Setting up of misfit dislocations in heteroepitaxial growth and critical thicknesses

In a previous work we have shown that the critical layer thickness (CLT) in heteroepitaxial growth of zinc-blende semiconductor compounds, as defined by the minimal energy configuration between the coherent deformation of the layer and the full misfit dislocation (MD) system, varies clearly only with the lattice mismatch η as η−32. We report new results regarding situations defined mainly by the fact that the MD array is, as often observed experimentally, not complete in length or in density. In the simplest case the interfacial MD have a maximum length but only along one direction and the layer is partially relaxed, with a strain energy roughly linear as a function of thickness. Pseudo CLT are found to be smaller than the one of a completely relaxed layer. In the situation of an incomplete interfacial cross-shaped MD, dislocation loops with threading dislocation (TD) lines are assumed and the system involves strain energy value always higher than that of a full MD system. It is shown that the setting up of the full MD system is not progressive but is rather a brutal one, as in a phase transition. Another observation is that partial MD systems lead to apparent CLT different from a complete MD network. In the case of low density MD array, i.e. with MD infinite in length and located at various distances from each other, stepped stages in the setting up of the total system are also found when varying the array density. The apparent CLT are submitted to change from 0.7tc up to 1.4tc, where tc is the equilibrium CLT in an ideal unit cell. Phenomenological models are proposed with results which are in good agreement with the computational data.