LIMITATIONS OF THE UNIFORM EFFECTIVE-FIELD APPROXIMATION DUE TO DOPING OF FERROELECTRIC THIN-FILM CAPACITORS

The electric-field distribution in a ferroelectric capacitor often is treated as a uniform effective field for circuit-level modeling. By so lving Poisson's equation and treating the ferroelectric capacitor as a back-to-back Schottky-barrier system, the nonuniform electric-field d istribution is calculated inside a ferroelectric thin film, assuming t hat the thin-film capacitor is completely depleted and has a constant doping concentration. It is found that the departure of the local fiel d from the uniform effective field increases with an increase in the d oping concentration of the film. Within this model, the uniform field approach to extraction of microscopic ferroelectric parameters is inac curate for doping levels great enough that the surface field exceeds t he coercive field even at zero bias. Based on this criterion, the crit ical doping concentration for parameter extraction using the uniform f ield approximation to be about 5x10(17) cm(-3). That is, according to the assumed model, for the high doping concentrations reported for typ ical lead-zirconate-titanate thin films (10(18)-10(19) cm(-3)), the ex traction of microscopic film properties based on a uniform electric fi eld approximation is inaccurate. (C) 1995 American Institute of Physic s.