We live in a time of great change. In the electronics world, the last several decades have seen unprecedented growth and advancement, described by Moore's law. This observation stated that transistor density in integrated circuits doubles every 1. 5-2 years. This came with the simultaneous improvement of individual device perf- mance as well as the reduction of device power such that the total power of the resulting ICs remained under control. No trend remains constant forever, and this is unfortunately the case with Moore's law. The trouble began a number of years ago when CMOS devices were no longer able to proceed along the classical scaling trends. Key device parameters such as gate oxide thickness were simply no longer able to scale. As a result, device o- state currents began to creep up at an alarming rate. These continuing problems with classical scaling have led to a leveling off of IC clock speeds to the range of several GHz. Of course, chips can be clocked higher but the thermal issues become unmanageable. This has led to the recent trend toward microprocessors with mul- ple cores, each running at a few GHz at the most. The goal is to continue improving performance via parallelism by adding more and more cores instead of increasing speed. The challenge here is to ensure that general purpose codes can be ef?ciently parallelized. There is another potential solution to the problem of how to improve CMOS technology performance: three-dimensional integrated circuits (3D ICs).

Statistical timing analysis is an area of growing importance in nanometer te- nologies' as the uncertainties associated with process and environmental var- tions increase' and this chapter has captured some of the major efforts in this area. This remains a very active field of research' and there is likely to be a great deal of new research to be found in conferences and journals after this book is published. In addition to the statistical analysis of combinational circuits' a good deal of work has been carried out in analyzing the effect of variations on clock skew. Although we will not treat this subject in this book' the reader is referred to [LNPS00' HN01' JH01' ABZ03a] for details. 7 TIMING ANALYSIS FOR SEQUENTIAL CIRCUITS 7.1 INTRODUCTION A general sequential circuit is a network of computational nodes (gates) and memory elements (registers). The computational nodes may be conceptualized as being clustered together in an acyclic network of gates that forms a c- binational logic circuit. A cyclic path in the direction of signal propagation 1 is permitted in the sequential circuit only if it contains at least one register . In general, it is possible to represent any sequential circuit in terms of the schematic shown in Figure 7.1, which has I inputs, O outputs and M registers. The registers outputs feed into the combinational logic which, in turn, feeds the register inputs. Thus, the combinational logic has I + M inputs and O + M outputs.

This volume provides a complete understanding of the fundamental causes of routing congestion in present-day and next-generation VLSI circuits, offers techniques for estimating and relieving congestion, and provides a critical analysis of the accuracy and effectiveness of these techniques. The book includes metrics and optimization techniques for routing congestion at various stages of the VLSI design flow. The subjects covered include an explanation of why the problem of congestion is important and how it will trend, plus definitions of metrics that are appropriate for measuring congestion, and descriptions of techniques for estimating and optimizing routing congestion issues in cell-/library-based VLSI circuits.

This volume provides a complete understanding of the fundamental causes of routing congestion in present-day and next-generation VLSI circuits, offers techniques for estimating and relieving congestion, and provides a critical analysis of the accuracy and effectiveness of these techniques. The book includes metrics and optimization techniques for routing congestion at various stages of the VLSI design flow. The subjects covered include an explanation of why the problem of congestion is important and how it will trend, plus definitions of metrics that are appropriate for measuring congestion, and descriptions of techniques for estimating and optimizing routing congestion issues in cell-/library-based VLSI circuits.

Statistical timing analysis is an area of growing importance in nanometer te- nologies' as the uncertainties associated with process and environmental var- tions increase' and this chapter has captured some of the major efforts in this area. This remains a very active field of research' and there is likely to be a great deal of new research to be found in conferences and journals after this book is published. In addition to the statistical analysis of combinational circuits' a good deal of work has been carried out in analyzing the effect of variations on clock skew. Although we will not treat this subject in this book' the reader is referred to [LNPS00' HN01' JH01' ABZ03a] for details. 7 TIMING ANALYSIS FOR SEQUENTIAL CIRCUITS 7.1 INTRODUCTION A general sequential circuit is a network of computational nodes (gates) and memory elements (registers). The computational nodes may be conceptualized as being clustered together in an acyclic network of gates that forms a c- binational logic circuit. A cyclic path in the direction of signal propagation 1 is permitted in the sequential circuit only if it contains at least one register . In general, it is possible to represent any sequential circuit in terms of the schematic shown in Figure 7.1, which has I inputs, O outputs and M registers. The registers outputs feed into the combinational logic which, in turn, feeds the register inputs. Thus, the combinational logic has I + M inputs and O + M outputs.

