  A large number of experimental studies suggest two-terminal resistive
switching devices made of a dielectric thin film sandwiched by a pair of
electrodes exhibit reversible multi-state switching behaviors; however coherent
understanding of physical and chemical origins of their electrical properties
needs to be further pursued to improve and customize the performance. In this
paper, phase-field methodology is used to study the formation and annihilation
of conductive channels resulting in reversible resistive switching behaviors
that can generally occur in any dielectric thin films. Our focus is on the
dynamical evolution of domains made of electrical charges under the influence
of spatially varying electric field and temperature resulting in distinctive
changes in electrical conductance.
