Nontree Routing for Reliability and Yield Improvement
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
We propose to introduce redundant interconnects for manufacturing yield and reliability improvement. By introducing redundant interconnects, the potential for open faults is reduced at the cost of increased potential for short faults; overall, manufacturing yield and fault tolerance can be improved. We focus on a post-processing, tree augmentation approach which can be easily integrated in current physical design flows. Our contributions are as follows: We formulate the problem as a variant of
... he classical 2-edge-connectivity augmentation problem in which we take into account such practical issues as wirelength increase budget, routing obstacles, and use of Steiner points. We show that an optimum solution can always be found on the Hanan grid defined by the terminals and the corners of the feasible routing region. We give a compact integer program formulation which is solved in practical runtime by the commercial optimization package CPLEX for nets with up to 100 terminals. We give a well-scaling greedy algorithm which has practical runtime up to 1,000 terminals, and comes on the average within 1-2% of the optimum computed by CPLEX. We give a comprehensive experimental study comparing the solution quality and runtime of our methods with the best methods reported in the literature for the related 2-edge-connectivity augmentation problem, including a sophisticated heuristic based on minimum-weight branchings  and a recent genetic algorithm  . Experiments on randomly generated and industry testcases show that our greedy augmentation method achieves significant increase in reliability (as measured by the percentage of biconnected tree edges) with very small increase in wirelength. For example, on 1,000 terminal nets the average percentage of biconnected tree edges is 34¡ 19% for a wirelength increase of only 1%, and 87¡ 73% for a wirelength increase of 20%. SPICE simulations on industry routed nets show that non-tree routing has the additional benefit of reducing maximum sink delay by an average of 28¡ 26% compared to Steiner routing, and by an average of 3¡ 72% compared to timing optimized routing. SPICE simulations further imply that non-tree routing has smaller delay variation due to process variability.