Clock power, skew and maximum latency are three key metrics for clock distribution in low-power and high-performance designs. An H-tree offers minimum clock skew and good robustness against variations, but at the cost of large wirelength and clock power. On the other hand, a “fishbone” clock network with spine-ribs structures has smaller wirelength, latency and clock power, but larger skew, as compared to an H-tree. No previous work enables systematic exploration of the regime between H-tree and spine to achieve an optimal tradeoff among clock power, skew, and latency. In this paper, we study the concept of a generalized H-tree (GH-tree)-a topologically balanced tree with an arbitrary sequence of branching factors-and propose a dynamic programming-based method to determine optimal clock power, skew, and latency, in the space of GH-tree solutions. Our method co-optimizes clock tree topology and buffering along branches according to fitted electrical models. We further propose a balanced K-means clustering and a linear programming (LP)-guided buffer placement approach to embed the GH-tree with respect to a given sink placement. We validate our solutions in commercial clock tree synthesis (CTS) tool flows, in a commercial foundry's 28LP technology. The results show up to 30% clock power reduction while achieving similar skew and maximum latency as CTS solutions from recent versions of leading commercial place-and-route tools. Our proposed approach also achieves up to 56% clock power reduction while achieving similar skew and maximum latency as compared to CTS solutions from a state-of-the-art academic tool.

Standard-cell libraries can be developed with different cell heights (e.g., in FinFET technology, corresponding to different numbers of fins). Larger cell heights provide higher drive strengths, but at the cost of larger area and power consumption as well as pin capacitance. Cells with smaller heights are relatively smaller in area, but have weaker drive strengths and are more likely to suffer from routing congestion and pin accessibility issues. Existing design methodologies and tool flows are able to mix cells with different heights at the block level (i.e., each block contains cells with heights being integer multiples of a particular “single row” cell height). To our knowledge, no design methodology in the literature or in production mixes cells with different, noninteger multiple heights in a fine-grained manner. In this paper, we propose a novel physical design optimization flow to implement design blocks with mixed cell heights in a fine-grained manner. Our optimization resolves the “chicken-and-egg” loop between floorplan site definition and the optimized choices of cell heights after placement with full comprehension of the constraints and costs of mixing cells of different heights (e.g., the “breaker cell” area overheads of row alignment between sub-blocks of 8 T and 12 T cell rows), our optimization achieves up to over 30% area and power reductions versus 12 T-only implementation while maintaining the same performance, and up to over 10% performance improvement along with power and area reductions versus 8 T-only implementation.

In advanced technology nodes, correctly choosing among available back-end-of-line (BEOL) stack options is important to meet stringent design quality of results requirements. However, it is nontrivial to evaluate BEOL stack options since the routing outcomes highly depend on the input design (e.g., netlist, placement, etc.). In this paper, we propose a systematic framework to measure routing capacity of a BEOL stack as well as inherent capability of routers. Based on our experimental results, we observe consistent results across mesh-like placement and placements from various placers. Also, our proposed framework enables new insights into important questions regarding BEOL stack options. Using our framework, we further study the relation between the routing hotspot size and routing failure empirically. Lastly, we present an analytical study based on exponentiation of a Markov transition matrix about the impact of design size on routing failure.

Energy and battery lifetime constraints are critical challenges to IC designs. Stacked power-domain implementation, which stacks voltage domains in a design, can effectively improve the power delivery efficiency and thus improve battery lifetime. However, such an approach requires balanced current between different domains across multiple operating scenarios. Furthermore, level shifter insertion (together with shifters' delay impacts), along with placement constraints imposed by power domain regions, can incur power and area penalties. To our knowledge, no existing work performs sub-block-level partitioning optimization for stacked-domain designs. In this paper, we present an optimization framework for stacked-domain designs. Based on an initial placement solution, we apply a flow-based partitioning that is aware of multiple operating scenarios, cell placement, and timing-critical paths to partition cells into two power domains with balanced current and minimized number of inserted level shifters. We further propose heuristics to define regions for each power domain so as to minimize placement perturbation, as well as a dynamic programming-based method to minimize the area cost of power domain generation. In an updated floorplan, we perform matching-based optimization to insert level shifters with minimized wirelength penalty. Overall, our method achieves more than ~10% and 3X battery lifetime improvements in function and sleep modes, respectively.

