In this paper, a theoretical approach, comprising the non-equilibrium Greens function method for electronic transport and Landau-Khalatnikov equation for electric polarization dynamics, is presented to describe polarization-dependent tunneling electroresistance (TER) in ferroelectric tunnel junctions. Using appropriate contact, interface, and ferroelectric parameters, measured current-voltage characteristic curves in both inorganic (Co/BaTiO$_{3}$/La$_{0.67}$Sr$_{0.33}$MnO$_{3}$) and organic (Au/PVDF/W) ferroelectric tunnel junctions can be well described by the proposed approach. Furthermore, under this theoretical framework, the controversy of opposite TER signs observed experimentally by different groups in Co/BaTiO$_{3}$/La$_{0.67}$Sr$_{0.33}$MnO$_{3}$ systems is addressed by considering the interface termination effects using the effective contact ratio, defined through the effective screening length and dielectric response at the metal/ferroelectric interfaces. Finally, our approach is extended to investigate the role of a CoO$_{x}$ buffer layer at the Co/BaTiO$_{3}$ interface in a ferroelectric tunnel memristor. It is shown that, to have a significant memristor behavior, not only the interface oxygen vacancies but also the CoO$_{x}$ layer thickness may vary with the applied bias.
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