APPLICATION OF MICRO-CANTILEVERS IN CHARACTERIZATION OF CRYSTALLIZATION-INDUCED STRESSES AND MECHANICAL PROPERTIES OF AMORPHOUS THIN FILMS GUO QIANG (B.Sc PEKING UNIVERSITY) (M.Eng MASSACHUSETTS INSTITUTE OF TECHNOLOGY) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN ADVANCED MATERIALS FOR MICRO- AND NANO- SYSTEMS (AMM&NS) SINGAPORE-MIT ALLIANCE NATIONAL UNIVERSITY OF SINGAPORE 2010 ACKNOWLEDGEMENT I feel it a great fortune to work with Prof Li Yi and Prof Carl V Thompson during the past years of my PhD endeavor Both professors are distinguished scientists in their respective fields of expertise and I have learnt from them the rigorous way in which scientific research should be conducted Furthermore, their highly motivated working spirits and serious attitudes towards research have deeply impressed and enlightened me, and will continue to inspire me in my future academic career The two postdocs involved in my PhD project, Dr Johannes Kalb and Dr Zhang Xiaoqiang, are greatly appreciated They had taught me a great deal of hands-on skills in doing experiments and data analysis Additionally, I am indebted to the people who have provided critical help for my research: Prof Sow Chorng Haur from the National University of Singapore (NUS) Department of Physics, for his help in the construction of scanning-laser systems, Mr Chen Gin Seng from NUS Department of Physics for my access to the vacuum annealing equipment, Prof Chua Soo Jin from the Institute of Materials Research and Engineering (IMRE) for my access to the sputter equipment, and Dr Yu Hongbin from the NUS Department of Mechanical Engineering for the use of ZYGO optical interferometer i Special thanks should be given to the Singapore-MIT Alliance (SMA) program Their generous financial support enabled me to obtain an MIT Master’s degree and spend one and half years at MIT to conduct research In particular, I would like to thank the program chairs, Prof Choi Wee Kiong and Prof Carl Thompson, and the administrative executives in charge of the AMMNS program, Ms Juliana Chai and Ms Hong Yanling Last but not least, I would like to thank my wife and my parents This work would not be possible without their constant support and love ii TABLE OF CONTENTS Acknowledgement - i Summary xi List of Tables - xvi List of Figures - xvii List of Symbols xxiii Chapter Background and motivations - 1.1 The definition of glasses and the glass transition behavior - 1.1.1 The definition of glasses 1.1.2 The glass transition behavior - 1.1.3 Kinetic theory of glass formation 1.1.3.1 Crystal nucleation - 1.1.3.1.1 Homogeneous nucleation - 1.1.3.1.2 Heterogeneous nucleation - 11 1.1.3.2 Crystal growth 12 1.1.3.3 Overall transformation kinetics 14 1.1.3.4 The temperature dependence of viscosity 17 1.1.4 Structure of glasses 19 iii 1.2 Metallic glasses - 20 1.2.1 Glass-forming abilities of metallic glasses - 21 1.2.1.1 Qualitative criteria - 23 1.2.1.1.1 The confusion principle 23 1.2.1.1.2 The three empirical rules - 23 1.2.1.2 Quantitative criteria 25 1.2.1.2.1 The Trg criterion - 25 1.2.1.2.2 The ∆Tx criterion 27 1.2.1.2.3 The driving force for crystallization 29 1.2.1.2.4 The density change upon crystallization - 30 1.2.1.3 Summary of glass-forming abilities of metallic glasses - 35 1.2.2 Structure of metallic glasses 35 1.2.2.1 Dense random packing model 36 1.2.2.2 Egami-Waseda model 38 1.2.2.3 Ma model 40 1.2.2.4 Efficient-cluster-packing (Miracle) model 42 1.2.3 Mechanical properties of metallic glasses 45 1.3 Phase-change materials - 47 1.3.1 General introduction - 47 1.3.2 Stresses upon reversible phase changes of phase-change materials 49 iv 1.3.2.1 Crystallization-induced stresses in phase-change thin films characterized by wafer curvature measurements 49 1.3.2.2 Limitations of wafer curvature measurements 51 1.3.3 Comparisons between phase-change materials and metallic glasses 52 1.3.3.1 Glass-forming abilities and the corresponding density changes upon crystallization - 52 1.3.3.2 Mechanical properties 53 1.3.4 Summary of Chapter and motivation of this research project 54 Chapter Background: mechanical properties of materials and beam mechanics for analysis of thin film stresses - 57 2.1 The elastic and plastic responses of materials 57 2.1.1 The definitions of stress and strain - 57 2.1.1.1 Stress 57 2.1.1.2 Strain 58 2.1.2 The