Effect of interface grading and lateral thickness variation on x-ray diffraction by InGaN/GaN multiple quantum wells

We develop a method for simulating the effects of interface grading and lateral variation in layer thickness on x-ray diffraction by InGaN/GaN multiple quantum wells (MQWs). Using the resulting simulation scheme, we perform detailed fitting of symmetric (0002) omega/20 scans measured for a selection of typical InGaN/GaN MQW heterostructures. We find that incorporation of the combined effects of interface grading and thickness variation substantially improves the goodness of fit relative to a conventional model that assumes ideal MQW structure. The improved simulations of experiments reveal that the examined InxGa1-xN/GaN MQWs (0.17 <= x <= 0.24) grown on the basal plane of GaN have graded heterointerface widths, w, in the range 0.5 <= w <= 1.1 nm concomitant with lateral variations in total MQW thickness of 0.7-6.3 nm rms. Atomic force microscopy of 10 x 10 mu m(2) areas of the as-grown MQWs finds surface roughnesses of 1.0-5.6 nm rms in agreement with corresponding rms thickness variations found by simulating the XRD measurements. For samples with smaller thickness variations, higher order MQW satellites are observed in high-dynamic-range diffraction experiments and best-fit simulations find evidence for asymmetric MQW interface widths. The lower interfaces are narrower than the upper interfaces in agreement with recent transmission electron microscopy and atom-probe studies of MQW interfaces by other groups. These under-recognized structural features heterointerface grading and lateral film-thickness variation will influence not only x-ray diffraction, but also polarization, bandstructure, and carrier localization within InGaN-based MQW heterostructures. (C) 2012 Elsevier B.V. All rights reserved.