Simulation of Leakage Current in Thin Films with Dead Layers

Abstract

There is a long-standing debate on the interpretation of leakage current data in metal/insulator/metal capacitors with high permittivity or ferroelectric materials such as SrTiO 3 , (Ba,Sr)TiO 3 or Pb (Zr,Ti)O 3 , respectively: Is the leakage current density, j, interface or bulk limited? Many data sets 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") as these data show linear behaviour in the dependencies on temperature, T, in an "Arrhenius plot" ln(j/T 2 ) vs. l/T and on the average field, <E>, in a plot ln(j) vs. sqrt (<E>) ("Schottky-plot"). 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, E 0 >> <E>, would be necessary. One possibility is the introduction of interface layers with low dielectric constant, "dead" layers, supported by theoretical investigations and capacitance data measured at different thickness. We have performed computer simulations to calculate the "bulk limited" steady state leakage current density through thin insulating films (with "dead" layers) employing the "Finite Difference Method". Parameters, which have been varied, are external ones, such as temperature, applied voltage, film thickness and interfacial barrier height (electrode material), and internal ones, such as dielectric constant and defect concentration of the "bulk" film, thickness and dielectric constant of the "dead layers". The most important result is: For nearly all values of the parameter field the calculated "bulk limited" current density through the thin film shows nearly perfect "Schottky-" and "Arrhenius" plots which - interpreted by the simple "Schottky" model - have the same deficiencies as mentioned above: too small Richardson constant and unphysical dielectric constant.