Electron beam lithography (EBL) is a promising, maskless solution for the technology beyond 14nm logic nodes. To overcome its throughput limitation, industry has proposed character projection (CP) technique, where some complex shapes (characters) can be printed in one shot. Recently, the traditional EBL system was extended into a multi-column cell (MCC) system to further improve the throughput. In an MCC system, several independent CPs are used to further speed-up the writing process. Because of the area constraint of stencil, the MCC system needs to be packed/planned carefully to take advantage of the characters. In this article, we prove that the overlapping aware stencil planning (OSP) problem is NP-hard. Then we propose E-BLOW, a tool to solve the MCC system OSP problem. E-BLOW involves several novel speedup techniques, such as successive relaxation and dynamic programming. Experimental results show that, compared with previous works, E-BLOW demonstrates better performance for both the conventional EBL system and the MCC system.

As minimum feature size and pitch spacing further scale down, triple patterning lithography is a likely 193 nm extension along the paradigm of double patterning lithography for 14-nm technology node. Layout decomposition, which divides input layout into several masks to minimize the conflict and stitch numbers, is a crucial design step for double/triple patterning lithography. In this paper, we present a systematic study on triple patterning layout decomposition problem, which is shown to be NP-hard. Because of the NP-hardness, the runtime required to exactly solve it increases dramatically with the problem size. We first propose a set of graph division techniques to reduce the problem size. Then, we develop integer linear programming (ILP) to solve it. For large layouts, even with the graph-division techniques, ILP may still suffer from serious runtime overhead. To achieve better trade-off between runtime and performance, we present a novel semidefinite programming (SDP)-based algorithm. Followed by a mapping process, we can translate the SDP solutions into the final decomposition solutions. Experimental results show that the graph division can reduce runtime dramatically. In addition, SDP-based algorithm can achieve great speedup even compared with accelerated ILP, with very comparable results in terms of the stitch number and the conflict number.

Electron beam lithography (EBL) is a promising maskless solution for the technology beyond 14nm logic node. To overcome its throughput limitation, recently the traditional EBL system is extended into MCC system. In this paper, we present E-BLOW, a tool to solve the overlapping aware stencil planning (OSP) problems in MCC system. E-BLOW is integrated with several novel speedup techniques, i.e., successive relaxation, dynamic programming and KD-Tree based clustering, to achieve a good performance in terms of runtime and solution quality. Experimental results show that, compared with previous works, E-BLOW demonstrates better performance for both conventional EBL system and MCC system.

As the CMOS feature enters the era of extreme scaling (14nm, 11nm and beyond), manufacturability challenges are exacerbated. The nanopatterning through the 193nm lithography is being pushed to its limit, through double/triple or more general multiple patterning, while non-conventional lithography technologies such as extreme ultra-violet (EUV), e-beam direct-write (EBDW), and so on, still have grand challenges to be solved for their adoption into IC volume production. This tutorial will provide an overview of key overarching issues in nanometer IC design for manufacturability (DFM) with these emerging lithography technologies, from modeling, mask synthesis, to physical design and beyond.

Electronic beam lithography (EBL) is one of the promising emerging technologies in the sub-22 nm regime. In EBL, the desired circuit patterns are directly shot into the wafer, which overcomes the diffraction limit of light in the current optical lithography system. However, the low throughput becomes its key technical hurdle. In the conventional EBL system, each rectangle in the layout will be projected by one electronic shot through a variable shape beam (VSB). This could be extremely slow. As an improved EBL technology, character projection (CP) shoots complex shapes, so-called characters, in one time, by putting them into a predesigned stencil. However, only a limited number of characters can be employed, due to the area constraint. Those patterns, not contained by any character, are still required to be written by VSB. A key problem is how to select an optimal set of characters and pack them on the CP stencil to minimize total processing time. In this paper, we investigate a problem of electronic beam lithography stencil design with overlapped characters. Different from previous works, besides selecting appropriate characters, their placements on the stencil are also optimized in our framework. Specifically, we propose a Hamilton-path-based iterative algorithm to handle 1-D stencil design problem, and an effective simulated annealing framework for the generalized 2-D case with an efficient look-ahead sequence pair evaluation technique. The experimental results show that, compared to conventional stencil design methodology without overlapped characters, we are able to reduce total projection time by 51%.

