Electronic band structure and effective mass parameters of Ge _1-xSn_x alloys

This work investigates the electronic band structures of bulk Ge _1xSn_x alloys using the empirical pseudopotential method (EPM) for Sn composition x varying from 0 to 0.2. The adjustable form factors of EPM were tuned in order to reproduce the band features that agree well with the reported experimental data. Based on the adjusted pseudopotential form factors, the band structures of Ge _1xSn_x alloys were calculated along high symmetry lines in the Brillouin zone. The effective masses at the band edges were extracted by using a parabolic line fit. The bowing parameters of hole and electron effective masses were then derived by fitting the effective mass at different Sn compositions by a quadratic polynomial. The hole and electron effective mass were examined for bulk Ge_1xSn_x alloys along specific directions or orientations on various crystal planes. In addition, employing the effective-mass Hamiltonian for diamond semiconductor, band edge dispersion at the Γ-point calculated by 8-band k.p. method was fitted to that obtained from EPM approach. The Luttinger-like parameters were also derived for Ge_1xSn_x alloys. They were obtained by adjusting the effective-mass parameters of k.p method to fit the k.p band structure to that of the EPM. These effective masses and derived Luttinger parameters are useful for the design of optical and electronic devices based on Ge_1xSn_x alloys.