Single-Layer Delay-Driven GNR Nontree Routing Under Resource Constraint for Yield Improvement

It is known that graphene nanoribbon (GNR)-based devices and interconnects can be treated to be a better alternative in nanoscale designs. In this article, given a source pin and a set of target pins inside a GNR grid-based routing plane, based on the consideration of the bending delay on one routing path, an integer linear programming (ILP)-based algorithm can be first proposed to minimize the total wirelength of a single-layer delay-driven GNR routing tree (DGNRRT). Furthermore, given a resource constraint in a single-layer DGNRRT and the connection defective rate on one routing segment, the other ILP-based algorithm can be proposed to insert a feasible set of yield-driven redundant paths to maximize the total yield gain of the inserted redundant paths under resource constraint. Finally, a feasible set of obstacle-aware redundant paths may be sequentially inserted to improve the connecting yield of a delay-driven GNR nontree routing (DGNRNTR) result under resource constraint. Compared with Das's algorithm in the construction of a GNR routing tree, the experimental results show that our proposed ILP-based algorithm uses reasonable CPU time to increase 2.50% of the wirelength and reduce 22.85% of the maximum delay for eight tested examples on the average. Compared with Yan's algorithm in the construction of a DGNRRT, the experimental results show that our proposed ILP-based algorithm uses reasonable CPU time to reduce 5.17% of the wirelength under the same maximum delay for eight tested examples on the average. Under two resource constraints as 50% and 65% in a DGNRNTR result, the experimental results show that the connecting yields of the eight tested DGNRRTs can be improved as 0.3939 and 0.5296 on the average by using our proposed ILP-based algorithm, respectively. Compared with the combination of the algorithm, PathInsertion, and our proposed algorithm, obstacle-aware path insertion (OAPI), the experimental results show that our proposed ILP-based algorithm can improve the connecting yields of the eight tested DGNRRTs as 0.067 and 0.0507 on the average under two resource constraints as 50% and 65%, respectively.