Trapping, free-carrier

In the above consideration it has been tacitly assumed that the charge carrier mobility docs not depend on the electric field. This is a good approximation for molecular crystals yet not for disordered systems in which transport occurs via hopping. Abkowitz et al. [37] have solved that problem for a field dependence of ft of the form p-po (FIFU) and trap-free SCL conduction. Their treatment predicts... 

It is obvious, and verified by experiment [73], that above a critical trap concentration the mobility increases with concentration. This is due to the onset of intertrap transfer that alleviates thermal detrapping of a carrier as a necessary step for charge transport. The simulation results presented in Figure 12-22 are in accord with this notion. The data for p(c) at ,=0.195 eV, i.e. EJa—T), pass through a minimum at a trap concentration c—10. Location of the minimum on a concentration scale depends, of course, on , since the competition between thermal detrapping and inter-trap transport scales exponentially with ,. The field dependence of the mobility in a trap containing system characterized by an effective width aeff is similar to that of a trap-free system with the same width of the DOS. 

The effect of traps on charge carrier motion does not become noticeable until the trap concentration reaches a threshold value. One can define a critical concentration Ci/2 at which the mobility has decreased to one half of the value of the trap-free system. Eq. (12.19) predicts that. ... 

IR transmission for the porous samples has been ascribed to a reduced free carrier concentration in the porous material due to trapping in surface states. After [Lei4]. 

The surface-state model, in which the luminescent recombination occurs via surface states, was proposed to explain certain properties of the PL from PS, for example long decay times or sensitivity of the PL on chemical environment. In the frame of this model the long decay times are a consequence of trapping of free carriers in localized states a few hundred meV below the bandgap of the confined crystallite. The sensitivity of the PL to the chemical environment is interpreted as formation of a trap or change of a trap level by a molecule bonding to the surface of a PS crystallite. The surface-state model suffers from the fact that most known traps, e.g. the Pb center, quench the PL [Me9], while the kinds of surface state proposed to cause the PL could not be identified. 

One of the most commonly employed techniques is TSL, which monitors photons as a function of temperature during the thermal scan. These photons are the result of radiative transitions (luminescence) of free carriers, previously released from the traps, to recombination centers. 

Because the escape probability of carriers from trapping sites is proportional to exp(-fi/ D, the location of a glow peak on the temperature scale provides encoded information on the value of thermal activation energy E. Hence, a glow curve represents a spectrum of energies that are required to free carriers from the various species of traps in the material. 

The excess free carriers (and excitons) do not represent stable excited states of the solids. A fraction of them recombine directly after thermahzation either radiatively or by multiphonon emission. In most materials, nonradiative transitions to defect states in the gap are the dominant mode of decay. The lifetime of free carriers T = 1/avS is determined by the density a of recombination centers, their thermal velocity v, and the capture cross section S, and may span 10-10 s. Electrons, captured by states above the demarcation level, and holes, captured by states below the hole demarcation level, may get trapped. The condition for trapping is given when the occupied electron trap has a very small cross section for recombining with a free hole. The trapping process has, until recently, not been well understood. 

After the decay of the excess free carriers due to recombination and trapping transitions, the solid is in the so-called excited state, which is characterized by the perturbation of the statistical equilibrium. The concentration of the remaining free carriers is now determined by the balance between thermal emission of carriers from the traps, retrapping transitions, and capture by recombination centers. 

In the case of material with a significant concentration of localized states, it is possible to assnme that transport of a carrier over any macroscopic distance will involve motion in states confined to a single energy. Here it is necessary to note that a particn-larly important departnre from this limiting situation is (according to Rose [4]) a trap-limited band motion. In this case, transport of carrier via extended states is repeatedly interrnpted by trapping in localized states. The macroscopic drift mobility for such a carrier is reduced from the value for free carriers, by taking into acconnt the proportion of time spent in traps. Under steady-state conditions, we may write... 

This relation also holds in the presence of shallow traps since the ratio of trapped (wt) to free carriers (n) (nt > n) influences both the response time (r0)... 

Capture and emission processes at a deep center are usually studied by experiments that use either electrical bias or absorbed photons to disturb the free-carrier density. The subsequent thermally or optically induced trapping or emission of carriers is detected as a change in the current or capacitance of a given device, and one is able to deduce the trap parameters from a measurement of these changes. 

Some relatively new analyses in the theory of nonradiative transitions have followed from the fact that there is no basic reason why our three primary processes cannot also take place in combination. Thus Gibb et al. (1977) propose a process of cascade capture into an excited electronic state and subsequent multiphonon emission from there. The results of this model were applied to capture and emission properties of the 0.75-eV trap in GaP. A more detailed analysis has since been given by Rees et al. (1980). Similarly, cascade capture followed by an Auger process with a free carrier seems a quite likely process. However, we are not aware that such a model has as yet been suggested. The third possible combination of processes, namely Auger with multiphonon, has been examined by Rebsch (1979) and by Chernysh... 

The Auger effect involving one free carrier, by definition, must include two trapped carriers. These two trapped carriers can be either on the same defect or on nearby defects. A further subdivision is that the two trapped carriers can... 

Fig. 14. Some Auger processes involving one-free carrier (boles as illustrated) The case of two trapped electrons on the same center is shown in (a), and the situation for trapping on nearby centers is shown in (b). The case of an exciton (isoelec-tronic) type center, with electron recombination to the trapped hole is shown in (c), and recombination with a free hole in (d) [note that in practice these two processes have to be considered in parallel (see, for example, Neumark, 1973)].

These equations can be solved by invoking the same constraints as before, namely (1) there is only one dominant trap, (2) free carriers are much more likely to recombine than be trapped, and (3) while the light is on, n and p are essentially constant, with n /0 and p /0 . Then Eq. (78) can be solved for the time the light pulse is on, and Eq. (48) [now the same as Eq. (54)], for the time after the light pulse. Thus for t > tp, as shown in Appendix C,... 

Thus, the electrical conductivity will be a measure of the number of free charge carriers of the catalysts. Adsorption processes which produce or destroy defects, or trap free electrons or holes, will alter the conductivity. Magnetic susceptibility, which will usually be changed by... 

The last three involve the capture of a charged carrier at an oppositely charged center. In all of these events except the free-hole trapped-electron recombination, the free carrier is the electron and the trapping center has a charge of +e/2. The key assumption is that the cross section for electron capture is determined by the coulombic attraction. On this basis, Hamilton derived an equation that includes one term to cover low-intensity reciprocity failure and another which is a first-order approximation of high-intensity reciprocity failure. Its predictions were in good accord with experimental data on the effects of sulfur sensitization. 

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