Simple analytical formulas for the extrinsic time-dependent dielectric breakdown lifetime are derived by extending intrinsic models to include the contribution of oxide defects, mathematically taking advantage of the characteristics of Weibull function. The lifetime is given by a simple function of electric field E with only four fitting parameters, two for intrinsic and two for extrinsic failures. Two types of formulas are compared to explain the data with the Weibull slope inversely proportional to E: one is a three-term formula assuming the extrinsic charge to breakdown., Q(BD) based on the 1/E theory, and the other is a two-term formula based on the E model using the idea of oxide thinning. It is discussed that the difference between the two formulas is only in the third term, and will be more clearly tested if the probed E range is increased. The E-n model is derived modifying the E model to cover experiments where the E or 1/E model does not simply apply, The experimental data with the Weibull slope not inversely proportional to E is successfully explained using the n value derived from the extrinsic Weibull slope. (C) 2002 Elsevier Science Ltd. All rights reserved.