HIGH-PERFORMANCE SPECTRAL METHODS FOR COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS

Recent research shows that by leveraging the key spectral properties of eigenvalues and eigenvectors of graph Laplacians, more efficient algorithms can be developed for tackling many graph-related computing tasks. In this dissertation, spectral methods are utilized for achieving faster algorithms in the applications of very-large-scale integration (VLSI) computer-aided design (CAD) First, a scalable algorithmic framework is proposed for effective-resistance preserving spectral reduction of large undirected graphs. The proposed method allows computing much smaller graphs while preserving the key spectral (structural) properties of the original graph. Our framework is built upon the following three key components: a spectrum-preserving node aggregation and reduction scheme, a spectral graph sparsification framework with iterative edge weight scaling, as well as effective-resistance preserving post-scaling and iterative solution refinement schemes. We show that the resultant spectrally-reduced graphs can robustly preserve the first few nontrivial eigenvalues and eigenvectors of the original graph Laplacian and thus allow for developing highly-scalable spectral graph partitioning and circuit simulation algorithms. Based on the framework of the spectral graph reduction, a Sparsified graph-theoretic Algebraic Multigrid (SAMG) is proposed for solving large Symmetric Diagonally Dominant (SDD) matrices. The proposed SAMG framework allows efficient construction of nearly-linear sized graph Laplacians for coarse-level problems while maintaining good spectral approximation during the AMG setup phase by leveraging a scalable spectral graph sparsification engine. Our experimental results show that the proposed method can offer more scalable performance than existing graph-theoretic AMG solvers for solving large SDD matrices in integrated circuit (IC) simulations, 3D-IC thermal analysis, image processing, finite element analysis as well as data mining and machine learning applications. Finally, the spectral methods are applied to power grid and thermal integrity verification applications. This dissertation introduces a vectorless power grid and thermal integrity verification framework that allows computing worst-case voltage drop or thermal profiles across the entire chip under a set of local and global workload (power density) constraints. To address the computational challenges introduced by the large 3D mesh-structured thermal grids, we apply the spectral graph reduction approach for highly-scalable vectorless thermal (or power grids) verification of large chip designs. The effectiveness and efficiency of our approach have been demonstrated through extensive experiments

Electrical and Computer Engineering Annual Report 2017

Early Career Awards Faculty Directory Faculty Highlights Special Report: Mobility at Michigan Tech Faculty Publications Staff Profile & Directory Graduate Student Research Accelerated Master\u27s Degree Graduate Student Awards & Degrees Undergraduate Highlights Senior Design Enterprise Undergraduate Student Awards & Advisory Grants & Contracts Departmental Statistics A Pioneer\u27s Storyhttps://digitalcommons.mtu.edu/ece-annualreports/1001/thumbnail.jp

Parametric Yield of VLSI Systems under Variability: Analysis and Design Solutions

Variability has become one of the vital challenges that the designers of integrated circuits encounter. variability becomes increasingly important. Imperfect manufacturing process manifest itself as variations in the design parameters. These variations and those in the operating environment of VLSI circuits result in unexpected changes in the timing, power, and reliability of the circuits. With scaling transistor dimensions, process and environmental variations become significantly important in the modern VLSI design. A smaller feature size means that the physical characteristics of a device are more prone to these unaccounted-for changes. To achieve a robust design, the random and systematic fluctuations in the manufacturing process and the variations in the environmental parameters should be analyzed and the impact on the parametric yield should be addressed. This thesis studies the challenges and comprises solutions for designing robust VLSI systems in the presence of variations. Initially, to get some insight into the system design under variability, the parametric yield is examined for a small circuit. Understanding the impact of variations on the yield at the circuit level is vital to accurately estimate and optimize the yield at the system granularity. Motivated by the observations and results, found at the circuit level, statistical analyses are performed, and solutions are proposed, at the system level of abstraction, to reduce the impact of the variations and increase the parametric yield. At the circuit level, the impact of the supply and threshold voltage variations on the parametric yield is discussed. Here, a design centering methodology is proposed to maximize the parametric yield and optimize the power-performance trade-off under variations. In addition, the scaling trend in the yield loss is studied. Also, some considerations for design centering in the current and future CMOS technologies are explored. The investigation, at the circuit level, suggests that the operating temperature significantly affects the parametric yield. In addition, the yield is very sensitive to the magnitude of the variations in supply and threshold voltage. Therefore, the spatial variations in process and environmental variations make it necessary to analyze the yield at a higher granularity. Here, temperature and voltage variations are mapped across the chip to accurately estimate the yield loss at the system level. At the system level, initially the impact of process-induced temperature variations on the power grid design is analyzed. Also, an efficient verification method is provided that ensures the robustness of the power grid in the presence of variations. Then, a statistical analysis of the timing yield is conducted, by taking into account both the process and environmental variations. By considering the statistical profile of the temperature and supply voltage, the process variations are mapped to the delay variations across a die. This ensures an accurate estimation of the timing yield. In addition, a method is proposed to accurately estimate the power yield considering process-induced temperature and supply voltage variations. This helps check the robustness of the circuits early in the design process. Lastly, design solutions are presented to reduce the power consumption and increase the timing yield under the variations. In the first solution, a guideline for floorplaning optimization in the presence of temperature variations is offered. Non-uniformity in the thermal profiles of integrated circuits is an issue that impacts the parametric yield and threatens chip reliability. Therefore, the correlation between the total power consumption and the temperature variations across a chip is examined. As a result, floorplanning guidelines are proposed that uses the correlation to efficiently optimize the chip's total power and takes into account the thermal uniformity. The second design solution provides an optimization methodology for assigning the power supply pads across the chip for maximizing the timing yield. A mixed-integer nonlinear programming (MINLP) optimization problem, subject to voltage drop and current constraint, is efficiently solved to find the optimum number and location of the pads

