  We report electrically switchable polarization and ferroelectric domain
scaling over a thickness range of 5-100 nm in BiFeO3 films deposited on [110]
vicinal substrates. The BiFeO3 films of variable thickness were deposited with
SrRuO3 bottom layer using pulsed laser deposition technique. These films have
fractal domain patterns and the domain width scales closely with the square
root of film thickness, in accordance with the Landau-Lifschitz-Kittel (LLK)
law. The Switching Spectroscopy Piezo-response Force Microscopy provides clear
evidence for the ferroelectric switching behavior in all the films. Using
Quasi-particle Self-consistent GW (QPGW) approximation we have investigated
physical parameters relevant for direct tunneling behavior, namely the
effective mass and effective barrier height of electrons. For rhombohedral BFO,
we report a large effective barrier height value of 3.6 eV, which is in
reasonable agreement with nanoscale transport measurements. QPGW investigations
into the tetragonal BFO structure with P4mm symmetry revealed a barrier height
of 0.38 eV, significantly lower compared to its rhombohedral counterpart. This
difference has very significant implications on the transport properties of
nearly tetragonal BFO phase.
