Electroreflectance Spectra and Band Structure of Germanium

Abstract

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 $L_{3^{\prime }}-L_1$ transitions, the valence band being split by 0.19 eV at the $L_{3^{\prime }}$ 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 ${\Gamma }_{{25}^{\prime }}$ and the doubly split level at ${\Gamma }_{15}$. The splitting of the ${\Gamma }_{15}$ level is 0.13 eV, as compared to the splitting of 0.29 eV for the ${\Gamma }_{{25}^{\prime }}$ level. The ${\Gamma }_{{25}^{\prime }}-{\Gamma }_{15}$ transitions are found to overlap with the ${\Delta }_5-{\Delta }_1$ transitions around 3.13 eV. There are two overlapping structures around 4.4 eV, one of which is attributed to the ${\Sigma }_2-{\Sigma }_3$ transition; the other could be either a second manifestation of the same ${\Sigma }_2-{\Sigma }_3$ transition, or due to the $X_4-X_1$ 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 ${\Lambda }_3-{\Lambda }_1$ transitions, and those at 5.35 and 5.52 eV to the $L_{3^{\prime }}-L_3$ transitions. Transitions at the $\Delta$, $X$, and $\Sigma$ 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 $M_0$, $M_1$, and $M_2$ types of singularities, if Lorentzian broadening is included.