We live in a time of great change. In the electronics world, the last several decades have seen unprecedented growth and advancement, described by Moore's law. This observation stated that transistor density in integrated circuits doubles every 1. 5-2 years. This came with the simultaneous improvement of individual device perf- mance as well as the reduction of device power such that the total power of the resulting ICs remained under control. No trend remains constant forever, and this is unfortunately the case with Moore's law. The trouble began a number of years ago when CMOS devices were no longer able to proceed along the classical scaling trends. Key device parameters such as gate oxide thickness were simply no longer able to scale. As a result, device o- state currents began to creep up at an alarming rate. These continuing problems with classical scaling have led to a leveling off of IC clock speeds to the range of several GHz. Of course, chips can be clocked higher but the thermal issues become unmanageable. This has led to the recent trend toward microprocessors with mul- ple cores, each running at a few GHz at the most. The goal is to continue improving performance via parallelism by adding more and more cores instead of increasing speed. The challenge here is to ensure that general purpose codes can be ef?ciently parallelized. There is another potential solution to the problem of how to improve CMOS technology performance: three-dimensional integrated circuits (3D ICs).

This Encyclopedia comes in 3 sets. To check out Set 1 and Set 3, please visit Set 1: Thermal Packaging Techniques and Set 3: Thermal Packaging Applications /remove Thermal and mechanical packaging - the enabling technologies for the physical implementation of electronic systems - are responsible for much of the progress in miniaturization, reliability, and functional density achieved by electronic, microelectronic, and nanoelectronic products during the past 50 years. The inherent inefficiency of electronic devices and their sensitivity to heat have placed thermal packaging on the critical path of nearly every product development effort in traditional, as well as emerging, electronic product categories.Successful thermal packaging is the key differentiator in electronic products, as diverse as supercomputers and cell phones, and continues to be of pivotal importance in the refinement of traditional products and in the development of products for new applications. The Encyclopedia of Thermal Packaging, compiled in four multi-volume sets (Set 1: Thermal Packaging Techniques, Set 2: Thermal Packaging Tools, Set 3: Thermal Packaging Applications, and Set 4: Thermal Packaging Configurations) will provide a comprehensive, one-stop treatment of the techniques, tools, applications, and configurations of electronic thermal packaging. Each of the author-written sets presents the accumulated wisdom and shared perspectives of a few luminaries in the thermal management of electronics.Set 2: Thermal Packaging ToolsThe second set in the encyclopedia, Thermal Packaging Tools, includes volumes dedicated to thermal design of data centers, techniques and models for the design and optimization of heat sinks, the development and use of reduced-order "compact" thermal models of electronic components, a database of critical material thermal properties, and a comprehensive exploration of thermally-informed electronic design. The numerical and analytical techniques described in these volumes are among the primary tools used by thermal packaging practitioners and researchers to accelerate product and system development and achieve "correct by design" thermal packaging solutions.The four sets in the Encyclopedia of Thermal Packaging will provide the novice and student with a complete reference for a quick ascent on the thermal packaging ';learning curve,'; the practitioner with a validated set of techniques and tools to face every challenge, and researchers with a clear definition of the state-of-the-art and emerging needs to guide their future efforts. This encyclopedia will, thus, be of great interest to packaging engineers, electronic product development engineers, and product managers, as well as to researchers in thermal management of electronic and photonic components and systems, and most beneficial to undergraduate and graduate students studying mechanical, electrical, and electronic engineering.