Design for Reliability and Low Power in Emerging Technologies

Die fortlaufende Verkleinerung von Transistor-Strukturgrößen ist einer der wichtigsten Antreiber für das Wachstum in der Halbleitertechnologiebranche. Seit Jahrzehnten erhöhen sich sowohl Integrationsdichte als auch Komplexität von Schaltkreisen und zeigen damit einen fortlaufenden Trend, der sich über alle modernen Fertigungsgrößen erstreckt. Bislang ging das Verkleinern von Transistoren mit einer Verringerung der Versorgungsspannung einher, was zu einer Reduktion der Leistungsaufnahme führte und damit eine gleichbleibenden Leistungsdichte sicherstellte. Doch mit dem Beginn von Strukturgrößen im Nanometerbreich verlangsamte sich die fortlaufende Skalierung. Viele Schwierigkeiten, sowie das Erreichen von physikalischen Grenzen in der Fertigung und Nicht-Idealitäten beim Skalieren der Versorgungsspannung, führten zu einer Zunahme der Leistungsdichte und, damit einhergehend, zu erschwerten Problemen bei der Sicherstellung der Zuverlässigkeit. Dazu zählen, unter anderem, Alterungseffekte in Transistoren sowie übermäßige Hitzeentwicklung, nicht zuletzt durch stärkeres Auftreten von Selbsterhitzungseffekten innerhalb der Transistoren. Damit solche Probleme die Zuverlässigkeit eines Schaltkreises nicht gefährden, werden die internen Signallaufzeiten üblicherweise sehr pessimistisch kalkuliert. Durch den so entstandenen zeitlichen Sicherheitsabstand wird die korrekte Funktionalität des Schaltkreises sichergestellt, allerdings auf Kosten der Performance. Alternativ kann die Zuverlässigkeit des Schaltkreises auch durch andere Techniken erhöht werden, wie zum Beispiel durch Null-Temperatur-Koeffizienten oder Approximate Computing. Wenngleich diese Techniken einen Großteil des üblichen zeitlichen Sicherheitsabstandes einsparen können, bergen sie dennoch weitere Konsequenzen und Kompromisse. Bleibende Herausforderungen bei der Skalierung von CMOS Technologien führen außerdem zu einem verstärkten Fokus auf vielversprechende Zukunftstechnologien. Ein Beispiel dafür ist der Negative Capacitance Field-Effect Transistor (NCFET), der eine beachtenswerte Leistungssteigerung gegenüber herkömmlichen FinFET Transistoren aufweist und diese in Zukunft ersetzen könnte. Des Weiteren setzen Entwickler von Schaltkreisen vermehrt auf komplexe, parallele Strukturen statt auf höhere Taktfrequenzen. Diese komplexen Modelle benötigen moderne Power-Management Techniken in allen Aspekten des Designs. Mit dem Auftreten von neuartigen Transistortechnologien (wie zum Beispiel NCFET) müssen diese Power-Management Techniken neu bewertet werden, da sich Abhängigkeiten und Verhältnismäßigkeiten ändern. Diese Arbeit präsentiert neue Herangehensweisen, sowohl zur Analyse als auch zur Modellierung der Zuverlässigkeit von Schaltkreisen, um zuvor genannte Herausforderungen auf mehreren Designebenen anzugehen. Diese Herangehensweisen unterteilen sich in konventionelle Techniken ((a), (b), (c) und (d)) und unkonventionelle Techniken ((e) und (f)), wie folgt: $\textbf{(a)}$ Analyse von Leistungszunahmen in Zusammenhang mit der Maximierung von Leistungseffizienz beim Betrieb nahe der Transistor Schwellspannung, insbesondere am optimalen Leistungspunkt. Das genaue Ermitteln eines solchen optimalen Leistungspunkts ist eine besondere Herausforderung bei Multicore Designs, da dieser sich mit den jeweiligen Optimierungszielsetzungen und der Arbeitsbelastung verschiebt. $\textbf{(b)}$ Aufzeigen versteckter Interdependenzen zwischen Alterungseffekten bei Transistoren und Schwankungen in der Versorgungsspannung durch „IR-drops“. Eine neuartige Technik wird vorgestellt, die sowohl Über- als auch Unterschätzungen bei der Ermittlung des zeitlichen Sicherheitsabstands vermeidet und folglich den kleinsten, dennoch ausreichenden Sicherheitsabstand ermittelt. $\textbf{(c)}$ Eindämmung von Alterungseffekten bei Transistoren durch „Graceful Approximation“, eine Technik zur Erhöhung der Taktfrequenz bei Bedarf. Der durch Alterungseffekte bedingte zeitlich Sicherheitsabstand wird durch Approximate Computing Techniken ersetzt. Des Weiteren wird Quantisierung verwendet um ausreichend Genauigkeit bei den Berechnungen zu gewährleisten. $\textbf{(d)}$ Eindämmung von temperaturabhängigen Verschlechterungen der Signallaufzeit durch den Betrieb nahe des Null-Temperatur Koeffizienten (N-ZTC). Der Betrieb bei N-ZTC minimiert temperaturbedingte Abweichungen der Performance und der Leistungsaufnahme. Qualitative und quantitative Vergleiche gegenüber dem traditionellen zeitlichen Sicherheitsabstand werden präsentiert. $\textbf{(e)}$ Modellierung von Power-Management Techniken für NCFET-basierte Prozessoren. Die NCFET Technologie hat einzigartige Eigenschaften, durch die herkömmliche Verfahren zur Spannungs- und Frequenzskalierungen zur Laufzeit (DVS/DVFS) suboptimale Ergebnisse erzielen. Dies erfordert NCFET-spezifische Power-Management Techniken, die in dieser Arbeit vorgestellt werden. $\textbf{(f)}$ Vorstellung eines neuartigen heterogenen Multicore Designs in NCFET Technologie. Das Design beinhaltet identische Kerne; Heterogenität entsteht durch die Anwendung der individuellen, optimalen Konfiguration der Kerne. Amdahls Gesetz wird erweitert, um neue system- und anwendungsspezifische Parameter abzudecken und die Vorzüge des neuen Designs aufzuzeigen. Die Auswertungen der vorgestellten Techniken werden mithilfe von Implementierungen und Simulationen auf Schaltkreisebene (gate-level) durchgeführt. Des Weiteren werden Simulatoren auf Systemebene (system-level) verwendet, um Multicore Designs zu implementieren und zu simulieren. Zur Validierung und Bewertung der Effektivität gegenüber dem Stand der Technik werden analytische, gate-level und system-level Simulationen herangezogen, die sowohl synthetische als auch reale Anwendungen betrachten

