FFTPL: An Analytic Placement Algorithm Using Fast Fourier Transform for Density Equalization

We propose a flat nonlinear placement algorithm FFTPL using fast Fourier transform for density equalization. The placement instance is modeled as an electrostatic system with the analogy of density cost to the potential energy. A well-defined Poisson's equation is proposed for gradient and cost computation. Our placer outperforms state-of-the-art placers with better solution quality and efficiency

Limits on Fundamental Limits to Computation

An indispensable part of our lives, computing has also become essential to industries and governments. Steady improvements in computer hardware have been supported by periodic doubling of transistor densities in integrated circuits over the last fifty years. Such Moore scaling now requires increasingly heroic efforts, stimulating research in alternative hardware and stirring controversy. To help evaluate emerging technologies and enrich our understanding of integrated-circuit scaling, we review fundamental limits to computation: in manufacturing, energy, physical space, design and verification effort, and algorithms. To outline what is achievable in principle and in practice, we recall how some limits were circumvented, compare loose and tight limits. We also point out that engineering difficulties encountered by emerging technologies may indicate yet-unknown limits.Comment: 15 pages, 4 figures, 1 tabl

On The Engineering of a Stable Force-Directed Placer

Analytic and force-directed placement methods that simultaneously minimize wire length and spread cells are receiving renewed attention from both academia and industry. However, these methods are by no means trivial to implement---to date, published works have failed to provide sufficient engineering details to replicate results. This dissertation addresses the implementation of a generic force-directed placer entitled FDP. Specifically, this thesis provides (1) a description of efficient force computation for spreading cells, (2) an illustration of numerical instability in this method and a means to avoid the instability, (3) metrics for measuring cell distribution throughout the placement area, and (4) a complementary technique that aids in minimizing wire length. FDP is compared to Kraftwerk and other leading academic tools including Capo, Dragon, and mPG for both standard cell and mixed-size circuits. Wire lengths produced by FDP are found to be, on average, up to 9% and 3% better than Kraftwerk and Capo, respectively. All told, this thesis confirms the validity and applicability of the approach, and provides clarifying details of the intricacies surrounding the implementation of a force-directed global placer

High-Performance Placement and Routing for the Nanometer Scale.

Modern semiconductor manufacturing facilitates single-chip electronic systems that only five years ago required ten to twenty chips. Naturally, design complexity has grown within this period. In contrast to this growth, it is becoming common in the industry to limit design team size which places a heavier burden on design automation tools. Our work identifies new objectives, constraints and concerns in the physical design of systems-on-chip, and develops new computational techniques to address them. In addition to faster and more relevant design optimizations, we demonstrate that traditional design flows based on ``separation of concerns'' produce unnecessarily suboptimal layouts. We develop new integrated optimizations that streamline traditional chains of loosely-linked design tools. In particular, we bridge the gap between mixed-size placement and routing by updating the objective of global and detail placement to a more accurate estimate of routed wirelength. To this we add sophisticated whitespace allocation, and the combination provides increased routability, faster routing, shorter routed wirelength, and the best via counts of published techniques. To further improve post-routing design metrics, we present new global routing techniques based on Discrete Lagrange Multipliers (DLM) which produce the best routed wirelength results on recent benchmarks. Our work culminates in the integration of our routing techniques within an incremental placement flow to improve detailed routing solutions, shrink die sizes and reduce total chip cost. Not only do our techniques improve the quality and cost of designs, but also simplify design automation software implementation in many cases. Ultimately, we reduce the time needed for design closure through improved tool fidelity and the use of our incremental techniques for placement and routing.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/64639/1/royj_1.pd

On the Use of Directed Moves for Placement in VLSI CAD

Search-based placement methods have long been used for placing integrated circuits targeting the field programmable gate array (FPGA) and standard cell design styles. Such methods offer the potential for high-quality solutions but often come at the cost of long run-times compared to alternative methods. This dissertation examines strategies for enhancing local search heuristics---and in particular, simulated annealing---through the application of directed moves. These moves help to guide a search-based optimizer by focusing efforts on states which are most likely to yield productive improvement, effectively pruning the size of the search space. The engineering theory and implementation details of directed moves are discussed in the context of both field programmable gate array and standard cell designs. This work explores the ways in which such moves can be used to improve the quality of FPGA placements, improve the robustness of floorplan repair and legalization methods for mixed-size standard cell designs, and enhance the quality of detailed placement for standard cell circuits. The analysis presented herein confirms the validity and efficacy of directed moves, and supports the use of such heuristics within various optimization frameworks

