Mobility of Impurity Ions in Germanium and Silicon

Lithium has been shown to migrate as a singly-charged positive ion in single crystals of both Ge and Si in temperature ranges of 150-600°C and 360-860°C, respectively. The mobility of the ${\mathrm{Li}}^{+}$ in crystalline Ge and Si has been measured as a function of temperature. Through the use of the Einstein relation between diffusion constant and mobility, values of the diffusion constants in ${\mathrm{cm}}^2$/sec of ${\mathrm{Li}}^{+}$ in Ge and Si are obtained as follows: $D=25\mathrm{}\times {10}^{-4\mathrm{}}\exp \left\{\frac{(-11\mathrm{}800)}{\mathrm{RT}}\right\}$ for Ge and $D=23\mathrm{}\times {10}^{-4\mathrm{}}\exp \left\{\frac{(-15\mathrm{}200)}{\mathrm{RT}}\right\}$ for Si, in satisfactory agreement with previously published results on the thermal diffusion of ${\mathrm{Li}}^{+}$. A curious reversion of conductivity type of solid solutions of Li in Ge is discussed. Copper has likewise been found to move as a positive ion in germanium in the temperature range 800°-900°C leading to diffusivities in agreement with previously published results.