Fowler-Nordheim model, tunneling injection

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] ... 

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] ... 

It is obvious that the device efficiency, rj, must also be very sensitive to the barrier height, since the efficiency is limited by upon the minority carrier density. As suggested by Eqs. (4.3) and (4.4), Fig. 4.13 plots rt(r]) vs >3/2. The excellent agreement between the theory and the data confirms the use of the Fowler-Nordheim tunneling model for describing the carrier injection into the band structure of the semiconducting polymer. 

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]. 

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