Schottky-barrier electroreflectance of Ge: Nondegenerate and orbitally degenerate critical points

Critical-point energies, broadening parameters, line-shape asymmetries, interband reduced masses, and polarization anisotropies are measured for the E₀, E₀+₀, E₁, E₁+₁, {E₀}^', {E₀}^'+{₀}^', {E₀}^'+{₀}^'+₀, E₂, {E₁}^', E₁+, and {E₁}^'+{₁}^'+{₁}^'' transitions in Ge using the Schottky-barrier electroreflectance (ER) method. The Keldysh-Konstantinov-Perel' (KKP) approximation for orbitally degenerate critical points is adapted to heavy holes and to Franz-Keldysh oscillations. Stark-shift effects are shown to be important only for energies within 4 ({) ^3}{E₆^2} of E₆, negligible in this experiment. The KKP prediction that orbitally degenerate ER line shapes are represented as a linear superposition of nondegenerate line shapes is verified by separating explicitly the light-hole and heavy-hole contributions to the E₀ structure at intermediate fields. The polarization anisotropies are in qualitative agreement with KKP predictions, but the light-hole spectrum is much too large. Therefore, either the KKP matrix-element magnitudes or the calculated densities of states do not represent correctly the experimental conditions. Low-field line-shape asymmetries for E₀ and E₀+₀ are in excellent agreement with two-dimensional model density-of-states calculations. We observe a cusp less than 2 meV wide at threshold on spectra for which the intrinsic energy scale 40 meV, verifying remarkably well the prediction of a functional singularity at threshold in ER theory. The E₁ and E₁+₁ line shapes show polarization anisotropies of 1. 320. 02 and 1. 200. 02 at 300 and 10 K, respectively, for 110 fields, compared to a theoretical value of 4/3. Significant field-dependent polarization anisotropies are observed for the {E₀}^' triplet, in qualitative agreement with the KKP approximation and in contrast to the predictions of nondegenerate theory. Heavy-electron-hole transitions appear to dominate the center structure of the {E₀}^' triplet. The polarization anisotropy of 1. 85 observed for the E₂ transition shows that the critical point responsible is a saddle point. The {E₁}^' structures are resolved into three components. The larger energy separation, 26610 meV, for the two lower components of points responsible is not the same as that for the E₁ transitions, which have a spin-orbit splitting of 1842 meV.