Band tails

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 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]... 

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. 

In amorphous semiconductors, information about the width of the band tail states (or disorder) may also be extracted from the optical absorption spectra. For photon energies near bandgap energy, the optical absorption coefficient of amorphous semiconductors exhibit an exponential dependence on the photon energy, following the so-called Urbach relationship ... 

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. 

While most of the research in metastable defect formation has focussed on light-induced defects, there has recently been growing interest in thermally generated defects. Smith and Wagner (1985 Smith et al., 1986) extended the proposed Staebler-Wronski mechanism of electron-hole recombination via band tail states, resulting in the formation of dangling... 

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... 

Fig. 9. Time decay of the occupied band tail density n Bx, measured by the voltage pulse charge sweepout technique, for various temperatures. The n-type doped a-Si.H sample was first annealed at 210°C for 10 min. and then cooled to the indicated temperatures (Street et al., 1988).

The slow relaxation of the occupied band tail density and of the conductivity a are accurately described by the stretched exponential time dependence... 

Fig. 13. Time dependence of the normalized band tail density data from Fig. 9 for increasing temperature. The solid lines are fits to the data using a stretched exponential time dependence (Kakalios et al., 1987).

T. Tiedje, Information about Band-Tail States from Time-of-Flight Experiments Arnold R. Moore, Diffusion Length in Undoped a-Si H W. Beyer and J. Overhof, Doping Effects in a-Si H H. Fritzche, Electronic Properties of Surfaces in a-Si H CR. Wronski, The Staebler-Wronski Effect... 

As shown in Fig. 2- 3, localized electron levels arise (A and C in the figure) near the band edges at relatively high state densities tailing into the band gap these are called diffuse band tail states. Further, localized electron levels may occur due to dangling bonds and impurities (B in the figure) in the band gap, which are called gap states. 

Fig. 2-33. Electron energy and state density in amorphous semiconductors A and C = diffuse band tail states B = gap states, cmc = mobility edge level for electrons MV = mobility edge level for holes ...

Electrons in the diffuse band tail states migrate in accord with the hopping mechanism rather than the band mechanism. The energy gap between the mobility edge Cue for electrons and the mobility edge mv for holes is called the mobility gap, Emt, instead of the band gap, C(. 

T. Tiedje, Information about band-Tail States from Time-of-Flight Experiments... 

Silver M, Pautmeier L, Bassler H (1989) On the origin of exponential band tails in amorphous-semiconductors. Solid State Commun 72 177... 

Electron band tailing in amorphous semiconductors Tauc (1972)... 

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... 

Mackintosh (1963) showed that the above effective mass, and an appropriate dielectric constant, are comparable with a Mott transition according to the equation n1/3aH=0.25 at x=0.1, but this equation has no theoretical basis in an exponential band tail. 

To clarify the effect of substituents we will discuss the spectrum of 4-nitro-benzenol, even though the compound has no value as a dye. It is a pale yellow compound ( raax 320 nm) with an ultraviolet absorption band tailing into the visible, as in Figure 28-8. Its close relatives are benzene, benzenol, and nitrobenzene ... 

---