374.
186 REFERENCES
46. Yilbas, B.S. (1997). The analysis of CO2 laser cutting. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 211(3), 223-232. 47. Sugioka, K. and Midorikawa, K. (2001). Novel technology for laser precision microfabrication of hard materials. Riken Review, 32, 36-42. 48. Fork, R.L., Greene, B.I. and Shank, C.V. (1981). Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking. Applied Physics Letters, 38(9), 671-672. 49. Knox, W.H., Fork, R.L., Downer, M.C., Miller, D.A.B., Chemla, D.S., Shank, C.V., Gossard, A.C. and Wiegmann, W. (1985). Femtosecond dynamics of resonantly excited excitons in room-temperature GaAs quantum wells.Physical Review Letters, 54(12), 1306-1309. 50. Knox, W.H., Fork, R.L., Downer, M.C., Stolen, R.H., Shank, C.V. and Valdmanis, J.A. (1985). Optical pulse compression to 8 fs at a 5-kHz repetition rate. Applied Physics Letters, 46(12), 1120-1121. 51. Sundaram, S.K. and Mazur, E. (2002). Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses. Nature Materials, 1(4), 217-224. 52. Stollhof, J., Weiler, S., Tan, C., Zawischa, I., Sutler, D.H., Kleinbauer, J. and Kumkar, M. (2007). Industrial micro machining with advanced solid state lasers. In Proceedings of SPIE - The International Society for Optical Engineering, San Jose, CA, 64511J1-64511J8. 53. Venkatakrishnan, K., Sudani, N. and Tan, B. (2008). A high-repetition-rate femtosecond laser for thin silicon wafer dicing. Journal of Micromechanics and Microengineering, 18(7), 0750321-0750327. 54. Chichkov, B.N., Momma, C., Nolte, S., Von Alvensleben, F. and Tunnermann, A. (1997). Femtosecond, picosecond and nanosecond laser ablation of solids. Applied Physics A: Materials Science and Processing, 63(2), 109-115. 55. Hirayama, Y. and Obara, M. (2003). Heat-affected zone of metals ablated with femtosecond laser pulses. In Proceedings of SPIE - The International Society for Optical Engineering, San Jose, CA, 417-425. 56. Amer, M.S., El-Ashry, M.A., Dosser, L.R., Hix, K.E., Maguire, J.F. and Irwin, B. (2005). Femtosecond versus nanosecond laser machining: Comparison of
187 REFERENCES
induced stresses and structural changes in silicon wafers. Applied Surface Science, 242(1-2), 162-167. 57. Rogers, M.S., Grigoropoulos, C.P., Minor, A.M. and Mao, S.S. (2009). Absence of amorphous phase in high power femtosecond laser-ablated silicon. Applied Physics Letters, 94(1), 0111111-0111113. 58. Singh, A.P., Kapoor, A., Tripathi, K.N. and Kumar, G.R. (2002). Laser damage studies of silicon surfaces using ultra-short laser pulses. Optics and Laser Technology, 34(1), 37-43. 59. Costache, F., Kouteva-Arguirova, S. and Reif, J. (2004). Sub-damage-threshold femtosecond laser ablation from crystalline Si: Surface nanostructures and phase transformation. Applied Physics A: Materials Science and Processing, 79(4-6), 1429-1432. 60. Ren, J. (2005). The Fundamental Physical Mechanisms and Characteristics in Laser Silicon Interaction. Ph.D. Thesis, Department of Electrical Engineering, Stanford University, California. 61. Dausinger, F. (2001). Drilling of high quality micro-holes. The Industrial Laser User, 22, 25-27. 62. Kruusing, A. (2004). Underwater and water-assisted laser processing: Part 1 - General features, steam cleaning and shock processing. Optics and Lasers in Engineering, 41(2), 307-327. 63. Kruusing, A. (2004). Underwater and water-assisted laser processing: Part 2 - Etching, cutting and rarely used methods. Optics and Lasers in Engineering, 41(2), 329-352. 64. Nath, A. and Khare, A. (2010). Transient evolution of multiple bubbles in laser induced breakdown in water. Laser and Particle Beams, 29(1), 1-9. 65. Sano, Y., Mukai, N., Okazaki, K. and Obata, M. (1997). Residual stress improvement in metal surface by underwater laser irradiation. Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms, 121(1-4), 432-436. 66. Zhu, S., Lu, Y.F., Hong, M.H. and Chen, X.Y. (2001). Laser ablation of solid substrates in water and ambient air. Journal of Applied Physics, 89(4), 2400- 2403.
188 REFERENCES
67. Fabbro, R., Fournier, J., Ballard, P., Devaux, D. and Virmont, J. (1990). Physical study of laser-produced plasma in confined geometry. Journal of Applied Physics, 68(2), 775-784. 68. Barnes, P.A. and Rieckhoff, K.E. (1968). Laser induced underwater sparks. Applied Physics Letters, 13(8), 282-284. 69. Park, H.K., Kim, D., Grigoropoulos, C.P. and Tam, A.C. (1996). Pressure generation and measurement in the rapid vaporization of water on a pulsed- laser-heated surface. Journal of Applied Physics, 80(7), 4072-4081. 70. Chen, X., Xu, R., Shen, Z., Lu, J. and Ni, X. (2003). Photodisruption effects of laser-matter interaction in liquids. In Proceedings of SPIE - The International Society for Optical Engineering, Wuhan, 290-295. 71. Lu, J., Xu, R.Q., Chen, X., Shen, Z.H., Ni, X.W., Zhang, S.Y. and Gao, C.M. (2004). Mechanisms of laser drilling of metal plates underwater. Journal of Applied Physics, 95(8), 3890-3894. 72. Daminelli, G., Kruger, J. and Kautek, W. (2004). Femtosecond laser interaction with silicon under water confinement. Thin Solid Films, 467(1-2), 334-341. 73. Morita, N., Ishida, S., Fujimori, Y. and Ishikawa, K. (1988). Pulsed laser processing of ceramics in water. Applied Physics Letters, 52(23), 1965-1966. 74. Zhu, G., Zhu, C., Yuan, X., Zhu, X. and Lu, P. (2005). UV laser assisted processing of ceramics in air and in water. In Proceedings of SPIE - The International Society for Optical Engineering, Beijing, 309-313. 75. Tsai, C.H. and Li, C.C. (2009). Investigation of underwater laser drilling for brittle substrates. Journal of Materials Processing Technology, 209(6), 2838- 2846. 76. Mueller, R.E., Bird, J. and Duley, W.W. (1992). Laser drilling into an absorbing liquid. Journal of Applied Physics, 71(2), 551-556. 77. Ren, J., Kelly, M. and Hesselink, L. (2005). Laser ablation of silicon in water with nanosecond and femtosecond pulses. Optics Letters, 30(13), 1740-1742. 78. Das, A.K. and Saha, P. (2010). Micromachining of silicon with excimer laser in air and water medium. International Journal of Manufacturing Technology and Management, 21(1-2), 42-53.
189 REFERENCES
79. Kruusing, A., Leppavuori, S., Uusimaki, A., Petretis, B. and Makarova, O. (1999). Micromachining of magnetic materials. Sensors and Actuators, A: Physical, 74(1), 45-51. 80. Kruusing, A., Leppavuori, S., Uusimaki, A. and Uusimaki, M. (1999). Rapid prototyping of silicon structures by aid of laser and abrasive-jet machining. Proceedings of SPIE - The International Society for Optical Engineering, 3680(2), 870-878. 81. Wee, L.M., Ng, E.Y.K., Prathama, A.H. and Zheng, H. (2011). Micro- machining of silicon wafer in air and under water. Optics & Laser Technology, 43(1), 62-71. 82. Karimzadeh, R., Anvari, J.Z. and Mansour, N. (2009). Nanosecond pulsed laser ablation of silicon in liquids. Applied Physics A: Materials Science and Processing, 94(4), 949-955. 83. Alfille, J.P., Pilot, G. and De Prunele, D. (1996). New pulsed YAG laser performances in cutting thick metallic materials for nuclear applications. Proceedings of SPIE - The International Society for Optical Engineering, 2789, 134-144. 84. Black, I. and Chua, K.L. (1997). Laser cutting of thick ceramic tile. Optics and Laser Technology, 29(4), 193-205. 85. Black, I., Livingstone, S.A.J. and Chua, K.L. (1998). A laser beam machining (LBM) database for the cutting of ceramic tile. Journal of Materials Processing Technology, 84(1-3), 47-55. 86. Richerzhagen, B. (1995). Device for Machining Material with a Laser. International Patent WO 95/32834. 87. Richerzhagen, B., Kutsuna, M., Okada, H. and Ikeda, T. (2002). Waterjet-guided laser processing. In Proceedings of SPIE - The International Society for Optical Engineering, Osaka, 91-94. 88. Yang, L.J., Li, C.Q., Tang, J., Wang, Y. and Chen, Y.B. (2011). Analysis on the coupling error of laser and water-jet in water-jet guided laser micromachining. Advanced Materials Research, 188, 190-194. 89. Li, C.Q., Yang, L.J., Wang, Y. and Tang, J. (2011). Simulation on the effects of misaligned coupling on the output intensity distribution in water-jet guided laser. Advanced Materials Research, 211-212, 400-405.
190 REFERENCES
90. Nilsson, T., Wagner, F., Housh, R. and Richerzhagen, B. (2004). Scribing of GaN wafer for white LED by water jet guided laser. In Proceedings of SPIE - The International Society for Optical Engineering, San Jose, CA, 200-206. 91. Ghassemieh, E., Versteeg, H.K. and Acar, M. (2006). The effect of nozzle geometry on the flow characteristics of small water jets. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 220(12), 1739-1753. 92. Tafreshi, H.V. and Pourdeyhimi, B. (2004). Effects of nozzle geometry on waterjet breakup at high Reynolds numbers. Exp. Fluids, 35(4), 354. 93. Vago, N., Spiegel, A., Couty, P., Wagner, F.R. and Richerzhagen, B. (2003). New technique for high-speed microjet breakup analysis. Experiments in Fluids, 35(4), 303-309. 94. Couty, P., Spiegel, A., Vágó, N., Ugurtas, B.I. and Hoffmann, P. (2004). Laser- induced break-up of water jet waveguide. Experiments in Fluids, 36(6), 919- 927. 95. Dushkina, N., Wagner, F.R., Boillat, C., Buchilly, J.M. and Richerzhagen, B. (2003). Water jet guided laser vs. saw dicing. In Proceedings of SPIE - The International Society for Optical Engineering, San Jose, CA, 75-85. 96. Sibailly, O. and Richerzhagen, B. (2004). Laser dicing of silicon and composite semiconductor materials. In Proceedings of SPIE - The International Society for Optical Engineering, San Jose, CA, 394-397. 97. Perrottet, D., Housh, R., Richerzhagen, B. and Manley, J. (2005). Heat damage- free Laser-Microjet cutting achieves highest die fracture strength. In Proceedings of SPIE - The International Society for Optical Engineering, San Jose, CA, 285-292. 98. Perrottet, D., Green, S. and Richerzhagen, B. (2006). Clean dicing of compound semiconductors using the water-jet guided laser technology. In ASMC (Advanced Semiconductor Manufacturing Conference) Proceedings, Boston, MA, 166-169. 99. Kray, D., Fell, A., Hopman, S., Mayer, K., Willeke, G.P. and Glunz, S.W. (2008). Laser chemical processing (LCP) - A versatile tool for microstructuring applications. Applied Physics A: Materials Science and Processing, 93(1), 99- 103.
191 REFERENCES
100. Hopman, S., Fell, A., Mayer, K., Mesec, M., Rodofili, A. and Kray, D. (2009). Comparison of laser chemical processing and Laser MicroJet for structuring and cutting silicon substrates. Applied Physics A: Materials Science and Processing, 95(3), 857-866. 101. Kuykendal, R. (1998). Water Laser Machine Tool. United States Patent No.5773791. 102. Kuykendal, R. (1992). Lighted Laminar Flow Nozzle. United States Patent No.5160086. 103. Porter, J.A., Louhisalmi, Y.A., Karjalainen, J.A. and Füger, S. (2007). Cutting thin sheet metal with a water jet guided laser using various cutting distances, feed speeds and angles of incidence. International Journal of Advanced Manufacturing Technology, 33(9-10), 961-967. 104. Perrottet, D., Boillat, C., Amorosi, S. and Richerzhagen, B. (2005). PV processing: Improved PV-cell scribing using water jet guided laser. Refocus, 6(3), 36-37. 105. Dupont, A., Caminat, P., Bournot, P. and Gauchon, J.P. (1995). Enhancement of material ablation using 248, 308, 532, 1064 nm laser pulse with a water film on the treated surface. Journal of Applied Physics, 78(3), 2022-2028. 106. Geiger, M., Becker, W., Rebhan, T., Hutfless, J. and Lutz, N. (1996). Increase of efficiency for the XeCl excimer laser ablation of ceramics. Applied Surface Science, 96-98, 309-315. 107. Geiger, M., Roth, S. and Becker, W. (1997). Microstructuring and surface modification by excimer laser machining under thin liquid films. In Proceedings of SPIE - The International Society for Optical Engineering, Limoges, 200-208. 108. Roth, S. and Geiger, M. (2000). Novel technique for high-quality microstructuring with excimer lasers. In Proceedings of SPIE - The International Society for Optical Engineering, San Jose, CA, USA: Society of Photo-Optical Instrumentation Engineers, 338-346. 109. Hong, M.H., Koh, M.L., Zhu, S., Lu, Y.F. and Chong, T.C. (2002). Steam- assisted laser ablation and its signal diagnostics. Applied Surface Science, 197- 198, 911-914.
192 REFERENCES
110. Koh, M.L., Hong, M.H., Zhu, S. and Lu, Y.F. (2002). Steam-assisted laser ablation metal substrate. In Proceedings of SPIE - The International Society for Optical Engineering, Singapore, 47-50. 111. Chryssolouris, G. and Sheng, P. (1990). Aspect of surface quality for laser machining of composite materials. Transactions of NAMRI/SME, 250-255. 112. Chryssolouris, G., Sheng, P. and Anastasia, N. (1993). Laser grooving of composite materials with the aid of a water jet. Journal of engineering for industry, 115(1), 62-72. 113. Molian, R., Neumann, C., Shrotriya, P. and Molian, P. (2008). Novel laser/water-jet hybrid manufacturing process for cutting ceramics. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 130(3), 0310081-03100810. 114. Kalyanasundaram, D., Shrotriya, P. and Molian, P. (2009). Obtaining a relationship between process parameters and fracture characteristics for hybrid CO2 laser/waterjet machining of ceramics. Journal of Engineering Materials and Technology, Transactions of the ASME, 131(1), 0110051-01100510. 115. Kalyanasundaram, D., Shrotriya, P. and Molian, P. (2010). Fracture mechanics- based analysis for hybrid laser/waterjet (LWJ) machining of yttria-partially stabilized zirconia (Y-PSZ). International Journal of Machine Tools and Manufacture, 50(1), 97-105. 116. Klingel, H. (1983). Method and Apparatus for Cutting by Means of a Laser Beam. United States Patent No.4403134. 117. Gangemi, D. (1991). Water Jet Slitter with Laser Finish and Method. United States Patent No.5068513.
118. Black, I. (1998). Determining cutting speeds for the CO2 laser machining of decorative ceramic tile. International Journal of Advanced Manufacturing Technology, 14(9), 651-655. 119. Ghoreishi, M., Low, D.K.Y. and Li, L. (2002). Comparative statistical analysis of hole taper and circularity in laser percussion drilling. International Journal of Machine Tools and Manufacture, 42(9), 985-995. 120. David, I. and Botis, M.N. (2004). Modelling of the laser hole drilling using factorial experiments. In Proceedings of SPIE - The International Society for Optical Engineering, Constanta, 465-471.
