Singular stress fields at corners in flip-chip packages

Abstract

An electronic device integrates diverse materials, and inevitably contains sharp features, such as interfaces and corners. When the device is subject to thermal and mechanical loads, the corners develop intense stress and are vulnerable sites to initiate failure. This paper analyzes stress fields at corners in flip-chip packages. The stress at a corner is a linear superposition of two modes of singular fields, with one mode being more singular than the other. The amplitudes of the two modes are represented by two stress intensity factors of dissimilar dimensions. To determine the stress intensity factors, we analyze the flip-chip structures under two loading conditions: stretching of the substrate and bending of the substrate. We show that the less singular mode may prevail over the more singular mode for some stretching-bending combinations. The relative significance of the two modes of stress fields also varies with materials, and with the substrate to chip thickness ratio.

Effects of Stiff Film Pattern Geometry on Surface Buckling Instabilities of Elastic Bilayers

“…Interestingly, the behavior of the film edges and the bare substrate in the gap regions depends on g /λ wrinkle . At low g /λ wrinkle (<1.7), shallow creases form at the edges of the stiff patterns (Figures a,b and S5) at very low global strain, which is consistent with the singular nature of the strain state expected at the boundary between the film and the substrate . Presumably, this strain concentration allows the critical strain for creasing to be locally exceeded, even at arbitrarily small global strains, thus nucleating creases near each edgethis phenomenon will be discussed in more depth in a later paper.…”

“…At low g/ λ wrinkle (<1.7), shallow creases form at the edges of the stiff patterns (Figures 3a,b and S5) at very low global strain, which is consistent with the singular nature of the strain state expected at the boundary between the film and the substrate. 40 Presumably, this strain concentration allows the critical strain for creasing to be locally exceeded, even at arbitrarily small global strains, thus nucleating creases near each edgethis phenomenon will be discussed in more depth in a later paper. At larger ε, however, a large crease is formed in the center of the gap, leading to contact between neighboring film regions (Figure 3a,b).…”

On ensuring structural integrity for configurations with stress singularities: a review

“…Recent reviews of such asymptotic identifications are available . Additional recent asymptotic identifications are also available …”

“…Often these additional identifications are for more complex local configurations than those in the references in the cited reviews: sometimes they simply fill in a gap in the literature. For classical elasticity with local configurations comprised of isotropic and piecewise homogeneous, linear elastic materials, all the stress singularities asymptotically identified that have been found to date since 2004 are discussed in the studies . Examples of stress singularities identified since 2004 for anisotropic elastic materials are given in the previous studies ; for functionally graded elastic materials; for finite strain in elastic materials; and for varying size scales …”