Mobility, Noise Temperature, and Diffusivity of Hot Holes in Germanium

Abstract

Measurements are performed on $p$-type germanium at several temperatures between 77 and 300 \ifmmode^\circ\else\textdegree\fi{}K. Mobility is plotted vs electric field up to 10 kV ${\mathrm{cm}}^{\ensuremath{-}1}$. Saturation is reached at low temperatures. Critical field ${E}_{c}$ and saturation velocity ${v}_{S}$ are deduced. ${E}_{c}$ varies as ${T}^{1.93}$ and ${v}_{S}$ lies between 8 \ifmmode\times\else\texttimes\fi{} ${10}^{6}$ and 9 \ifmmode\times\else\texttimes\fi{} ${10}^{6}$ cm ${\mathrm{sec}}^{\ensuremath{-}1}$. An explanation is given to the fact that $\frac{\ensuremath{\mu}(E)}{{\ensuremath{\mu}}_{0}}$ is found to increase with carrier density. The longitudinal noise temperature ${T}_{n\ensuremath{\parallel}}(E)$ is measured vs electric field up to 3 kV ${\mathrm{cm}}^{\ensuremath{-}1}$ at different lattice temperatures $T$ in the range 112-300 \ifmmode^\circ\else\textdegree\fi{}K. ${T}_{n\ensuremath{\parallel}}(E)\ensuremath{-}T$ varies as ${E}^{1.6}$ at low field. A flat appears around $E={E}_{c}$ Transverse noise temperature ${T}_{n\ensuremath{\perp}}(E)$ is lower than ${T}_{n\ensuremath{\parallel}}(E)$ Longitudinal ${D}_{\ensuremath{\parallel}}(E)$ and transverse ${D}_{\ensuremath{\perp}}(E)$ are deduced. ${D}_{\ensuremath{\parallel}}(E)$ is smaller than the Ohmic diffusivity ${D}_{0}$ and reaches $0.15{D}_{0}$ at 112\ifmmode^\circ\else\textdegree\fi{}K and 2 kV ${\mathrm{cm}}^{\ensuremath{-}1}$. A simple and original iterative method is given for solving the spatially invariant Boltzmann equation in the hot carrier range. Distribution function and transport coefficients are obtained for transitory regime and steady state for $p$-type germanium. The distribution function is never a displaced Maxwellian even at low fields. Comparison with experiment shows that the scattering mechanisms commonly taken into account cannot explain the drift velocity saturation observed experimentally. Multiphonon processes would probably reduce this discrepancy. The relaxation time $\ensuremath{\tau}$ involved in diffusion-coefficient formulas is found to depend on electric field. A formal expression is given for $\ensuremath{\tau}$.