As we approach the limits of traditional Moore’s-Law scaling, alternative computing techniques that consume energy more efficiently become attractive. Stochastic computing (SC), as a re-emerging computing technique, is a low-cost and error-tolerant alternative to conventional binary circuits in several important applications such as image processing and communications. SC allows a natural accuracy-energy tradeoff that has been exploited in the past. This article presents an accuracy-energy tradeoff technique for SC circuits that reduces their energy consumption with virtually no accuracy loss. To this end, we employ voltage or frequency scaling, which normally reduce energy consumption at the cost of timing errors. Then we show that due to their inherent error tolerance, SC circuits operate satisfactorily without significant accuracy loss even with aggressive scaling. This significantly improves their energy efficiency. In contrast, conventional binary circuits quickly fail as the supply voltage decreases. To find the most energy-efficient operating point of an SC circuit, we propose an error estimation method that allows us to quickly explore the circuit’s design space. The error estimation method is based on Markov chain and least-squares regression. Furthermore, we investigate opportunities to optimize SC circuits under such aggressive scaling. We find that logical and physical design techniques can be combined to significantly expand the already-powerful accuracy-energy tradeoff possibilities of SC. In particular, we demonstrate that careful adjustment of path delays can lead to significant error reduction under voltage and frequency scaling. We perform buffer insertion and route detouring to achieve more balanced path delays. These techniques differ from conventional path-balancing techniques whose goal is to minimize power consumption by resizing the non-critical paths. The goal of our path-balancing approach is to increase error cancellation chances in voltage-/frequency-scaled SC circuits. Our circuit optimization comprehends the tradeoff between power overheads due to inserted buffers and wires versus the energy reduction from supply voltage downscaling enabled by more balanced path delays. Simulation results show that our optimized SC circuits can tolerate aggressive voltage scaling with no significant signal-to-noise ratio (SNR) degradation. In one example, a 40% supply voltage reduction (1V to 0.6V) on the SC circuit leads to 66% energy saving (20.7pJ to 6.9pJ) and makes it more efficient than its conventional binary counterpart. In the same example, a 100% frequency boosting (400ps to 200ps) of the optimized circuits leads to no significant SNR degradation. We also show that process variation and temperature variation have limited impact on optimized SC circuits. The error change is less than 5% when temperature changes by 100°C or process condition changes from worst case to best case.

Energy and battery lifetime constraints are critical challenges to IC designs. Stacked power-domain implementation, which connects voltage domains in series, can effectively improve power delivery efficiency and thus improve battery lifetime. However, such an approach requires balanced currents between different domains across multiple operating scenarios. Furthermore, level shifter insertion, along with placement constraints imposed by power domain regions, can incur significant power and area penalties. To the best of our knowledge, no existing work performs subblock-level partitioning optimization for stackeddomain designs. In this paper, we present an optimization framework for stacked-domain designs. Based on an initial placement solution, we apply a flow-based partitioning that is aware of multiple operating scenarios, cell placement, and timing-critical paths to partition cells into two power domains with balanced cross-domain current and minimized number of inserted level shifters. We further propose heuristics to define regions for each power domain so as to minimize placement perturbation, as well as a dynamic programming-based method to minimize the area cost of power domain generation. In an updated floor plan, we perform matching-based optimization to insert level shifters with minimized wirelength penalty. Overall, our method achieves an excellent current balance across stacked domains with less than 10% discrepancy, which results in up to more than 2× battery lifetime improvements.

