The impact (three-body) recombination and optical recombination coefficients are calculated for hydrogenlike impurity centers in extrinsic germanium and silicon in thermal equilibrium. These have been compared with the phonon recombination coefficient calculated by Gummel and Lax for a similar model. It is found that the optical coefficient is always less than the phonon coefficient in the temperature range of interest. The impact ionization coefficient which is proportional to the free carrier concentration may be comparable with or greater than the phonon recombination coefficient at 4.2°K in the presence of background radiation and definitely exceeds it at higher temperatures. Comparison with experimental data indicates that none of the mechanisms considered can yet explain the observed time constants.

• Received 7 February 1955

DOI:https://doi.org/10.1103/PhysRev.98.1757