On the Weibull shape factor of intrinsic breakdown of dielectric films and its accurate experimental determination. Part I: theory, methodology, experimental techniques

Critically examined several important aspects concerning the experimental determination of Weibull shape factors (slopes). Statistical characteristics of breakdown distribution such as area scaling property and the extreme-value distribution are reviewed. We discuss the experimental measurement methodology of time-to-breakdown (T_BD) or charge-to-charge (Q_BD) distributions with the emphasis on the accuracy. The influence of sample numbers on the estimation of Weibull distribution parameters such as characteristic T_BD and Weibull slopes are investigated in the context of confidence limits. Some examples of the measurement fallacy on Weibull slopes are given. Three different experimental techniques to measure Weibull slopes are described and compared in terms of their advantages and disadvantages. Finally, we will give a comparison of these three methods. Having established these fundamental aspects of the Weibull slope measurements, we will present our extensive experimental data on thickness, voltage, temperature, and polarity dependence of Weibull slopes in part II.