Simulation of Steady State Leakage Current in Thin Films
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U3.9.1
Simulation of Steady State Leakage Current in Thin Films
Herbert Schroeder, Sam Schmitz, and Paul Meuffels Institut für Elektrokeramische Materialien im Institut für Festkörperforschung, Forschungszentrum Jülich GmbH D-52425 Jülich, Germany ABSTRACT Numerical simulation studies were performed in order to shed light on the controlling mechanism for the steady state leakage current through metal/insulator/metal capacitors with high permittivity dielectric or ferroelectric materials such as SrTiO3, (Ba,Sr)TiO3 or Pb (Zr,Ti)O3. As a model we used an extension of the combined injection-diffusion model, i.e. we have solved the Poisson and continuity equations inside the dielectric assuming thin, low permittivity (“dead”) layers at the electrode interfaces. As “new” boundary conditions we used injection / recombination terms at both electrodes, also taking into account the barrier lowering due to the coulomb mirror potential. The simulation data are presented in dependence on several extrinsic and intrinsic parameters (voltage, temperature, film thickness, barrier height, dead layer properties, etc.) for symmetrical electrodes together with first results on asymmetrical ones. The most important result is that for nearly all parameter sets the leakage current is (film) bulk-limited, mostly due to the low carrier mobilities in these insulating materials. Only for very special conditions the interfacelimited current, e.g. thermionic injection at the cathode for electrons, is a good approximation. The numerical data are compared to experimental true leakage current results on STO and BST. INTRODUCTION Leakage current densities, j, in metal/insulator/metal capacitors with high permittivity dielectric or ferroelectric materials such as SrTiO3, (Ba,Sr)TiO3 or Pb (Zr,Ti)O3 often show linear behavior in the dependences on temperature, T, in an “Arrhenius” plot ln(j/T2) vs. 1/T and on the mean applied field, , in a plot ln(j) vs. sqrt() (“Schottky” plot) [1,2]. Therefore, they have been interpreted as interface limited by thermionic emission over a barrier lowered by the combined effect of mirror potential and applied field (“Schottky-effect”). However, the absolute values of j are in many cases much smaller than the prediction (value of the effective “Richardson constant”) and – much more serious – the optical dielectric constant deduced from the “Schottky-plot” is very often smaller than 1, an unphysical value. In order to correct the last much higher electrical fields at or near the interface, E0 = E(x≈0) >> , would be necessary because E0 is the only field value entering the thermionic emission equation via the mirror potential lowering term. One possibility is the introduction of thin interface layers with a much lower dielectric constant than the bulk, so-called “dead” layers. This is supported by theoretical investigations [3,4] and capacitance data measured at different thickness [5-7], especially for non-oxide electrodes such as Pt. The recently discussed electrode field penetration [7-9] would not change the argum
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