193 REFERENCES
121. Kuar, A.S., Doloi, B. and Bhattacharyya, B. (2006). Modelling and analysis of pulsed Nd:YAG laser machining characteristics during micro-drilling of zirconia (ZrO2). International Journal of Machine Tools and Manufacture, 46(12-13), 1301-1310. 122. Sundar, M., Nath, A.K., Bandyopadhyay, D.K., Chaudhuri, S.P., Dey, P.K. and Misra, D. (2009). Effect of process parameters on the cutting quality in lasox cutting of mild steel. International Journal of Advanced Manufacturing Technology, 40(9-10), 865-874. 123. Wee, L.M., Crouse, P.L. and Li, L. (2008). A statistical analysis of striation formation during laser cutting of ceramics. International Journal of Advanced Manufacturing Technology, 36(7-8), 699-706. 124. Martan, J., Kunes, J. and Semmar, N. (2007). Experimental mathematical model of nanosecond laser interaction with material. Applied Surface Science, 253(7), 3525-3532. 125. Dhupal, D., Doloi, B. and Bhattacharyya, B. (2007). Optimization of process parameters of Nd:YAG laser microgrooving of Al 2TiO5 ceramic material by response surface methodology and artificial neural network algorithm. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 221(8), 1341-1351. 126. Dhupal, D., Doloi, B. and Bhattacharyya, B. (2008). Parametric analysis and optimization of Nd:YAG laser micro-grooving of aluminum titanate (Al2TiO5) ceramics. International Journal of Advanced Manufacturing Technology, 36(9- 10), 883-893. 127. Dhupal, D., Doloi, B. and Bhattacharyya, B. (2008). Pulsed Nd:YAG laser turning of micro-groove on aluminum oxide ceramic (Al2O3). International Journal of Machine Tools and Manufacture, 48(2), 236-248. 128. Tsai, M.J., Li, C.H. and Chen, C.C. (2008). Optimal laser-cutting parameters for QFN packages by utilizing artificial neural networks and genetic algorithm. Journal of Materials Processing Technology, 208(1-3), 270-283. 129. Ghoreishi, M. and Nakhjavani, O.B. (2008). Optimisation of effective factors in geometrical specifications of laser percussion drilled holes. Journal of Materials Processing Technology, 196(1-3), 303-310. 130. Steen, W.M. (2003). Laser Material Processing. 3rd ed. London: Springer.
194 REFERENCES
131. Rosenthal, D. (1946). The theory of moving sources of heat and its application to metal treatments. Transaction ASME, 48, 849-866. 132. Cline, H.E. and Anthony, T.R. (1977). Heat treating and melting material with a scanning laser or electron beam. Journal of Applied Physics, 48(9), 3895-3900. 133. Mazumder, J. and Steen, W.M. (1980). Heat transfer model for CW laser material processing. Journal of Applied Physics, 51(2), 941-947. 134. Moody, J.E. and Hendel, R.H. (1982). Temperature profiles induced by a scanning cw laser beam. Journal of Applied Physics, 53(6), 4364-4371. 135. Liarokapis, E. and Raptis, Y.S. (1985). Temperature rise induced by a cw laser beam revisited. Journal of Applied Physics, 57(12), 5123-5126. 136. Grigoropoulos, C.P., Buckholz, R.H. and Domoto, G.A. (1986). A heat transfer algorithm for the laser-induced melting and recrystallization of thin silicon layers. Journal of Applied Physics, 60(7), 2304-2309. 137. Yilbas, B.S. (1993). Analytical solution for the heat conduction mechanism appropriate to the laser heating process. International Communications in Heat and Mass Transfer, 20(4), 545-555. 138. Yilbas, B.S. and Sahin, A.Z. (1994). Laser heating mechanism including evaporation process. International Communications in Heat and Mass Transfer, 21(4), 509-518. 139. Yilbas, B.S., Sahin, A.Z. and Davies, R. (1995). Laser heating mechanism including evaporation process initiating laser drilling. International Journal of Machine Tools and Manufacture, 35(7), 1047-1062. 140. Yilbas, B.S., Sami, M. and Al-Farayedhi, A. (1998). Closed-form and numerical solutions to the laser heating process. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 212(2), 141-151. 141. Ruf, A., Berger, P., Dausinger, F. and Hugel, H. (2001). Analytical investigations on geometrical influences on laser drilling. Journal of Physics D: Applied Physics, 34(18), 2918-2925. 142. Kaplan, A.F.H. (1996). An analytical model of metal cutting with a laser beam. Journal of Applied Physics, 79(5), 2198-2208.
195 REFERENCES
143. Araya, G. and Gutierrez, G. (2006). Analytical solution for a transient, three- dimensional temperature distribution due to a moving laser beam. International Journal of Heat and Mass Transfer, 49(21-22), 4124-4131. 144. Fell, A., Kray, D. and Willeke, G.P. (2008). Transient 3D/2D simulation of laser-induced ablation of silicon. Applied Physics a-Materials Science & Processing, 92(4), 987-991. 145. Richardson, L.F. (1910). The approximate arithmetical solution by finite differences of physical problems including differential equations, with an application to the stresses in a masonry dam. Philosophical Transactions of the Royal Society of London, Series A, 210, 307-357. 146. Diniz Neto, O.O. and Lima, C.A.S. (1994). Nonlinear three-dimensional temperature profiles in pulsed laser heated solids. Journal of Physics D: Applied Physics, 27(9), 1795-1804. 147. Tzou, D.Y. and Chiu, K.S. (2001). Temperature-dependent thermal lagging in ultrafast laser heating. International Journal of Heat and Mass Transfer, 44(9), 1725-1734. 148. Chen, D.J., Wu, S.C., Xiang, Y.B. and Li, M.Q. (2002). Simulation of three- dimensional transient temperature field during laser bending of sheet metal. Materials Science and Technology, 18(2), 215-218. 149. Kim, B.C., Kim, T.H., Kim, J.S., Kim, K.B. and Lee, H.Y. (2002). Investigation on the effect of laser pulse shape during Nd:YAG laser microwelding of thin Al sheet by numerical simulation. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 33(5), 1449-1459. 150. Sabbaghzadeh, J., Azizi, M. and Torkamany, M.J. (2008). Numerical and experimental investigation of seam welding with a pulsed laser. Optics and Laser Technology, 40(2), 289-296. 151. Qiu, W., Watson, J., Thompson, D.S. and Deans, W.F. (1994). Modelling the interaction between laser and target material in laser microspectral analysis. Optics and Laser Technology, 26(3), 157-166. 152. Groß, M.S., Black, I. and Müller, W.H. (2001). Full-through laser cutting process simulation. In Proceedings of SPIE - The International Society for Optical Engineering, Prague, 236-239.
196 REFERENCES
153. Bin-Mansoor, S. and Yilbas, B.S. (2006). Laser pulse heating of steel surface: Consideration of phase-change process. Numerical Heat Transfer; Part A: Applications, 50(8), 787-807. 154. Li, C.F., Johnson, D.B. and Kovacevic, R. (2003). Modelling of heat transfer in waterjet guided laser drilling of silicon. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 217(5), 583-600. 155. Li, C.F., Johnson, D.B. and Kovacevic, R. (2003). Modeling of waterjet guided laser grooving of silicon. International Journal of Machine Tools and Manufacture, 43(9), 925-936. 156. Ozisik, M.N. (1994). Finite Difference Methods in Heat Transfer. USA: CRC Press. 157. Courant, R.L. (1943). Variational methods for the solution of problems of equilibrium and vibration. Bulletin of the American Mathematical Society, 49, 1- 23. 158. Akarapu, R., Li, B.Q. and Segall, A. (2004). A thermal stress and failure model for laser cutting and forming operations. Journal of Failure Analysis and Prevention, 4(5), 51-62. 159. Chen, Y., Lu, J. and Ni, X. (2007). Analysis of thermal stress damage in single- crystal silicon induced by 1064nm long pulse laser. In Proceedings of SPIE - The International Society for Optical Engineering, Beijing, 68351X1-68351X7. 160. Polak, M., Chmelickova, H., Stranyanek, M. and Vasicek, L. (2002). Modeling of laser cutting and drilling. In Proceedings of SPIE - The International Society for Optical Engineering, Olomouc, 146-151. 161. Kim, M.J. (2005). 3D finite element analysis of evaporative laser cutting. Applied Mathematical Modelling, 29(10), 938-954. 162. Ganesh, R.K., Bowley, W.W., Bellantone, R.R. and Hahn, Y. (1996). A model for laser hole drilling in metals. Journal of Computational Physics, 125(1), 161- 176. 163. Ganesh, R.K., Faghri, A. and Hahn, Y. (1997). A generalized thermal modeling for laser drilling process - I. Mathematical modeling and numerical methodology. International Journal of Heat and Mass Transfer, 40(14), 3351- 3360.
197 REFERENCES
164. Ganesh, R.K., Faghri, A. and Hahn, Y. (1997). A generalized thermal modeling for laser drilling process - II. Numerical simulation and results. International Journal of Heat and Mass Transfer, 40(14), 3361-3373. 165. Schvan, P. and Thomas, R.E. (1985). Time-dependent heat flow calculation of cw laser-induced melting of silicon. Journal of Applied Physics, 57(10), 4738- 4741. 166. Van Elsen, M., Baelmans, M., Mercelis, P. and Kruth, J.P. (2007). Solutions for modelling moving heat sources in a semi-infinite medium and applications to laser material processing. International Journal of Heat and Mass Transfer, 50(23-24), 4872-4882. 167. Shamsundar, N. and Sparrow, E.M. (1975). Analysis of multidimensional conduction phase change via the enthalpy model. Journal of Heat Transfer, 97 Ser C(3), 333-340. 168. Eyres, N.R., Hartree, D.R., Ingham, J., Jackson, R., Sarjant, R.J. and Wagstaff, J.B. (1946). The calculation of variable heat flow in solids. Phil. Trans. R. Soc. A, 240, 1-57. 169. Furzeland, R.M. (1980). A comparative study of numerical methods for moving boundary problems. J. Inst. Math. Appl., 26(4), 411-429. 170. Pham, Q.T. (1985). A fast, unconditionally stable finite-difference scheme for heat conduction with phase change. International Journal of Heat and Mass Transfer, 28(11), 2079-2084. 171. Semak, V.V., Damkroger, B. and Kempka, S. (1999). Temporal evolution of the temperature field in the beam interaction zone during laser material processing. Journal of Physics D: Applied Physics, 32(15), 1819-1825. 172. Atanasov, P.A., Eugenieva, E.D. and Nedialkov, N.N. (2001). Laser drilling of silicon nitride and alumina ceramics: A numerical and experimental study. Journal of Applied Physics, 89(4), 2013-2016. 173. Fell, A. and Willeke, G.P. (2010). Fast simulation code for heating, phase changes and dopant diffusion in silicon laser processing using the alternating direction explicit (ADE) method. Applied Physics A: Materials Science and Processing, 98(2), 435-440. 174. Shin, S. and Chung, H. (2009). Modeling of melting, evaporating, and resolidifying procedure in laser-induced metal processing. Journal of
198 REFERENCES
Manufacturing Science and Engineering, Transactions of the ASME, 131(2), 0245011-0245015. 175. Yang, L.J., Wang, M.L., Wang, Y., Tang, J. and Chen, Y.B. (2009). Numerical simulation on the temperature field of water-jet guided laser micromachining. Advanced Materials Research, 69-70, 333-337. 176. Shu, J.J. (2004). Microscale heat transfer in a free jet against a plane surface. Superlattices and Microstructures, 35(3-6), 645-656. 177. Watson, E.J. (1964). The radial spread of a liquid jet over a horizontal plane.J. Fluid Mech., 20(3), 481-499. 178. Chaudhury, Z.H. (1964). Heat transfer in a radial liquid jet. J. Fluid Mech., 20(3), 501-511. 179. Cadek, F.F. (1968). A Fundamental Investigation of Jet Impingement Heat Transfer. Ph.D. Thesis, Mechanical Engineering, The University of Cincinnati, USA. 180. Obot, N.T. (1980). Flow and Heat Transfer for Impinging Round Turbulent Jets. Ph.D. Thesis, Chemical Engineering, McGill University, Canada. 181. Miyazaki, H. and Silberman, E. (1972). Flow and heat transfer on a flat plate normal to a two-dimensional laminar jet issuing from a nozzle of finite height. International Journal of Heat and Mass Transfer, 15(11), 2097-2107. 182. Stevens, J. and Webb, B.W. (1991). Local heat transfer coefficients under an axisymmetric, single-phase liquid jet. Journal of Heat Transfer, 113(1), 71-78. 183. Garimella, S.V. and Rice, R.A. (1995). Confined and submerged liquid jet impingement heat transfer. Journal of Heat Transfer, 117(4), 871-877. 184. Garimella, S.V. and Nenaydykh, B. (1996). Nozzle-geometry effects in liquid jet impingement heat transfer. International Journal of Heat and Mass Transfer, 39(14), 2915-2923. 185. Stevens, J., Pan, Y. and Webb, B.W. (1992). Effect of nozzle configuration on transport in the stagnation zone of axisymmetric, impinging free-surface liquid jets. Part 1. Turbulent flow structure. Journal of Heat Transfer, 114(4), 874-879. 186. Elison, B. and Webb, B.W. (1994). Local heat transfer to impinging liquid jets in the initially laminar, transitional, and turbulent regimes. International Journal of Heat and Mass Transfer, 37(8), 1207-1216.
199 REFERENCES
187. Gardon, R. and Akfirat, J.C. (1965). The role of turbulence in determining the heat-transfer characteristics of impinging jets. International Journal of Heat and Mass Transfer, 8(10), 1261-1272. 188. Zhao, Y., Masuoka, T., Tsuruta, T. and Ma, C.F. (2002). Conjugated heat transfer on a horizontal surface impinged by circular free-surface liquid jet. JSME International Journal, Series B: Fluids and Thermal Engineering, 45(2), 307-314. 189. Vader, D.T., Incropera, F.P. and Viskanta, R. (1991). A method for measuring steady local heat transfer to an impinging liquid jet. Experimental Thermal and Fluid Science, 4(1), 1-11. 190. Webb, B.W. and Ma, C.F. (1995). Single-phase liquid jet impingement heat transfer. Advances in Heat Transfer, 26, 105-217. 191. Tong, A.Y. (2003). A numerical study on the hydrodynamics and heat transfer of a circular liquid jet impinging onto a substrate. Numerical Heat Transfer; Part A: Applications, 44(1), 1-19. 192. Louahlia-Gualous, H. and Baonga, J.B. (2008). Experimental study of unsteady local heat transfer for impinging miniature jet. Heat Transfer Engineering, 29(9), 782-792. 193. Lee, D.H., Song, J. and Jo, M.C. (2004). The effects of nozzle diameter on impinging jet heat transfer and fluid flow. Journal of Heat Transfer, 126(4), 554-557. 194. Stevens, J. and Webb, B.W. (1991). The effect of inclination on local heat transfer under an axisymmetric, free liquid jet. International Journal of Heat and Mass Transfer, 34(4-5), 1227-1236. 195. Pan, Y., Stevens, J. and Webb, B.W. (1992). Effect of nozzle configuration on transport in the stagnation zone of axisymmetric, impinging free-surface liquid jets. Part 2. Local heat transfer. Journal of Heat Transfer, 114(4), 880-886. 196. Lee, D., Greif, R., Lee, S.J. and Lee, J.H. (1995). Heat transfer from a flat plate to a fully developed axisymmetric impinging jet. Journal of Heat Transfer, 117(3), 772-776. 197. Ramulu, M., Kunaporn, S., Arola, D., Hashish, M. and Hopkins, J. (2000). Waterjet machining and peening of metals. Journal of Pressure Vessel Technology, Transactions of the ASME, 122(1), 90-95.
200 REFERENCES
198. Arola, D., McCain, M.L., Kunaporn, S. and Ramulu, M. (2001). Waterjet and abrasive waterjet surface treatment of titanium: A comparison of surface texture and residual stress.Wear, 249(10-11), 943-950. 199. Kunaporn, S., Ramulu, M. and Hashish, M. (2005). Mathematical modeling of ultra-high-pressure waterjet peening. Journal of Engineering Materials and Technology, Transactions of the ASME, 127(2), 186-191. 200. Meng, P., Geskin, E.S., Leu, M.C., Li, F. and Tismeneskiy, L. (1998). An analytical and experimental study of cleaning with moving waterjets. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 120(3), 580-589. 201. Daoming, G. and Jie, C. (2006). ANFIS for high-pressure waterjet cleaning prediction. Surface and Coatings Technology, 201(3-4), 1629-1634. 202. Leu, M.C., Meng, P., Geskin, E.S. and Tismeneskiy, L. (1998). Mathematical modeling and experimental verification of stationary waterjet cleaning process. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 120(3), 571-579. 203. Bowden, F.P. and Brunton, J.H. (1958). Damage to solids by liquid impact at supersonic speeds. Nature, 181(4613), 873-875. 204. Taylor, T.A. (1995). Surface roughening of metallic substrates by high pressure pure waterjet. Surface and Coatings Technology, 76-77, 95-100. 205. Momber, A.W., Wong, Y.C., Budidharma, E. and Tjo, R. (2002). Surface profiling of low-carbon steel with supersonic waterjets.Wear, 249(10-11), 853- 859. 206. Adler, W.F. (1995). Waterdrop impact modeling.Wear, 186-187(2), 341-351. 207. Mabrouki, T., Raissi, K. and Cornier, A. (2000). Numerical simulation and experimental study of the interaction between a pure high-velocity waterjet and targets: Contribution to investigate the decoating process.Wear, 239(2), 260- 273. 208. Maniadaki, K., Kestis, T., Bilalis, N. and Antoniadis, A. (2007). A finite element-based model for pure waterjet process simulation. International Journal of Advanced Manufacturing Technology, 31(9-10), 933-940.
