Equilibrium theory of the Stranski-Krastanov epitaxial morphology

Abstract

We present a theory of the equilibrium morphology adopted by N atoms of one material when they crystallize epitaxially onto the surface of a dissimilar material. The discussion is limited to the case of the so-called Stranski-Krastanov morphology where a strongly bound but elastically strained wetting layer coats the substrate. The arrangement of atoms atop this layer is determined by minimizing an approximate total energy expression derived for a set of vertically coupled Frenkel-Kontorova chains of finite yet variable length. In this way, both elastic and plastic strain accommodation are treated with a common formalism. Our semi-analytic treatment permits us to compare very rapidly the energy of essentially all configurations of N atoms (up to about N = 5000) including uniform films, coherent islands and dislocated islands. The results are presented in the form of a morphological phase diagram as a function of misfit, surface energy and total particle number for the case of diamond structure materials. Coherent islands are found to be stable in a non-negligible portion of the phase diagram and the relevant phase boundaries are well predicted by simple analytic expressions. A kinetic interpretation of the results is possible when the variable N is redefined appropriately.