Delay-Constrained GNR Routing With CNT-Via Insertion in Nano-Scale Designs

It is well known that graphene nanoribbon (GNR) can be used as interconnects in nano-scale designs. In this paper, given a set of delay-constrained GNR nets in a multiple-layer routing plane, based on the construction of a combined carbon nanotube (CNT)/graphene hetero-structure for CNT-vias between two adjacent layers, an efficient routing algorithm can be proposed to minimize the number of the used layers with satisfying the non-crossing constraints between two GNR nets and the delay constraints on the GNR nets in GNR routing with CNT-via insertion. In the initial assignment, based on the definition of the delay-constrained routing pattern on a GNR net with tight delay constraint and the delay-constrained via path on a GNR net, the delay-constrained routing patterns can be firstly assigned for layer minimization and the delay-driven minimum-length routing paths and the delay-constrained via paths can be further assigned onto the available layers. In the iterative routing, the unrouted GNR nets can be further routed on the available layers and some possible new layers by using one iterative maze-routing and rip-up-and-rerouting process. Compared with the published routing algorithms with no via insertion, the experimental results show that our proposed routing algorithm with CNT-via insertion can insert some CNT-vias and use shorter wirelength to decrease 53.8% and 24.9% of the number of the used layer under reasonable CPU time on the given GNR nets with two different sets of the delay constraints for 8 tested examples on the average, respectively.