Analysis of the breakdown spot spatial distribution in Pt/HfO ₂/Pt capacitors using nearest neighbor statistics

The breakdown spot spatial distribution in Pt/HfO₂/Pt capacitors is investigated using nearest neighbor statistics in combination with more conventional estimation methods such as the point-event and event-event distance distributions. The spots appear as a random point pattern over the top metal electrode and arise as a consequence of significant localized thermal effects caused by the application of high-voltage ramped stress to the devices. The reported study mainly involves the statistical characterization of the distances between each failure site and the nearest, second nearest,⋯ kth nearest event and the comparison with the corresponding theoretical distributions for a complete spatial randomness (CSR) process. A method for detecting and correcting deviations from CSR based on a precise estimation of the average point intensity and the effective damaged device area is proposed.