Using Fermi-Dirac statistics in the depolarization-field calculations

In previous calculations, Boltzmann statistics have been used to compute the depolarization field in a thin ferroelectric film sandwiched between semiconducting electrodes. This approximation breaks down if the interface carrier density becomes degenerate as is often the case. Since the modifications of ferroelectric properties by depolarization effects depend rather critically on the distribution of the compensation charge in the electrodes, it might well be argued that such a drastic change, like the change of the order of the phase transition, might be a consequence of an inappropriate statistics. Here we use Fermi-Dirac statistics and show that it predicts quantitative differences but the qualitative behavior remains unaltered. In particular, it is shown that the first-order phase transition predicted previously is not a consequence of an inadequate statistics. Limits of applicability of Boltzmann and Fermi-Dirac statistics are discussed. © 1974 The American Physical Society.