Thermalization in localized states

Low temperature tunneling thermalization in the band tail is observed by time resolved luminescence, which is a transition between band tail electrons and holes, as described in Section 8.3.2. Fig. 8.11 (a) shows the change in energy of the luminescence peak with increasing time after the excitation pulse, measured at 12 K. The decrease of the energy at times up to 10 s is caused by carrier thermalization - the changes at 

Thermalization by multiple trapping dominates over direct timneling above 50-100 K. The luminescence energy reflects the carrier distribution and so is expected to have a temperature-dependent shift of the peak energy, given from Eq. (8.16) by 

In summary, the experimental data confirm the models of carrier thermalization. Thermalization in extended states is very rapid and is completed in less than 10 s. Thermalization by tunneling between localized states becomes increasingly slow as the carriers move into the band tail and at high temperatures is overtaken by the multiple trapping mechanism of sequential thermal excitation and trapping. 

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