Analytical Determination of Empirical Coefficients for Several Lifetime Models of Power Semiconductors

Power cycling reliability is one of the most widely used frameworks to evaluate the lifetimes of power semiconductor switching devices from a thermal stress perspective. Experimental tests can be used to predict their lifetimes under operating conditions. An estimation of the number of cycles to failure Nf can also be given by several lifetime models, which express the number of cycles to end of life as a function of empirical coefficients. In the existing literature, these empirical coefficients are generally estimated using the classical least squares method (to find the best-fitting line through data points), where outliers are removed using the Random Sample Consensus algorithm. The aim of this paper is to present a general strategy for the calculation of empirical coefficients for different lifetime models, such as Coffin–Manson, Coffin–Manson–Arrhenius, Norris–Landzberg, and simplified Bayerer, aiming at minimizing the number of required experimental tests. The results show that the number of experimental trials required varies between two and four, depending on the number of empirical coefficients to be determined, which is specific to the lifetime model used. Furthermore, a limited number of experimental data points are selected to avoid any degradation in accuracy. The accuracy of coefficient estimation is significantly improved by excluding outliers: some relative errors decrease by 25%. Additionally, each empirical coefficient is determined under specific thermal stress conditions, such as a constant junction temperature swing ΔTj, constant current per bond wire I, constant cycling frequency f, or constant mean junction temperature Tjm. Furthermore, a limited number of experimental data are selected to avoid any degradation in accuracy due to outliers. Moreover, this general method can be applied to all power devices, such as IGBTs or MOSFETs. Finally, the limitations of the analytical solution for the Scheuermann lifetime model are discussed.