Eshelby's problem for two-dimensional piezoelectric inclusions of arbitrary shape

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 456, Issue 1997, 2000, Pages 1051-1068

  Ru, C Q ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Electroelastic field; Eshelby inclusion; Piezoelectric material; Plane problem; Strained semiconductor devices

Indexed keywords

EID: 0001325738     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2000.0550     Document Type: Article

References (31)

1. Adachi, S. 1985 GaAs, AlAs, and AlxGai_xAs: material parameters for use in research and device applications. J. Appl. Phys. 58, R1-R29.
2. Benveniste, Y. 1993 Exact results in the micromechanics of fibrous piezoelectric composites exhibiting pyroelectricity. Proc. R. Soc. Lond. A 441, 59-81.
3. Caridi, E. A., Chang, T. Y., Goossen, K. W. & Eastman, L. F. 1990 Direct demonstration of a misfit strain-generated electric field in a [111] growth axis zinc-blende heterostructure. Appl. Phys. Lett. 56, 659-661.
4. Chung, M. Y. & Ting, T. C. T. 1996 Piezoelectric solid with an elliptic inclusion or hole. Int. J. Solids Struct. 33, 3343-3361.
5. Davies, J. H. 1998 Elastic and piezoelectric fields around a buried quantum dot: a simple picture. J. Appl. Phys. 84, 1358-1365.
6. Downes, J. & Faux, D. A. 1995 calculation of strain distribution in multiple-quantum well strained-layer structures. J. Appl. Phys. 77, 2444-2447.
7. Dünn, M. L. 1994 Electroelastic Green's functions for transversely isotropic piezoelectric media and their application to the solution of inclusion and inhomogeneity problems. Int. J. Engng Sci. 32, 119-131.
8. Dunn, M. L. & Taya, M. 1993 An analysis of piezoelectric composite materials containing ellipsoidal inhomogeneities. Proc. R. Soc. Land. A 443, 265-287.
9. Dunn, M. L. & Wienecke, H. A. 1997 Inclusions and inhomogeneities in transversely isotropic piezoelectric solids. Int. J. Solids Struct. 34, 3571-3582.
10. England, A. H. 1971 Complex variable methods in elasticity. Wiley-Interscience.
11. Faux, D. A., Downes, J. R. & O'Reilly, E. P. 1996 A simple method for calculating strain distribution in quantum-wire structures. J. Appl. Phys. 80, 2515-2517.
12. Faux, D. A., Downes, J. R. & O'Reilly, E. P. 1997 Analytic solutions for strain distribution in quantum-wire structures. J. Appl. Phys. 82, 3754-3762.
13. Freund, L. B. & Gosling, T. J. 1995 Critical thickness condition for growth of strained quantum wires in substrate V-grooves. Appl. Phys. Lett. 66, 2822-2824.
14. Gosling, T. J. & Willis, J. R. 1995 Mechanical stability and electronic properties of buried strained quantum wire arrays. J. Appl. Phys. 77, 5601-5610.
15. Grundmann, M., Stier, O. & Bimberg, D. 1994 Symmetry breaking in pseudomorphic V-groove quantum wires. Phys. Rev. B 50, 14187-14192.
16. Grundmann, M., Stier, O. & Bimberg, D. 1995 InAs/GsAs pyramidal quantum dots: strain distribution, optical phonons, and electronic structures. Phys. Rev. B 52, 11969-11981.
17. Ivanov, V. I. & Trubetakov, M. K. 1995 Handbook of conformai mapping with computer-aided visualization. Boca Raton, FL: CRC.
18. Kantorovich, L. V. & Krylov, V. I. 1958 Approximate methods of higher analysis. Interscience.
19. Li, J. Y. & Dünn, M. L. 1998 Anisotropie coupled-field inclusion and inhomogeneity problems. Phil. Mag. A 77, 1341-1350.
20. Lothe, J. & Barnett, D. M. 1976 Integral formulation for surface waves in piezoelectric crystals. J. Appl. Phys. 47, 1799-1807.
21. Lu, P. & Williams, F. W. 1998 Green functions of piezoelectric material with an elliptic hole or inclusion. Int. J. Solids Struct. 35, 651-664.
22. Masumura, R. A. & Chou, Y. T. 1982 Anti-plane eigenstrain problem of an elliptic inclusion in an anisotropic half space. J. Appl. Mech. 49, 52-54.
23. Muskhelishvili, N. I. 1963 Some basic problems of the mathematical theory of elasticity. Groningen: Noordhoff.
24. Nishi, K., Yamaguchi, A. A., Ahopelto, J., Usui, A. & Sakaki, H. 1994 Analysis of localized confinement potential in semiconductor strained wires and dots buried in lattice-mismatched materials. J. Appl. Phys. 76, 7437-7445.
25. O'Reilly, E. P. &: Adams, A. R. 1994 Band-structure engineering in strained semiconductor lasers. IEEE Jl Quantum Electronics 30, 366-379.
26. Ru, C. Q. 1999 Analytic solution for Eshelby's problem of an inclusion of arbitrary shape in a plane or half-plane. J. Appl. Mech. 66, 315-322.
27. Savin, G. N. 1961 Stress concentration around holes. Pergamon.
28. Smith, D. L. & Mailhiot, C. 1988 Piezoelectric effects in strained-layer superlattices. J. Appl. Phys. 63, 2717-2719.
29. Stroh, A. N. 1958 Dislocation and cracks in anisotropic elasticity. Phil. Mag. 7, 625-646.
30. Suo, Z., Kuo, C. M., Barnett, D. M. & Willis, J. R. 1992 Fracture mechanics for piezoelectric ceramics. J. Mech. Phys. Solids 40, 739-765.
31. Wang, B. 1992 Three-dimensional analysis of an ellipsoidal inclusion in a piezoelectric material. Int. J. Solid Struct. 29, 293-308.