ANALYSIS OF TRANSIENT-BEHAVIOR OF VERTICAL INTERCONNECTS IN STACKED CIRCUIT-BOARD LAYERS USING QUASI-STATIC TECHNIQUES

Fuzz-buttons can interconnect up to fifty circuit board substrate laye rs in conjunction with metallic vias, As a result, the use of three-di mensional multichip modules (MCM's) with fuzz-buttons may be able to a chieve very high packaging densities, On the other hand, the vertical interconnects, surrounded by different dielectric materials and passin g through many ground mesh holes, are three-dimensional nonuniform tra nsmission lines. Therefore, the electromagnetic analysis of fuzz-butto n interconnects is not straightforward. In this paper, we propose a me thod to analyze fuzz-buttons under quasistatic assumptions. We apply t he electrostatic method to find the charge distribution and the distri buted capacitance of the fuzz-buttons, and a quasimagnetostatic approa ch to calculate the inductance, By using image theory, a free space Gr een's function is formulated, The effect of the via holes is taken int o account by utilizing the equivalence principle, A set of integral eq uations is established and solved by a combination of the point-matchi ng method and Galerkin's method, An iterative algorithm is imposed to solve the matrix equations, After the equivalent nonuniform transmissi on line model is established, we then apply the transmission (ABCD) ma trix method, allowing the propagation parameters to be obtained easily , Finally, we employ the fast fourier transform (FFT) to convert the f requency results into the time domain, Waveform distortion, time delay , and crosstalk values for a 60 ps risetime input signal are evaluated , The quasistatic approach is compared against the finite difference t ime domain (FDTD) algorithms and good agreement is observed.