Some remarks on finite element modeling of electromigration in solder joints

Abstract

This paper investigates several issues in finite element modeling of electromigration in solder joints: current density and thermal stress singularities; negative divergences of atomic fluxes due to electron current and thermal stresses; and submodeling accuracy. A copper post wafer level package is used as a test vehicle for simulation. Coupled electrical-, thermal-, and mechanical finite element modeling is performed. Results show that the values of maximum current density in solder balls significantly depend on finite element mesh sizes, indicating a singularity exists. Negative values of the divergences of atomic fluxes due to electron current and thermal stresses are obtained under certain loading conditions. Submodeling presents accurate results if cut boundary is appropriately chosen.

The effect of atomic density gradient in electromigration

“…Thus, the prediction by the conventional AFD method is incorrect in the solder model. Dandu et al (2010) noticed this problem using traditional AFD method. However, with the consideration of the ADG, the AFDs in (a) and (c) cases are positive at the upper left edge of the solder ball.…”

Coupling model of electromigration and experimental verification – Part I: Effect of atomic concentration gradient

“…Although the industry succeeds in advancing the integrated circuit (IC) technology node every two years, EM solutions have been trial-error and empirical-based, mainly because of its complicated multi-scale and multi-physics nature (Zhang and Roosmalen, 2009;Zhang et al, 2006;Zhang and Roosmalen, 2010). While scaling alone can improve performance for each new silicon technology node, heterogeneous integration using a combination of 3D monolithic and 2.5D/3D advanced packaging technology can boost the system performance significantly with low costs (Dang;Lau, 2022) (RDL) and micro-bumps/pillars at the packaging level (Chen et al, 2012;Chen et al, 2010;Dandu and Fan, 2011;Dandu et al, 2010;Liang et al, 2020;. With the "hyper-scaling" of IC to sub-nanoscale and the emerging of quantum computing and photonics technologies, establishing the fundamental understanding of the underlying EM failure mechanisms becomes urgent and vital for the future of micro-/nano-electronics.…”

Effect of Thermomigration on Electromigration in SWEAT Structures

“…Electromigration (EM) in interconnects has become a major reliability issue in recent years because of the miniaturization trend to meet the demand of higher performance of microelectronic devices. EM essentially is an enhanced mass transport process driven by high current density [1][2][3][4][5][6][7][8]. The electron wind force, attributed to the momentum exchange between conducting electrons and metal atoms, pushes atoms diffusing from cathode to anode.…”