A Review of Bayesian Methods in Electronic Design Automation

The utilization of Bayesian methods has been widely acknowledged as a viable solution for tackling various challenges in electronic integrated circuit (IC) design under stochastic process variation, including circuit performance modeling, yield/failure rate estimation, and circuit optimization. As the post-Moore era brings about new technologies (such as silicon photonics and quantum circuits), many of the associated issues there are similar to those encountered in electronic IC design and can be addressed using Bayesian methods. Motivated by this observation, we present a comprehensive review of Bayesian methods in electronic design automation (EDA). By doing so, we hope to equip researchers and designers with the ability to apply Bayesian methods in solving stochastic problems in electronic circuits and beyond.Comment: 24 pages, a draft version. We welcome comments and feedback, which can be sent to [email protected]

Importance sampling for high speed statistical Monte-Carlo simulations

As transistor dimensions of Static Random AccessMemory (SRAM) become smaller with each new technology generation, they become increasingly susceptible to statistical variations in their parameters. These statistical variations can result in failing memory. SRAM is used as a building block for the construction of large Integrated Circuits (IC). To ensure SRAM does not degrade the yield (fraction of functional devices) of ICs, very low failure probabilities of Pfail = 10-10 are strived for. For instance in SRAMmemory design one aims to get a 0.1% yield loss for 10Mbit memory, which means that 1 in 10 billion cells fails (Pfail = 10-10; this corresponds with an occurrence of -6.4s when dealing with a normal distribution). To simulate such probabilities, traditional Monte-Carlo simulations are not sufficient and more advanced techniques are required. Importance Sampling is a technique that is relatively easy to implement and provides sufficiently accurate results. Importance sampling is a well known technique in statistics to estimate the occurrences of rare events. Rare or extreme events can be associated with dramatic costs, like in finance or because of reasons of safety in environment (dikes, power plants). Recently this technique also received new attention in circuit design. Importance sampling tunes Monte Carlo to the area in parameter space from where the rare events are generated. By this a speed up of several orders can be achieved when compared to standard Monte Carlo methods. We describe the underlying mathematics. Experiments reveal the intrinsic power of the method. The efficiency of the method increases when the dimension of the parameter space increases. The method could be a valuable extension to the statistical capacities of any circuit simulator A Matlab implementation is included in the Appendix

Robust Circuit Design for Low-Voltage VLSI.

Voltage scaling is an effective way to reduce the overall power consumption, but the major challenges in low voltage operations include performance degradation and reliability issues due to PVT variations. This dissertation discusses three key circuit components that are critical in low-voltage VLSI. Level converters must be a reliable interface between two voltage domains, but the reduced on/off-current ratio makes it extremely difficult to achieve robust conversions at low voltages. Two static designs are proposed: LC2 adopts a novel pulsed-operation and modulates its pull-up strength depending on its state. A 3-sigma robustness is guaranteed using a current margin plot; SLC inherently reduces the contention by diode-insertion. Improvements in performance, power, and robustness are measured from 130nm CMOS test chips. SRAM is a major bottleneck in voltage-scaling due to its inherent ratioed-bitcell design. The proposed 7T SRAM alleviates the area overhead incurred by 8T bitcells and provides robust operation down to 0.32V in 180nm CMOS test chips with 3.35fW/bit leakage. Auto-Shut-Off provides a 6.8x READ energy reduction, and its innate Quasi-Static READ has been demonstrated which shows a much improved READ error rate. A use of PMOS Pass-Gate improves the half-select robustness by directly modulating the device strength through bitline voltage. Clocked sequential elements, flip-flops in short, are ubiquitous in today’s digital systems. The proposed S2CFF is static, single-phase, contention-free, and has the same number of devices as in TGFF. It shows a 40% power reduction as well as robust low-voltage operations in fabricated 45nm SOI test chips. Its simple hold-time path and the 3.4x improvement in 3-sigma hold-time is presented. A new on-chip flip-flop testing harness is also proposed, and measured hold-time variations of flip-flops are presented.PhDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111525/1/yejoong_1.pd

Rare Event Probability Learning by Normalizing Flows

A rare event is defined by a low probability of occurrence. Accurate estimation of such small probabilities is of utmost importance across diverse domains. Conventional Monte Carlo methods are inefficient, demanding an exorbitant number of samples to achieve reliable estimates. Inspired by the exact sampling capabilities of normalizing flows, we revisit this challenge and propose normalizing flow assisted importance sampling, termed NOFIS. NOFIS first learns a sequence of proposal distributions associated with predefined nested subset events by minimizing KL divergence losses. Next, it estimates the rare event probability by utilizing importance sampling in conjunction with the last proposal. The efficacy of our NOFIS method is substantiated through comprehensive qualitative visualizations, affirming the optimality of the learned proposal distribution, as well as a series of quantitative experiments encompassing $10$ distinct test cases, which highlight NOFIS's superiority over baseline approaches.Comment: 16 pages, 5 figures, 2 table

