Improved tri-layered interfacial stress model with the effect of different temperatures in the layers

Abstract

The study of thermal mismatch induced stresses and their role in mechanical failure is one relevant topic to composite materials and electronic packages. An understanding of the nature of the interfacial stresses under different temperature conditions is necessary in order to minimize or eliminate the risk of mechanical failure. An accurate estimate of thermal stresses in the interfaces plays an important role in the design and reliability studies of micro-electronic devices. In the microelectronic industry, from a practical point of view, there is a need for simple and powerful analytical models to determine interfacial stresses in layered structures quickly and accurately. In the present paper, a model is proposed for the shearing and peeling stresses occurring at the interface of three bonded thin plates of dissimilar materials to account for different uniform temperatures in the layers by incorporating two temperature ratios. The model is then further upgraded to accommodate the effect of thickness wise linear temperature gradients in the layers by incorporating three linear temperature gradients at the interfaces. This upgraded model can be viewed as a more generalized form to take care of different temperature conditions which may occur in a tri-layered structure. The improved uniform temperature model of tri-material assembly provided by Sujan (Int Microelectron Packag Soc JMEP 5(1):37–42, 2008) is utilized to develop the proposed tri-layered model. The selected shearing stress results are presented for the case of die, die attach and substrate as commonly found in electronic packaging.