Simulation of inhomogeneous strain in Ge-Si core-shell nanowires

  • Yuhui He
  • Yuning Zhao
  • Chun Fan
  • Xiaoyan Liu
  • Ruqi Han
Research Article

Abstract

This paper studies the elastic deformation field in lattice-mismatched Ge-Si core-shell nanowires (NWs). Infinite wires with a cylindrical cross section under the assumption of translational symmetry are considered. The strain distributions are found by minimizing the elastic energy per unit cell using finite element method. This paper finds that the trace of the strain is discontinuous with a simple, almost piecewise variation between core and shell, whereas the individual components of the strain can exhibit complex variations. The simulation results are prerequisite of strained band structure calculation, and pave a way for further investigation of strain effect on the related transport property simulation.

Keywords

core-shell nanowire strain continuum elasticity 

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References

  1. 1.
    Lauhon L J, Gudiksen M S, Wang D, Lieber C M. Epitaxial coreshell and core-multishell nanowire heterostructures. Nature, 2002, 420(6911): 57–61CrossRefGoogle Scholar
  2. 2.
    Lu W, Xiang J, Timko B P, Wu Y, Lieber C M. One-dimensional hole gas in germanium/silicon nanowire heterostructures. Proceedings of the National Academy of Sciences of the United States of America, 2005, 102(29): 10046–10051CrossRefGoogle Scholar
  3. 3.
    Lin H M, Chen Y L, Yang J, Liu Y C, Yin K M, Kai J J, Chen F R, Chen L C, Chen Y F, Chen C C. Synthesis and characterization of core-shell GaP@GaN and GaN@GaP nanowires. Nano Letters, 2003, 3(4): 537–541CrossRefGoogle Scholar
  4. 4.
    Tateno K, Gotoh H, Watanabe Y. GaAs/AlGaAs nanowires capped with AlGaAs layers on GaAs(311)B substrates. Applied Physics Letters, 2004, 85(10): 1808–1810CrossRefGoogle Scholar
  5. 5.
    Sköld N, Karlsson L S, Larsson M W, Pistol M E, Seifert W, Tragardh J, Samuelson L. Growth and optical properties of strained GaAs-GaxIn1 - xP core-shell nanowires. Nano Letters, 2005, 5(10): 1943–1947CrossRefGoogle Scholar
  6. 6.
    Xiang J, Lu W, Hu Y, Wu Y, Yan H, Lieber C M. Ge/Si nanowire heterostructures as high-performance field-effect transistors. Nature, 2006, 441(7092): 489–493CrossRefGoogle Scholar
  7. 7.
    Liang G, Xiang J, Kharche N, Klimeck G, Lieber C M, Lundstrom M. Performance analysis of a Ge/Si core/shell nanowire field-effect transistor. Nano Letters, 2007, 7(3): 642–646CrossRefGoogle Scholar
  8. 8.
    Liu X W, Hu J, Pan B C. The composition-dependent mechanical properties of Ge/Si core-shell nanowires. Physica E: Low-dimensional Systems and Nanostructures, 2008, 40(10): 3042–3048CrossRefGoogle Scholar
  9. 9.
    De Caro L, Tapfer L. Elastic lattice deformation of semiconductor heterostructures grown on arbitrarily oriented substrate surfaces. Physical Review B, 1993, 48(4): 2298–2303CrossRefGoogle Scholar
  10. 10.
    Landau L, Lifshitz E. Theory of Elasticity. New York: Pergamon, 1959Google Scholar
  11. 11.
    Pryor C, Kim J, Wang L W, Williamson A J, Zunger A. Comparison of two methods for describing the strain profiles in quantum dots. Journal of Applied Physics, 1998, 83(5): 2548–2550CrossRefGoogle Scholar
  12. 12.
    Jogai B. Three-dimensional strain field calculations in coupled InAs/GaAs quantum dots. Journal of Applied Physics, 2000, 88(9): 5050–5055CrossRefGoogle Scholar
  13. 13.
    Cleland A N. Foundations of Nanomechanics. Berlin: Springer, 2003Google Scholar
  14. 14.
    Søndergaard N, He Y H, Fan C, Han R Q, Guhr T, Xu H Q. Strain distributions in lattice mismatched semiconductor core-shell nanowires. Journal of Vacuum Science and Technology B, 2009, 27(2): 827–830CrossRefGoogle Scholar
  15. 15.
    Zienkiewicz O C, Taylor R L. The Finite Element Method. Maidenhead: McGraw-Hill, 1994Google Scholar
  16. 16.
    Vurgaftman I, Meyer J R, Ram-Mohan L R. Band parameters for IIIV compound semiconductors and their alloys. Journal of Applied Physics, 2001, 89(11): 5815–5875CrossRefGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH 2009

Authors and Affiliations

  • Yuhui He
    • 1
  • Yuning Zhao
    • 1
  • Chun Fan
    • 2
  • Xiaoyan Liu
    • 1
  • Ruqi Han
    • 1
  1. 1.Institute of MicroelectronicsPeking UniversityBeijingChina
  2. 2.Computer Center of Peking UniversityBeijingChina

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