HIGH PERFORMANCE CLOCK DISTRIBUTION FOR HIGH-SPEED VLSI SYSTEMS

Tohoku University堀口 進課

Design and modelling of variability tolerant on-chip communication structures for future high performance system on chip designs

The incessant technology scaling has enabled the integration of functionally complex System-on-Chip (SoC) designs with a large number of heterogeneous systems on a single chip. The processing elements on these chips are integrated through on-chip communication structures which provide the infrastructure necessary for the exchange of data and control signals, while meeting the strenuous physical and design constraints. The use of vast amounts of on chip communications will be central to future designs where variability is an inherent characteristic. For this reason, in this thesis we investigate the performance and variability tolerance of typical on-chip communication structures. Understanding of the relationship between variability and communication is paramount for the designers; i.e. to devise new methods and techniques for designing performance and power efficient communication circuits in the forefront of challenges presented by deep sub-micron (DSM) technologies. The initial part of this work investigates the impact of device variability due to Random Dopant Fluctuations (RDF) on the timing characteristics of basic communication elements. The characterization data so obtained can be used to estimate the performance and failure probability of simple links through the methodology proposed in this work. For the Statistical Static Timing Analysis (SSTA) of larger circuits, a method for accurate estimation of the probability density functions of different circuit parameters is proposed. Moreover, its significance on pipelined circuits is highlighted. Power and area are one of the most important design metrics for any integrated circuit (IC) design. This thesis emphasises the consideration of communication reliability while optimizing for power and area. A methodology has been proposed for the simultaneous optimization of performance, area, power and delay variability for a repeater inserted interconnect. Similarly for multi-bit parallel links, bandwidth driven optimizations have also been performed. Power and area efficient semi-serial links, less vulnerable to delay variations than the corresponding fully parallel links are introduced. Furthermore, due to technology scaling, the coupling noise between the link lines has become an important issue. With ever decreasing supply voltages, and the corresponding reduction in noise margins, severe challenges are introduced for performing timing verification in the presence of variability. For this reason an accurate model for crosstalk noise in an interconnection as a function of time and skew is introduced in this work. This model can be used for the identification of skew condition that gives maximum delay noise, and also for efficient design verification

Timing-Constrained Global Routing with RC-Aware Steiner Trees and Routing Based Optimization

In this thesis we consider the global routing problem, which arises as one of the major subproblems in the physical design step in VLSI design. In global routing, we are given a three-dimensional grid graph G with edge capacities representing available routing space, and we have to connect a set of nets in G without overusing any edge capacities. Here, each net consists of a set of pins corresponding to vertices of G, where one pin is the sender of signals, while all other pins are receivers. Traditionally, next to obeying all edge capacity constraints, the objective has been to minimize wire length and possibly via (edges in z-direction) count, and timing constraints on the chip were only modeled indirectly. We present a new approach, where timing constraints are modeled directly during global routing: In joint work with Stephan Held, Dirk Mueller, Daniel Rotter, Vera Traub and Jens Vygen, we extend the modeling of global routing as a Min-Max Resource Sharing Problem to also incorporate timing constraints. For measuring signal delays we use the well-established Elmore delay model. One of the key subproblems here is the computation of Steiner trees minimizing a weighted sum of routing space usages and signal delays. For k pins, this problem is NP-hard to approximate within o(log k), and even the special case k = 2 is NP-hard, as was shown by Haehnle and Rotter. We present a fast approximation algorithm with strong approximation bounds for the case k = 2. For k > 2 we use a multi-stage approach based on modifying the topology of a short Steiner tree and using our algorithm for the two-pin case for computing new connections. Moreover, we present a layer assignment algorithm that assigns z-coordinates to the edges of a given two-dimensional tree. We also discuss the topic of routing based optimization. Here, the starting point is a complete routing, and timing optimization tools make changes that require incremental adaptations of the underlying routing. We investigate several aspects of this problem and derive a new routing flow that includes our timing-aware global router and routing based optimization steps. We evaluate our results from this thesis in practice on industrial 14nm microprocessor designs from IBM. Our theoretical results are validated in practice by a strong performance of our timing-aware global routing framework and our new routing flow, yielding significant improvements over the traditional global routing method and the previously used routing flow. Therefore, we conclude that our approaches and results from this thesis are not only theoretically sound but also give compelling results in practice

