Conductivity and Hall Effect in the Intrinsic Range of Germanium

Abstract

Conductivity and Hall effect have been measured in the intrinsic range of germanium from 250\ifmmode^\circ\else\textdegree\fi{} to 1000\ifmmode^\circ\else\textdegree\fi{}K. From lattice-scattering mobility and conductivity below 500\ifmmode^\circ\else\textdegree\fi{}K, a new empirical expression for carrier concentration is determined: $np=3.10\ifmmode\times\else\texttimes\fi{}{10}^{32}{T}^{3}\mathrm{exp}(\ensuremath{-}\frac{0.785}{\mathrm{kT}})$. An estimate is made of the contribution of optical modes to the lattice-scattering mobility. Conductivity from 500\ifmmode^\circ\else\textdegree\fi{} to 1000\ifmmode^\circ\else\textdegree\fi{} and Hall effect from 250\ifmmode^\circ\else\textdegree\fi{} to 1000\ifmmode^\circ\else\textdegree\fi{} are computed and compared with experiment. Included in the computation are: the empirical expression for carrier concentration modified by the change in intrinsic ionization energy produced by electrostatic interaction of charge carriers, extrapolated empirical lattice scattering mobility, scattering by electron-hole collisions, and an extrapolation of the ratio Hall mobility/conductivity mobility.