Poole-Frenkel current

The conductivity and j-U characteristic given by Eq. (187) is similar to the result following the Poole-Frenkel effect on SCL currents [376,377]. Such a situation is clearly not expected in the case of the standard solution for trapping by a discrete set of separated microtraps expressed by Eqs. (167) and (168). This is the case if one extrapolates Eq. (185) to l 0, with = (Neff/N0) exp(—Et/kT). The physical meaning of this extrapolation is that we deal with one discrete trap level (Et), the trap potential being the infinitely sharp point well for which the barrier lowering can be neglected. 

In order to predict absolute dielectric strengths we need to have more detailed information than is yet available about electronic states and mobilities in polymers. For the present we can only conclude that there is satisfactory agreement between the form of the theoretical results, based on a rather general electronic model, and the best experimental results. To the extent that the model is a very reasonable one, we can say that we can understand intrinsic breakdown behaviour. Measurement of pre-breakdown currents, especially with pointed electrodes which impose regions of very high field strength at their tips when embedded in the material, suggests that electronic carrier production either by injection from the electrodes (Schottky emission) or from impurities (Poole-Frenkel effect) may play a part in the breakdown process. More work is required, however, before this can be fully understood. 

SCLC given by Equation (8.50). The analysis of Many and Rakavy (1962) shows that the peak current is approximately 1.2 times the SCLC and that the maximum occurs at approximately 0.8 times the carrier transit time. Goldie (1999) has incorporated the experimentally observed Poole-Frenkel field dependence into this model and finds a range of possible numerical factors for the current maximum of from 1-1.2 times the SCLC and 0.7-0.8 times the transit time. Experimental data come close to these model profiles, see Abkowitz et al. (1994), Goldie (1999). 

Tunneling in multilayered LB films is defect-mediated via trap sites within the conduction band of the molecules (Poole conduction), or by Schottky emission between widely spaced trap sites (Poole Frenkel conduction) in thicker samples [13]. With good molecular conductors the current from molecular conduction should dominate the small contribution from tunneling. However, the conduction mechanism between adjacent layers is not always obvious, due to the complexity of the interface structure. 

In view of the above, conductivity measurements were conducted in asymmetric systems Au-polymer-Si for polystyrene and polysilazane, and Au-polymer-In for polysiloxane. The difference in barrier height between Au-polymer and Si-polymer estimated on the basis of measurements of the Au-Si barrier is ca. 0.5 eV (M) which, in the case of the conductivity limited by the electrodes, should produce a difference in the intensity of the currents of opposite polarizations equal to about 8 orders of magnitude. The difference in work function of Au and In, on the other hand, is ca. 1 eV so, on the assumption of the Schottky mechanism of conductivity, the difference in the intensity of opposite polarizations should amount to 17 orders of magnitude ( ). As can be seen in Fig. 4 in the case of an asymmetric polysilazane sample there is a difference in the intensity of the currents although this difference does take the expected course, it is several times smaller than expected, and is thus virtually negligible. A similar result was obtained for the polystyrene sample, while in the case of the asymmetric system based on polysiloxane there was no difference in the intensity of the opposite-biassed fields over the entire range of fields used - up to 3 x 10 V/m. It can thus be assumed that the conductivity in the films under study is dominated by the Poole-Frenkel volume generation independent of the contact effects. Such were also the conclusions of the workers who studied the conductivity in polystyrene (29) and polysiloxane (21). 

The usual expression for the Poole-Frenkel effect is thus the rate of escape from traps. This gives the current in the situation where only a small fraction of traps are ionized at any given moment, and where the field in the electrically neutral oxide controls the current. In a thick enough film the ionized traps near the interface will provide space charge which will accumulate until the field across the interface is increased to the value necessary to keep the rate of injection at the required level. With a thin enough film... 

Equation (8.15) may well cause one to wonder whether Poole-Frenkel (P-F) emission [268] or Schottky emission [208] of the charges underlies the charge transport. For the latter the charge emission is assumed to take place across the Schottky barrier between the electrodes and the semiconductive materials. By testing the linearity of log(7/7 ) versus F IkT plots [208] where J is the current density, it was found that the linearity is worse than that displayed in Figure 8.66, implying that Schottky emission is irrelevant and that P-F emission is more likely. The P-F-like feature... 

Highly nonlinear current-voltage characteristics can be obtained with an anodically formed tantalum pentaoxide (TajOs) layer. These characteristics result from the Poole-Frenkel conduction mechanism [21, 22]. 

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