Urbach energy

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]... 

The variation of the Tauc gap and the Urbach energy obtained by Silva et al. are shown in Figure 38, together with the variation of the refraction index. 

In fact, an apparent doping effect was also reported by Schwan et al. [39] in a-C(N) H films deposited by the highly ionized plasma beam deposition technique in C2H2-N2 atmospheres. Schwan et al. also observed thermally activated behavior for the conductivity. As reported by Silva et al. [14], they also observed increasing optical gap, and decreasing ESR spin signal, but the Urbach energy was found to increase. 

Optical absorption spectra is used to calculate the energy band gap (Fig. 14) and the Urbach energy for the as synthesized nanopowders, resulting in Eg=3.94eV Urbach energy= 1.33 eV. 

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 ... 

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] ... 

Skettrup T. Urbach s rule derived from thermal fluctuations in the band-gap energy. Phys Rev B 1978 18 2622-31. 

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. 

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... 

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).

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). 

Another interesting case, in which the self-consistent solution of Eq. (6.13) is reasonably simple, concerns a diagonal disorder described by a Gaussian distribution P(h ). A Gaussian distribution has been introduced by Sumi and Toyozawa to simulate the fluctuation of the electron (or exciton) orbital energy due to a phonon field and explain the Urbach absorption tail of a number of semiconductors. 

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]. 

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