Algorithms and methodologies for interconnect reliability analysis of integrated circuits

The phenomenal progress of computing devices has been largely made possible by the sustained efforts of semiconductor industry in innovating techniques for extremely large-scale integration. Indeed, gigantically integrated circuits today contain multi-billion interconnects which enable the transistors to talk to each other -all in a space of few mm2. Such aggressively downscaled components (transistors and interconnects) silently suffer from increasing electric fields and impurities/defects during manufacturing. Compounded by the Gigahertz switching, the challenges of reliability and design integrity remains very much alive for chip designers, with Electro migration (EM) being the foremost interconnect reliability challenge. Traditionally, EM containment revolves around EM guidelines, generated at single-component level, whose non-compliance means that the component fails. Failure usually refers to deformation due to EM -manifested in form of resistance increase, which is unacceptable from circuit performance point of view. Subsequent aspects deal with correct-by-construct design of the chip followed by the signoff-verification of EM reliability. Interestingly, chip designs today have reached a dilemma point of reduced margin between the actual and reliably allowed current densities, versus, comparatively scarce system-failures. Consequently, this research is focused on improved algorithms and methodologies for interconnect reliability analysis enabling accurate and design-specific interpretation of EM events. In the first part, we present a new methodology for logic-IP (cell) internal EM verification: an inadequately attended area in the literature. Our SPICE-correlated model helps in evaluating the cell lifetime under any arbitrary reliability speciation, without generating additional data - unlike the traditional approaches. The model is apt for today's fab less eco-system, where there is a) increasing reuse of standard cells optimized for one market condition to another (e.g., wireless to automotive), as well as b) increasing 3rd party content on the chip requiring a rigorous sign-off. We present results from a 28nm production setup, demonstrating significant violations relaxation and flexibility to allow runtime level reliability retargeting. Subsequently, we focus on an important aspect of connecting the individual component-level failures to that of the system failure. We note that existing EM methodologies are based on serial reliability assumption, which deems the entire system to fail as soon as the first component in the system fails. With a highly redundant circuit topology, that of a clock grid, in perspective, we present algorithms for EM assessment, which allow us to incorporate and quantify the benefit from system redundancies. With the skew metric of clock-grid as a failure criterion, we demonstrate that unless such incorporations are done, chip lifetimes are underestimated by over 2x. This component-to-system reliability bridge is further extended through an extreme order statistics based approach, wherein, we demonstrate that system failures can be approximated by an asymptotic kth-component failure model, otherwise requiring costly Monte Carlo simulations. Using such approach, we can efficiently predict a system-criterion based time to failure within existing EDA frameworks. The last part of the research is related to incorporating the impact of global/local process variation on current densities as well as fundamental physical factors on EM. Through Hermite polynomial chaos based approach, we arrive at novel variations-aware current density models, which demonstrate significant margins (> 30 %) in EM lifetime when compared with the traditional worst case approach. The above research problems have been motivated by the decade-long work experience of the author dealing with reliability issues in industrial SoCs, first at Texas Instruments and later at Qualcomm.L'espectacular progrés dels dispositius de càlcul ha estat possible en gran part als esforços de la indústria dels semiconductors en proposar tècniques innovadores per circuits d'una alta escala d'integració. Els circuits integrats contenen milers de milions d'interconnexions que permeten connectar transistors dins d'un espai de pocs mm2. Tots aquests components estan afectats per camps elèctrics, impureses i defectes durant la seva fabricació. Degut a l’activitat a nivell de Gigahertzs, la fiabilitat i integritat són reptes importants pels dissenyadors de xips, on la Electromigració (EM) és un dels problemes més importants. Tradicionalment, el control de la EM ha girat entorn a directrius a nivell de component. L'incompliment d’alguna de les directrius implica un alt risc de falla. Per falla s'entén la degradació deguda a la EM, que es manifesta en forma d'augment de la resistència, la qual cosa és inacceptable des del punt de vista del rendiment del circuit. Altres aspectes tenen a veure amb la correcta construcció del xip i la verificació de fiabilitat abans d’enviar el xip a fabricar. Avui en dia, el disseny s’enfronta a dilemes importants a l’hora de definir els marges de fiabilitat dels xips. És un compromís entre eficiència i fiabilitat. La recerca en aquesta tesi se centra en la proposta d’algorismes i metodologies per a l'anàlisi de la fiabilitat d'interconnexió que permeten una interpretació precisa i específica d'esdeveniments d'EM. A la primera part de la tesi es presenta una nova metodologia pel disseny correcte-per-construcció i verificació d’EM a l’interior de les cel·les lògiques. Es presenta un model SPICE correlat que ajuda a avaluar el temps de vida de les cel·les segons qualsevol especificació arbitrària de fiabilitat i sense generar cap dada addicional, al contrari del que fan altres tècniques. El model és apte per l'ecosistema d'empreses de disseny quan hi ha a) una reutilització creixent de cel·les estàndard optimitzades per unes condicions de mercat i utilitzades en un altre (p.ex. de wireless a automoció), o b) la utilització de components del xip provinents de terceres parts i que necessiten una verificació rigorosa. Es presenten resultats en una tecnologia de 28nm, demostrant relaxacions significatives de les regles de fiabilitat i flexibilitat per permetre la reavaluació de la fiabilitat en temps d'execució. A continuació, el treball tracta un aspecte important sobre la relació entre les falles dels components i les falles del sistema. S'observa que les tècniques existents es basen en la suposició de fiabilitat en sèrie, que porta el sistema a fallar tant aviat hi ha un component que falla. Pensant en topologies redundants, com la de les graelles de rellotge, es proposen algorismes per l'anàlisi d'EM que permeten quantificar els beneficis de la redundància en el sistema. Utilitzant com a mètrica l’esbiaixi del senyal de rellotge, es demostra que la vida dels xips pot arribar a ser infravalorada per un factor de 2x. Aquest pont de fiabilitat entre component i sistema es perfecciona a través d'una tècnica basada en estadístics d'ordre extrem on es demostra que les falles poden ser aproximades amb un model asimptòtic de fallada de l'ièssim component, evitant així simulacions de Monte Carlo costoses. Amb aquesta tècnica, es pot predir eficientment el temps de fallada a nivell de sistema utilitzant eines industrials. La darrera part de la recerca està relacionada amb avaluar l'impacte de les variacions de procés en les densitats de corrent i factors físics de la EM. Mitjançant una tècnica basada en polinomis d'Hermite s'han obtingut uns nous models de densitat de corrent que mostren millores importants (>30%) en l'estimació de la vida del sistema comprades amb les tècniques basades en el cas pitjor. La recerca d'aquesta tesi ha estat motivada pel treball de l'autor durant més d'una dècada tractant temes de fiabilitat en sistemes, primer a Texas Instruments i després a Qualcomm.Postprint (published version

