Poole-Frenkel-effect as dominating current mechanism in thin oxide films—An illusion?!

In many of the publications, over 50 per year for the last five years, the Poole-Frenkel-effect (PFE) is identified or suggested as dominating current mechanism to explain measured current-electric field dependencies in metal-insulator-metal (MIM) thin film stacks. Very often, the insulating thin film is a metal oxide as this class of materials has many important applications, especially in information technology. In the overwhelming majority of the papers, the identification of the PFE as dominating current mechanism is made by the slope of the current-electric field curve in the so-called Poole-Frenkel plot, i.e., logarithm of current density, j, divided by the applied electric field, F, versus the square root of that field. This plot is suggested by the simplest current equation for the PFE, which comprises this proportionality (ln(j/F) vs. F^1/2) leading to a straight line in this plot. Only one other parameter (except natural constants) may influence this slope: the optical dielectric constant of the insulating film. In order to identify the importance of the PFE simulation studies of the current through MIM stacks with thin insulating films were performed and the current-electric field curves without and with implementation of the PFE were compared. For the simulation, an advanced current model has been used combining electronic carrier injection/ejection currents at the interfaces, described by thermionic emission, with the carrier transport in the dielectric, described by drift and diffusion of electrons and holes in a wide band gap semiconductor. Besides the applied electric field (or voltage), many other important parameters have been varied: the density of the traps (with donor- and acceptor-like behavior); the zero-field energy level of the traps within the energy gap, this energy level is changed by the PFE (also called internal Schottky effect); the thickness of the dielectric film; the permittivity of the dielectric film simulating different oxide materials; the barriers for electrons and holes at the interfaces simulating different electrode materials; the temperature. The main results and conclusions are: (1) For a single type of trap present only (donor-like or acceptor-like), none of the simulated current density curves shows the expected behavior of the PFE and in most cases within the tested parameter field the effect of PFE is negligibly small. (2) For both types of traps present (compensation) only in the case of exact compensation, the expected slope in the PF-plot was nearly found for a wider range of the applied electric field, but for a very small range of the tested parameter field because of the very restricting additional conditions: first, the quasi-fermi level of the current controlling particle (electrons or holes) has to be 0.1 to 0.5 eV closer to the respective band limit than the zero-field energy level of the respective traps and, second, the compensating trap energy level has to be shallow. The conclusion from all these results is: the observation of the PFE as dominating current mechanism in MIM stacks with thin dielectric (oxide) films (typically 30 nm) is rather improbable!