On the interfacial phase growth and vacancy evolution during accelerated electromigration in Cu/Sn/Cu microjoints

Abstract

In this work, we integrate different computational tools based on multi-phase-field simulations to account for the evolution of morphologies and crystallographic defects of Cu/Sn/Cu sandwich interconnect structures that are widely used in three dimensional integrated circuits (3DICs). Specifically, this work accounts for diffusion-driven formation and disappearance of multiple intermetallic phases during accelerated electromigration and takes into account the non-equilibrium formation of vacancies due to electromigration. The work compares nucleation, growth, and coalescence of intermetallic layers during transient liquid phase bonding and virtual joint structure evolution subjected to accelerated electromigration conditions at different temperatures. The changes in the rate of dissolution of Cu from intermetallics and the differences in the evolution of intermetallic layers depending on whether they act as cathodes or anodes are accounted for and are compared favorably with experiments. The model considers non-equilibrium evolution of vacancies that form due to differences in couplings between diffusing atoms and electron flows. This work is significant as the point defect evolution in 3DIC solder joints during electromigration has deep implications to the formation and coalescence of voids that ultimately compromise the structural and functional integrity of the joints.

Integration of machine learning with phase field method to model the electromigration induced Cu6Sn5 IMC growth at anode side Cu/Sn interface

“…The third term of Eq. 5, namely felec is the electrostatic free energy density [18,19,20,35] . In Eq.…”

“…In the formula for the composition dependent effective charge number, and , are respectively the effective charge numbers of Sn and Cu in i th phase. In [19] , Z* is considered as a constant and does not vary with the phases, whereas in [20] it is considered as a phase dependent property. Within a phase, it is possible that Z* has a different value for Cu and Sn [10] .…”

“…The interfacial energy between the phases is considered to be uniform everywhere in the computational domain. The values for electrical resistivities of FCC (Cu rich) and IMC phases are taken from [19] , whereas that of the Sn-rich LIQUID phase is taken from [20] . It must be noted that and are taken to be equal to that of pure Cu and Sn respectively , and are represented as and in the table.…”

“…For the binary Cu-Sn system consisting of Cu-rich, Sn-rich and intermetallic phases, a multiphase field formalism [17] has been utilized to investigate the evolution of interfacial intermetallic compound (IMC) layers under electromigration conditions [18][19][20]. The research works [18][19][20] utilize a free energy density term to describe the electromigration driving force on phase evolution, and this term includes the effective charge number. As highlighted earlier, it is not clearly understood how the magnitude of Z* has been assigned in these works.…”

“…Park et al [19] have assigned a constant magnitude of 50 for effective charge number, implying that both Cu and Sn are considered to have the same value Z* for all of the FCC, IMCs and BCT phases. Though Attari et al [20] took different values of the effective charge numbers in different phases, they assumed that the numbers for Cu and Sn are of a same magnitude in the same phase. Chao et al [10] stated that for the binary Cu-Sn system, in general, the effective charge numbers of Cu and Sn are not equal and are also different in different phases.…”