Stability of the polarization in a thin ferroelectric film on a semiconductor is theoretically investigated using an insulating homogeneous Ginzburg-Landau theory. Dependence of the stability on various parameters such as the ferroelectric thickness, the materials (BaTiO3, KNbO3, PbTiO3, Bi4Ti3O12), the interfacial defects, the work function difference, the epitaxial orientation, and the buffer insulator thickness is numerically and analytically studied, and the results are qualitatively compared with the past experiments on ferroelectric field effect devices. The spontaneous polarization in a ferroelectric single-domain on a semiconductor is shown to be bistable in agreement with recent experiments. Furthermore, its thickness limit of the ferroelectric stability is found to be very small, implying a great potential of this structure for the miniaturization. The single-domained spontaneous polarization is destabilized when even a very thin insulating layer exists between the ferroelectric and the semiconductor. The formation of the multidomain is found to be insufficient to stabilize the spontaneous polarization in thin ferroelectrics used in experiments. The spontaneous polarization can be stabilized at one polarity by the defects or the surface states at the ferroelectric/insulator interface, which explains its temporary stability experimentally suggested. The thermodynamic liner susceptibility is crucial for the stability, while the ferroelectric stability is predicted to be enhanced by modifying it effectively by changing the epitaxial orientation of the ferroelectric film. An addition of metallic layer between the ferroelectric and the insulator changes this restriction, although this invites another instability of the conductance modulation. To explain the experimental instabilities, they are classified into four categories. The present study suggests also a limitation of the assumption of an insulating ferroelectric under a very large depolarization field.
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