201 REFERENCES
209. Ma, L., Bao, R.H. and Guo, Y.M. (2008). Waterjet penetration simulation by hybrid code of SPH and FEA. International Journal of Impact Engineering, 35(9), 1035-1042. 210. Li, X., Si, H. and Xie, Y. (2011). Numerical Simulation of Rock Fracture Under High Pressure Water Jet. Key Engineering Materials, 462-463, 785-790. 211. Tate, A. (1967). A theory for the deceleration of long rods after impact. Journal of the Mechanics and Physics of Solids, 15(6), 387-399. 212. Tate, A. (1977). A possible explanation for the hydrodynamic transition in high speed impact. International Journal of Mechanical Sciences, 19(2), 121-123. 213. Tate, A. (1969). Further results in the theory of long rod penetration. Journal of the Mechanics and Physics of Solids, 17(3), 141-150. 214. Huang, Y.C., Hammitt, F.G. and Mitchell, T.M. (1973). Note on shock-wave velocity in high-speed liquid-solid impact. Journal of Applied Physics, 44(4), 1868-1869. 215. Field, J.E., Lesser, M.B. and Dear, J.P. (1985). Studies of two-dimensional liquid-wedge impact and their relevance to liquid-drop impact problems. Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences, 401(1821), 225-249. 216. Kennedy, C.F. and Field, J.E. (2000). Damage threshold velocities for liquid impact. Journal of Materials Science, 35(21), 5331-5339. 217. Rein, M. (1993). Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dynamics Research, 12(2), 61-93. 218. Çengel, Y.A. (2007). Heat and Mass Transfer: A Practical Approach. 3 ed. New York: McGraw-Hill. 219. Gilbert, T., Krstic, V.D. and Zak, G. (2007). Machining of aluminium nitride with ultra-violet and near-infrared Nd:YAG lasers. Journal of Materials Processing Technology, 189(1-3), 409-417. 220. Davis, T.A. and Cao, J. (2010). Effect of laser pulse overlap on machined depth. Transactions of the North American Manufacturing Research Institution of SME, 38, 291-298. 221. Sheng, P.S. and Joshi, V.S. (1995). Analysis of heat-affected zone formation for laser cutting of stainless steel. Journal of Materials Processing Tech., 53(3-4), 879-892.
202 REFERENCES
222. Cai, L. and Sheng, P. (1996). Analysis of laser evaporative and fusion cutting. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 118(2), 225-234. 223. Yang, G.W. (2007). Laser ablation in liquids: Applications in the synthesis of nanocrystals. Progress in Materials Science, 52(4), 648-698. 224. Vogel, A., Lauterborn, W. and Timm, R. (1989). Optical and acoustic investigations of the dynamics of laser-produced cavitation bubbles near a solid boundary. Journal of Fluid Mechanics, 206, 299-338. 225. Chalmers, B. (1964). Principles of Solidification. Wiley Series on the Science and Technology of Materials: John Wiley & Sons. 226. Davidson, S.M. (1970). Study of radiation damage in silicon with the scanning electron microscope. Nature, 227(5257), 487-488. 227. Thompson, M.O., Mayer, J.W., Cullis, A.G., Webber, H.C., Chew, N.G., Poate, J.M. and Jacobson, D.C. (1983). Silicon melt, regrowth, and amorphization velocities during pulsed laser irradiation. Physical Review Letters, 50(12), 896- 899. 228. Cullis, A.G., Chew, N.G., Webber, H.C. and Smith, D.J. (1984). Orientation dependence of high speed silicon crystal growth from the melt. Journal of Crystal Growth, 68(2), 624-638. 229. Yan, J., Asami, T. and Kuriyagawa, T. (2007). Response of machining-damaged single-crystalline silicon wafers to nanosecond pulsed laser irradiation. Semiconductor Science and Technology, 22(4), 392-395. 230. Yan, J., Asami, T., Harada, H. and Kuriyagawa, T. (2009). Fundamental investigation of subsurface damage in single crystalline silicon caused by diamond machining. Precision Engineering, 33(4), 378-386. 231. Kaczmarski, M., Bedoya-MartÃnez, O.N. and Hernández, E.R. (2005). Phase diagram of silicon from atomistic simulations. Physical Review Letters, 94(9), 1- 4. 232. Droz, C., Vallat-Sauvain, E., Bailat, J., Feitknecht, L., Meier, J. and Shah, A. (2004). Relationship between Raman crystallinity and open-circuit voltage in microcrystalline silicon solar cells. Solar Energy Materials and Solar Cells, 81(1), 61-71.
203 REFERENCES
233. Islam, M.N. and Kumar, S. (2001). Influence of crystallite size distribution on the micro-Raman analysis of porous Si. Applied Physics Letters, 78(6), 715-717. 234. Kobliska, R.J. and Solin, S.A. (1973). Raman spectrum of wurtzite silicon. Physical Review B, 8(8), 3799-3802. 235. Yan, J., Asami, T. and Kuriyagawa, T. (2008). Nondestructive measurement of machining-induced amorphous layers in single-crystal silicon by laser micro- Raman spectroscopy. Precision Engineering, 32(3), 186-195. 236. Tsu, R., Gonzalez-Hernandez, J., Chao, S.S., Lee, S.C. and Tanaka, K. (1982). Critical volume fraction of crystallinity for conductivity percolation in phosphorus-doped Si:F:H alloys. Applied Physics Letters, 40(6), 534-535. 237. Bustarret, E., Hachicha, M.A. and Brunel, M. (1988). Experimental determination of the nanocrystalline volume fraction in silicon thin films from Raman spectroscopy. Applied Physics Letters, 52(20), 1675-1677. 238. Brodsky, M.H., Cardona, M. and Cuomo, J.J. (1977). Infrared and Raman spectra of the silicon-hydrogen bonds in amorphous silicon prepared by glow discharge and sputtering. Physical Review B, 16(8), 3556-3571. 239. Houben, L., Luysberg, M., Hapke, P., Carius, R., Finger, F. and Wagner, H. (1998). Structural properties of microcrystalline silicon in the transition from highly crystalline to amorphous growth. Philosophical Magazine A: Physics of Condensed Matter, Structure, Defects and Mechanical Properties, 77(6), 1447- 1460. 240. Thompson, M.O., Galvin, G.J., Mayer, J.W., Peercy, P.S., Poate, J.M., Jacobson, D.C., Cullis, A.G. and Chew, N.G. (1984). Melting temperature and explosive crystallization of amorphous silicon during pulsed laser irradiation.Physical Review Letters, 52(26), 2360-2363. 241. Grigoropoulos, C.P., Park, H.K. and Xu, X. (1993). Modeling of pulsed laser irradiation of thin silicon layers. International Journal of Heat and Mass Transfer, 36(4), 919-924. 242. Yilbas, B.S. and Mansoor, S.B. (2009). Laser pulse heating and phase changes in the irradiated region: Temperature-dependent thermal properties case. International Journal of Thermal Sciences, 48(4), 761-772.
204 REFERENCES
243. Yilbas, B.S., Mansoor, S.B. and Mansoor, R. (2008). Laser pulse heating: Cavity formation into steel, nickel and tantalum surfaces. Optics and Laser Technology, 40(5), 723-734. 244. Miotello, A. and Kelly, R. (1995). Critical assessment of thermal models for laser sputtering at high fluences. Applied Physics Letters, 67, 3535. 245. Ki, H., Mohanty, P.S. and Mazumder, J. (2001). Modelling of high-density laser-material interaction using fast level set method. Journal of Physics D: Applied Physics, 34(3), 364-372. 246. Wang, X., Shen, Z.H., Lu, J. and Ni, X.W. (2010). Laser-induced damage threshold of silicon in millisecond, nanosecond, and picosecond regimes. Journal of Applied Physics, 108(3), 0331031-0331037. 247. Ohsaka, K., Chung, S.K., Rhim, W.K. and Holzer, J.C. (1997). Densities of Si determined by an image digitizing technique in combination with an electrostatic levitator. Applied Physics Letters, 70(4), 423-425. 248. Touloukian, Y.S. and Buyco, E.H. (1970). Thermophysical Properties of Matter. Vol. 2. New York: IFI/Plenum. 249. Touloukian, Y.S. and Makita, T. (1976). Thermophysical Properties of Matter. Vol. 6. New York: IFI/Plenum. 250. Lim, D.J., Ki, H. and Mazumder, J. (2006). Mass removal modes in the laser ablation of silicon by a Q-switched diode-pumped solid-state laser (DPSSL). Journal of Physics D: Applied Physics, 39(12), 2624-2635. 251. FLIR. (2008). ALTAIR User Manual (DL001U-M). 252. Hale, G.M. and Querry, M.R. (1973). Optical constants of water in the 200-nm to 200-ȝm wavelength region. Applied Optics, 12(3), 555-563. 253. Palmer, K.F. and Williams, D. (1974). Optical properties of water in the near infrared. J Opt Soc Am, 64(8), 1107-1110. 254. Liu, H. (2004). A study of the cutting performance in abrasive waterjet contouring of alumina ceramics and associated jet dynamic characteristics. Ph.D. Thesis, School of Mechanical, Manufacturing and Medical Engineering, Queensland University of Technology 255. Hibbeler, R.C. (2005). Mechanics of Materials. SI 2nd ed. Singapore: Prentice Hall.
205 REFERENCES
256. Wijaranakula, W. (1992). Morphology of oxide precipitates in Czochralski silicon degenerately doped with boron. Journal of Applied Physics, 72(9), 4026- 4030. 257. Ruoff, A.L. (1979). On the yield strength of diamond. Journal of Applied Physics, 50(5), 3354-3356. 258. Mathews, V.K. and Gross, T.S. (1987). Tensile properties of Czochralski grown silicon from 900-1200°C. Scripta Metallurgica, 20(12), 1677-1682. 259. Kang, K. and Cai, W. (2007). Brittle and ductile fracture of semiconductor nanowires - molecular dynamics simulations. Philosophical Magazine, 87(14- 15), 2169-2189. 260. Mathews, V.K. and Gross, T.S. (1987). High temperature (900 - 1300°C) mechanical behaviour of dendritic web grown silicon ribbons: - strain rate and temperature dependence of the yield stress. Scripta Metallurgica, 21(2), 117- 122.
206 Appendix A
Technical Data of Nanosecond Fiber Laser
A.1 Technical Specifications of MANLIGHT Fiber Laser
Table A.1. Laser machine specifications.
A-1 APPENDIX A
Figure A.1. Laser pulse shape in time domain (laser pulse frequency=20 kHz and average power=20 W).
Figure A.2. Average output power under different pump currents (laser pulse frequency=20 kHz).
A-2 APPENDIX A
A.2 Results of Laser Power/Energy Measurements
-5 Beam diameter (df) 1.72 x 10 m -6 2 Beam area (Al) 2.32 x 10 cm Pulse duration (IJ) 4.20 x 10-8 s
Pulse shape coefficient (kp) 0.914
Table A.2. Laser power/energy at pulse frequency of 20 kHz.
Pump current (A) 0 5 10 15 20 25 30
Pmax (W) 0.341 0.714 1.51 2.52 4.32 6.29 8.04
Pmin (W) 0.336 0.712 1.51 2.49 4.3 6.26 7.98
Pavg (W) 0.337 0.713 1.51 2.51 4.31 6.27 8.01 SD (mW) 1 0 1 7 4 10 12 RMS % 0.3227 0.0631 0.0874 0.2853 0.0908 0.1664 0.1508 PTP % 1.641 0.2185 0.2994 1.278 0.333 0.5754 0.6715 2 Iavg (W/cm ) 145207.2 307218.9 650631.8 1081514 1857101 2701630 3451365 E (J) 1.54E-05 3.26E-05 6.9E-05 0.000115 0.000197 0.000287 0.000366 E/A (J/cm2) 6.635971 14.0399 29.73388 49.42518 84.86954 123.4645 157.7274
Ppeak (W) 3.67E+02 7.76E+02 1.64E+03 2.73E+03 4.69E+03 6.82E+03 8.72E+03 2 Ipeak (W/cm ) 1.58E+08 3.34E+08 7.08E+08 1.18E+09 2.02E+09 2.94E+09 3.76E+09 Pump current (A) 35 40 45 50 55 60 62
Pmax (W) 10 11.9 13.7 15.5 16.8 18.1 18.5
Pmin (W) 10 11.8 13.7 15.4 16.8 18 18.4
Pavg (W) 10 11.8 13.7 15.5 16.8 18 18.4 SD (mW) 13 22 13 2 25 17 37 RMS % 0.1272 0.1849 0.096 0.0147 0.146 0.0956 0.2018 PTP % 0.4173 0.5961 0.4041 0.0719 0.3899 0.2744 0.6991 2 Iavg (W/cm ) 4308820 5084408 5903084 6678671 7238818 7755876 7928229 E (J) 0.000457 0.000539 0.000626 0.000708 0.000768 0.000823 0.000841 E/A (J/cm2) 196.9131 232.3574 269.7709 305.2153 330.814 354.4435 362.3201
Ppeak (W) 1.09E+04 1.28E+04 1.49E+04 1.69E+04 1.83E+04 1.96E+04 2.00E+04 2 Ipeak (W/cm ) 4.69E+09 5.53E+09 6.42E+09 7.27E+09 7.88E+09 8.44E+09 8.63E+09
A-3 APPENDIX A
Table A.3. Laser power/energy at pulse frequency of 30 kHz.
Pump current (A) 0 5 10 15 20 25 30
Pmax (W) 0.548 0.955 1.82 2.93 4.17 6.65 8.88
Pmin (W) 0.545 0.955 1.82 2.93 4.16 6.61 8.85
Pavg (W) 0.548 0.955 1.82 2.93 4.17 6.62 8.86 SD (mW) 1 0 0 0 1 11.2 10 RMS % 0.1363 0.0073 0.0157 0.011 0.0304 0.1693 0.3584 PTP % 0.5611 0 0 0 0.1411 0.6578 0.1136 2 Iavg (W/cm ) 236123.3 411492.3 784205.3 1262484 1796778 2852439 3817615 E (J) 1.67E-05 2.91E-05 5.54E-05 8.93E-05 0.000127 0.000202 0.00027 E/A (J/cm2) 7.193891 12.5368 23.89212 38.46369 54.74184 86.90431 116.31
Ppeak (W) 3.98E+02 6.93E+02 1.32E+03 2.13E+03 3.02E+03 4.80E+03 6.43E+03 2 Ipeak (W/cm ) 1.71E+08 2.98E+08 5.69E+08 9.16E+08 1.30E+09 2.07E+09 2.77E+09 Pump current (A) 35 40 45 50 55 60 62
Pmax (W) 10.9 12.8 15.1 16.8 18.4 19.8 20.3
Pmin (W) 10.8 12.8 15.1 16.8 18.4 19.8 20.2
Pavg (W) 10.9 12.8 15.1 16.8 18.4 19.8 20.3 SD (mW) 11 19 5 11 10 11 7 RMS % 0.1 0.1463 0.0342 0.0652 0.0525 0.0549 0.0349 PTP % 0.2977 0.4573 0.1185 0.2029 0.1618 0.1663 0.0512 2 Iavg (W/cm ) 4696614 5515290 6506318 7238818 7928229 8531464 8746905 E (J) 0.000332 0.00039 0.00046 0.000512 0.000561 0.000603 0.000618 E/A (J/cm2) 143.0902 168.0325 198.2258 220.5426 241.5467 259.9253 266.489
Ppeak (W) 7.91E+03 9.29E+03 1.10E+04 1.22E+04 1.33E+04 1.44E+04 1.47E+04 2 Ipeak (W/cm ) 3.41E+09 4.00E+09 4.72E+09 5.25E+09 5.75E+09 6.19E+09 6.34E+09
Table A.4. Laser power/energy at pulse frequency of 40 kHz.
