BiFeO₃ thin films were grown on Pt/c-sapphire substrates by pulsed laser deposition with different growth rates. With increasing growth rate the leakage current is decreased and the conduction mechanism changes from bulk-limited Poole-Frenkel emission to interface-limited Schottky emission. In the present letter, we show that only the growth rate of the BiFeOv₃ films close to the metal contacts has to be increased in order to reduce the leakage current and to observe saturated polarization-electric field hysteresis loops.