Split singularities: Stress field near the edge of a silicon die on a polymer substrate

In current design the circuitry is extended very close to the edges of a silicon die to maximize useful surface area. When the die is bonded to a polymer substrate, with the circuitry facing the polymer, thermal misfit stress concentrates at the die edges and may damage the circuitry. The stress distribution near a die edge is quantified using a combination of asymptotic analysis and finite element calculation. The asymptotic field consists of two modes of singular stresses, scaling with the distance from the edge r as, respectively, r(-lambda 1) and r(-lambda 2), where lambda(1) > lambda(2). It is shown that the more singular field (i.e. the lambda(1)-singularity) prevails in an exceedingly small zone, smaller than 10(-6) limes the die thickness. Once both modes are included, however, the asymptotic field matches the full field in a zone about 10(-1) times the die thickness. This finding resolves several controversies in the literature on electronic packaging. The near-edge stress distribution is presented for various substrate thicknesses, elastic moduli and thermal expansion coefficients. The results can be used to explore design options. (C) 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.