Delay-Constrained GNR Routing for Layer Minimization

It is known that graphene nanoribbon (GNR)-based devices and interconnects can be a better alternative in nano-scale designs. In this article, given a set of GNR nets with delay constraints in a GNR routing plane, a delay-constrained routing algorithm can be proposed to minimize the number of the used layers with satisfying the non-crossing constraints between the two GNR nets and the delay constraints on the given GNR nets in multiple-layer delay-constrained GNR routing. The routing process in our proposed algorithm can be divided into two sequential steps: initial assignment and iterative routing. In the initial assignment step, based on the source-to-target transformation of the multiple-pin nets and the definition of the delay-constrained routing patterns on the GNR nets with the tight delay constraints, a set of necessary delay-constrained routing patterns on the GNR nets can be first assigned onto a minimal set of used layers and the remaining GNR nets can be further assigned onto the available layers. In the iterative routing step, based on the assignment result of the GNR nets, the assigned GNR nets can be routed by using one routability-driven obstacle-aware routing process without considering the delay constraints and the delay-violated GNR nets can be rerouted by using one iterative delay-constrained rip-up-and-rerouting process with considering the delay constraints. Compared with the combination of the source-to-target transformation of the multiple-pin nets and one multiple-layer planar routing process using two single-layer GNR routing algorithms, the experimental results show that our proposed delay-constrained algorithm can use less CPU time and reasonable wirelengths to decrease 38.6%; and 35.0% of the number of used layers on the given GNR nets with two different sets of delay constraints for eight tested examples on the average, respectively.