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Investigation of Thermal Transport in Layered Sytems and Micro-Structured Semiconductor Devices by Photothermal Techniques and Finite Element Simulations

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Investigation of Thermal Transport in Layered Sytems and Micro-Structured Semiconductor Devices by Photothermal Techniques and Finite Element Simulations Investigation of Thermal Transport in Layered Sytems and Micro-structured Semiconductor Devices by Photothermal Techniques and Finite Element Simulations Dissertation Zur Erlangung des Grades eines Doktors der Naturwissenschaften in der Fakultät für Physik und Astronomie der Ruhr-Universität Bochum vorgelegt von Jean Lazare Nzodoum Fotsing aus Jaunde Kamerun Bochum 2004 Mit der Genehmigung des Dekanats vom 03.05.2004 wurde die Dissertation in englischer Sprache verfasst Eingereicht am: 21. 05. 2004 Disputation am: 14. 07. 2004 1. Gutachter: Prof. Dr. J. Pelzl 2. Gutachter: Prof. Dr. A. Wieck ii To my uncles Takam André Pombo Gaston who passed away respectively in 2003 and in 2004. May their souls rest in peace iii Contents Contents.................................................................................................................................... iv Abreviations and Nomenclature ..........................................................................................viii 1 Introduction ...................................................................................................... 1 1.1 Motivation ....................................................................................................................... 1 1.2 Objectives of the Work.................................................................................................... 2 1.3 Thesis Overview.............................................................................................................. 2 2 Fundamentals and Goals of the Photothermal Techniques ......................... 5 2.1 Introduction ..................................................................................................................... 5 2.2 The concept of thermal waves......................................................................................... 5 2.3 Relevant physical parameters.......................................................................................... 7 2.4 Review of the main detection methods ........................................................................... 7 2.5 Conclusions ................................................................................................................... 11 3 Surface and Subsurface Effects of Thermal Transport in Layered Systems............................................................................................. 12 3.1 Introduction ................................................................................................................... 12 3.2 Photothermal IR radiometric signal............................................................................... 13 3.3 Description of the measuring system ............................................................................ 16 3.4 Description of the investigated samples........................................................................ 17 3.5 Theoretical models of thermal waves for layered systems............................................ 17 3.6 Interpretation of the modulated IR radiometric signals................................................. 21 3.7 Discussion of physical effects in the investigated samples........................................... 24 3.7.1 Surface effects.......................................................................................................... 24 3.7.1.1 Optical effects: coating semi-transparency..................................................... 24 3.7.1.2 Topological effects......................................................................................... 26 3.7.2 Subsurface effects: lateral thermal transport ........................................................... 28 3.7.2.1 Theoretical developments............................................................................... 28 3.7.2.2 Comparison of 1-D and 3-D thermal wave propagation................................. 33 3.7.2.3 Effects of heating spot radius and subsurface thermal properties .................. 34 3.8 Interpretation of signal phases based on 3D thermal transport ..................................... 37 3.8.1 Determination of the properties of lateral heat transport......................................... 38 3.8.2 Discussion of results................................................................................................ 40 3.9 Conclusions ................................................................................................................... 41 4 Determination of Thermal Transport Properties of Two-layer Structures using the Concept of the Phase Extremum.................................................. 43 4.1 Motivation ..................................................................................................................... 43 4.2 The concept of the Phase Extremum............................................................................. 44 iv 4.2.1 Physical significance of the observable phase extrema........................................... 44 4.2.2 Theoretical background........................................................................................... 46 4.3 Application to experimental measurements .................................................................. 49 4.3.1 Methodology and discussions.................................................................................. 49 4.3.2 Determination of the thermophysical properties ..................................................... 51 4.3.3 Efficient localization of the phase extremum .......................................................... 52 4.3.4 Application to measurements at high temperatures................................................. 54 4.4 Discussions on the reliability of the Extremum Method............................................... 57 4.4.1 Solutions from any measured point of the calibrated phase .................................... 57 4.4.2 Comparison of results .............................................................................................. 60 4.5 General results for on-line interpretation in industrial applications.............................. 61 4.5.1 Graphic of thermal reflection coefficients............................................................... 61 4.5.2 Graphic of ratio of the effusivities........................................................................... 63 4.5.3 Graphic of thermal diffusion times.......................................................................... 63 4.5.4 Example of on-line interpretation............................................................................ 66 4.6 Interpretation of modulated IR signals obscured by the background fluctuation ......... 67 4.6.1 Theory of the transformation of the inverse normalized phase ............................... 68 4.6.2 Application of the functional transform to measurements: The problem of convergence ............................................................................................................. 71 4.6.3 Phase interpretation obscured by the background fluctuation................................. 77 4.7 Conclusions ................................................................................................................... 79 5 Detection of Local Inhomogeneities of Thermal Transport and Localization of Heat sources in Micro-scaled Systems based on Spot Displacement.......................................................................................... 81 5.1 Motivation ..................................................................................................................... 81 5.2 Review of the main results of 3-D thermal wave propagation...................................... 81 5.3 Displacement between heating and detection spots ...................................................... 82 5.3.1 Theoretical background........................................................................................... 83 5.3.2 Simulation of controlled displacements between the two spots .............................. 85 5.3.3 Localization of heat sources .................................................................................... 87 5.3.4 Comparison of experimental measurements and theoretical results........................ 88 5.4 Scaling of thermal localization of hot spots .................................................................. 91 5.5 Comparisons with measurements based on Thermoreflectance.................................... 94 5.6 Conclusions ................................................................................................................... 95 6 Efficient Simulation of Thermal Wave Problems with the ANSYS-aided Finite Element Technique.............................................................................. 97 6.1 Introduction ................................................................................................................... 97 6.2 Finite element concepts................................................................................................. 97 6.2.1 Theoretical foundation............................................................................................. 97 6.2.2 Fundamental steps................................................................................................... 99 6.3 Finite element modeling................................................................................................ 99 6.3.1 Pre-processing........................................................................................................ 100 6.3.2 Computation..........................................................................................................
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