The Wiedemann–Franz–Lorenz relation for lead-free solder and intermetallic materials

Abstract

Lead-free solders are replacing lead-rich solders in the electronics industry. 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 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, analysis of the experimental data shows that the WFL relation is obeyed in both solder alloy and IMC materials, especially matching 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, and vice versa. A coupled thermal–electrical three-dimensional finite element analysis is performed to study the behavior of lead-free solder/IMC interconnects. Solder and IMC material properties predicted using the WFL relation are adopted in the computational model. By applying the WFL relation, the number of experiments required to determine the material properties for different lead-free solder/IMC interconnects can be significantly reduced, which can lead to pronounced savings of time and cost.