Experimental evidence of TBD power-law for voltage dependence of oxide breakdown in ultrathin gate oxides

In this paper, we present experimental evidence on the voltage-dependence of the voltage acceleration factors observed on ultrathin oxides from 5 nm down to ∼1 nm over a wide range of voltages from ∼2 V to 6 V. Two independent experimental approaches, area scaling method and long-term stress, are used to investigate this phenomenon. We show the exponential law with a constant voltage-acceleration factor violates the widely accepted fundamental breakdown property of Poisson random statistics while the voltage-dependent voltage acceleration described by an empirical power-law relation preserves this well-known property. The apparent thickness-dependence of voltage acceleration factors measured in different voltage ranges can be nicely understood and unified with these independent experimental results in the scenario of a voltage-driven breakdown. In the framework of the critical defect density and defect generation rate for charge-to-breakdown, we explore the possible explanation of increasing voltage acceleration factors at reduced voltage by assuming a geometric model for the critical defect density.