Polarity Control at Runtime:from Circuit Concept to Device Fabrication

Semiconductor device research for digital circuit design is currently facing increasing challenges to enhance miniaturization and performance. A huge economic push and the interest in novel applications are stimulating the development of new pathways to overcome physical limitations affecting conventional CMOS technology. Here, we propose a novel Schottky barrier device concept based on electrostatic polarity control. Specifically, this device can behave as p- or n-type by simply changing an electric input bias. This device combines More-than-Moore and Beyond CMOS elements to create an efficient technology with a viable path to Very Large Scale Integration (VLSI). This thesis proposes a device/circuit/architecture co-optimization methodology, where aspects of device technology to logic circuit and system design are considered. At device level, a full CMOS compatible fabrication process is presented. In particular, devices are demonstrated using vertically stacked, top-down fabricated silicon nanowires with gate-all-around electrode geometry. Source and drain contacts are implemented using nickel silicide to provide quasi-symmetric conduction of either electrons or holes, depending on the mode of operation. Electrical measurements confirm excellent performance, showing Ion/Ioff > 10^7 and subthreshold slopes approaching the thermal limit, SS ~ 60mV/dec (~ 63mV/dec) for n(p)-type operation in the same physical device. Moreover, the shown devices behave as p-type for a polarization bias (polarity gate voltage, Vpg) of 0V, and n-type for a Vpg = 1V, confirming their compatibility with multi-level static logic circuit design. At logic gate level, two- and four-transistor logic gates are fabricated and tested. In particular, the first fully functional, two-transistor XOR logic gate is demonstrated through electrical characterization, confirming that polarity control can enable more compact logic gate design with respect to conventional CMOS. Furthermore, we show for the first time fabricated four- transistors logic gates that can be reconfigured as NAND or XOR only depending on their external connectivity. In this case, logic gates with full swing output range are experimentally demonstrated. Finally, single device and mixed-mode TCAD simulation results show that lower Vth and more optimized polarization ranges can be expected in scaled devices implementing strain or high-k technologies. At circuit and system level, a full semi-custom logic circuit design tool flow was defined and configured. Using this flow, novel logic libraries based on standard cells or regular gate fabrics were compared with standard CMOS. In this respect, results were shown in comparison to CMOS, including a 40% normalized area-delay product reduction for the analyzed standard cell libraries, and improvements of over 2× in terms of normalized delay for regular Controlled Polarity (CP)-based cells in the context of Structured ASICs. These results, in turn, confirm the interest in further developing and optimizing CP devices, as promising candidates for future digital circuit technology

