Photon-Radiative Recombination of Electrons and Holes in Germanium

The spectral distribution of the rate of photon generation for the photon-radiative recombination of electrons and holes in germanium is determined from known optical properties by application of the principle of detailed balance. Quantities characterizing the process are evaluated: The thermal equilibrium recombination rate at 300\ifmmode^\circ\else\textdegree\fi{}K is 1.57\ifmmode\times\else\texttimes\fi{}${10}^{13}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ ${\mathrm{sec}}^{\ensuremath{-}1}$, which corresponds to a recombination cross section of 2.9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}21}$ ${\mathrm{cm}}^{2}$ and a decay time for a small disturbance in carrier concentration in intrinsic material of 0.75 sec. The extension to the steady-state case of added current carriers is given, and estimates are included of the dependence of the quantities on temperature.