Band tails dispersive transport

Global AMI.5 sun illumination of intensity 100 mW/cm ). The DOS (or defect) is found to be low with a dangling bond (DB) density, as measured by electron spin resonance (esr) of - 10 cm . The inherent disorder possessed by these materials manifests itself as band tails which emanate from the conduction and valence bands and are characterized by exponential tails with an energy of 25 and 45 meV, respectively the broader tail from the valence band provides for dispersive transport (shallow defect controlled) for holes with alow drift mobiUty of 10 cm /(s-V), whereas electrons exhibit nondispersive transport behavior with a higher mobiUty of - 1 cm /(s-V). Hence the material exhibits poor minority (hole) carrier transport with a diffusion length <0.5 //m, which puts a design limitation on electronic devices such as solar cells. 

The Urbach edge represents the joint density of states, but is dominated by the slope of the valence band, which has the wider band tail. Expression (3.37) for is therefore also an approximate description of the thermal broadening of the valence band tail. It is worth noting that the slope is quite strongly temperature-dependent above 200 K. This may have a significant impact on the analysis of dispersive hole transport, in which the temperature dependence of the slope is generally ignored. 

There are several techniques for measuring the mobility in a-Si H, most notably the time-of-flight method. All the techniques measure the average motion of the carriers over a time longer than that taken to trap a carrier in the band tail states, so that the drift mobility is always measured, rather than the free carrier mobility. The drift mobility depends on the distribution of traps and the free mobility can only be extracted if the density of states distribution is known. Chapter 3 describes how the time-of-flight experiment is used to determine the shape of the band tail through the analysis of the dispersive transport process. 

It is possible to extract the free mobility and the shape of the band tail from the dispersive transport data without any assumptions about the form of the tail (Marshall, Berkin and Main 1987). The average... 

Fig. 7.8. (a) Electron and (b) hole drift mobility data (points) fitted to the multiple trapping dispersive transport mechanism, assuming an exponential band tail (lines) (Tiedje 1984). 

Ej is a demarcation energy, similar to that defined in the analysis of dispersive transport (see Section 3.2.1). It is assumed that all carriers which are thermally excited recombine non-radiatively, but the same result is obtained if some fraction are subsequently retrapped and recombine radiatively. The luminescence efficiency is given by the fraction of carriers deeper than E, . An exponential band tail density of states proportional to exp (E/kf,) results in a quantum efficiency of... 

Eq. (8.65) assumes that electrons and holes form a quasi-equilibrium with the band tail states. This is valid for electrons near room temperature, but only approximate for holes since dispersive hole transport indicates that a quasi-equilibrium is not fully established in the band tail. 

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