Abstract-Design rules have been the primary contract between technology developers and designers and are likely to remain so to preserve abstractions and productivity. While current approaches for defining design rules are largely unsystematic and empirical in nature, this paper offers a novel framework for early and systematic evaluation of design rules and layout styles in terms of major layout characteristics of area, manufacturability, and variability. The framework essentially creates a virtual standard-cell library and performs the evaluation based on the virtual layouts. Due to the focus on the exploration of rules at an early stage of technology development, we use first order models of variability and manufacturability (instead of relying on accurate simulation) and layout topology/congestion-based area estimates (instead of explicit and slow layout generation). Such a framework can be used to co-evaluate and co-optimize design rules, patterning technologies, layout methodologies, and library architectures.

Abstract-Design rules have been the primary contract between technology and design and are likely to remain so to preserve abstractions and productivity. While current approaches for defining design rules are largely unsystematic and empirical in nature, this paper offers a novel framework for early and systematic evaluation of design rules and layout styles in terms of major layout characteristics of area, manufacturability, and variability. Due to the focus on co-exploration in early stages of technology development, we use first order models of variability and manufacturability (instead of relying on accurate simulation) and layout topology/congestion-based area estimates (instead of explicit and slow layout generation). The framework is used to efficiently co-evaluate several debatable rules (evaluation for a 104-cell library takes 20 minutes). Results show that: a) diffusionrounding mainly from diffusion power-straps is a dominant source of variability, b) cell-area overhead of fixed gate-pitch implementation compared to 1D-poly implementation is tolerable (5%) given the improvement in variability, and c) 1D-poly restriction, which improves manufacturability and variability, has almost no area overhead compared to 2D-poly. In addition, we explore gate-spacing rules using our evaluation framework. This exploration yields almost identical values as those of a commercial 65nm process, which serves as a validation for our approach.

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The use of multiple-patterning (MP) optical lithography for sub-20 nm technologies has inevitably become slow to adopt the next generation of lithography systems. The biggest technical challenge of MP is failure to reach a manufacturable layout-coloring solution, especially in dense layouts. This paper offers a postlayout solution for the removal of conflicts, i.e., patterns that cannot be assigned to different masks without violating spacing rules. The proposed method essentially consists of three steps: 1) layout coloring; 2) exposure layers; 3) geometric rules definition; and 4) layout legalization using compaction and MP rules as constraints. The method is general and can be used for different MP technologies, including lithography-etch, lithography-etch double-patterning (DP), triple patterning/MP (i.e., multiple litho-etch steps), and self-aligned DP (SADP). For demonstration purposes, we apply the proposed method in this paper to remove conflicts in DP. We offer an O(n) layout-coloring heuristic algorithm for DP, which is up to 80× faster than the integer linear program-based approach. The conflict-removal problem is formulated as a linear program, which permits an extremely fast runtime (less than 1 min in real time for macro layouts). The method was tested on standard cells and macro layouts from a commercial 22-nm library designed without any MP awareness. For many cells, the method removes all conflicts without any area increase. For some complex cells and macros, the method still removes all conflicts but with a modest 6% average increase in area.

In double patterning lithography (DPL), overlay error between two patterning steps at the same layer translates into CD variability. Since CD uniformity budget is very tight, overlay control becomes a tough challenge for DPL. In this paper, we electrically evaluate overlay error for BEOL DPL with the goal of studying relative effects of different overlay sources and interactions of overlay control with design parameters. Experimental results show the following: (a) overlay electrical impact is not significant in case of positive-tone DPL (< 3.4% average capacitance variation) and should be the base for determining overlay budget requirement; (b) when considering congestion, overlay electrical impact reduces in positivetone DPL; (c) Design For Manufacturability (DFM) techniques like wire spreading can have a large effect on overlay electrical impact (20% increase of spacing can reduce capacitance variation by 22%); (d) translation overlay has the largest electrical impact compared to other overlay sources; and (e) overlay in y direction (x for horizontal metallization) has negligible electrical impact and, therefore, preferred routing direction should be taken into account for overlay sampling and alignment strategies.