Exploiting heterogeneity in Chip-Multiprocessor Design

In the past decade, semiconductor manufacturers are persistent in building faster and smaller transistors in order to boost the processor performance as projected by Moore’s Law. Recently, as we enter the deep submicron regime, continuing the same processor development pace becomes an increasingly difficult issue due to constraints on power, temperature, and the scalability of transistors. To overcome these challenges, researchers propose several innovations at both architecture and device levels that are able to partially solve the problems. These diversities in processor architecture and manufacturing materials provide solutions to continuing Moore’s Law by effectively exploiting the heterogeneity, however, they also introduce a set of unprecedented challenges that have been rarely addressed in prior works. In this dissertation, we present a series of in-depth studies to comprehensively investigate the design and optimization of future multi-core and many-core platforms through exploiting heteroge-neities. First, we explore a large design space of heterogeneous chip multiprocessors by exploiting the architectural- and device-level heterogeneities, aiming to identify the optimal design patterns leading to attractive energy- and cost-efficiencies in the pre-silicon stage. After this high-level study, we pay specific attention to the architectural asymmetry, aiming at developing a heterogeneity-aware task scheduler to optimize the energy-efficiency on a given single-ISA heterogeneous multi-processor. An advanced statistical tool is employed to facilitate the algorithm development. In the third study, we shift our concentration to the device-level heterogeneity and propose to effectively leverage the advantages provided by different materials to solve the increasingly important reliability issue for future processors

Heterogeneous Chip Multiprocessor: Data Representation, Mixed-Signal Processing Tiles, and System Design

With the emergence of big data, the need for more computationally intensive processors that can handle the increased processing demand has risen. Conventional computing paradigms based on the Von Neumann model that separates computational and memory structures have become outdated and less efficient for this increased demand. As the speed and memory density of processors have increased significantly over the years, these models of computing, which rely on a constant stream of data between the processor and memory, see less gains due to finite bandwidth and latency. Moreover, in the presence of extreme scaling, these conventional systems, implemented in submicron integrated circuits, have become even more susceptible to process variability, static leakage current, and more. In this work, alternative paradigms, predicated on distributive processing with robust data representation and mixed-signal processing tiles, are explored for constructing more efficient and scalable computing systems in application specific integrated circuits (ASICs). The focus of this dissertation work has been on heterogeneous chip multi-processor (CMP) design and optimization across different levels of abstraction. On the level of data representation, a different modality of representation based on random pulse density modulation (RPDM) coding is explored for more efficient processing using stochastic computation. On the level of circuit description, mixed-signal integrated circuits that exploit charge-based computing for energy efficient fixed point arithmetic are designed. Consequently, 8 different chips that test and showcase these circuits were fabricated in submicron CMOS processes. Finally, on the architectural level of description, a compact instruction-set processor and controller that facilitates distributive computing on System-On-Chips (SoCs) is designed. In addition to this, a robust bufferless network architecture is designed with a network simulator, and I/O cells are designed for SoCs. The culmination of this thesis work has led to the design and fabrication of a heterogeneous chip multi- processor prototype comprised of over 12,000 VVM cores, warp/dewarp processors, cache, and additional processors, which can be applied towards energy efficient large-scale data processing

Robustness Analysis of Controllable-Polarity Silicon Nanowire Devices and Circuits

