Experimental determination of the N-p-partial density of states in the conduction band of GaN: Determination of the polytype fractions in mixed phase samples

Abstract

Hexagonal, cubic, and mixed phase GaN samples grown by molecular beam epitaxy are studied using near-edge x-ray absorption fine structure (NEXAFS) spectroscopy. The spectra were recorded at the N-K-edge, at several angles of incidence. It is shown that the N-K-edge NEXAFS spectra, which are proportional to the p-partial density of states in the conduction band, are characteristic of the cubic or hexagonal structure of the examined crystal. The spectra of the cubic sample do not depend on the angle of incidence (θ), contrary to the spectra of the hexagonal sample in which the areas under the NEXAFS resonances depend linearly on cos2 θ. From the fitting of the lines Ai=A+B cos2 θ, where Ai are the areas under the resonances and A and B are constants, the directions of maximum electron charge density with respect to the normal to the surface are determined for the hexagonal sample. The energy positions of the absorption edge and the NEXAFS resonances in the spectra from the cubic sample are different from those of the hexagonal sample and in either case are independent of θ. Contrary to that, the energy positions of the NEXAFS resonances in a mixed phase sample have a characteristic angular dependence and shift between the energies corresponding to the cubic and hexagonal polytypes. Based on this observation, we propose that the spectrum of the mixed-phase sample can be approximated as the weighted average of the spectra from the pure cubic and hexagonal samples. From this approximation the coexisting fractions of α- and β-GaN in a mixed-phase sample are determined and they are found in good agreement with results from high resolution transmission electron microscopy and x-ray diffraction.