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+Δ₀, E₁, E₁+Δ₁, E₀^', E₀^'+Δ₀^', E₀^'+Δ₀^'+Δ₀, E₂, E₁^', E₁+Δ, and E₁^'+Δ₁^'+Δ₁^'' 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(Ω)³Eg² of Eg, 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+Δ₀ 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 Ω40 meV, verifying remarkably well the prediction of a functional singularity at threshold in ER theory. The E₁ and E₁+Δ₁ line shapes show polarization anisotropies of 1.32±{}0.02 and 1.20±{}0.02 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, 266±{}10 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 184±{}2 meV.