Attempt-to escape frequency

The hopping energy is thus one-half of the energy released when a polaron is formed. For this so-called adiabatic case, when the electron goes backwards and forwards several times during the period of excitation, the chance per unit time that the electron will have moved from one site to another after the system has relaxed is given by (3), where co is the attempt-to-escape frequency. The diffusion coefficient D is thus... 

The energy scale for the deep traps, given by Eq. (4.17), depends on having the correct value for the attempt-to-escape frequency and here there has been considerable controversy. Theoretical estimates of... 

Yuh et al. (1987) investigated hole transport in TPD doped PC containing low concentrations of 5-(p-diethylaminophenyl)-l-phenyl-3-(p-diethylamino-styryl)-2-pyrazoline (DEASP). Time-of-flight photocurrent measurements showed a transition from nondispersive to dispersive and back to nondispersive behavior as the DEASP concentration increased from 0 to 1%. The results were described by Schmidlin s (1977) single-trap-controlled model. The attempt-to-escape frequency and trap depth were reported as 4 x 1012 s-1 and 0.56 eV. 

It is expected that these parameters are independent of each other and of concentration parameters. This means that one hopes that, for example, for a particular electron trap, the activation energy, the attempt to escape frequency factor, and the retrapping probability are not dependent on the concentration of the trap. Most of these methods were developed for the evaluation of the activation energy, which in many cases, may be calculated by a number of methods, which thus provides a cross-check on the results. In the following section, we will discuss the various methods developed for the evaluation of trapping parameters. 

The frequency vx is interpreted as an attempt frequency that describes the number of times per second that the atom tries to escape. The rest of the expression represents the probability of escape at any given attempt. The term a /ay specifies the ratio of the window sizes at A and X through which the atom has to pass. The final term is a temperature-dependent Boltzmann factor that specifies the ratio of equilibrium number densities at A and X. 

The temperature-dependence of the viscosity of simple liquids can be discussed using the cell model as follows. Consider the cell of molecules shown in Fig. 6.2(a), where U is the average height of the potential barrier a molecule must surmount to escape from the cell. The molecule at A tries to climb over this barrier times per second, where Vq is its vibration frequency. The probabihty that the molecule at A acquires sufficient energy, as a result of a thermal fluctuation, to climb over the potential barrier is proportional to the Boltzmann factor exp (—where k is the Boltzmann constant and T is the thermodynamic temperature. Therefore, the number of successful attempts per second to surmount the potential hill, known as the jump frequency i, is ... 

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