A Nonlinear Viscous Model for Sn-Whisker Growth
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WHISKER growth on beta-tin (b-Sn) is a phenomenon associated with stress relaxation. The growth of Sn-whiskers has been observed extensively in various environments, which appears to be a local response to external loading, including compressive stress,[1–13] electric field,[14] electric current,[14–16] resonance vibration,[17] temperature cycling,[18–20] and humidity.[21,22] The use of pure Sn and Sn-based Pb-free alloys in microelectronics devices and systems has raised the concern of reliability pertaining to the formation and growth of Sn-whiskers, particularly among high-reliability product communities such as the aerospace, biomedical, and military industries. In working toward mitigating the formation of Sn-whiskers, it is of importance to understand the mechanisms controlling the formation and growth of Sn-whiskers. Various models for the growth of Sn-whiskers have been proposed. Tu[23] proposed that the fracture of the surface oxide layer led to the relief of localized stresses and the formation and growth of whiskers was driven by a long-range stress gradient. Galyon and Palmer[24] considered the effect of microstructure and internal stresses, and proposed that the mass transport through the grain boundary network controls the growth of whiskers. Boettinger et al.[25] proposed a growth model based on the localized creep of columnar grain structures to relieve the compressive stress in thin films. Tu and Li[7] used the concept of the grain boundary fluid flow[26,27] to analyze the growth behavior of whiskers. Yang[28] analyzed the growth of whiskers controlled by lattice diffusion. Based on Tu’s work,[23] Buchovecky et al.[29] proposed the concept of soft Sn-grains in a Sn-surface coating, and incorporated time-independent plastic deformation with grain boundary diffusion in simulating the growth of Sn-whiskers. Considering the role of intermetallic growth, stress evolution, and plastic FUQIAN YANG, Professor, is with the Materials Program, Department of Chemical and Materials Engineering, University of Kentucky, Lexington, KY 40506. Contact E-mail: [email protected] Manuscript submitted October 26, 2015. METALLURGICAL AND MATERIALS TRANSACTIONS A
deformation in the whisker formation, Chason et al.[30] suggested that the nucleation of whiskers begins after stress saturates. Osenbach[31] proposed that the whisker growth is controlled by the ratio of the long-range grain boundary diffusion creep relaxation rate to the short range creep relaxation rate. Li and co-workers[32–34] proposed an interfacial flow mechanism for the whisker and hillock growth. Recently, Sarobol et al.[35] considered the effects of grain geometry and size and grain boundary properties in analyzing the growth of whiskers and hillocks. The linear flow relationship used by Tu and Li[7] and the power–law relationship used by Cheng et al.[34] in analyzing the whisker growth are the two limiting cases of the Eyring flow relationship for the flow of the grain boundary fluid.[26,36,37] Each relationship is likely adequate for describing the growth beh
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