The effect of atomic density gradient in electromigration

Abstract

This paper studies the electromigration (EM) failure of interconnect structure and solder joint in a wafer level chip scale package (WL-CSP) based on atomic flux divergence (AFD) method. The impact of atomic density gradient (ADG) on the divergence of the atomic fluxes is investigated. The simulation results show that the traditional AFD method, which neglects the effect of atomic density gradient, can result in significant errors in predicting solder joint failures in a WL-CSP; while the AFD method with the consideration of the atomic density gradient has shown more reasonable results. ME. He has co-authored over 150 papers in journals and conferences, two books, and has filed over 40 US patents in the area of analogue and power electronic packaging. His research interests are advanced IC packaging, modelling and simulation, reliability, and material characterisation.Lihua Liang received his BS and MS in Mechanical Engineering from Zhejiang University . He has published more than 100 scientific papers, two books and filed five US patents. His interests and expertise lie in the areas of reliability, material characterisation and thermal and mechanical modelling for microelectronic packaging.

Effect of Passivation and Mechanical Constraint on Electromigration in Interconnect

“…( 1)), in which θ is the total volumetric strain, and Ja is the total atomic flux, As the present study focuses on the impact of mechanical constraints on EM, thus the atomic flux driven by temperature gradient was neglected. The total atomic flux is given as follows, [26][27][28]…”

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

“…Different theories and models describing EM have evolved over the decades (Blech and Herring, 1976;Blech, 1976;Ceric et al, 2008;Clement and Thompson, 1995;Cui, 2021;Cui et al, 2019Cui et al, , 2020Kirchheim, 1992;Korhonen et al, 1993;Lin and Basaran, 2005;Pharr et al, 2011;Sarychev et al, 1999;Shatzkes and Lloyd, 1986;Sukharev et al, 2007;Zhang et al, 2012). Blech first presented a steady-state solution considering the counterbalance of atomic flux by a stress gradient against the electrical current (Blech and Herring, 1976;Blech, 1976).…”

“…Additionally, Sukharev et al (Sukharev et al, 2007) suggested a new equation for diffusion-induced strain and developed analytical solutions for vacancy concentration, atomic concentration, and hydrostatic stress at the steady-state. Ceric et al (Ceric et al, 2008) and Zhang et al (Zhang et al, 2012) used sequentially coupled finite element analysis, without considering the coupling of diffusion-induced strain, to investigate the time-to-failure owing to EM in chips and solder bumps, respectively. Pharr et al (Pharr et al, 2011) presented a theory that couples creep and EM to calculate the stress distribution in solder joint.…”

Implementation of Fully Coupled Electromigration Theory in COMSOL

“…Electromigration is an enhanced mass transport process in metal interconnects induced by high electrical current density, which, over time, causes void nucleation near the cathode side and hillock development near the anode side, resulting in opens and shorts in microelectronic devices [1][2][3][4][5]. The driving force of electromigration is attributed to the momentum transfer between conducting electrons and diffusion metal atoms, which is vividly called the electron wind force.…”