In order for sub-10 nm thin films of ZrO₂ to have a dielectric constant larger than 30 they need to be crystalline. This is done by either depositing the layer at higher temperatures or by a postdeposition annealing step. Both methods induce high leakage currents in ZrO₂ based dielectrics. In order to understand the leakage a thickness series of ultrathin ZrO₂ and nanolaminate ZrO₂ / Al₂ O₃ / ZrO₂ (ZAZ) films, deposited by atomic layer deposition, was investigated. After deposition these films were subjected to different rapid thermal annealing (RTA) processes. Grazing incidence x-ray diffraction and transmission electron microscopy yield that the crystallization of ZrO ₂ during deposition is dependent on film thickness and on the presence of an Al₂ O₃ sublayer. Moreover, the incorporation of Al₂ O₃ prevents crystallites from spanning across the entire film during RTA. C-V and I-V spectroscopies show that after a 650 °C RTA in N₂ the capacitance equivalent oxide thickness of 10 nm ZAZ films is reduced to 1.0 nm while maintaining low leakage currents of 3.2× 10^-8 A/ cm² at 1 V. Conductive atomic force microscopy studies yield that currents are not associated with significant morphological features in amorphous layers. However, after crystallization, the currents at crystallite grain boundaries are increased in ZrO₂ and ZAZ films.