Correspondence between coherently strained multilayers and a single coherently strained layer on lattice mismatched substrate

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Abstract
The equilibrium in-plane lattice parameter for lattice mismatched multilayers, as first derived by Matthews and Blakeslee [J. Cryst. Growth 32, 265 (1976)], has been used to obtain an expression for the misfit between the multilayers as a whole and a lattice mismatched substrate. The resulting expression immediately suggests a correspondence between the multilayers as a whole and a single coherently strained layer of equal thickness but having a misfit equal to the misfit between the constituent layers spatially averaged over a single repeat distance. The present results are obtained without reference to the energy density of a misfit dislocation. In particular, the present correspondence allows one to predict the critical thickness of coherently strained multilayers if single-layer critical thicknesses are known.