The equilibrium sizes of micro- and nano-domains caused by electric field ofatomic force microscope tip in ferroelectric semiconductor crystals have beencalculated. The domain was considered as a prolate semi-ellipsoid with ratherthin domain walls. For the first time we modified the Landauer model allowingfor semiconductor properties of the sample and the surface energy of the domainbutt. The free carriers inside the crystal lead to the formation of thescreening layer around the domain, which partially shields its interior fromthe depolarization field. We expressed the radius and length of the domainthough the crystal material parameters (screening radius, spontaneouspolarization value, dielectric permittivity tensor) and atomic force microscopetip characteristics (charge, radius of curvature). The obtained dependence ofdomain radius via applied voltage is in a good quantitative agreement with theones of submicron ferroelectric domains recorded by high-voltage atomic forceand scanning probe microscopy in LiNbO3 and LiTaO3 crystals.
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