Thermodynamical approach to nanodomain tailoring in thin   ferroelectric-semiconductor films
  We propose the thermodynamical theory of nanodomain tailoring with the help of atomic force microscope electric field in thin ferroelectric-semiconductor films. We modified the existing thermodynamical models of domain formation allowing for the Debye screening, recharging of sluggish surface charge layers caused by emission current between the tip apex and sample surface.For the first time we calculated the realistic sizes of nanodomains recorded in BaTiO3, PbZrxTi1-xO3 and LiTaO3 ferroelectric-semiconductor thin films in contrast to the over-estimated ones obtained in the evolved approaches. We have shown that the depolarization field energy of the domain butt, Debye screening effects and field emission at high voltages lead to the essential decrease of the equilibrium domain sizes. For the first time we obtained, that the domain radius does not decrease continuously with applied voltage decrease: the domain appears with non-zero radius at definite critical voltage applied to the tip. This result completely agrees with experimentally observed threshold domain recording in PbZrxTi1-xO3 and LiTaO3 thin films. Such threshold domain formation is similar to the first order phase transition. We hope, that our results will help one to determine the necessary recording conditions and appropriate ferroelectric medium in order to obtain the stable domains with minimum lateral size in a wide range of applied voltages. 
Anna N. Morozovska, Eugene A. Eliseev