Determination of tolerance limits for the reliability of semiconductor devices using longitudinal data

Design and production of semiconductor devices for the automotive industry are characterized by high reliability requirements, such that the proper functioning of these devices is ensured over the whole specified lifetime. Therefore, manufacturers let their products undergo extensive testing procedures that simulate the tough requirements their products have to withstand. Such tests typically are highly accelerated, to test the behavior of the products over the whole lifetime. In case of drift of electrical parameters, manufacturers then need to find appropriate tolerance limits for their final electrical product tests, such that the proper functioning of their devices over the whole specified lifetime is ensured. In this study, we present a statistical model for the determination of tolerance limits that minimize yield loss. The model considers longitudinal measurements of continuous features, based on censored data from stress tests. The tolerance limits are derived from multivariate distributions where the dependence structure is described by different copulas. Based on extensive numerical testing, we are able to provide insights into the properties of our model for different drift behaviors of the devices.