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 (hh2h¯l), e.g., (112¯2), and inclined m-planes (hh¯0l), e.g., (11¯01) or (22¯01).

Polar and semipolar (112) InAlN layers grown on AlN templates using MOVPE

“…The In content of the (112) layers was determined using the recently developed XRD analysis method based on that of Oehler et al. .…”

Structural and optical properties of (112̅2) InGaN quantum wells compared to (0001) and (112̅0)

“…The barrier growth rate was independently confirmed by in situ reflectance oscillation during growth of a thick layer at barrier growth conditions. For the (112̅ 2) orientation we recorded symmetrical w -Q 2 scans of the (112̅ 2) reflection along [112̅ 3̅ ] and [11̅ 00] and then did simulation using our own software [26,27]. APT and TEM confirmed the XRD simulation results within the errors of »1% for the In content.…”

Stress relaxation of AlGaN on nonpolar m-plane GaN substrate

“…( 11). The Al composition was also estimated from measurements of the symmetrical 10 10 and 30 30 reflections at 32 nm and 118 nm thickness and their simulations using the method of Oehler et al 14,15 which assumes fully strained layers. Independently, the samples were measured with room-temperature cathodoluminescence (CL), as shown in Fig.…”