root of the field () is depicted. The idea of such a plot originates from the expression of the Poole-Frenkel current density, which contains this proportionality ( vs ), and would thus result in a straight line in this plot. For a fixed value of the voltage barrier in absence of any applied electric field, the slope is influenced by just one parameter: the dielectric permittivity. Despite of the same functional dependence of the current density upon the electric field intensity, one could differentiate between Poole-Frenkel conduction upon Schottky conduction as they would result in straight lines with different slopes in a Poole-Frenkel plot. The theoretical slopes can be evaluated knowing the high frequency dielectric constant of the material (, where is the vacuum permittivity), and comparing these with the slopes detected experimentally. As an alternative, one can evaluate the value for equating the theoretical slopes to the experimental detected ones, provided that it is known if the conductivity is electrode-limited or bulk-limited. Such a value of the high frequency dielectric constant should then conform the relation , where is the refractive index of the material. Improved Poole-Frenkel models Although many progresses have been made on the topic since the classical work of Frenkel, the Poole-Frenkel formula has been spreadly used to interpret several non-ohmic experimental currents observed in dielectrics and also semiconductors. The debate about the underlying assumptions of the classical Poole-Frenkel model has given life to several improved Poole-Frenkel models. These hypotheses are presented in the following. Only electron (single-carrier) conduction is considered, assuming the existence of ohmic contacts capable to refill detrapped electrons at the electrodes, and space charge effects are neglected, supposing that the field is uniform. A revisitation of this latter assumption can be found, for example, in the “theory of space charge limited current enhanced by Frenkel effect” developed by Murgatroyd. The carriers mobility is assumed to be field-independent. Neglecting every kind of diffusion process for the de-trapped carriers, the pre-exponential factor in the Poole-Frenkel formula is thus proportional to . This depiction would be suitable for the description of the conduction either in dielectrics or semiconductors. However, Poole–Frenkel effect is likely to be observed only in materials characterized by low mobility values, for, in high mobility solids, the re-trapping of carriers would be gradually inhibited by carrier depletion. Still, different dependences of the pre-exponential factor from the field can be found: assuming that