Urbach tails

Reference Maximum nitrogen content (at. ) E, (eV) Urbach tail width (mcV) Spin density (spins/cm )... 

Rakhshani AE. Study of Urbach tail, bandgap energy and grain-boundary characteristics in CdS by modulated photocurrent spectroscopy. J Phys Condens Mater 2000 12 4391 100. 

The structural disorder formalism has been mostly utilized to discuss electronic transport in organic solids [29,38] (cf. Sec. 4.6), and only a few works show its applicability to interpret optical spectra [62,67], and, recently, quantum efficiency of organic LEDs [68]. The absorption spectrum of an organic material with impurities disorder, local electric fields, or strong exciton-phonon coupling exhibits an exponential tail, commonly referred to as the Urbach tail [69,70]. Such a spectrum can often be decomposed into broad bands featuring... 

In summary, beyond an exponential (Urbach) tail, which can be due either to phonons or to disorder, there is no low-energy absorption that can be assigned to a neutral state. This conclusion is probably valid for all... 

The slope of the Urbach tail increases at deposition temperatures well above 250 °C and is associated with a lower hydrogen concentration in the film (see Fig. 3.20). It seems probable that the equilibrium temperature also increases and both effects lead to an expectation of a higher defect density, in agreement with observations (see Fig. 2.2). The correlation between Ty and Nj, predicted in Eq. 

Examples of the low temperature luminescence spectra are shown in Fig. 8.12. The luminescence intensity is highest in samples with the lowest defect density and so we concentrate on this material. The role of the defects is discussed in Section 8.4. The luminescence spectrum is featureless and broad, with a peak at 1.3-1.4 eV and a half width of 0.25-0.3 eV. It is generally accepted that the transition is between conduction and valence band tail states, with three main reasons for the assignment. First, the energy is in the correct range for the band tails, as the spectrum lies at the foot of the Urbach tail (Fig. 8.12(6)). Second, the luminescence intensity is highest when the defect density is lowest, so that the luminescence cannot be a transition to a defect. Third, the long recombination decay time indicates that the carriers are in localized rather than extended states (see Section 8.3.3). 

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]. 

H. Tang, F. Levy, H. Berger et al., Urbach tail of anatase Ti02, Phys. Rev. B Conden. Matter 199S, 52(11), 7771-7774. 

If the Urbach tail is interpreted in this way, we may say that at low temperatures the broadening is determined by the zero-point vibrations at higher temperatures the contribution of thermal vibrations becomes more and more important. 

It is more difficult to account for the temperature dependence of Urbach tails in ionic crystals. As it was shown above (Eq. 4.21) Fq (T ) and therefore this simple model does not give the proper temperature dependence, and one may hope a more correct consideration of ihe influence of non-uniform fields on exciton broadening may give the correct answer. Dow and Redfield (1972) point out some plausible reasons that it may be indeed so. Their arguments are based on the consideration that F is proportional not only to (T ) /, as shown above but also to the magnitude of the polaron cut-off vector q (cf. Section 4.4.4) which may be proportional to (T ) /. ... 

He T, Ehrhart P, Meuffels P (1995) Optical band gap and Urbach tail in Y-doped BaCe03. J Appl Phys 79 3219-3223... 

We then show that complete universality exists for the density of states near band edges for weak disorder in less than two dimensions and modified universality exists in more than two dimensions. Deep in the tail, non-universal behavior emerges as the localized states become sensitive to potential fluctuations on individual sites. This non-universal exponential behavior is responsible for the observed Urbach tails. 

The result of Eq. (7) was welcomed because the H-L variation exp [-( E(/e,o) ]> ad never been observed in the tails of disordered three-dimensional bands. Instead, exponential tails are observed everywhere in the optical absorption S (Urbach tails) and the density of states. 

Region C of Figure 24.10 can be related to intraband transitions and to the density of states (DOS). The procedure for determining the DOS has been to measure the absorption in excess of that identified with an extrapolated Urbach tail. 

Most localized states in the forbidden band gap are however close to the edges of the valence or conduction bands [137]. They are related to a high defect concentration of passive layers and suggest a smaller gap, called mobility gap, compared to the band gap (Eg) determined by light absorption measurements. They cause an extension of small photocurrents to photon energies hv with qE < CgEg, which is known as Urbach tailing. Such effects are discussed in Section 5.7.3. 

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