Statistical analysis and design of subthreshold operation memories

This thesis presents novel methods based on a combination of well-known statistical techniques for faster estimation of memory yield and their application in the design of energy-efficient subthreshold memories. The emergence of size-constrained Internet-of-Things (IoT) devices and proliferation of the wearable market has brought forward the challenge of achieving the maximum energy efficiency per operation in these battery operated devices. Achieving this sought-after minimum energy operation is possible under sub-threshold operation of the circuit. However, reliable memory operation is currently unattainable at these ultra-low operating voltages because of the memory circuit's vanishing noise margins which shrink further in the presence of random process variations. The statistical methods, presented in this thesis, make the yield optimization of the sub-threshold memories computationally feasible by reducing the SPICE simulation overhead. We present novel modifications to statistical sampling techniques that reduce the SPICE simulation overhead in estimating memory failure probability. These sampling scheme provides 40x reduction in finding most probable failure point and 10x reduction in estimating failure probability using the SPICE simulations compared to the existing proposals. We then provide a novel method to create surrogate models of the memory margins with better extrapolation capability than the traditional regression methods. These models, based on Gaussian process regression, encode the sensitivity of the memory margins with respect to each individual threshold variation source in a one-dimensional kernel. We find that our proposed additive kernel based models have 32% smaller out-of-sample error (that is, better extrapolation capability outside training set) than using the six-dimensional universal kernel like Radial Basis Function (RBF). The thesis also explores the topological modifications to the SRAM bitcell to achieve faster read operation at the sub-threshold operating voltages. We present a ten-transistor SRAM bitcell that achieves 2x faster read operation than the existing ten-transistor sub-threshold SRAM bitcells, while ensuring similar noise margins. The SRAM bitcell provides 70% reduction in dynamic energy at the cost of 42% increase in the leakage energy per read operation. Finally, we investigate the energy efficiency of the eDRAM gain-cells as an alternative to the SRAM bitcells in the size-constrained IoT devices. We find that reducing their write path leakage current is the only way to reduce the read energy at Minimum Energy operation Point (MEP). Further, we study the effect of transistor up-sizing under the presence of threshold voltage variations on the mean MEP read energy by performing statistical analysis based on the ANOVA test of the full-factorial experimental design.Esta tesis presenta nuevos métodos basados en una combinación de técnicas estadísticas conocidas para la estimación rápida del rendimiento de la memoria y su aplicación en el diseño de memorias de energia eficiente de sub-umbral. La aparición de los dispositivos para el Internet de las cosas (IOT) y la proliferación del mercado portátil ha presentado el reto de lograr la máxima eficiencia energética por operación de estos dispositivos operados con baterias. La eficiencia de energía es posible si se considera la operacion por debajo del umbral de los circuitos. Sin embargo, la operación confiable de memoria es actualmente inalcanzable en estos bajos niveles de voltaje debido a márgenes de ruido de fuga del circuito de memoria, los cuales se pueden reducir aún más en presencia de variaciones randomicas de procesos. Los métodos estadísticos, que se presentan en esta tesis, hacen que la optimización del rendimiento de las memorias por debajo del umbral computacionalmente factible mediante la simulación SPICE. Presentamos nuevas modificaciones a las técnicas de muestreo estadístico que reducen la sobrecarga de simulación SPICE en la estimación de la probabilidad de fallo de memoria. Estos esquemas de muestreo proporciona una reducción de 40 veces en la búsqueda de puntos de fallo más probable, y 10 veces la reducción en la estimación de la probabilidad de fallo mediante las simulaciones SPICE en comparación con otras propuestas existentes. A continuación, se proporciona un método novedoso para crear modelos sustitutos de los márgenes de memoria con una mejor capacidad de extrapolación que los métodos tradicionales de regresión. Estos modelos, basados en el proceso de regresión Gaussiano, codifican la sensibilidad de los márgenes de memoria con respecto a cada fuente de variación de umbral individual en un núcleo de una sola dimensión. Los modelos propuestos, basados en kernel aditivos, tienen un error 32% menor que el error out-of-sample (es decir, mejor capacidad de extrapolación fuera del conjunto de entrenamiento) en comparacion con el núcleo universal de seis dimensiones como la función de base radial (RBF). La tesis también explora las modificaciones topológicas a la celda binaria SRAM para alcanzar velocidades de lectura mas rapidas dentro en el contexto de operaciones en el umbral de tensiones de funcionamiento. Presentamos una celda binaria SRAM de diez transistores que consigue aumentar en 2 veces la operación de lectura en comparacion con las celdas sub-umbral de SRAM de diez transistores existentes, garantizando al mismo tiempo los márgenes de ruido similares. La celda binaria SRAM proporciona una reducción del 70% en energía dinámica a costa del aumento del 42% en la energía de fuga por las operaciones de lectura. Por último, se investiga la eficiencia energética de las células de ganancia eDRAM como una alternativa a los bitcells SRAM en los dispositivos de tamaño limitado IOT. Encontramos que la reducción de la corriente de fuga en el path de escritura es la única manera de reducir la energía de lectura en el Punto Mínimo de Energía (MEP). Además, se estudia el efecto del transistor de dimensionamiento en virtud de la presencia de variaciones de voltaje de umbral en la media de energia de lecture MEP mediante el análisis estadístico basado en la prueba de ANOVA del diseño experimental factorial completo.Postprint (published version

