Transient thermal gradients across solder interconnections in electronic systems

A thermal analysis for a component mounted on a carrier via solder interconnections is provided, with emphasis on understanding how the thermal gradients across the solder interconnections develop during the power-on transient. A 1-D model is sought for its simplicity, while the important features of the problem are kept intact. Closed-form solutions are obtained when the thermal mass of the component is much less than the thermal mass of the carrier. The asymptotic solutions are compared with the numerical solutions of the same set of equations. Finite element solutions and experimental data are also obtained to assess the validity of the 1-D model as a predictor of the thermal gradients across the solder interconnections. Results of the analysis show that the thermal gradients across the solder interconnections reach a maximum at some early time before steady-state conditions are reached and that the thermally induced transient strains can be several times worse than the steady-state strains