Floating Random Walk-Based Capacitance Extraction for General Non-Manhattan Conductor Structures

Abstract

The non-Manhattan conductor geometry existing in some capacitance extraction problems brings difficulty to the floating random walk (FRW) method using cubic transition domains. In this paper, techniques are proposed to enhance the FRW method for handling the structures with non-Manhattan conductors. Based on the aligned-box distances and corresponding calculating approaches, the techniques for generating the Gaussian surface and constructing axis-aligned transition cubes are proposed. A practical strategy is then proposed to judge the domination relationship of non-Manhattan conductor blocks for building the space management structure with candidate list. Finally, the strategy using rotated transition cube and related space management technique are proposed to make further acceleration. Experiments on 3-D interconnect structures including from 8 to 1000 non-Manhattan blocks show that the proposed method is from $2.9 {\times }$ to $96 {\times }$ faster than a simple extension of the original FRW method. The proposed method is also up to $39 {\times }$ faster than a boundary element method-based solver. Additional experiments are carried out to further validate the accuracy and efficiency of the proposed techniques, and to demonstrate their suitability for large and multi-dielectric structures.