Modeling temperature dependent chemical reaction of intermetallic compound growth

Abstract

This paper is concerned with the modeling of the formation and growth of InterMetallic Compound (IMC) layers in tin (Sn) based solder bumps on copper (Cu) interconnects within a microelectronic component subjected to a thermo-cycle test. IMC formation is the result of diffusion and chemical reaction processes. There is a change in shape and volume between the products and reactants, and, consequently, in addition to temperature the growth is influenced by the resulting residual stresses and strains. Strictly speaking IMC formation is based on multi-component diffusion in solids, including vacancies as a migrating species leading to Kirkendall voiding, and in addition to mechanical stress it can be enhanced by electric currents. It should also be noted that if the bump is used as an electric connection in a microelectronic component additional mechanical stress will result from the thermal mismatch of the various materials used to fabricate this component. In this paper we will use a formerly developed methodology to study IMC growth in solder bumps that are sheared due to the different thermal expansion coefficients of the adjacent material structures. The change of temperature is chosen such that it mimics the temperature range, ramp and hold times typically encountered in a temperature cycle test. The methodology for computing the growth of the reaction front is based on a kinetic equation. It was derived in former work from an expression for the chemical affinity tensor. It allows to incorporate the influence of stresses and strains on the chemical reaction rate and the normal component of the reaction front velocity in a rational manner. Due to the complexity of the geometry the involved solution procedures must be numerical ones. Consequently, the Finite Element (FE) technique will be applied during the solution.