Creep behaviour of Sn–3.8Ag–0.7Cu under the effect of electromigration: Experiments and modelling Fei Su a,⇑ , Ronghai Mao b , Xiaoyan Wang a , Guangzhou Wang a , Haiyan Pan a a Institute of Solid Mechanics, Beijing University of Aeronautics and Astronautics, PR China b ALSTOM (Switzerland) Ltd. Building 239D, Zentralstrasse 40, 5242 Birr, Switzerland article info Article history: Received 3 April 2010 Received in revised form 21 December 2010 Accepted 21 January 2011 abstract In this paper, creep behaviour of Sn–3.8Ag–0.7Cu (SAC) lead-free solder under the collective effect of electromigration, stress and temperature was investigated. Firstly, the conventional creep test was improved so that high current density can be applied to the ribbon sample and serve as one of the exper- imental control variables. Experimental results indicate that creep rate of the SAC was greatly affected by electromigration (EM) and its linear dependence on current density and stress was revealed. Then a uni- fied phenomenological creep model with variables of stress, temperature and current density was set up based on the fact that both the mechanisms of conventional creep and electromigration are vacancy dif- fusion type. Coefficients in the unified creep model were determined from the experimental results by curve fitting, and numerical results of the unified creep model are found to fit the experimental results quite well. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Thermal fatigue of solder bump is one of the most important reli- ability issues of electronic packages, and a lot of empirical models for thermal fatigue life prediction have been built up [1]. In those energy-based models such as Darveaux’s model [2], energy density of inelastic strain within one thermal cycle at critical site of a solder was often used as control variable. Inelastic strain includes both plastic strain and creep strain for viscoplastic solder materials. Nevertheless, the creep strain dominates in low cycle fatigues, in which the period of thermal cycle is relatively longer than that of high cycle fatigues. As such, creep property of solder material turns out to be critical for its thermal fatigue life prediction. Convention- ally, temperature and stress are deemed to be the only two parame- ters that affect the steady creep rate of solder materials. However, with the state-of-the-art development of compact electronic pack- aging, the size of solder ball becomes smaller and smaller. Conse- quently the density of electric current increases rapidly. When it reaches 100 A/mm 2 , which is widely recognised as a threshold value, electromigration effect will be so significant that it will cause failure to solders. The electromigration effect, abbreviated as EM, is the dif- fusion effect of metal atom from cathode to anode due to the contin- uous collision of electron with enough kinetic energy, alternatively it can be treated as the diffusion effect of the vacancy in a reversed direction [3,4]. Complicated multi-physical coupling effects will usually be induced by EM. For example owing to Joule effect, the unevenly distributed temperature will lead to thermal diffusion and local stress fields. EM may cause back stress in confined metal line and contrariwise, EM will be retarded or terminated when back stress gradient is steep enough. But from the point view of micro- mechanism, both EM and high temperature creep of solder materials are controlled by vacancy diffusion. Fortunately it has been proven by experiments that the activation energies of vacancy diffusion in these two cases are exactly the same [4]. The only differences be- tween them are the driving force and diffusion path. In the case of EM, vacancy diffusion is driven by electron wind and grain boundary is the principal diffusion path, whereas in the case of conventional creep at high temperature and low stress, the driving force is vacancy concentration gradient and diffusion paths include boundary and interior of grain. Now it is reasonable to infer that EM may cause deformation to solders. As a matter of fact, EM induced inelastic deformation of solder has been observed by experiments [5,6] and a theoretical model has been set up to investigate the EM induced creep [7], in which creep rate was described as a linear function of current density. The objective of the present investigation is to study the creep behaviour of solder materials under the collective and coupled ef- fects of stress, temperature and EM. This problem is of practical sense for reliability evaluation of solder balls but not well studied. In this paper, experimental investigation was performed on SAC material, followed by a phenomenological creep model with vari- ables of stress, temperature and current density. The model was developed from the mechanisms of diffusion deformation, in 0026-2714/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.microrel.2011.01.010 ⇑ Corresponding author. E-mail address: Sufei@buaa.edu.cn (F. Su). Microelectronics Reliability 51 (2011) 1020–1024 Contents lists available at ScienceDirect Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel