Efficient inductance calculation in interconnect structures by applying the Monte Carlo method

We present an advanced algorithm for an extraction tool to compute inductances of interconnect structures. As already pointed out [Proc. Third Int. Conf. Modeling Simul. Microsyst. (2000) 416] the pursued energy concept leads to a 6-fold integral which can also be evaluated by use of the Monte Carlo method. A classical implementation of the Monte Carlo method, where the whole geometry has to be hunted for an associated element loses efficiency. Our approach is applied without time consuming element location for the random point coordinates to compute this integral. The precalculated current density distribution is computed with the finite element method. Geometrical modeling is done with an unstructured tetrahedral mesh to gain high flexibility and to ensure a latter integration of the process flow. Hence, some simplifications compared to the real geometry, as other published approaches usually do implicitly, are not required. q 2003 Elsevier Science Ltd. All rights reserved.