Fowler-Nordheim model

Extension of the tunnelling problem to three dimensions was first attempted by Itskovich who showed that the band structure of the emitter would affect both the FN plot and TED. Gadzuk and Politzer and Cutler have argued that the spatial extent of the wave-function is important in determining the yield of field emitted electrons, and the latter authors conclude that the Fowler-Nordheim model succeeds for 2>d metals only because the contribution from the 3d band to the total field emitted current is small so that the current reflects the nearly-free-electron character of the 4s-p bands. 

Fluctuating Gap Model Fowler-Nordheim fluorine-doped tin dioxide full width at half maximum geminate pair... 

For the same the single layer devices based on Alq3, Peyghambarian et al. [83] found that the 1/V characteristics can also be described by an SCL current flow in the low cu ire lit regime. However, in the low current regime the 1/V characteristics can be qualitatively modeled by the Fowler-Nordheim equation (even if, quantitatively, the real device current differs from the calculated by seven orders of magnitude) [83] and thermionic emission ]78]. 

Fig. 1.38. The Fowler Nordheim equation for field emission. The relevant dimensions are much smaller than the tip radius. Therefore, a one-dimensional model is adequate. Neglecting the image-force effect, the potential U(z) outside the metal surface is linear with respect to distance z- The relevant parameters are work function of the material, tj), and the field intensity near the surface, F.

The voltage dependence of the injection-limited current resulting from this treatment, as well as experimentally observed I(V) characteristics are Fowler-Nordheim (FN)-like, i.e., similar to that obtained by tunneling through a triangular barrier. This similarity suggested a number of treatments that analyzed injection into OLEDs in terms of this model, which predicts that... 

Peyghambarian et al. modeled the dependence of the current flow and the efficiency of devices on various device parameters as the (balance of the) charge carrier mobility and the barrier height at the interfaces for devices, where the current flow is determined by Fowler-Nordheim tunneling (see Fig. 9-24) [83]. In this case, the current flow through the LEDs is injection limited and dominated by Fowler-Nordheim tunneling and the following characteristics are observed [83] ... 

The operating voltage is very sensitive to the barrier height. This sensitivity is predicted by the Fowler-Nordheim tunneling model. Equations (4.3) and (4.4) indicate that for the same tunneling current, the ratio f/>i/2/ V must be the same. Thus,... 

Two limit models are considered (see Fig. 9.3), the first is the Fowler-Nordheim mechanism, which assumes tunneling through a perfect triangular barrier (the image potential is neglected) and does not consider the localized aspect of the sites. The main characteristic of this model is that the current density is independent of the temperature and scales as a function of the electric field as follows ... 

To study charge injection mechanisms, we have tried to fit Richardson-Schottky thermionic emission and Fowler-Nordheim tunnelling mechanisms. We have found that under forward bias, the temperature-independent Fowler-Nordheim (FN) tunnelling mechanism is applicable, which presumes tunnelling of charge carriers directly into the bands of the semiconductor. According to the model, the current density J) is related to the applied field F) as [11,12] ... 

Fig. 3 Fowler Nordheim plots [log(J/F ) vs. I/F] under forward bias for the same structures as described in Fig. 2. The line is the best fit of the model to the experimental points above 10 V/cm.

However, the values for the current that are obtained with the actual device parameters using the Fowler-Nordheim equation are several orders of magnitude higher than the values for the measured current in real devices. This is due to the fact that the I-V characteristics of PLEDs are determined not only by the injection mechanisms but also by the charge transport mechanism in the active polymer layer (see Section V). The discrepancy between the measured and calculated values for the current in the model for field-induced tunneling can be accounted for by a backflow current of the injected charge carriers into the injection contact. This effect then reduces the net device current and seems to be especially important in low mobility conjugated polymers [93]. 

This model proposes the Fowler-Nordheim process as the source of the charge carriers when it is known [cf. Section II.l(ii)] that experimentally observed currents differ from those predicted by Fowler-Nordheim theory (cf. Figs. 15 and 16). Furthermore, Kao s theory assumes a larger number of created negative charges than positive charges, which is against the law of electrical neutrality of a material. 

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