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

The statistics of electrical breakdown field (E-bd) 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(-2) mm(2)-10 mu 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 similar to 10(15) cm(-2) and E-bd is similar to 40 MV/cm for nanometer-length scales; as such, breakdown in these materials is most likely initiated by bond breaking rather than punctual defects. (C) 2007 American Institute of Physics.