Field emission measurements of current-voltage characteristics are reported for tetrapod structures of ZnO. The nonlinear Fowler-Nordheim (FN) plot is analyzed according to a model of calculation based on saturation of conduction band current and predominance of valence band current at high-field values. The simulated FN plot exhibits similar features to those observed experimentally. The model of calculation suggests that the slope variation of the FN plot, in the high-field and low-field regions, does not depend on the magnitude of saturation. Instead, it is a characteristic of the energy band structure and voltage-to-barrier-field conversion factor of the emitting material.