Role of experimental resolution in measurements of critical layer thickness for strained-layer epitaxy

Abstract

Experimental measurements of critical layer thicknesses (CLT’s) in strained-layer epitaxy are considered. Finite experimental resolution can have a major effect on measured CLT’s and can easily lead to spurious results. The theoretical approach to critical layer thicknesses of J. W. Matthews [J. Vac. Sci. Technol. 12, 126 (1975)] has been modified in a straightforward way to predict the apparent critical thickness for an experiment with finite resolution in lattice parameter. The theory has also been modified to account for the general empirical result that fewer misfit dislocations are generated than predicted by equilibrium calculation. The resulting expression is fit to recent x-ray diffraction data on InGaAs/GaAs and SiGe/Si. The results suggest that CLT’s in these systems may not be significantly larger than predicted by equilibrium theory, in agreement with high-resolution measurements.