Pump current (A) 0 5 10 15 20 25 30
Pmax (W) 0.154 0.425 1.14 2.18 3.83 5.77 8.08
Pmin (W) 0.153 0.424 1.12 2.17 3.79 5.7 8.03
Pavg (W) 0.153 0.424 1.13 2.17 3.7 5.74 8.06 SD (mW) 0 0 4 2.5 11.9 17 15.2 RMS % 0.1054 0.0363 0.3927 0.113 0.3138 0.2957 0.1885 PTP % 0.3598 0.1251 1.557 0.386 1.229 1.143 0.6595 2 Iavg (W/cm ) 65924.95 182694 486896.7 935014 1594263 2473263 3472909 E (J) 3.5E-06 9.69E-06 2.58E-05 4.96E-05 8.45E-05 0.000131 0.000184 E/A (J/cm2) 1.506385 4.174557 11.12559 21.36507 36.42892 56.51405 79.35597
Ppeak (W) 8.32E+01 2.31E+02 6.15E+02 1.18E+03 2.01E+03 3.12E+03 4.39E+03 2 Ipeak (W/cm ) 3.59E+07 9.94E+07 2.65E+08 5.09E+08 8.67E+08 1.35E+09 1.89E+09 Pump current (A) 35 40 45 50 55 60 62
Pmax (W) 9.99 12.1 14.5 16.4 18.1 19.7 20.2
Pmin (W) 9.92 12 14.5 16.4 18.1 19.6 20.2
Pavg (W) 9.96 12 14.5 16.4 18.1 19.7 20.2 SD (mW) 19 12 15 21 13 14 16 RMS % 0.1914 0.0979 0.1036 0.1275 0.0728 0.0694 0.0808 PTP % 0.694 0.3617 0.5414 0.4361 0.2308 0.2501 0.301 2 Iavg (W/cm ) 4291585 5170584 6247789 7066465 7798964 8488376 8703817 E (J) 0.000228 0.000274 0.000331 0.000375 0.000414 0.00045 0.000462 E/A (J/cm2) 98.06271 118.1478 142.762 161.4687 178.2063 193.9594 198.8822
Ppeak (W) 5.42E+03 6.53E+03 7.89E+03 8.92E+03 9.85E+03 1.07E+04 1.10E+04 2 Ipeak (W/cm ) 2.33E+09 2.81E+09 3.40E+09 3.84E+09 4.24E+09 4.62E+09 4.74E+09
A-4 APPENDIX A
Table A.5. Laser power/energy at pulse frequency of 50 kHz.
Pump current (A) 0 5 10 15 20 25 30
Pmax (W) 0.211 0.549 1.33 2.4 3.73 5.88 8.11
Pmin (W) 0.211 0.545 1.32 2.38 3.71 5.85 8.05
Pavg (W) 0.211 0.546 1.33 2.39 3.72 5.86 8.09 SD (mW) 0 0.6 1.6 5.4 4.3 11.9 16.2 RMS % 0.0466 0.1168 0.119 0.2279 0.1161 0.2037 0.2003 PTP % 0.1617 0.6121 0.4675 0.7257 0.4755 0.5524 0.7505 2 Iavg (W/cm ) 90916.1 235261.6 573073.1 1029808 1602881 2524969 3485835 E (J) 3.86E-06 9.98E-06 2.43E-05 4.37E-05 6.8E-05 0.000107 0.000148 E/A (J/cm2) 1.661946 4.300582 10.47578 18.82489 29.30067 46.15643 63.72107
Ppeak (W) 9.18E+01 2.38E+02 5.79E+02 1.04E+03 1.62E+03 2.55E+03 3.52E+03 2 Ipeak (W/cm ) 3.96E+07 1.02E+08 2.49E+08 4.48E+08 6.98E+08 1.10E+09 1.52E+09 Pump current (A) 35 40 45 50 55 60 62
Pmax (W) 10.4 12.4 14.9 16.8 18.5 20.1 20.7
Pmin (W) 10.3 12.4 14.9 16.7 18.4 20 20.7
Pavg (W) 10.3 12.4 14.9 16.7 18.5 20 20.7 SD (mW) 9 13 0 19 26 23 12 RMS % 0.0849 0.1012 0.0027 0.1149 0.1416 0.1142 0.0577 PTP % 0.2602 0.3382 0.009 0.4534 0.5647 0.4505 0.2045 2 Iavg (W/cm ) 4438085 5342937 6420142 7195730 7971317 8617640 8919258 E (J) 0.000188 0.000227 0.000272 0.000305 0.000338 0.000366 0.000378 E/A (J/cm2) 81.12819 97.66889 117.3602 131.5379 145.7157 157.5305 163.044
Ppeak (W) 4.48E+03 5.40E+03 6.49E+03 7.27E+03 8.05E+03 8.70E+03 9.01E+03 2 Ipeak (W/cm ) 1.93E+09 2.33E+09 2.79E+09 3.13E+09 3.47E+09 3.75E+09 3.88E+09
Table A.6. Laser power/energy at pulse frequency of 60 kHz.
Pump current (A) 0 5 10 15 20 25 30
Pmax (W) 0.315 0.693 1.52 2.63 4 6.38 8.57
Pmin (W) 0.311 0.688 1.51 2.62 3.99 6.31 8.54
Pavg (W) 0.314 0.691 1.52 2.63 4 6.34 8.56 SD (mW) 1 1.3 2.5 4 4.4 17.4 9.7 RMS % 0.1717 0.1824 0.1668 0.1524 0.109 0.2752 0.1133 PTP % 1.361 0.6069 0.5481 0.4197 0.4243 1.036 0.3717 2 Iavg (W/cm ) 135297 297739.5 654940.7 1133220 1723528 2731792 3688350 E (J) 4.78E-06 1.05E-05 2.32E-05 4.01E-05 6.09E-05 9.66E-05 0.00013 E/A (J/cm2) 2.061024 4.535565 9.976929 17.26271 26.25508 41.6143 56.18587
Ppeak (W) 1.14E+02 2.51E+02 5.51E+02 9.54E+02 1.45E+03 2.30E+03 3.10E+03 2 Ipeak (W/cm ) 4.91E+07 1.08E+08 2.38E+08 4.11E+08 6.25E+08 9.91E+08 1.34E+09 Pump current (A) 35 40 45 50 55 60 62
Pmax (W) 10.6 12.7 15 16.9 18.7 20.4 21
Pmin (W) 10.6 12.7 15 16.8 18.6 20.4 21
Pavg (W) 10.6 12.7 15 16.8 18.6 20.4 21 SD (mW) 4 15 13 18 19 11 19 RMS % 0.0419 0.1217 0.0892 0.1045 0.1015 0.0523 0.0896 PTP % 0.2501 0.5356 0.3418 0.4985 0.45 0.1897 0.3721 2 Iavg (W/cm ) 4567349 5472202 6463230 7238818 8014405 8789993 9048522 E (J) 0.000161 0.000193 0.000229 0.000256 0.000283 0.000311 0.00032 E/A (J/cm2) 69.57595 83.35987 98.45654 110.2713 122.0861 133.9009 137.8392
Ppeak (W) 3.84E+03 4.61E+03 5.44E+03 6.09E+03 6.75E+03 7.40E+03 7.62E+03 2 Ipeak (W/cm ) 1.66E+09 1.98E+09 2.34E+09 2.63E+09 2.91E+09 3.19E+09 3.28E+09
A-5 APPENDIX A
Table A.7. Laser power/energy at pulse frequency of 70 kHz.
Pump current (A) 0 5 10 15 20 25 30
Pmax (W) 0.394 0.776 1.61 2.64 4 6.43 8.64
Pmin (W) 0.382 0.774 1.61 2.62 3.98 6.38 8.58
Pavg (W) 0.388 0.775 1.61 2.63 3.98 6.4 8.6 SD (mW) 3 0.7 1.9 5 6.8 15.3 15 RMS % 0.7641 0.088 0.1172 0.1895 0.1714 0.2394 0.1744 PTP % 3.165 0.3726 0.4649 0.6188 0.5206 0.7798 0.7281 2 Iavg (W/cm ) 167182.2 333933.6 693720 1133220 1714910 2757645 3705585 E (J) 5.07E-06 1.01E-05 2.1E-05 3.43E-05 5.2E-05 8.36E-05 0.000112 E/A (J/cm2) 2.182922 4.360218 9.058002 14.79661 22.39183 36.00696 48.38436
Ppeak (W) 1.21E+02 2.41E+02 5.01E+02 8.18E+02 1.24E+03 1.99E+03 2.67E+03 2 Ipeak (W/cm ) 5.20E+07 1.04E+08 2.16E+08 3.52E+08 5.33E+08 8.57E+08 1.15E+09 Pump current (A) 35 40 45 50 55 60 62
Pmax (W) 10.7 12.8 15.2 17.2 18.9 20.5 21.2
Pmin (W) 10.7 12.8 15.2 17.1 18.8 20.5 21.1
Pavg (W) 10.7 12.8 15.2 17.1 18.8 20.5 21.1 SD (mW) 16 10 12 8 16 13 15 RMS % 0.1453 0.0802 0.0761 0.0458 0.0866 0.0655 0.0719 PTP % 0.5201 0.2999 0.2481 0.1557 0.3859 0.213 0.2615 2 Iavg (W/cm ) 4610438 5515290 6549407 7368082 8100582 8833081 9091610 E (J) 0.00014 0.000167 0.000198 0.000223 0.000245 0.000268 0.000276 E/A (J/cm2) 60.19914 72.01393 85.51654 96.2061 105.7705 115.3348 118.7105
Ppeak (W) 3.33E+03 3.98E+03 4.73E+03 5.32E+03 5.84E+03 6.37E+03 6.56E+03 2 Ipeak (W/cm ) 1.43E+09 1.71E+09 2.04E+09 2.29E+09 2.52E+09 2.75E+09 2.83E+09
Table A.8. Laser power/energy at pulse frequency of 80 kHz.
Pump current (A) 0 5 10 15 20 25 30
Pmax (W) 0.468 0.893 1.76 2.89 4.39 6.64 8.79
Pmin (W) 0.459 0.889 1.76 2.87 4.35 6.58 8.78
Pavg (W) 0.463 0.891 1.76 2.88 4.37 6.61 8.79 SD (mW) 3.15 0.9 2.9 6.5 11.1 16.1 2 RMS % 0.6793 0.1065 0.1647 0.2264 0.2534 0.2443 0.0202 PTP % 1.954 0.3823 0.511 0.7326 0.9399 0.8881 0.0905 2 Iavg (W/cm ) 199498.4 383915.9 758352.3 1240940 1882954 2848130 3787453 E (J) 5.29E-06 1.02E-05 2.01E-05 3.29E-05 4.99E-05 7.55E-05 0.0001 E/A (J/cm2) 2.279269 4.386239 8.664176 14.17774 21.51275 32.53989 43.27165
Ppeak (W) 1.26E+02 2.42E+02 4.79E+02 7.83E+02 1.19E+03 1.80E+03 2.39E+03 2 Ipeak (W/cm ) 5.43E+07 1.04E+08 2.06E+08 3.38E+08 5.12E+08 7.75E+08 1.03E+09 Pump current (A) 35 40 45 50 55 60 62
Pmax (W) 10.9 13 15.3 17.3 19.1 20.8 21.4
Pmin (W) 10.8 12.9 15.3 17.2 19.1 20.7 21.3
Pavg (W) 10.9 13 15.3 17.2 19.1 20.7 21.3 SD (mW) 17 19 14 8 11 9 13 RMS % 0.1556 0.1432 0.0923 0.0476 0.0593 0.0433 0.0622 PTP % 0.5304 0.558 0.3004 0.137 0.2445 0.1365 0.2122 2 Iavg (W/cm ) 4696614 5601466 6592495 7411171 8229846 8919258 9177787 E (J) 0.000125 0.000149 0.000175 0.000197 0.000218 0.000236 0.000243 E/A (J/cm2) 53.65881 63.99675 75.31925 84.67262 94.026 101.9025 104.8562
Ppeak (W) 2.97E+03 3.54E+03 4.16E+03 4.68E+03 5.20E+03 5.63E+03 5.79E+03 2 Ipeak (W/cm ) 1.28E+09 1.52E+09 1.79E+09 2.02E+09 2.24E+09 2.43E+09 2.50E+09
A-6 APPENDIX A
Table A.9. Laser power/energy at pulse frequency of 90 kHz.
Pump current (A) 0 5 10 15 20 25 30
Pmax (W) 0.545 0.996 1.91 3.12 4.68 6.85 9.01
Pmin (W) 0.541 0.991 1.9 3.09 4.64 6.83 8.95
Pavg (W) 0.543 0.994 1.91 3.1 4.66 6.84 8.97 SD (mW) 1.04 1.5 3.1 7.9 10.1 5.5 18 RMS % 0.1906 0.1532 0.1636 0.2564 0.2164 0.0798 0.2043 PTP % 0.6855 0.5565 0.6675 0.8928 0.8792 0.319 0.7187 2 Iavg (W/cm ) 233968.9 428296.7 822984.6 1335734 2007910 2947233 3865012 E (J) 5.51E-06 1.01E-05 1.94E-05 3.15E-05 4.73E-05 6.95E-05 9.11E-05 E/A (J/cm2) 2.376084 4.349591 8.357866 13.56512 20.39144 29.93079 39.25134
Ppeak (W) 1.31E+02 2.40E+02 4.62E+02 7.50E+02 1.13E+03 1.65E+03 2.17E+03 2 Ipeak (W/cm ) 5.66E+07 1.04E+08 1.99E+08 3.23E+08 4.86E+08 7.13E+08 9.35E+08 Pump current (A) 35 40 45 50 55 60 62
Pmax (W) 11.1 13.2 15.5 17.4 19.3 20.9 21.5
Pmin (W) 11.1 13.2 15.4 17.4 19.2 20.8 21.5
Pavg (W) 11.1 13.2 15.4 17.4 19.2 20.8 21.5 SD (mW) 17 20 9 16 18 11 10 RMS % 0.1506 0.1499 0.0559 0.0895 0.0935 0.0549 0.0457 PTP % 0.5631 0.5078 0.2361 0.349 0.4109 0.1846 0.1329 2 Iavg (W/cm ) 4782790 5687643 6635583 7497347 8272935 8962346 9263963 E (J) 0.000113 0.000134 0.000156 0.000177 0.000195 0.000211 0.000218 E/A (J/cm2) 48.57189 57.76117 67.38803 76.13972 84.01625 91.0176 94.08069
Ppeak (W) 2.68E+03 3.19E+03 3.72E+03 4.21E+03 4.64E+03 5.03E+03 5.20E+03 2 Ipeak (W/cm ) 1.16E+09 1.38E+09 1.60E+09 1.81E+09 2.00E+09 2.17E+09 2.24E+09
Table A.10. Laser power/energy at pulse frequency of 100 kHz.
