EPEEC: comprehensive SPICE-compatible reluctance extraction for high-speed interconnects above lossy multilayer substrates

With continuous advances in radio-frequency (RF) mixed-signal very large scale integration (VLSI) technology, the creation of eddy currents in lossy multilayer substrates has made the already complicated interconnect analysis and modeling issue more challenging. To account for substrate losses, traditional electromagnetic methods are often computationally prohibitive for today´s VLSI geometries. In this paper, an accurate and efficient interconnect modeling approach-the eddy-current-aware partial equivalent element circuit (EPEEC)-is proposed. Based on complex image theory, it extends the traditional partial equivalent element circuit (PEEC) model to simultaneously take multilayer substrate eddy-current losses and frequency-dependent effects into consideration. To accommodate even larger scale on-chip interconnect networks, EPEEC develops a new simulation program with integrated circuit emphasis (SPICE)-compatible reluctance extraction algorithm by applying sparsification in the inverse inductance domain with an extended window algorithm. Compared with several industry standard inductance and full-wave solvers, such as FastHenry and Sonnet, EPEEC demonstrates within 1.5% accuracy while providing over 100× speedup.