Shortest Paths and Steiner Trees in VLSI Routing

Routing is one of the major steps in very-large-scale integration (VLSI) design. Its task is to find disjoint wire connections between sets of points on a chip, subject to numerous constraints. This problem is solved in a two-stage approach, which consists of so-called global and detailed routing steps. For each set of metal components to be connected, global routing reduces the search space by computing corridors in which detailed routing sequentially determines the desired connections as shortest paths. In this thesis, we present new theoretical results on Steiner trees and shortest paths, the two main mathematical concepts in routing. In the practical part, we give computational results of BonnRoute, a VLSI routing tool developed at the Research Institute for Discrete Mathematics at the University of Bonn. Interconnect signal delays are becoming increasingly important in modern chip designs. Therefore, the length of paths or direct delay measures should be taken into account when constructing rectilinear Steiner trees. We consider the problem of finding a rectilinear Steiner minimum tree (RSMT) that --- as a secondary objective --- minimizes a signal delay related objective. Given a source we derive some structural properties of RSMTs for which the weighted sum of path lengths from the source to the other terminals is minimized. Also, we present an exact algorithm for constructing RSMTs with weighted sum of path lengths as secondary objective, and a heuristic for various secondary objectives. Computational results for industrial designs are presented. We further consider the problem of finding a shortest rectilinear Steiner tree in the plane in the presence of rectilinear obstacles. The Steiner tree is allowed to run over obstacles; however, if it intersects an obstacle, then no connected component of the induced subtree must be longer than a given fixed length. This kind of length restriction is motivated by its application in VLSI routing where a large Steiner tree requires the insertion of repeaters which must not be placed on top of obstacles. We show that there are optimal length-restricted Steiner trees with a special structure. In particular, we prove that a certain graph (called augmented Hanan grid) always contains an optimal solution. Based on this structural result, we give an approximation scheme for the special case that all obstacles are of rectangular shape or are represented by at most a constant number of edges. Turning to the shortest paths problem, we present a new generic framework for Dijkstra's algorithm for finding shortest paths in digraphs with non-negative integral edge lengths. Instead of labeling individual vertices, we label subgraphs which partition the given graph. Much better running times can be achieved if the number of involved subgraphs is small compared to the order of the original graph and the shortest path problems restricted to these subgraphs is computationally easy. As an application we consider the VLSI routing problem, where we need to find millions of shortest paths in partial grid graphs with billions of vertices. Here, the algorithm can be applied twice, once in a coarse abstraction (where the labeled subgraphs are rectangles), and once in a detailed model (where the labeled subgraphs are intervals). Using the result of the first algorithm to speed up the second one via goal-oriented techniques leads to considerably reduced running time. We illustrate this with the routing program BonnRoute on leading-edge industrial chips. Finally, we present computational results of BonnRoute obtained on real-world VLSI chips. BonnRoute fulfills all requirements of modern VLSI routing and has been used by IBM and its customers over many years to produce more than one thousand different chips. To demonstrate the strength of BonnRoute as a state-of-the-art industrial routing tool, we show that it performs excellently on all traditional quality measures such as wire length and number of vias, but also on further criteria of equal importance in the every-day work of the designer

CAD methodologies for low power and reliable 3D ICs

The main objective of this dissertation is to explore and develop computer-aided-design (CAD) methodologies and optimization techniques for reliability, timing performance, and power consumption of through-silicon-via(TSV)-based and monolithic 3D IC designs. The 3D IC technology is a promising answer to the device scaling and interconnect problems that industry faces today. Yet, since multiple dies are stacked vertically in 3D ICs, new problems arise such as thermal, power delivery, and so on. New physical design methodologies and optimization techniques should be developed to address the problems and exploit the design freedom in 3D ICs. Towards the objective, this dissertation includes four research projects. The first project is on the co-optimization of traditional design metrics and reliability metrics for 3D ICs. It is well known that heat removal and power delivery are two major reliability concerns in 3D ICs. To alleviate thermal problem, two possible solutions have been proposed: thermal-through-silicon-vias (T-TSVs) and micro-fluidic-channel (MFC) based cooling. For power delivery, a complex power distribution network is required to deliver currents reliably to all parts of the 3D IC while suppressing the power supply noise to an acceptable level. However, these thermal and power networks pose major challenges in signal routability and congestion. In this project, a co-optimization methodology for signal, power, and thermal interconnects in 3D ICs is presented. The goal of the proposed approach is to improve signal, thermal, and power noise metrics and to provide fast and accurate design space explorations for early design stages. The second project is a study on 3D IC partition. For a 3D IC, the target circuit needs to be partitioned into multiple parts then mapped onto the dies. The partition style impacts design quality such as footprint, wirelength, timing, and so on. In this project, the design methodologies of 3D ICs with different partition styles are demonstrated. For the LEON3 multi-core microprocessor, three partitioning styles are compared: core-level, block-level, and gate-level. The design methodologies for such partitioning styles and their implications on the physical layout are discussed. Then, to perform timing optimizations for 3D ICs, two timing constraint generation methods are demonstrated that lead to different design quality. The third project is on the buffer insertion for timing optimization of 3D ICs. For high performance 3D ICs, it is crucial to perform thorough timing optimizations. Among timing optimization techniques, buffer insertion is known to be the most effective way. The TSVs have a large parasitic capacitance that increases the signal slew and the delay on the downstream. In this project, a slew-aware buffer insertion algorithm is developed that handles full 3D nets and considers TSV parasitics and slew effects on delay. Compared with the well-known van Ginneken algorithm and a commercial tool, the proposed algorithm finds buffering solutions with lower delay values and acceptable runtime overhead. The last project is on the ultra-high-density logic designs for monolithic 3D ICs. The nano-scale 3D interconnects available in monolithic 3D IC technology enable ultra-high-density device integration at the individual transistor-level. The benefits and challenges of monolithic 3D integration technology for logic designs are investigated. First, a 3D standard cell library for transistor-level monolithic 3D ICs is built and their timing and power behavior are characterized. Then, various interconnect options for monolithic 3D ICs that improve design quality are explored. Next, timing-closed, full-chip GDSII layouts are built and iso-performance power comparisons with 2D IC designs are performed. Important design metrics such as area, wirelength, timing, and power consumption are compared among transistor-level monolithic 3D, gate-level monolithic 3D, TSV-based 3D, and traditional 2D designs.PhDCommittee Chair: Lim, Sung Kyu; Committee Member: Bakir, Muhannad; Committee Member: Kim, Hyesoon; Committee Member: Lee, Hsien-Hsin; Committee Member: Mukhopadhyay, Saiba

Analysis of Dynamic Logic Circuits in Deep Submicron CMOS Technologies

Dynamic logic circuits are utilized to minimize the delay in the critical path of high-performance designs such as the datapath circuits in state-of-the-art microprocessors. However, as integrated circuits (ICs) scale to the very deep submicron (VDSM) regime, dynamic logic becomes susceptible to a variety of failure modes due to decreasing noise margins and increasing leakage currents. The objective of this thesis is to characterize the performance of dynamic logic circuits in VDSM technologies and to evaluate various design strategies to mitigate the effects of leakage currents and small noise margins