In the era of deep sub-wavelength lithography for nanometer VLSI designs, manufacturability and yield issues are critical and need to be addressed during the key physical design implementation stage, in particular detailed routing. However, most existing studies for lithography-friendly routing suffer from either huge run-time due to the intensive lithographic computations involved, or severe loss of quality of results because of the inaccurate predictive models. In this paper, we propose AENEID - a fast, generic and high performance lithography-friendly detailed router for enhanced manufacturability. AENEID combines novel hotspot detection and routing path prediction techniques through modern data learning methods and applies them at the detailed routing stage to drive high fidelity lithography-friendly routing. Compared with existing litho-friendly routing works, AENEID demonstrates 26% to 66% (avg. 50%) of lithography hotspot reduction at the cost of only 18%-38% (avg. 30%) of run-time overhead.

As minimum feature size and pitch spacing further decrease, triple patterning lithography (TPL) is a possible 193nm extension along the paradigm of double patterning lithography (DPL). However, there is very little study on TPL layout decomposition. In this paper, we show that TPL layout decomposition is a more difficult problem than that for DPL. We then propose a general integer linear programming formulation for TPL layout decomposition which can simultaneously minimize conflict and stitch numbers. Since ILP has very poor scalability, we propose three acceleration techniques without sacrificing solution quality: independent component computation, layout graph simplification, and bridge computation. For very dense layouts, even with these speedup techniques, ILP formulation may still be too slow. Therefore, we propose a novel vector programming formulation for TPL decomposition, and solve it through effective semidefinite programming (SDP) approximation. Experimental results show that the ILP with acceleration techniques can reduce 82% runtime compared to the baseline ILP. Using SDP based algorithm, the runtime can be further reduced by 42% with some tradeoff in the stitch number (reduced by 7%) and the conflict (9% more). However, for very dense layouts, SDP based algorithm can achieve 140x speed-up even compared with accelerated ILP.

Electronic Beam Lithography (EBL) is an emerging maskless nanolithography technology which directly writes the desired circuit pattern into wafer using e-beam, thus it overcomes the diffraction limit of light in current optical lithography system. However, low throughput is its key technical hurdle. In conventional EBL system, each rectangle in the layout will be projected by one electronic shot, through a Variable Shaped Beam (VSB). This would be extremely slow. As an improved EBL technology, Character Projection(CP) shoots complex shapes, so called characters, by putting them into a pre-designed stencil to increase throughput. However, only a limited number of characters can be put on the stencil due to its area constraint.

As double patterning lithography(DPL) becomes the leading candidate for sub-30 nm lithography process, we need a fast and lithography friendly decomposition framework. In this paper, we propose a multi-objective min-cut based decomposition framework for stitch minimization, balanced density, and overlay compensation, simultaneously. The key challenge of DPL is to accomplish high quality decomposition for large-scale layouts under reasonable runtime with the following objectives: a) the number of stitches is minimized, b) the balance between two decomposed layers is maximized for further enhanced patterning, c) the impact of overlay on coupling capacitance is reduced for less timing variation. We use a graph theoretic algorithm for minimum stitch insertion and balanced density. An additional decomposition constraints for self-overlay compensation are obtained by integer linear programming(ILP). With the constraints, global decomposition is executed by our modified FM graph partitioning algorithm. Experimental results show that the proposed framework is highly scalable and fast: we can decompose all 15 benchmark circuits in five minutes in a density balanced fashion, while an ILP-based approach can finish only the smallest five circuits. In addition, we can remove more than 95% of the timing variation induced by overlay for tested structures.

