Domain formation in thin ferroelectric films: The role of depolarization energy

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Abstract
Formulae for equlibrium stripe domain width Weq in a nonductive ferroelectric plate of thickness d are deduced, taking into account electrostatic interaction of surfaces. It is shown that the classical formula giving W eq ∞ d 1/2 is not applicable when the sample thickness decreases below the value dcrit which is a function of dielectric properties and domain wall energy density. For many ferroelectrics the value of dcrit lies in a range which can be easily reached far below the transition point by contemporary thin film techniques; it further increases as the transition point is approached. In the region d < dcrit the width Weq increases with decreasing d. For samples with thickness d << dcrit the domain structure becomes insensitive to electrical boundary conditions and will be primarily determined by other factors.