Two‐dimensional finite‐element calculation of stress and strain in a stripe epilayer and substrate

Abstract

We report the first finite-element calculations of stress and strain in a layer, and the substrate on which it is grown, without any of the approximations used in earlier calculations. We take into account strain relaxation due to the finite (not “zero”) thickness h of the stripe layer, the effect of its narrow width 2l and stresses created in the substrate because of the film edges. The coupling of the two relaxations (in the film and substrate) is found to have a large effect on the magnitudes of stress and strain. The previous calculations either neglect distortion of the substrate and/or assume a negligible thickness of the layer, so that there is no variation in stress in the layer as a function of distance from the interface. The results reported in this paper reveal the deficiencies of the earlier models. They show, for the first time, that the lattice planes of the layer and of the substrate near the interface are curved even though the substrate has “infinite” dimensions. They also show that, for a layer with h/l = 1 or greater, the stress in the top layer changes sign; that is if the layer in the centre near the interface is under compression, the top of the layer is under tensile stress. Results of the finite-element calculations are compared with analytical models and relevant available experimental data. Analytical models are found to be inaccurate. Agreement with the experimental data is satisfactory.