Test and Diagnosis of Integrated Circuits

The ever-increasing growth of the semiconductor market results in an increasing complexity of digital circuits. Smaller, faster, cheaper and low-power consumption are the main challenges in semiconductor industry. The reduction of transistor size and the latest packaging technology (i.e., System-On-a-Chip, System-In-Package, Trough Silicon Via 3D Integrated Circuits) allows the semiconductor industry to satisfy the latest challenges. Although producing such advanced circuits can benefit users, the manufacturing process is becoming finer and denser, making chips more prone to defects.The work presented in the HDR manuscript addresses the challenges of test and diagnosis of integrated circuits. It covers:- Power aware test;- Test of Low Power Devices;- Fault Diagnosis of digital circuits

On-Chip Power Supply Noise: Scaling, Suppression and Detection

Design metrics such as area, timing and power are generally considered as the primary criteria in the design of modern day circuits, however, the minimization of power supply noise, among other noise sources, is appreciably more important since not only can it cause a degradation in these parameters but can cause entire chips to fail. Ensuring the integrity of the power supply voltage in the power distribution network of a chip is therefore crucial to both building reliable circuits as well as preventing circuit performance degradation. Power supply noise concerns, predicted over two decades ago, continue to draw significant attention, and with present CMOS technology projected to keep on scaling, it is shown in this work that these issues are not expected to diminish. This research also considers the management and on-chip detection of power supply noise. There are various methods of managing power supply noise, with the use of decoupling capacitors being the most common technique for suppressing the noise. An in-depth analysis of decap structures including scaling effects is presented in this work with corroborating silicon results. The applicability of various decaps for given design constraints is provided. It is shown that MOS-metal hybrid structures can provide a significant increase in capacitance per unit area compared to traditional structures and will continue to be an important structure as technology continues to scale. Noise suppression by means of current shifting within the clock period of an ALU block is further shown to be an additional method of reducing the minimum voltage observed on its associated supply. A simple, and area and power efficient technique for on-chip supply noise detection is also proposed