Kai-Yuan Chao

Coupling-aware Dummy Metal Insertion for Lithography

As integrated circuits manufacturing technology is advancing into 65nm and 45nm nodes, extensive resolution enhancement techniques (RETs) are needed to correctly manufacture a chip design. The widely used RET called off-axis illumination (OAI) introduces forbidden pitches which lead to very complex design rules. It has been observed that imposing uniformity on layout designs can substantially improve printability under OAI. For metal layers, uniformity can be achieved simply by inserting dummy metal wire segments at all free spaces. Simulation results indeed show significant improvement in printability with such a dummy metal insertion approach. To minimize mask cost, it is advantageous to use dummy metal segments that are of the same size as regular metal wires due to their simple geometry. But these dummy wires are printable and hence increase coupling capacitances and potentially affect yield. The alternative is to use a set of parallel sub-resolution thin wires (which is not printed) to replace a printable dummy wire segment. These invisible dummy metal segments do not increase coupling capacitances but bring a higher lithography cost, which includes mask cost and RET/process expense. This paper presents a strategy for dummy metal insertion that can optimally trade off lithography cost and coupling capacitance. In particular, we present an optimal algorithm that can minimize lithography cost subject to any given coupling capacitance bound. Moreover, this dummy metal insertion achieves a highly uniform density because of the locality of coupling capacitance, which automatically ameliorates chemical mechanical polish (CMP) problem.

Multi-threaded collision-aware global routing with bounded-length maze routing

Modern global routers use various routing methods to improve routing speed and the quality. Maze routing is the most time-consuming process for existing global routing algorithms. This paper presents two bounded-length maze routing (BLMR) algorithms (optimal-BLMR and heuristic-BLMR) to perform much faster routing than traditional maze routing algorithms. The proposed sequential global router, which adopts a heuristic-BLMR, identifies less-wirelength routing results with less runtime than state-of-the-art global routers. This study also proposes a parallel multi-threaded collision-aware global router based on a previous sequential global router. Unlike the conventional partition-based concurrency strategy, the proposed algorithm uses a task-based concurrency strategy. Experimental results reveal that the proposed sequential global router uses less wirelength and runs about 1.9X to 18.67X faster than other state-of-the-art global routers. Compared to the proposed sequential global router, the proposed parallel global router yields almost the same routing quality with average 2.71 and 3.12-fold speedup on overflow-free and hard-to-route benchmarks, respectively, when running on an Intel quad-core system.

Flip-Flop and Repeater Insertion for Early Interconnect Planning

We present a unified framework that considers flipflop and repeater insertion and the placement of flip-flop/repeater blocks during RT or higher level design. We introduce the concept of independent feasible regions in which flip-flops and repeaters can be inserted in an interconnect to satisfy both delay and cycle time constraints. Experimental results show that, with flip-flop insertion, we greatly increase the ability of interconnects to meet timing constraints. Our results also show that it is necessary to perform interconnect optimization at early design steps as the optimization will have even greater impact on the chip layout as feature size continually scales down.

NCTU-GR 2.0: Multithreaded Collision-Aware Global Routing With Bounded-Length Maze Routing

Modern global routers employ various routing methods to improve routing speed and quality. Maze routing is the most time-consuming process for existing global routing algorithms. This paper presents two bounded-length maze routing (BLMR) algorithms (optimal-BLMR and heuristic-BLMR) that perform much faster routing than traditional maze routing algorithms. In addition, a rectilinear Steiner minimum tree aware routing scheme is proposed to guide heuristic-BLMR and monotonic routing to build a routing tree with shorter wirelength. This paper also proposes a parallel multithreaded collision-aware global router based on a previous sequential global router (SGR). Unlike the partitioning-based strategy, the proposed parallel router uses a task-based concurrency strategy. Finally, a 3-D wirelength optimization technique is proposed to further refine the 3-D routing results. Experimental results reveal that the proposed SGR uses less wirelength and runs faster than most of other state-of-the-art global routers with a different set of parameters , , , . Compared to the proposed SGR, the proposed parallel router yields almost the same routing quality with average 2.71 and 3.12-fold speedup on overflow-free and hard-to-route cases, respectively, when running on a 4-core system.

Fast and Optimal Redundant Via Insertion

Redundant via insertion is highly effective in improving chip yield and reliability. In this paper, we study the problem of double-cut via insertion (DVI) in a post-routing stage, where a single via can have, at most, one redundant via inserted next to it and the goal is to insert as many redundant vias as possible. The DVI problem can be naturally formulated as a zero-one integer linear program (0-1 ILP). Our main contributions are acceleration methods for reducing the problem size and the number of constraints. Moreover, we extend the 0-1 ILP formulation to handle via density constraints. Experimental results show that our 0-1 ILP is very efficient in computing an optimal DVI solution, with up to 73.98 times speedup over existing heuristic algorithms.

