Layer-Constrained GNR Area Routing with CNT-Via Insertion for Via Minimization

It is known that graphene nanoribbon (GNR) can be used as interconnects in nano-scale designs. To reduce the manufacturing cost in GNR routing, the constraint on the number of the used layers becomes more important. In this paper, given a set of GNR nets on a constrained set of routing layers inside a limited area, based on the concept of using GNR wires with CNT-via insertion in GNR routing, an efficient routing algorithm can be proposed to maximize the routability of the GNR nets and minimizing the total wirelength in assignment of the feasible routed paths with satisfying the non-crossing constraint on the GNR nets. Firstly, based on the construction of a crossing graph on the length-oriented consideration of the multiple-pin nets, all the intervals representing the GNR nets with covering compatibility can be assigned onto the minimized tracks and the represented intervals on the extra tracks can be reassigned onto the constrained tracks by using two separation-and-reassignment operations. Furthermore, based on the assignment result of the represented intervals on the constrained tracks and the hierarchical covering tree of the independent nets and the separated sub-nets on the constrained layers, the full and partial boundary-oriented paths of the GNR nets can be assigned on the constrained layers for routability and the assigned paths of the GNR nets can be modified to reduce the number of the used bends and the total wirelength of the GNR nets. Compared with the combination of Yen’s routing algorithm and the rip-up and reroute (RAR) process in layer-constrained GNR area routing with CNT-via insertion, the proposed algorithm can increase 2.1% of routability for 12 tested examples under 24 different constraints on the average. In addition, the proposed algorithm can reduce 31.6% of the number of the inserted CNT-vias, 5.5% of the number of the used bends and 2.3% of the total wirelength for 12 tested examples under 13 different constraints with 100% routability on the average.