Hydrostatic deformation potentials and the question of exciton binding energies and splittings in aluminium nitride

Abstract

By comparing a series of optical experiments performed on bulk aluminum nitride crystals and heteroepitaxial films, we determine the hydrostatic excitonic deformation potentials of AlN. The agreement between the whole available experimental data and our analysis consolidates this determination. Using the previously determined values of the valence-band deformation potentials which account for the strain-induced variation in the crystal-field splitting: ${d}_{3}=\ensuremath{-}8.19\text{ }\text{eV}$ and ${d}_{4}=4.10\text{ }\text{eV}$ we obtain values of $\ensuremath{-}6.04$ and 2.15 eV for the hydrostatic excitonic deformation potentials ${a}_{1}$ and ${a}_{2}$ in the context of the quasicubic approximation. This constitutes the first series of values coherent with the whole set of experimental data. The experimental value of $1s\text{\ensuremath{-}}2s$ splitting disagrees with the theory of excitons in anisotropic semiconductors. This disagreement, we attribute it to our poor knowledge of the valence-band dispersion relations of AlN and to the difficulty we face for including in the calculation plausible values for the anisotropic hole effective mass, dielectric constant.