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

Abstract

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) ω/2θ 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≤1.1nm concomitant with lateral variations in total MQW thickness of 0.7–6.3nm rms. Atomic force microscopy of 10×10μm2 areas of the as-grown MQWs finds surface roughnesses of 1.0–5.6nm 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.