Abstract-1 We propose shift-trim double patterning lithography (ST-DPL), a cost-effective double patterning technique for achieving pitch relaxation with a single photomask. The mask is re-used for the second exposure by applying a translational mask-shift. An additional non-critical trim exposure is applied to remove extra printed features. ST-DPL can be used to pattern critical layers and is very suitable for regular and gridded layouts, where redesign effort and area overhead are minimal. In this paper, the viability of ST-DPL is demonstrated through a design implementation at the poly and contacts layers in bidirectional layouts. Standard-cell layouts are constructed so as to avoid layout decomposition conflicts, which are found to be the limiting factor for the pitch relaxation that can be achieved with double-patterning (ST-DPL as well as standard DPL). 2× pitch relaxation being associated with a considerable area overhead, 1.8× pitch relaxation is achieved in our implementation while ensuring no layout decomposition conflicts and a small area overhead. Specifically, in comparison to layouts assumed to be feasible with a hypothetical single-patterning process, we observe virtually no area overhead when ST-DPL is applied to the poly layer (<0.3% cell-area overhead) and no more than 4.7% cellarea overhead when ST-DPL is applied at both the poly and contacts layers. The proposed method has many benefits over standard pitch-split double-patterning: (1) cuts mask-cost to nearly half, (2) reduces overlay errors between the two patterns, (3) alleviates the bimodal line-width distribution problem in double patterning, and (4) slightly enhances the throughput of critical-layer scanners.

Double patterning (DP) in a litho-etch-litho-etch (LELE) process is an attractive technique to scale the K 1 factor below 0.25. For dense bidirectional layers such as the first metal layer (M1), however, density scaling with LELE suffers from poor tip-to-tip (T2T) and tip-to-side (T2S) spacing. As a result, triple-patterning (TP) in a LELELE process has emerged as a strong alternative. Because of the use of a third exposure/etch, LELELE can achieve good T2T and T2S scaling as well as improved pitch scaling over LELE in case further scaling is needed. TP layout decomposition, a.k.a. TP coloring, is much more challenging than DP layout decomposition. One of the biggest complexities of TP decomposition is that a stitch can be between different two-mask combinations (i.e. first/second, first/third, second/third) and, consequently, stitches are color-dependent and candidate stitch locations can be determined only during/after coloring. In this paper, we offer a novel methodology for TP layout decomposition. Rather than simplifying the TP stitching problem by using DP candidate stitches only (as in previous works), the methodology leverages TP stitching capability by considering additional candidate stitch locations to give coloring higher flexibility to resolve decomposition conflicts. To deal with TP coloring complexity, the methodology employs multiple DP coloring steps, which leverages existing infrastructure developed for DP layout decomposition. The method was used to decompose bidirectional M1 and M2 layouts at 45nm, 32nm, 22nm, and 14nm nodes. For reasonably dense layouts, the method achieves coloring solutions with no conflicts (or a reasonable number of conflicts solvable with manual legalization). For very dense and irregular M1 layouts, however, the method was unable to reach a conflict-free solution and a large number of conflicts was observed. Hence, layout simplifications for the M1 layer may be unavoidable to enable TP for the M1 layer. Although we apply the method for TP, the method is more general and can be applied for multiple patterning with any number of masks.

Abstract-Double/Multiple-patterning (DP/MP) lithography in a multiple litho-etch steps process is a favorable solution for technology scaling to the 20nm node and below. Mask-assignment conflicts represent the biggest challenge for MP and limiting them through design rules is crucial for the adoption of MP technology. In this paper, we offer a methodology for the early evaluation and exploration of layout and MP rules intended for speeding up the rules-development cycle. Using a novel wiringestimation method, we create layout estimates with fine-grained congestion prediction. MP-conflicts are then predicted using a machine-learning approach. In this work, we demonstrate the use of the method for double-patterning lithography in litho-etchlitho-etch process; the methodology is more general, however, and can be applied for other multiple-patterning technologies including tripe/multiple-patterning with multiple litho-etch steps, selfaligned double patterning (SADP), and directed self-assembly. Results of testing the methodology on standard-cell layouts show an 81% accuracy in DP-conflicts prediction. The methodology was then used to explore DP and layout rules and investigate their effects on DP-compatibility and layout area. The methodology allows for rules optimization; for example, pushing the minimum tip-to-side same-color spacing rule value from 1.7× to 1.5× the minimum side-to-side spacing design rule (i.e., from 110nm down to 90nm) would more than double the number of DP-compatible cells in the library.