Urbach edge

Fig. 3.23. Temperature dependence of (a) the slope, of the Urbach edge, and (6) the band gap energy and (c) the correlation between the band gap and the band tail slope (Cody et al. 1981).

Eq. (3.35) relates the broadening of the Urbach edge and the shift of the band gap, both of which originate from the thermal and bonding disorder. 

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. 

Fig. 5.18 compares the optical absorption spectra of phosphorus doped a-Si H with the corresponding compensated material. The compensated a-Si H has a substantially broader Urbach edge, but a... 

Ee is approximately equal to Eo and F is a constant having a range of 10-25 eV . Absorption edges which obey the above exponential equation are called Urbach edges. There is as such no clear understanding of the origin... 

Fig. 10, Hole photocurrenl transients measured with 2- and 8-V applied bias (solid and open circles, respectively) at 299 K in the time-of-flight experiment. [Reprinted with permission from Solid State Communications, Vol. 47, T. Tiedje, B. Abeles, and J. M. Cebulka, Urbach edge and the density of states of hydrogenated amorphous silicon. Copyright 1983, Pergamon Press, Ltd.]...

The electronic transitions which are responsible for the Urbach edge have been investigated by Izumitani and Hirota (1985) and Izumitani et al. (1986) by UV reflection spectroscopy with synchrotron radiation in Zrp4 BaFj and AlFj-CaFj-P2O5 glasses. In the FZ glasses, in addition to weaker features at 7.3, 9.3, 13.2 and... 

The frequency and temperature dependence of Urbach edges is empirically described by the equation... 

The theories of the Urbach edge are based on the idea that a sharp absorption edge is broadened by some mechanism. In ionic crystals there is little doubt that optical phonons are responsible for the Urbach edges. If their frequency is then by a general argument given below... 

Bustarret E, Ligeon M, Mihalcescu I, Oswald J (1995) Urbach edges in light-emitting porous silicon and related materials. Thin Solid Films 255 234-237... 

Figure 3.2 Hole excitation by weak (a) and intense (b, c) Urbach-edge light.

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