Failure Analysis of MIM and MIS Structures Using Point-to-Event Distance and Angular Probability Distributions

Multiple breakdown (BD) spots are generated in large (>10^-4 cm²) circular and square area metal-insulator-metal and metal-insulator-semiconductor devices using ramped and constant-voltage electrical stresses. Due to the important local thermal effects that take place at the very moment of the formation of the conductive paths spanning the insulating layer, the failure events become visible on the top metal electrode of the structures as a point pattern. The resulting point-to-event distance and angular histograms are compared with the theoretical distributions corresponding to a complete spatial randomness (CSR) process. The location of the voltage probe tip over the top electrode is considered here as the singular point from which the positions of the BD spots are referred to. In this way, we are able to assess the influence of the probe point on the final BD spot distribution. In most of the cases, this distribution is consistent with CSR, but after prolonged electrical stress, a deviation is detected. This departure from CSR is ascribed to the concentration of the current lines in the top electrode toward the center of the structure. The methods reported here are general and can be used for analyzing the generation of similar point patterns occurring in other structures or material systems.