An analytical model for the energetics of quantum dots: Beyond the small slope assumption

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

Volumn 462, Issue 2076, 2006, Pages 3523-3553

  Gill, S P A ^a   Cocks, A C F ^b  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Elastic strain energy; Heteroepitaxial systems; Phase diagrams; Quantum dots; Shape transitions

Indexed keywords

EID: 33947260967     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2006.1723     Document Type: Article

References (29)

1. Cammarata, R. C. & Sieradzki, K. 1994 Surface and interface stresses. Annu. Rev. Mater. Sci. 24, 215-234.
2. Chiu, C.-H. 1999 The self-assembly of uniform heteroepitaxial islands. Appl. Phys. Lett. 75, 3473. (doi:10.1063/1.125300)
3. Chiu, C.-H. 2004 Stable and uniform arrays of self-assembled nanocrystalline islands. Phys. Rev. D 69, 165 413. (doi:10.1103/PhysRevB.69.165413)
4. Chiu, C.-H. & Poh, C. T. 2005 Strain energy of nanoislands on strained film-substrate systems. Phys. Rev. D 71, 045400. (doi:10.1103/PhysRevB.71.045406)
5. Cocks, A. C. F. & Gill, S. P. A. Submitted. A kinetic model for the formation and growth of quantum dots: beyond the small slope assumption. Proc. R. Soc. A.
6. Constantini, G., Ratelli, A., Manzano, C., Acosta-Diaz, P., Katsaros, G., Songmuang, R., Schmidt, O. G., Känel, H. v. & Kern, K. 2005 Pyramids and domes in the InAs/GaAs(001) and Ge/Si(001) systems. J. Cryst. Growth 278, 38-45. (doi:10.1016/j.jcrysgro.2004.12.047)
7. Daruka, I., Tersoff, J. & Barabasi, A.-L. 1999 Shape transition in growth of strained islands. Phys. Rev. Lett. 82, 2753-2756. (doi:10.1103/PhysRevLett.82.2753)
8. Eisenberg, H. R. & Kandel, D. 2005 Formation, ripening and stability of epitaxially strained island arrays. Phys. Rev. B 71, 115423. (doi:10.1103/PhysRevB.71.115423)
9. Floro, J. A., Lucadamo, G. A., Chason, E., Freund, L. B., Sinclair, M., Twesten, R. D. & Hwang, R. Q. 1998 SiGe island shape transition induced by elastic repulsion. Phys. Rev. Lett. 80, 4717. (doi:10.1103/ PhysRevLett.80.4717)
10. Freund, L. B. & Suresh, S. 2003 Thin film materials-stress, defect formation and surface evolution. Cambridge, UK: Cambridge University Press.
11. Gill, S. P. A. 2003 Self-organised growth on strained substrates: the influence of anisotropic strain, surface energy and surface diffusivity. Thin Solid Film 423, 136-145. (doi:10.1016/S0040-6090(02)01017-9)
12. Howe, P., Le Ru, E. C., Murray, R. & Jones, T. S. 2005 Indium segregation during multilayer InAs/GaAs(001) quantum dot formation. J. Cryst. Growth 278, 57-60. (doi:10.1016/j.jcrysgro.2004.12.053)
13. Koenraad, P. M., Bruls, D. M., Davies, J. H., Gill, S. P. A., Long, F., Hopkinson, M., Skolnick, M. & Wolter, J. H. 2003 Composition profiling at the atomic scale in IU-V nanostructures by cross-sectional STM. Physica E 17, 526-532. (doi:10.1016/S1386-9477(02)00860-3)
14. Lach-hab, M., Papaconstantopoulos, D. A. & Mehl, J. M. 2002 Electronic structure calculations of lead chalcogenides PbS, PbSe and PbTe. J. Phys. Chem. Solids 63, 833-841. (doi:10.1016/ 50022-3697(01)00237-2)
15. Lin, K. C., Chiu, Y. H., Lin, J. H. & Pai, W. W. 2005 A quantitative analysis of the shape transition of Ge islands on Si(100) with NC-AFM. Nanotechnology 16, S63-S67. (doi:10.1088/ 0957-4484/16/3/012)
16. Long, F., Gill, S. P. A. & Cocks, A. C. F. 2001 Effect of surface-energy anisotropy on the kinetics of quantum dot formation. Phys. Rev. D 64, 1307-1310.
17. 4(001) thin films: tunable growth from pyramidal clusters to a {111} fully faceted surface. Phys. Rev. D 70, 045403. (doi:10.1103/PhysRevB.70.045403)
18. 3(100). Surf. Sci. 589,120-128. (doi:10.1016/j.susc.2005.05.062)
19. Mariette, H. 2005 Formation of self-assembled quantum dots induced by the Stranski-Krastanow transition: a comparison of various semiconductor systems. C.R. Phys. 6, 23-32. (doi:10.1016/ j.crhy.2004.11.003)
20. Raab, A. & Springholz, G. 2000 Oswald ripening and shape transitions of self-assembled PbSe quantum dots on PbTe(111) during annealing. Appl. Phys. Lett. 77, 2991-2993. (doi:10.1063/1.1323733)
21. Raab, A., Lechner, R. T. & Springholz, G. 2002 Self-organized lateral ordering for vertically aligned PbSe/PbEuTe quantum-dot superlattices. Appl. Phys. Lett. 80, 1273. (doi:10.10G3/1.1447319)
22. Ross, F. M., Tersoff, J. & Tromp, R. M. 1998 Coarsening of self-assembled Ge quantum dots on Si(001). Phys. Rev. Lett. 80, 984-987. (doi:10.1103/PhysRevLett.80.984)
23. Rudd, R. E., Briggs, G. A. D., Button, A. P., Medeiros-Ribeiro, G. & Stanley Williams, R. 2003 Equilibrium model of bimodal distributions of epitaxial island growth. Phys. Rev. Lett. 90, 146 101. (doi:10.1103/PhysRevLett.90.146101)
24. Shchukin, V. A., Bimberg, D., Munt, T. P. & Jesson, D. E. 2004 Elastic interaction and self-relaxation energies of coherently strained conical islands. Phys. Rev. D 70, 085416. (doi:10.1103/ PhysRevB.70.085416)
25. Wang, L. G., Kratzer, P., Scheffler, M. & Moll, N. 1999 Formation and stability of self-assembled coherent islands in highly mismatched heteroepitaxy. Phys. Rev. Lett. 82, 4042. (doi:10.1103/ PhysRevLett.82.4042)
26. Zhang, Y. W. & Bower, A. F. 2001 Three-dimensional analysis of shape transitions in strained-heteroepitaxial islands. Appl. Phys. Lett. 78, 2706. (doi:10.1063/1.1354155)
27. Zhang, Y. W., Xu, S. J. & Chiu, C.-H. 1999 Vertical self-alignment of quantum dots in superlattice. Appl. Phys. Lett. 74, 1809. (doi:10.1063/1.123093)
28. Zhang, Y. W., Bower, A. F. & Liu, P. 2003 Morphological evolution driven by strain induced surface diffusion. Thin Solid Films 424, 9-14. (doi:10.1016/S0040-G090(02)00897-0)
29. 2O structures by in situ oxidation of Cu(100). Phys. Rev. Lett. 89, 106 101. (doi:10.1103/PhysRevLett.89.106101)