X-ray absorption, glancing-angle reflectivity, and theoretical study of the N K- and GaM2,3-edge spectra in GaN

Abstract

A comprehensive study of the nitrogen K edge and gallium ${\mathrm{M}}_{2,3}$ edge in gallium nitride is presented. Results of two different experimental techniques, x-ray absorption by total photocurrent measurements and glancing-angle x-ray reflectivity, are presented and compared with each other. First-principles calculations of the (polarization averaged) dielectric response ${\mathrm{\ensuremath{\epsilon}}}_{2}$(\ensuremath{\omega}) contributions from the relevant core-level to conduction-band transitions and derived spectral functions are used to interpret the data. These calculations are based on the local density approximation (LDA) and use a muffin-tin orbital basis for the band structure and matrix elements. The angular dependence of the x-ray reflectivity is studied and shown to be in good agreement with the theoretical predictions based on Fresnel theory and the magnitude of the calculated x-ray optical response functions. The main peaks in the calculated and measured spectra are compared with those in the relevant partial density of conduction-band states. Assignments are made to particular band transitions and corrections to the LDA are discussed. From the analysis of the N K and Ga ${\mathrm{M}}_{2,3}$ edges the latter are found to be essentially constant up to \ensuremath{\sim}10 eV above the conduction-band minimum. The differences in spectral shape found between the various measurements were shown to be a result of polarization dependence. Since the c axis in all the measurements was normal to the sample surface, p-polarized radiation at glancing angles corresponds to E\ensuremath{\Vert}c while s polarization corresponds to E\ensuremath{\perp}c at all incident angles. Thus, this polarization dependence is a result of the intrinsic anisotropy of the wurtzite structure. Spectra on powders which provide an average of both polarizations as well as separate measurements of reflectivity with s polarization and p polarization were used to arrive at this conclusion.