Electroreflectance Spectra and Band Structure of Germanium

The electroreflectance spectra of Ge were studied in detail in the region 1.5 to 6.5 eV. Structures are observed at energies which correspond to critical points in interband transitions. By varying the magnitude of the ac voltage which provides the modulating field at the surface of the sample, and by using different polarizations of the incident light, many overlapping structures have been resolved. Peaks at 2.05 and 2.24 eV are attributed to L_3^'-L₁ transitions, the valence band being split by 0.19 eV at the L_3^' point because of the spin-orbit interaction. Structures observed between 2.7 and 3.3 eV are attributed to transitions between the doubly split valence band at Γ_25^' and the doubly split level at Γ₁₅. The splitting of the Γ₁₅ level is 0.13 eV, as compared to the splitting of 0.29 eV for the Γ_25^' level. The Γ_25^'-Γ₁₅ transitions are found to overlap with the Δ₅-Δ₁ transitions around 3.13 eV. There are two overlapping structures around 4.4 eV, one of which is attributed to the Σ₂-Σ₃ transition; the other could be either a second manifestation of the same Σ₂-Σ₃ transition, or due to the X₄-X₁ transition. Structures observed at 5.85 and 6.18 eV are yet to be identified. Structures observed at 2.12 and 2.32 eV are attributed to the Λ₃-Λ₁ transitions, and those at 5.35 and 5.52 eV to the L_3^'-L₃ transitions. Transitions at the Δ, X, and Σ points are found to have anisotropic electroreflectance spectra. The line shapes for electroreflectance spectra are in qualitative agreement with those predicted by Aspnes and by Seraphin and Bottka for critical points having M₀, M₁, and M₂ types of singularities, if Lorentzian broadening is included.