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Elastic Fields in Quantum Dot Structures with Arbitrary Shapes and Interface Effects

  • H. J. Chu
  • H. L. Duan
  • J. Wang
  • B. L. Karihaloo
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 13)

Abstract

Elastic fields in quantum dot (QD) structures affect their physical and mechanical properties, and they also play a significant role in their fabrication. The elastic fields in QD structures may be induced by mismatches in the coefficients of thermal expansion and the lattice constants of species, by defects, and by external loading. The calculation of the elastic fields in QD structures is complicated by several factors: by the complex shapes of QDs; by the anisotropy of the material species; and by the interface effects at the nano scale. In this paper we present a general approach to the calculation of the elastic fields in QD structures of arbitrary shape. This approach can also deal with the anisotropy of the QD material, the non-uniformity of its composition, the mismatch in the elastic constants of the matrix and the QD, and the interface effect. The effects of these factors on the elastic fields are depicted by analytical and numerical results.

Keywords

Interface Stress Interface Effect Elastic Field Stiffness Tensor Comparison Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Chu H.J. and Wang J., 2005, Strain distribution in arbitrarily shaped quantum dots with nonuniform composition, J. Appl. Phys. 98: 034315.CrossRefADSGoogle Scholar
  2. 2.
    Chu H.J. and Wang, J., 2005, An approach for calculating strain distributions in arbitrarily shaped quantum dots. Chin. Phys. Lett. 22: 667–670.CrossRefADSGoogle Scholar
  3. 3.
    Chu H.J., 2006, Mechanics of semiconductor quantum dot structures. PhD Thesis, Peking University.Google Scholar
  4. 4.
    Davies J.H., 2003, Elastic field in a semi-infinite solid due to thermal expansion or a coherently misfitting inclusion, J. Appl. Mech. 70: 655–660.MATHCrossRefGoogle Scholar
  5. 5.
    Downes J.R. and Faux D.A., 1995, Calculation of strain distributions in multiple-quantum-well strained-layer structures, J. Appl. Phys. 77: 2444–2447.CrossRefADSGoogle Scholar
  6. 6.
    Downes J.R., Faux D.A., and O'Reilly E.P., 1997, A simple method for calculating strain distributions in quantum dot structures, J. Appl. Phys. 81: 6700–6702.CrossRefADSGoogle Scholar
  7. 7.
    Duan H.L., Wang J., Huang Z.P., and Karihaloo B.L., 2005, Eshelby formalism for nano-inhomogeneities, Proc. R. Soc. A 461: 3335–3353.MATHCrossRefADSMathSciNetGoogle Scholar
  8. 8.
    Freund L.B. and Johnson H.T., 2001, Influence of strain on functional characteristics of nano-electronic devices, J. Mech. Phys. Solids 49: 1925–1935.MATHCrossRefADSGoogle Scholar
  9. 9.
    Gosling T.J., and Willis J.R., 1995, Mechanical stability and electronic properties of buried strained quantum wire arrays, J. Appl. Phys. 77: 5601–5610.CrossRefADSGoogle Scholar
  10. 10.
    Grundmann M., Stier O., and Bimberg D., 1995, InAs/GaAs pyramidal quantum dots: Strain distribution, optical phonons, and electronic structure, Phys. Rev. B 52: 11969–11981.CrossRefADSGoogle Scholar
  11. 11.
    Gunnella R., Castrucci P., Pinto N., Davoli I., Sébilleau D., and Crescenzi M.D., 1996, X-ray photoelectron-diffraction study of intermixing and morphology at the Ge/Si(001) and Ge/Sb/Si(001) interface, Phys. Rev. B 54: 8882–8891.CrossRefADSGoogle Scholar
  12. 12.
    Ikeda A., Sumitomo K., Nishioka T., Yasue T., Koshikawa T., and Kido Y., 1997, Intermixing at Ge/Si(001) interfaces studied by surface energy loss of medium energy ion scattering, Surf. Sci. 385: 200–206.CrossRefADSGoogle Scholar
  13. 13.
    Makeev M.A., Wenbin Yu, and Madhukar A., 2004, Atomic scale stresses and strains in Ge/Si(001) nanopixels: An atomistic simulation study, J. Appl. Phys. 96: 4429–4443.CrossRefADSGoogle Scholar
  14. 14.
    Migliorato M.A., Cullis A.G., Fearn M., and Jefferson J.H., 2002, Atomistic simulation of strain relaxation in InxGa1-xAs/GaAs quantum dots with nonuniform composition, Phys. Rev. B 65: 115316.CrossRefADSGoogle Scholar
  15. 15.
    Migliorato M.A., Cullis A.G., Fearn M., and Jefferson J.H., 2002, Atomistic simulation of InxGa1-xAs/GaAs quantum dots with nonuniform composition, Phys. E 13: 1147–1150.CrossRefGoogle Scholar
  16. 16.
    Patthey L., Bullock E.L., Abukawa T., Kono S., and Johansson L.S.O., 1995, Mixed Ge-Si dimer growth at the Ge/Si(001)-(2×1) surface, Phys. Rev. Lett. 75: 2538–2541.PubMedCrossRefADSGoogle Scholar
  17. 17.
    Pearson G.S. and Faux D.A., 2000, Analytical solutions for strain in pyramidal quantum dots, J. Appl. Phys. 88: 730–736.CrossRefADSGoogle Scholar
  18. 18.
    Sharma P. and Ganti S., 2004, Size-dependent Eshelby's tensor for embedded nano-inclusions incorporating surface/interface, J. Appl. Mech. 71: 663–671.MATHCrossRefGoogle Scholar
  19. 19.
    Sharma P., Ganti S., and Bhate, N., 2003, Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl. Phys. Lett. 82: 535–537.CrossRefADSGoogle Scholar
  20. 20.
    Uberuaga B.P., Leskovar M., Smith A.P., Jónsson H., and Olmstead M., 2000, Diffusion of Ge below the Si(100) surface: theory and experiment, Phys. Rev. Lett. 84: 2441–2444.PubMedCrossRefADSGoogle Scholar
  21. 21.
    Vegard L., 1921, The constitution of the mixed crystals and the filling of space of the atoms. Z. Physik 5: 17–26.CrossRefADSGoogle Scholar
  22. 22.
    Wang J. and Chu H.J., 2006, A perturbation theory for calculating strain distributions in heterogeneous and anisotropic quantum dot structures. J. Appl. Phys. 100: 053520.CrossRefADSGoogle Scholar
  23. 23.
    Yeom H.W., Sasaki M., Suzuki S., Sato S., Hosoi S., Iwabuchi M., Higashiyama K., Fukutani H., Nakamura M., Abukawa T., and Kono S., 1997, Existence of a stable intermixing phase for monolayer Ge on Si(001), Surf. Sci. 381: L533.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, B.V. 2009

Authors and Affiliations

  • H. J. Chu
    • 1
  • H. L. Duan
    • 2
    • 3
  • J. Wang
    • 3
  • B. L. Karihaloo
    • 4
  1. 1.College of Hydraulic Science and EngineeringYangzhou UniversityP.R. China
  2. 2.Institute of NanotechnologyForschungszentrum KarlsruheGermany
  3. 3.LTCS and College of EngineeringPeking UniversityBeijingP.R. China
  4. 4.School of EngineeringCardiff University, Queen's BuildingsCardiffUK

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