Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Physics and Astronomy

First Advisor

Joseph Callaway


Neutral impurity scattering is a relatively untouched subject because it is only significant at very low temperatures. With the development of a new class of impurity band conduction devices that operate at cryogenic temperatures, it becomes necessary to describe the scattering in a more realistic fashion. We have calculated both elastic and inelastic scattering of electrons by substitional As in n-type Si, taking into account the anisotropy of the host band structure. Specifically, in regard to inelastic scattering, we calculated the differential and integrated cross sections for transitions from the ground state to the valley-orbit split states $\Gamma\sb{15}$ and $\Gamma\sb{12}$. Intervalley scattering was also considered but was not found to be substantial within the first Born approximation. The cross sections for excitation of the $\Gamma\sb{15}$ state were found to be negligible. This result is probably due to the cancellation of potentially large terms by symmetry. However, the $\Gamma\sb{12}$ excitation is rather substantial. In contrast to scattering in free space, the incident and outgoing wavevectors are confined to a small cone, while the actual particle velocity can have a broad angular span. The formal theory of elastic scattering was extended to as required by the anistropy of the conduction band. Potentials for the calculation were obtained by scaling the potentials of the hydrogen atom. We obtained a set of coupled differential equations similar to those in electron-molecule scattering with axial symmetry. Due to the complication of the interplay between the anisotropy and the multivalley nature of the host, we have to neglect inter-valley scattering. It is found that for a specific outgoing direction, incidence along the longitudinal directions of the ellipsoidal valleys gives the maximum rate; whereas the transverse directions have the maximum scattering rates for any fixed incident directions. At low incident energies, the scattering is dominated by the singlet state with our choice of the exchange potentials.