Application of a surrogate layer for lower bending stress in a tri-material body

Low strength materials in multi-layer (multi-body) structures subjected to a change in temperature often fail because of the elevated thermal expansion (contraction) mismatch of the materials and the resulting curvatures and bending stresses. In some cases, an introduction of an additional 'surrogate' layer of a high expansion and/or high modulus material (not needed from the standpoint of the normal design and operation of the system) can be an effective means to flatten the composite structure and thereby reduce the bending stress in the vulnerable material. Particularly, this approach can be applied to ball grid array (BGA) packages in which an epoxy molding compound encapsulating IC devices on a thin substrate could be prone to cracking as a result of excessive bending at room temperature. We considered the use of an epoxy molding compound on a thin ceramic substrate and suggest that an additional 'surrogate' layer of a high expansion and high modulus polymeric material be applied onto the outer side of the substrate and that this material be processed concurrently with the molding operation. A simple formula is obtained for choosing the thickness of this layer for the given mechanical properties of the material(s), including the additional material itself.