Theoretical and experimental determination of Cu diffusivity in eutectic Sn–Ag system at 235–280 °C

Abstract

This study evaluated the Cu diffusion and dissolution behaviors in eutectic Sn–Ag alloy with a mathematical model in combination with experimental data. The diffusion was performed at temperatures ranging from 235°C to 280°C with a Cu/Sn–3.5Ag solder bump joint, where the Cu substrate was a solid but the Sn–3.5Ag solder bump was a liquid at all of the temperatures examined. The Cu diffusion coefficient (DCu) with respect to temperature, the activation energy of the Cu diffusion (Q), and the average Cu concentration (Cavg) as a function of diffusion time (t) were investigated via this metallurgical system. The coefficients DCu were 1.2(±0.4)×10−9m2/s (235°C), 2.4(±0.6)×10−9m2/s (250°C), 2.6(±0.7)×10−9m2/s (265°C), and 3.9(±1.6)×10−9m2/s (280°C), which are of the same order as those acquired from the capillary-reservoir technique for the bulk Cu/Sn system by Ma and Swalin in 1969. The activation energy Q was estimated based on the Arrhenius relation and was approximately 13.3kJ/mol at 235–280°C, reflecting the insensitivity of DCu to temperature. A calculated Cavg–t profile predicted that Cavg approaches saturation after 70s (235°C), which agrees well with experiments. The modeling results were consistent with the experimental and literature data, indicating that the proposed mathematical model is an effective method to represent the Cu diffusion/dissolution behavior in a confined solder alloy.