EQUILIBRIUM-THEORY OF THE STRANSKI-KRASTANOV EPITAXIAL MORPHOLOGY

We present a theory of the equilibrium morphology adopted by N atoms o f 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 elasti cally strained wetting layer coats the substrate. The arrangement of a toms atop this layer is determined by minimizing an approximate total energy expression derived for a set of vertically coupled Frenkel-Kont orova 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 ene rgy of essentially all configurations of N atoms (up to about N = 5000 ) including uniform films, coherent islands and dislocated islands. Th e results are presented in the form of a morphological phase diagram a s a function of misfit, surface energy and total particle number for t he case of diamond structure materials. Coherent islands are found to be stable in a non-negligible portion of the phase diagram and the rel evant phase boundaries are well predicted by simple analytic expressio ns. A kinetic interpretation of the results is possible when the varia ble N is redefined appropriately.