  Phase-field simulation (PFS) have revolutionized the understanding of domain
structure and switching behavior in ferroelectric thin films and ceramics.
Generally, PFS is based on solution of a (set) of Ginzburg-Landau equations for
a defined order parameter field(s) under physical boundary conditions (BCs) of
fixed potential or charge. While well-matched to the interfaces in bulk
materials and devices, these BCs are generally not applicable to free
ferroelectric surfaces. Here, we developed a self-consistent phase-field model
with boundary conditions based on electrochemical equilibria. We chose
Pb(Zr0.2Ti0.8)O3 ultrathin film consisting of (001) oriented single tetragonal
domain (Pz) as a model system, and systematically studied the effects of oxygen
partial pressure, temperature and surface ion on the ferroelectric state, and
compared it with the case of complete screening. We have further explored the
polarization switching induced by the oxygen partial pressure and observed
pronounced size effect induced by chemical screening. Our work thus helps to
understand the emergent phenomena in ferroelectric thin films brought about by
the electrochemical ionic surface compensations.
