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We calculate the realistic sizes of nano-domains recorded by the electricfield of atomic force microscope tip in BaTiO3 and LiNbO3ferroelectric-semiconductors in contrast to the over-estimated ones obtained inthe previous works. We modified the existing models of domain formationallowing for the Debye screening, recharging of sluggish surface screeninglayers caused by emission current between the tip apex and the domain buttsurface and the redistribution of domain depolarization field induced by thecharged tip apex. We have shown that the depolarization field energy of thedomain butt, Debye screening effects and field emission at high voltages leadto the essential decrease of the equilibrium domain sizes. We obtained, thatthe domain length and radius do not decrease continuously with voltagedecrease: the domain appears with non-zero length and radius at definitecritical voltage. Such "threshold" domain formation is similar to the firstorder phase transition and correlates with recent theoretical and experimentalinvestigations.Comment: 20 pages, 4 figures, new references are added, content is changed,  sent to Physica Status Solid

Screening and size effects on the nanodomain tailoring in ferroelectrics semiconductors