Dramatic rises in the power consumption and integration density of contemporary systems-on-chip (SoCs) have led to the need for careful attention to chip-level thermal integrity. High temperatures or uneven temperature distributions may result not only in reliability issues, but also timing failures, due to the temperature-dependent nature of chip time-to-failure and delay, respectively. To resolve these issues, high-quality, accurate thermal modeling and analysis, and thermally oriented placement optimizations, are essential prior to tapeout. This paper first presents an overview of thermal modeling and simulation methods, such as finite-difference time domain, finite element, model reduction, random walk, and Green-function based algorithms, that are appropriate for use in placement algorithms. Next, two-dimensional and three-dimensional thermal-aware placement algorithms such as matrix-synthesis, simulated annealing, partition-driven, and force directed are presented. Finally, future trends and challenges are described
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Tsai et al. (2006) studied this question.
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