Kinetics of distant-pair recombination

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Abstract
The kinetics of the recombination of separately trapped electrons and holes are treated theoretically, and the results are compared with the low-temperature 1·4 eV luminescence of a-Si: H. The carriers are assumed to be distributed at random spatially, and the recombination transition rate is assumed to depend exponentially on the electron-hole separation. We obtain an exact solution, in the form of a non-linear integral equation, for the case of luminescence decay following a single excitation pulse; and we give approximate solutions for repetitively pulsed excitation (as in time-resolved spectroscopy) and for continuous excitation. Good agreement is found between the experimentally observed behaviour of a-Si: H and the predictions of the distant-pair model, without any adjustable parameters. In particular, the model predicts that the decay curve will be independent of the excitation pulse intensity when the pulse creates fewer than ∼ 1018 cm−3 carriers. We show, therefore, that frequency-response spectroscopy is necessary for the unambiguous identification of the recombination kinetics of a distant-pair system.