Numerical analysis to lead free solder/intermetallic interconnect with application of wiedemann-franz-lorenz relation

Due to the limitation of available experimental data for thermal conductivity of lead free solder and Intermetallic Compound (IMC) materials, the Wiedemann-Franz-Lorenz (WFL) relation is presented in this paper as a possible solution to predict thermal conductivity with known electrical conductivity. The method is based upon the fact that heat and electrical transport both involve the free electrons. The thermal and electrical conductivities of Cu, Ni, Sn, and different Sn rich lead free solder and IMC materials are studied by employing the WFL relation. Generally, the analysis to the experimental data shows that the WFL relation is obeyed in both solder alloy and IMC materials especially matches close to the relation for Sn, with a positive deviation from the theoretical Lorenz number. Thus, with the available electrical conductivity data, the thermal conductivity of solder and IMC materials can be obtained based on the proper WFL relation, vice versa. With the reduction of size of electronic devices and solder interconnects, it has been observed experimentally that solders fail by crack nucleation and propagation near the interface of IMC and bulk solder. A coupled thermal-electrical finite element analysis is performed to study the behavior of lead free solder/IMC interconnects under different electrical current densities. The joule heating, temperature concentration and electrical current concentration effects with a crack propagating near the interface of solder and IMC are investigated numerically. Solder and IMC material properties predicted using the WFL relation are adopted in the computational model. The effects of different thermal and electrical conductivities of solder and IMC materials on interfacial crack tip temperature are analyzed in the present study. By applying the WFL relation, the amount of experiments required to determine the material properties for different lead free solder/IMC interconnects can be significantly reduced, which can lead to pronounced saving of time and cost.