Substantial downscaling of the feature size in current CMOS technology has confronted digital designers with serious challenges including short channel effect and high amount of leakage power. To address these problems, emerging nano-devices, e.g., Silicon NanoWire FET (SiNWFET), is being introduced by the research community. These devices keep on pursuing Mooreâs Law by improving channel electrostatic controllability, thereby reducing the Off âstate leakage current. In addition to these improvements, recent developments introduced devices with enhanced capabilities, such as Controllable-Polarity (CP) SiNWFETs, which make them very interesting for compact logic cell and arithmetic circuits. At advanced technology nodes, the amount of physical controls, during the fabrication process of nanometer devices, cannot be precisely determined because of technology fluctuations. Consequently, the structural parameters of fabricated circuits can be significantly different from their nominal values. Moreover, giving an a-priori conclusion on the variability of advanced technologies for emerging nanoscale devices, is a difficult task and novel estimation methodologies are required. This is a necessity to guarantee the performance and the reliability of future integrated circuits. Statistical analysis of process variation requires a great amount of numerical data for nanoscale devices. This introduces a serious challenge for variability analysis of emerging technologies due to the lack of fast simulation models. One the one hand, the development of accurate compact models entails numerous tests and costly measurements on fabricated devices. On the other hand, Technology Computer Aided Design (TCAD) simulations, that can provide precise information about devices behavior, are too slow to timely generate large enough data set. In this research, a fast methodology for generating data set for variability analysis is introduced. This methodology combines the TCAD simulations with a learning algorithm to alleviate the time complexity of data set generation. Another formidable challenge for variability analysis of the large circuits is growing number of process variation sources. Utilizing parameterized models is becoming a necessity for chip design and verification. However, the high dimensionality of parameter space imposes a serious problem. Unfortunately, the available dimensionality reduction techniques cannot be employed for three main reasons of lack of accuracy, distribution dependency of the data points, and finally incompatibility with device and circuit simulators. We propose a novel technique of parameter selection for modeling process and performance variation. The proposed technique efficiently addresses the aforementioned problems. Appropriate testing, to capture manufacturing defects, plays an important role on the quality of integrated circuits. Compared to conventional CMOS, emerging nano-devices such as CP-SiNWFETs have different fabrication process steps. In this case, current fault models must be extended for defect detection. In this research, we extracted the possible fabrication defects, and then proposed a fault model for this technology. We also provided a couple of test methods for detecting the manufacturing defects in various types of CP-SiNWFET logic gates. Finally, we used the obtained fault model to build fault tolerant arithmetic circuits with a bunch of superior properties compared to their competitors

Rapid SoC Design: On Architectures, Methodologies and Frameworks

Modern applications like machine learning, autonomous vehicles, and 5G networking require an order of magnitude boost in processing capability. For several decades, chip designers have relied on Moore’s Law - the doubling of transistor count every two years to deliver improved performance, higher energy efficiency, and an increase in transistor density. With the end of Dennard’s scaling and a slowdown in Moore’s Law, system architects have developed several techniques to deliver on the traditional performance and power improvements we have come to expect. More recently, chip designers have turned towards heterogeneous systems comprised of more specialized processing units to buttress the traditional processing units. These specialized units improve the overall performance, power, and area (PPA) metrics across a wide variety of workloads and applications. While the GPU serves as a classical example, accelerators for machine learning, approximate computing, graph processing, and database applications have become commonplace. This has led to an exponential growth in the variety (and count) of these compute units found in modern embedded and high-performance computing platforms. The various techniques adopted to combat the slowing of Moore’s Law directly translates to an increase in complexity for modern system-on-chips (SoCs). This increase in complexity in turn leads to an increase in design effort and validation time for hardware and the accompanying software stacks. This is further aggravated by fabrication challenges (photo-lithography, tooling, and yield) faced at advanced technology nodes (below 28nm). The inherent complexity in modern SoCs translates into increased costs and time-to-market delays. This holds true across the spectrum, from mobile/handheld processors to high-performance data-center appliances. This dissertation presents several techniques to address the challenges of rapidly birthing complex SoCs. The first part of this dissertation focuses on foundations and architectures that aid in rapid SoC design. It presents a variety of architectural techniques that were developed and leveraged to rapidly construct complex SoCs at advanced process nodes. The next part of the dissertation focuses on the gap between a completed design model (in RTL form) and its physical manifestation (a GDS file that will be sent to the foundry for fabrication). It presents methodologies and a workflow for rapidly walking a design through to completion at arbitrary technology nodes. It also presents progress on creating tools and a flow that is entirely dependent on open-source tools. The last part presents a framework that not only speeds up the integration of a hardware accelerator into an SoC ecosystem, but emphasizes software adoption and usability.PHDElectrical and Computer EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168119/1/ajayi_1.pd

