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Thickness driven stabilization of saw-tooth–like domains upon phase transitions in ferroelectric thin films with depletion charges

Ionized impurities have nearly always been neglected in discussing the limit of functionality of ferroelectric thin films. One would certainly expect that the thickness limit for functionality would be altered in the presence of ionized impurities, but how this would occur remains unclear. In this article, we analyze the domain structures as well as the phase transition temperatures in films with depletion charges for various film thicknesses. Depletion charges induce a position-dependent built-in field that leads to an inhomogeneous distribution of ferroelectric polarization. Such an inhomogeneity in the polarization results in strong depolarizing fields in films. We show that formation of saw-tooth–type domains is a way to circumvent the depolarizing fields, even in films with ideal electrodes. There is a critical film thickness above which the saw-tooth domains develop. On the other hand, the phase transition of the ultrathin structures with electrodes having a finite screening length, namely real elec...