A quantitative procedure to probe for compositional inhomogeneities in InxGa1−xN alloys

The distribution of indium in a GaN/InxGa1−xN/AlyGa1−yN quantum well with x±Δx=0.24±0.07 is quantitatively investigated by extraction of displacement fields from lattice images. Simulations accurately describe the measured strain relaxation across a wedge-shaped sample for a sample thickness up to 150 nm. The proportionality between indium concentration and resulting lattice constant c(x) is approximated by c(x)=0.5185+0.111x nm. In general, it is challenging to discriminate the effects of random alloying against clustering. In InxGa1−xN this is particularly true at low indium concentrations x<0.2. For an accurate quantitative analysis, sample preparation and imaging were developed such that radiation damage can be recognized if present. Further, an analysis of detection limits and knowledge of the sample thickness are crucial for obtaining reproducible results. Data averaging is necessary to reach sufficient precision. Consequently, the size of the indium-rich clusters is poorly known if x is small. Beyond the interest in physical properties of InxGa1−xN alloys, the analysis of strain and its relaxation exemplifies how quantitative analysis is possible at an atomic level and is in excellent agreement with theoretical predictions.