Extensions of the effective thickness theory of oxide breakdown

The effective thickness concept of oxide breakdown is generalized to a causal time-to-breakdown function, depending only on effective electric field. The function is approximated by a linear and inverse exponential electric-field dependence and applied differentially to data obtained in a pair of step stress tests. The effective thickness distribution is evaluated in both cases and found to be independent of the form chosen. The actual electric-field dependence of the time-to-breakdown function is measured and can be fit with either form over the small range of effective electric fields encountered in the highly accelerated tests. The analysis technique using a pair of tests is presented to illustrate that the effective thickness theory does not require a particular form for the time-to-breakdown function. It demonstrates that the defect density function can be fully obtained at highly accelerated conditions, sampling only a small range of high electric fields. The technique does not of itself allow extrapolation to lower electric fields even though the distribution in effective thickness is known