Optical absorption Urbach edge

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... 

Figure 8.18. Optical absorption edges for a variety of amorphous semiconductors at room temperature showing Urbach behaviour. The arrows mark the value for...

In these studies the optical absorption edge was defined as the energy of light at a transmission of 1%, that is an optical density of 2 (OD=2). Although common, this definition does not reflect the true absorption edge, which has to be evaluated more strictly, for example, using the so-called Urbach equation. 

The analysis of the shape of the absorption edge of the high-pressure phase (Fig. 13) shows the existence of two spectral ranges with different types of energy dependence on the absorption coefficient. At high values of absorption it follows the empirical Tauc relation [57] in the case of parabolic band edges (Fig. 13(b)), while at smaller absorption a so-called Urbach or exponential absorption tail [58, 59] is observed (Fig. 13(c)). The existence of this kind of absorption edge is normally related to amorphous semiconductors. The optical absorption gap determined from our experiment is 0.6-0.7 eV and it decreases with pressure (see below). The slope of the Urbach tail, which can be considered as a measure of a random microfield [59] is found to be T=2.6 eV at 160 GPa. This is very close to what one would expect for an amorphous phase with a coordination of 2.5 [59]. 

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... 

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