Statistics of electrical breakdown field in HfO2 and SiO2 films from millimeter to nanometer length scales

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.