Band tails density of states

In a-C H, the tail states are dominated by n electrons, which results, as pointed out by Robertson [99, 100], in an enhanced localization as compared to a-Si H, giving rise to higher band tail density of states and also to higher defect density in the midgap. 

Optical transitions between the valence and conduction bands are responsible for the main absorption band and are the primary measure of the band gap energy. The optical data are also used to extract information about the band tail density of states. However, the absorption coefficient depends on both conduction and valence band densities of states and the transition matrix elements and these cannot be separated by optical absorption measurements alone. The independent measurements of the conduction and valence state distributions described in Section 3.1.1 make it possible to extract the matrix elements and to explore the relation between N E) and the optical spectrum. 

The first term is an energy which is estimated to be close to the mobility edge, so that the second term represents the shift of the transport path below E. Band tail hopping is most significant when the band tail density of states distribution is broad and at low temperatures such that T transport energy moves up to the mobility edge when the temperature is above 2 and the contribution from the band tail hopping is small. 

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... 

FIG. 1. Schematic density of states distribution. Bands of (mobile) extended states exist due to short-range order. Long-range disorder causes tails of localized states, whereas dangling bonds show up around midgap. The dashed curves represent the equivalent states in a crystal. 

A detailed description of the local bond rearrangement has been derived [439], using the concept of the HDOS with a low-energy tail that corresponds to the H present at weak Si —Si bonds. The width of this tail is 2 i o, i-c., twice the width of the valence band tail in the electronic density of states, which in turn is about equal to the Urbach energy Eq [442,443]. The HDOS then is [439]... 

It was found that in this energy range, a follows the same behavior of the joint (valence -I- conduction) density of states. Thus, Eo, may be interpreted as a measure of the structural disorder [98], as it represents the inverse of band tail sharpness. 

Recent studies of doped a-Si H have found that the background density of localized states, that is, the electrically active dopants and dangling bond defects, are metastable (Ast and Brodsky, 1979 Street et al., 1986, 1987a Muller et al., 1986). After annealing above 150°C in the dark, the dark conductivity at room temperature of n- and p-type doped a-Si H decreases by nearly a factor of two over a time scale of several weeks for n-type and several hours for p-type a-Si H. As shown in Fig. 9 (Street et al., 1987a), the relaxation rate of the occupied band tail density nBT is a sensitive function of temperature, so that the time to reach... 

However, in Ref. 59 also the first valence band spectrum of U has been measured by UPS, and shows a very sharp and, compared with Th, about 10 times more intense 5f peak at 0.3 eV below Ep. Thus the UPS peak at 0.75 eV and the XPS 0.6 eV peak for Th metal may be attributed to the same origin, namely 6d, as suggested by density of state calculations, the small shift between the two being induced by the different contribution of a possible 5 f tail in the UPS and XPS spectra. 

Economou et al. (1985) and Soukoulis et al. (1985, 1986, 1987) have used somewhat similar methods to calculate both the density of states, the mobility edge and the conductivity as a function of energy for the case of diagonal disorder their work is limited to disorder parameters V0 less than one-fifth of the bandwidth B, and is therefore relevant to the band tail... 

The disorder inherent in hydrogenated amorphous silicon gives rise to tails in the density of state distribution near the band edges. Calculations by... 

Fig. 1.6. Schematic density of states distribution for an amorphous semiconductor showing the bands, the band tails, and the defect states in the band gap. The dashed curves are the equivalent density of states in a crystal.

An example of the valence band tail of a-Si H obtained using this technique is shown in Fig. 3.9. The position of the mobility edge, E, is not obtained in this experiment, which does not distinguish localized from extended states, but is estimated to be at about 5.6 eV. There is a linear density of states near and above y, and an exponential band tail over several orders of magnitude of N E) below y. The slope of the... 

Fig. 3.9. Photoemission yield measurements of the valence band density of states. Note the exponential band tail and linear valence band edge (Winer and Ley 1989).

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. 

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