Band Structure of Silicon from an Adjusted Heine-Abarenkov Calculation

The band structure of silicon has been computed using the Heine-Abarenkov pseudopotential method. The theoretical Fourier coefficients of the potential were then varied on the order of 30% to give agreement with measured cyclotron masses and the indirect gap. The resultant band structure is close to that obtained by Brust, Cohen, and Phillips using only the three lowest potential coefficients. We find that the higher potential coefficients are not weak but are nearly linearly dependent in their effect on the band-structure parameters investigated. The distribution in $k$ space of contributions to ${\epsilon }_2\left(\omega \right)$ was studied and found to be poorly described by contributions from the symmetry points at $\Gamma$, $X$, and $L$. Nevertheless, the optical gaps at $\Gamma$, $X$, and $L$ are fairly close in energy to the three prominent peaks, 3.5, 4.3, and 5.4 eV in ${\epsilon }_2\left(\omega \right)$. For the 4.3-eV peak, at least, this proximity in energy is found to be relatively insensitive to variations in the potential which maintain cubic symmetry.