Statistical Yield Analysis and Design for Nanometer VLSI

Process variability is the pivotal factor impacting the design of high yield integrated circuits and systems in deep sub-micron CMOS technologies. The electrical and physical properties of transistors and interconnects, the building blocks of integrated circuits, are prone to significant variations that directly impact the performance and power consumption of the fabricated devices, severely impacting the manufacturing yield. However, the large number of the transistors on a single chip adds even more challenges for the analysis of the variation effects, a critical task in diagnosing the cause of failure and designing for yield. Reliable and efficient statistical analysis methodologies in various design phases are key to predict the yield before entering such an expensive fabrication process. In this thesis, the impacts of process variations are examined at three different levels: device, circuit, and micro-architecture. The variation models are provided for each level of abstraction, and new methodologies are proposed for efficient statistical analysis and design under variation. At the circuit level, the variability analysis of three crucial sub-blocks of today's system-on-chips, namely, digital circuits, memory cells, and analog blocks, are targeted. The accurate and efficient yield analysis of circuits is recognized as an extremely challenging task within the electronic design automation community. The large scale of the digital circuits, the extremely high yield requirement for memory cells, and the time-consuming analog circuit simulation are major concerns in the development of any statistical analysis technique. In this thesis, several sampling-based methods have been proposed for these three types of circuits to significantly improve the run-time of the traditional Monte Carlo method, without compromising accuracy. The proposed sampling-based yield analysis methods benefit from the very appealing feature of the MC method, that is, the capability to consider any complex circuit model. However, through the use and engineering of advanced variance reduction and sampling methods, ultra-fast yield estimation solutions are provided for different types of VLSI circuits. Such methods include control variate, importance sampling, correlation-controlled Latin Hypercube Sampling, and Quasi Monte Carlo. At the device level, a methodology is proposed which introduces a variation-aware design perspective for designing MOS devices in aggressively scaled geometries. The method introduces a yield measure at the device level which targets the saturation and leakage currents of an MOS transistor. A statistical method is developed to optimize the advanced doping profiles and geometry features of a device for achieving a maximum device-level yield. Finally, a statistical thermal analysis framework is proposed. It accounts for the process and thermal variations simultaneously, at the micro-architectural level. The analyzer is developed, based on the fact that the process variations lead to uncertain leakage power sources, so that the thermal profile, itself, would have a probabilistic nature. Therefore, by a co-process-thermal-leakage analysis, a more reliable full-chip statistical leakage power yield is calculated

