Dispersive trapping in a band tail

To explain the trap-limited transport it is useful to consider the model of a single trapping level of density, Nj., at energy E. below the conducting states, as illustrated in Fig. 3.10. The drift mobility is the free carrier mobility reduced by the fraction of time that the carrier spends in the traps, so that, 

The approximate expression applies when p . Thus the drift mobility is thermally activated with the energy of the traps. When there is a distribution of trap energies, N E), the drift mobility reflects the average release time of the carriers, which is given by. 

However, when Tis less than T., the exponent in Eq. (3.6) is positive, so that the integral diverges and the average trap release time becomes infinite. The drift mobility should consequently drop abruptly to zero. To see that this is not what actually happens, consider the median release time of the carriers, defined by 

E is a well-defined finite energy, = kTf. In 2, so that although the 

The reason for the divergent Xj but finite x is that the average release time from the traps is dominated by the exponentially small density of states with very large trap energies. In any measurement that involves a finite number, n, of trapping and release events, the average carrier will not fall into a trap deeper than where 

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