edfas.org 29 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 26 NO. 2 Figure 4 shows the shape of the evolution of the temperature. It is clear that with each cycle the temperature increases and accumulates until it reaches a maximum value of 138°C. This is due to the thermal inertia on the one hand and to the effusivity of each layer and the diffusivity within these layers on the other hand. Thermal inertia is the ability of a material to retain its temperature. This technique consists in accumulating the heat induced by the silicon chip, which is considered as an internal heat source that produces the joules effect in the copper layers and then solder joints to end up to the FR4 layer. This thermal wave is the heat flow depicted in the curve (Fig. 5). The temperature effect is more than just material deterioration and it affects the performance of the electronic package in terms of reliability as well. The elevation of total temperature (Fig. 4) induces thermal stresses in the package made up of different materials with different thermal expansion coefficients (Figs. 6 and 7). Thermal conductivity of materials has crucial impacts on the thermal transfer rate. Thermal expansion is quantified using the formula below: ΔL=L - L0 = αLΔT (Eq 19) εth = ΔL/L0 = αΔT (Eq 20) Tin has the highest stiffness in the direction of greatest thermal expansion. This can generate internal stresses in the tin crystals that can cause heterogeneous deformations at the grain boundaries during thermal cycling. These thermal stresses induced by the difference in thermal Fig. 6 Thermal strain curve. Fig. 7 Strain energy curve.
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