Low temperature non-radiative tunneling

3 describes the radiative tunneling process which results in a wide distribution of recombination times. A similar mechanism accounts for the non-radiative quenching. 

The luminescence efficiency is given by the fraction of electron-hole pairs which are created farther than R from the nearest defect (Street et al. 1978). The distribution of distances is the nearest neighbor distribution function, G R), for randomly dispersed defects, which is (Williams 1968) 

52) gives a good fit to the data in Fig. 8.20, for values of Rf. of 100-120 A. The fit assumes that there is a single value of the critical transfer radius R, which is a poor approximation because is widely distributed with a corresponding varying value of R. . Nevertheless, the average radiative lifetime of 10 s from Fig. 8.14 and co = 10 s gives 

The defect tunneling mechanism is suppressed when the localization length is decreased, as happens in a-Si Ge alloys (Street, Tsai, Stutzmann and Kakalios 1987c) and probably in other alloys. Although the dependence on defect density has the same form as for a-Si H, a larger defect density is needed to quench the band tail luminescence and is explained by a smaller localization length. 

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