Gallium Energy Bands and Fermi Surface via the Augmented-Plane-Wave Method

Results of numerical calculations of the band structure of gallium are reported; the calculations have been carried out according to the augmented-plane-wave (APW) method of Slater. Calculations have been carried out at 115 points in 1/8 of the Brillouin zone. An approximate Fermi energy is determined by counting states; cuts of surfaces of constant energy have been constructed for two energies near this approximate Fermi energy. one set of cuts is presented in this paper. The potential used was an ad hoc one constructed from superposed free atoms and a ρ1/3 exchange potential; the free-atom calculations used were those of Freeman and Watson. The lattice constants are taken as supplied by Barrett, viz., a=4.5151×10^-8 cm, b=4.4881×10^-8 cm, and c=7.6318×10^-8 cm. The bands resemble perturbed free-electron bands, but the two Fermi surfaces exhibit considerable departures from the free-electron Fermi surface. Because of the inherent defects in the ad hoc potential, it is unlikely that the present calculations can be expected to explain all the experimental information, but it is hoped that they will furnish a better zeroth-order model than does the free-electron picture.