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

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

References

[1] Lauhon L J, Gudiksen M S, Wang D, Lieber C M. Epitaxial core-shell and core-multishell nanowire heterostructures. Nature, 2002, 420(6911): 57–61

[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): 10046–10051

[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): 537–541

[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): 1808–1810

[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-Ga_xIn_1-xP core-shell nanowires. Nano Letters, 2005, 5(10): 1943–1947

[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): 489–493

[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): 642–646

[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): 3042–3048

[9] De Caro L, Tapfer L. Elastic lattice deformation of semiconductor heterostructures grown on arbitrarily oriented substrate surfaces. Physical Review B, 1993, 48(4): 2298–2303

[10] Landau L, Lifshitz E. Theory of Elasticity. New York: Pergamon, 1959

[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): 2548–2550

[12] Jogai B. Three-dimensional strain field calculations in coupled InAs/GaAs quantum dots. Journal of Applied Physics, 2000, 88(9): 5050–5055

[13] Cleland A N. Foundations of Nanomechanics. Berlin: Springer, 2003

[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): 827–830

[15] Zienkiewicz O C, Taylor R L. The Finite Element Method. Maidenhead: McGraw-Hill, 1994

[16] Vurgaftman I, Meyer J R, Ram-Mohan L R. Band parameters for III-V compound semiconductors and their alloys. Journal of Applied Physics, 2001, 89(11): 5815–5875

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg