Optical Characterization of Thermal Transport from the Nanoscale to the Macroscale by Aaron Jerome Schmidt Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY (June Aoo?] May 2008 @ Massachusetts Institute of Technology 2008. All rights reserved. Author ............... ....... ...... :Ijipartment of Mechanical Engineering May 21, 2008 Certified by............ Gang Chen Warren and Towneley Rohsenow Professor Thesis Supervisor Accepted by Lallit Anand MASSACHt.SETTS INSTITTEChairman D t t C itt G d t ' eparmen omm ee on ra uae u ens OF TECHNOLOGY JUL 2 9 2008 LIBRARIES McHNES Optical Characterization of Thermal Transport from the Nanoscale to the Macroscale by Aaron Jerome Schmidt Submitted to the Department of Mechanical Engineeringon May 21, 2008, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering Abstract The thermal properties of thin films and material interfaces play an important role in many technologies such as microelectronics and solid-state energy conversion. This thesis examines the characterization of thermal transport over length scales from nanometers upward in solids and liquids using pump-probe optical techniques. The design and implementation of a system that is uniquely suited to thermal measure- ments is described in detail, and the theory for interpreting the measurement results is developed using a linear systems approach, accounting for pulse accumulation effects and anisotropic thermal properties. Cross-plane thin film and bulk thermal conductivity measurements spanning more than two orders of magnitude are presented, along with a discussion on the impor- tance of sample preparation on thermal boundary conductance and thermal conduc- tivity measurements. An approach for measurement of in-plane thermal properties of anisotropic thin films is presented, and as a demonstration the method is used to extract both the cross-plane and in-plane thermal conductivity of highly ordered pyrolytic graphite. In addition, the measurement techniques are extended to liq- uids, providing a way to measure liquid volumes less than 500 nm thick as well as solid-liquid thermal interface conductances. Finally, optical techniques for the study of nanofluids are discussed. Transmission pump-probe measurements on gold nanorods in suspension are presented. The heat transfer dynamics of the rods are measured, and the critical role played by surfactants in the thermal transport between the rod and the surrounding fluid is studied system- atically. An optical transient grating technique is used to explore the bulk thermal and viscous properties of nanofluids. Thermal conductivity measurements show that the observed thermal conductivity enhancement of nanofluids is repeatable and is not a function of the measurement technique, while acoustic attenuation measurements indicate that the nanoparticles do not form clusters in solution. Thesis Supervisor: Gang Chen Title: Warren and Towneley Rohsenow Professor Acknowledgments Many thanks are in order. First on the list is my advisor and mentor, Prof. Gang Chen. His knowledge and drive are inspirational, as is his dedication to his students. Gang displayed patience and understanding during my first three years of Ph.D. research, a time in which I struggled with experimental challenges and produced no significant results. He also pushed me to achieve more than I realized I was capable of, and I am a better person and researcher for it. I am also grateful to the other members of my thesis committee, Prof. John H. Lienhard V and Prof. Keith A. Nelson, for their encouragement and guidance, and to the many inspirational teachers I have had at MIT over the past ten years, especially Prof. Neville Hogan, Prof. John Brisson and Prof. Bora Mikid. It has been a privilege to work with everyone in the Nanoengineering Group, whose members past and present have been a source of lasting friendships and scientific inspiration. I owe special thanks to Ronggui Yang, Arvind Narayanaswamy, and especially Chris Dames, now all professors pursuing their own research, for mentoring me as a new graduate student, and to Xiaoyuan Chen, who gave me a crash-course in optics and helped me set up early versions of our system. I feel a strong connection with Lu Hu and Tom Harris, who joined the group with me and have been great friends through the years, and with Shin Nakamura, for welcoming me into his family and opening my eyes to a new culture. Finally, I would like to thank Matteo Chiesa. His infectious enthusiasm has made working with him a true pleasure, and his presence has had a positive influence on our entire group. I have benefitted enormously from collaboration with colleagues in several other research groups. I owe a great debt to Prof. David Cahill and Xuan Zheng at the University of Illinois at Urbana-Champaign for sharing with me key details on how to build a pump-probe system; without their patient help, much of the work in this thesis would not have been possible. It has been a pleasure and a great learning experience to work in the laboratory of Prof. Keith A. Nelson with Darius Torchinsky, Jeremy Johnson and Christoph Klieber, and to study gold nanorods with Josh Alper of the Hamad-Schifferli Group. I would also like to thank Prof. Sarit Das, who has been generous with his time and instrumental in shaping the final chapter of this thesis. I am grateful to the National Science Foundation, the Department of Defense, and the MIT-Ford Alliance for their generous financial support. Finally, I am grateful to Sheena, for helping me grow as a person, and to my parents, who belong in a category by themselves for their unconditional love and support in everything I've done. Contents 1 Introduction and Background 19 1.1 Optical Techniques for Thermal Measurement . .......... . . 