Grain-size effects in ferroelectric switching

Abstract

describes domain growth in crystals composed of a large number of relatively small grains. If the grain boundaries stop or significantly affect domain wall motion then the observed switching transients will deviate from those predicted by the infinite grain model of Ishibashi and Takagi. The model assumes a constant nucleation rate throughout the switching process and constant domain wall velocity. A t a characteristic time dependent only on the size of the grains and the domain wall velocity the switching current transient changes from its early-time infinite-grain behavior to an exponential decay. The results are compared with Monte Carlo simulations of switching in the two-dimensional Ising model.

Theoretical Methods of Domain Structures in Ultrathin Ferroelectric Films: A Review

“…It is very convenient to combine MC simulation with various models including Ising model, thermodynamics free energy, and effective Hamiltonian approach, since it requires only calculations of the changes in the total energy with trial moves of the configuration to find the equilibrium state. Primitive MC simulations of ferroelectric domain structures are mainly based on the Ising model [ 232 , 233 ] and the Q-state Potts model [ 234 , 235 ], which is a generalization of the Ising model with Q metastable states and recovers to it as Q = 2 [ 236 ]. For ferroelectric thin films, the four-state Potts model was usually employed [ 237 , 238 ].…”