"beta-Sn (Sn) whiskers growing from tin coatings in electronic devices have been a serious concern to its reliability as they nucleate in unpredictable locations, can grow to a length of several millimeters, and hence, are able to short-circuit different parts of an electronic assembly. It was found that alloying Sn with lead (Pb) mitigated whisker formation. However, with the drive to- wards lead-free electronics from early 2000, due to the hazardous nature of Pb, reliability problems due to tin whiskers resurfaced, thereby, rekindling an interest to understand their governing mechanisms in order to propose efficient mitigation strategies. With such a drive, significant research has been published highlighting different whisker characteristics (morphology, propensity, and kinetics). However, till date, there lacks a unified theory that could explain the formation of these filamentous structures, with sometimes even contradicting observations between different research groups. Despite some contradictions, it is widely accepted that tin whiskers are a result of stress-driven diffusion in the film, with diffusion occurring primarily through the grain boundary network. Stresses in these films can originate from various sources, such as, upon deposition, indentation, thermal expansion mismatch, and by formation of voluminous Cu6Sn5 intermetallic compounds at the interface between a copper substrate and the film. Among these sources, thermal straining has been used to deliberately control the stresses in films deposited on a Silicon (Si) substrate (having a lower thermal expansion coefficient thanbeta-Sn) to analyze the effect of applied stress on whisker propensity. In the present work such experimental conditions of thermally straining beta-Sn films is mimicked, and the resulting mechanics and kinetics are investigated using fully coupled chemo- thermo-mechanical simulations in a crystal plasticity continuum mechanical framework. The goal of the is to identify crystallographic and geometric factors that modulate the stress-driven transport of atoms along the grain boundary network. In that regard, first a thermo-mechanical study is done that highlights the dominating influence of global film-texture compared to grain geometry and grain-size distribution. It is also established that whisker nucleation is indeed a local phenomenon as no long-range stress gradients are found. Following, more involved chemo-thermo-mechanical simulations are performed to understand the kinematics and kinetics of atom redistribution in these thermally strained films for two loading conditions. Based on these simulations it is inferred that plastic relaxation plays a dominant role in stress evolution compared to diffusion kinetics. The dominant role of film-texture on determining whisker nucleation sites (low compressive locations in the biaxially strained film) can be attributed to the high anisotropy of the body-centered tetragonal beta-Sn crystal structure that involves an elastic anisotropy, a thermal anisotropy, and a very complex plastic anisotropy. The complex plastic anisotropy arises due to the availability of multiple slip families with a small number of slip systems per family. Plasticity readily happens in Sn even at room temperature, which corresponds to about 0.6 T m, and, therefore, requires the establishment of an accurate constitutive description. In that regard, the second half of this work focuses on establishing the reliability of Inverse Indentation Analysis (IIA) as a means to identify such constitutive plastic parameters for different crystal structures. In this method, the error in experimental and simulated indentation response (both in load--displacement and surface topography) is minimized to obtain the constitutive material parameters. The reliability of this IIA method is first established for face-centered cubic (fcc) materials, where it is found that any crystal orientation is adequately sensitive for the optimization to identify the parameters. Such is not the case for less symmetric hexagonal materials, where the efficacy of the IIA method relies heavily on the selected crystal orientation, and it is proposed to select crystal orientations that are sensitive to all slip families considered in the constitutive description. The next step will be to apply the IIA method to beta-Sn."--Pages ii-iii.
Read
