Poole-Frenkel

Emin D (2008) Generalized adiabatic polaron hopping Meyer-Neldel compensation and Poole-Frenkel behavior. Phys Rev Lett 100 166602... 

The results of several studies were interpreted by the Poole-Frenkel mechanism of field-assisted release of electrons from traps in the bulk of the oxide. In other studies, the Schottky mechanism of electron flow controlled by a thermionic emission over a field-lowered barrier at the counter electrode oxide interface was used to explain the conduction process. Some results suggested a space charge-limited conduction mechanism operates. The general lack of agreement between the results of various studies has been summarized (57). 

AEfp Pool-Frenkel decrease of the potential barrier... 

The release of the trapped carriers may be stimulated by the electric field. In the Pool-Frenkel model the decrease of the potential barrier of the trapped electron by the electric field (AEFp) obeys the formula... 

The main experimental results of charge carrier generation in PVC was explained in the frame of the Pool-Frenkel model [28-30]. The dependence of the recombination time on electric field was due to the change of the mobility in the electric field. Germinate recombination of the electron-hole pairs was investigated by means of luminescence decay characteristics [31]. 

The dependence of the drift mobility p on the electric field is represented by formula p (p-E1/2/kTcf) which corresponds to the Pool-Frenkel effect. The good correspondence between experimental and theoretical quantity for Pool-Frenkel coefficient 3 was obtained. But in spite of this the interpretation of the drift mobility in the frame of the Coulombic traps may be wrong. The origin of the equal density of the positive and negative traps is not clear. The relative contribution of the intrinsic traps defined by the sample morphology is also not clear [17,18]. This is very important in the case of dispersive transport. A detailed analysis of the polymer polarity morphology and nature of the dopant molecules on mobility was made by many authors [55-58]. 

The empirical relationship [Eq. (15)] obtained by fitting the experimental electric field dependence to the measured data suggests a Poole-Frenkel (PF) type mechanism17. The PF effect deals with a carrier trapped in a coulombic barrier19. The applied field causes a reduction of 0pFE 2in the barrier height and therefore the probability of escape is increased in the presence of the applied field. The slope... 

We treat here the case of shallow Gaussian traps. The equations reduce to those applicable to single level traps by making the standard deviation at = 0. If the Poole-Frenkel effect (PEE) is included the J-V relation for a device containing shallow traps is given... 

Here is the hole trap density, g is the degeneracy factor (taken as unity in the calculations), Etp is the ionization energy of the hole traps, Ev is the valence band edge (i.e. HOMO), Ny is the effective density of states for holes, at is the standard deviation of the Gaussian distribution of traps, and the factor expOS /F/fcr) arises due to the Poole-Frenkel effect. Analytical solution of (3.58) and (3.60) can not be obtained. Numerically computed results are shown in Fig. 3.29. 

Fig. 3.31. Schematic illustration of the lowering of trap ionization energy by the Poole-Frenkel effect.

In the case of exponentially distributed traps, the effect of high fields on the trap depths (Poole-Frenkel effect) can be taken into account by the same procedure. The trapped hole density is modified and Eq. (3.40) changes to [38],... 

Kumar et al. [39] made numerical calculations for traps at a single energy level and for traps distributed exponentially in the energy space. The effect of high field is qualitatively similar in the two cases. We show the effect of high field on the electric field in Fig. 3.32. The electric field and Poole-Frenkel effect suppress the actual electric field considerably. Near the exit end the field is suppressed by more than one order of... 

The electric field at the interface of the oxide and the active layer is large. As discussed earlier, the field assists the ionization of the traps due to the Poole-Frenkel Effect. The trap depth is reduced by an amount /9 /F and the number of trapped carriers is reduced. Following Horowitz and Delannoy [157] we consider the traps at a single level located near the band edge [158] in an n-type polymer. The treatment is quite general and can be extended to p-type polymers quite easily. When PFE is included, Eq. (6.3) changes to,... 

Figure 50 Quenching efficiency (<5) as a function of dc electric field applied to the electrophosphorescent (EPH) and phosphorescent system. The curves are fits to the Poole—Frenkel (see lower inset) and Onsager (see upper inset) models for charge pair dissociation in external electric fields. The quenching efficiency is defined as a relative difference between the emission efficiency at a given field F[0(F)] and at a field F0[4>(F0)] where a decrease in the EPH efficiency becomes observed (<) (F0) (7 1)]/

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