Pump current (A) 0 5 10 15 20 25 30
Pmax (W) 0.722 1.17 2.06 3.17 4.54 6.59 9.22
Pmin (W) 0.716 1.16 2.06 3.14 4.51 6.54 9.16
Pavg (W) 0.719 1.16 2.06 3.15 4.52 6.57 9.19 SD (mW) 1.54 1.3 1.1 8.8 7.8 13.2 18.6 RMS % 0.2143 0.1134 0.0549 0.2778 0.1716 0.201 0.2021 PTP % 0.9034 0.3908 0.208 1.095 0.6006 0.7096 0.6601 2 Iavg (W/cm ) 309804.2 499823.1 887616.9 1357278 1947587 2830895 3959806 E (J) 6.57E-06 1.06E-05 1.88E-05 2.88E-05 4.13E-05 6E-05 8.4E-05 E/A (J/cm2) 2.83161 4.568383 8.112819 12.40552 17.80094 25.87438 36.19262
Ppeak (W) 1.56E+02 2.52E+02 4.48E+02 6.86E+02 9.84E+02 1.43E+03 2.00E+03 2 Ipeak (W/cm ) 6.74E+07 1.09E+08 1.93E+08 2.95E+08 4.24E+08 6.16E+08 8.62E+08 Pump current (A) 35 40 45 50 55 60 62
Pmax (W) 11.3 13.4 15.6 17.7 19.5 21.1 21.7
Pmin (W) 11.3 13.4 15.5 17.6 19.4 21.1 21.6
Pavg (W) 11.3 13.4 15.6 17.6 19.5 21.1 21.7 SD (mW) 6 15 11 15 14 13 11 RMS % 0.0533 0.115 0.0723 0.0855 0.0701 0.0628 0.0522 PTP % 0.2829 0.434 0.3554 0.2972 0.2843 0.203 0.1877 2 Iavg (W/cm ) 4868967 5773819 6721759 7583523 8402199 9091610 9350140 E (J) 0.000103 0.000122 0.000143 0.000161 0.000178 0.000193 0.000198 E/A (J/cm2) 44.50236 52.77271 61.43688 69.3134 76.7961 83.09732 85.46028
Ppeak (W) 2.46E+03 2.92E+03 3.39E+03 3.83E+03 4.24E+03 4.59E+03 4.72E+03 2 Ipeak (W/cm ) 1.06E+09 1.26E+09 1.46E+09 1.65E+09 1.83E+09 1.98E+09 2.03E+09
A-7 APPENDIX A
A.3 Regression Models for Calculating Pump Current
6 5 4 Pump current20 kHz (A) = -2.9765E+21 Ep + 8.87485E+18 Ep - 1.02484E+16 Ep + 3 2 5.82345E+12 Ep - 1697326724 Ep + 295284.9566 Ep – 3.725160003
6 5 4 Pump current30 kHz (A) = -1.17812E+22 Ep + 2.73735E+19 Ep - 2.49991E+16 Ep + 3 2 1.14995E+13 Ep - 2789499123 Ep + 411062.4945 Ep – 5.684192091
6 5 4 Pump current40 kHz (A) = -1.39515E+23 Ep + 2.18864E+20 Ep - 1.33173E+17 Ep + 3 2 3.98001E+13 Ep - 6082893496 Ep + 548800.8225 Ep – 0.913856123
6 5 4 Pump current50 kHz (A) = -3.75831E+23 Ep + 4.79993E+20 Ep - 2.39736E+17 Ep + 3 2 5.97999E+13 Ep - 7846613710 Ep + 638837.4066 Ep – 1.646506922
6 5 4 Pump current60 kHz (A) = -8.97936E+23 Ep + 9.91947E+20 Ep - 4.31849E+17 Ep + 3 2 9.44093E+13 Ep - 10835516169 Ep + 764480.8615 Ep – 2.837502994
6 5 4 Pump current70 kHz (A) = -2.38816E+24 Ep + 2.27955E+21 Ep - 8.54961E+17 Ep + 3 2 1.60669E+14 Ep - 15854484699 Ep + 947940.8453 Ep – 3.950800796
6 5 4 Pump current80 kHz (A) = -3.95631E+24 Ep + 3.4458E+21 Ep - 1.17907E+18 Ep + 3 2 2.02263E+14 Ep - 18249404370 Ep + 1019788.422 Ep – 4.443610617
6 5 4 Pump current90 kHz (A) = -8.44849E+24 Ep + 6.4223E+21 Ep - 1.9197E+18 Ep + 3 2 2.88153E+14 Ep - 22849358321 Ep + 1137989.843 Ep – 5.173344552
A-8 APPENDIX A
6 5 4 Pump current100 kHz (A) = -5.93112E+24 Ep + 4.99014E+21 Ep - 1.6422E+18 Ep + 3 2 2.71983E+14 Ep - 23731631812 Ep + 1266102.582 Ep – 6.877168449
70
60
50
Frequency (kHz) 40 20 30 30 40 50 Pump current (A) 20 60 70 80 10 90 100 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Beam energy (mJ)
Figure A.3. Plots of pump current versus laser pulse energy under different pulse frequencies.
A-9 Appendix B
Experimental Results of Hybrid Laser- Waterjet Machining of Silicon
B.1 Experimental Data of the First Set of Experiments
Focal Waterjet Laser plane offset pulse Pulse Groove Groove position distance energy overlap width depth HAZ width (mm) (mm) (mJ) (%) (ȝm) (ȝm) (ȝm) -0.6 0 0.3 99.3 0 0 0 -0.6 0 0.3 99.5 0 0 0 -0.6 0 0.3 99.7 0 0 0 -0.6 0 0.3 99.9 0 0 0 -0.6 0 0.4 99.3 0 0 0 -0.6 0 0.4 99.5 0 0 0 -0.6 0 0.4 99.7 0 0 0 -0.6 0 0.4 99.9 0 0 125.069 -0.6 0 0.5 99.3 0 0 0 -0.6 0 0.5 99.5 0 0 0 -0.6 0 0.5 99.7 0 0 103.369 -0.6 0 0.5 99.9 0 0 139.566 -0.6 0 0.6 99.3 0 0 0 -0.6 0 0.6 99.5 0 0 109.167 -0.6 0 0.6 99.7 0 0 118.53 -0.6 0 0.6 99.9 0 0 144.436 -0.6 0.2 0.3 99.3 0 0 83.282 -0.6 0.2 0.3 99.5 0 0 96.508 -0.6 0.2 0.3 99.7 0 0 102.074 -0.6 0.2 0.3 99.9 0 0 124.76 -0.6 0.2 0.4 99.3 0 0 99.158 -0.6 0.2 0.4 99.5 0 0 109.302 -0.6 0.2 0.4 99.7 0 0 116.528 -0.6 0.2 0.4 99.9 0 0 138.064 -0.6 0.2 0.5 99.3 0 0 97.643 -0.6 0.2 0.5 99.5 0 0 115.466 -0.6 0.2 0.5 99.7 0 0 127.495 -0.6 0.2 0.5 99.9 0 0 142.387 -0.6 0.2 0.6 99.3 0 0 108.405 -0.6 0.2 0.6 99.5 0 0 120.302 -0.6 0.2 0.6 99.7 0 0 127.811 -0.6 0.2 0.6 99.9 0 0 147.283
B-1 APPENDIX B
Focal Waterjet Laser plane offset pulse Pulse Groove Groove position distance energy overlap width depth HAZ width (mm) (mm) (mJ) (%) (ȝm) (ȝm) (ȝm) -0.6 0.4 0.3 99.3 0 0 38.006 -0.6 0.4 0.3 99.5 0 0 42.069 -0.6 0.4 0.3 99.7 0 0 50.695 -0.6 0.4 0.3 99.9 0 0 53.426 -0.6 0.4 0.4 99.3 0 0 49.12 -0.6 0.4 0.4 99.5 0 0 50.173 -0.6 0.4 0.4 99.7 0 0 52.193 -0.6 0.4 0.4 99.9 110.47 31.649 54.893 -0.6 0.4 0.5 99.3 87.417 12.474 49.619 -0.6 0.4 0.5 99.5 95.743 19.117 50.002 -0.6 0.4 0.5 99.7 108.56 43.238 51.98 -0.6 0.4 0.5 99.9 137.517 48.726 55.432 -0.6 0.4 0.6 99.3 96.113 35.237 49.676 -0.6 0.4 0.6 99.5 102.08 38.412 52.521 -0.6 0.4 0.6 99.7 113.57 48.859 54.127 -0.6 0.4 0.6 99.9 141.257 62.598 58.035 -0.6 0.6 0.3 99.3 59.253 16.83 20.014 -0.6 0.6 0.3 99.5 66.133 19.057 22.739 -0.6 0.6 0.3 99.7 74.9 32.405 22.016 -0.6 0.6 0.3 99.9 80.55 75.687 25.068 -0.6 0.6 0.4 99.3 69.46 24.045 20.955 -0.6 0.6 0.4 99.5 79.56 31.311 22.127 -0.6 0.6 0.4 99.7 84.023 53.352 24.797 -0.6 0.6 0.4 99.9 87.743 81.333 25.228 -0.6 0.6 0.5 99.3 70.22 33.878 22.234 -0.6 0.6 0.5 99.5 78.19 55.242 23.623 -0.6 0.6 0.5 99.7 88.023 82.595 25.205 -0.6 0.6 0.5 99.9 96.12 116.833 25.466 -0.6 0.6 0.6 99.3 82.547 57.025 21.72 -0.6 0.6 0.6 99.5 88.627 65.584 24.415 -0.6 0.6 0.6 99.7 97.153 79.747 24.961 -0.6 0.6 0.6 99.9 100.21 124.924 26.697 -0.4 0 0.3 99.3 0 0 0 -0.4 0 0.3 99.5 0 0 0 -0.4 0 0.3 99.7 0 0 0 -0.4 0 0.3 99.9 0 0 0 -0.4 0 0.4 99.3 0 0 0 -0.4 0 0.4 99.5 0 0 0 -0.4 0 0.4 99.7 0 0 0 -0.4 0 0.4 99.9 0 0 116.019 -0.4 0 0.5 99.3 0 0 0 -0.4 0 0.5 99.5 0 0 0 -0.4 0 0.5 99.7 0 0 98.481 -0.4 0 0.5 99.9 0 0 126.138 -0.4 0 0.6 99.3 0 0 0 -0.4 0 0.6 99.5 0 0 101.467 -0.4 0 0.6 99.7 0 0 114.149 -0.4 0 0.6 99.9 0 0 129.471 -0.4 0.2 0.3 99.3 0 0 81.815 -0.4 0.2 0.3 99.5 0 0 87.826 -0.4 0.2 0.3 99.7 0 0 94.892 -0.4 0.2 0.3 99.9 0 0 103.028 -0.4 0.2 0.4 99.3 0 0 84.959 -0.4 0.2 0.4 99.5 0 0 88.349 -0.4 0.2 0.4 99.7 0 0 97.773 -0.4 0.2 0.4 99.9 101.78 6.116 33.793 -0.4 0.2 0.5 99.3 0 0 103.555 -0.4 0.2 0.5 99.5 0 0 115.853 -0.4 0.2 0.5 99.7 0 0 120.394 -0.4 0.2 0.5 99.9 114.107 14.505 39.212 -0.4 0.2 0.6 99.3 0 0 114.246
B-2 APPENDIX B
Focal Waterjet Laser plane offset pulse Pulse Groove Groove position distance energy overlap width depth HAZ width (mm) (mm) (mJ) (%) (ȝm) (ȝm) (ȝm) -0.4 0.2 0.6 99.5 0 0 121.558 -0.4 0.2 0.6 99.7 111.587 8.906 39.916 -0.4 0.2 0.6 99.9 157.373 29.845 46.97 -0.4 0.4 0.3 99.3 69.843 27.202 24.97 -0.4 0.4 0.3 99.5 79.94 33.845 27.581 -0.4 0.4 0.3 99.7 98.713 44.92 31.756 -0.4 0.4 0.3 99.9 109.533 50.261 36.858 -0.4 0.4 0.4 99.3 82.78 33.222 32.954 -0.4 0.4 0.4 99.5 92.927 36.849 36.486 -0.4 0.4 0.4 99.7 110.78 43.938 39.348 -0.4 0.4 0.4 99.9 136.557 57.51 41.497 -0.4 0.4 0.5 99.3 91.397 35.714 34.655 -0.4 0.4 0.5 99.5 98.117 38.365 36.996 -0.4 0.4 0.5 99.7 115.443 44.412 42.76 -0.4 0.4 0.5 99.9 143.337 66.421 46.715 -0.4 0.4 0.6 99.3 108.19 44.021 36.524 -0.4 0.4 0.6 99.5 117.37 49.841 41.304 -0.4 0.4 0.6 99.7 126.41 54.49 45.177 -0.4 0.4 0.6 99.9 149.31 72.302 47.701 -0.4 0.6 0.3 99.3 72.967 49.093 15.78 -0.4 0.6 0.3 99.5 77.927 53.906 17.405 -0.4 0.6 0.3 99.7 83.657 63.115 18.742 -0.4 0.6 0.3 99.9 96.11 94.42 19.757 -0.4 0.6 0.4 99.3 77.337 51.825 16.57 -0.4 0.6 0.4 99.5 88.67 68.714 16.703 -0.4 0.6 0.4 99.7 96.54 79.741 17.447 -0.4 0.6 0.4 99.9 102.58 108.339 17.828 -0.4 0.6 0.5 99.3 79.893 72.468 15.412 -0.4 0.6 0.5 99.5 93.843 78.097 18.88 -0.4 0.6 0.5 99.7 100.327 100.194 19.524 -0.4 0.6 0.5 99.9 106.733 117.567 20.71 -0.4 0.6 0.6 99.3 86.85 69.695 18.189 -0.4 0.6 0.6 99.5 97.083 72.589 19.574 -0.4 0.6 0.6 99.7 100.273 97.806 18.251 -0.4 0.6 0.6 99.9 108.92 135.244 19.606 -0.2 0 0.3 99.3 0 0 97.766 -0.2 0 0.3 99.5 0 0 105.932 -0.2 0 0.3 99.7 0 0 110.82 -0.2 0 0.3 99.9 0 0 123.561 -0.2 0 0.4 99.3 0 0 101.343 -0.2 0 0.4 99.5 0 0 106.737 -0.2 0 0.4 99.7 0 0 116.575 -0.2 0 0.4 99.9 0 0 141.419 -0.2 0 0.5 99.3 0 0 115.241 -0.2 0 0.5 99.5 0 0 116.692 -0.2 0 0.5 99.7 0 0 129.101 -0.2 0 0.5 99.9 197.197 33.063 25.4 -0.2 0 0.6 99.3 0 0 115.987 -0.2 0 0.6 99.5 0 0 140.246 -0.2 0 0.6 99.7 190.033 18.078 32.626 -0.2 0 0.6 99.9 238.59 41.584 34.543 -0.2 0.2 0.3 99.3 0 0 105.614 -0.2 0.2 0.3 99.5 0 0 118.78 -0.2 0.2 0.3 99.7 109.627 36.579 30.963 -0.2 0.2 0.3 99.9 157.087 78.273 31.644 -0.2 0.2 0.4 99.3 0 0 103.818 -0.2 0.2 0.4 99.5 0 0 118.571 -0.2 0.2 0.4 99.7 152.637 47.933 30.861 -0.2 0.2 0.4 99.9 186.55 86.175 31.863 -0.2 0.2 0.5 99.3 0 0 114.123 -0.2 0.2 0.5 99.5 0 0 119.542 -0.2 0.2 0.5 99.7 179.313 55.443 27.137
B-3 APPENDIX B
Focal Waterjet Laser plane offset pulse Pulse Groove Groove position distance energy overlap width depth HAZ width (mm) (mm) (mJ) (%) (ȝm) (ȝm) (ȝm) -0.2 0.2 0.5 99.9 197.81 96.537 31.368 -0.2 0.2 0.6 99.3 0 0 129.632 -0.2 0.2 0.6 99.5 0 0 131.922 -0.2 0.2 0.6 99.7 183.587 66.84 25.397 -0.2 0.2 0.6 99.9 228.36 104.654 26.512 -0.2 0.4 0.3 99.3 89.113 67.156 19.008 -0.2 0.4 0.3 99.5 99.127 75.121 20.351 -0.2 0.4 0.3 99.7 101.42 94.694 22.565 -0.2 0.4 0.3 99.9 124.353 106.336 24.966 -0.2 0.4 0.4 99.3 100.327 82.839 21.13 -0.2 0.4 0.4 99.5 110.473 89.097 22.357 -0.2 0.4 0.4 99.7 114.12 99.087 23.265 -0.2 0.4 0.4 99.9 145.14 134.705 22.921 -0.2 0.4 0.5 99.3 100.123 94.702 21.722 -0.2 0.4 0.5 99.5 112.76 100.577 25.606 -0.2 0.4 0.5 99.7 123.153 119.988 24.818 -0.2 0.4 0.5 99.9 147.3 154.615 27.068 -0.2 0.4 0.6 99.3 113.58 103.261 23.906 -0.2 0.4 0.6 99.5 119.95 114.697 24.287 -0.2 0.4 0.6 99.7 128.36 134.506 24.211 -0.2 0.4 0.6 99.9 153.597 174.061 25.664 -0.2 0.6 0.3 99.3 75.593 54.044 16.686 -0.2 0.6 0.3 99.5 81.203 70.37 17.274 -0.2 0.6 0.3 99.7 87.59 86.99 17.781 -0.2 0.6 0.3 99.9 100.743 102.387 20.037 -0.2 0.6 0.4 99.3 78.867 79.027 17.072 -0.2 0.6 0.4 99.5 87.913 80.596 18.024 -0.2 0.6 0.4 99.7 96.327 93.144 19.795 -0.2 0.6 0.4 99.9 105.1 114.165 18.853 -0.2 0.6 0.5 99.3 84.07 78.69 17.012 -0.2 0.6 0.5 99.5 93.977 86.668 19.312 -0.2 0.6 0.5 99.7 102.147 95.093 18.426 -0.2 0.6 0.5 99.9 107.687 116.711 21.095 -0.2 0.6 0.6 99.3 84.6 68.939 17.15 -0.2 0.6 0.6 99.5 94.137 79.314 18.997 -0.2 0.6 0.6 99.7 103.65 90.585 19.63 -0.2 0.6 0.6 99.9 109.987 131.133 19.143 0 0 0.3 99.3 99.243 18.825 32.799 0 0 0.3 99.5 108.663 23.784 33.86 0 0 0.3 99.7 118.803 28.501 36.09 0 0 0.3 99.9 149.23 76.616 39.732 0 0 0.4 99.3 113.033 25.719 33.522 0 0 0.4 99.5 127.493 39.233 35.681 0 0 0.4 99.7 145.41 76.963 38.217 0 0 0.4 99.9 182.28 106.438 40.93 0 0 0.5 99.3 151.877 40.841 35.635 0 0 0.5 99.5 162.06 69.006 36.907 0 0 0.5 99.7 174.833 80.334 38.35 0 0 0.5 99.9 203.593 132.52 42.462 0 0 0.6 99.3 158.52 56.59 35.772 0 0 0.6 99.5 170.477 82.715 37.514 0 0 0.6 99.7 186.567 89.084 38.671 0 0 0.6 99.9 214.87 137.17 43.957 0 0.2 0.3 99.3 90.907 65.309 30.11 0 0.2 0.3 99.5 96.963 77.235 30.79 0 0.2 0.3 99.7 113.487 101.853 32.139 0 0.2 0.3 99.9 141.963 133.978 35.202 0 0.2 0.4 99.3 117.84 78.901 31.482 0 0.2 0.4 99.5 124.48 100.022 33.112 0 0.2 0.4 99.7 142.477 131.559 35.71 0 0.2 0.4 99.9 176.577 153.301 37.221 0 0.2 0.5 99.3 149.953 87.374 32.562
B-4 APPENDIX B
