Computationally efficient characterization of standard cells for statistical static timing analysis

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 44-45).We propose a computationally efficient statistical static timing analysis (SSTA) technique that addresses intra-die variations at near-threshold to sub-threshold supply voltage, simulated on a scaled 32nm CMOS standard cell library. This technique would characterize the propagation delay and output slew of an individual cell for subsequent timing path analyses. Its efficiency stems from the fact that it only needs to find the delay or output slew in the vicinity of the ?- sigma operating point (where ? = 0 to 3) rather than the entire probability density function of the delay or output slew, as in conventional Monte-Carlo simulations. The algorithm is simulated on combinational logic gates that include inverters, NANDs, and NORs of different sizes. The delay and output slew estimates in most cases differ from the Monte-Carlo results by less than 5%. Higher supply voltage, larger transistor widths, and slower input slews tend to improve delay and output slew estimates. Transistor stacking is found to be the only major source of under-prediction by the SSTA technique. Overall, the cell characterization approach has a substantial computational advantage compared to SPICE-based Monte-Carlo analysis.by Sharon H. Chou.M.Eng

Statistical Classification Based Modelling and Estimation of Analog Circuits Failure Probability

At nanoscales, variations in transistor parameters cause variations and unpredictability in the circuit output, and may ultimately cause a violation of the desired specifications, leading to circuit failure. The parametric variations in transistors occur due to limitations in the manufacturing process and are commonly known as process variations. Circuit simulation is a Computer-Aided Design (CAD) technique for verifying the behavior of analog circuits but exhibits incompleteness under the effects of process variations. Hence, statistical circuit simulation is showing increasing importance for circuit design to address this incompleteness problem. However, existing statistical circuit simulation approaches either fail to analyze the rare failure events accurately and efficiently or are impractical to use. Moreover, none of the existing approaches is able to successfully analyze analog circuits in the presence of multiple performance specifications in timely and accurate manner. Therefore, we propose a new statistical circuit simulation based methodology for modelling and estimation of failure probability of analog circuits in the presence of multiple performance metrics. Our methodology is based on an iterative way of estimating failure probability, employing a statistical classifier to reduce the number of simulations while still maintaining high estimation accuracy. Furthermore, a more practical classifier model is proposed for analog circuit failure probability estimation. Our methodology estimates an accurate failure probability even when the failures resulting from each performance metric occur simultaneously. The proposed methodology can deliver many orders of speedup compared to traditional Monte Carlo methods. Moreover, experimental results show that the methodology generates accurate results for problems with multiple specifications, while other approaches fail totally

Low-cost, high-precision DAC design based on ordered element matching and verification against undesired operating points for analog circuits

Over the past 50 years, the integrated circuit (IC) industry has grown rapidly, following the famous ``Moore\u27s law. The process feature size keeps shrinking, whereby the performance of digital circuits is constantly enhanced and their cost constantly decreases. However, with the system integration and the development of system on chip (SoC), nearly all of today\u27s ICs contain analog/mixed-Signal circuits. Although a mixed-signal SoC is primarily digital, the analog circuit design and verification consume most of the resources, and the dominant source of IC breakdowns is attributable to the analog circuits. One important reason for the high cost and risk of breakdowns of analog circuits is that the technology advancement does not benefit many analog and mixed-signal circuits, and in fact imposes higher requirements on their performance. With process scaling, many important parameters of integrated circuit components degrade, which cause a drop in many key aspects of performance of analog circuits. Many analog circuits rely on matched circuit components (transistors, resistors, or capacitors) to achieve the required linearity performance; examples are amplifiers, digital-to-analog converters (DACs), etc. However, shrinking of the feature sizes increases the circuit components mismatch, thereby making it more difficult to maintain circuit accuracy. Therefore, to reduce the cost of analog circuit design, designers should propose new structures whose key performance can be improved by the technology scaling. In this dissertation, we propose a low-cost, high-precision DAC structure based on ordered element matching (OEM) theory. High matching accuracy can be achieved by applying OEM calibration to the resistors in unary weighted segments and calibrating the gain error between different segments by calibration DAC (CalDAC). As a design example to verify the proposed structure, a high-precision DAC is designed in a 130 nm Global Foundry (GF) CMOS process. The 130 nm GF process features high-density digital circuits and is a typical process which is constantly enhanced by the scaling of device dimensions and voltage supply; implementation of a high-precision DAC in such process is important to decreasing the costs of high-precision DAC designs. As a result, our proposed DAC structure is demonstrated to be able to significantly lower the cost of high-precision DAC design. Another reason for the high cost and risk of breakdowns of analog circuits arises from the complexity of analog circuit working states. Most digital circuits serve as logic functions, so that digital transistors work in only two states, either low or high. In contrast, analog circuits have much more complicated functions; they may work in multiple operating points, since various feedback approaches are applied in analog circuits to enhance their performance. Circuits with undetected operating points can be devastating, particularly when they are employed in critical applications such as automotive, health care, and military products. However, since the existing circuit simulators provide only a single operating point, recognizing the existence of undesired operating points depends largely on the experiences of designers. In some circuits, even the most experienced designers may not be aware that a circuit they designed has undesired operating points, which often go undetected in the standard simulations in the design process. To identify undesired operating points in an analog circuit and reduce its risk of breakdowns, a systematic verification method against undesired operating points in analog circuits is proposed in this dissertation. Unlike traditional methods of finding all operating points, this method targets only searches for voltage intervals containing undesired operating points. To achieve this, our method first converts the circuit into a corresponding graph and locates the break point to break all the positive feedback loops (PFLs). For one dimensional verification, divide and contraction algorithms could be applied to identify undesired operating points. Two dimensional vector field methods are used to solve the two dimensional verifications. Based on the proposed verification methods against undesired operating points, an EDA tool called ``ITV is developed to identify undesired operating points in analog and mixed-signal circuits. Simulation results show ITV to be effective and efficient in identifying undesired operating points in a class of commonly used benchmark circuits that includes bias generators, voltage references, temperature sensors, and op-amp circuits

System level performance and yield optimisation for analogue integrated circuits

Advances in silicon technology over the last decade have led to increased integration of analogue and digital functional blocks onto the same single chip. In such a mixed signal environment, the analogue circuits must use the same process technology as their digital neighbours. With reducing transistor sizes, the impact of process variations on analogue design has become prominent and can lead to circuit performance falling below specification and hence reducing the yield.This thesis explores the methodology and algorithms for an analogue integrated circuit automation tool that optimizes performance and yield. The trade-offs between performance and yield are analysed using a combination of an evolutionary algorithm and Monte Carlo simulation. Through the integration of yield parameter into the optimisation process, the trade off between the performance functions can be better treated that able to produce a higher yield. The results obtained from the performance and variation exploration are modelled behaviourally using a Verilog-A language. The model has been verified with transistor level simulation and a silicon prototype.For a large analogue system, the circuit is commonly broken down into its constituent sub-blocks, a process known as hierarchical design. The use of hierarchical-based design and optimisation simplifies the design task and accelerates the design flow by encouraging design reuse.A new approach for system level yield optimisation using a hierarchical-based design is proposed and developed. The approach combines Multi-Objective Bottom Up (MUBU) modelling technique to model the circuit performance and variation and Top Down Constraint Design (TDCD) technique for the complete system level design. The proposed method has been used to design a 7th order low pass filter and a charge pump phase locked loop system. The results have been verified with transistor level simulations and suggest that an accurate system level performance and yield prediction can be achieved with the proposed methodology