The internal electric field originating from the mismatch effect and its influence on ferroelectric thin film properties

Abstract

The ferroelectric thin film properties were calculated in phenomenological\ntheory framework. Surface energy that defined boundary conditions for\nEuler-Lagrange differential equation was written as surface tension energy. The\nlatter was expressed via surface polarization and tension tensor related to\nmismatch of a substrate and a film lattice constants and thermal expansion\ncoefficients. The calculations of the film polarization distribution,\ntemperature, thickness and external electric field dependence and hysteresis\nloops as well as average dielectric susceptibility dependence on temperature\nand film thickness have been performed allowing for mismatch-induced\npolarization Pm, leading to appearance of internal thickness dependent field.\nIt has been shown that this field influences drastically all the properties\nbehaviour. In particular the polarization profile becomes asymmetrical, average\npolarization temperature dependence resembles the one in the external electric\nfield, and there is possibility of external field screening by the internal\none. The obtained asymmetry of hysteresis loop makes it possible to suppose\nthat the self-polarization phenomenon recently observed in some films is\nrelated to mismatch effect. The thickness induced ferroelectric-paraelectric\nphase transition has been shown to exist when the Pm value is smaller than the\npolarization PS in the bulk. The large enough mismatch effect could be the\nphysical reason of ferroelectric phase conservation in ultrathin film. The\npossibility to observe the peculiarities of the films properties temperature\nand thickness dependencies related to mismatch effect is discussed.\n