Scan chain timing is increasingly critical to test time and product cost. However, hold buffer insertions (e.g., due to large clock skew) limit scan timing improvement. Dynamic voltage drop (DVD) during scan shift further degrades scan shift timing, inducing "false failures" in silicon. Hence, new optimizations are needed in late stages of implementation when accurate (skew, DVD) information is available. We propose skew-aware scan ordering to minimize hold buffers, and DVD-aware gating insertion to improve scan shift timing slacks. Our optimizations at the post-CTS and post-routing stages reduce hold buffers by up to 82%, and DVD-induced timing degradation by up to 58%, with negligible area and power overheads.

Over the past decade, “Moore's Law” has become increasingly well-understood as being a law of “value scaling”: success of new electronics- and semiconductor-based products depends on improved cost-efficiency, utility, and value. Design Automation (DA) provides fundamental tools and methodologies that glue together disparate technological advances - across architectures, circuits, process and integration - into actually-realized product and system benefits. However, it is still unknown how to measure and credit “progress” of DA with respect to realized product- and system-level benefits. Thus, it is also challenging for industry, academia and funding entities to envision, and define, R&D objectives and prioritizations. In this paper, we contend that “measuring progress and value” is tractable at the level of EDA technology and R&D efforts. We describe four example assessments of progress and value of IC implementation technology: (i) assessment of progress of EDA tools (e.g., for P&R and STA) across multiple releases; (ii) establishing “upper bounds” on future progress (e.g., for 3DIC layout); (iii) robust rank-ordering of alternative design enablements (e.g., including routing tools and interconnect stack options); and (iv) lowering barriers to measuring progress and value of academic research results in “more real-world” contexts.

Clock network power reduction is critical in modern SoC designs. Application of flop trays (i.e., multi-bit flip-flops) can significantly reduce the number of sinks in a clock network, and thus reduce the number of clock buffers, clock wirelength, and clock network power. Shared inverters within flop trays also reduce power at the flip-flop level. However, large-size flop trays typically induce placement and routing congestion, and impose additional placement constraints on their fanin/fanout logic cones; this results in power overheads on datapaths. At the same time, to our knowledge, few previous works have studied flop trays with more than four bits. The “chicken-and-egg” loop between flop tray generation and placement optimization is another challenge to flop tray-based design [7]. In this work, we propose an optimization flow to generate and place flop trays from a library of arbitrary given sizes and aspect ratios (ARs), to achieve clock network power reduction. Our optimization starts with an initial placement solution using only single-bit flops. It then performs capacitated K-means clustering to generate solutions with different flop tray sizes and ARs. More specifically, we iteratively use (i) min-cost flow to cluster flops, and (ii) a linear programming-based optimization to determine locations of the generated flop trays. Last, we formulate an integer linear program to select the best combination of flop tray solutions (i.e., sizes and placements) with minimum displacement and number of isolated sinks. Our optimization is aware of flop tray sizes and ARs, as well as timing-critical start-end pairs. Results in foundry 28FDSOI technology show up to 32% total block power reduction as compared to designs using only single-bit flops, up to 16% total block power reduction over designs with flop trays generated by logical clustering during synthesis, and 13% clock power reduction on average compared to the previous work in [10].

As combinations of signoff corners grow in modern SoCs, minimization of clock skew variation across corners is important. Large skew variation can cause difficulties in multi-corner timing closure because fixing violations at one corner can lead to violations at other corners. Such "ping-pong" effects lead to significant power and area overheads and time to signoff. We propose a novel framework encompassing both global and local clock network optimizations to minimize the sum of skew variations across different PVT corners between all sequentially adjacent sink pairs. The global optimization uses linear programming to guide buffer insertion, buffer removal and routing detours. The local optimization is based on machine learning-based predictors of latency change; these are used for iterative optimization with tree surgery, buffer sizing and buffer displacement operators. Our optimization achieves up to 22% total skew variation reduction across multiple testcases implemented in foundry 28nm technology, as compared to a best-practices CTS solution using a leading commercial tool.

