  We calculate the realistic sizes of nano-domains recorded by the electric
field of atomic force microscope tip in BaTiO3 and LiNbO3
ferroelectric-semiconductors in contrast to the over-estimated ones obtained in
the previous works. We modified the existing models of domain formation
allowing for the Debye screening, recharging of sluggish surface screening
layers caused by emission current between the tip apex and the domain butt
surface and the redistribution of domain depolarization field induced by the
charged tip apex. 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. We obtained, that
the domain length and radius do not decrease continuously with voltage
decrease: the domain appears with non-zero length and radius at definite
critical voltage. Such "threshold" domain formation is similar to the first
order phase transition and correlates with recent theoretical and experimental
investigations.
