Development of Specialized Basis Functions and Efficient Substrate Integration Techniques for Electromagnetic Analysis of Interconnect and RF Inductors

The performance of several mixed-signal and RF-analog platforms depends on substrate effects that need to be represented in the library model with critical field solver accuracy. For instance, substrate-induced currents in RF inductors can severely affect quality and hence RF filter selectivity. We have developed an efficient approach to full-wave impedance extraction that accounts for substrate effects through the use of two-layer media Green’s functions in a mixed-potential-integral-equation (MPIE) solver. In particular, we have developed accelerated techniques for both volume and surface integrations in the solver.

In this work, we have also introduced a technique for the numerical generation of basis functions that are capable of parameterizing the frequency-variant nature of cross-sectional conductor current distributions. Hence skin and proximity effects can be captured utilizing many fewer basis functions in comparison to the prevalently-used piecewise-constant basis functions. One important characteristic of these basis functions is that they only need to be pre-computed once for a frequency range of interest per unique conductor cross-sectional geometry, and they can be stored off-line with a minimal associated cost. In addition, the robustness of these frequency-independent basis functions is enforced using an optimization routine.

We have shown in that the cost of solving a complex interconnect system using the new basis functions can be reduced by a factor of 170 when compared to the use of piecewise-constant basis functions over a wide range of operating frequencies. Furthermore the volume and surface integration routines improve efficiency by an additional factor of 9.8. The solver accuracy is validated against measurements taken on fabricated devices.