Sachin Sapatnekar

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.

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.

With dramatic increases in on-chip packing densities, routing congestion has become a major problem in integrated circuit design, impacting convergence, performance, and yield, and complicating the synthesis of critical interc- nects. The problem is especially acute as interconnects are becoming the performance bottleneck in modern integrated circuits. Even with more than 30% of white space, some of the design blocks in modern microprocessor and ASIC designs cannot be routed successfully. Moreover, this problem is likely to worsen considerably in the coming years due to design size and technology scaling. There is an inherent tradeo? between choosing a minimum delay path for interconnect nets, and the need to detour the routes to avoid “tra?c jams”; congestion management involves intelligent allocation of the available int- connect resources, up-front planning of the wire routes for even distributions, and transformations that make the physical synthesis ?ow congestion-aware. The book explores this tradeo? that lies at the heart of all congestion m- agement, in seeking to address the key question: how does one optimize the traditional design goals such as the delay or the area of a circuit, while still ensuring that the circuit remains routable? It begins by motivating the c- gestion problem, explaining why this problem is important and how it will trend. It then progresses with comprehensive discussions of the techniques available for estimating and optimizing congestion at various stages in the design ?ow.

With dramatic increases in on-chip packing densities, routing congestion has become a major problem in integrated circuit design, impacting convergence, performance, and yield, and complicating the synthesis of critical interc- nects. The problem is especially acute as interconnects are becoming the performance bottleneck in modern integrated circuits. Even with more than 30% of white space, some of the design blocks in modern microprocessor and ASIC designs cannot be routed successfully. Moreover, this problem is likely to worsen considerably in the coming years due to design size and technology scaling. There is an inherent tradeo? between choosing a minimum delay path for interconnect nets, and the need to detour the routes to avoid “tra?c jams”; congestion management involves intelligent allocation of the available int- connect resources, up-front planning of the wire routes for even distributions, and transformations that make the physical synthesis ?ow congestion-aware. The book explores this tradeo? that lies at the heart of all congestion m- agement, in seeking to address the key question: how does one optimize the traditional design goals such as the delay or the area of a circuit, while still ensuring that the circuit remains routable? It begins by motivating the c- gestion problem, explaining why this problem is important and how it will trend. It then progresses with comprehensive discussions of the techniques available for estimating and optimizing congestion at various stages in the design ?ow.

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.