Thermalization in extended states

The result of one of the first experiments to measure the thermalization times is shown in Fig. 8.8 (Vardeny and Tauc 1981). The 

0 eVps . The thermalization is difficult to detect, as it corresponds to a small change in the absorption because the cross-section is weakly energy-dependent and is also masked by the coherence artifact. In undoped a-Si H there is no particular reason to expect a strongly energy-dependent cross-section. 

More recent measurements vary the energy of the pump and probe independently (Fauchet et al. 1986). Some data are shown in Fig. 8.9 for a 2.0 eV pump and different probe energies. The transient response of the induced absorption is almost constant when the probe energy is above 2 eV as found by Vardeny and Tauc, but there is a fast decay of the absorption at lower probe energies. The decay is interpreted in terms of the bleaching of the absorption transitions which occurs when a carrier occupies a conduction band state and so inhibits the excitation of electrons from the valence band. The transient absorption is the 

The transient induced absorption is different in doped or compensated a-Si H. The compensated material has fewer deep defects to cause rapid recombination so that the time dependence arises only from thermalization. The absorption transients are shown in Fig. 8.10 for a pump and probe energy of 2 eV (Thomsen et al. 1986). In contrast to the almost constant absorption of the undoped material (Fig. 8.8), there is now a rapid change from absorption to induced bleaching after 

1-2 ps. There has been considerable debate about the origin of this effect, but the present consensus seems to be that the bleaching is caused by trapping in donor or acceptor states which have a lower absorption cross-section than the intrinsic band tail states. Thus the time constant for bleaching represents the thermalization time into the dopant states which are estimated to be at least 50 meV beyond the mobility edges. 

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After this time, the carrier crosses the mobility edge and is trapped in localized states, so that further movement is much slower, although the distance between the sites is larger. During thermalization in extended states the carriers diffuse apart a distance. 

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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