elastic response of materials and Hooke’s law 61 2.1.3 The plastic response of materials - 62 2.2 The stresses in thin films 64 2.2.1 The origins of stresses in thin films 64 v 2.2.1.1 The mismatch of lattice parameters of the film and substrate - 64 2.2.1.2 The thermal mismatch between the film and substrate -65 2.2.1.3 The volume change in the film due to phase transformations - 65 2.2.1.4 The residual stress due to sputter deposition 65 2.2.2 The determination of thin film stresses with the simple and extended Stoney formulae 66 2.2.2.1 Constitutive relations between the mismatch strain and the film stress 66 2.2.2.2 The simple Stoney formula 68 2.2.2.3 The extended Stoney formula for films of arbitrary thickness 73 2.2.2.4 The substrate curvature for non-uniform mismatch strains and elastic properties through layer thickness 75 2.3 Experimental techniques to characterize thin film stresses - 76 2.3.1 Diffraction-based methods 77 2.3.2 Spectroscopy-based methods - 78 2.3.3 Curvature-based methods - 79 2.4 Thin film stress measurement using micro-fabricated cantilevers 80 Chapter The fabrication of SiN micro-cantilevers and the supplementary experimental methods 84 vi 3.1 The fabrication of SiN cantilevers - 84 3.1.1 The deposition of low stress, silicon-rich SiN film on single-crystalline (100) Si wafers - 84 3.1.2 Pattern transfer 86 3.1.3 Undercut SiN using potassium hydroxide (KOH) etch 88 3.2 Supplementary experimental methods and equipments - 91 3.2.1 Sputter machines used to deposit the amorphous films - 91 3.2.2 X-ray diffraction (XRD) - 92 3.2.3 Energy dispersive X-ray spectroscopy (EDS) 95 3.2.4 Rutherford Backscattering (RBS) 98 3.2.5 Deflection measurement with Veeco interferometer (NT 2000) - 99 3.2.6 Deflection measurement with conventional optical microscopes - 101 3.2.7 Equipments used to perform furnace annealing of amorphous thin films at elevated temperatures - 102 3.2.7.1 The furnace with a vacuum to crystallize amorphous Cu-Zr thin films - 102 3.2.7.2 The furnace with a vacuum to crystallize amorphous Zr-Cu-Al thin films 103 3.6.7.3 High precision furnace to anneal amorphous phase-change Ge2Te2Sb5 films 103 vii Chapter Crystallization-induced stresses in Ge2Sb2Te5 phase-change thin films 104 4.1 Experimental details - 105 4.2 The analytical model used to calculate the crystallization-induced stresses in phase-change thin films - 106 4.3 Results and discussions 110 4.4 Application: phase-change materials in optically-triggered micro-actuators 115 4.4.1 The analytical model to calculate cantilever tip deflections as a result of crystallization of the phase-change film at the cantilever base 116 4.4.2 The laser setup used to crystallize the phase-change thin films locally at the cantilever base 118 4.4.3 Results - 120 4.4.4 Discussions 123 Chapter Density change upon crystallization of amorphous Cu-Zr thin films 126 5.1 Experimental details - 127 5.1.1 Micro-cantilever experiments - 127 5.1.2 Wedge-casting experiments - 129 viii 5.2 Analytical model for the calculation of density changes 131 5.3 Results and discussions - 134 5.4 Summary 140 Chapter Density change upon crystallization of amorphous Zr-Cu-Al thin films 142 6.1 Sample layout and experimental procedures - 143 6.2 Results and discussions - 149 6.2.1 Global and local trends of density change: individual effects of Zr, Cu, and Al atomic species on the density change upon crystallization of the alloys - 149 6.2.2 Comparison between density change data and particular compositions of high glass-forming ability 155 6.3 Conclusions - 161 Chapter Measurements of Young’s modulus 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Adam S Zeiger, Krystyn J Van Vliet, Yi Li, Carl V Thompson, under review, Scripta Materialia 211 ... micro- fabricated cantilevers were used to investigate the stresses and density changes upon crystallization in amorphous thin films Two classes of materials with distinct properties and significant... of Young’s modulus and coefficients of thermal expansion of amorphous Cu-Zr thin films - 162 7.1 Measurement of Young’s modulus of amorphous Cu-Zr thin films - 162 7.1.1... equipment, Prof Chua Soo Jin from the Institute of Materials Research and Engineering (IMRE) for my access to the sputter equipment, and Dr Yu Hongbin from the NUS Department of Mechanical Engineering