Alloy content determination of fully strained and partially relaxed semi-polar group III-nitrides by x-ray diffraction

Abstract

Semi-polar group III nitrides and their alloys (AlGaN, InGaN) show great promise for future opto-electronic devices. For these orientations, specific X-ray diffraction (XRD) methods have been developed to measure the alloy content. The XRD methods proposed in the literature all use approximations at different levels. Here, we introduce a novel exact model, against which we compare each simplifying assumption previously used. The relevant approximations are then assembled to produce an accurate linearized model, which shares the same mathematical form as that of the standard polar or non-polar nitride analysis. This linearized model can be further simplified to provide an analytic expression for correction of the alloy content when a tilt (partial relaxation) is found between the alloy epilayer and the semi-polar GaN template. For a given model - alloy content and tilt angle - we can compute the expected XRD data. Vice-versa, the alloy content can be obtained from the experimental measurements - tilt angle and difference in d-spacing. This work focuses on the typical semi-polar planes studied in the literature: inclined a-planes (h h 2 h ̄ l), e.g., (11 2 ̄ 2), and inclined m-planes (h h ̄ 0 l), e.g., (1 1 ̄ 01) or (2 2 ̄ 01). © 2013 Author(s).