Ballistic electron motion

The new model is called quasi-ballistic because the electron motion in the quasi-free state is partly ballistic—that is, not fully diffusive, due to fast trapping. It is intended to be applied to low- and intermediate-mobility liquids, where the mobility in the trapped state is negligible. According to this, the mean... 

Table 10.4 lists the values of trap density and binding energy obtained in the quasi-ballistic model for different hydrocarbon liquids by matching the calculated mobility with experimental determination at one temperature. The experimental data have been taken from Allen (1976) and Tabata et ah, (1991). In all cases, the computed activation energy slightly exceeds the experimental value, and typically for n-hexane, 0/Eac = 0.89. Some other details of calculation will be found in Mozumder (1995a). It is noteworthy that in low-mobility liquids ballistic motion predominates. Its effect on the mobility in n-hexane is 1.74 times greater than that of diffusive trap-controlled motion. As yet, there has been no calculation of the field dependence of electron mobility in the quasi-ballistic model. 

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. 

If d is smaller than the electron mean free path l (l l = It1 + l l, li is the elastic mean free path), the electrons flow through the contact ballistically. In opposite cases (d f>> l) they perform a diffusive motion, but if the energy relaxation length Ae remains larger than d,... 

Microwaves can be produced by four types of macroscopic cavity resonators that use the ballistic motion of electrons across a cavity opening the klystron, the magnetron, the traveling-wave tube (TWT), and the gyrotron. They can also be generated by field-effect transistors at low frequencies, by Gunn42 diodes, and by IMP ATT diodes. 

The frequency T - corresponding to the ballistic motion of electron between two successive scatterings by impurities is here the characteristic one. At oJQ, the usual Drude... 

The relation (X (0) = Kf between mean squared displacement and time presents a range of possibilities for varying a, in which canonical Brownian motion (a = 1) and ballistic motion (a = 2) represent just two possibilities. AU cases apart from a = 1 are clubbed under the label anomalous Brownian motion and encompass a range of interesting phenomena from biology to electronics [9]. The value of a is determined by two quantities - the variance in the step size waiting time /x, between consecutive steps - as discussed below. 

We assume a random walk, i.e., an incoherent motion, for the spin carrier. In practice this assumption is not restrictive. Coherence or incoherence of the motion is essentially a question of time scale. A motion appears coherent, i.e., ballistic, as long as it is not interrupted by any kind of collision. After a collision the memory is left and the motion appears incoherent. In spin dynamics studies the time scale to probe the motion corresponds to the Larmor periods in the applied magnetic fields, typically 10" and 10" s for the nuclear and electron spins, respectively. This is longer than the usual collision times of charge carriers in conducting materials. 

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