Radiative Recombination in Germanium

The dependence of recombination radiation, $U$, on the excess carrier density, $\delta p$, and on the equilibrium carrier density, ($n_0+p_0$), was studied in 0.2 to 12 ohm-cm $n$- and $p$-type germanium by simultaneous measurements of output radiation and of photoconductivity as functions of incident light intensity. The results confirm the van Roosbroeck-Shockley theory of band-to-band recombination which predicts that $U=\frac{\mathcal{R}\left[\right(n_0+p_0)\delta p+\delta p^2]}{{n_i}^2}$, where $n_i$ is the carrier density in intrinsic material. As predicted by the theory, a log-log plot of $U$ vs $\delta p$ gave a straight line with slope of 1.0 for small $\delta p$ and showed a curvature asymptotically approaching a slope of 2 for $\delta p$ greater than ($n_0+p_0$). The value of $\mathcal{R}$ was estimated from the output radiation to be 2.5×${10}^{13}$ ${\mathrm{cm}}^{-3\mathrm{}}$ ${\sec }^{-1\mathrm{}}$ which compares favorably with the previously published theoretical value of 1.57×${10}^{13}$ ${\mathrm{cm}}^{-3\mathrm{}}$ ${\sec }^{-1\mathrm{}}$. The dependence of $\delta p$ on incident light intensity shows the behavior of the effective sample lifetime, which, in most cases, increases slowly with injection level.