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Use of Spectroscopic Ellipsometry and Modeling in Determining Composition and Thickness of Barium Strontium Titanate Thin-Films

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Use of Spectroscopic Ellipsometry and Modeling in Determining Composition and Thickness of Barium Strontium Titanate Thin-Films Use of Spectroscopic Ellipsometry and Modeling in Determining Composition and Thickness of Barium Strontium Titanate Thin-Films A Thesis Submitted to the Faculty of Drexel University by Dominic G. Bruzzese III in partial fulfillment of the requirements for the degree of MS in Materials Science and Engineering June 2010 c Copyright June 2010 Dominic G. Bruzzese III. All Rights Reserved. Acknowledgements I would like to acknowledge the guidance and motivation I received from my advi- sor Dr. Jonathan Spanier not just during my thesis but for my entire stay at Drexel University. Eric Gallo for his help as my graduate student mentor and always making himself available to help me with everything from performing an experiment to ana- lyzing some result, he has been an immeasurable resource. Keith Fahnestock and the Natural Polymers and Photonics Group under the direction of Dr. Caroline Schauer for allowing the use of their ellipsometer, without which this work would not have been possible. I would like to thank everyone in the MesoMaterials Laboratory, espe- cially Stephen Nonenmann, Stephanie Johnson, Guannan Chen, Christopher Hawley, Brian Beatty, Joan Burger, and Andrew Akbasheu for help with experiments, as well as Oren Leffer and Terrence McGuckin for enlightening discussions. Claire Weiss and Dr. Pamir Alpay at the University of Connecticut have both contributed much to the the field and I am grateful for their work; also Claire produced the MOSD samples on which much of the characterization and modeling was done. Dr. Melanie Cole and the Army Research Office and Dr. Marc Ulrich for funding the project under W911NF-08-0124 and W911NF-08-0067. Dr. Nick Sbrockey and Structured Materi- als Industries, Inc for their support in funding, and supplying the MOCVD samples and characterizations when necessary. Without their help collectively, i would not have been able to produce this work. Dedications To my father i Table of Contents List of Figures ......................................................................... iv Abstract ................................................................................ vii 1. Introduction and Motivation...................................................... 1 1.1 Scope of this work ........................................................... 2 2. Barium Strontium Titanate....................................................... 4 2.1 Structure ..................................................................... 4 2.1.1 Temperature and Compositional Dependence ..................... 5 2.2 Film Synthesis ............................................................... 5 2.2.1 MOSD ................................................................ 5 2.2.2 MOCVD.............................................................. 6 2.3 Effect of Grading ............................................................ 8 2.3.1 Effect of Polarization ................................................ 8 2.3.2 Temperature Insensitivity ........................................... 10 2.3.3 Increased Dielectric Response and Tunability ..................... 12 2.4 Complex Dielectric Function ................................................ 13 2.4.1 Kramer-Kronig Relation ............................................ 14 2.4.2 Parameterization .................................................... 15 2.5 Absorption ................................................................... 16 2.5.1 The Fundamental Bandgap ......................................... 17 2.5.2 Intraband Absorption ............................................... 19 2.5.3 Defect States and Absorption....................................... 19 2.5.4 The Tauc Relation................................................... 19 2.5.5 Variation in the Bandgap Due to Stress and Temperature ....... 21 2.5.6 Ellipsometric Parameters and Related Equations ................. 21 3. Characterization Techniques ...................................................... 24 ii 3.1 Scanning Electron Microscopy .............................................. 24 3.2 Atomic Force Microscopy ................................................... 24 3.3 X-ray Diffraction............................................................. 24 3.4 Raman Spectroscopy ........................................................ 25 3.5 Variable Angle Spectroscopic Ellipsometry ................................ 25 3.5.1 Determination of the Ellipsometric parameters ................... 26 4. Modeling ........................................................................... 29 4.1 Physical Representation ..................................................... 29 4.1.1 Effect of Microstructure ............................................. 31 4.2 Optimum Parameterization ................................................. 31 4.2.1 Lorentz Oscillator Model............................................ 32 4.2.2 Lorentz + Drude Oscillator Model ................................. 33 4.2.3 Tauc-Lorentz Parameterization ..................................... 33 4.2.4 Cauchy Model ....................................................... 35 4.3 Fitting Algorithm ............................................................ 36 4.3.1 The Gradient Method ............................................... 36 4.3.2 The Inverse Hessian Method........................................ 37 4.3.3 The Levenberg-Marquardt Algorithm .............................. 38 4.4 Covariance and Correlation ................................................. 39 4.5 Free Parameter Space ....................................................... 41 5. Composition and Thickness Determination in Monolithic BST ................ 42 5.1 Film Synthesis ............................................................... 42 5.2 Characterization ............................................................. 42 5.3 Building the Physical Model ................................................ 46 5.3.1 BST on Pt Substrate ................................................ 48 5.3.2 BST on Si Substrate ................................................ 49 iii 5.3.3 Index Grading ....................................................... 50 5.3.4 Roughness Layer ..................................................... 51 5.4 Method ....................................................................... 52 5.4.1 Notes on the Tauc Plot ............................................. 56 5.4.2 Effect of Annealing Procedure ...................................... 57 5.5 Analysis ...................................................................... 59 5.5.1 Error in Composition................................................ 61 6. Composition and Thickness Determination in Multi-layer BST................ 63 6.1 Film Synthesis ............................................................... 63 6.1.1 Annealing Procedure ................................................ 63 6.2 Characterization ............................................................. 63 6.2.1 Focused Ion Beam Preparation of TEM Samples ................. 64 6.2.2 Transmission Electron Microscopy ................................. 65 6.3 Analysis and Proposed Model .............................................. 65 7. Conclusion ......................................................................... 67 7.1 Future Work ................................................................. 67 8. Appendix ........................................................................... 69 8.1 Sample List................................................................... 69 8.2 Igor Source Code for Tauc Plot............................................. 72 8.3 XRD results .................................................................. 73 Bibliography ........................................................................... 75 iv List of Figures 2.1 Structure of BST in cubic perovskite phase.................................... 4 2.2 Curie temperature dependence on BST composition. Plotted as a function of STO content .................................................................. 6 2.3 Thin-film deposition techniques................................................. 7 2.4 Different types of grading in multi-layer films. ................................ 9 2.5 Electric displacement plotted against electric field for both \up" and \down" compositionally graded BST multi-layer thin- films. .......................... 11 2.6 Effect of extent of grading on temperature insensitivity of the dielectric response .......................................................................... 12 2.7 Comparison of the fundamental bandgap and the observed bandgap, where energy is plotted for DOS for the CB and VB. ................................ 17 2.8 Identification of the bandgap provides a means by which composition may be determined. ................................................................... 18 2.9 Defect states (which are more present in amorphous BST) add a tail to the absorption curve, and effectively lower the `bandgap' of the material ... 20 2.10 Schematic of Fresnel reflection with Snell's law................................ 22 3.1 J.A. Woollam ellipsometer used for this work. ................................ 26 3.2 Schematic representation of VASE. ............................................ 27 4.1 Process diagram of the method for obtaining extinction coefficient. ......... 30 4.2 Sample model geometry, pictured here is the monolithic case. ............... 31 5.1 Key equipment for MOSD sample production belonging to Dr. Alpay and the Functional Materials Group
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