Atomistic Monte Carlo calculation of critical layer thickness for coherently strained siliconlike structures

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Abstract
Monte Carlo based techniques were used to study the stability of thin, coherently strained layers of mismatched siliconlike semiconductor material. The atomic interaction used for this study is the Stillinger–Weber potential [Phys. Rev. B 31, 5262 (1985)], modified to allow modeling of mismatched materials. Layers from 3 to 80 Å thickness were considered. For layers greater than about 20 Å thickness, the critical layer thickness is accurately described by the continuum theory of Matthews and Blakeslee [J. Cryst. Growth 27, 118 (1974)]. For thinner layers, however, the strain energy associated with misfit dislocations varies from the continuum value, resulting in smaller critical layer thickness, to the extent that critical mismatch as a function of layer thickness becomes nonmonotonic for the thinnest films considered.