Recombination in electron-hole droplets in polar and non-polar indirect band gap semiconductors and carrier concentration power law

The dependence of the recombination relaxation rate on the carrier concentration, n, is examined in detail. It is found that in polar indirect band gap semiconductors the phonon-induced recombination rate varies as $\text{n}{}^{\mathrm{<mtext>4</mtext><mtext>3</mtext>}}$ at low temperatures. This is a new power law. On the other hand, in the non-polar materials, the relaxation rate varies as a linear combination of n², $\text{n}{}^{\mathrm{<mtext>5</mtext><mtext>3</mtext>}}$ and $\text{n}{}^{\mathrm{<mtext>4</mtext><mtext>3</mtext>}}$ terms. We find the experimental evidence for the occurence of $\text{n}{}^{\mathrm{<mtext>5</mtext><mtext>3</mtext>}}$ and $\text{n}{}^{\mathrm{<mtext>4</mtext><mtext>3</mtext>}}$ contributions for the first time.