Polarization Relaxation Induced by Depolarization Field in Ultrathin Ferroelectric BaTiO${}_3$ Capacitors

Abstract

Time-dependent polarization relaxation behaviors induced by a depolarization field $E_d$ were investigated on high-quality ultrathin SrRuO${}_3$/BaTiO${}_3$/SrRuO${}_3$ capacitors. The $E_d$ values were determined experimentally from an applied external field to stop the net polarization relaxation. These values agree with those from the electrostatic calculations, demonstrating that a large $E_d$ inside the ultrathin ferroelectric layer could cause severe polarization relaxation. For numerous ferroelectric devices of capacitor configuration, this effect will set a stricter size limit than the critical thickness issue.