Evolution of film stress with accumulation of misfit dislocations at semiconductor interfaces

For mismatched heterosystems the equilibrium plastic relaxation process that occurs with accumulation of two pure edge misfit dislocation (MD) arrays at the interface is investigated. The treatment is based on the comparison of energies calculated for MD arrays of various densities. Two requirements are proposed to test the correctness of the stress and energy calculations. The values of the film critical thicknesses for the appearance of the first MDs is in good agreement with the Matthews model, but disagreement increases with the growth of MD density. In the framework of our model, the relaxation process is slow at the beginning stage, then it intensifies and achieves a relaxation level of 90% at approximately half film thickness compared with the Matthews model. The whole accumulated MD energy is halved for almost the whole range of atomic fraction χ in GeχSi1−χ epitaxial layers grown on Si substrates.