Nonhomogeneous spatial distribution of filamentary leakage current paths in circular area Pt/HfO₂/Pt capacitors

Filamentary leakage current paths can occur in circular area Pt/HfO ₂/Pt capacitors as the result of severe electrical stress. The spatial distribution of these paths is investigated using 2D statistical methods. The filamentary paths are associated with important thermal effects occurring inside the HfO₂ layer and manifest externally as a random spot pattern on the top Pt electrode. It is shown in this paper that for the devices with the largest areas significant departures from homogeneity are detected close to the peripheries of the structures. These deviations are observed as a lower density of spots than expected for a homogeneous Poisson process. Although the ultimate reason for this anomaly is still under investigation, our results demonstrate that the complete spatial randomness frequently assumed in oxide reliability analysis should not be taken for granted.