The electrical resistivity, Hall coefficient, and weak-field magnetoresistance of homogeneous single crystals of $n$-type ${\mathrm{Mg}}_2$Ge have been measured. The samples were either Al doped or undoped, and had exhaustion carrier concentrations from 1.3×${10}^{16}$ to 8.2×${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The electrical resistivity and Hall coefficient were measured from 4.2 to 300 K. Impurity-band conduction was observed at the lower temperatures. The Hall mobility from 150 to 300 K had a $T^{-\frac{3}{2}}$ temperature dependence which indicates that intravalley acoustic-mode scattering is the dominant scattering mechanism in this temperature range. From a consideration of the selection rules and this Hall-mobility temperature dependence, we conclude that the symmetry of the conduction-band minima is $X_3$ rather than $X_1$. The weak-field magnetoresistance of ${\mathrm{Mg}}_2$Ge, which was measured at 77.4 K and at three other stable temperatures (43.6, 194.5, and 299.5 K), was found to be much smaller than the magnetoresistance of Ge and ${\mathrm{Mg}}_2$Sn. The magnetoresistance coefficients $b$, $c$, and $d$ were obtained from these measurements and found to satisfy the symmetry relations $b+c+d=0\mathrm{}$, $d<\mathrm{}0\mathrm{}$. This result confirms the theoretical prediction that $n$-type ${\mathrm{Mg}}_2$Ge is a many-valley semiconductor with constant-energy spheroids in the $〈100〉$ directions. The anisotropy parameter $K$ was between 1.51 and 1.78 at 77 K. Inhomogeneous samples showed anomalies in the Hall mobilities and in the magnetoresistances.

• Received 21 January 1972

DOI:https://doi.org/10.1103/PhysRevB.6.442