Focal Waterjet Laser plane offset pulse Pulse Groove Groove position distance energy overlap width depth HAZ width (mm) (mm) (mJ) (%) (ȝm) (ȝm) (ȝm) 0 0.2 0.5 99.5 153.143 97.444 34.603 0 0.2 0.5 99.7 168.683 122.865 36.947 0 0.2 0.5 99.9 193.43 158.448 38.503 0 0.2 0.6 99.3 152.953 91.422 33.304 0 0.2 0.6 99.5 155.287 110.841 34.403 0 0.2 0.6 99.7 167.34 129.96 37.114 0 0.2 0.6 99.9 201.997 173.531 40.363 0 0.4 0.3 99.3 71.737 81.69 17.917 0 0.4 0.3 99.5 79.337 86.554 19.78 0 0.4 0.3 99.7 94.177 111.996 19.817 0 0.4 0.3 99.9 103.443 139.303 21.396 0 0.4 0.4 99.3 82.107 88.272 19.096 0 0.4 0.4 99.5 95.167 99.228 20.573 0 0.4 0.4 99.7 102.727 115.43 20.705 0 0.4 0.4 99.9 114.96 154.976 21.639 0 0.4 0.5 99.3 90.19 115.957 19.078 0 0.4 0.5 99.5 103.513 127.456 19.782 0 0.4 0.5 99.7 111.797 150.627 21.502 0 0.4 0.5 99.9 119.653 174.143 23.198 0 0.4 0.6 99.3 99.357 141.941 18.787 0 0.4 0.6 99.5 107.623 158.293 20.607 0 0.4 0.6 99.7 111.317 174.696 21.972 0 0.4 0.6 99.9 122.473 191.439 22.422 0 0.6 0.3 99.3 68.7 69.697 15.86 0 0.6 0.3 99.5 76.893 84.158 16.793 0 0.6 0.3 99.7 84.283 95.586 17.574 0 0.6 0.3 99.9 97.45 106.616 18.475 0 0.6 0.4 99.3 73.67 85.766 15.972 0 0.6 0.4 99.5 80.35 101.203 17.085 0 0.6 0.4 99.7 94.923 111.734 18.595 0 0.6 0.4 99.9 105.357 119.48 19.701 0 0.6 0.5 99.3 80.713 90.969 17.017 0 0.6 0.5 99.5 86.753 101.976 17.95 0 0.6 0.5 99.7 98.217 115.84 18.044 0 0.6 0.5 99.9 106.543 124.786 19.168 0 0.6 0.6 99.3 84.04 88.107 16.462 0 0.6 0.6 99.5 91.72 100.653 18.19 0 0.6 0.6 99.7 96.273 125.984 19.552 0 0.6 0.6 99.9 109.83 135.296 19.603
B.2 Experimental Data of the Second Set of Experiments
Waterjet Laser impact Water Pulse pulse Groove Groove angle pressure overlap energy width depth HAZ width (deg) (MPa) (%) (mJ) (ȝm) (ȝm) (ȝm) 30 5 99.3 0.3 51.913 60.003 16.652 30 5 99.3 0.6 55.173 83.767 16.168 30 5 99.9 0.3 64.227 77.817 15.625 30 5 99.9 0.6 71.233 138.713 17.433 30 10 99.3 0.3 59.4 64.107 15.393 30 10 99.3 0.6 66.637 106.333 15.3 30 10 99.9 0.3 81.493 104.593 14.13 30 10 99.9 0.6 80.687 190.12 15.457 30 15 99.3 0.3 64.84 75.107 13.413 30 15 99.3 0.6 69.263 114.1 12.76 30 15 99.9 0.3 80.97 118.557 12.775 30 15 99.9 0.6 88.937 210.55 14.345
B-5 APPENDIX B
Waterjet Laser impact Water Pulse pulse Groove Groove angle pressure overlap energy width depth HAZ width (deg) (MPa) (%) (mJ) (ȝm) (ȝm) (ȝm) 30 20 99.3 0.3 74.57 78.483 12.942 30 20 99.3 0.6 85.827 124.843 13.708 30 20 99.9 0.3 96.24 160.047 12.815 30 20 99.9 0.6 111.677 259.267 10.57 40 5 99.3 0.3 54.91 59.27 15.832 40 5 99.3 0.6 68.213 74.703 15.998 40 5 99.9 0.3 72.177 74.723 15.71 40 5 99.9 0.6 75.453 121.33 15.162 40 10 99.3 0.3 67.367 72.707 12.443 40 10 99.3 0.6 89.217 102.45 16.128 40 10 99.9 0.3 83.01 84.443 13.918 40 10 99.9 0.6 104.19 174.22 12.808 40 15 99.3 0.3 75.263 74.897 13.867 40 15 99.3 0.6 95.59 107.85 15.298 40 15 99.9 0.3 84.493 95.97 13.588 40 15 99.9 0.6 108.78 189.063 14.073 40 20 99.3 0.3 77.007 80.283 11.423 40 20 99.3 0.6 102.453 114.103 12.52 40 20 99.9 0.3 98.013 144.473 13.65 40 20 99.9 0.6 129.903 251.983 13.073 50 5 99.3 0.3 82.223 76.433 17.753 50 5 99.3 0.6 102.623 78.97 16.91 50 5 99.9 0.3 104.193 72.92 14.197 50 5 99.9 0.6 130.393 134.337 13.972 50 10 99.3 0.3 81.257 79.383 17.093 50 10 99.3 0.6 111.073 81.18 16.025 50 10 99.9 0.3 123.143 81.433 11.145 50 10 99.9 0.6 146.09 146.657 12.283 50 15 99.3 0.3 88.617 85.633 13.203 50 15 99.3 0.6 107.693 88.147 15.248 50 15 99.9 0.3 128.1 85.167 10.533 50 15 99.9 0.6 142.587 157.517 9.465 50 20 99.3 0.3 96.06 88.86 13.603 50 20 99.3 0.6 107.017 90.423 14.645 50 20 99.9 0.3 133.133 101.503 12.852 50 20 99.9 0.6 143.96 182.663 13.018 60 5 99.3 0.3 75.82 51.447 17.207 60 5 99.3 0.6 100.23 73.193 15.988 60 5 99.9 0.3 112.36 63.1 14.618 60 5 99.9 0.6 132.807 145.31 17.65 60 10 99.3 0.3 83.45 53.267 15.117 60 10 99.3 0.6 108.307 75.387 15.81 60 10 99.9 0.3 124.84 61.497 17.218 60 10 99.9 0.6 156.587 143.257 14.767 60 15 99.3 0.3 100.82 54.36 15.207 60 15 99.3 0.6 137.513 73.42 12.445 60 15 99.9 0.3 145.483 64.003 14.417 60 15 99.9 0.6 174.947 144.32 9.895 60 20 99.3 0.3 99.483 53.867 10.44 60 20 99.3 0.6 141.257 75.933 12.848 60 20 99.9 0.3 144.997 64.44 12.092 60 20 99.9 0.6 183.993 143.337 10.982
B-6 Appendix C
Temperature Measurement Data Obtained from an Infrared Camera
C.1 Dry Laser Machining of Silicon
Temperature profiles (Kelvin) measured by an infrared camera at 30 ȝm from the laser axis.
Distance v=10 mm/s from the fpp=0 mm top work surface Ep=0.5 mJ Ep=0.6 mJ Ep=0.7 mJ Ep=0.8 mJ (ȝm) 0 2056.14 1921.79 2296.55 2187.14 10 1692.34 1718.62 2013.84 1990.14 20 1530.22 1574.78 1702.23 1734.42 30 1411.87 1415.51 1549.25 1545.11 40 1380.14 1355.81 1453.73 1452.16 50 1269.55 1282.02 1287.23 1399.88 60 1204.78 1208.13 1208.71 1335.66 70 1178.14 1198.72 1193.42 1266.74 80 1145.92 1210.39 1214.00 1248.09 90 1182.88 1190.33 1191.00 1238.45 100 1174.22 1150.88 1182.00 1226.19 fpp=-0.2 mm 0 1847.68 1913.36 2088.62 2178.25 10 1726.43 1752.85 2017.39 2023.47 20 1510.56 1555.03 1682.92 1714.47 30 1378.20 1382.50 1515.65 1511.25 40 1301.36 1376.92 1474.70 1472.58 50 1242.44 1254.99 1260.81 1372.48 60 1211.77 1215.80 1215.84 1342.58 70 1210.72 1231.07 1225.39 1298.35 80 1072.76 1137.43 1140.50 1174.58 90 1130.19 1137.31 1138.39 1185.36 100 1029.47 1106.34 1137.24 1181.35
C-1 APPENDIX C
Distance v=10 mm/s from the fpp=-0.4 mm top work surface Ep=0.5 mJ Ep=0.6 mJ Ep=0.7 mJ Ep=0.8 mJ (ȝm) 0 1741.48 1806.58 1981.85 2071.24 10 1381.16 1407.52 1671.52 1677.25 20 1298.17 1343.13 1470.55 1501.58 30 1220.76 1317.67 1450.69 1445.94 40 1196.29 1271.90 1369.54 1367.23 50 1172.39 1184.40 1190.73 1301.46 60 1104.86 1108.97 1108.91 1235.28 70 1158.83 1178.77 1173.41 1245.48 80 1120.48 1184.32 1187.52 1221.41 90 1114.11 1121.32 1122.15 1168.95 100 994.00 1070.24 1101.86 1145.12 fpp=-0.6 mm 0 1105.47 1171.00 1426.24 1435.16 10 1112.53 1139.20 1403.45 1408.48 20 1118.94 1164.13 1292.19 1322.27 30 1082.86 1150.40 1282.73 1377.31 40 1061.25 1137.37 1234.77 1332.49 50 1012.66 1124.62 1230.92 1341.58 60 1008.47 1113.02 1212.28 1338.59 70 994.15 1105.11 1199.35 1271.23 80 989.37 1094.60 1197.86 1231.23 90 986.11 1089.25 1198.91 1245.16 100 980.12 1038.14 1169.25 1212.50
Distance v=30 mm/s from the fpp=0 mm top work surface Ep=0.5 mJ Ep=0.6 mJ Ep=0.7 mJ Ep=0.8 mJ (ȝm) 0 1370.84 1436.69 1811.36 1701.35 10 1199.74 1225.81 1521.49 1497.29 20 1121.25 1165.46 1293.25 1324.86 30 1097.19 1100.98 1234.91 1230.24 40 976.29 981.70 1079.94 1077.57 50 975.24 987.53 993.02 1105.34 60 887.24 890.10 890.37 1017.25 70 941.92 962.69 957.64 1030.24 80 886.96 961.09 964.51 998.24 90 872.05 879.31 879.87 927.26 100 869.34 885.67 917.47 960.69 fpp=-0.2 mm 0 1368.64 1434.46 1609.41 1698.40 10 1205.07 1231.64 1496.07 1502.02 20 1109.10 1152.90 1281.51 1312.31 30 1084.79 1089.75 1222.63 1217.64 40 910.78 985.53 1083.79 1081.16 50 956.27 968.55 974.30 1085.77 60 889.29 893.13 893.22 1019.64 70 945.66 966.71 960.73 1033.25 80 840.75 905.58 907.80 941.74 90 872.14 878.86 880.03 926.33 100 807.28 883.77 914.88 958.33
C-2 APPENDIX C
Distance v=30 mm/s from the fpp=-0.4 mm top work surface Ep=0.5 mJ Ep=0.6 mJ Ep=0.7 mJ Ep=0.8 mJ (ȝm) 0 1277.08 1341.83 1517.26 1606.36 10 948.46 974.38 1239.20 1244.09 20 944.78 989.55 1117.32 1147.97 30 947.22 1044.54 1177.36 1172.23 40 884.77 960.27 1057.91 1055.12 50 906.62 919.16 925.95 1035.69 60 882.03 886.75 886.99 1012.41 70 927.65 948.31 943.09 1014.19 80 851.92 916.46 919.73 952.62 90 867.63 875.10 875.85 921.94 100 796.56 873.50 904.89 947.62 fpp=-0.6 mm 0 1080.47 1146.32 1401.04 1409.66 10 856.10 883.09 1146.79 1151.81 20 902.52 948.14 1075.90 1105.29 30 837.26 904.80 1037.38 1131.23 40 749.64 825.90 923.31 1020.85 50 722.02 833.90 940.29 1050.28 60 747.98 853.25 952.01 1078.05 70 755.84 866.82 960.99 1032.69 80 715.41 821.36 923.97 957.01 90 676.17 779.69 889.07 934.86 100 723.21 781.29 912.47 955.41
Distance v=50 mm/s from the fpp=0 mm top work surface Ep=0.5 mJ Ep=0.6 mJ Ep=0.7 mJ Ep=0.8 mJ (ȝm) 0 1177.96 1244.40 1618.43 1508.37 10 1083.74 1110.51 1405.74 1381.25 20 1012.16 1056.53 1184.15 1215.47 30 1036.86 1040.05 1174.67 1169.25 40 977.42 983.05 1081.30 1078.47 50 947.57 959.50 965.36 1077.24 60 851.07 853.78 853.59 980.36 70 837.20 858.79 853.71 925.48 80 806.50 880.85 884.57 917.36 90 909.90 917.09 917.98 964.47 100 779.20 795.88 827.25 870.14 fpp=-0.2 mm 0 1177.64 1243.28 1417.78 1506.64 10 1085.81 1112.97 1377.61 1382.72 20 1001.23 1044.56 1173.53 1203.83 30 1025.02 1030.07 1162.89 1157.71 40 908.88 983.12 1082.11 1078.51 50 945.82 957.99 964.00 1074.87 60 852.57 856.21 856.00 982.39 70 840.34 861.90 855.85 927.66 80 812.15 876.80 878.99 912.34 90 911.26 917.92 918.43 964.45 100 719.36 795.59 827.21 869.74
C-3 APPENDIX C
Distance v=50 mm/s from the fpp=-0.4 mm top work surface Ep=0.5 mJ Ep=0.6 mJ Ep=0.7 mJ Ep=0.8 mJ (ȝm) 0 1127.52 1192.32 1368.41 1456.70 10 830.00 856.50 1120.95 1125.58 20 951.62 995.82 1124.30 1154.17 30 930.33 1027.28 1160.80 1154.77 40 900.33 976.27 1073.54 1070.40 50 937.11 949.64 956.19 1065.40 60 846.21 850.99 851.13 976.32 70 833.22 854.16 848.74 919.36 80 816.43 881.52 884.51 917.01 90 909.65 916.69 917.65 963.27 100 716.29 793.47 824.34 866.68 fpp=-0.6 mm 0 958.08 1024.22 1278.64 1286.60 10 775.18 802.45 1066.57 1070.84 20 920.51 966.35 1094.17 1122.66 30 847.08 914.59 1047.23 1140.43 40 789.51 865.58 963.19 1060.47 50 739.36 851.17 957.35 1066.77 60 705.59 811.08 910.05 1035.46 70 660.30 771.03 865.05 936.35 80 679.00 784.59 887.54 919.71 90 714.41 817.96 927.48 972.31 100 640.15 698.13 829.38 871.72
Distance v=70 mm/s from the fpp=0 mm top work surface Ep=0.5 mJ Ep=0.6 mJ Ep=0.7 mJ Ep=0.8 mJ (ȝm) 0 994.93 1061.98 1435.58 1325.25 10 858.49 885.41 1180.51 1155.84 20 940.12 984.56 1111.39 1142.58 30 905.08 908.42 1043.64 1037.23 40 832.34 838.50 936.42 932.95 50 845.34 857.68 863.32 974.45 60 792.68 795.96 795.09 921.75 70 857.51 878.78 873.97 945.36 80 796.19 871.20 874.35 906.94 90 777.37 784.83 785.57 831.23 100 746.05 762.69 793.55 836.16 fpp=-0.2 mm 0 996.37 1061.61 1236.46 1324.51 10 860.56 887.98 1152.82 1157.14 20 929.08 973.33 1101.67 1131.63 30 903.21 908.32 1041.30 1035.42 40 763.49 837.86 936.82 932.99 50 844.66 856.95 863.48 973.38 60 792.71 796.36 796.52 922.01 70 860.47 882.10 876.02 947.37 80 804.67 869.28 871.02 904.35 90 778.81 785.50 785.49 831.22 100 686.21 762.08 794.15 835.80
C-4 APPENDIX C
Distance v=70 mm/s from the fpp=-0.4 mm top work surface Ep=0.5 mJ Ep=0.6 mJ Ep=0.7 mJ Ep=0.8 mJ (ȝm) 0 957.17 1021.78 1197.52 1285.75 10 862.17 888.78 1152.46 1157.00 20 883.34 928.02 1056.19 1085.65 30 810.55 907.75 1041.47 1034.70 40 758.00 833.58 930.59 927.40 50 844.32 857.13 863.36 972.53 60 791.69 796.60 796.57 921.69 70 859.44 880.11 874.25 944.70 80 805.38 870.80 873.61 905.76 90 777.46 784.05 785.58 830.25 100 684.58 762.18 793.36 834.82 fpp=-0.6 mm 0 860.27 926.26 1180.57 1188.50 10 813.26 840.76 1104.61 1108.35 20 865.81 911.81 1039.47 1067.25 30 739.09 806.74 940.08 1032.36 40 650.85 727.41 825.05 921.73 50 646.19 758.23 863.77 972.89 60 627.23 732.75 831.82 956.57 70 683.71 794.35 888.21 959.43 80 667.18 772.07 874.97 907.03 90 578.30 682.37 791.81 836.06 100 607.10 664.87 795.62 837.75
C.2 Hybrid Laser-Waterjet Machining of Silicon
Average bottom surface temperature of silicon.
