Determination of strain state and composition of highly mismatched group-III nitride heterostructures by x-ray diffraction

We present an accurate model for the dynamical x-ray diffraction analysis of highly mismatched materials systems. Our approach features an exact incidence parameter as well as an exact calculation of the changes of Bragg angle and lattice plane inclination due to strain. We show that the commonly used approximations for these parameters are, in general, unable to describe diffraction profiles of different reflections consistently, and utterly fail for a strain on the order of 1% or more. The model as presented explicitly considers crystals with zincblende and wurtzite structure of arbitrary orientation and the resulting distortions. The validity of our model is demonstrated by various experimental examples, including closely lattice-matched GaAs/AlAs structures on GaAs(001) and GaAs(113), as well as highly mismatched GaN layers, (Al, Ga)N/GaN and GaN/(In, Ga)N heterostructures on 6H-SiC(0001) and gamma-LiAlO2(100).