A computational simulation of Kirkendall voiding in metallic materials is presented. After a brief explanation of the phenomena and its consequences on the reliability of microelectronic components we introduce a constitutive model for void nucleation and growth which is based on vacancy diffusion and rate-dependent inelastic deformation. This model can be used to predict the temporal development of voids in solder during thermal cycling and/or impact loading. A numerical study illustrates the potential of the model for the failure analysis.
The ProblemSolder joints of microelectronic circuit units are to an increasing extent made of tin alloys (e.g., Sn-Ag or Sn-Ag-Cu). These joints hold the multi-layered unit in position and, in addition, the solder joints provide electrical conductivity between the metallic (coppered) layers of the units. "Aging" of solder, such as phase separation, coarsening or the formation of InterMetallic Compounds (IMCs), as well as the formation and growth of pores and cracks in the vicinity of heterogeneities significantly effect the life expectation of the joints and considerably influence the reliability of the whole component. During manufacturing the (molten) Sn-rich solder wets the copper pad and IMCs are formed due to an interfacial reaction. These IMCs are relatively stiff and considerable stresses are induced in these regions due to mismatching thermal expansion. Furthermore the IMCs show different diffusion coefficients w.r.t. Cu and, therefore, the diffusion of Cu from the pad via the interface Cu/Cu 3 Sn into Cu 3 Sn is much slower than the diffusion of Cu from Cu 3 Sn into the Cu 6 Sn 5 scallops, which also cannot be "corrected" by the vice versa diffusion of Sn via the Cu 6 Sn 5 /Cu 3 interface. As a consequence vacancies on the lattice sides remain within the Cu 3 Sn compounds, which coalesce due to vacancy diffusion to macroscopic voids. Moreover, primarily initiated by stress peaks in the vicinity of the voids they further grow and merge to cracks, which may proceed such that failure occurs.
Constitutive Model for Void Nucleation and GrowthIn [2, 3] the authors developed a detailed model for KIRKENDALL voiding in IMCs. The main ideas are sketched here shortly. To this end we distinct between void nucleation and ∼growth. The nucleation process is understood, beyond the atomic scale, to be the result of vacancy diffusion. The resulting vacancy "cluster" is, if a critical amount of vacancies would be reached, treated as a nucleated macroscopic void. However, these voids do not exclusively grow due to diffusion. In particular, local mechanical stresses or surface energy effects result in proceeding void growth and coalescence.