Modeling of micro- and nano-scale domain recording by high-voltage atomic force microscopy in ferroelectrics-semiconductors

TL;DR

This paper models the size of micro- and nano-domains in ferroelectric semiconductors created by high-voltage atomic force microscopy, incorporating semiconductor properties and surface energy effects for accurate predictions.

Contribution

It introduces a modified Landauer model that accounts for semiconductor characteristics and surface energy, enabling precise calculation of domain sizes in ferroelectric semiconductors.

Findings

The model accurately predicts domain size dependence on applied voltage.

Good quantitative agreement with experimental data in LiNbO3 and LiTaO3.

Inclusion of screening effects improves domain size estimations.

Abstract

The equilibrium sizes of micro- and nano-domains caused by electric field of atomic force microscope tip in ferroelectric semiconductor crystals have been calculated. The domain was considered as a prolate semi-ellipsoid with rather thin domain walls. For the first time we modified the Landauer model allowing for semiconductor properties of the sample and the surface energy of the domain butt. The free carriers inside the crystal lead to the formation of the screening layer around the domain, which partially shields its interior from the depolarization field. We expressed the radius and length of the domain though the crystal material parameters (screening radius, spontaneous polarization value, dielectric permittivity tensor) and atomic force microscope tip characteristics (charge, radius of curvature). The obtained dependence of domain radius via applied voltage is in a good quantitative agreement with the ones of submicron ferroelectric domains recorded by high-voltage atomic force and scanning probe microscopy in LiNbO3 and LiTaO3 crystals.