Integrated Circuits Parasitic Capacitance Extraction Using Machine Learning and its Application to Layout Optimization

The impact of parasitic elements on the overall circuit performance keeps increasing from one technology generation to the next. In advanced process nodes, the parasitic effects dominate the overall circuit performance. As a result, the accuracy requirements of parasitic extraction processes significantly increased, especially for parasitic capacitance extraction. Existing parasitic capacitance extraction tools face many challenges to cope with such new accuracy requirements that are set by semiconductor foundries (\u3c 5% error). Although field-solver methods can meet such requirements, they are very slow and have a limited capacity. The other alternative is the rule-based parasitic capacitance extraction methods, which are faster and have a high capacity; however, they cannot consistently provide good accuracy as they use a pre-characterized library of capacitance formulas that cover a limited number of layout patterns. On the other hand, the new parasitic extraction accuracy requirements also added more challenges on existing parasitic-aware routing optimization methods, where simplified parasitic models are used to optimize layouts. This dissertation provides new solutions for interconnect parasitic capacitance extraction and parasitic-aware routing optimization methodologies in order to cope with the new accuracy requirements of advanced process nodes as follows. First, machine learning compact models are developed in rule-based extractors to predict parasitic capacitances of cross-section layout patterns efficiently. The developed models mitigate the problems of the pre-characterized library approach, where each compact model is designed to extract parasitic capacitances of cross-sections of arbitrary distributed metal polygons that belong to a specific set of metal layers (i.e., layer combination) efficiently. Therefore, the number of covered layout patterns significantly increased. Second, machine learning compact models are developed to predict parasitic capacitances of middle-end-of-line (MEOL) layers around FINFETs and MOSFETs. Each compact model extracts parasitic capacitances of 3D MEOL patterns of a specific device type regardless of its metal polygons distribution. Therefore, the developed MEOL models can replace field-solvers in extracting MEOL patterns. Third, a novel accuracy-based hybrid parasitic capacitance extraction method is developed. The proposed hybrid flow divides a layout into windows and extracts the parasitic capacitances of each window using one of three parasitic capacitance extraction methods that include: 1) rule-based; 2) novel deep-neural-networks-based; and 3) field-solver methods. This hybrid methodology uses neural-networks classifiers to determine an appropriate extraction method for each window. Moreover, as an intermediate parasitic capacitance extraction method between rule-based and field-solver methods, a novel deep-neural-networks-based extraction method is developed. This intermediate level of accuracy and speed is needed since using only rule-based and field-solver methods (for hybrid extraction) results in using field-solver most of the time for any required high accuracy extraction. Eventually, a parasitic-aware layout routing optimization and analysis methodology is implemented based on an incremental parasitic extraction and a fast optimization methodology. Unlike existing flows that do not provide a mechanism to analyze the impact of modifying layout geometries on a circuit performance, the proposed methodology provides novel sensitivity circuit models to analyze the integrity of signals in layout routes. Such circuit models are based on an accurate matrix circuit representation, a cost function, and an accurate parasitic sensitivity extraction. The circuit models identify critical parasitic elements along with the corresponding layout geometries in a certain route, where they measure the sensitivity of a route’s performance to corresponding layout geometries very fast. Moreover, the proposed methodology uses a nonlinear programming technique to optimize problematic routes with pre-determined degrees of freedom using the proposed circuit models. Furthermore, it uses a novel incremental parasitic extraction method to extract parasitic elements of modified geometries efficiently, where the incremental extraction is used as a part of the routing optimization process to improve the optimization runtime and increase the optimization accuracy

