Conductivity prefactor

Fig. 7.3. Measured values of the conductivity prefactor a, versus the conductivity activation energy, showing the Meyer-Neldel relation. Data from sever different laboratories are shown (Tanielian 1982).

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. 

A conductivity prefactor of 100-200 ft" cm" gives the free carrier mobility from Eq. (7.5),... 

Suppose next that E is temperature-dependent and that Yt is positive. According to the definition in Eq. (7.15), moves into the band gap as the temperature is raised. The correct conductivity prefactor will be lower than the measured value and the experimentally determined position of is further into the band than the actual value. The opposite occms when is negative - conduction takes place above the apparent transport energy with a higher prefactor than that measured. 

The effect of the statistical shift can be calculated from Eq. (7.18) and the density of states distribution, just as for the equilibrium state except that the density of electrons is now constant. The resulting values of Yp are in the range 3k-6k, so that the correction to the prefactor of exp(Yp/ ) from the statistical shift is a factor of 10-100. The calculated conductivity is shown in Fig. 7.5 and a good fit to the data is found with a conductivity prefactor of 100 cm and the same transport energy as was obtained from the analysis of the equilibrium regime. The modeling of the conductivity therefore shows that the only difference... 

Fig. 7.5. Comparison of calculated and measured conductivity of n-type a-Si H in the frozen state. The calculation assumes a conductivity prefactor of 100 cm" (data from Fig. 6.3).

Fig. 7.7. Relation between the conductivity prefactor and activation energy for different conduction regimes described in the text.

The analysis of the experimental data in Section 7.1 found a conductivity prefactor of about 100 Q" cm", but without any correction for the temperature dependence of the mobility edge. The comparison with the predicted value of o , suggests that Yc is less than 1 and is positive, which corresponds to a shift of Ec into the gap with increasing temperature. Similarly the free carrier mobility found in... 

This explains why the conductivity prefactor is quite close to the predictions of the homogeneous mobility edge model, even in the presence of fluctuations. 

The second expression uses the experimental information about the conductivity prefactor derived in Eq. (7.19). The descriptions of the photoconductivity in terms of the recombination lifetimes or the quasi-Fermi energies are equivalent. 

Here k is Boltzmann s constant and denotes the Fermi energy. The conductivity prefactor (Tq depends on the carrier mobility and on the density of states at the energy E and above. The heat of transport term A of the... 

Fig. 20. Fit of thermopower data of Fig. 19, using different ratios of conductivity prefactors. [From Beyer et al. (198 la).]...

One of the striking features of the conductivity data of doped a-Si H films is the wide variation of apparent conductivity prefactors (tJ. In Fig. 21 (tJ values of phosphorus-doped films from Fig. 14 have been plotted as a function of the apparent conductivity activation energy E, both for the low temperature and high temperature region. Also included are data for Li doping (Beyer and Overhof, 1979). The results agree well with those of Rehm etal. 911), Carlson and Wronski (1979), and Anderson and Paul (1982). A... 

Fig. 21. Apparent conductivity prefactor cr J as a function of conductivity activation energy E for phosphorus-doped films of Fig. 14 (squares) and for Li doping (triangles). [Data from Beyer et al. (1979b).] Open symbols, low temperature range closed symbols, high temperature range.

Fig. 25. Calculated curve of apparent conductivity prefactor crj versus conductivity activation energy E for extrapolation from the 300°K < T < 400°K range. Experimental data for comparison— , O PH, , ASH3 A, A Sb(CH3)j V, Bi(CH3)3. Qosed symbols, 1% doping open symbols, 0.1% doping. [Experimental data from Carlson and Wronski (1979) figure from Overhof and Beyer (1983).]...

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