Power Management and SRAM for Energy-Autonomous and Low-Power Systems

We demonstrate the two first-known, complete, self-powered millimeter-scale computer systems. These microsystems achieve zero-net-energy operation using solar energy harvesting and ultra-low-power circuits. A medical implant for monitoring intraocular pressure (IOP) is presented as part of a treatment for glaucoma. The 1.5mm3 IOP monitor is easily implantable because of its small size and measures IOP with 0.5mmHg accuracy. It wirelessly transmits data to an external wand while consuming 4.7nJ/bit. This provides rapid feedback about treatment efficacies to decrease physician response time and potentially prevent unnecessary vision loss. A nearly-perpetual temperature sensor is presented that processes data using a 2.1μW near-threshold ARM°R Cortex- M3TM μP that provides a widely-used and trusted programming platform. Energy harvesting and power management techniques for these two microsystems enable energy-autonomous operation. The IOP monitor harvests 80nW of solar power while consuming only 5.3nW, extending lifetime indefinitely. This allows the device to provide medical information for extended periods of time, giving doctors time to converge upon the best glaucoma treatment. The temperature sensor uses on-demand power delivery to improve low-load dc-dc voltage conversion efficiency by 4.75x. It also performs linear regulation to deliver power with low noise, improved load regulation, and tight line regulation. Low-power high-throughput SRAM techniques help millimeter-scale microsystems meet stringent power budgets. VDD scaling in memory decreases energy per access, but also decreases stability margins. These margins can be improved using sizing, VTH selection, and assist circuits, as well as new bitcell designs. Adaptive Crosshairs modulation of SRAM power supplies fixes 70% of parametric failures. Half-differential SRAM design improves stability, reducing VMIN by 72mV. The circuit techniques for energy autonomy presented in this dissertation enable millimeter-scale microsystems for medical implants, such as blood pressure and glucose sensors, as well as non-medical applications, such as supply chain and infrastructure monitoring. These pervasive sensors represent the continuation of Bell’s Law, which accurately traces the evolution of computers as they become smaller, more numerous, and more powerful. The development of millimeter-scale massively-deployed ubiquitous computers ensures the continued expansion and profitability of the semiconductor industry. NanoWatt circuit techniques will allow us to meet this next frontier in IC design.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86387/1/grgkchen_1.pd

Statistical Performance Modeling of SRAMs

Yield analysis is a critical step in memory designs considering a variety of performance constraints. Traditional circuit level Monte-Carlo simulations for yield estimation of Static Random Access Memory (SRAM) cell is quite time consuming due to their characteristic of low failure rate, while statistical method of yield sensitivity analysis is meaningful for its high efficiency. This thesis proposes a novel statistical model to conduct yield sensitivity prediction on SRAM cells at the simulation level, which excels regular circuit simulations in a significant runtime speedup. Based on the theory of Kriging method that is widely used in geostatistics, we develop a series of statistical model building and updating strategies to obtain satisfactory accuracy and efficiency in SRAM yield sensitivity analysis. Generally, this model applies to the yield and sensitivity evaluation with varying design parameters, under the constraints of most SRAM performance metric. Moreover, it is potentially suitable for any designated distribution of the process variation regardless of the sampling method

Cross-Layer Resiliency Modeling and Optimization: A Device to Circuit Approach

The never ending demand for higher performance and lower power consumption pushes the VLSI industry to further scale the technology down. However, further downscaling of technology at nano-scale leads to major challenges. Reduced reliability is one of them, arising from multiple sources e.g. runtime variations, process variation, and transient errors. The objective of this thesis is to tackle unreliability with a cross layer approach from device up to circuit level

Low Voltage Circuit Design Techniques for Cubic-Millimeter Computing.

Cubic-millimeter computers complete with microprocessors, memories, sensors, radios and power sources are becomingly increasingly viable. Power consumption is one of the last remaining barriers to cubic-millimeter computing and is the subject of this work. In particular, this work focuses on minimizing power consumption in digital circuits using low voltage operation. Chapter 2 includes a general discussion of low voltage circuit behavior, specifically that at subthreshold voltages. In Chapter 3, the implications of transistor scaling on subthreshold circuits are considered. It is shown that the slow scaling of gate oxide relative to the device channel length leads to a 60% reduction in Ion/Ioff between the 90nm and 32nm nodes, which results in sub-optimal static noise margins, delay, and power consumption. It is also shown that simple modifications to gate length and doping can alleviate some of these problems. Three low voltage test-chips are discussed for the remainder of this work. The first test-chip implements the Subliminal Processor (Chapter 4), a sub-200mV 8-bit microprocessor fabricated in a 0.13µm technology. Measurements first show that the Subliminal Processor consumes only 3.5pJ/instruction at Vdd=350mV. Measurements of 20 dies then reveal that proper body biasing can eliminate performance variations and reduce mean energy substantially at low voltage. Finally, measurements are used to explore the effectiveness of body biasing, voltage scaling, and various gate sizing techniques for improving speed. The second test-chip implements the Phoenix Processor (Chapter 5), a low voltage 8-bit microprocessor optimized for minimum power operation in standby mode. The Phoenix Processor was fabricated in a 0.18µm technology in an area of only 915x915µm2. The aggressive standby mode strategy used in the Phoenix Processor is discussed thoroughly. Measurements at Vdd=0.5V show that the test-chip consumes 226nW in active mode and only 35.4pW in standby mode, making an on-chip battery a viable option. Finally, the third test-chip implements a low voltage image sensor (Chapter 6). A 128x128 image sensor array was fabricated in a 0.13µm technology. Test-chip measurements reveal that operation below 0.6V is possible with power consumption of only 1.9µW at 0.6V. Extensive characterization is presented with specific emphasis on noise characteristics and power consumption.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/62233/1/hansons_1.pd