Stochastic computing (SC) acts on data encoded by bit-streams, and is an attractive, low-cost and error-tolerant alternative to conventional binary circuits in some important applications such as image processing and communications. We study the use of energy reduction techniques such as voltage or frequency scaling in SC circuits. We show that due to their inherent error-tolerance, SC circuits operate satisfactorily without significant accuracy loss even with aggressive scaling that improves their energy efficiency by orders of magnitude. To find the minimum-energy operating point of an SC circuit, we propose a Markov chain model that allows us to quickly explore the space of operating points. We also investigate opportunities to optimize SC circuits under such aggressive scaling. We find that logical and physical design techniques can be used to significantly expand the already powerful accuracy-energy tradeoff possibilities in SC circuits. Our simulation results show that our optimized SC circuits can tolerate aggressive voltage scaling with no significant SNR degradation after 40% supply voltage reduction (1V to 0.6V), leading to 66% energy saving (20.7pJ to 6.9pJ). Similarly, a 100% frequency boosting (400ps to 200ps) of the optimized circuits leads to no significant SNR degradation for several representative circuits.

In advanced nodes, standard-cell libraries can be developed with different cell heights (e.g., in FinFET technology, corresponding to different numbers of fins). Larger cell heights provide higher drive strengths, but at the cost of larger area and power consumption as well as pin capacitance. Cells with smaller heights are relatively smaller in area, but have weaker drive strengths and are more likely to suffer from routing congestion and pin accessibility issues. Existing design methodologies and tool flows are able to mix cells with different heights at the block level (i.e., each block contains cells of a particular cell height). To our knowledge, no design methodology in the literature mixes cells of different heights in a fine-grained manner. In this work, we propose a novel physical design optimization flow to implement design blocks with mixed cell heights in a fine-grained manner. Our optimization resolves the “chicken-and-egg” loop between floorplan site definition and the optimized choices of cell heights after placement. Comprehending the constraints and costs of mixing cells of different heights (e.g., the “breaker cell” area overheads of row alignment between sub-blocks of 8T and 12T cell rows), our optimization achieves 25% area reduction versus 12T-only implementation while maintaining the same performance, and 20% performance improvement versus 8T-only implementation while maintaining similar total cell area.

Resilient design techniques are used to (i) ensure correct operation under dynamic variations and to (ii) improve design performance (e.g., timing speculation). However, significant overheads (e.g., 16% and 14% energy penalties due to throughput degradation and additional circuits) are incurred by existing resilient design techniques. For instance, resilient designs require additional circuits to detect and correct timing errors. Further, when there is an error, the additional cycles needed to restore a previous correct state degrade throughput, which diminishes the performance benefit of using resilient designs. In this work, we describe an improved methodology for resilient design implementation to minimize the costs of resilience in terms of power, area, and throughput degradation. Our methodology uses two levers: selective-endpoint optimization (i.e., sensitivity-based margin insertion) and clock skew optimization. We integrate the two optimization techniques in an iterative optimization flow which comprehends toggle rate information and the trade-off between cost of resilience and margin on combinational paths. Since the error-detection network can result in up to 9% additional wirelength cost, we also propose a matching-based algorithm for construction of the error-detection network to minimize this resilience overhead. Further, our implementations comprehend the impacts of signoff corners (in particular, hold constraints, and use of typical vs. slow libraries) and process variation, which are typically omitted in previous studies of resilience trade-offs. Our proposed flow achieves energy reductions of up to 21% and 10% compared to a conventional (with only margin used to attain robustness) design and a brute-force implementation (i.e., a typical resilient design, where resilient endpoints are (greedily) instantiated at timing-critical endpoints), respectively. We show that these benefits increase in the context of an adaptive voltage scaling strategy.

