  "Head-to-head" and "tail-to-tail" 180-degree domain-walls in a finite
isolated ferroelectric sample are theoretically studied using Landau theory.
The full set of equations, suitable for numerical calculations is developed.
The explicit expressions for the polarization profile across the walls are
derived for several limiting cases and wall-widths are estimated. It is shown
analytically that different regimes of screening and different dependences for
width of charged domain walls on the temperature and parameters of the system
are possible, depending on spontaneous polarization and concentration of
carriers in the material. It is shown that the half-width of charged domain
walls in typical perovskites is about the nonlinear Thomas-Fermi
screening-length and about one order of magnitude larger than the half-width of
neutral domain-walls. The formation energies of "head-to-head" walls under
different regimes of screening are obtained, neglecting the poling ability of
the surface. It is shown that either "head-to-head" or "tail-to-tail"
configuration can be energetically favorable in comparison with the monodomain
state of the ferroelectric if the poling ability of the surface is large
enough. If this is not the case, the existence of charged domain walls in bulk
ferroelectrics is merely a result of the domain-growth kinetics. Size-effect
corresponding to the competition between state with charged domain wall, single
domain state, multidomain state, and the state with the zero polarization is
considered. The results obtained for the case of an isolated ferroelectric
sample were compared with the results for an electroded sample. It was shown
that charged domain wall in electroded sample can be either metastable or
stable, depends on the work function difference between electrodes and
ferroelectric and the poling ability of the electrode/ferroelectric interface.
