Band tails temperature dependence

Fig. 13. Time dependence of the normalized band tail density data from Fig. 9 for increasing temperature. The solid lines are fits to the data using a stretched exponential time dependence (Kakalios et al., 1987).

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. 

Fig. 5.13. The temperature dependence of the band tail (BT) and neutral donor (ND) density of phosphorus doped a-Si H. The equivalent temperature dependence of Ae arsenic donors is shown by the dotted line (Stutzmann et al. 1987).

Fig. 6.6. The temperature dependence of the equilibrium conduction band tail electron concentration at different n-type doping levels (Street 1989).

The comparable equilibrium behavior of p-type a-Si H films is shown in Fig. 6.7. The density of band tail holes, has a smaller activation energy than the n-type material and is constant at the highest doping levels. The increase in conductivity activation energy at the equilibration temperature is less obvious than in the n-type material (see Fig. 5.2), but the frozen state is identified by the dependence on thermal history. The equilibration temperature is lower than in n-type material by about 50 °C and the relaxation times in Fig. 6.5 are also correspondingly shorter. 

The Fermi energy in doped samples is within the band tail, so there should be no significant contribution to the conductivity from the temperature dependence of the band gap. Thus, in the absence of any temperature dependence of E, is equal to the measured conductivity prefactor. 

Fig. 7.9. Temperature dependence of the acousto-electric voltage, and drift mobility of (a) electrons and (b) holes obtained by the SAW technique, llie solid lines are calculated for trapping in an exponential band tail of slope 7J. or 7 (Takada and Fritzsche 1987).

Fig 8.18 shows the thermal quenching of a-Sij. C iH alloys for different x (Liedke et al. 1989). The parameter 7 is about 25 K in a-Si H and increases with the carbon concentration. It should not be too surprising that the temperature dependence originates from the exponential distribution of band tail states, or that the derivation of Eq. (8.44) follows the multiple trapping approach. Thermal quenching... 

Fig. 8.20 shows the dependence of the band tail luminescence intensity on the defect density as measured by the g = 2.0055 ESR resonance in undoped a-Si H. The luminescence intensity drops rapidly when the defect density is above 10 cm" , becoming unobservable at defect densities above 10 cm" (Street et al. 1978). These data establish that the defect provides an alternative recombination path competing with the radiative band tail transition. At the low temperatures of the measurements, the electrons and holes are trapped in the band tails and are immobile. Both the radiative and the non-radiative transitions must therefore occur by tunneling. Section... 

Photoemission and neutron diffraction measurements are limited only to UBe13. The combined XPS-BIS experiments of Wuilloud et al. (1984) displayed a picture similar to other very narrow-band compounds with 5f states extended to 2 eV below Ep, while the 5f intensity is spread above 5 eV about EF. Pronounced satellites corresponding to poorly screened final states accompany the core 4f lines of U, but the XPS spectrum of the Be Is level remains unaffected by hybridization with U electron states. A temperature-dependent narrow feature was distinguished at EF by means of high-resolution studies (Arko et al. 1984). The existence of a low intensity 5f-tail extended far below EF, which can be resolved by resonant photo-emission, is taken as an indication for the hybridization of 5f states with Be-derived conduction-band states (Parks et al. 1984). 

Several completely different experiments support our interpretation of the time-of-flight transport process and the conclusions we have drawn about the distribution of band-tail states. The time-resolved photoinduced absorption experiments of Ray etal. 9% ) support the view that the photogenerated holes are concentrated in the vicinity of an energy E, which moves deeper into the localized state distribution, linearly with temperature and logarithmically with time. Furthermore, the time decay of the photoinduced absorption, which is controlled by the more mobile of the two carriers (electrons), has the t form expected from the multiple trapping model (see, for example, Orenstein eta/., 1982). Thea = r/300°K temperature dependence for a reported by Tauc (1982) is in excellent agreement with the electron time-of-flight results. 

Many important fundamental issues are unresolved. Virtually no experimental information is available about the energy dependence of the mobility in the vicinity of the mobility edge at some finite temperature. Very little is known about the nature of the electronic structure of the band-tail states or about the strength of the electron-phonon interaction for these states. Finally, it is not clear why the disorder produces exponential rather than Gaussian band tails or even why the valence-band tail is wider than the conduction-band tail, although some theoretical models have been suggested (see, for example, Yonezawa and Cohen, 1981). Much remains to be done. 

Surprisingly, we do not observe from out Q T) data, even for doping in the one-percent region, any indication of the formation of a donor band affecting the electronic transport. LeComber et al. (1977) have inferred the presence of a donor band in highly phosphorus-doped a-Si H from their Hall mobility data. We note, however, that the temperature dependence of the Hall mobility as shown in Fig. 17 can be understood according to Eq. (27) by the presence of potential fluctuations. A possible explanation why a donor band is not observed in transport could be that the donor states are hidden by the distribution of tail states. 

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