This paper proposes a theory to describe the polarization and switching behavior of ferroelectrics
that are also wide-gap semiconductors. The salient feature of our theory is that it does not make
any a priori assumption about either the space charge distribution or the polarization profile. The
theory is used to study a metal-ferroelectric-metal capacitor configuration, where the ferroelectric
is n-type doped. The main result of our work is a phase diagram as a function of doping level and
thickness that shows different phases, namely, films with polarization profiles that resemble that of
undoped classical ferroelectrics, paraelectric, and a new head-to-tail domain structure. We have
identified a critical doping level, which depends on the energy barrier in the Landau energy and the
built-in potential, which is decided by the electronic structures of both the film and the electrodes.
When the doping level is below this critical value, the behavior of the films is almost classical. We
see a depleted region, which extends through the film when the film thickness is very small, but is
confined to two boundary layers near the electrodes for large film thickness. When the doping level
is higher than the critical value, the behavior is classical for only very thin films. Thicker films at
this doping level are forced into a tail-to-tail configuration with three depletion layers, lose their
ferroelectricity, and may thus be described as nonlinear dielectric or paraelectric. For films which
are doped below the critical level, we show that the field required for switching starts out at the
classical coercive field for very thin films, but gradually decreases
