Wavefunction decay constants

In the Miller-Abrahams expression, the hopping rates are a product of a prefactor v0, an electron overlap quantity Wy = Wji9 and the term exp[-(ey - zj)/kT when y > e, and unity for the case where ey < e7. For a pair of sites separated Ry in an isotropic medium, Wy = exp(-2yft7y). where y is an inverse wavefunction decay constant. To incorporate positional or off-diagonal disorder, Pautmeier et al. (1988, 1990) assumed that sites / and j make independent contributions as... 

In the lattice gas model, the hopping frequency of a carrier decreases exponentially with the hopping distance p as v = vQ exp(-2p/p0). Here, pQ is a wavefunction decay constant and vQ a frequency factor. From the Einstein relationship, the zero-field mobility is... 

Figure 7 shows the concentration dependencies of a. The width of the DOS was described by the dipolar disorder model and gave van der Waals components of 0.104 eV, independent of the TPM-E concentration. These results differ from the aiylamine doped polymers where the van der Waals component increases with increasing dilution. These results are discussed in Section III. From a plot of log(ju0/p > - Y 14.59 versus p, the wavefunction decay constant was determined as 1.2 A. 

Figure 10 shows the concentration dependencies of a for TPM-A, TPM-E and TPM-F doped PS. The results show that a increases with decreasing p. Figure 11 shows plots of log(p0/p2) -1 /4.59 versus p for TPM-A, TPM-E, and TPM-F doped PS. The predicted linear relationships are observed. From the slopes, the wavefunction decay constants are 1.0 A. 

Borsenberger (1992a) measured the concentration dependence of the hole mobility of TAPC doped PC. The width of the DOS increased with decreasing concentration, as illustrated in Fig. 31. The concentration dependence was attributed to dipole moments of the carbonyl groups. The concentration dependence of was attributed to packing constraints. From a plot of l°g(/ 0/p2) - 14.59 versus p, the wavefunction decay constant was determined... 

Troup et al. (1980) measured hole mobilities of TTA doped PC. The concentration dependence was described by the lattice gas model with a wavefunction decay constant of 1.1 A. The temperature dependence was described by an Arrhenius relationship with an activation energy of 0.35 eV at 1.0 x 105 V/cm. 

Aratani et al. (1996) investigated effects of molecular orbital distributions on hole mobilities of a series of triphenylamine derivatives doped into PC. The results show that the HOMO of the triphenylamine derivatives has essentially no effect on either the width of the DOS or the degree of positional disorder, but has a large effect on the prefactor mobility. Aratini et al. argued that increasing the HOMO distribution on the triphenylamine moiety results in an increase in the wavefunction decay constant. The mobility increases as the fraction of the HOMO electron density distributed on the triphenylamine moiety increases. The ionization potential of the triphenylamine derivatives was found to have little effect on the transport behavior. 

Arrhenius relationship. The activation energies were between 0.52 and 0.45 eV for concentrations between 15 and 60%. The concentration dependence of the zero-field mobility was described by a wavefunction decay constant of 1.3 A. The results were described by a small-polaron argument. Based on the concen-... 

N-isopropylcaibazole (NIPC) was studied as a model for the monomer repeat unit of PVK by Mort et al. (1976). The concentration dependence was described by a wavefunction decay constant of 1.5 A, compared to 1.2 A for PVK (Gill, 1972). Composite plots of the logarithm of the photocurrent versus the logarithm of time were universal when normalized to the transit time. The activation energy was 0.1 eV smaller than for PVK. The results were described by the Scher-Montroll model (1975). 

Santos-Lemus and Hirsch (1986) measured hole mobilities of NIPC doped PC. Over a range of concentrations, fields, and temperatures, the transport was nondispersive. The field and temperature dependencies followed logn / El/2 and -(T0IT)2 relationships. For concentrations of less than 40%, a power-law concentration dependence was reported. The concentration dependence was described by a wavefunction decay constant of 1.6 A. To explain a mobility that shows features expected for trap-free transport with a field dependence predicted from the Poole-Frenkel effect, the authors proposed a model based on field-enhanced polaron tunneling. The model is based on an earlier argument of Mott (1971). 

For doped polymers, the concentration dependence of the prefactor mobility is usually described by the wavefunction decay constant. Wavefunction decay constants are separately discussed in Section XII G. 

Table 17 Wavefunction Decay Constants of a Series of Doped Polymers...

TNF dispersed in the polyester. Figure 19 shows a plot of log(p/p2) versus p for TNF doped polyester. From the slope, the wavefunction decay constant was determined as 1.8 A, the same as for electron transport in TNF.PVK mixtures. In comparing the results for the TNF dispersions and TNF PVK mixtures, Gill concluded that complexing TNF with PVK did not affect electron transport through the TNF sites. In agreement with Gill s results, Emerald and Mort (1974) later reported an electron mobility of 6.0 x 10-5 cm2/Vs for TNF at 4.0 x 105 V/cm. 

The concentration dependencies of the mobility are usually described by a wavefunction decay constant pQ. Table 7 summarizes literature values. The... 

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