Dynamical x-ray rocking curve simulations of nonuniform InGaAs and InGaAsP using Abeles’ matrix method

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Abstract
Computer simulations of the intrinsic (400) reflecting power of In1−xGaxAs layers having graded compositions are presented. We find that multiple x-ray peaks can result from a linearly graded region which implies that an interpretation which ascribes individual peaks to sublayers having a constant lattice parameter may not always be correct. We find that, in general, the simulations are asymmetric and that they have a full width at half maximum less than ∼100 arcsec. We have simulated an actual rocking curve of a single In1−xGaxAs1−yPy layer grown on a (100) InP substrate by vapor-phase epitaxy which exhibited multiple peaks, and we find that a good fit is possible if the layer had a graded lattice parameter. Comparing dynamical to kinematical simulations for a 3-μm-thick linearly graded layer, we find that most of the features resulting from the grading can be explained using kinematical theory. However, only the dynamical simulations can properly account for the reflecting power in the vicinity of the substrate peak and for the lack of fine structure which is observed in the absence of a discontinuity in Bragg spacing at the layer/substrate interface.