Laser Bottom pulse Pulse Water surface energy overlap pressure temperature (mJ) (%) (MPa) (K) 0.3 99.3 5 314 0.3 99.3 10 310 0.3 99.3 15 304 0.3 99.3 20 300 0.3 99.5 5 325 0.3 99.5 10 321 0.3 99.5 15 320 0.3 99.5 20 311 0.3 99.7 5 348 0.3 99.7 10 344 0.3 99.7 15 335 0.3 99.7 20 323 0.3 99.9 5 375 0.3 99.9 10 367 0.3 99.9 15 355 0.3 99.9 20 345 0.4 99.3 5 316 0.4 99.3 10 314 0.4 99.3 15 308 0.4 99.3 20 302 0.4 99.5 5 329 0.4 99.5 10 325 0.4 99.5 15 322 0.4 99.5 20 315 0.4 99.7 5 352
C-5 APPENDIX C
Laser Bottom pulse Pulse Water surface energy overlap pressure temperature (mJ) (%) (MPa) (K) 0.4 99.7 10 348 0.4 99.7 15 337 0.4 99.7 20 327 0.4 99.9 5 379 0.4 99.9 10 371 0.4 99.9 15 357 0.4 99.9 20 349 0.5 99.3 5 320 0.5 99.3 10 318 0.5 99.3 15 310 0.5 99.3 20 306 0.5 99.5 5 334 0.5 99.5 10 329 0.5 99.5 15 324 0.5 99.5 20 317 0.5 99.7 5 357 0.5 99.7 10 352 0.5 99.7 15 339 0.5 99.7 20 329 0.5 99.9 5 384 0.5 99.9 10 375 0.5 99.9 15 359 0.5 99.9 20 351 0.6 99.3 5 325 0.6 99.3 10 322 0.6 99.3 15 312 0.6 99.3 20 308 0.6 99.5 5 339 0.6 99.5 10 333 0.6 99.5 15 326 0.6 99.5 20 319 0.6 99.7 5 362 0.6 99.7 10 356 0.6 99.7 15 341 0.6 99.7 20 331 0.6 99.9 5 389 0.6 99.9 10 379 0.6 99.9 15 361 0.6 99.9 20 353
C-6 Appendix D
Experimental Results of Dry Laser Machining of Silicon
Laser Focal Laser pulse plane traverse Groove energy position speed depth HAZ width (mJ) (mm) (mm/s) (ȝm) (ȝm) 0.5 0 10 30 125 0.5 0 30 13 119 0.5 0 50 8 107 0.5 0 70 6 83 0.5 -0.2 10 24 120 0.5 -0.2 30 10 115 0.5 -0.2 50 8 106 0.5 -0.2 70 6 80 0.5 -0.4 10 14 118 0.5 -0.4 30 8 112 0.5 -0.4 50 5 105 0.5 -0.4 70 4 79 0.5 -0.6 10 10 119 0.5 -0.6 30 5 111 0.5 -0.6 50 4 102 0.5 -0.6 70 4 80 0.6 0 10 56 137 0.6 0 30 20 125 0.6 0 50 16 112 0.6 0 70 12 96 0.6 -0.2 10 47 135 0.6 -0.2 30 17 126 0.6 -0.2 50 13 111 0.6 -0.2 70 10 98 0.6 -0.4 10 24 133 0.6 -0.4 30 10 125 0.6 -0.4 50 6 111 0.6 -0.4 70 4 100 0.6 -0.6 10 14 130 0.6 -0.6 30 5 124 0.6 -0.6 50 4 110 0.6 -0.6 70 4 98
D-1 APPENDIX D
Laser Focal Laser pulse plane traverse Groove energy position speed depth HAZ width (mJ) (mm) (mm/s) (ȝm) (ȝm) 0.7 0 10 88 144 0.7 0 30 33 137 0.7 0 50 25 122 0.7 0 70 18 108 0.7 -0.2 10 79 144 0.7 -0.2 30 28 135 0.7 -0.2 50 20 121 0.7 -0.2 70 14 110 0.7 -0.4 10 54 142 0.7 -0.4 30 15 134 0.7 -0.4 50 10 118 0.7 -0.4 70 7 111 0.7 -0.6 10 38 143 0.7 -0.6 30 10 135 0.7 -0.6 50 6 119 0.7 -0.6 70 4 110 0.8 0 10 114 155 0.8 0 30 45 144 0.8 0 50 33 132 0.8 0 70 25 121 0.8 -0.2 10 105 153 0.8 -0.2 30 40 144 0.8 -0.2 50 28 130 0.8 -0.2 70 21 120 0.8 -0.4 10 80 150 0.8 -0.4 30 27 142 0.8 -0.4 50 15 130 0.8 -0.4 70 10 119 0.8 -0.6 10 60 151 0.8 -0.6 30 10 144 0.8 -0.6 50 6 133 0.8 -0.6 70 5 120
D-2 Appendix E
MATLAB Codes for Simulation Using Finite Difference Method
% ===== Explicit Forward-central Time-space FDM ===== % By: Viboon Tangwarodomnukun % School of Mechanical and Manufacturing Engineering % The University of New South Wales % Copyright 2011. All right reserved. % ======close all; clear all; dx = 2e-6; %(m) Grid size dy = 2e-6; sizex = 100; %Number of grid in X sizey = 100; %Number of grid in Y hp = 1; %Position of laser spot
%Material properties rho = 2329; %(kg/m3) Density stef = 5.67e-8; %(W/m2K4) Stefan-Boltzmann constant k = 130; %(W/mK) Thermal conductivity cp = 700; %(J/kgC) Heat capacity alpha = k/(rho*cp); %(m2/K) thermal diffusivity Tm = 1687; %(K) Melting temperature Tv = 3538; %(K) Vaporization temperature Lm = 1.79e6; %(J/kg) Latent heat of melting Lv = 1.28e7; %(J/kg) Latent heat of vaporization
%Laser parameters kp = 0.914; %Pulsed laser coefficient hp = (sizex*sizey)-sizex+hp; vx = 1e-3; %(m/s) Traverse speed in X xp = 0; %(m) Observed position tau = 50e-9; %(s) Pulse duration fpp = 0; %(m) Focal plane position dbf = 20e-6; %(m) Focused laser beam diameter
E-1 APPENDIX E
db = (dbf)*(sqrt((1)+(((4*abs(fpp)*1080e-9)/(pi*((dbf)^2)))^2))); Al = pi*(db^2)/4; %(m2) Laser spot area feq = 20e3; %(Hz) Pulse frequency tprep = 1/feq; %(s) Ep = (0.3e-3)/kp; P = kp*Ep/tau;
%Thermal convection rhow = 1e3; %(kg/m3) Water density kw = 0.674; %(W/mK) Thermal conductivity of water cpw = 4.2e3; %(J/kgK) Heat capacity of water nuw = 0.89e-6; %(m2/s) Kinematic viscosity muw = nuw*rhow; %(Pa.s) Dynamic viscosity Pr = cpw*muw/kw; %Prandtl number Abw = 1/(20e-3); %(1/m) Water absorption coefficient Rfw = 0.0198; %Water reflectivity at 1080 nm vw = sqrt((10e6)*2/rhow); %(m/s) Waterjet velocity dn = 0.57e-3; %(m) Waterjet nozzle diameter Anw = (pi*(dn^2))/4; %(m2) Nozzle cross-sectional area Thickw = 0.1*dn; Lc = Thickw; %(m) Characteristic length Re = (rhow*vw*dn)/(muw); %Reynolds number znt = 2e-3; %(m) Nozzle-to-target distance angw = (40-0)*pi/180; %(rad) Impact angle beamdiv = 0*pi/180; %(rad) Beam divergence dimp = dn+(2*znt*tan(beamdiv/2)); %(m) Impact diameter xwl = 0.4e-3; %(m) Impact position Nu = (((0.109.*(Re.^0.847))^(9))+((1.175.*(Re.^0.465))^(-9)))^(1/9); h = Nu.*kw./Lc; %(W/m2K) Heat transfer coefficient h0 = h;
%Surrounding temperature and times Tsur = 300; %(K) Surrounding temperature dt = 0.25*(min(dx,dy)^2)/(alpha*(1+(h*(min(dx,dy))/k))); %(s)time step tfinal = 1e-3; %(s)
%Temperature matrixes T=ones(sizex*sizey,1).*Tsur; T2=ones(sizex*sizey,1).*Tsur;
%Temperature-dependent material properties %Density rho=zeros(sizex*sizey,1); for i=1:1:sizex for z=0:1:sizey-1 if T(i+(sizex*z))<=Tm rho(i+(sizex*z),1)=(2.311-((2.63e-5).* ... (T(i+(sizex*z),1)-Tm))).*1000; end if T(i+(sizex*z))>Tm rho(i+(sizex*z),1)=(2.580-((1.71e-4).* ... (T(i+(sizex*z),1)-Tm))-((1.61e-7).*((T(i+(sizex*z),1)- ... Tm).^2))).*1000; end end end %Thermal conductivity k=zeros(sizex*sizey,1); for i=1:1:sizex for z=0:1:sizey-1
E-2 APPENDIX E
k(i+(sizex*z),1)=29900./(T(i+(sizex*z),1)-99); end end %Heat capacity cp=zeros(sizex*sizey,1); for i=1:1:sizex for z=0:1:sizey-1 if T(i+(sizex*z))<=Tm cp(i+(sizex*z),1)=(1./rho(i+(sizex*z),1)).* ... (1.4743+((0.17066/300).*T(i+(sizex*z)))).*1000000; end if T(i+(sizex*z))>Tm cp(i+(sizex*z),1)=(2.432e6./rho(i+(sizex*z),1)); end end end %Thermal diffusivity alpha=zeros(sizex*sizey,1); for i=1:1:sizex for z=0:1:sizey-1 alpha(i+(sizex*z),1)=(128/10000)./(T(i+(sizex*z),1)-159); end end %Reflectivity Rf=zeros(sizex*sizey,1); for i=1:1:sizex for z=0:1:sizey-1 if T(i+(sizex*z))<=3019 Rf(i+(sizex*z),1)=(0.367+(4.29e-5).*T(i+(sizex*z)))+ ... ((2.691e-15).*T(i+(sizex*z)).^(4)); end if T(i+(sizex*z))>3019 Rf(i+(sizex*z),1)=0.72; end end end %Absorption coefficient Ab=zeros(sizex*sizey,1); for i=1:1:sizex for z=0:1:sizey-1 if T(i+(sizex*z),1)
E-3 APPENDIX E
%Fictitious node correction betac=ones(sizex*sizey,1); betac1=ones(sizex*sizey,1); beta0=ones(sizex*sizey,1); beta0x=ones(sizex*sizey,1); beta1=ones(sizex*sizey,1); beta1x=ones(sizex*sizey,1); beta2=ones(sizex*sizey,1); gamma=ones(sizex*sizey,1); betac = betac.*(1+(dx.*h./(2.*k))+(dy.*h./(2.*k))); betac1 = betac1.*(1+(dx.*h./(6.*k))+(dy.*h./(6.*k))); beta0 = beta0.*(1+(dy.*h0./(2.*k))); beta0x = beta0x.*(1+(dx.*h0./(2.*k))); beta1 = beta1.*(1+(dy.*h./(2.*k))); beta1x = beta1x.*(1+(dx.*h./(2.*k))); beta2 = beta2.*(k.*dt./(rho.*((dy.^2).*(dx.^2)))).* ... 2.*((dx)^2).*(dy.*h0./(k)); gamma = gamma.*(k.*dt./(rho.*((dy.^2).*(dx.^2))));
%Matrix [A] imod = sparse(((dx)^2)*eye(sizex)); m4 = sparse(eye(sizex)); m4 = -(2*((dx^2)+(dy^2)))*m4; for i=1:1:sizex-1 m4(i+1,i) = 1*((dy)^2); m4(i,i+1) = 1*((dy)^2); end m4(1,2) = 2*((dy)^2); m4(sizex,sizex-1)=2*((dy)^2); A=sparse(eye(sizex*sizey)); for i=1:1:sizex for j=1:1:sizex for z=0:1:sizey-1 if (i==1) && (j==1) m4(1,1)=-(2*((dx^2)+(dy^2))); end if (i==sizex) && (j==sizex) m4(sizex,sizex)=-(2*((dx^2)+(dy^2))); end A(i+(sizex*z),j+(sizex*z))=m4(i,j); end for z=0:1:sizey-2 A(i+(sizex*(z+1)),j+(sizex*z))=imod(i,j); A(i+(sizex*z),j+(sizex*(z+1)))=imod(i,j); end end end for i=1:1:sizex A(i,i)=-(2*((dx^2)+(dy^2))); A(i,i+sizex)=2*((dx)^2); A((sizex*sizey)-sizex+i,(sizex*sizey)-sizex+i)= ... -(2*((dx^2)+(dy^2)))*beta0((sizex*sizey)-sizex+i,1); A((sizex*sizey)-sizex+i,(sizex*sizey)-sizex-sizex+i)= ... 2*((dx)^2); for iG=0:1:((db/2)/dx) if (hp+iG<(sizex*sizey)) A(hp+iG,hp+iG)=-(2*((dx^2)+(dy^2)))*beta1(hp+iG,1); end if ((hp-iG)>=(((int16((hp+(sizex/2))/sizex))-1)*sizex)+1) A(hp-iG,hp-iG)=-(2*((dx^2)+(dy^2)))*beta1(hp-iG,1);
E-4 APPENDIX E
end end end
%Matrix [c] c=sparse(zeros(sizex*sizey,1));
%Enthalpy matrixes H = ones(sizex*sizey,1).*(cp.*(Tsur-Tm)); H2 = ones(sizex*sizey,1).*(cp.*(Tsur-Tm));
%Volumetric fraction voll=int8(zeros(sizex*sizey,1)); voll2=int8(zeros(sizex*sizey,1)); volv=int8(zeros(sizex*sizey,1)); volr=int8(zeros(sizex*sizey,1));
%Initial values t = 0; %Initial time tp = 0; btpex = int8(0); tp = 0;
%Heat source positioning hpdr=zeros(size(0:1:(db/2)/dx,2),1); hpdl=zeros(size(0:1:(db/2)/dx,2),1); for iG=0:1:((db/2)/dx) hpdr(iG+1,1)=hp+iG; hpdl(iG+1,1)=hp-iG; end
%Laser spot area Al=Al.*ones(sizex*sizey,1); fppy=(sizey*dy) + fpp; for j=1:1:sizey for i=1:1:sizex Al(((j-1)*sizex)+i,1)= ... pi*(((dbf)*(sqrt((1)+(((4*abs(fppy)*1080e-9)/ ... (pi*((dbf)^2)))^2))))^2)/4; end fppy=fppy-dy; end
%Finite difference calculation while (t+dt <= tfinal) t = t+dt; %Update time tp = tp+dt; if tp>=tprep tp=(tp-tprep); temporalf=1; btpex=int8(1); h=0; h0=0; else temporalf=0; btpex=int8(0); h=Nu.*kw./Lc; h0=h; end if mod(t,tprep)<=tau
E-5 APPENDIX E
temporalf=1; h=0; h0=0; end betac = (1+(dx.*h./(2.*k))+(dy.*h./(2.*k))); betac1 = (1+(dx.*h./(6.*k))+(dy.*h./(6.*k))); beta0 = (1+(dy.*h0./(2.*k))); beta0x = (1+(dx.*h0./(2.*k))); beta1 = (1+(dy.*h./(2.*k))); beta1x = (1+(dx.*h./(2.*k))); beta2 = (k.*dt./(rho.*((dy.^2).*(dx.^2)))).* ... 2.*((dx)^2).*(dy.*h0./(k)); gamma = (k.*dt./(rho.*((dy.^2).*(dx.^2)))); for i=1:1:sizex*sizey if A(i,i)==0 betac(i,1)=0; betac1(i,1)=0; beta0(i,1)=0; beta0x(i,1)=0; beta1(i,1)=0; beta1x(i,1)=0; beta2(i,1)=0; gamma(i,1)=0; end end %Gaussian beam profile for iG=0:1:((db/2)/dx) if (H(hpdr(iG+1,1),1)>=0) Tl(iG+1,1) = (((P.*dt)./(Al(hpdr(iG+1,1),1).* ... (rho(hpdr(iG+1,1),1)).*dy)).* ... (exp(-((1.*((iG.*dx).^2))./((db./2).^2)))).* ... (temporalf).*(exp(-Abw.*Thickw)).* ... (1-Rf(hpdr(iG+1,1),1)).*(1-Rfw)); else if btpex==0 Tl(iG+1,1) = (((P.*Ab(hpdr(iG+1,1),1).*dt)./ ... (Al(hpdr(iG+1,1),1).*(rho(hpdr(iG+1,1),1)))).* ... (exp(-((1.*((iG.*dx).^2))./((db./2).^2)))).* ... (temporalf).*(exp(-Abw.*Thickw)).* ... (1-Rf(hpdr(iG+1,1),1)).*(1-Rfw)); else Tl(iG+1,1) = (((P.*Ab(hpdr(iG+1,1),1).*(dt+tp))./ ... (Al(hpdr(iG+1,1),1).*(rho(hpdr(iG+1,1),1)))).* ... (exp(-((1.*((iG.*dx).^2))./((db./2).^2)))).* ... (temporalf).*(exp(-Abw.*Thickw)).* ... (1-Rf(hpdr(iG+1,1),1)).*(1-Rfw)); end end if (H(hpdl(iG+1,1),1)>=0) Tll(iG+1,1) = (((P.*dt)./(Al(hpdl(iG+1,1),1).* ... (rho(hpdl(iG+1,1),1)).*dy)).* ... (exp(-((1.*((iG.*dx).^2))./ ... ((db./2).^2)))).*(temporalf).*(exp(-Abw.*Thickw)).* ... (1-Rf(hpdl(iG+1,1),1)).*(1-Rfw)); else if btpex==0 Tll(iG+1,1) = (((P.*Ab(hpdl(iG+1,1),1).*dt)./ ... (Al(hpdl(iG+1,1),1).*(rho(hpdl(iG+1,1),1)))).* ... (exp(-((1.*((iG.*dx).^2))./((db./2).^2)))).* ... (temporalf).*(exp(-Abw.*Thickw)).* ...