Post-routing redundant via insertion and line end extension with via density consideration

Redundant via insertion and line end extension employed in the post-routing stage are two well known and highly recommended techniques to reduce yield loss due to via failure. However, if the amount of inserted redundant vias is not well controlled, it could violate via density rules and adversely worsen the yield and reliability of the design. In this paper, we first study the problem of redundant via insertion, and present two methods to accelerate a state-of-the-art approach (which is based on a maximum independent set (MIS) formulation) to solve it. We then consider the problem of simultaneous redundant via insertion and line end extension. We formulate the problem as a maximum weighted independent set (MWIS) problem and modify the accelerated MIS-based approach to solve it. Lastly, we investigate the problem of simultaneous redundant via insertion and line end extension subject to the maximum via density rule, and present a two-stage approach for it. In the first stage, we ignore the maximum via density rule, and enhance the MWIS-based approach to find the set of regions which violate the maximum via density rule after performing simultaneous redundant via insertion and line end extension. In the second stage, excess redundant vias are removed from those violating regions such that after the removal, the maximum via density rule is met while the total amount of redundant vias removed is minimized. This density-aware redundant via removal problem is formulated as a set of zero-one integer linear programming (0-1 ILP) problems each of which can be solved independently without sacrificing the optimality. The superiorities of our approaches are all demonstrated through promising experimental results

Optimal post-routing redundant via insertion

Redundant via insertion is highly recommended for improving chip yield and reliability. In this paper, we study the problem of double-cut via insertion (DVI) in a post-routing stage, where a single via can have at most one redundant via inserted next to it and the goal is to insert as many redundant vias as possible. The DVI problem can be naturally formulated as a zero-one integer linear program (0-1 ILP). Our main contributions are acceleration methods for reducing the problem size and the number of constraints. Moreover, we extend the 0-1 ILP formulation to handle via density constraints. Experimental results show that our 0-1 ILP is very efficient in computing optimal DVI solution, with up to 35.3 times speedup over existing heuristic algorithms

On process-aware 1-D standard cell design

When VLSI technology scales down to sub-40nm process node, systematic variation introduced by the lithography is a persistent challenge to the manufacturability. The limitation of the resolution enhancement technologies (RETs) forces people to adopt a regular cell design methodology. In this paper, targeted on 1-D cell design, we use simulation data to analyze the relationship between the line-end gap distribution and printability. Based on the gap distribution preferences, an optimal algorithm is provided to efficiently extend the line ends and insert dummies, which will significantly improve the gap distribution and help printability. Experimental results on 45nm and 32nm processes show that significant improvement can be obtained on edge placement error (EPE).

Mask cost reduction with circuit performance consideration for self-aligned double patterning

Double patterning lithography (DPL) is the enabling technology for printing in sub-32nm nodes. In the EDA literature, researchers have been focusing on double-exposure double-patterning (DEDP) DPL for printing arbitrary 2D features where the layout decomposition problem for double exposure is an interesting graph coloring problem. But due to overlay errors, it is very difficult for DEDP to print even 1D features. A more promising DPL technology is self-aligned double patterning (SADP) for 1D design. SADP first prints dense lines and then trims away the portions not on the design by a cut mask. The complexity of cut mask is very high, adding to the skyrocketing manufacturing cost. In this paper we present a mask cost reduction method with circuit performance consideration for SADP. This is the first paper to focus on the mask cost reduction issue for SADP from a design perspective. We simplify the polygons on the cut mask, by formulating the problem as a constrained shortest path problem. Experimental results show that with a set of layouts in 28nm technology, we can largely reduce the complexity of cut polygons, with little impact on performance.

Lithography-aware layout modification considering performance impact

As regular design rules become necessary in sub-45nm node circuit design, 1-D design has shown its advantages and has drawn intensive research interest. In 1-D design, line-end gaps are the main sources of printing difficulties. Recently, we [5] demonstrated that printability can be significantly improved by intelligent (litho-aware) rearrangement of the gap distribution with techniques such as line-end extension and dummy insertion. Note that poly/gate redistribution techniques require layout modification of the original layout and thus will impact circuit performance and power consumption. Such potentially undesirable impacts on performance and power were not considered in [5] and deserve a careful investigation, which is the subject of our study. In this paper, we present performance-driven gate redistribution algorithms which consider bounds on line-end extension. Experimental results demonstrate the feasibility of our algorithms, and lithography simulation and circuit analysis show the trend of the trade off between printability, delay, and power.