Identification of Probabilistic Input Data for a Glue-Die-Package Problem

Abstract

In mathematical models, physical or geometrical parameters often involve uncertainties due to measurement errors, estimations or imperfections of an industrial production. An uncertainty quantification can be performed by a stochastic description, where parameters are substituted by random variables or random processes. The probability distributions of the parameters have to be predetermined as an input to the stochastic model. However, the variability of input parameters often cannot be measured directly, whereas the output quantities are available. We consider a test problem from nanoelectronics, where a piece of glue connects a die and a package. The geometrical parameters as well as the material parameters are uncertain for the piece of glue. We fit the input probability distributions of the random parameters to measurements of the output, which represents a kind of inverse problem. For this purpose, a minimization problem is defined including a piecewise linear approximation of the cumulative distribution functions. We present numerical results for this test problem.