Several methods are presented for highly efficient calculation of substrate noise transport in integrated circuits. A three-dimensional Green's function-based boundary element method, accelerated through use of the fast Fourier transform, allows the computation of sensitivities with respect to all substrate parameters at a considerably higher speed than any methods reported in the literature. Substrate sensitivities are used in a number of physical optimization tools, such as placement and trend analysis. The aim is a fast and accurate estimation of the impact of technology migration and/or layout redesign on substrate noise and, ultimately, on the circuit's overall performance. The suitability of the approach is shown through industrial-strength mixed-mode integrated circuits fabricated on a standard CMOS process.

The Green function over a multilayer substrate is derived by solving Poisson's equation analytically in the coordinate and numerically in the z and y coordinates. The x and y functional dependence is transformed into a discrete cosine transform (DCT) representation for rapid evaluation. The Green function is further transformed into a numerically stable form appropriate for finite-precision machine evaluation. This Green function is used to solve for the impedance matrix for an arbitrary three-dimensional arrangement of conductors placed anywhere in the substrate. Using this technique, the substrate coupling and loss in IC circuits can be analyzed. A spiral inductor is presented as an example. Experimental measurement results verify the accuracy of the technique.

A number of methods are presented for highly efficient calculation of substrate current transport. A three-dimensional Green's Function based substrate representation, in combination with the use of the Fast Fourier Transform, significantly speeds up the computation of sensitivities with respect to all parameters associated with a given architecture. Substrate sensitivity analysis is used in a number of physical optimization tools, such as placement and trend analysis for the estimation of the impact of technology migration and/or layout re-design.