Statistical prediction of temperature effects inside through-silicon vias by means of orthogonal polynomials

This paper presents a stochastic SPICE model for through-silicon vias (TSVs). The model is based on recent state-of-the-art equivalent-circuit models for TSVs and allows to inherently include possible random variations of physical parameters. The underlying idea is the description of the stochastic circuit equations in terms of orthogonal polynomials, whose unknown coefficients are obtained from the deterministic solution of a modified system. An application example involving the stochastic simulation of a TSV in presence of uncertain temperature conditions concludes the paper.