Assessing the Correlation Between Location and Size of Catastrophic Breakdown Events in High-K MIM Capacitors

The connection between the spatial location of catastrophic breakdown spots occurring in metal-insulator-metal capacitors with a high-permittivity dielectric film (HfO 2 ) and their respective sizes is investigated. Large area structures ( $10^{4}$ - $10^{5}~\mu \text{m}^{2}$ ) are used for this correlation assessment since, for statistical considerations, a large number of spots in the same device is imperatively required. The application of ramped or constant voltage stress across the capacitor generates defects inside the dielectric that result in the formation of multiple failure sites. High power dissipation takes place locally, leaving a permanent mark on the top electrode of the device. The set of marks constitutes a point pattern with attributes that can be analyzed from a statistical viewpoint. The correlation between the spot locations and their sizes is assessed through the mark correlation function and the method of reverse conditional moments. The study reveals that for severely damaged devices, there exists a link between the spot location and size that leads to a short range departure from a complete spatial randomness (CSR) process. It is shown that the affected region around each failure site is actually larger than the visible area of the spot. A structural modification of the dielectric layer in the vicinity of the spot caused by the huge thermal effects occurring just before the microexplosion might be the reason behind this extension of the damage.