Poole-Frenkel law

The electric field dependence is, in all systems, very well described by a Poole-Frenkel law ... 

In this expression, ptoo, Ao, fipp and T are constants. The name of Eq. (8.85) derives from its similarity to the Poole-Frenkel law [50]. 

Numerous measurements over a large range of electric fields and temperatures have established that, in many materials, the carrier mobility can be described by a universal law bearing the Poole-Frenkel like form of the electric field dependence... 

Santos-Lemus and Hirsch (1986) measured hole mobilities of NIPC doped PC. Over a range of concentrations, fields, and temperatures, the transport was nondispersive. The field and temperature dependencies followed logn / El/2 and -(T0IT)2 relationships. For concentrations of less than 40%, a power-law concentration dependence was reported. The concentration dependence was described by a wavefunction decay constant of 1.6 A. To explain a mobility that shows features expected for trap-free transport with a field dependence predicted from the Poole-Frenkel effect, the authors proposed a model based on field-enhanced polaron tunneling. The model is based on an earlier argument of Mott (1971). 

The escape of electrons from traps by tunneling bears the same relation to the Poole-Frenkel theory as does the Fowler-Nordheim theory to the Schottky theory. It gives a law similar to the Fowler-Nordheim law. 

The effect of the particular metal used for the counterelectrode in the Schottky-law region has been investigated by several authors. Mead, as stated above, has suggested that the rapid rise to the Poole-Frenkel region occurs when the electrostatic field in the oxide due to the work function difference is just cancelled by the applied field. The voltage at which the rapid rise occurs was thus equated to the difference in work functions of the clean metal surfaces. It would seem that this picture should apply only to the... 

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. 

---