Elastic field in a semi-infinite solid due to thermal expansion or a coherently misfitting inclusion

Journal of Applied Mechanics, Transactions ASME

Volumn 70, Issue 5, 2003, Pages 655-660

  Davies, J H ^a  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CMOS INTEGRATED CIRCUITS; POISSON EQUATION; POISSON RATIO; SURFACES; THERMAL EXPANSION; TRACTION (FRICTION);

COHERENTLY MISFITTING INCLUSION; SEMI-INFINITE SOLID;

ELASTICITY;

EID: 0242667910     PISSN: 00218936     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1602481     Document Type: Article

References (40)

1. Boley, B. A., and Weiner, J. H., 1997, Theory of Thermal Stresses, Dover, Mineola, NY.
2. Nowacki, W., 1986, Thermoelasticity, Pergamon, Oxford, UK, 2nd edition.
3. Hu, S. M. 1989, "Stress From a Parallelepipedic Thermal Inclusion in a Half-space," J. Appl. Phys., 66, pp. 2741-2743.
4. Hu, S. M., 1990, "Stress From Isolation Trenches in Silicon Substrates," J. Appl. Phys., 67, pp. 1092-1101.
5. Freund, L. B. 2000, "The Mechanics of Electronic Materials," Int. J. Solids Struct., 37, pp. 185-196.
6. Jain, S. C., Maes, H. E., Pinardi, K., and De Wolf, I. 1996, "Stresses and Strains in Lattice-Mismatched Stripes, Quantum Wires, Quantum Dots, and Substrates in Si Technology," J. Appl. Phys., 79, pp. 8145-8165.
7. Glas, F. 1987, "Elastic State of the Thermodynamic Properties of Inhomogeneous Epitaxial Layers: Application to Immiscible III-V Alloys," J. Appl. Phys., 62, pp. 3201-3208.
8. Glas, F. 1991, "Coherent Stress Relaxation in a Half Space: Modulated Layers, Inclusions, Steps and a General Solution," J. Appl. Phys., 70, pp. 3556-3571.
9. Pinnington, T., Sanderson, A., Tiedje, T., Pearsall, T.P., Kasper, E., and Presting, H. 1992, "Ambient Pressure Scanning Tunneling Microscope Imaging of Hydrogen-Passivated Si/Ge Multilayers," Thin Solid Films, 222, pp. 259-264.
10. Chen, H., Feenstra, R. M., Piva, P. G., Goldberg, R. D., Mitchell, I. V., Aers, G. C., Poole, P. J., and Charbonneau, S. 1999, "Enhanced Group-V Intermixing in InGaAs/InP Quantum Wells Studied by Cross-Sectional Scanning Tunneling Microscopy," Appl. Phys. Lett., 75, pp. 79-81.
11. Gosling, T. J., and Willis, J. R. 1995, "Mechanical Stability and Electronic Properties of Buried Strained Quantum Well Arrays," J. Appl. Phys., 77, pp. 5601-5610.
12. Faux, D. A., Downes, J. R., and O'Reilly, E. P. 1996, "A Simple Method for Calculating Strain Distributions in Quantum-Wire Structures," J. Appl. Phys., 80, pp. 2515-2517.
13. Faux, D. A., Downes, J. R., and O'Reilly, E. P. 1997, "Analytic Solutions for Strain Distributions in Quantum-Wire Structures," J. Appl. Phys., 82, pp. 3754-3762.
14. Grundmann, M., Stier, O., and Bimberg, D. 1995, "InAs/GaAs Pyramidal Quantum Dots: Strain Distribution, Optical Phonons, and Electronic Structure," Phys. Rev. B, 52, pp. 11969-11981.
15. 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, pp. 6700-6702.
16. Pryor, C., Kim, J., Wang, L. W., Williamson, A., and Zunger, A. 1998, "Comparison of Two Methods for Describing the Strain Profiles in Quantum Dots," J. Appl. Phys., 83, pp. 2548-2554.
17. Davies, J. H. 1998, "Elastic and Piezoelectric Fields Around a Buried Quantum Dot: A Simple Picture," J. Appl. Phys., 84, pp. 1358-1365.
