Fowler-Nordheim formula

Table 2.4 Constants in the Dushman-Richardson and Fowler-Nordheim Formulas [95]...

Fowler-Nordheim Formula and Thermionic Field Emission... 

The corrective factor f (A W/ Wq) is shown in Table 2-13 (Granovsky, 1971). Numerical examples of the field emission calculations (2-103) are presented in Table 2-12. The field emission current density dependence on electric field is really sharp in this case a 4 x change of electric field results in an increase of the field emission current density by more than 23 orders of magnitude. According to the corrected Fowler-Nordheim formula and Table 2-12, the field electron emission becomes significant when the electric field exceeds 10 V/cm. 

Table 2-13. Correction Factor 1 AW / Wo) in the Fowler-Nordheim Formula for Field Emission...

Oc = WQ—Eji, here Wv and Wq represent the work function of anode and cathode, respectively. As a consequence, holes (electrons) carmot hop to HOMO (LUMO). However, when bias voltage is applied across the device, HOMO (LUMO) of organic semiconductor will slant, and then the holes (electrons) distributed around Fermi level will have considerable possibility to cross a triangular barrier and get injected into HOMO (LUMO). When the external electric field becomes higher, the energy level will slant badly and the barrier will become lower. The relationship between the current of the device / and the electric field strength E can be demonstrated in Fowler-Nordheim formula ... 

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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