Ah. Harker et al., 2-DIMENSIONAL FINITE-ELEMENT CALCULATION OF STRESS AND STRAIN IN A STRIPE EPILAYER AND SUBSTRATE, Philosophical magazine. A. Physics of condensed matter. Defects and mechanical properties, 71(4), 1995, pp. 871-881
We report the first finite-element calculations of stress and strain i
n a layer, and the substrate on which it is grown, without any of the
approximations used in earlier calculations. We take into account stra
in 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 relaxatio
ns (in the film and substrate) is found to have a large effect on the
magnitudes of stress and strain. The previous calculations either negl
ect distortion of the substrate and/or assume a negligible thickness o
f 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 t
he first time, that the lattice planes of the layer and of the substra
te near the interface are curved even though the substrate has 'infini
te' dimensions. They also show that, for a layer with h/l = 1 or great
er, 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 lay
er is under tensile stress. Results of the finite-element calculations
are compared with analytical models and relevant available experiment
al data. Analytical models are found to be inaccurate. Agreement with
the experimental data is satisfactory.