18. Davies, J. H. 1999, "Quantum Dots Induced by Strain," Appl. Phys. Lett., 75, pp. 4142-4144.
19. Legrand, B., Grandidier, B., Nuys, J. P., Stiévenard, D., Gérard, J. M., and Thierry-Mieg, V. 1998, "Scanning Tunneling Microscopy and Scanning Tunneling Spectroscopy of Self-Assembled InAs Quantum Dots," Appl. Phys. Lett., 73, pp. 96-98.
20. Chiu, Y. P. 1977, "On the Stress Field Due to Initial Strains in a Cuboid Surrounded by an Infinite Elastic Space," ASME J. Appl. Mech., 44, pp. 587-590.
21. Chiu, Y. P. 1978, "On the Stress Field in Surface Deformation in a Half Space With a Cuboidal Zone in Which Initial Strains are Uniform," ASME J. Appl. Mech., 45, pp. 302-306.
22. Mindlin, R. D., and Cheng, D. H. 1950, "Nuclei of Strain in the Semi-Infinite Solid," J. Appl. Phys., 21, pp. 926-930.
23. Mindlin, R. D., and Cheng, D. H. 1950, "Thermoelastic Stress in the Semi-Infinite Solid," J. Appl. Phys., 21, pp. 931-933.
24. Sen, B. 1951, "Note on the Stresses Produced by a Nuclei of Thermoelastic Strain in a Semi-Infinite Elastic Solid," Q. Appl. Math., 8, pp. 365-369.
25. Goodier, J. N. 1937, "On the Integration of the Thermo-Elastic Equations," Philos. Mag., 23, pp. 1017-1032.
26. Timoshenko, S. P., and Goodier, J. N., 1970, Theory of Elasticity, McGraw-Hill, New York, 3rd edition.
27. Westergaard, H. M., 1952, Theory of Elasticity and Plasticity, Harvard University Press, Cambridge, MA.
28. Barber, J. R. 1987, "Thermoelastic Distortion of the Half-Space," J. Therm. Stresses, 10, pp. 221-228.
29. Barber, J. R., 2002. Elasticity, 2nd Ed., Kluwer, Dordrecht, The Netherlands.
30. Nowacki, W., 1954, "Thermal Stresses in Anisotropic Bodies (I)," Arch. Mech. Stos. (Arch. Mech.) 6, pp. 481-492.
31. Hieke, M. 1955, Z. Angew. Math. Mech., 35, pp. 285-294.
32. Garcia Blanco, S., Glidle, A., Davies, J. H., Aitchison, J. S., and Cooper, J. M. 2001, "Electron Beam Induced Densification of Ge-Doped Flame Hydrolysis Silica for Waveguide Fabrication," Appl. Phys. Lett., 79, pp. 2889-2891.
33. Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.
34. Davies, J. H., Bruls, D. M., Vugs, J. W. A. M., and Koenraad, P. M. 2002, "Relaxation of a Strained Quantum Well at a Cleaved Surface," J. Appl. Phys., 91, pp. 4171-4176.
35. Myklestad, N. O. 1942, "Two Problems of Thermal Stress in the Infinite Solid," ASME J. Appl. Mech., 9, pp. A136-A143.
36. Faivre, G. 1964, "Déformations de Cohérence d'un Précipité Quadratique," Phys. Status Solidi, 35, pp. 249-259.
37. Seo, K., and Mura, T. 1979, "The Elastic Field in a Half Space due to Ellipsoidal Inclusions With Uniform Dilational Eigenstrains," ASME J. Appl. Mech., 46, pp. 568-572.
38. Glas, F. 2001, "Elastic Relaxation of Truncated Pyramidal Quantum Dots and Quantum Wires in a Half Space: An Analytical Calculation," J. Appl. Phys., 90, pp. 3232-3241.
39. Pearson, G. S., and Faux, D. A. 2000, "Analytical Solutions for Strain in Pyramidal Quantum Dots," J. Appl. Phys., 88, pp. 730-736.
40. Lita, B., Goldman, R. S., Phillips, J. D., and Battacharya, P. K. 1999, "Interdiffusion and Surface Segregation and Stacked, Self-Assembled InAs/GaAs Quantum Dots," Appl. Phys. Lett., 75, pp. 2797-2799.