Electronic structure of the diamond crystal based on an improved cellular calculation

Abstract

The band structure of diamond has been determined using Slater's cellular method. Calculations were carried out with the unit cell partitioned into two and then four space-filling polyhedra. The dependence of the energy-level structure on the choice of matching points and cellular basis functions is carefully examined. Once a sufficient number of cellular basis functions (tetrahedral harmonics) is introduced, the precise arrangement of the matching points is no longer critical, and substantially the same energy-level structure is obtained for a wide variety of matching-point configurations. Tetrahedral harmonic expansions including $l_{max}=12\mathrm{}$ are sufficient to ensure reasonable convergence at the zone points $\Gamma$, $X$, and $L$. Some energy levels converge with $l_{max}\ge 8$. Most early attempts to calculate the band structure of diamond-type crystals using the cellular method were quantitatively unsatisfactory because too few basis functions were used. The present cellular results based on fourfold partitioning compare favorably with orthogonalized-plane-wave (OPW) results and with experiment. The lowest conduction-band level at the zone center is found to be ${\Gamma }_{15}$ in agreement with OPW calculations but in disagreement with recent nonlocal-empirical-pseudopotential calculations.