Optical constants and critical-point transitions in biaxially tensile-strained epitaxial thin films of germanium

We present the optical properties of epitaxial germanium (Ge) thin films as a function of tensile strain from 0% to 1.96%, measured using variable-angle spectroscopic ellipsometry in the energy range of 0.5-4.1 eV. The band structure of unstrained Ge is modified using epitaxial tensile strain imparted by the underlying compositionally controlled InxGa1-xAs strain template. The degeneracy of Ge's light-hole (LH) and heavy-hole (HH) bands near the Γ point is lifted due to tensile strain while the Γ and L valleys descend. Such changes in the band structure impact the optical properties of tensile-strained Ge, such as the dielectric constant, refractive index, and absorption coefficient. At the Γ point, it is noticed that the absorption coefficient gradually increases with tensile strain, indicating a shift in the effective band edge of Ge. Further, it is observed that the indirect transitions are dominated by L-LH, whereas the direct transitions are contributed from the Γ-LH as well as the Γ-HH due to the interplay between the transition energy and joint density of states. In addition, the tensile strain is seen to affect the band structure at different regions in the Brillouin zone (BZ) resulting in the movement of the critical points (CPs) to lower energy in the optical spectrum. The E1 and E1+ Δ1 CPs in tensile-strained Ge are redshifted compared with unstrained Ge. The observed movement of the E1, and E0 CP peaks is in close agreement with the first principles calculated band structure. Further, the apparent value of the E0 spin-orbit (SO) energy, Δ0 is seen to decrease with increasing tensile strain at the Γ point. Interestingly, the E1 SO energy, Δ1 at the Λ direction in the BZ remains constant, indicating a very low shear deformation-related shift in the band structure due to biaxial tensile strain. As tensile-strained Ge thin films have a wide range of potential applications in electronics, sensing, and photonics, further understanding of tensile strain in Ge and its impact on its dielectric and optical properties is essential.