Band tails carrier density

The band tail carrier density n r is the difference between the donor and defect densities (Eq. (6.5)) and is generally smaller than either (see Fig. 5.16). is therefore a sensitive measure of the equilibration, and... 

The rapid thermalization of carriers in extended states ensures that virtually all of the recombination occurs after the carriers are trapped into the band tail states. The two dominant recombination mechanisms in a-Si H are radiative transitions between band tail states and non-radiative transitions from the band edge to defect states. These two processes are described in this section and the following one. The radiative band tail mechanism tends to dominate at low temperature and the non-radiative processes dominate above about 100 K. The change with temperature results from the different characteristics of the transitions. The radiative transition rate is low, but there is a large density of band tail states at which recombination can occur. In contrast, the defect density is low but there is a high non-radiative transition rate for a band tail carrier near the defect. Band tail carriers are immobile at low temperatures, so that the recombination is... 

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. 

A comparison of Fig. 5.12 and the defect density in Fig. 5.9 shows that the total density of the band tail electrons - neutral donors plus occupied intrinsic band tail states-is about ten times less than the density of deep defects induced by the doping. This is a remarkable result because it implies that almost all the donors are compensated by deep defects. However, before considering the consequences of this observation, it is helpful to discuss an alternate experimental technique for measuring the density of shallow electrons or holes, because of the possibility that ESR is missing some of the carriers due to electron pairing or broadening of the resonance. 

The electrical data described in Section 5.2.4 are consistent with this expected behavior. The low defect density and the pinning of p are both observed. The higher doping efficiency explains the wider band tails and the associated reduction in the carrier mobility, because the many extra dopant states directly add localized states to the band tails. In addition, the large Coulomb potential fluctuations due to the high concentration of charged dopants lead to a further broadening of the band tails. 

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. 

The multiple trapping model of transport in an exponential band tail is described by Eq. (3.20) in Section 3.2.1 and a fit to this expression is given in Fig. 7.8. TTie free carrier mobilities are 13 and 1 cm V s" for electrons and holes respectively, with the band tail slopes of 300 °C and 450 C (Tiedje el al. 1981). Implicit in the analysis is the assumption that the exponential band tail extends up to the mobility edge, but the density of states model developed in Fig. 3.16 shows that this is a poor approximation. The band taU changes slope below E. and this may change the estimated values of the mobility. 

Examples of the low temperature luminescence spectra are shown in Fig. 8.12. The luminescence intensity is highest in samples with the lowest defect density and so we concentrate on this material. The role of the defects is discussed in Section 8.4. The luminescence spectrum is featureless and broad, with a peak at 1.3-1.4 eV and a half width of 0.25-0.3 eV. It is generally accepted that the transition is between conduction and valence band tail states, with three main reasons for the assignment. First, the energy is in the correct range for the band tails, as the spectrum lies at the foot of the Urbach tail (Fig. 8.12(6)). Second, the luminescence intensity is highest when the defect density is lowest, so that the luminescence cannot be a transition to a defect. Third, the long recombination decay time indicates that the carriers are in localized rather than extended states (see Section 8.3.3). 

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... 

The average of 10 s gives /23, so that the measured value of 20-25 K is of the correct magnitude for the band tail slope in a-Si H. The larger in the alloys is because they have broader band tails. The derivation of Eq. (8.46) makes several approximations, of which the most severe is the neglect of the distribution of lifetimes, so that one should not expect an accurate fit. Also it is tacitly assumed that only one type of carrier is thermally excited. The non-radiative process obviously involves both carriers. The question of what is the rate-limiting step in the process is complicated and, in fact, the thermal quenching of the luminescence depends on the defect density and on the excitation intensity. 

The charge-induced defect creation mechanism is too slow to be significant at low temperature and the electronic recombination effects reestablish themselves. Low temperature measurements (0-100 K) have been performed using an IR probe beam to modulate the excess carrier density that is in the band tail states (Hundhausen, Ley and Carius... 

Such an observation of strong VG and T dependent EA can be explained using the multi trap and release model which assumes a semiconductor with Fermi level closer to the band edge and upon applying VG the Fermi level moves through the distribution of band tail states. As a result EA is reduced as the density of injected charge carriers are increased above the mobility edge [4, 6-11],... 

K. The observation that the density of band tail and mid-gap states is very sensitive to the microstructure of the film [116] may explain why the mentioned peak is not observed in every sample. Moreover, transient photoinduced absorption and photoconductance have not been measured in the same film, and it is not certain that the carrier lifetime or photoexcited carrier concentration does not exhibit a peak at T approx. 250 K in some samples. 

Conduction can also operate in the band tails below the mobility edge when such tails are wide and have a sufficiently high density of states to allow rapid hopping of a carrier from one site to another via thermally-activated processes. In this case the mobility of a carrier depends exponentially upon the amount of energy it must gain to leave a given state and hop to the next. Thus, it was proposed that the mobility will have the form [5]... 

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