Calculation of neutron cross sections for interband transitions in semiconductors

Abstract

It has been proposed that the introduction of the high-flux high-energy pulsed-neutron sources will allow the study of electronic transitions between valence and conduction bands in semiconductors produced by inelastic scattering of neutrons. A theoretical calculation of the cross sections that would be expected in such an experiment is described. Results are presented for silicon and germanium. In calculating cross sections, which are based on an empirical pseudopotential description of the electronic band structure, it has been important to include both the spin and the orbital part of the magnetic scattering. It is found that, for the values of momentum transfer considered (up to about 10 ${\mathrm{nm}}^{\ensuremath{-}1}$), it is the orbital contribution that dominates. It is also shown that the matrix elements for the transitions have an important effect. Cross sections are shown for a range of energy and momentum transfer from which it is concluded that the experiment is likely to be possible, but questions of resolution will be of great importance if useful information about band structure is to be obtained.