Finite element transient thermal analysis of electronic boards and packages using moment-matching techniques

Development of highly integrated and denser semiconductor module configurations with greater power consumption rates make thermal design increasingly important. In this paper a new solution method for transient thermal analysis of electronic systems is described. The method is based on combining finite element technique and efficient moment-matching technique originally developed in the circuit simulation area for solving large set of linear differential equations. Finite element modeling in space/time domain of a complete electronic system usually results in a large set of ordinary differential equations which can be solved using various time stepping algorithms. However, efficiency of conventional algorithms is limited by their computational cost and stability criteria. In this paper, application of the moment-matching technique to solve thermal finite element equations is presented. Several examples are considered to illustrate the methodology. A good agreement between the results obtained using conventional iterative techniques and the proposed method has been found. In addition, applying moment-matching technique results in one to two orders of magnitude speed-up compared to conventional iterative techniques.