SMART NoCs achieve ultra-low latency by enabling single-cycle multiple-hop transmission via bypass channels. However, contention along bypass channels can seriously degrade the performance of SMART NoCs by breaking the bypass paths. Therefore, contention-free task mapping and scheduling are essential for optimal system performance. In this article, we propose an SMT (Satisfiability Modulo Theories)-based framework to find optimal contention-free task mappings with minimum application schedule lengths on 2D/3D SMART NoCs with mixed dimension-order routing. On top of SMT’s fast reasoning capability for conditional constraints, we develop efficient search-space reduction techniques to achieve practical scalability. Experiments demonstrate that our SMT framework achieves 10× higher scalability than ILP (Integer Linear Programming) with 931.1× (ranges from 2.2× to 1532.1×) and 1237.1× (ranges from 4× to 4373.8×) faster average runtimes for finding optimum solutions on 2D and 3D SMART NoCs and our 2D and 3D extensions of the SMT framework with mixed dimension-order routing also maintain the improved scalability with the extended and diversified routing paths, resulting in reduced application schedule lengths throughout various application benchmarks.

In advanced nodes, scaling of critical dimension and pitch has not progressed at historical Moore’s Law rates. Thus,scaling boostersare explored to improve achievable power, performance, area, and cost (PPAC) in new technologies. However, scaling boosters increase complexity of standard-cell architectures, power delivery, design rules, and other aspects of the design enablement, and may not result in design-level benefits. Therefore, design-technology co-optimization (DTCO) methodologies are required to evaluate design-level benefits of scaling boosters. The key challenge for DTCO is that large engineering efforts and long timelines are needed to develop design enablements (e.g., cell libraries) and perform implementation studies in order to assess technology options. We describe a new framework that can systematically evaluate a measure of intrinsic routability,$K_{\mathrm{ th}}$, across both technology and design choices. We focus on routability since it is a critical factor in the scaling of area and cost. Our framework includes realistic standard-cell libraries that are automatically generated using satisfiability modulo theory (SMT) methods, and a new pin shape selection method. Routability assessments are based on the PROBE approach and an improved construction of underlying netlist topologies. Our experimental studies demonstrate the assessment of routability impacts for advanced-node technology and design options. We demonstrate learning-based$K_{\mathrm{ th}}$prediction to reduce runtime, disk space and commercial tool licenses needed to implement our framework. Our work enables faster and more comprehensive evaluation of technology options early in the technology development process.

As technology nodes continue to advance relentlessly, geometric pitch scaling starts to slow down. In order to retain the trend of Moore’s law, design technology co-optimization (DTCO) and system technology co-optimization (STCO) are introduced together to continue scaling beyond 5 nm using pitch scaling, patterning, and novel 3-D cell structures [i.e., complementary-FET (CFET)]. However, numerous DTCO and STCO iterations are needed to continue block-level area scaling with considerations of physical layout factors: 1) various standard cell (SDC) library sets (i.e., different cell heights and conventional FET); 2) design rules (DRs); 3) back end of line (BEOL) settings; and 4) power delivery network (PDN) configurations. The growing turnaround time (TAT) among SDC design, DR optimization, and block-level area evaluation becomes one of the major bottlenecks in DTCO and STCO explorations. In this work, we develop a machine learning model that combines bootstrap aggregation and gradient boosting techniques to predict the sensitivity of minimum valid block-level area of various physical layout factors. We first demonstrate that the proposed model achieves 16.3% less mean absolute error (MAE) than the previous work for testing sets. Then, we show that the proposed model successfully captures the block-level area sensitivity of new SDC library sets, new BEOL settings, and new PDN settings with 0.013, 0.004, and 0.027 MAE, respectively. Finally, compared to the previous work, the proposed approach improves the robustness of predicting new circuit designs by up to 6.76%. The proposed framework provides more than$100\times $speedup compared to conventional DTCO and STCO exploration flows.

With the relentless scaling of technology nodes, physical design engineers encounter non-trivial challenges caused by rapidly increasing design complexity, particularly in the routing stage. Back-end designers must manually stitch/modify all of the design rule violations (DRVs) that remain after automatic place-and-route (P&R), during the implementation of engineering change orders (ECOs). In this paper, we propose CoRe-ECO, a concurrent refinement framework for efficient automation of the ECO process. Our framework efficiently resolves pin accessibility-induced DRVs by simultaneously performing detailed placement, detailed routing, and cell replacement. In addition to perturbation-minimized solutions, our proposed SMT-based optimization framework also suggests the adoption of alternative master cells to better achieve DRV-clean layouts. We demonstrate that our framework successfully resolves from 33.3% to 100.0% (58.6% on average) of remaining DRVs on M1-M3 layers, across a range of benchmark circuits with various cell architectures, while also providing average total wirelength reduction of 0.003%.

In this article, we propose an automated standard cell synthesis framework, SP&R, which simultaneously solves P&R without deploying any sequential/separate operations, by a novel dynamic pin allocation scheme. The proposed SP&R utilizes the multiobjective optimization feature of satisfiability modulo theories (SMT) to obtain optimal cell layouts. To achieve practical scalability of the framework, we develop various search-space reduction techniques, including breaking symmetry, conditional assignment/localization, and cell/objective function partitioning. Compared to the previous work, SP&R achieves 20.8× to 131.7× runtime improvements on average across the design-rule sets. As a result, SP&R successfully produces cell layouts up to 36 field-effect transistors (FETs) and 27 nets within 1.75 h by orchestrating all innovative tactics together, resulting in the generation of a whole 7-nm standard cell library. Compared to the known layouts, our work improves cell size and # M2 tracks by 0.1 contacted poly pitch and 0.3 tracks, respectively.

