Kinetics of Domain Wall Motion in Ferroelectric Switching. I. General Formulation

Abstract

Detailed theoretical study has been made of the nucleation model for wall motion in ferroelectrics. Kinetics of the wall motion has been worked out both analytically and by simulation. The wall velocity v is expressed in terms of nucleation rate I and sideways growth velocity u_s of nuclei on the wall by the formula v=cw₀I or v=1.4c(u_sI)^1⁄2 according as w₀²I⁄u_s>>1 or w₀²I⁄u_s<<1. (c: minimum advancement of wall, w₀: width of critical nucleus.) The nucleation rate I and the sideways growth velocity u_s have been calculated on the basis of the theory of absolute reaction rates. It is shown that at very high fields two-dimensional nuclei can not nucleate, instead one-dimensional nuclei are formed, whose nucleation rate depends on field following a power law. From these results, general formulae for absolute wall velocities in various field ranges have been derived.