In modern system-on-chip implementations, multimode design is commonly used to achieve better circuit performance and power across voltage-scaled, “turbo” and other operating modes. To the best of our knowledge, there is no available systematic analysis or methodology for the selection of associated signoff modes for multimode circuit implementations. In this brief, we observe significant impacts of signoff mode selection on circuit area, power, and performance. For example, incorrect choice of signoff voltages for required overdrive frequencies can incur 12% suboptimality in power or 20% in area. Using the concept of mode dominance as a guideline, we propose a scalable, model-based adaptive search methodology to explore the design space for signoff mode selection. Our proposed methodology is duty cycle-aware in its minimization of lifetime energy. Results show that our proposed methodology provides >8% improvement in performance, for given Vdd, area and power constraints, compared with the traditional “signoff and scale” method. Further, the signoff modes determined by our methods result in <;6% overhead in power compared with the optimal signoff modes.

Resilient design techniques are used to (i) ensure correct operation under dynamic variations; and (ii) improve design performance (e.g., through timing speculation). However, significant overheads (e.g., 17% and 15% energy penalties due to throughput degradation and additional circuits) are incurred by existing resilient design techniques. For instance, resilient designs require additional circuits to detect and correct timing errors. Further, when there is an error, the additional cycles needed to restore a previous correct state degrade throughput, which diminishes the performance benefit of using resilient designs. In this work, we propose a methodology for resilient design implementation to minimize the costs of resilience in terms of power, area and throughput degradation. Our methodology uses two levers: selective-endpoint optimization (i.e., sensitivity-based margin insertion) and clock skew optimization. We integrate the two optimization techniques in an iterative optimization flow which comprehends toggle rate information and the tradeoff between cost of resilience and margin on combinational paths. Our proposed flow achieves energy reductions of up to 19% and 21% compared to a conventional design (with only margin used to attain robustness) and a brute-force implementation, respectively. These benefits increase in the context of an adaptive voltage scaling strategy.

The rapid growth in complexity and diversity of IC designs, design flows and methodologies has resulted in a benchmark-centric culture for evaluation of performance and scalability in physicaldesign algorithm research. Landmark papers in the literature present vertical benchmarks that can be used across multiple design flow stages; artificial benchmarks with characteristics that mimic those of real designs; artificial benchmarks with known optimal solutions; as well as benchmark suites created by major companies from internal designs and/or open-source RTL. However, to our knowledge, there has been no work on horizontal benchmark creation, i.e., the creation of benchmarks that enable maximal, comprehensive assessments across commercial and academic tools at one or more specific design stages. Typically, the creation of horizontal benchmarks is limited by mismatches in data models, netlist formats, technology files, library granularity, etc. across different tools, technologies, and benchmark suites. In this paper, we describe methodology and robust infrastructure for horizontal benchmark extension" that permits maximal leverage of benchmark suites and technologies in "apples-to-apples" assessment of both industry and academic optimizers. We demonstrate horizontal benchmark extensions, and the assessments that are thus enabled, in two well-studied domains: place-and-route (four combinations of academic placers/routers, and two commercial P&R tools) and gate sizing (two academic sizers, and three commercial tools). We also point out several issues and precepts for horizontal benchmark enablement.

In modern SOC implementations, multi-mode design is commonly used to achieve better circuit performance and power across voltage-scaling, “turbo” and other operating modes. Although there are many tools for multi-mode circuit implementation, to our knowledge there is no available systematic analysis or methodology for the selection of associated signoff modes. We observe that the selection of signoff modes has significant impact on circuit area, power and performance. For example, incorrect choice of signoff voltages for required overdrive frequencies can result in a netlist with 15% suboptimality in power or 21% in area. In this paper, we propose a concept of mode dominance which can be used as a guideline for signoff mode selection. Further, we also propose efficient circuit implementation flows to optimize the selection of signoff modes within several distinct use cases. Our results show that our proposed methodology provides 5–7% improvement in performance compared to the traditional “signoff and scale” method. The signoff modes determined by our methods result in only 0.6% overhead in performance and 8% overhead in power after implementation, compared to the optimal signoff modes.