Domain switching and spatial dependence of permittivity in ferroelectric thin films

Abstract

A domain model consistent with the measured capacitance-voltage ( CV) characteristic of PZT (Pb( Zr,Ti)O₃) capacitors is proposed. The model is introduced using a macroscopic electric field that is spatially uniform through the depth of the film. Then this multiple-domain model is generalized, and a spatially varying electric field model with a domain structure varying through the depth of the film is proposed. The spatial variation of the electric field is caused by dopant-ion charges in this work. A position-dependent permittivity is then deduced. Based upon this permittivity, the extraction of doping profiles in ferroelectric thin film capacitors using ferroelectric capacitance-voltage (CV) measurements is studied. The doping profile relation to measured CV curves for ferroelectric thin film capacitors is found to be analogous to the well-known result of metal-semiconductor Schottky junctions with an easily determined effective dielectric constant. Computer simulation shows the electrical doping concentration of ferroelectric thin film capacitors can be profiled accurately with the proposed model. The profiling shows compensation of the p-type PZT samples by the n-type niobium doping. Limitations of the Schottky profiling on ferroelectrics are investigated. Based on the approximate doping profiles extracted from CV measurement and the deduced permittivity, the measured CV characteristics are reconstructed through computer simulations. It is found that there is a minimum doping level below which it is not possible to obtain the doping profile from CV measurements. This minimum level depends on the shape of the CV curve, and a method to determine this minimum level from the CV curve is presented. For the films measured in this work, the minimum level is about 10¹⁸ cm⁻³. It is also found using the model that niobium doping slightly slows the volume growth of polarization with the electric field and has a tendency to increase the coercive field.