  Recent observations of unusual ferroelectricity in thin films of HfO_2 and
related materials have attracted broad interest to the materials and led to the
emergence of a number of competing models for observed behaviors. Here we
develop the electrochemical mechanism of observed ferroelectric-like behaviors,
namely the collective phenomena of elastic and electric dipoles originated from
oxygen vacancies formation in the vicinity of film surfaces, as well as from
grain boundaries and other types of inhomogeneities inside the film. The
ferroelectric phase is induced by the "electrochemical" coupling, that is the
joint action of the omnipresent electrostriction and "chemical" pressure, which
lead to the sign change of the positive coefficient alfa in the quadratic term
alfa*P^2 in the order-disorder type thermodynamic functional depending on
polarization P. Negative coefficient alfa becomes the driving force of the
transition to the long-range ordered ferroelectric phase with the spontaneous
polarization P in the direction normal to the film surface. Using the above
ideas, we estimated that the reversible ferroelectric polarization, as high as
(0.05 - 0.2) C/m^2, can be induced by oxygen vacancies in HfO_2 films of
thickness less than (20 - 30) nm. Semi-quantitative agreement with available
experimental data is demonstrated.
