Modeling of thermally induced skew variations in clock distribution network

Clock distribution network is sensitive to large thermal gradients on the die as the performance of both clock buffers and interconnects are affected by temperature. A robust clock network design relies on the accurate analysis of clock skew subject to temperature variations. In this work, we address the problem of thermally induced clock skew modeling in nanometer CMOS technologies. The complex thermal behavior of both buffers and interconnects are taken into account. In addition, our characterization of the temperature effect on buffers and interconnects provides valuable insight to designers about the potential impact of thermal variations on clock networks. The use of industrial standard data format in the interface allows our tool to be easily integrated into existing design flow

Associative skew clock routing for difficult instances

This thesis studies the associative skew clock routing problem, which seeks a clock routing tree such that zero skew is preserved only within identified groups of sinks. Although the number of constraints is reduced, the problem becomes more difficult to solve due to the enlarged solution space. Perhaps, the only previous study used a very primitive delay model which could not handle difficult instances when sink groups are intermingled. We reuse existing techniques to solve this problem including difficult instances based on an improved delay model. Experimental results show that our algorithm can reduce the total clock routing wirelength by 9%Â15% compared to greedy-DME, which is one of the best zero skew routing algorithms

High performance IC clock networks with grid and tree topologies

In this dissertation, an essential step in the integrated circuit (IC) physical design flow—the clock network design—is investigated. Clock network design entailsa series of computationally intensive, large-scale design and optimization tasks for the generation and distribution of the clock signal through different topologies. The lack or inefficacy of the automation for implementing high performance clock networks, especially for low-power, high speed and variation-aware implementations, is the main driver for this research. The synthesis and optimization methods for the two most commonly used clock topologies in IC design—the grid topology and the tree topology—are primarily investigated.The clock mesh network, which uses the grid topology, has very low skew variation at the cost of high power dissipation. Two novel clock mesh network designmethodologies are proposed in this dissertation in order to reduce the power dissipation. These are the first methods known in literature that combine clock meshsynthesis with incremental register placement and clock gating for power saving purposes. The application of the proposed automation methods on the emerging resonant rotary clocking technology, which also has the grid topology, is investigated in this dissertation as well.The clock tree topology has the advantage of lower power dissipation compared to other traditional clock topologies (e.g. clock mesh, clock spine, clock tree with cross links) at the cost of increased performance degradation due to on-chip variations. A novel clock tree buffer polarity assignment flow is proposed in this dissertation in order to reduce these effects of on-chip variations on the clock tree topology. The proposed polarity assignment flow is the first work that introduces post-silicon, dynamic reconfigurability for polarity assignment, enabling clock gating for low power operation of the variation-tolerant clock tree networks.Ph.D., Electrical Engineering -- Drexel University, 201

Clock tree synthesis for prescribed skew specifications

In ultra-deep submicron VLSI designs, clock network layout plays an increasingly important role in determining circuit performance including timing, power consumption, cost, power supply noise and tolerance to process variations. It is required that a clock layout algorithm can achieve any prescribed skews with the minimum wire length and acceptable slew rate. Traditional zero-skew clock routing methods are not adequate to address this demand, since they tend to yield excessive wire length for prescribed skew targets. The interactions among skew targets, sink location proximities and capacitive load balance are analyzed. Based on this analysis, a maximum delay-target ordering merging scheme is suggested to minimize wire and buffer area, which results in lesser cost, power consumption and vulnerability to process variations. During the clock routing, buffers are inserted simultaneously to facilitate a proper slew rate level and reduce wire snaking. The proposed algorithm is simple and fast for practical applications. Experimental results on benchmark circuits show that the algorithm can reduce the total wire and buffer capacitance by 60% over an extension of the existing zero-skew routing method

High-performance and Low-power Clock Network Synthesis in the Presence of Variation.

Semiconductor technology scaling requires continuous evolution of all aspects of physical design of integrated circuits. Among the major design steps, clock-network synthesis has been greatly affected by technology scaling, rendering existing methodologies inadequate. Clock routing was previously sufficient for smaller ICs, but design difficulty and structural complexity have greatly increased as interconnect delay and clock frequency increased in the 1990s. Since a clock network directly influences IC performance and often consumes a substantial portion of total power, both academia and industry developed synthesis methodologies to achieve low skew, low power and robustness from PVT variations. Nevertheless, clock network synthesis under tight constraints is currently the least automated step in physical design and requires significant manual intervention, undermining turn-around-time. The need for multi-objective optimization over a large parameter space and the increasing impact of process variation make clock network synthesis particularly challenging. Our work identifies new objectives, constraints and concerns in the clock-network synthesis for systems-on-chips and microprocessors. To address them, we generate novel clock-network structures and propose changes in traditional physical-design flows. We develop new modeling techniques and algorithms for clock power optimization subject to tight skew constraints in the presence of process variations. In particular, we offer SPICE-accurate optimizations of clock networks, coordinated to reduce nominal skew below 5 ps, satisfy slew constraints and trade-off skew, insertion delay and power, while tolerating variations. To broaden the scope of clock-network-synthesis optimizations, we propose new techniques and a methodology to reduce dynamic power consumption by 6.8%-11.6% for large IC designs with macro blocks by integrating clock network synthesis within global placement. We also present a novel non-tree topology that is 2.3x more power-efficient than mesh structures. We fuse several clock trees to create large-scale redundancy in a clock network to bridge the gap between tree-like and mesh-like topologies. Integrated optimization techniques for high-quality clock networks described in this dissertation strong empirical results in experiments with recent industry-released benchmarks in the presence of process variation. Our software implementations were recognized with the first-place awards at the ISPD 2009 and ISPD 2010 Clock-Network Synthesis Contests organized by IBM Research and Intel Research.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89711/1/ejdjsy_1.pd

