Effect of Neutral Impurity on the Microwave Conductivity and Dielectric Constant of Germanium at Low Temperatures

Abstract

Conductivity and dielectric constant of germanium at 4.2\ifmmode^\circ\else\textdegree\fi{}K were measured at a frequency of 9200 Mc/sec. The dielectric constant measured for a pure sample is 16.0\ifmmode\pm\else\textpm\fi{}0.3. Higher dielectric constants, up to 80, were measured on $n$- and $p$-type samples doped with antimony or gallium. The conductivity and the change of dielectric constant are attributed to carriers in the impurity states. A positive contribution, $\ensuremath{\Delta}{K}_{b}$, to the dielectric constant is given by the polarization of neutral impurity atoms and a negative contribution, $\ensuremath{\Delta}{K}_{c}$, is associated with the conduction effect. Using $\ensuremath{\Delta}{K}_{b}$ to estimate the ionization energy of the impurity, a value of 0.0099 ev is obtained for a sample containing 1.6\ifmmode\times\else\texttimes\fi{}${10}^{16}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ antimony and 0.0084 ev is obtained for a sample containing 3.7\ifmmode\times\else\texttimes\fi{}${10}^{16}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ gallium. Samples of higher impurity concentrations showed much higher conductivity and the effect of overlapping of impurity states is shown in the variation of impurity polarizability. The relaxation time and effective mass for the conduction in impurity states are estimated from the dc conductivity and its ratio to the microwave conductivity. Large effective masses, around $1000m$, are obtained for samples of \ensuremath{\sim}${10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ impurity concentration.