Dielectric response of ferroelectric thin films with full and partial depletion

We studied the dielectric response of metal/ferroelectric/metal thin films capacitors with low to moderate densities of n-type impurities. Using the Landau-Ginzburg-Devonshire formalism for ferroelectrics, equations of semiconductors and electrostatics, we show how partially depleted films can generate a higher dielectric constant than those fully depleted but having the same impurity density. Such a thickness dependence trend is just the inverse of what is expected from films with low or no impurities. The results are provided for (001) BaTiO₃ films grown on (001) SrTiO₃ substrates with pseudomorphic Pt top and bottom metallic electrodes.