A Fully Planar Approach to Field-Coupled Nanocomputing: Scalable Placement and Routing Without Wire Crossings

Field-coupled Nanocomputing (FCN) is a class of promising post-CMOS technologies that transmit information through electric or magnetic fields instead of current flow. They utilize basic building blocks called cells, which can form gates that implement Boolean functions. However, the design constraints for FCN circuits differ significantly from those for CMOS. One major challenge is that wires in FCN have to be realized as gates, i. e., they are constructed from cells and incur the same costs as gates. Additionally, all FCN technologies are fabricated on a single layer, e.g., a silicon surface, requiring all elements-gates and wires-to be placed within that same layer. Consequently, FCN employs special gates, called wire crossings, to enable signals to cross. While existing wirecrossing implementations are complex and were previously considered costly, initial efforts have aimed at minimizing their use. However, recent physical simulations and experiments on a quantum annealing platform have shown that currently used wire crossings in FCN significantly compromise signal stability, to the extent that circuits cannot function reliably. This work addresses that issue by introducing the first placement and routing algorithm that produces fully planar FCN circuits, eliminating the need for all wire crossings. For a comparative evaluation, a state-of-the-art placement and routing algorithm was also modified to enforce planarity. However, our proposed algorithm is more scalable and can handle inputs with up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$149 k$</tex> gates, enabling it to process circuits that are <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$182 \times$</tex> more complex than those handled by the modified state-of-theart algorithm.