21 1.2 Transport Following Pulsed Laser Heating .......... ... .. 22 1.2.1 Optical Absorption and Carrier Non-equilibrium ..... ... . 22 1.2.2 Thermal Interface Conductance and Transport in the Substrate 26 1.3 Organization of the Thesis ....... ................. 28 2 The Experimental System 31 2.1 Optics ....... ....... ... .... ... ......... 33 2.2 Beam Spot Characterization .... ............ ......... 37 2.3 Instrumentation ............... . .... .......... 40 2.4 Sources of Noise ................. . ..... ......... 43 2.5 Summary ............. . ........... ........ 45 3 Theory and Data Analysis 47 3.1 The Thermal System as an LTI System ............... . . .. . . 47 3.1.1 Introduction ............ ............... 47 3.1.2 Signal Analysis Using the Impulse Response . . . . ... . . . 52 3.1.3 Signal Analysis Using the Frequency Response ..... . . . . 57 3.2 Accumulation Effects ................... ........ 60 3.2.1 Example of Accumulation with a Model System . .. . . . . . 61 3.2.2 Tests for Accumulation . .................. ... 63 3.2.3 Convergence of the Impulse-Response Solution. .. . . . . . 64 3.3 Heat Transfer Analysis ...................... ... . 65 3.3.1 One Dimensional Heat Transfer in Layered Structures . . . . . 66 3.3.2 Extension to Radial Conduction . . . . . . . . . . . . . . . . . 68 3.4 Post Processing .............. ................ 7 1 3.4.1 Fitting Variables ......... ................ 7 1 3.4.2 Determining the Phase Offset . . . . . . . . . . . . . . . . . . 72 3.5 Sensitivity Analysis . ........... . . . . . . . . . . . . . . . . 75 3.6 Sample Results .............. ................ 77 3.6.1 The Impact of the Interface . . . . . . . . . . . . . . . . . . . 78 3.7 Sample Preparation ............ ................ 83 3.7.1 Choice of the Metal Transducer . . . . . . . . . . . . . . . . . 83 3.7.2 Film Thickness Characterization. . . . . . . . . . . . . . . . . 85 3.8 Steady Heating and Linearity ...... . . . . . . . . . . . . . . . . 87 3.9 Summary ................. ................ 9 1 4 Application of the Pump-Probe Technique to Liquids, Anisotropic Properties, and Microstructures 93 4.1 Thermal Conductivity of Liquids . . . . . . . . . . . . . . . . . . . . 93 4.1.1 Experimental Setup and Procedure . . . . . . . . . . . . . . . 94 4.1.2 Theory ... .............. .............. 94 4.1.3 Sensitivity ............... .............. 97 4.1.4 Results . . . . .. ... ... .. ... .............. 99 4.2 In-Plane Thermal Properties ......... . . . . . . . . . . . . . . 106 4.2.1 Highly Ordered Pyrolytic Graphite . . . . . . . . . . . . . . . 106 4.2.2 SiGe Superlattices .......... .............. 111 4.3 Characterization of Microstructures ..... . . . . . . . . . . . . . . 116 4.3.1 Thermal Properties .......... .............. 119 4.3.2 Mechanical Characterization ..... . . . . . . . . . . . . . . 121 4.4 Summary ................... .............. 123 5 Experimental Investigations of Nanofluids 125 5.1 Introduction . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . .. 125 5.2 Transient Absorption of Gold Nanorods . ................ 125 5.2.1 Sample Preparation and Experimental Setup .......... 126 5.2.2 Re sults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.2.3 An alysis . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 131 5.3 Bulk Nanofluid Thermal Conductivity Measurements ........ . 135 5.3.1 Sample Preparation ................... ..... 137 5.3.2 Transient Hotwire System .................... 138 5.3.3 Picosecond Transient Grating System . ............. 140 5.3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 5.4 Viscosity and Clustering ......................... 148 5.4.1 Shear Viscosity .......................... 149 5.4.2 Longitudinal Viscosity and Clustering . ............. 150 5.4.3 Conclusion ................ ............. 156 5.5 Sum m ary . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. 157 6 Summary and Outlook 159 6.1 Sum m ary . . . . . . . . . .. .. . . . . . . . . . . . . . . . . . . .. 159 6.2 Outlook and Conclusion ......................... 161 A Details on Signal Analysis 163 A.1 The Effect of Higher Harmonics ..................... 163 A.2 Proof of Equation 3.14 .......................... 165 A.3 The Sampling Theorem .......................... 166 A.4 Equivalence of the Impulse and Frequency Response Solutions . . . . 167 A.5 Interpretation of the Real and Imaginary Parts . ........... 168