LANDAU THEORY OF THIN FERROELECTRIC-FILMS

Landau-Devonshire theory(1) is a useful phenomenological model to desc ribe the properties of ferroelectric phase transitions. Below the tran sition temperature, the Landau model can be generalized to describe th e thermodynamic stability of a ferroelectric crystallite in a bistable polarized configuration, and to predict the response of the crystalli te to external fields and charges. The three primary elements to be co nsidered in modeling thin-film ferroelectric devices are the polar res ponse of the ferroelectric itself, the contribution of electrode inter faces, acid the interaction of mobile and immobile charged defects and carriers with the ferroelectric and the electrodes. First, the hyster esis properties of a single domain or crystallite are derived. This re sult is generalized to find the polar response in a polycrystalline fi lm where there may be variations in the size and orientation of the cr ystallites and in the coercivity, remanence and offset of the domains. After postulating that metal electrodes form Schottky barriers with r espect to the ferroelectric, we can then calculate the electric fields and potentials throughout the ferroelectric film. These calculations show that space charges form near the electrodes and the magnitude of the electric field in these regions is large. A further examination of the space charges results in a model for the C-V response of the ferr oelectric capacitor, as the C-V response is dominated by space charge effects. The charge concentrations, contact potentials, high-field per mittivity, and space charge widths can be extracted from the C-V data. Finally, the interactions between defects and domains leading to doma in pinning and fatigue are investigated.