Tunneling injection, Fowler-Nordheim

Fig. 24 Schematic representation of electron injection from a metallic electrode into a semiconductor (a) via Schottky emission, (b) via Fowler-Nordheim tunneling, and (c) via hopping in a disordered organic solid.

FIGURE 2.1. Two possible carrier injection mechanisms at the organic/metal electrode interface (a) Schottky-type carrier injection via impurity or structural disordered levels with thermal assistance and (b) Fowler-Nordheim tunneling carrier injection with the assistance of a local high electric field (106—107 V/cm). 

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] ... 

Figure 12-5. Representation of the calculated injection current on a In 7 vs 7 scale. The dashed hne indicates the slopes predicted by Fowler Nordheim tunneling theory for A=0.8eV assuming that the effective mass equals the free electron mass.

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. 

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... 

Whereas early publications have explained experimental results within the framework of the Fowler-Nordheim mechanism alone [43], recent publications [44-46] have attributed the injection of carriers to a combination of both mechanisms at low fields and high temperature, thermoionic emission is considered dominant. On the contrary, for high electric fields (typically >2MV/cm), injection would essentially occur via tunneling. 

A. J. Heeger, I. D. Parker and Y. Yang, Carrier injection into semiconducting polymers Fowler-Nordheim field-emission tunneling, Synth. Met. 67, 23—29 (1994). 

We now turn attention to conditions at the electrodes. These play vital roles in establishing the pre-breakdown conditions in the liquid under high electric stress and in triggering the breakdown itself. It has been natural to invoke electron injection at the cathode as an important component since high fields will lower the potential barrier to electron transfer across the interface whether it occurs by a thermally activated or tunnelling process. However, employment of the Schottky formula for field-assisted thermionic emission or the Fowler-Nordheim one for tunnel emission which are appropriately applicable only for electron transfer to a vacuum is a much too simplified solution to the problem. 

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