  The contribution of a built-in electric field to ferroelectric phase
transition in asymmetric ferroelectric tunnel junctions is studied using a
multiscale thermodynamic model. It is demonstrated in details that there exists
a critical thickness at which an unusual ferroelectric-\'\' polar
non-ferroelectric\rq\rq phase transition occurs in asymmetric ferroelectric
tunnel junctions. In the \'\' polar non-ferroelectric\rq\rq phase, there is
only one non-switchable polarization which is caused by the competition between
the depolarizing field and the built-in field, and closure-like domains are
proposed to form to minimize the system energy. The transition temperature is
found to decrease monotonically as the ferroelectric barrier thickness is
decreased and the reduction becomes more significant for the thinner
ferroelectric layers. As a matter of fact, the built-in electric field does not
only result in smearing of phase transition but also forces the transition to
take place at a reduced temperature. Such findings may impose a fundamental
limit on the work temperature and thus should be further taken into account in
the future ferroelectric tunnel junction-type or ferroelectric capacitor-type
devices.
