Determination of the composition and thickness of semi-polar and non-polar III-nitride films and quantum wells using X-ray scattering

There is increasing interest in III-nitride films and multiple quantum well structures grown in non-polar or semi-polar orientations for application in light-emitting devices. We describe a method to obtain the compositions and the thicknesses of layers within III-nitride quantum well or superlattice structures grown in non-polar or semi-polar orientations, based on X-ray scattering. For each new crystallographic orientation considered, new axes were obtained and both the lengths and angles of these new axes calculated relative to the original conventional reference axes. These angles provide the coefficients of the matrix to transform the elastic constants published in the conventional setting (as used for polar c -plane oriented III-nitrides) into the appropriate new values. The new characteristic lengths and new elastic constants are then put into the general equation that relates the composition of a fully strained layer to the experimentally measured out-of-plane alloy d -spacing. Thus we have (a) determined the alloy composition from the difference between the experimentally measured alloy d -spacing and that of the substrate and (b) calculated the strained d -spacing for a given alloy composition for input to simple kinematical simulation software. In addition for quantum well structures the thickness ratio of well-to-barrier must be determined. Here we use the minima in the low angle reflectivity data. The repeat thickness and thus the thicknesses of the well and barrier layers, can be obtained from either the low or the high-angle data. We then cross-check by comparing the experimental and the simulated high-angle diffraction data. This method has been applied successfully to heteroepitaxial non-polar and semi-polar GaN/AlGaN and InGaN/GaN multiple quantum well structures and may also be used to find the composition of epilayers. The method works even in the presence of tilt between the superlattice and the GaN "template', although in this case additional high-angle diffraction data at different settings must be collected.