Space Charge Effects in Ferroelectric Thin Films
  The effects of space charges on hysteresis loops and field distributions in ferroelectrics have been investigated numerically using the phenomenological Landau-Ginzburg-Devonshire theory. Cases with the ferroelectric fully and partially depleted have been considered. In general, increasing the number of charged impurities results in a lowering of the polarization and coercive field values. Squarer loops were observed in the partially depleted cases and a method was proposed to identify fully depleted samples experimentally from dielectric and polarization measurements alone. Unusual field distributions found for higher dopant concentrations have some interesting implications for leakage mechanisms and limit the range of validity of usual semiconductor equations for carrier transport. 
P. Zubko, D. J. Jung, J. F. Scott