Mobility of Impurity Ions in Germanium and Silicon

Abstract

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\ifmmode^\circ\else\textdegree\fi{}C and 360-860\ifmmode^\circ\else\textdegree\fi{}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: $D=25\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\mathrm{exp}{\frac{(\ensuremath{-}11800)}{\mathrm{RT}}}$ for Ge and $D=23\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\mathrm{exp}{\frac{(\ensuremath{-}15200)}{\mathrm{RT}}}$ 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\ifmmode^\circ\else\textdegree\fi{}-900\ifmmode^\circ\else\textdegree\fi{}C leading to diffusivities in agreement with previously published results.