Gallium Arsenide Band Structure Calculation

Energy levels, associated with some points of high symmetry, in the Brillouin zone of gallium arsenide are calculated. The variational method proposed by Brown and Krumhansl is used. The trial wave functions consist of Bloch sums constructed from nonoverlapping atomic-like functions and of plane waves. In order to calculate the crystal potential, the lattice sites are assumed to be occupied by ${\mathrm{Ga}}^{-}$ and ${\mathrm{As}}^{+}$ ions in $4s4p^3$ configurations. The bottom of the conduction band is found to have $X_1$ symmetry. The indirect band gap is found to have a width of 1.63±0.8 eV. The conduction level ${\Gamma }_1$ is found to lie below the conduction level ${\Gamma }_{15}$.