Vacuum Ultraviolet Spectroscopy and Analytical Critical Point Modeling of the Electronic Structure of Aluminum Nitride.

AlN is a wurzite isomorph with a band gap of 6.2 (eV). A technologically important material with applications in electronic packaging, electro-optics, and structural ceramics, it is also being investigated for use as an active device material. The electronic structure of AlN is therefore of both practical interest and fundamental importance. Extending ab initio calculations to address materials like AlN requires the ability to quantitatively compare experiment and theory. Toward this goal, a new approach for analyzing experimental and theoretical electronic structure results, through critical point modeling of the optical joint density of states, J_{rm cv}, has been developed. A vacuum ultraviolet spectrometer was used to obtain experimental optical properties for single crystal and polycrystalline AlN, over the range 4-40 (eV). Theoretical optical properties were derived from a first-principles calculation, using an orthogonalized linear combination of atomic orbitals in the local density approximation. Comparison of experiment and theory was realized by a numerical optimization of analytical critical point models of the undifferentiated J_{rm cv}^ectra. By modeling J_{rm cv}^ectra as balanced sets of critical points, this approach highlights relationships among critical points to discern transitions between individual pairings of valence and conduction bands. Since the areas of features are preserved, it also permits the use of partial sum rules to count electrons involved in optical transitions between these pairs. The electronic structure of AlN thus revealed, has a 2D character indicated by logarithmic divergences at 8.7 and 14 eV. These mark the centers of two sets of 2D critical points which are associated with N2p to A13s transitions and Al = N to A13p transitions, respectively. A broad third feature is centered at 33 (eV) and associated with N2s to A13d transitions. These orbital origins are suggested by consideration of the orbitally decomposed density of states. Good agreement between experiment and theory is found for the energy location of most features, with discrepancies in the band gap location, 6.2 versus 4.4 (eV), and in some of the features above 10 (eV).