Stress analysis of thermal inclusions with interior voids and cracks

Thermal mismatch induced residual stresses are identified as one of the maj or causes of voiding and failure of some critical components in electronic packaging, such as passivated interconnect lines and isolation trenches. In this paper, a general method is presented for thermal stress analysis of a n embedded Structural element in the presence of internal or nearby voids a nd cracks. Here, the elastic mismatch between dissimilar materials is ignor ed. Hence, the embedded structural element is modeled as a thermal inclusio n of arbitrary shape surrounded by an infinite elastic medium of the same e lastic constants. Thermal stresses are caused by thermal mismatch between t he inclusion and the surrounding material due to a uniform change in temper ature. With the present method, the problem is reduced to one of an infinit e homogeneous medium containing the same voids and cracks, subjected to a s at of remote stresses determined by the geometrical shape of the thermal in clusion. In particular, the remote stresses are uniform, when the thermal i nclusion is an ellipse. The method gives an elementary expression for the i nternal stress field of a thermal inclusion with a single interior void or crack. Several examples of practical interest are used to illustrate the me thod. The results show that all internal void or crack cart significantly c hange stress distribution within the inclusion and gives rise to stress con centration around the void or crack.