Characterization of the Failure Site Distribution in MIM Devices Using Zoomed Wavelet Analysis

The angular wavelet analysis is applied to the study of the spatial distribution of breakdown (BD) spots in Pt/HfO₂/Pt capacitors with square and circular areas. The method is originally developed for rectangular areas, so a zoomed approach needs to be considered when the observation window does not coincide with the device area. The BD spots appear as a consequence of the application of electrical stress to the device. The stress generates defects within the dielectric film, a process that ends with the formation of a percolation path between the electrodes and the melting of the top metal layer because of the high release of energy. The BD spots have lateral sizes ranging from 1 μm to 3 μm and they appear as a point pattern that can be studied using spatial statistics methods. In this paper, we report the application of the angular wavelet method as a complementary tool for the analysis of the distribution of failure sites in large-area metal–insulator–metal (MIM) devices. The differences between considering a continuous or a discrete wavelet and the role played by the number of BD spots are also investigated.