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The statistics of electrical breakdown field (Ebd) of HfO2 and SiO2 thin films has been evaluated over multiple length scales using macroscopic testing of standardized metal-oxide-semiconductor (TiN∕SiO2∕Si) and metal-insulator-metal (TiN∕HfO2∕TiN) capacitors (10−2mm2–10μm2 area) on a full 200mm wafer along with conductive-atomic-force microscopy. It is shown that Ebd follows the same Weibull distribution when the data are scaled using the testing area. This overall scaling suggests that the defect density is ∼1015cm−2 and Ebd is ∼40MV∕cm for nanometer-length scales; as such, breakdown in these materials is most likely initiated by bond breaking rather than punctual defects.
Sire et al. (Mon,) studied this question.