Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-17T15:47:28.887Z Has data issue: false hasContentIssue false

Spontaneous Formation of Arrays of Strained Islands: Thermodynamics Versus Kinetics

Published online by Cambridge University Press:  10 February 2011

V. A. Shchukin
Affiliation:
Technische Universität Berlin, 10623 Berlin, Germany
N. N. Ledentsov
Affiliation:
Technische Universität Berlin, 10623 Berlin, Germany
D. Bimberg
Affiliation:
Technische Universität Berlin, 10623 Berlin, Germany
Get access

Abstract

Options are discussed which allow to distinguish equilibrium arrays of strained islands from kinetically-controlled arrays. Finite-temperature thermodynamic theory is developed for equilibrium arrays of two-dimensional monolayer-high islands in heteroepitaxial systems at submonolayer coverage. It is shown that the entropy contribution to the Helmholtz free energy of the system favors formation of small islands and results in the shrinkage of the islands with increasing temperature. The average size of islands decreases tremendously with respect to zero-temperature size at temperatures far below the characteristic energy of island formation. Such a temperature dependence can be the basis for decisive experiments aimed to distinguish between thermodynamic and kinetic effects on the formation of arrays of 2D islands. The theory is able to explain results of high-resolution electron microscopy of submonolayer arrays of InAs/GaAs(001) islands. Their formation is predominantly influenced by thermodynamics.

Type
Research Article
Copyright
Copyright © Materials Research Society 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

[⋄]

Permanent address: A.F. Ioffe Physical Technical Institute, St. Petersburg 194021, Russia.

References

REFERENCES

1.Bimberg, D., Grundmann, M., and Ledentsov, N.N., Quantum Dot Heterostructures, Wiley, Chichester (1998).Google Scholar
2.Pehlike, E., Moll, N., Kley, A., and Scheffler, M., Appl. Phys. A 65, pp. 525534 (1997).Google Scholar
3.Shchukin, V.A. and Bimberg, D., Rev. Mod. Phys. 71, pp. 11251171 (1999).Google Scholar
4.Shchukin, V.A., Ledentsov, N.N., P.S. Kop'ev, and Bimberg, D., Phys. Rev. Lett. 75, pp. 29682971 (1995).Google Scholar
5.Madhukar, A., Chen, P., Xie, Q., Konkar, A., Ramachandran, T.R., Kobayashi, N.P., and Viswanathan, R., in Low Dimensional Structures prepared by Epitaxial Growth or Regrowth on Patterned Substrates, Proc. NATO Advanced Workshop, February 20–24, 1995, Ringberg Castle, Germany, edited by Eberl, K., Petroff, P., and Demeester, P., Kluwer, Dordrecht, pp. 1928 (1995); N. Kobayashi, T.R. Ramachandran, P. Chen, and A. Madhukar, Appl. Phys. Lett. 68, pp. 3299–3301 (1996).Google Scholar
6.Jesson, D.E., Chen, K.M., and Pennycook, S.J., MRS Bulletin 21, p. 31 (1996); D.E. Jesson, G. Chen, K.M. Chen, and S.J. Pennycook, Phys. Rev. Lett. 80, pp. 5156–5159 (1998).Google Scholar
7.Wang, L.G., Kratzer, P., Scheffler, M., and Moll, N., Phys. Rev. Lett. 82, pp. 40424045 (1999).Google Scholar
8.Andreev, A.F., Pis'ma Zh. Eksp. Teor. Fiz. 32, pp. 654–656 (1980) [JETP Lett. 32, pp. 640642 (1980)].Google Scholar
9.Marchenko, V.I., Pis'ma Zh. Eksp. Teor. Fiz. 33, pp. 397–398 (1981) [JETP Lett. 33, pp. 381382 (1981)].Google Scholar
10.Tersoff, J. and Tromp, R.M., Phys. Rev. Lett. 70, pp. 27822785 (1993).Google Scholar
11.Alerhand, O.L., Vanderbilt, D., Meade, R.D., and Joannopoulos, J.D., Phys. Rev. Lett. 61, pp. 19731976 (1988).Google Scholar
12.Vanderbilt, D., Surf. Sci. 268, L300 (1992).Google Scholar
13.Zeppenfeld, P., Krzyzowski, M., Romainczuk, C., Comsa, G., and Lagally, M., Phys. Rev. Lett. 72, pp. 27372740 (1994).Google Scholar
14.Ng, K.-O. and Vanderbilt, D., Phys. Rev. B 52, pp. 21772190 (1995).Google Scholar
15.Kern, K., Niehus, H., Schatz, A., Zeppenfeld, P., George, J., and Comsa, G., Phys. Rev. Lett. 67, pp. 855858 (1991).Google Scholar
16.Wang, P.D., Ledentsov, N.N., Torres, C.M. Sotomayor, P.S. Kop'ev, and Ustinov, V.M., Appl. Phys. Lett. 64, pp. 15261528 (1994).Google Scholar
17. V. Bressler-Hill, Lorke, A., Varma, S., Pond, K., Petroff, P.M., and Weinberg, W.H., Phys. Rev. B 50, 84798488 (1994).Google Scholar
18.Strafburg, M., Kutze, V., Pohl, U.W., Hoffmann, A., Broser, I., Ledentsov, N.N., Bimberg, D., Rosenauer, A., Fisher, U.. Gerthsen, D., Krestnikov, I.L., Maximov, M.V., P.S. Kop'ev, and Zh.I. Alferov. Appl. Phys. Lett. 72, pp. 942944 (1998).Google Scholar
19.Kfimmell, T., Weigand, R., Bacher, G., Forchel, A., Leonardi, K., Hommel, D., and Selke, H., Appl. Phys. Lett. 73. pp. 31053107 (1998).Google Scholar
20.Family, F. and P. Meakin. Phys. Rev. Lett. 61, pp. 428431 (1988).Google Scholar
21.Bartelt, M.C. and Evans, J.W., Phys. Rev. B 46, pp. 12675 (1992).Google Scholar
22.Ratsch, C., Zangwill, A.. Smilauer, P., and Vvedensky, D.D., Phys. Rev. Lett. 72, pp. 31943197 (1994).Google Scholar
23.Mo, Y.-W., Kleiner, J.. Webb, M.B., and Lagally, M.G., Phys. Rev. Lett. 66, pp. 19982001 (1991).Google Scholar
24.Ernst, H.-J.. Fabre, F., and Lapujoulade, J., Phys. Rev. B 46, pp. 1929 (1992); J.-K. Zuo, J.F. Wendelken, H. Diirr. and C.-L. Liu. Phys. Rev. Lett. 72, pp. 3064–3067 (1994).Google Scholar
25.Zuo, I.-K. and Wendelken, J.F.. Phys. Rev. Lett. 66, pp. 22272230 (1991).Google Scholar
26.Vidali, W. Li. G.. and Biham, O.Phys. Rev. B 48, p. 8336 (1993).Google Scholar
27.Shchukin, V.A. et at., to be published.Google Scholar
28.Ledentsov, N.N.. Wang, P.D., Torres, C.M. Sotomayor, Yu, A.. Egorov, Maximov, M.V., Ustinov, V.M., Zhukov, A.E., and Kop'ev, P.S.Phys. Rev. B 50, pp. 1217112174 (1994).Google Scholar
29.Gerthsen, D. et al., unpublished.Google Scholar