Abstract
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. F1/2) 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!
Highlights
In solid state and materials engineering textbooks, one can find in the sections about “Conduction” or “(Leakage) Current” through metal-insulator-metal (MIM) stacks usually two classes in models for the current:(a) Current is interface controlled, e.g., thermionic emission; tunneling carrier injection.(b) Current is bulk controlled, e.g., space charge limited current (SCLC); Poole-Frenkel-effect (PFE).it is not surprising that in the literature this classification of the suggested current mechanisms into these classes is applied nearly without exception
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
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
Summary
In solid state and materials engineering textbooks, one can find in the sections about “Conduction” or “(Leakage) Current” through metal-insulator (wide band gap semiconductor)-metal (MIM) stacks usually two classes in models for the (leakage) current:. As the model describes injection of electron and holes (double injection), recombination reactions between the two species may be important This effect is included in the simulation tool, but it has been verified that this process is only important if the injection currents and the densities for both are about comparable, which for wide band gap thin film semiconductors is only true if the electrode Fermi levels are close to the middle of the gap. The combined model shows very different current simulation curves varying in shape and profile and absolute number dependent on interface properties (electrode barrier height, electrode symmetry, etc.), film properties (permittivity, carrier mobility, thickness), film defect properties (width (homogeneity), energy level in the gap with respect to the Fermi level (shallow, deep) and type (donor-like, acceptorlike)) and temperature. This powerful simulation tool was used to check if and to what amount the implementation of the PFE (as described before) would change the leakage current curves and if the possibly changed dependencies would show the characteristic slope in a PF-plot, as it is claimed in hundreds of papers.
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