Quasi-free mobility

Where mobility data are available over a considerable range of temperature, the activation energy is often found to be temperature-dependent. Thus, in n-pentane the activation energy increases with temperature whereas in ethane it decreases (Schmidt, 1977). Undoubtedly, part of the explanation lies in the temperature dependence of density, but detailed understanding is lacking. In very high mobility liquids, the mobility is expected to decrease with temperature as in the case of the quasi-free mobility. Here again, as pointed out by Munoz (1991), density is the main determinant, and similar results can be expected at the same density by different combinations of temperature and pressure. This is true for LAr, TMS, and NP, but methane seems to be an exception. 

Here (g)T = (e/m)Tf2/(r( + Tt) is called the ballistic mobility and (/t)H = + Tt) is the usual trap-controlled mobility. (q)F is the applicable mobility when the velocity autocorrelation time ( 1) is much less than the trapping time scale in the quasi-free state (fTf l). In the converse limit, (jj)t applies, that is—trapping effectively controls the mobility and a finite mobility results due to random trapping and detrapping even if the quasi-free mobility is infinite (see Eq. 10.8). 

Apart from fundamental constants and the liquid temperature, the variable parameters in the effective mobility equation are the quasi-free mobility, the trap density, and the binding energy in the trap. Figure 10.2, shows the variation of prff with e0 at T = 300 K for /tqf = 100 cm3v 1s 1 and nt = 1019cm-3. It is clear that the importance of the ballistic mobility (jl)l increases with the binding... 

In comparing the results of the quasi-ballistic model with experiment, generally pq[ = 100 cn v s-1 has been used (Mozumder, 1995a) except in a case such as isooctane (Itoh et al, 1989) where a lower Hall mobility has been determined when that value is used for the quasi-free mobility. There is no obvious reason that the quasi-free mobility should be the same in all liquids, and in fact values in the range 30-400 cmV -1 have been indicated (Berlin et al, 1978). However, in the indicated range, the computed mobility depends sensitively on the trap density and the binding energy, and not so much on the quasi-free mobility if the effective mobility is less than 10 crr v s-1. A partial theoretical justification of 100 cm2 v 1s 1 for the quasi-free mobility has been advanced by Davis and Brown (1975). Experimentally, it is the measured mobility in TMS, which is considered to be trap-free (vide supra). 

Electrons have not been detected by optical absorption in alkanes in which the mobility is greater than 10 cm /Vs. For example, Gillis et al. [82] report seeing no infrared absorption in pulse-irradiated liquid methane at 93 K. This is not surprising since the electron mobility in methane is 500 cm /Vs [81] and trapping does not occur. Geminately recombining electrons have, however, been detected by IR absorption in 2,2,4-trimethyl-pentane in a subpicosecond laser pulse experiment [83]. The drift mobility in this alkane is 6.5 cm /Vs, and the quasi-free mobility, as measured by the Hall mobility, is 22 cm /Vs (see Sec. 6). Thus the electron is trapped two-thirds of the time. 

The magnitude of the mobility then depends on the value of the quasi-free mobility in such liquids multiplied by the fraction of time the electron is quasi-free since the trapped electron is relatively immobile. Thus ... 

The main experimental elfects are accounted for with this model. Some approximations have been made a higher-level calculation is needed which takes into account the fact that the charge distribution of the trapped electron may extend outside the cavity into the liquid. A significant unknown is the value of the quasi-free mobility in low mobility liquids. In principle, Hall mobility measurements (see Sec. 6.3) could provide an answer but so far have not. Berlin et al. [144] estimated a value of = 27 cm /Vs for hexane. Recently, terahertz (THz) time-domain spectroscopy has been utilized which is sensitive to the transport of quasi-free electrons [161]. For hexane, this technique gave a value of qf = 470 cm /Vs. Mozumder [162] introduced the modification that motion of the electron in the quasi-free state may be in part ballistic that is, there is very little scattering of the electron while in the quasi-free state. 

Here t is the time elapsed from the moment the light is switched on, z 1 is the probability of the transition of an electron to a quasi-free (mobile) state per unit time under the action of light, Rz = (ae/2)lnver is the distance of electron tunneling from a trap to an acceptor within the time z. 

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