Automated Hardware Prototyping for 3D Network on Chips

Vor mehr als 50 Jahren stellte Intel® Mitbegründer Gordon Moore eine Prognose zum Entwicklungsprozess der Transistortechnologie auf. Er prognostizierte, dass sich die Zahl der Transistoren in integrierten Schaltungen alle zwei Jahre verdoppeln wird. Seine Aussage ist immer noch gültig, aber ein Ende von Moores Gesetz ist in Sicht. Mit dem Ende von Moore’s Gesetz müssen neue Aspekte untersucht werden, um weiterhin die Leistung von integrierten Schaltungen zu steigern. Zwei mögliche Ansätze für "More than Moore” sind 3D-Integrationsverfahren und heterogene Systeme. Gleichzeitig entwickelt sich ein Trend hin zu Multi-Core Prozessoren, basierend auf Networks on chips (NoCs). Neben dem Ende des Mooreschen Gesetzes ergeben sich bei immer kleiner werdenden Technologiegrößen, vor allem jenseits der 60 nm, neue Herausforderungen. Eine Schwierigkeit ist die Wärmeableitung in großskalierten integrierten Schaltkreisen und die daraus resultierende Überhitzung des Chips. Um diesem Problem in modernen Multi-Core Architekturen zu begegnen, muss auch die Verlustleistung der Netzwerkressourcen stark reduziert werden. Diese Arbeit umfasst eine durch Hardware gesteuerte Kombination aus Frequenzskalierung und Power Gating für 3D On-Chip Netzwerke, einschließlich eines FPGA Prototypen. Dafür wurde ein Takt-synchrones 2D Netzwerk auf ein dreidimensionales asynchrones Netzwerk mit mehreren Frequenzbereichen erweitert. Zusätzlich wurde ein skalierbares Online-Power-Management System mit geringem Ressourcenaufwand entwickelt. Die Verifikation neuer Hardwarekomponenten ist einer der zeitaufwendigsten Schritte im Entwicklungsprozess hochintegrierter digitaler Schaltkreise. Um diese Aufgabe zu beschleunigen und um eine parallele Softwareentwicklung zu ermöglichen, wurde im Rahmen dieser Arbeit ein automatisiertes und benutzerfreundliches Tool für den Entwurf neuer Hardware Projekte entwickelt. Eine grafische Benutzeroberfläche zum Erstellen des gesamten Designablaufs, vom Erstellen der Architektur, Parameter Deklaration, Simulation, Synthese und Test ist Teil dieses Werkzeugs. Zudem stellt die Größe der Architektur für die Erstellung eines Prototypen eine besondere Herausforderung dar. Frühere Arbeiten haben es versäumt, eine schnelles und unkompliziertes Prototyping, insbesondere von Architekturen mit mehr als 50 Prozessorkernen, zu realisieren. Diese Arbeit umfasst eine Design Space Exploration und FPGA-basierte Prototypen von verschiedenen 3D-NoC Implementierungen mit mehr als 80 Prozessoren

Multi-objective Digital VLSI Design Optimisation

Modern VLSI design's complexity and density has been exponentially increasing over the past 50 years and recently reached a stage within its development, allowing heterogeneous, many-core systems and numerous functions to be integrated into a tiny silicon die. These advancements have revealed intrinsic physical limits of process technologies in advanced silicon technology nodes. Designers and EDA vendors have to handle these challenges which may otherwise result in inferior design quality, even failures, and lower design yields under time-to-market pressure. Multiple or many design objectives and constraints are emerging during the design process and often need to be dealt with simultaneously. Multi-objective evolutionary algorithms show flexible capabilities in maintaining multiple variable components and factors in uncertain environments. The VLSI design process involves a large number of available parameters both from designs and EDA tools. This provides many potential optimisation avenues where evolutionary algorithms can excel. This PhD work investigates the application of evolutionary techniques for digital VLSI design optimisation. Automated multi-objective optimisation frameworks, compatible with industrial design flows and foundry technologies, are proposed to improve solution performance, expand feasible design space, and handle complex physical floorplan constraints through tuning designs at gate-level. Methodologies for enriching standard cell libraries regarding drive strength are also introduced to cooperate with multi-objective optimisation frameworks, e.g., subsequent hill-climbing, providing a richer pool of solutions optimised for different trade-offs. The experiments of this thesis demonstrate that multi-objective evolutionary algorithms, derived from biological inspirations, can assist the digital VLSI design process, in an industrial design context, to more efficiently search for well-balanced trade-off solutions as well as optimised design space coverage. The expanded drive granularity of standard cells can push the performance of silicon technologies with offering improved solutions regarding critical objectives. The achieved optimisation results can better deliver trade-off solutions regarding power, performance and area metrics than using standard EDA tools alone. This has been not only shown for a single circuit solution but also covered the entire standard-tool-produced design space