Electron Momentum Distribution in Silicon and Germanium by Positron Annihilation

Abstract

The angular correlation of positron-annihilation radiation from single crystals of silicon and germanium has been measured for three different orientations of each crystal. The distributions for the three orientations differ greatly from one another, but each germanium distribution differs from the corresponding silicon distribution only by a scale factor which arises from the difference in the lattice constant. Data are compared with curves calculated using the nearly free-electron approximation for the electron's momentum. It is assumed that the occupied electron states in the crystal fill the Jones zone, a regular dodecahedron bounded by the set of {220} planes in momentum space, and the energy gap is taken to be an adjustable parameter. The fit is extremely good for the radiation emitted in the (110) plane but not so good for the (111) and (100) orientations. Possible reasons for the discrepancies are discussed.