The change in permittivity of bismuth zinc niobate (BZN) films with the cubic pyrochlore structure under an applied electric field was measured as a function of temperature. Dielectric measurements were performed using parallel-plate capacitor structures with Pt electrodes on sapphire substrates. The electric field tunability of the permittivity was weakly temperature dependent and increased with decreasing temperature up to the onset of dielectric relaxation. At temperatures below the onset of the dielectric relaxation (similar to150 K at 1 MHz), larger electric fields were required to achieve the highest tunabilities. A simple model of hopping, noninteracting dipoles was not suited to describe. the dielectric tunability of BZN thin films. A better description of the experimentally observed behavior at temperatures above the onset of the dielectric relaxation was obtained using a simple random-field model with hopping dipoles in a uniform distribution of random fields. (C) 2005 American Institute of Physics.