Calculation of band bending in ferroelectric semiconductor

In order to investigate the electronic characteristics of ferroelectric thin films that behave as semiconductors, we derive an equation to calculate the band bending in ferroelectrics, to replace the Poisson equation. We find that the space-charge density term, rho, in the Poisson equation should be replaced by rho - delP(r), where P-r is the remanent polarization. In order to simplify the band bending calculation, only one dimension is considered here. For example, in the case of the 3 V band bending in a metal-semiconductor Schottky barrier junction with a 1 mum thick ferroelectric semiconductor, the depletion region extends over the whole semiconductor, even with a dielectric constant of 10 and a donor density of 1 x 10(17) cm(-3) due to dP(r)/dx. However, the depletion layer width in a semiconductor without remanent polarization is only about 0.18 mum under the same conditions.