Kinetic Monte Carlo simulation of the nucleation stage of the self-organized growth of quantum dots

doi:10.1016/S0038-1101(98)00076-8

Solid-State Electronics

Volume 42, Issues 7–8, July–August 1998, Pages 1587-1591

https://doi.org/10.1016/S0038-1101(98)00076-8 Get rights and content

Abstract

In this paper we report computer simulations which explain the self-organized growth of quantum dots in the Stranski–Krastanov growth mode of strained semiconductor systems as used, e.g., for quantum dot lasers. Because of the broad range of materials where this effect occurs we adopt an approach via a simple kinetic Monte Carlo simulation. The formation of regular arrays of equally sized quantum dots is explained by the nonlinear interplay of deposition and surface diffusion, and the strain field.

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Acknowledgements

This work was supported by Deutsche Forschungsgemeinschaft in the framework of Sfb 296.

References (21)

E. Steimetz et al.
Appl. Surf. Sci.
(1996)
S. Clarke et al.
Surf. Sci.
(1991)
N.N. Ledentsov et al.
Solid State Electron.
(1996)
Y. Arakawa et al.
Appl. Phys. Lett.
(1982)
Y. Arakawa et al.
IEEE J. Quantum. Electron.
(1986)
D. Bimberg, see these...
Shchukin, V. A., Ledentsov, N. N., Grundmann M. and Bimberg, D., in Optical Spectroscopy of Low Dimensional...
D. Leonard et al.
Appl. Phys. Lett.
(1993)
S. Ruvimov et al.
Phys. Rev. B
(1995)
N.N. Ledentsov et al.
Phys. Rev. B
(1996)

There are more references available in the full text version of this article.

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Citation Excerpt :
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Kinetic Monte Carlo simulation of the nucleation stage of the self-organized growth of quantum dots

Abstract

Section snippets

Acknowledgements

Appl. Surf. Sci.

Surf. Sci.

Solid State Electron.

Appl. Phys. Lett.

IEEE J. Quantum. Electron.

Appl. Phys. Lett.

Phys. Rev. B

Phys. Rev. B