A COMBINED FINITE-DIFFERENCE AND ANALYTIC-EXPRESSION APPROACH TO CROSSOVER CAPACITANCE IN A MULTILAYER DIELECTRIC ENVIRONMENT

The capacitances in the crossover regions of orthogonal transmission l ines of finite thickness, fabricated on structures of the approximate dimensions of an integrated circuit, are evaluated in this paper by me ans of a combined finite difference and analytic expression method, Th e three-dimensional (3-D) finite difference method (FDM), using very f ine mesh grids, is applied to an artificially defined region only a fe w microns in thickness, where orthogonal transmission lines on differe nt metal layers of an integrated circuit cross one-another, In the 600 -mu m thick dielectric region above the ground plane on the lower surf ace of an integrated circuit, analytic expressions of the solution to the Laplace equation are formulated, An artificial boundary is assumed to separate the substrate of the 60-mu m thick integrated circuit fro m the thin active region oh its uppermost surface where the active cir cuits and interconnects are actually fabricated, creating two separate regions which are treated using different approaches, An iterative pr ocedure ,is employed to create a continuous interface between solution s across the boundary of the two regions generated by the two methods, The algorithm converges rapidly to very accurate solutions, The error s between this simulation method and laboratory measurements are withi n 8% for very small absolute values in the femtoFarad (fF) range, The field solutions are then converted into the equivalent circuit paramet ers, Finally, the waveshapes of propagating signal pulses are simulate d by a networking program in a general electromagnetic modeling tool s uite referred to as the Mayo Graphical Integrated Computer Aided Desig n Suite, or MagiCAD [1], in which the equivalent circuit model and cap acitance values of the crossover problem are integrated.