Simulation of Steady State Leakage Current in Thin Films

Abstract

ABSTRACTNumerical 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 interface-limited 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.