Ferroelectric (FE) thin films have been used in numerous applications, including FE random access memories (FeRAM) [1] and FE field effect transistors [2,3]. As the devices become smaller, the required FE films should become thinner. The ultimate size of such miniaturization will depend on how thin the films can be made without losing their required FE properties. One such fundamental limit is the ''critical thickness'', in which spontaneous polarization (Ps) of an ultrathin film vanishes [3-6]. Here we show that, in FE capacitor-type devices, there should be another thickness limit, imposed by the decay of net polarization (驴P). Using high quality BaTiO3 FE films with thicknesses between 5.0 and 30 nm, we observed a rapid decay of 驴P values in time (t): 驴P(t) ~t-n (Ref. 7). We demonstrated that the rapid polarization decay should originate from the FE domain dynamics, governed by nucleation process. In addition, we empirically found a simple scaling relation between n and the nucleation energy barrier (U*) of FE domains. Then, we were able to write the new thickness limit as U* ≫ A路kBT, with A of the order of 10. The form of this limit is analogous to that of the superparamagnetic limit for magnetic nano-particles [8].
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