Placement for fast and reliable through-silicon-via (TSV) based 3D-IC layouts

The objective of this research is to explore the feasibility of addressing the major performance and reliability problems or issues, such as wirelength, stress-induced carrier mobility variation, temperature, and quality trade-offs, found in three-dimensional integrated circuits (3D ICs) that use through-silicon vias (TSVs) at placement stage. Four main works that support this goal are included. In the first work, wirelength of TSV-based 3D ICs is the main focus. In the second work, stress-induced carrier mobility variation in TSV-based 3D ICs is examined. In the third work, temperature inside TSV-based 3D ICs is investigated. In the final work, the quality trade-offs of TSV-based 3D-IC designs are explored. In the first work, a force-directed, 3D, and gate-level placement algorithm that efficiently handles TSVs is developed. The experiments based on synthesized benchmarks indicate that the developed algorithm helps generate GDSII layouts of 3D-IC designs that are optimized in terms of wirelength. In addition, the impact of TSVs on other physical aspects of 3D-IC designs is also studied by analyzing the GDSII layouts. In the second work, the model for carrier mobility variation caused by TSV and STI stresses is developed as well as the timing analysis flow considering the stresses. The impact of TSV and STI stresses on carrier mobility variation and performance of 3D ICs is studied. Furthermore, a TSV-stress-driven, force-directed, and 3D placement algorithm is developed. It exploits carrier mobility variation, caused by stress around TSVs after fabrication, to improve the timing and area objectives during placement. In addition, the impact of keep-out zone (KOZ) around TSVs on stress, carrier mobility variation, area, wirelength, and performance of 3D ICs is studied. In the third work, two temperature-aware global placement algorithms are developed. They exploit die-to-die thermal coupling in 3D ICs to improve temperature during placement. In addition, a framework used to evaluate the results from temperature-aware global placements is developed. The main component of the framework is a GDSII-level thermal analysis that considers all structures inside a TSV-based 3D IC while computing temperature. The developed placers are compared with several state-of-the-art placers published in recent literature. The experimental results indicate that the developed algorithms help improve the temperature of 3D ICs effectively. In the final work, three block-level design styles for TSV-based die-to-wafer bonded 3D ICs are discussed. Several 3D-IC layouts in the three styles are manually designed. The main difference among these layouts is the position of TSVs. Finally, the area, wirelength, timing, power, temperature, and mechanical stress of all layouts are compared to explore the trade-offs of layout quality.PhDCommittee Chair: Lim, Sung Kyu; Committee Member: Bakir, Muhannad; Committee Member: Kim, Hyesoon; Committee Member: Mukhopadhyay, Saibal; Committee Member: Swaminathan, Madhava

High-performance Global Routing for Trillion-gate Systems-on-Chips.

Due to aggressive transistor scaling, modern-day CMOS circuits have continually increased in both complexity and productivity. Modern semiconductor designs have narrower and more resistive wires, thereby shifting the performance bottleneck to interconnect delay. These trends considerably impact timing closure and call for improvements in high-performance physical design tools to keep pace with the current state of IC innovation. As leading-edge designs may incorporate tens of millions of gates, algorithm and software scalability are crucial to achieving reasonable turnaround time. Moreover, with decreasing device sizes, optimizing traditional objectives is no longer sufficient. Our research focuses on (i) expanding the capabilities of standalone global routing, (ii) extending global routing for use in different design applications, and (iii) integrating routing within broader physical design optimizations and flows, e.g., congestion-driven placement. Our first global router relies on integer-linear programming (ILP), and can solve fairly large problem instances to optimality. Our second iterative global router relies on Lagrangian relaxation, where we relax the routing violation constraints to allowing routing overflow at a penalty. In both approaches, our desire is to give the router the maximum degree of freedom within a specified context. Empirically, both routers produce competitive results within a reasonable amount of runtime. To improve routability, we explore the incorporation of routing with placement, where the router estimates congestion and feeds this information to the placer. In turn, the emphasis on runtime is heightened, as the router will be invoked multiple times. Empirically, our placement-and-route framework significantly improves the final solution’s routability than performing the steps sequentially. To further enhance routability-driven placement, we (i) leverage incrementality to generate fast and accurate congestion maps, and (ii) develop several techniques to relieve cell-based and layout-based congestion. To broaden the scope of routing, we integrate a global router in a chip-design flow that addresses the buffer explosion problem.PHDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/98025/1/jinhu_1.pd

Nanometer VLSI placement and optimization for multi-objective design closure

In a VLSI physical synthesis flow, placement directly defines the interconnection, which affects many other design objectives, such as timing, power consumption, congestion, and thermal issues. With the scaling of technology, the relative interconnect delay increases dramatically. As a result, placement has become a bottleneck in deep sub-micron physical synthesis. In this dissertation, I propose several optimization algorithms from global placement, placement migration, timing driven placements, to incremental power optimizations for multi-objective VLSI design closure. The first work is DPlace, a new global placement algorithm that scales well to the modern large-scale circuit placement problems. DPlace simulates the natural diffusion process to spread cells smoothly over the placement region, and uses both analytical and discrete techniques to improve the wire length. However, global placement is never sufficient for multi-objective design closure, a variety of design objectives have to be improved incrementally, such as timing, routing congestion, signal integrity, and heat distribution. Placement migration is a critical step to address the cell overlaps appearing during incremental optimizations. To achieve high placement stability, I propose a computational geometry based placement migration flow to cope with placement changes, and a new stability metric to measure the “similarity” between two placements accurately. Our placement migration algorithm has clear advantage over conventional legalization algorithms such that the neighborhood characteristics of the original placement are preserved. For timing closure in high performance designs, I present a linear programming based incremental timing driven placement to improve the timing on critical paths directly. I further present an efficient timing driven placement algorithm (Pyramids). Two formulations of Pyramids are proposed, which are suitable for different optimization stages in a physical synthesis flow. Both approaches find the optimal location for timing of a cell in constant time, through computational geometry based approaches. For fast convergence of design closure, placement should be integrated with other optimization techniques. I propose to combine placement, gate sizing and Vt swapping techniques to reduce the total power consumption, especially the leakage power, which is becoming increasingly critical for nanometer VLSI design closure.Electrical and Computer Engineerin