With the relentless scaling of technology nodes, design technology co-optimization (DTCO) for the conventional (Conv.) cell structure is starting to reach its limitations due to limited routing resources, lateral p-n separations, and performance requirements. As a result, system technology co-optimization (STCO) has been proposed to exploit the benefits of 3-D architectures. Complementary-FET (CFET) technology, which stacks p-FET on n-FET or vice versa, can release the restriction of p-n separation and reduce in-cell routing congestion by enabling p-n direct connections. However, CFET standard cell (SDC) synthesis demands holistic considerations to maximize the area benefit of scaling at the block level due to the extremely limited routability that comes from the stacked structure and reduced cell height. In this article, we propose a satisfiability modulo theory (SMT)-based CFET SDC synthesis framework that simultaneously solves place-and-route to generate optimized layouts. We first demonstrate that the CFET structure achieves 10.94% and 21.27% reduction on average cell area and metal length, respectively, and 15.10% smaller block-level area compared to Conv. structure as scaling down to 3.5T architecture. For routability, the proposed constraint-based minimum pin length/minimum pin opening and objective-based edge-based pin-separation/M2 track use reduce up to 48% #DRVs at the block level compared to the previous work. Then, through extensive DTCO explorations on ground design rules and #BEOLs, 3.5T CFET SDCs achieve up to 6.50% smaller block-level areas than 4.5T CFET SDCs. Finally, with the assistance of STCO and DTCO, 3.5T CFET SDCs achieve 21.0% on average reduced block-level areas compared to 4.5T Conv. SDCs.

Standard cell synthesis requires careful engineering approaches to ensure routability across various digital IC designs since physical design (PD) for sub-7nm technology nodes demands holistic efforts to address urgent and nontrivial design challenges. The smaller number of routing tracks and more complex design rules due to the sophisticated multi-patterning technology make place-and-route (P&R) for designing a standard cell extremely hard and time-consuming. Many conventional approaches have been suggested for improving transistor-level P&R and pin accessibility, nonetheless insufficient because of the heuristic/divide-and-conquer manners. In this paper, we propose a novel framework, SP&R, which simultaneously solves P&R for designing standard cell's layout without deploying any sequential procedures (between place and route steps) by using dynamic pin allocation-based cell synthesis. The proposed SP&R utilizes the Optimization Modulo Theories (OMT), an extension of the Satisfiability modulo theories (SMT), to obtain optimal standard cell layout by virtue of SAT (Boolean Satisfiability)-based fast reasoning ability. We validate that our SP&R framework achieves 10.5% of reduction on average in terms of metal length compared to the sequential approach, through practical standard cell designs targeting sub-7nm technology nodes.

As the technology node is evolving, standard cell (SDC) design scaling is obstructed by design constraints such as limited routing resources, lateral P-N separation, and performance requirements. Complimentary-FET (CFET) technology, which stacks the P-FET on N-FET or vice versa, is able to release the restriction of P-N connection for SDC layout scaling. However, (both in-cell and block-level) routable CFET SDC design, while maintaining the scaling advantages, is a non-trivial problem because of the extremely limited routability (including pin-accessibility) comes from the intrinsic stacked FET structure.

With the scaling of VLSI technologies, the design-technology co-optimization (DTCO) requires prompt development of standard cell libraries to explore scaling effects of various cell architectures. However, standard cell layout design demands holistic efforts for processing transistor placement and in-cell routing due to the limited routing tracks and complicated design rules. Thus, an automatic design framework of standard cell layout became essential in the advanced scaling. Conventional heuristic/divide-and-conquer approaches lack the optimality of solutions because of the limited solution space. In this paper, we propose a novel standard cell scaling framework that simultaneously finds an optimal solution in placement and routing with the pin-accessibility. To ensure the minimum number of pin-access points, we devise strict Boolean counter-based design constraints. We validate our framework using scaling parameters and cell architectures across sub-7nm technology nodes.

Pin accessibility encounters nontrivial challenges due to the smaller number of routing tracks, higher pin density, and more complex design rules. Consequently, securing design rule-correct routability has become a critical bottleneck for sub-10-nm IC designs (particularly in the detailed routing stage) costing days of runtime. To reduce turnaround time, IC designers demand new design methodologies to analyze the routing feasibility of a given layout architecture (e.g., conditional design rules, pin assignment patterns, etc). There are several conventional methods capable of assessing routability that consider pin accessibility. However, precise diagnosis of unroutable layouts remains an open problem for IC design practitioners. In this article, we propose two novel frameworks that: 1) efficiently analyzes design rule-correct routability via an integer linear programming (ILP)-derived Boolean satisfiability (SAT) formulation written in light-weight conjunctive normal form, on top of multicommodity flow theory and 2) precisely diagnose explicit reasons for design-rule violations (DRVs) in the form of human-interpretable explanations, while specifying conflicting design rules with a physical location. While covering a variety of conditional design rules, we have refined our formulation by using SAT encoding techniques, supernode simplification, Boolean constraint propagation-based preprocessing, etc. We demonstrate that our routability analysis framework produces design rule-correct routability assessment within 0.02% of ILP runtime on average. Also, our routability diagnosis framework precisely examines DRVs, revealing design-rule conflicts for a variety of pin layouts and switchboxes. We show our frameworks scalability by utilizing practical benchmarks ranging up to 40000 grid-size layouts (i.e., 200 Htrack × 200 Vtrack), producing results within an hour.

As more cores are integrated in a single chip with sophisticated process like nano technology, testing signal integrity between the cores needs much effort due to complicate coupling effects. In this paper, we propose a novel test pattern generation method for testing signal integrity. Using this method, short and effective test patterns are generated with low hardware overhead. It can be used for self-test scheme and experimental results show the effectiveness of the proposed scheme.