Recombination-induced heating of free carriers in a semiconductor

Recombination of externally excited (injected) charge carriers in a semiconductor can strongly change the temperature of the remaining carriers. The temperature is increased if the recombination rate decreases with energy and/or degenerate statistics applies. The normalized heating rate $\frac{\left[\frac{d\left(k_{B}T\right)}{\mathrm{dt}}\right]}{k_{B}T\cong {\tau }^{-1\mathrm{}}}$ (the recombination rate) will thus drastically reduce energy relaxation (cooling) of hot carriers at low temperatures. Cooling may occur if the recombination rate increases with energy.