Band tails, shape

The opposite point of view is that the luminescence line shape and energy are determined by the band tail shapes and the convolution of... 

Since the slope, E, of the Urbach absorption reflects the shape of the valence band tails, it follows that varies with the structural disorder. For example, one measure of the disorder is the average bond angle variation, which is measured from the width of the vibrational spectrum using Raman spectroscopy (Lannin 1984). Fig. 3.22 shows an increasing E with bonding disorder, which is caused by changes in the deposition conditions and composition (Bustarret, Vaillant and Hepp 1988 also see Fig. 3.20). The defect density is another measure of the disorder and also increases with the band tail slope (Fig. 3.22). A detailed theory for the dependence of defect density on is given in Section 6.2.4. 

The dark ESR spectra of doped a-Si H in Fig. 5.10 show resonances near g = 2, with different line shapes and g-values from those of the dangling bond (Stuke 1977). These lines are attributed to band tail states because they are observed when the Fermi energy is moved up to the band tails by doping and also in the low temperature LESR spectra of undoped a-Si H, when electrons or holes are optically excited into the band tails. The larger g-shift for the valence band tail states than for the conduction band states is expected from Eq. (4.12). 

The weak bond model is useful because the distribution of formation energies can be evaluated from the known valence band and defect density of states distributions. Fig. 6.12 illustrates the distribution of formation energies, N iU). The shape is that of the valence band edge given in Fig. 3.16 and the position of the chemical potential of the defects coincides with the energy of the neutral defect gap state. Fig. 6.12 also shows that in equilibrium virtually all the band tail states which are deeper than convert into defects, while a temperatiue-dependent fraction of the states above convert. 

The weak bond model assumes a non-equilibrium distribution of weak bonds arising from the disorder of the a-Si H network. It has been proposed that the shapes of the band tails are themselves a consequence of thermal equilibrium of the structure (Bar-Yam, Adler and Joannopoulos 1986). The formation energy of a tail state is assumed proportional to the difference in the one-electron energies, so that the energy, required to create a band tail state of energy Ey from the valence band mobility edge is... 

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... 

The first observation of a metastable component to the optically induced ESR in a-Si H was reported by Street ct a/., (1981) in heavily P- and B-doped samples and in doped and compensated samples. [For a recent review of metastable, optically induced effects in a-Si H see Pankove (1982).] As near as can be determined, this metastable signal is a fraction ( 20%) of the transient optically induced response, and the dependences of the line shapes on doping appear to be similar for the two eflFects. These ESR centers can be generated with light intensities of 150 mW cm , and they anneal in a few minutes at 80 ° K. It is particularly surprising that a subset of the photoexcited electrons are trapped in band-tail states or in a Tj configuration in p-type material in which there exists a large density of holes to facilitate rapid recombination. 

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