The electronic structures of cubic and hexagonal phases of GaN have been investigated by high-resolution electron energy-loss spectroscopy in a monochromated transmission electron microscope. Both the Ga-L 2,3 and N K-edges were measured. The data are compared to the latest versions of two different calculation schemes: band structure and multiple-scattering calculations. We have found that both methods are capable of giving results that can be compared quantitatively to the experiment. Small discrepancies with experiment could be eliminated by future developments in the implementation of these methods. DOI: 10.1103/PhysRevB.73.073308 PACS number͑s͒: 79.20.Uv, 78.70.Dm, 82.80.Pv The recent availability of electron-beam monochromators for high-resolution electron energy-loss spectroscopy ͑HREELS͒ in a transmission electron microscope ͑TEM͒ makes it feasible to obtain the near-edge fine structure ͑EL-NES͒ of a core-loss spectrum with a precision comparable to that of x-ray absorption spectroscopy. This opportunity opens up the exciting possibility of studying the internal electronic structure of materials, combined with complete structural information ͑from TEM diffraction and imaging͒ and nanometer lateral resolution. Because ELNES is related to the angular-momentum resolved density of unoccupied states ͑LDOS͒ at the site of the excited atom, 1 high-resolution data allows us to make a comparison with state-of-the-art computer calculations. As a consequence, we should obtain greatly improved reliability of spectral interpretation. Two different ab initio methodologies can be compared: band structure ͑BS͒ calculations and self-consistent real-space multiple-scattering ͑MS͒ calculations. It is often assumed that the latter approach is less precise than the former because of the use of a finite cluster size; that it is convenient for obtaining fast results but that its usefulness is limited to qualitative comparisons. However, both approaches ͑in their latest developments͒ allow inclusion of the effects of the core-hole left by the excited electron, using approximations that are an improvement on the Z + 1 approximation previously used in such calculations.
2,3GaN and its alloys have attracted much research in recent years due to their applications. 4,5 At present, GaN nanowires are receiving particular attention since they have possible application as high-mobility field-effect transistors and miniaturized UV-blue nanolasers. Recent work has stressed the importance of sub-band-gap states in this material in relation to potential applications. [6][7][8][9] States close to the Fermi energy relate directly to the scattering and recombination mechanisms that determine the concentration of carriers. Thus the use of bulk or nanostructured material requires, as a prerequisite to understanding more complex problems, a precise knowledge of the density of unoccupied states. Although there have been previous calculations for GaN, using BS 10-13 and/or MS calculations, 14,15 they involved qualitative comparisons to data of ...