Evolution of a stripe array of polarization domains triggered by the oxygen vacancy migration in an acceptor doped ferroelectric is investigated in a self-consistent manner. A comprehensive model based on the Landau-Ginzburg-Devonshire approach includes semiconductor features due to the presence of electrons and holes, and effects of electrostriction and flexoelectricity especially significant near the free surface and domain walls. A domain array spontaneously formed in the absence of an external field is shown to undergo a reconstruction in the course of the gradual oxygen vacancy migration driven by the depolarization fields. The charge defect accumulation near the free ferroelectric surface causes a series of phenomena: (i) symmetry breaking between the positive and negative c-domains, (ii) appearance of an effective dipole layer at the free surface followed by the formation of a surface electrostatic potential, (iii) tilting and recharging of the domain walls, especially pronounced at higher acceptor concentrations. An internal bias field determined by the gain in the free energy of the structure exhibits dependences of its amplitude on time and dopant concentration well comparable with available experimental results on aging in BaTiO3.
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