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

Register-transfer-level power profiling for system-on-chip power distribution network design and signoff

Abstract. This thesis is a study of how register-transfer-level (RTL) power profiling can help the design and signoff of power distribution network in digital integrated circuits. RTL power profiling is a method which collects RTL power estimation results to a single power profile which then can be analysed in order to find interesting time windows for specifying power distribution network design and signoff. The thesis starts with theory part. Complementary metal-oxide semiconductor (CMOS) inverter power dissipation is studied at first. Next, power distribution network structure and voltage drop problems are introduced. Voltage drop is demonstrated by using power distribution network impedance figures. Common on-chip power distribution network structure is introduced, and power distribution network design flow is outlined. Finally, decoupling capacitors function and impact on power distribution network impedance are thoroughly explained. The practical part of the thesis contains RTL power profiling flow details and power profiling flow results for one simulation case in one design block. Also, some methods of improving RTL power estimation accuracy are discussed and calibration with extracted parasitic is then used to get new set of power profiling time windows. After the results are presented, overall RTL power estimation accuracy is analysed and resulted time windows are compared to reference gate-level time windows. RTL power profiling result analysis shows that resulted time windows match the theory and RTL power profiling seems to be a promising method for finding time windows for power distribution network design and signoff.Rekisterisiirtotason tehoprofilointi järjestelmäpiirin tehonsiirtoverkon suunnittelussa ja verifioinnissa. Tiivistelmä. Tässä työssä tutkitaan, miten rekisterisiirtotason (RTL) tehoprofilointi voi auttaa digitaalisten integroitujen piirien tehonsiirtoverkon suunnittelussa ja verifioinnissa. RTL-tehoprofilointi on menetelmä, joka analysoi RTL-tehoestimoinnista saadusta tehokäyrästä hyödyllisiä aikaikkunoita tehonsiirtoverkon suunnitteluun ja verifiointiin. Työ alkaa teoriaosuudella, jonka aluksi selitetään, miten CMOS-invertteri kuluttaa tehoa. Seuravaksi esitellään tehonsiirtoverkon rakenne ja pahimmat tehonsiirtoverkon jännitehäviön aiheuttajat. Jännitehäviötä havainnollistetaan myös piirikaavioiden ja impedanssikäyrien avustuksella. Lisäksi integroidun piirin tehonsiirtoverkon suunnitteluvuo ja yleisin rakenne on esitelty. Lopuksi teoriaosuus käsittelee yksityiskohtaisesti ohituskondensaattoreiden toiminnan ja vaikutuksen tehonsiirtoverkon kokonaisimpedanssiin. Työn kokeellisessa osuudessa esitellään ensin tehoprofiloinnin vuo ja sen jälkeen vuon tulokset yhdelle esimerkkilohkolle yhdessä simulaatioajossa. Lisäksi tässä osiossa käsitellään RTL-tehoestimoinnin tarkkuutta ja tehdään RTL-tehoprofilointi loisimpedansseilla kalibroidulle RTL-mallille. Lopuksi RTL-tehoestimoinnin tuloksia ja saatuja RTL-tehoprofiloinnin aikaikkunoita analysoidaan ja verrataan porttitason mallin tuloksiin. RTL-tehoprofiloinnin tulosten analysointi osoittaa, että saatavat aikaikkunat vastaavat teoriaa ja että RTL-tehoprofilointi näyttää lupaavalta menetelmältä tehosiirtoverkon analysoinnin ja verifioinnin aikaikkunoiden löytämiseen

Design and Analysis of Power Distribution Networks in VLSI Circuits.

Rapidly switching currents of the on-chip devices can cause fluctuations in the supply voltage which can be classified as IR and Ldi/dt drops. The voltage fluctuations in a supply network can inject noise in a circuit which may lead to functional failures of the design. Power supply integrity verification is, therefore, a critical concern in high-performance designs. Also, with decreasing supply voltages, gate-delay is becoming increasingly sensitive to supply voltage variation. With ever-diminishing clock periods, accurate analysis of the impact of supply voltage on circuit performance has also become critical. Increasing power consumption and clock frequency have exacerbated the Ldi/dt drop in every new technology generation. The Ldi/dt drop has become the dominant portion of the overall supply-drop in high performance designs. On-die passive decap, which has traditionally been used for suppressing Ldi/dt, has become expensive due to its area and leakage power overhead. This has created an urgent need for novel circuit techniques to suppress the Ldi/dt drop in power distribution networks. We provide accurate algorithmic solutions for determining the worst-case supply-drop and the impact of supply noise on circuit performance. We propose a path-based and a block-based approach for computing the maximum circuit delay under power supply fluctuations. We also propose an early-mode supply-drop estimation approach and a statistical approach for power grid analysis. All the proposed approaches are vectorless and account for both IR and Ldi/dt drops. We also propose a performance-aware decoupling capacitance allocation technique which uses timing slacks to drive the optimization. Finally, we present analog as well as all-digital circuit techniques for inductive supply noise suppression. The proposed all-digital circuit techniques were implemented in a test-chip, fabricated in a 0.13µm CMOS process. Measurements on the test-chip demonstrate a reduction in the supply fluctuations by 57% for a ramp loads and by 75% during resonance. We also present a low-power, all-digital on-chip oscilloscope for accurate measurement of supply noise. Supply noise measurements obtained from the on-chip oscilloscope were validated to conform well to those obtained from a traditional supply-drop monitor and direct on-chip probing.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58508/1/spant_1.pd

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

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

Empirical timing analysis of CPUs and delay fault tolerant design using partial redundancy

The operating clock frequency is determined by the longest signal propagation delay, setup/hold time, and timing margin. These are becoming less predictable with the increasing design complexity and process miniaturization. The difficult challenge is then to ensure that a device operating at its clock frequency is error-free with quantifiable assurance. Effort at device-level engineering will not suffice for these circuits exhibiting wide process variation and heightened sensitivities to operating condition stress. Logic-level redress of this issue is a necessity and we propose a design-level remedy for this timing-uncertainty problem. The aim of the design and analysis approaches presented in this dissertation is to provide framework, SABRE, wherein an increased operating clock frequency can be achieved. The approach is a combination of analytical modeling, experimental analy- sis, hardware /time-redundancy design, exception handling and recovery techniques. Our proposed design replicates only a necessary part of the original circuit to avoid high hardware overhead as in triple-modular-redundancy (TMR). The timing-critical combinational circuit is path-wise partitioned into two sections. The combinational circuits associated with long paths are laid out without any intrusion except for the fan-out connections from the first section of the circuit to a replicated second section of the combinational circuit. Thus only the second section of the circuit is replicated. The signals fanning out from the first section are latches, and thus are far shorter than the paths spanning the entire combinational circuit. The replicated circuit is timed at a subsequent clock cycle to ascertain relaxed timing paths. This insures that the likelihood of mistiming due to stress or process variation is eliminated. During the subsequent clock cycle, the outcome of the two logically identical, yet time-interleaved, circuit outputs are compared to detect faults. When a fault is detected, the retry sig- nal is triggered and the dynamic frequency-step-down takes place before a pipe flush, and retry is issued. The significant timing overhead associated with the retry is offset by the rarity of the timing violation events. Simulation results on ISCAS Benchmark circuits show that 10% of clock frequency gain is possible with 10 to 20 % of hardware overhead of replicated timing-critical circuit

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