Valense band structure of Ge_x Si_1-x for hole transport calculation

We have calculated the hole densities of states and the velocities as functions of energy in strained and relaxed p-type Ge_xSi_1-x layers grown on ⟨001⟩ Si substrates. It is shown that the nonparabolic and nonspherical effects are very large in the energy range of (0, 0.2 eV) measured from the heavy hole band edge. Deeper into the valence band, the bands gradually become parabolic and spherical. For most applications, the impurity doping concentration is below 10²⁰ cm^-3. For 10²⁰ cm^-3 p-type doped Si, the Fermi level is 77.3 meV at 77 K. It is therefore concluded that the nonparabolic and nonspherical effects must be taken into proper consideration when investigating the transport properties of p-type Ge_xSi_1-x samples. The calculated data of both relaxed and strained Ge_xSi_1-x valence band structures are curve fitted and a data library is built up for further study of the hole transport properties. The mobility and the diffusion coefficient are largely affected when the doping concentration is increased. It is found that at high doping concentration the contributions from the light hole and spin split-off bands become very important, they can become even larger than the contribution from the heavy hole band, even if their densities of states are smaller than that of the heavy hole band.