Elastic Strain Engineering in Silicon and Silicon-Germanium Nanomembranes By Deborah Marie Paskiewicz A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Materials Science) at the UNIVERSITY OF WISCONSIN-MADISON 2012 Date of final oral examination: 11/14/12 The dissertation is approved by the following members of the Final Oral Committee: Max G. Lagally, Professor, Materials Science and Engineering Mark A. Eriksson, Professor, Physics Thomas F. Kuech, Professor, Chemical and Biological Engineering Paul G. Evans, Associate Professor, Materials Science and Engineering Irena Knezevic, Associate Professor, Electrical and Computer Engineering ©Copyright by Deborah Marie Paskiewicz 2012 All Rights Reserved i Abstract Elastic Strain Engineering in Silicon and Silicon-Germanium Nanomembranes Deborah M. Paskiewicz Under the supervision of Professor Max G. Lagally At the University of Wisconsin-Madison Strain in crystalline materials alters the atomic symmetry, thereby changing materials properties. Controlling the strain (its magnitude, direction, extent, periodicity, symmetry, and nature) allows tunability of these new properties. Elastic strain engineering in crystalline nanomembranes (NMs) provides ways to induce and relax strain in thin sheets of single- crystalline materials without exposing the material to the formation of extended defects. I use strain engineering in NMs in two ways: (1) elastic strain sharing between multiple layers using the crystalline symmetry of the layers to induce unique strain distributions, and (2) complete elastic relaxation of single-crystalline alloy NMs. In both cases, NM strain engineering methods enable the introduction of unique strain profiles or strain relaxation in ways not compatible with conventional bulk processing, where strain destroys the long-range crystallinity. Elastically strain-shared NMs are fabricated by releasing multi-layer thin film heterostructures from the original host substrate. If one layer of the original heterostructure contains strain, the strain will share between the layers of the freestanding NM. The extent of strain sharing will depend on the relative thicknesses, the ratio of the elastic moduli between ii the materials, and elastic symmetry of the layers. I calculate strain distributions in flat NMs between layers with 2-fold and 4-fold elastic symmetry. I verify my calculations with experimental proof of two examples: (1) strain sharing between biaxially isotropic layers, Si/SiGe/Si(001), and (2) strain sharing between biaxially anisotropic layers, Si/SiGe/Si(110). Strain engineering in NMs is also used to relax strain elastically in thin materials that are difficult to fabricate with conventional bulk crystal growth techniques. The SiGe alloy is one such material. Thin films of SiGe grow uniformly and elastically strained on Si substrates. I release the SiGe layer from the Si growth template with NM fabrication processes and allow the SiGe allow to relax elastically to the appropriate bulk lattice constant. I confirm the high structural quality and strain uniformity of these new materials, and demonstrate their use as substrates for technologically relevant epitaxial films by growing strained Si layers and thick, lattice-matched SiGe alloy layers on them. I compare the structural quality of epitaxial films grown on SiGe NMs to those grown on plastically relaxed SiGe substrates. iii Acknowledgements I would like to thank all the people whose assistance and support have made this work possible. My research advisor, Max Lagally, has provided me with the encouragement and advice needed to carry out my thesis research and grow professionally. Thank you for helping me develop my research skills and creating an environment where I was free to work on many projects. I also appreciate the scientific guidance and professional advice of Professors Paul Evans, Mark Eriksson, and Kevin Turner. All of which helped me advance my research and shape my career path. Thanks to all of the Lagally group members, past and present, who have provided feedback on my research and helped me with experiments. I’d especially like to thank Don Savage for assistance in the lab and many valuable discussions. I appreciate all the conversations, both research and non-research related, with my officemates Arnold Kiefer, Anna Clausen, José Sánchez-Pérez, Boy Tanto, and RB Jacobson. Thank you to Anna for teaching me TEM sample prep, and José for helping me fix the MBE more times than we can count. Thank you to all of the staff members and scientists who assisted me with the experimental work in this thesis. In particular, staff at the Wisconsin Center for Applied Microelectronics (WCAM) for cleanroom training and staff at the Materials Science Center (MSC) for help with the materials characterization (XRD, TEM, and Raman) needed for this work. I thank Martin Holt at the Nanoprobe station at the Advanced Photon Source for helping me collect the data for the x-ray microdiffraction experiments, and Paul Evans for letting me iv use some of his beam time to do so. Thank you to Soitec, and in particular George Celler, for providing SOI(110). I acknowledge fellowship support from the following programs: the Rae and Anne Herb UW Materials Science Program Fellowship, the National Defense Science and Engineering Graduate (NDSEG) Fellowship, and the National Science Foundation Graduate Research Fellowship (NSFGRF). Funding for this research was also provided by the DOE. Lastly, thank you to my family for your encouragement and emotional support through the many highs and lows I have experienced while in school. A special thank you to my husband, David, for your constant support and patience during these years, and for making me laugh every day. v Table of Contents Abstract ................................................................................................................................. i Acknowledgements .............................................................................................................. iii Introduction .......................................................................................................................... 1 Chapter 1 Si/SiGe Thin Film Heterostructures ........................................................................ 7 1.1 Crystalline structure and materials properties of Si, SiGe, and Ge ............................................................... 7 1.2 Bulk crystal growth .................................................................................................................................... 11 1.2.1 Silicon ........................................................................................................................................................ 12 1.2.2 Silicon-Germanium .................................................................................................................................... 14 1.3 Heteroepitaxial growth ............................................................................................................................. 20 1.3.1 Growth modes .......................................................................................................................................... 21 1.3.2 Epitaxial-growth techniques ..................................................................................................................... 22 1.3.3 Plastic strain relaxation ............................................................................................................................. 28 1.3.4 Critical thickness ....................................................................................................................................... 32 1.3.5 Growth on compliant substrates .............................................................................................................. 36 1.3.6 Plastically relaxed SiGe substrates ............................................................................................................ 38 1.4 Changes in materials properties with strain .............................................................................................. 43 1.4.1 Electronic band structure .......................................................................................................................... 43 1.4.2 Optical properties ..................................................................................................................................... 48 1.4.3 Adverse effects of crystalline defects on materials properties ................................................................. 49 1.5 Experimental techniques for measuring strain .......................................................................................... 50 1.5.1 X-ray diffraction ........................................................................................................................................ 50 1.5.2 X-ray micro/nanodiffraction ..................................................................................................................... 53 1.5.3 Micro-Raman spectroscopy ...................................................................................................................... 55 1.6 Chapter summary ...................................................................................................................................... 60 1.7 References ................................................................................................................................................