Metal-insulator-metal (MIM) large area (>10-4 cm2) capacitors with different
aspect ratios were subjected to severe stress conditions (Eox>4-5 MV/cm) with
the aim of generating a large density of breakdown spots (from 105 to 106
spots/cm2) in the same device. The resulting mark pattern on the top metal
electrode associated with the failure events was analyzed first using
conventional functional estimators for two-dimensional spatial statistics.
Second, as a double check, the attention was focused on the same breakdown
spot patterns but in relation to the probe point location. In this latter
case, the objective was to rule out any stochastic dependence of the
breakdown spot distribution on the position of the source of degradation and
therefore to confirm whether or not the spots follow a complete spatial
randomness (CSR) process. In order to simplify the mathematical treatment of
the point-to-event distributions, the voltage probe was assumed to be located
at one corner of the observation window which significantly reduces the
number of cases to analyze. Infrared images revealed that the generation of
the spots is associated with micro-explosions within the insulating material
(HfO2) and with the local volatilization of the top metal electrode (Pt).