An Application of the Cellular Method to Silicon

Abstract

The calculations of Kimball and Mullaney applying the cellular method to elemental silicon are extended to a higher approximation. Although the energy gap is decreased through use of a larger number of harmonics, the values obtained are still much higher than that given by experiment. The proposal of Pearson, Haynes, and Shockley that the highest point of the filled band and the lowest point of the conduction band do not occur at the center of the zone may have a bearing on the results, since the calculations reported here are performed for zero wave number. The effective mass of the conduction electrons is determined under the assumption that the lowest point lies at the center of the zone.