Stephen W. S. McKeever - A Course in Luminescence Measurements and Analyses for Radiation Dosimetry

In cascade capture, the free charge loses its energy via the successive emission of phonons accompanied by loss of energy of the free charge by cascading down a series of discrete, excited states of the defect, eventually reaching the ground state. For example, a free electron may be captured by cascading down the trapped electron excited states, eventually reaching its ground state. The process requires that the electron will not be re-emitted from any of the excited states back to the conduction band and the probability of this happening will increase with temperature. This leads to a power-law dependence of the capture cross-section on temperature in which the capture cross-section decreases as T increases, σ∝T−a.

The multi-phonon process requires a sufficient number of phonons to allow the defect energy level to cross into the delocalized band and capture the electron (and similarly for hole capture). Phonons are bosons and the distribution of phonons of energy Eph at temperature T is given by Bose-Einstein statistics as 1/(1+ exp{−Eph/kT}). Thus, the availability of sufficiently energetic phonons increases with temperature, giving rise to an exponential dependence of the capture cross-section on temperature (exp{−Eph/kT}). The cascade-capture mechanism is likely to be combined with the multi-phonon mechanism, especially for the last excited-state to ground-state transition. Thus, a combination of a power-law dependence on T and an exponential dependence on T might be expected. Note that if Eph is small, the dependence will approximate to the power law T−a.

Shockley-Read-Hall recombination requires a combination of two of the above capture processes. First, capture of (say) a hole is required, followed by capture of an electron by the trapped hole and consequent electron-hole recombination.

From the literature, look up discussions of radiative transitions, Auger processes, cascade capture, and multi-phonon relaxation. Under what conditions might one process be expected compared to another?

1 1. The author is grateful to P.D. Townsend for this comment.

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