Urbach absorption edge

According to the theory of the Urbach absorption edge in crystals, the slope E is proportional to the thermal displacement of atoms r(7). The frozen phonon model assumes that an amorphous semiconductor has an additional temperature independent term, r , representing the displacements which originate from the static disorder, so that... 

Skuja, L., Kajihara, K., Ikuta, Y, Hirano, M., and Hosono, H., Urbach absorption edge of silica Reduction of glassy disorder by fluorine doping, J. Non-Cryst. Solids 345 346, 328 (2004). 

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... 

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]. 

Fig. 14. Transmission spectra of polymeric nitrogen as a fimction of temperature. Spectra are shifted vertically for clarity. The characteristic peak of the T) phase is marked by a vertical arrow. Inset (a) shows the pressure dependence of the absorption spectra of nitrogen at very high pressures and room temperature. Gray lines represent the Tauc fits to the speetra in an appropriate spectral range. The determination of the energy gap from these measurements is obscured by additional losses caused by the presence of a fine ruby powder in the chamber. The high-energy absorption edge is most probably due to stress-induced absorption of diamond anvils (Ref. 62). (b) Urbach plots at 200 GPa and different temperatures (shifted vertically). Gray lines are guides to the eye.

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... 

Urbach F. The long-wavelength edge of photographic sensitivity and of the electronic absorption of solids. Phys Rev 1953 92 1324. 

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... 

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