Effects of Dislocations on Mobilities in Semiconductors

Abstract

The scattering of electrons or holes in semiconductors by the dilation of the lattice around rigid, randomly-arranged edge-type dislocations is treated by the method of the deformation potential. The contribution of this scattering to the electrical resistance is determined from the Boltzmann transport equation by the method of Mackenzie and Sondheimer, except for the use of Maxwell-Boltzmann, rather than Fermi-Dirac statistics. The temperature dependence of the reciprocal of the mobility $\ensuremath{\mu}$ is given by $\frac{1}{\ensuremath{\mu}}={\ensuremath{\alpha}}_{l}{T}^{\frac{3}{2}}+{\ensuremath{\alpha}}_{i}{T}^{\ensuremath{-}\frac{3}{2}}+{\ensuremath{\alpha}}_{d}{T}^{\ensuremath{-}1}$ where the $\ensuremath{\alpha}$'s are temperature-independent quantities referring to scattering from the lattice, impurity atoms, and dislocations, respectively. A discussion is given of the relative magnitudes of these three terms, and of the possibility of obtaining experimental information concerning dislocations in semiconductors by electrical measurements.