E-6 APPENDIX E
(1-Rf(hpdl(iG+1,1),1)).*(1-Rfw)); else Tll(iG+1,1) = (((P.*Ab(hpdl(iG+1,1),1).*(dt+tp))./ ... (Al(hpdl(iG+1,1),1).*(rho(hpdl(iG+1,1),1)))).* ... (exp(-((1.*((iG.*dx).^2))./((db./2).^2)))).* ... (temporalf).*(exp(-Abw.*Thickw)).* ... (1-Rf(hpdl(iG+1,1),1)).*(1-Rfw)); end end end %Moving heat source due to traverse speed for iG=0:1:((db/2)/dx) if (hpdr(iG+1,1) >= sizex*sizey-sizex+1) for iab=0:sizex:hpdr(iG+1,1) if (H(hpdr(iG+1,1),1)>=0) c(hpdr(iG+1,1),1)=-(Tl(iG+1,1).* ... (exp(-4.*(((xp-(vx.*t)).^2)./(db.^2))))); else c(hpdr(iG+1,1)-iab,1)=-((Tl(iG+1,1)- ... ((h.*dt.*(T(hpdr(iG+1,1),1)-Tsur))./ ... (dy.*rho(hpdr(iG+1,1),1)))).* ... (exp(-Ab(hpdr(iG+1,1)-iab,1).*dy.* ... (iab./sizex))).*(exp(-4.*(((xp-(vx.*t)).^2)./ ... (db.^2))))); c(hpdr(iG+1,1),1)=-(Tl(iG+1,1).* ... (exp(-4.*(((xp-(vx.*t)).^2)./(db.^2))))); end end end end Hp = H + (gamma.*(A*T)) - c; for i=(sizex*sizey)-sizex+1:1:(sizex*sizey) if A(i,i) ~= 0 Hp(i,1) = Hp(i,1) + (beta2(i,1)*Tsur) - ... ((((stef.*dt.*em(i,1))./(dy.*rho(i,1)))).* ... (((T(i,1)).^(4))-((Tsur).^(4)))); end end H = Hp; %Moving heat source due to material removal for iG=0:1:((db/2)/dx) for i=1:1:sizex*sizey c(i,1)=0; end for i=hpdr(iG+1,1):-sizex:mod(hpdr(iG+1,1),sizex)+sizex if (i>sizex) && (((tenstr(i,1)) < sqrt((((vw^2)* ... (rhow/2)*((cos(angw)).*(sin(angw)))).^2) + ... (((vw^2)*(rhow/2)*((cos(angw))^2)/2).^2))) || ... (H(i,1)>(0))) H(i,1)=-970900; if volr(i:sizex:hpdr(iG+1,1),1) ~= 100 volr(i:sizex:hpdr(iG+1,1),1) = 100; end A(i,i)=0; A(i+1,i+1)=-(2*((dx^2)+(dy^2)))*beta1x(i+1,1); if (iG >= 1) A(i,i-1)=0; end A(i+1,i+1-1)=2*((dy)^2).*(dx.*h./(k(i+1-1))); if (iG >= 1)
E-7 APPENDIX E
A(i,i+1)=0; end if (iG == 0) A(i,i+1)=0; end A(i+1,i+1+1)=2*((dy)^2); if (i > sizex) && (i < (sizex*sizey)-sizex+1) A(i,i+sizex)=0; if A(i+sizex+1,i+sizex+1)==0 A(i+1,i+1)=-(2*((dx^2)+(dy^2)))*betac(i+1,1); A(i+1,i+1-sizex)=2*((dx)^2); A(i+1,i+1+sizex)=2*((dx)^2).* ... (dy.*h./(k(i+1+sizex))); else A(i+1,i+1-sizex)=1*((dx)^2); A(i+1,i+1+sizex)=1*((dx)^2); end end if (i>=(sizex*sizey)-sizex+1) A(i+1,i+1)=-(2*((dx^2)+(dy^2)))*betac(i+1,1); A(i+1,i+1-sizex)=2*((dx)^2); end if (i > sizex) && (i < (sizex*sizey)-sizex+1) A(i,i-sizex)=0; end if (i >= (sizex*sizey)-sizex+1) A(i,i-sizex)=0; A(i,i)=0; end if (i <= sizex) A(i,i+sizex)=0; end hpdr((iG+1),1)=i-sizex; else break; end end for i=hpdr(iG+1,1):sizex:sizex*sizey-sizex+1 if (volr(i,1)==100) && (volr(i+1,1)~=100) A(i+1,i+1)=-(2.*((dx.^2)+(dy.^2))).*beta1x(i+1,1); A(i+1,i+1-1)=2*((dy)^2).*(dx.*h./(k(i+1-1))); A(i+1,i+1+1)=2*((dy)^2); end end if (hpdr((iG+1),1) > sizex) A(hpdr((iG+1),1),hpdr((iG+1),1))=-(2*((dx^2)+(dy^2)))* ... beta1(hpdr((iG+1),1),1); A(hpdr((iG+1),1),hpdr((iG+1),1)-sizex)=2*((dx)^2); if (hpdr((iG+1),1) < (sizex*sizey)-sizex+1) A(hpdr((iG+1),1),hpdr((iG+1),1)+sizex)= ... 2*((dx)^2).*(dy.*h./(k(hpdr((iG+1),1)+sizex))); end if (iG > 0) A(hpdr((iG+1),1),hpdr((iG+1),1)+1)=1*((dy)^2); A(hpdr((iG+1),1),hpdr((iG+1),1)-1)=1*((dy)^2); end end for i=sizex*sizey-sizex+mod(hp,sizex):1:sizex*sizey- ... sizex+mod(hp,sizex)+size(hpdr,1)+1 if (volr(i,1)==100) && (volr(i+1,1)~=100)
E-8 APPENDIX E
A(i+1,i+1)=-(2.*((dx.^2)+(dy.^2))).*betac(i+1,1); A(i+1,i+1-sizex)=2*((dx)^2); A(i+1,i+1-1)=2*((dy)^2).*(dx.*h./(k(i+1-1))); A(i+1,i+1+1)=2*((dy)^2); end end if (hpdr((iG+1),1)+1 > sizex) && (hpdr((iG+1),1)+1 < ... (sizex*sizey)-sizex+1) && ... (A(hpdr((iG+1),1)+1+sizex,hpdr((iG+1),1)+1+sizex) ~= 0) A(hpdr((iG+1),1)+1,hpdr((iG+1),1)+1)= ... -(2*((dx^2)+(dy^2)))*betac1(hpdr((iG+1),1)+1,1); A(hpdr((iG+1),1)+1,hpdr((iG+1),1)+1-sizex)= ... 2*((dx)^2)*(2/3); A(hpdr((iG+1),1)+1,hpdr((iG+1),1)+1+sizex)= ... 1*((dx)^2)*(2/3); A(hpdr((iG+1),1)+1,hpdr((iG+1),1)+1+1)=2*((dy)^2)*(2/3); A(hpdr((iG+1),1)+1,hpdr((iG+1),1)+1-1)=1*((dy)^2)*(2/3); end if (iG > 0) if (hpdr((iG+1),1) > sizex) && (hpdr((iG+1),1) < ... (sizex*sizey)-sizex+1) if (hpdr((iG+1),1) > hpdr((iG+1-1),1)+1) A(hpdr((iG+1),1),hpdr((iG+1),1))= ... -(2*((dx^2)+(dy^2)))*betac(hpdr((iG+1),1),1); A(hpdr((iG+1),1),hpdr((iG+1),1)-sizex)=2*((dx)^2); A(hpdr((iG+1),1),hpdr((iG+1),1)+sizex)= ... 2*((dx)^2).*(dy.*h./(k(hpdr((iG+1),1)+sizex))); A(hpdr((iG+1),1),hpdr((iG+1),1)+1)=2*((dy)^2); A(hpdr((iG+1),1),hpdr((iG+1),1)-1)= ... 2*((dy)^2).*(dx.*h./(k(hpdr((iG+1),1)-1))); end end end end for i=1:1:sizex*sizey if (H(i,1) E-9 APPENDIX E if H2(iH,1) %Update temperature-dependent material properties %Density rho=zeros(sizex*sizey,1); for i=1:1:sizex for z=0:1:sizey-1 if T(i+(sizex*z))<=Tm rho(i+(sizex*z),1)=(2.311-((2.63e-5).* ... (T(i+(sizex*z),1)-Tm))).*1000; end if T(i+(sizex*z))>Tm rho(i+(sizex*z),1)=(2.580-((1.71e-4).* ... (T(i+(sizex*z),1)-Tm))-((1.61e-7).* ... E-10 APPENDIX E ((T(i+(sizex*z),1)-Tm).^2))).*1000; end end end %Thermal conductivity k=zeros(sizex*sizey,1); for i=1:1:sizex for z=0:1:sizey-1 k(i+(sizex*z),1)=29900./(T(i+(sizex*z),1)-99); end end %Heat capacity cp=zeros(sizex*sizey,1); for i=1:1:sizex for z=0:1:sizey-1 if T(i+(sizex*z))<=Tm cp(i+(sizex*z),1)=(1./rho(i+(sizex*z),1)).* ... (1.4743+((0.17066/300).*T(i+(sizex*z)))).*1000000; end if T(i+(sizex*z))>Tm cp(i+(sizex*z),1)=(2.432e6./rho(i+(sizex*z),1)); end end end %Thermal diffusivity alpha=zeros(sizex*sizey,1); for i=1:1:sizex for z=0:1:sizey-1 alpha(i+(sizex*z),1)=(128/10000)./(T(i+(sizex*z),1)-159); end end %Reflectivity Rf=zeros(sizex*sizey,1); for i=1:1:sizex for z=0:1:sizey-1 if T(i+(sizex*z))<=3019 Rf(i+(sizex*z),1)=(0.367+(4.29e-5).* ... T(i+(sizex*z)))+((2.691e-15).*T(i+(sizex*z)).^(4)); end if T(i+(sizex*z))>3019 Rf(i+(sizex*z),1)=0.72; end end end %Absorption coefficient Ab=zeros(sizex*sizey,1); for i=1:1:sizex for z=0:1:sizey-1 if T(i+(sizex*z),1) E-11 APPENDIX E em(i+(sizex*z),1)=0.66; end if T(i+(sizex*z))>=Tm em(i+(sizex*z),1)=0.27; end end end betac = (1+(dx.*h./(2.*k))+(dy.*h./(2.*k))); betac1 = (1+(dx.*h./(6.*k))+(dy.*h./(6.*k))); beta0 = (1+(dy.*h0./(2.*k))); beta0x = (1+(dx.*h0./(2.*k))); beta1 = (1+(dy.*h./(2.*k))); beta1x = (1+(dx.*h./(2.*k))); beta2 = (k.*dt./(rho.*((dy.^2).*(dx.^2)))).* ... 2.*((dx)^2).*(dy.*h0./(k)); gamma = (k.*dt./(rho.*((dy.^2).*(dx.^2)))); for i=1:1:sizex*sizey if A(i,i)==0 betac(i,1)=0; betac1(i,1)=0; beta0(i,1)=0; beta0x(i,1)=0; beta1(i,1)=0; beta1x(i,1)=0; beta2(i,1)=0; gamma(i,1)=0; if i>sizex A(i,i-sizex)=0; end if i<=(sizex*sizey)-sizex A(i,i+sizex)=0; end A(i,i-1)=0; A(i,i+1)=0; end end %Update surface node correction for i=1:1:sizex A(i,i)=-(2*((dx^2)+(dy^2))); A(i,i+sizex)=2*((dx)^2); if A((sizex*sizey)-sizex+i,(sizex*sizey)-sizex+i) ~= 0 A((sizex*sizey)-sizex+i,(sizex*sizey)-sizex+i)= ... -(2*((dx^2)+(dy^2)))*beta0((sizex*sizey)-sizex+i,1); A((sizex*sizey)-sizex+i,(sizex*sizey)-sizex- ... sizex+i)=2*((dx)^2); end for j=sizex*sizey-sizex+mod(hp,sizex):1:sizex*sizey- ... sizex+mod(hp,sizex)+size(hpdr,1)+1 if (volr(j,1)==100) && (volr(j+1,1)~=100) A(j+1,j+1)=-(2.*((dx.^2)+(dy.^2))).*betac(j+1,1); A(j+1,j+1-sizex)=2*((dx)^2); A(j+1,j+1-1)=2*((dy)^2).*(dx.*h./(k(j+1-1))); A(j+1,j+1+1)=2*((dy)^2); end end end end E-12