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

Abstract
The statistics of electrical breakdown field ( E bd ) of Hf O 2 and Si O 2 thin films has been evaluated over multiple length scales using macroscopic testing of standardized metal-oxide-semiconductor ( Ti N ∕ Si O 2 ∕ Si ) and metal-insulator-metal ( Ti N ∕ Hf O 2 ∕ Ti N ) capacitors ( 10 − 2 mm 2 – 10 μ m 2 area) on a full 200 mm wafer along with conductive-atomic-force microscopy. It is shown that E bd follows the same Weibull distribution when the data are scaled using the testing area. This overall scaling suggests that the defect density is ∼ 10 15 cm − 2 and E bd is ∼ 40 MV ∕ cm for nanometer-length scales; as such, breakdown in these materials is most likely initiated by bond breaking rather than punctual defects.