Semiconducting Properties of Mg 2 Si Single Crystals

High-purity $n$-type single crystals of the semiconducting compound ${\mathrm{Mg}}_{2}$Si were prepared from melts of stoichiometric proportions of the constituents in graphite crucibles; $p$-type crystals were obtained when the melt was doped with silver or copper. Carrier concentrations in the saturation region were as low as 8\ifmmode\times\else\texttimes\fi{}${10}^{16}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ for $n$-type and 4\ifmmode\times\else\texttimes\fi{}${10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ for $p$-type samples. Electrical resistivity $\ensuremath{\rho}$ and Hall coefficient $R$ were measured from 77\ifmmode^\circ\else\textdegree\fi{}K to 1000\ifmmode^\circ\else\textdegree\fi{}K. Hall mobility $\frac{R}{\ensuremath{\rho}}$ showed a temperature dependence in the intrinsic range of approximately ${T}^{\ensuremath{-}\frac{5}{2}}$ for all samples. At 300\ifmmode^\circ\else\textdegree\fi{}K, $\frac{R}{\ensuremath{\rho}}$ was as high as 406 ${\mathrm{cm}}^{2}$/volt-sec for $n$-type and 56 ${\mathrm{cm}}^{2}$/volt-sec for $p$-type material. The ratio of electron mobility to hole mobility was approximately five. The energy gap, determined from the least-square slopes at high temperature of the curves $log(R{T}^{\frac{3}{2}}) \mathrm{vs} \frac{1}{T}$, was 0.78 ev. The electron mobility at any temperature in the range 77\ifmmode^\circ\else\textdegree\fi{} to 400\ifmmode^\circ\else\textdegree\fi{}K can be explained quantitatively by a combination of scattering by optical modes and scattering by ionized impurities.