This review covers methods and recent developments of the theoretical study of domain structures in ultrathin ferroelectric films. The review begins with an introduction to some basic concepts and theories (e.g., polarization and its modern theory, ferroelectric phase transition, domain formation, and finite size effects, etc.) that are relevant to the study of domain structures in ultrathin ferroelectric films. Basic techniques and recent progress of a variety of important approaches for domain structure simulation, including first-principles calculation, molecular dynamics, Monte Carlo simulation, effective Hamiltonian approach and phase field modeling, as well as multiscale simulation are then elaborated. For each approach, its important features and relative merits over other approaches for modeling domain structures in ultrathin ferroelectric films are discussed. Finally, we review recent theoretical studies on some important issues of domain structures in ultrathin ferroelectric films, with an emphasis on the effects of interfacial electrostatics, boundary conditions and external loads.
Keywords: domain structure; simulation; theoretical methods; ultrathin ferroelectric film.