Landau theory of free standing and epitaxial ferroelectric film
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Date
2009
Authors
Musleh, Ahmad M. A.
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Abstract
Landau-Ginzburg-Devonshire’s (LGD) theory and Landau Khalatnikov’s
dynamic equation are used to study the polarization reversal of second order
ferroelectric (FE) systems. These FE systems that we considered are FE films with
finite value of surface polarization and also films where the surface polarization can
be considered as zero value. This zero surface polarisation could be the result of
non-ferroelectric sites present at film surfaces. Another FE system considered is a
one dimensional finite size system which is made up of (2N+1) sites with the edges
at the –Nth and +Nth sites. When an external electric field is applied, all the sites
including the edges feel the same field.
Various forms of electric fields such as step field, sinusoidal field, triangular
field and bipolar field are used to study the switching phenomena in these FE
systems. The influence of the amplitude and frequency 0 E ω of the applied electric
field, temperature T, film thickness L and surface parameter δ on polarization
reversal have been investigated. Runge-Kutta (R-K) method and finite difference
technique are the numerical techniques used to obtain the equilibrium initial
polarization profile for the film of finite surface polarization and for the system of
finite-size. A trial cosine function is used to obtain the initial polarization profile of
FE film with zero surface polarization.
The controversial thickness dependence of coercive field in FE film
reported in experimental studies, can be explained theoretically by the signs of δ , the extrapolation length. For negative δ , increases with decreasing film
thickness, while for positive δ , decreases with decreasing film thickness. The
coercive field of FE film is found to be thickness dependent. It is interesting to note
that the numerical values of switching time and the applied field are best fitted by an
exponential function with high regression factor. From this curve, it has clearly
shown that the FE film will only be switched by a minimum electric field .
Regarding the FE film with zero surface polarization, two peaks in the switching
current are found for a relatively thick film. The extra peak in the switching current
is due to the dipole moments near the surface are switched earlier than the dipole
moments in the interior. The effects of misfit strain on the phase transition, spontaneous polarization,
transition temperatures and critical thickness of epitaxial Barium Titanate BaTiO3 are
examined by using LGD free energy with the order parameter up to the eight-order
because of the high compressive stress caused by the substrate interface. Phase
transition of epitaxial BaTiO3 film is found to be of second-order, though the stress free
BaTiO3 film undergoes first-order phase transition. The misfit strain in BaTiO3
films increases the average polarization and the transition temperature in films are
shown for thicknesses up to the 1.2 nm. From our calculations, we predicted that the
critical thickness of strained BaTiO3 film is 0.8 nm.
Description
PhD
Keywords
Science Physic , Landau theory , Ferroelectric film