Only two decades ago most electronic circuits were designed with a slide-rule, and the designs were verified using breadboard techniques. Simulation tools were a research curiosity and in general were mistrusted by most designers and test engineers. In those days the programs were not user friendly, models were inadequate, and the algorithms were not very robust. The demand for simulation tools has been driven by the increasing complexity of integrated circuits and systems, and it has been aided by the rapid decrease in the cost of com puting that has occurred over the past several decades. Today a wide range of tools exist for analYSiS, deSign, and verification, and expert systems and synthesis tools are rapidly emerging. In this book only one aspect of the analysis and design process is examined. but it is a very important aspect that has received much attention over the years. It is the problem of accurate circuit and timing simulation.

Digital Timing Macromodeling for VLSI Design Verification first of all provides an extensive history of the development of simulation techniques. It presents detailed discussion of the various techniques implemented in circuit, timing, fast-timing, switch-level timing, switch-level, and gate-level simulation. It also discusses mixed-mode simulation and interconnection analysis methods. The review in Chapter 2 gives an understanding of the advantages and disadvantages of the many techniques applied in modern digital macromodels. The book also presents a wide variety of techniques for performing nonlinear macromodeling of digital MOS subcircuits which address a large number of shortcomings in existing digital MOS macromodels. Specifically, the techniques address the device model detail, transistor coupling capacitance, effective channel length modulation, series transistor reduction, effective transconductance, input terminal dependence, gate parasitic capacitance, the body effect, the impact of parasitic RC-interconnects, and the effect of transmission gates. The techniques address major sources of errors in existing macromodeling techniques, which must be addressed if macromodeling is to be accepted in commercial CAD tools by chip designers. The techniques presented in Chapters 4-6 can be implemented in other macromodels, and are demonstrated using the macromodel presented in Chapter 3. The new techniques are validated over an extremely wide range of operating conditions: much wider than has been presented for previous macromodels, thus demonstrating the wide range of applicability of these techniques.

This useful book addresses electrothermal problems in modern VLSI systems. It discusses electrothermal phenomena and the fundamental building blocks that electrothermal simulation requires. The authors present three important applications of VLSI electrothermal analysis: temperature-dependent electromigration diagnosis, cell-level thermal placement, and temperature-driven power and timing analysis.

As the complexity and the density of VLSI chips increase with shrinking design rules, the evaluation of long-term reliability of MOS VLSI circuits is becoming an important problem. The assessment and improvement of reliability on the circuit level should be based on both the failure mode analysis and the basic understanding of the physical failure mechanisms observed in integrated circuits. Hot-carrier induced degrada tion of MOS transistor characteristics is one of the primary mechanisms affecting the long-term reliability of MOS VLSI circuits. It is likely to become even more important in future generation chips, since the down ward scaling of transistor dimensions without proportional scaling of the operating voltage aggravates this problem. A thorough understanding of the physical mechanisms leading to hot-carrier related degradation of MOS transistors is a prerequisite for accurate circuit reliability evaluation. It is also being recognized that important reliability concerns other than the post-manufacture reliability qualification need to be addressed rigorously early in the design phase. The development and use of accurate reliability simulation tools are therefore crucial for early assessment and improvement of circuit reliability : Once the long-term reliability of the circuit is estimated through simulation, the results can be compared with predetermined reliability specifications or limits. If the predicted reliability does not satisfy the requirements, appropriate design modifications may be carried out to improve the resistance of the devices to degradation.

Test generation is one of the most difficult tasks facing the designer of complex VLSI-based digital systems. Much of this difficulty is attributable to the almost universal use in testing of low, gate-level circuit and fault models that predate integrated circuit technology. It is long been recognized that the testing prob lem can be alleviated by the use of higher-level methods in which multigate modules or cells are the primitive components in test generation; however, the development of such methods has proceeded very slowly. To be acceptable, high-level approaches should be applicable to most types of digital circuits, and should provide fault coverage comparable to that of traditional, low-level methods. The fault coverage problem has, perhaps, been the most intractable, due to continued reliance in the testing industry on the single stuck-line (SSL) fault model, which is tightly bound to the gate level of abstraction. This monograph presents a novel approach to solving the foregoing problem. It is based on the systematic use of multibit vectors rather than single bits to represent logic signals, including fault signals. A circuit is viewed as a collection of high-level components such as adders, multiplexers, and registers, interconnected by n-bit buses. To match this high-level circuit model, we introduce a high-level bus fault that, in effect, replaces a large number of SSL faults and allows them to be tested in parallel. However, by reducing the bus size from n to one, we can obtain the traditional gate-level circuit and models.

