Finite Element Modeling of Stress Evolution in Sn Films due to Growth of the Cu6Sn5 Intermetallic Compound

Abstract

We use finite element simulations to quantitatively evaluate different mechanisms for the generation of stress in Sn films due to growth of the Cu 6 Sn 5 intermetallic phase at the Cu-Sn interface. We find that elastic and plastic behavior alone are not sufficient to reproduce the experimentally measured stress evolution. However, when grain boundary diffusion is included, the model results agree well with experimental observations. Examination of conditions necessary to produce the observed stresses provides insight into potential strategies for minimizing stress generation and thus mitigating Sn whisker growth.

Evaluation of local strain evolution from metallic whisker formation

“…The strain detected during the period of observation falls into a range of ±0.6%, indicating that the Sn grains near the whisker growth locations yield plasticity. Such a result is consistent with reported stress measurements [5,12]. From Figure 1c, moderate compressive strain was usually detected a couple of grains apart from the growth location, which is denoted by the open black circle in Figure 1d.…”

“…grain boundary diffusion [12,19], grain boundary fluid theory [8] and interface fluid flow [20], each of which has been supported by experimental observations in different cases. The considerable compressive found strain here can be caused by shrinkage of the grains, indicating that grain-boundary-related activity is the main factor in the growth process.…”

“…X-ray diffraction (XRD) [10] and synchrotron measurement [4,11], as well as numerical method, i.e. the finite element method [12], have been applied for measuring residual strain in thin metallic films with whisker growth. However, each technique has its limitations, especially for the analytic methods.…”

Coupled diffusion-deformation multiphase field model for elastoplastic materials applied to the growth of Cu6Sn5

“…These IMC are of great importance due to their role in soldering of electronic components. The recent transition to lead-free solders, driven by environmental concerns and legislation, have further increased the interest for the Cu-Sn system, both from experimental [6][7][8][9][10][11][12][13] and modeling [14][15][16][17][18] perspectives.…”

“…None of these models, however, take the mechanical behavior of the material into account. In [18], the stress build-up caused by the growth of IMC is simulated using the finite element method. The model in [18] is uncoupled and only deformation is taken into account while the growth of IMC is added based on curve fitting of experimental data.…”