Urbach band tail

Hall s expression is often used even for narrow-bandgap semiconductors with nonparabobc bands and with an arbitrary degeneration [19, 21, 22]. Most of the calculations in this work were performed using the accurate model of absorption coefficient, based on Kane s model with taking into account the Urbach band tailing [23]. For some calculations an empirical approximation for HgCdTe absorption coefficient was used [24]... 

A detailed description of the local bond rearrangement has been derived [439], using the concept of the HDOS with a low-energy tail that corresponds to the H present at weak Si —Si bonds. The width of this tail is 2 i o, i-c., twice the width of the valence band tail in the electronic density of states, which in turn is about equal to the Urbach energy Eq [442,443]. The HDOS then is [439]... 

In amorphous semiconductors, information about the width of the band tail states (or disorder) may also be extracted from the optical absorption spectra. For photon energies near bandgap energy, the optical absorption coefficient of amorphous semiconductors exhibit an exponential dependence on the photon energy, following the so-called Urbach relationship ... 

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. 

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).

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. 

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). 

Further complication in semiconductor band shape analysis concerns the spectral region near the fundemental absorption onset. Ideal semiconductor crystal at 0 K should not absorb any photons with energies lower than Eg. Real systems, however, show pronounced absorption tails at energies lower than the bandgap energy (Figure 7.7). The absorption profile within the tail region can be very well approximated by the empirical Urbach s rule [23-26] ... 

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... 

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]. 

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. 

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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