In Double Patterning Lithography (DPL), conflict and stitch minimization are two main challenges. Post-routing mask decomposition algorithms may not be enough to achieve high quality solution for DPL-unfriendly designs, due to complex metal patterns. In this paper, we propose an efficient framework of WISDOM to perform wire spreading and mask assignment simultaneously for enhanced decomposability. A set of Wire Spreading Candidates (WSC) are identified to eliminate coloring constraints or create additional splitting locations. Based on these candidates, an Integer Linear Programming (ILP) formulation is proposed to simultaneously minimize the number of conflicts and stitches, while introducing as less layout perturbation as possible. To improve scalability, we further propose three acceleration techniques without loss of solution quality: odd-cycle union optimization, coloring-independent group computing, and suboptimal solution pruning. The experimental results show that, compared to a post-routing mask decomposition method, we are able to reduce the number of conflicts and stitches by 41% and 23% respectively, with only 0.43% wire length increase. Moreover, with proposed acceleration methods, we achieve 9× speed-up.

Double patterning lithography (DPL) is considered as a most likely solution for 32 nm/22 nm technology. In DPL, the layout patterns are decomposed into two masks (colors), and manufactured through two exposures and etch steps. If the spacing between two features (polygons) is less than certain minimum coloring distance, they have to be assigned opposite colors. However, a proper coloring is not always feasible because two neighboring patterns within the minimum distance may be in the same mask due to complex pattern configurations. In that case, a feature may need to be split into two parts to resolve the conflict, resulting in stitch insertion which causes yield loss due to overlay and line-end effect. While previous layout decomposition approaches perform coloring and splitting separately, in this paper, we propose a simultaneous conflict and stitch minimization algorithm with an integer linear programming (ILP) formulation. Since ILP is in class NP-hard, the algorithm includes three speed-up techniques: (1) grid merging; (2) independent component computation; and (3) layout partition. In addition, our algorithm can be extended to handle design rules such as overlap margin and minimum width for practical use as well as off-grid layout. Our approach can reduce 33% of stitches and remove conflicts by 87.6% compared with two phase greedy decomposition.

In double patterning lithography (DPL), coloring conflict and stitch minimization are the two main challenges. Post layout decomposition algorithm [1] [2]may not be enough to achieve high quality solution for DPL-unfriendly designs, due to complex 2D patterns in lower metal layers. Therefore, DPL-friendliness is needed at routing stage [3]. Another key yield improvement technique is redundant via insertion [4] [5]. However, this would increase the complexity in DPL-compliance. To make designs manufacturable in DPL, we should not insert a redundant via if it results in coloring conflict. This paper is the first work to consider DPL and redundant via together. We have developed two algorithms, post-routing DPL-aware insertion and DPL-friendly routing with redundant via consideration to take into account redundant via DPL-compliance. Experimental results show that, compared to a DPL-aware optimization flow without redundant via consideration, we can improve insertion rate by 43% while still achieving zero coloring conflicts. Moreover, we can reduce the number of vias and stitches by 9% and 17% respectively.

Double patterning lithography (DPL) is considered as a most likely solution for 32nm/22nm technology. In DPL, the layout patterns are decomposed into two masks (colors). Two features (polygons) have to be assigned opposite colors if their spacing is less than certain minimum coloring distance. However, a proper coloring is not always feasible because two neighboring patterns within the minimum distance may be in the same mask due to complex pattern configurations. In that case, a feature may be split into two parts to resolve the conflict but the resulting stitch causes yield loss due to overlay error and increases manufacturing cost. While previous layout decomposition approaches perform coloring and splitting separately, in this paper, we propose an algorithm to minimize the number of conflicts and stitches simultaneously. Our algorithm is based on grid layout model and integer linear programming. Two techniques, independent component computation and layout partition, are proposed to reduce runtime of the algorithm. The experimental results show that, compared with the two phase decomposition flow, the proposed algorithm reduces the conflicts significantly using less stitches under reasonable runtime.

