Potential Distribution and Multi-Terminal DC Resistance Computations for LSI Technology

Computer time and storage requirements are the two main considerations in the design of a packaging analysis software tool for the problem of calculating the electric potential distribution in arbitrary geometrical shapes. The FEM (Finite Element Method) is the accepted approach for solving such problems. A new formulation for the linear triangular element is presented which is used to derive a very simple and computationally inexpensive linear rectangular element equation interrelating only the geometrical centers of the elements. The result is a much sparser assembly matrix with a maximum of five non-zero entries per equation compared with the usual nine of the FEM formulation. In addition, a method to obtain the minimum bandwidth of the matrix is given for the efficient and static use of external storage, permitting the solution of any size problem. The methods are applicable to multi-plane, multi-terminal configurations for the production of equivalent-resistance networks and for the calculation of the potential distribution throughout the configurations.