Diffusion-limited lifetime in semiconductors

At high recombination rates, minority carrier recombination at defects in crystals ceases to obey Shockley-Read theory, and diffusion theory should be applied. These theories for neutral plane, line, and point defects are compared and used to interpret experimental results on hole recombination in $n$-type GaP. The steady-state kinetics and spatial distribution of the recombining carriers are briefly discussed but most attention is placed on the transient lifetime of the carriers for comparison with experiment. With no recourse to disposable parameters, the concentration and temperature dependences for plane sinks (surfaces) and line sinks (dislocations) in $n-\mathrm{G}\mathrm{a}\mathrm{P}$ are in excellent agreement with the diffusion theory. The resulting lifetimes are approximately independent of the sink strength (capture distance) and represent a lower limit to the observable lifetime for a fixed (low) defect concentration. For point sinks such limitation is not predicted and the experimental lifetime data do not agree with the diffusion theory. However, extending the diffusion theory to the case of a negatively charged defect, using a modified "Lax" treatment, produces concentration and temperature dependences in good agreement with experiment, and again a similar lifetime limitation is predicted providing the effective capture radius does not exceed 2×${10}^{-5\mathrm{}}$ cm ($\sigma \sim {10}^{-11\mathrm{}}$ ${\mathrm{cm}}^2$).