In this paper, we present an efficient lithography aware detailed (ELIAD) router to enhance silicon image after optical proximity correction (OPC) in a correct-by-construction manner. We first quantitatively show that a pre-OPC litho-metric is highly uncorrelated with a post-OPC metric, which stresses the importance of a post-OPC litho-metric for design-time optimization. We then propose a compact post-OPC litho-metric for a detailed router (DR) based on statistical characterization, where the interferences among predefined litho-prone shapes are captured as a lookup table. Our litho-metric derived from the characterization shows high fidelity to the total edge placement error (EPE) in large scale, compared with Calibre OPC/optical rule check. Therefore, ELIAD powered by the proposed litho-metric can enhance the overall post-OPC printed silicon image. Experimental results on 65-nm industrial circuits show that ELIAD outperforms a rip-up/rerouting approach such as Resolution-enhancement-technique-Aware Detailed Routing with 8times more EPE hot spot reduction and 12times speedup. Moreover, compared with a conventional DR, ELIAD is only about 50% slower.

In this article, we present BoxRouter 2.0, and discuss its architecture and implementation. As high-performance VLSI design becomes more interconnect-dominant, efficient congestion elimination in global routing is in greater demand. Hence, we propose a global router which has a strong ability to improve routability and minimize the number of vias with blockages, while minimizing wirelength. BoxRouter 2.0 is extended from BoxRouter 1.0, but can perform multi-layer routing with 2D global routing and layer assignment. Our 2D global routing is equipped with two ideas: node shifting for congestion-aware Steiner tree and robust negotiation-based A* search for routing stability. After 2D global routing, 2D-to-3D mapping is done by the layer assignment which is powered by progressive via/blockage-aware integer linear programming. Experimental results show that BoxRouter 2.0 has better routability with comparable wirelength than other routers on ISPD07 benchmark, and it can complete (no overflow) the widely used ISPD98 benchmark for the first time in the literature with the shortest wirelength. We further generate a set of harder ISPD98 benchmarks to push the limit of BoxRouter 2.0, and propose the hardened ISPD98 benchmarks to map state-of-the-art solutions for future routing research.

In this paper, we present ELIAD, an efficient lithography aware detailed router to optimize silicon image after optical proximity correction (OPC) in a correct-by-construction manner. We first propose a compact post-OPC litho-metric for a detailed router based on statistical characterization. We characterize the interferences among weak grids filled with one of predefined litho-prone shapes (e.g., jog-corner, via, line-end). Our litho-metric derived from the characterization shows high fidelity to total edge placement error (EPE) in large scale, compared with Calibre-OPC/ORC. As a chip itself is in the largest scale, ELIAD powered by the proposed metric can enhance the overall post-OPC printed silicon image. Experimental results on 65nm industrial circuits show that ELIAD outperforms a ripup/rerouting approach such as RADAR [17] with 8x more EPE hotspot reduction and 12x speedup. Also, compared with a conventional detailed router, ELIAD is only about 50% slower.

In this paper, we present BoxRouter 2.0, a hybrid and robust global router with discussion on its architecture and implementation. As high performance VLSI design becomes more interconnect-dominant, efficient congestion elimination in global routing is in greater demand. Hence, we propose BoxRouter 2.0 which has strong ability to improve routability and minimize the number of vias with blockages, while minimizing wirelength. BoxRouter 2.0 is improved over [1], but can perform multi-layer routing with 2D global routing and layer assignment. Our 2D global routing is equipped with two ideas: robust negotiation- based A∗ search for routing stability, and topology-aware wire ripup for flexibility. After 2D global routing, 2D-to-3D mapping is done by the layer assignment which is powered by progressive via/blockage-aware integer linear programming. Experimental results show that BoxRouter 2.0 has better routability with comparable wirelength than other routers on ISPD07 benchmark, and it can complete (no overflow) ISPD98 benchmark for the first time in the literature with the shortest wirelength.