Exploratory study and application of the angular wavelet analysis for assessing the spatial distribution of breakdown spots in Pt/HfO_2/Pt structures

摘要

The angular wavelet analysis is applied for assessing the spatial distribution of breakdown spots in Pt/HfO_2/Pt capacitors with areas ranging from 10~4 to 10~5 μm~2. The breakdown spot lateral sizes are in the range from 1 to 3 /an, and they appear distributed on the top metal electrode as a point pattern. The spots are generated by ramped and constant voltage stresses and are the consequence of microexplosions caused by the formation of shorts spanning the dielectric film. This kind of pattern was analyzed in the past using the conventional spatial analysis tools such as intensity plots, distance histograms, pair correlation function, and nearest neighbours. Here, we show that the wavelet analysis offers an alternative and complementary method for testing whether or not the failure site distribution departs from a complete spatial randomness process in the angular domain. The effect of using different wavelet functions, such as the Haar, Sine, French top hat, Mexican hat, and Morlet, as well as the roles played by the process intensity, the location of the voltage probe, and the aspect ratio of the device, are all discussed.