  We propose the phenomenological description of ferroelectric disordering in
ferroelectric-semiconductors caused by charged impurities with the charge
density random fluctuations. The material improper conductivity is proportional
to the averaged impurity charge density. For high enough conductivity free
carriers screen fluctuations in the absence of an external field. When external
electric field is applied, inner field fluctuations and dynamical induction
fluctuations appear in the inhomogeneously polarized system "charged defect +
screening cloud". We show that the macroscopic state of
ferroelectric-semiconductor with random charged defects and sufficiently high
improper conductivity can be described by three coupled equations for three
parameters averaged over sample volume. Induction determines the ferroelectric
ordering in the system, its square fluctuation determines disordering caused by
electric field fluctuations appeared around charged fluctuations, and averaged
product of fluctuations of induction and charge density reflects the
correlations between the free carriers screening cloud and charged defects
fluctuations. For the first time we derive the following nonlinear system of
coupled equations. The obtained system of coupled equations adequately
describes the peculiarities of polarization switching (footprint and minor
hysteresis loops) in such bulk ferroelectric materials as PLZT ceramics and SBN
single crystals doped with cerium.
