Radiative Recombination in Germanium

The dependence of recombination radiation, U, on the excess carrier density, δp, and on the equilibrium carrier density, (n₀+p₀), 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=R[(n₀+p₀)δp+δp²]nᵢ², where nᵢ is the carrier density in intrinsic material. As predicted by the theory, a log-log plot of U vs δp gave a straight line with slope of 1.0 for small δp and showed a curvature asymptotically approaching a slope of 2 for δp greater than (n₀+p₀). The value of R was estimated from the output radiation to be 2.5×{}10¹³ cm^-3 sec^-1 which compares favorably with the previously published theoretical value of 1.57×{}10¹³ cm^-3 sec^-1. The dependence of δp on incident light intensity shows the behavior of the effective sample lifetime, which, in most cases, increases slowly with injection level.