Conductivity Mobilities of Electrons and Holes in Heavily Doped Silicon

Electron and hole mobilities in silicon have been determined in a region in which ionized impurity scattering is predominant. Resistivities were measured by a four-point probe and impurity concentrations were obtained with radioactive tracers or from thermal neutron activation analysis. Measurements were taken with several Group III and Group V impurities up to concentrations of 6\ifmmode\times\else\texttimes\fi{}${10}^{19}$ (${\mathrm{cm}}^{\ensuremath{-}3}$) and 6\ifmmode\times\else\texttimes\fi{}${10}^{18}$ (${\mathrm{cm}}^{\ensuremath{-}3}$) for $n$- and $p$-type silicon, respectively. The conductivity mobility can be calculated from these data by considering the percentage of ionized impurities. The electron mobility approaches 80 ${\mathrm{cm}}^{2}$/v-sec and the hole mobility 60 ${\mathrm{cm}}^{2}$/v-sec for the highest impurity concentrations. The comparison with measured Hall mobilities leads to a ratio $\frac{{\ensuremath{\mu}}_{H}}{{\ensuremath{\mu}}_{c}}$ which agrees with theory. A comparison with the existing theory of impurity scattering yields better agreement for $n$-type silicon than for $p$-type. In the latter the measured mobilities are considerably smaller than the theoretical values.