  By considering an interfacial layer between the electrode and the
$BiFeO_{3}$($BFO$) layer, the polarization and the hysteresis behavior of $BFO$
film are simulated. It is found that the non-ferroelectric interface will
increase the coercive field, and remarkably suppress the polarization of the
ultrathin film under low applied fields. Due to the competition between the
interfacial effect and the internal compressive stress, the maximum
polarization on the P-E loop of a $BFO$ film can be independent on the film
thickness under an adequate applied field.
