To handle modern routing with nanometer effects, we need to consider designs of variable wire widths and spacings, for which gridless routers are desirable due to their great flexibility. The gridless routing is much more difficult than the grid-based one because the solution space of gridless routing is significantly larger than that of grid-based one. In this paper, we present the first multilevel, full-chip gridless detailed router. The router integrates global routing, detailed routing, and congestion estimation together at each level of the multilevel routing. It can handle non-uniform wire widths and consider routability and optical proximity correction (OPC). Experimental results show that our approach obtains significantly better routing solutions than previous works. For example, for a set of 11 commonly used benchmark circuits, our approach achieves 100% routing completion for all circuits while the famous state-of-the-art three-level routing and multilevel routing (multilevel global routing + flat detailed routing) cannot complete routing for any of the circuits. Besides, experimental results show that our multilevel gridless router can handle non-uniform wire widths efficiently and effectively (still maintain 100% routing completion for all circuits). In particular, our OPC-aware multilevel gridless router archives an average reduction of 11.3% pattern features and still maintains 100% routability for the 11 benchmark circuits.

Due to the sub-wavelength lithography, manufacturing sub-90 nm feature sizes require intensive use of resolution-enhancement techniques, among which optical proximity correction (OPC) is the most popular technique in industry. Considering the OPC effects during routing can significantly alleviate the cost of post-layout OPC operations. In this paper, we present an efficient, accurate, and economical analytical formula for intensity computation and develop the first modeling of post-layout OPC based on a quasiinverse lithography technique. Extensive simulations with SPLAT, the golden lithography simulator in academia and industry, show that our intensity formula has high fidelity. Incorporating the OPC costs computed by the quasi-inverse lithography technique for our post-layout OPC modeling into a router, the router can be guided to maximize the effects of the correction. Compared with a rulebased OPC method, the experimental results show that our approach can achieve 14% and 16% reductions in the maximum and average layout distortions, respectively.

Abstract-Due to its great flexibility, gridless routing is desirable for nanometer circuit designs that use variable wire widths and spacings. Nevertheless, it is much more difficult than grid-based routing because of its larger solution space. In this paper, we present a novel "V-shaped" multilevel framework (called VMF) for full-chip gridless routing. Unlike the traditional "Λ-shaped" multilevel framework (inaccurately called the "Vcycle" framework in the literature), our VMF works in the V-shaped manner: top-down uncoarsening followed by bottom-up coarsening. Based on the novel framework, we develop a multilevel full-chip gridless router (called VMGR) for large-scale circuit designs. The top-down uncoarsening stage of VMGR starts from the coarsest regions and then processes down to finest ones level by level; at each level, it performs global pattern routing and detailed routing for local nets and then estimate the routing resource for the next level. Then, the bottom-up coarsening stage performs global maze routing and detailed routing to reroute failed connections and refine the solution level by level from the finest level to the coarsest one. We employ a dynamic congestion map to guide the global routing at all stages and propose a new cost function for congestion control. Experimental results show that VMGR achieves the best routability among all published gridless routers based on a set of commonly used MCNC benchmarks. Besides, VMGR can obtain significantly less wirelength, smaller critical path delay, and smaller average net delay than the previous works. In particular, VMF is general and thus can readily apply to other problems.

In modern technology, layout effects have more and more impacts on circuit performance. However, most of the existing analog automation tools consider the circuit sizing and layout generation in two separate steps, which often result in time-consuming sizinglayout iterations. In this paper, a layout-aware analog synthesis tool is presented to generate the required designs from specifications to layout through a user-friendly GUI. In order to provide a strong link between sizing and layout steps, a parasitic-aware circuit sizing flow is proposed based on a flexible layout template to prevent the performance from failing to meet the specifications after layout. Routability-aware analog placement is then performed with a simple routing algorithm to generate the corresponding layout with minimized cost. As demonstrated in the experimental results, this analog synthesis tool is able to generate the required circuits in seconds with high quality layouts and effectively guarantees the post-layout performance with less over-design.