Fowler-Nordheim mechanism

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 ... 

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. 

Field emission is the emission of electrons from a solid under an intense electric field, usually at ambient temperatures. It occurs by the quantum mechanical tunneling of electrons through a potential barrier (Fig. 13.1). This leads to an exponential dependence of emission current density J on the local electric field, as given by the Fowler Nordheim equation,... 

Field emission results from tunneling of electrons from a metal into a vacuum under application of a strong electric field. The tunneling mechanism is described in the WKB approximation for emission from metal surfaces which leads to the well known Fowler-Nordheim equation ... 

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). 

Fowler-Nordheim tunneling-current density, well known as the programming mechanism of a NAND-flash memory-cell, is represented by... 

At high fields and low temperatures, where the thermal activation Schottky and Poole-Frenkel mechanisms are frozen out, and for films too thick for tunneling from metal to metal, a Fowler-Nordheim law is expected. Mead has observed this relationship for Ta205 films, it could be due either to tunneling from the metal into the conduction band or from localized states to the conduction band. Mead favored the latter case. 

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] ... 

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]. 

Summarizing, pure-field-enhanced emission mechanisms have been observed only in a few liquids.The probable reason is that since the Schottky and Fowler-Nordheim theories were developed for a metal-vacuum interface, their application implies that the liquid can be considered as a structurless dielectric not... 

While field ion microscopy has provided an effective means to visualize surface atoms and adsorbates, field emission is the preferred technique for measurement of the energetic properties of the surface. The effect of an applied field on the rate of electron emission was described by Fowler and Nordheim [65] and is shown schematically in Fig. Vlll 5. In the absence of a field, a barrier corresponding to the thermionic work function, prevents electrons from escaping from the Fermi level. An applied field, reduces this barrier to 4> - F, where the potential V decreases linearly with distance according to V = xF. Quantum-mechanical tunneling is now possible through this finite barrier, and the solufion for an electron in a finite potential box gives... 

---