Finite Substrate Effects on Critical Thickness in Epitaxial Systems

Abstract

During the growth of an epitaxial overlayer on a thick substrate (GeSi on Si), an interfacial misfit dislocation becomes energetically favourable on exceeding the critical thickness. In substrates of finite thickness, the value of critical thickness is altered with respect to thick substrates. Thin substrates can bend and partially relax the coherency stresses, thus contributing to the altered value of the critical thickness. The current work aims at simulating the stress state of a growing finite epitaxial overlayer on a substrate of finite thickness, using finite element method. The numerical model is used to calculate the critical thickness for substrates with finite thickness. Eigenstrains will be imposed in selected regions in the domain towards this end. Size of the substrate for which it is not energetically favourable to accommodate a misfit dislocation is determined from the simulations (i.e. the system remains coherent for substrates below this thickness). Important effects arising in the transition regime of substrate thicknesses are also investigated.