Transition thickness of semiconductor heteroepitaxy

In Stranski-Krastanov mode, the transition from two-dimensional growth to t hree-dimensional growth occurs at a certain thickness: a transition thickne ss. In subsequent growth, misfit dislocations are incorporated at the inter -face between the substrate and the epitaxially grown layer. This limited t hickness for coherent growth is called: the critical thickness. An analytic al equation for the transition thickness is derived by the thermodynamical approach in which strain energy and surface energy are taken into account. The three-dimensional island, often called a quantum dot, is stably formed, when the strain energy of the two-dimensional layer exceeds the sum of the relaxed strain energy and the excess surface energy of the three-dimension al island. The equation is applied to obtain the transition thickness of In As/GaAs, InP/ GaP, and Ge/Si which fit fairly well with the experimental re sults. (C) 2000 Published by Elsevier Science S.A. All rights reserved.