Electromigration damage mechanics of lead-free solder joints under pulsed DC: A computational model

Abstract A numerical method for studying migration of voids driven by pulse electric current and thermal gradient in 95.5Sn–4Ag–0.5Cu (SAC405) solder joints is developed. The theoretical model involves coupling electron wind force, chemical potential, joule heating and stress gradient driving mass diffusion processes. Entropy based damage criteria is adopted to characterize the mass transportation mechanism, which utilize irreversible entropy production rate as a measure of material degradation. The pulse current induced EM damage results were compared with DC EM response under otherwise the same conditions. It is observed that increasing duty factor, current density and frequency leads to a faster damage accumulation. A mean time to failure (MTF) equation for solder joints under pulse current loadings is proposed which incorporates both thermomigration (TM) and EM damage. The failure mechanism is verified by our experimental results. It is observed that MTF is inversely proportional to r m , f p , and j n , where duty factor exponent m equals to 1.1, frequency exponent p equals to 1.43 and current density exponent is 1.96. This equation is effective only when pulse period is below thermal relaxation time, commonly in μ s range.

[1]  Minghui Lin,et al.  Damage Mechanics Modeling of Concurrent Thermal and Vibration Loading on Electronics Packaging , 2006 .

[2]  Yangyuan Wang,et al.  Numerical calculation of electromigration under pulse current with Joule heating , 1999 .

[3]  Hua Ye,et al.  Failure Modes of Flip Chip Solder Joints Under High Electric Current Density , 2005 .

[4]  T. M. Makhviladze,et al.  General model for mechanical stress evolution during electromigration , 1999 .

[5]  S. Timoshenko,et al.  Mechanics of Materials, 3rd Ed. , 1991 .

[6]  N. Wu,et al.  Direct resistance profile for an electrical pulse induced resistance change device , 2005 .

[7]  Cemal Basaran,et al.  Electromigration analysis of solder joints under ac load: A mean time to failure model , 2012 .

[8]  J. M. Schoen.  A model of electromigration failure under pulsed condition , 1980 .

[9]  K. Tu,et al.  Effect of electromigration on mechanical behavior of solder joints , 2005, Proceedings. International Symposium on Advanced Packaging Materials: Processes, Properties and Interfaces, 2005..

[10]  Cora Salm,et al.  Effect of current crowding on electromigration lifetime investigated by simulation and experiment , 2010 .

[11]  Minghui Lin,et al.  Computational simulation of electromigration induced damage in copper interconnects , 2007, SCSC.

[12]  Reduced impedance and superconductivity of SnAgCu solder alloy at high frequency , 2012, Electronic Materials Letters.

[13]  C. Basaran,et al.  A Viscoplasticity Model for Solder Alloys , 2010 .

[14]  Amir Averbuch,et al.  Computation for electromigration in interconnects of microelectronic devices , 2001 .

[15]  C. Hu,et al.  An electromigration failure model for interconnects under pulsed and bidirectional current stressing , 1994 .

[16]  C. Basaran,et al.  Damage Mechanics of Low Temperature Electromigration and Thermomigration , 2009, IEEE Transactions on Advanced Packaging.

[17]  Chenming Hu,et al.  Electromigration interconnect lifetime under AC and pulse DC stress , 1989 .

[18]  Ying Zhao,et al.  Thermomechanical behavior of micron scale solder joints under dynamic loads , 2000 .

[19]  Cemal Basaran,et al.  A Thermodynamic Framework for Damage Mechanics of Solder Joints , 1998 .

[20]  Amir Averbuch,et al.  Electromigration of intergranular voids in metal films for microelectronic interconnects , 2003 .

[21]  C. Basaran,et al.  An Irreversible Thermodynamics Theory for Damage Mechanics of Solids , 2004 .

[22]  Minghui Lin,et al.  Electromigration induced stress analysis using fully coupled mechanical-diffusion equations with nonlinear material properties , 2005 .

[23]  C. Basaran,et al.  Damage mechanics of electromigration induced failure , 2008 .

[24]  Cemal Basaran,et al.  Thermomigration induced degradation in solder alloys , 2008 .

[25]  C. Basaran,et al.  Damage mechanics of microelectronics solder joints under high current densities , 2003 .

[26]  G.H. Bernstein,et al.  Pulsed-current duty cycle dependence of electromigration-induced stress generation in aluminum conductors , 1996, IEEE Electron Device Letters.

[27]  Hua Ye,et al.  Thermomigration in Pb–Sn solder joints under joule heating during electric current stressing , 2003 .

[28]  Laura Brooke.  Pulsed Current Electromigration Failure Model , 1987, 25th International Reliability Physics Symposium.

[29]  Fausto Fantini,et al.  A percolative approach to electromigration in metallic lines , 2001 .

[30]  King-Ning Tu,et al.  Effect of current crowding on vacancy diffusion and void formation in electromigration , 2000 .

[31]  Y. Wei,et al.  Skin effect and material degradation of lead-free solder joint under AC , 2012, 13th InterSociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems.

[32]  Hua Ye,et al.  A thermodynamic model for electrical current induced damage , 2003, 2004 Proceedings. 54th Electronic Components and Technology Conference (IEEE Cat. No.04CH37546).

[33]  Cemal Basaran,et al.  A thermodynamics based damage mechanics constitutive model for low cycle fatigue analysis of microelectronics solder joints incorporating size effects , 2005 .

[34]  Cemal Basaran,et al.  A computational damage mechanics model for thermomigration , 2009 .

[35]  R. Balzer,et al.  Equilibrium vacancy concentration measurements on tin single crystals , 1979 .

[36]  C. Basaran,et al.  Mean time to failure of SnAgCuNi solder joints under DC , 2012, 13th InterSociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems.

[37]  C. Basaran,et al.  Damage of SAC405 solder joint under PDC , 2012, 13th InterSociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems.

[38]  Minghui Lin,et al.  Damage mechanics of electromigration in microelectronics copper interconnects , 2007 .

[39]  Cemal Basaran,et al.  Simulating Damage Mechanics of Electromigration and Thermomigration , 2008, Simul..

[40]  L. Niu,et al.  A 2-D mesoscopic model coupling mechanical and diffusion for electromigration in thin films , 2009 .

[41]  Yi-Shao Lai,et al.  Thermomigration Versus Electromigration in Microelectronics Solder Joints , 2009, IEEE Transactions on Advanced Packaging.

[42]  Hua Ye,et al.  Numerical simulation of stress evolution during electromigration in IC interconnect lines , 2003 .

[43]  Cemal Basaran,et al.  A thermodynamics based damage mechanics model for particulate composites , 2007 .

[44]  Cemal Basaran,et al.  Electromigration time to failure of SnAgCuNi solder joints , 2009 .