Analog Design Issues in Digital VLSI Circuits and Systems brings together in one place important contributions and up-to-date research results in this fast moving area. Analog Design Issues in Digital VLSI Circuits and Systems serves as an excellent reference, providing insight into some of the most challenging research issues in the field.

Mixed-Mode Simulation and Analog Multilevel Simulation addresses the problems of simulating entire mixed analog/digital systems in the time-domain. A complete hierarchy of modeling and simulation methods for analog and digital circuits is described. Mixed-Mode Simulation and Analog Multilevel Simulation also provides a chronology of the research in the field of mixed-mode simulation and analog multilevel simulation over the last ten to fifteen years. In addition, it provides enough information to the reader so that a prototype mixed-mode simulator could be developed using the algorithms in this book. Mixed-Mode Simulation and Analog Multilevel Simulation can also be used as documentation for the SPLICE family of mixed-mode programs as they are based on the algorithms and techniques described in this book.

Our purpose in writing this book was two-fold. First, we wanted to compile a chronology of the research in the field of mixed-mode simulation over the last ten to fifteen years. A substantial amount of work was done during this period of time but most of it was published in archival form in Masters theses and Ph. D. dissertations. Since the interest in mixed-mode simulation is growing, and a thorough review of the state-of-the-art in the area was not readily available, we thought it appropriate to publish the information in the form of a book. Secondly, we wanted to provide enough information to the reader so that a proto type mixed-mode simulator could be developed using the algorithms in this book. The SPLICE family of programs is based on the algorithms and techniques described in this book and so it can also serve as docu mentation for these programs. ACKNOWLEDGEMENTS The authors would like to dedicate this book to Prof. D. O. Peder son for inspiring this research work and for providing many years of support and encouragement The authors enjoyed many fruitful discus sions and collaborations with Jim Kleckner, Young Kim, Alberto Sangiovanni-Vincentelli, and Jacob White, and we thank them for their contributions. We also thank the countless others who participated in the research work and read early versions of this book. Lillian Beck provided many useful suggestions to improve the manuscript. Yun cheng Ju did the artwork for the illustrations.

Moore's law [Noy77], which predicted that the number of devices in tegrated on a chip would be doubled every two years, was accurate for a number of years. Only recently has the level of integration be gun to slow down somewhat due to the physical limits of integration technology. Advances in silicon technology have allowed Ie design ers to integrate more than a few million transistors on a chip; even a whole system of moderate complexity can now be implemented on a single chip. To keep pace with the increasing complexity in very large scale integrated (VLSI) circuits, the productivity of chip designers would have to increase at the same rate as the level of integration. Without such an increase in productivity, the design of complex systems might not be achievable within a reasonable time-frame. The rapidly increasing complexity of VLSI circuits has made de- 1 2 INTRODUCTION sign automation an absolute necessity, since the required increase in productivity can only be accomplished with the use of sophisticated design tools. Such tools also enable designers to perform trade-off analyses of different logic implementations and to make well-informed design decisions.

From the perspective of complex systems, conventional Ie's can be regarded as "discrete" devices interconnected according to system design objectives imposed at the circuit board level and higher levels in the system implementation hierarchy. However, silicon monolithic circuits have progressed to such complex functions that a transition from a philosophy of integrated circuits (Ie's) to one of integrated sys tems is necessary. Wafer-scale integration has played an important role over the past few years in highlighting the system level issues which will most significantly impact the implementation of complex monolithic systems and system components. Rather than being a revolutionary approach, wafer-scale integration will evolve naturally from VLSI as defect avoidance, fault tolerance and testing are introduced into VLSI circuits. Successful introduction of defect avoidance, for example, relaxes limits imposed by yield and cost on Ie dimensions, allowing the monolithic circuit's area to be chosen according to the natural partitioning of a system into individual functions rather than imposing area limits due to defect densities. The term "wafer level" is perhaps more appropriate than "wafer-scale". A "wafer-level" monolithic system component may have dimensions ranging from conventional yield-limited Ie dimensions to full wafer dimensions. In this sense, "wafer-scale" merely represents the obvious upper practical limit imposed by wafer sizes on the area of monolithic circuits. The transition to monolithic, wafer-level integrated systems will require a mapping of the full range of system design issues onto the design of monolithic circuit.