Variation and power issues in VLSI clock networks

Clock Distribution Network (CDN) is an important component of any synchronous logic circuit. The function of CDN is to deliver the clock signal to the clock sinks. Clock skew is defined as the difference in the arrival time of the clock signal at the clock sinks. Higher uncertainty in skew (due to PVT variations) degrades circuit performance by decreasing the maximum possible delay between any two sequential elements. Aggressive frequency scaling has also led to high power consumption especially in CDN. This dissertation addresses variation and power issues in the design of current and potential future CDN. The research detailed in this work presents algorithmic techniques for the following problems: (1) Variation tolerance in useful skew design, (2) Link insertion for buffered clock nets, (3) Methodology and algorithms for rotary clocking and (4) Clock mesh optimization for skew-power trade off. For clock trees this dissertation presents techniques to integrate the different aspects of clock tree synthesis (skew scheduling, abstract topology and layout embedding) into one framework- tolerance to variations. This research addresses the issues involved in inserting cross-links in a buffered clock tree and proposes design criteria to avoid the risk of short-circuit current. Rotary clocking is a promising new clocking scheme that consists of unterminated rings formed by differential transmission lines. Rotary clocking achieves reduction in power dissipation clock skew. This dissertation addresses the issues in adopting current CAD methodology to rotary clocks. Alternative methodology and corresponding algorithmic techniques are detailed. Clock mesh is a popular form of CDN used in high performance systems. The problem of simultaneous sizing and placement of mesh buffers in a clock mesh is addressed. The algorithms presented remove the edges from the clock mesh to trade off skew tolerance for low power. For clock trees as well as link insertion, our experiments indicate significant reduction in clock skew due to variations. For clock mesh, experimental results indicate 18.5% reduction in power with 1.3% delay penalty on a average. In summary, this dissertation details methodologies/algorithms that address two critical issues- variation and power dissipation in current and potential future CDN

Synthesis Methodologies for Robust and Reconfigurable Clock Networks

In today\u27s aggressively scaled technology nodes, billions of transistors are packaged into a single integrated circuit. Electronic Design Automation (EDA) tools are needed to automatically assemble the transistors into a functioning system. One of the most important design steps in the physical synthesis is the design of the clock network. The clock network delivers a synchronizing clock signal to each sequential element. The clock signal is required to be delivered meeting timing constraints under variations and in multiple operating modes. Synthesizing such clock networks is becoming increasingly difficult with the complex power management methodologies and severe manufacturing variations. Clock network synthesis is an important problem because it has a direct impact on the functional correctness, the maximum operating frequency, and the overall power consumption of each synchronous integrated circuit. In this dissertation, we proposed synthesis methodologies for robust and reconfigurable clock networks. We have made three contributions to this topic. First, we have proposed a clock network optimization framework that can achieve better timing quality than previous frameworks. Our proposed framework improves timing quality by reducing the propagation delay on critical paths in a clock network using buffer sizing and layer assignment. Second, we have proposed a clock tree synthesis methodology that integrates the clock tree synthesis with the clock tree optimization. The methodology improves timing quality by avoiding to synthesize clock trees with topologies that are sensitive to variations. Third, we have proposed a clock network that can reconfigure the topology based on the active mode of operation. Lastly, we conclude the dissertation with future research directions

Design Methodologies and Architecture Solutions for High-Performance Interconnects

ABSTRACT In Deep Sub-Micron (DSM) technologies, interconnects play a crucial role in the correct functionality and largely impact the performance of complex System-on-Chip (SoC) designs. For technologies of 0.25µm and below, wiring capacitance dominates gate capacitance, thus rapidly increasing the interconnect-induced delay. Moreover, the coupling capacitance becomes a significant portion of the on-chip total wiring capacitance, and coupling between adjacent wires cannot be considered as a second-order effect any longer. As a consequence, the traditional top-down design methodology is ineffective, since the actual wiring delays can be computed only after layout parasitic extraction, when the physical design is completed. Fixing all the timing violations often requires several time-consuming iterations of logical and physical design, and it is essentially a trial-and-error approach. Increasingly tighter time-to-market requirements dictate that interconnect parasitics must be taken into account during all phases of the design flow, at different level of abstractions. However, given the aggressive technology scaling trends and the growing design complexity, this approach will only temporarily ameliorate the interconnect problem. We believe that in order to achieve gigascale designs in the nanometer regime, a novel design paradigm, based on new forms of regularity and newly created IP (Intellectual Property) blocks must be developed, to provide a direct path from system-level architectural exploration to physical implementation

메쉬 기반의 클락 네트워크 설계 방법론

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2015. 2. 김태환.The clock distribution network in a synchronous digital circuit delivers a clock signal to every storage element i.e., clock sink in the circuit. However, since the continued technology scaling increases PVT (process-voltage-temperature) variation, the increase of clock skew variation is highly likely to cause performance degradation or system failure at run time. Recently, to mitigate the clock skew variation, many researchers have taken a profound interest in the clock mesh network. However, though the structure of clock mesh network is excellent in tolerating timing variation, it demands significantly high power consumption due to the use of excessive mesh wire and buffer resources. Thus, optimizing the resources required in the mesh clock synthesis while maintaining the variation tolerance is crucially important. The three major tasks that greatly affect the cost of resulting clock mesh are (1) mesh segment allocation, (2) mesh buffer allocation and sizing, and (3) clock sink binding to mesh segments. Previous clock mesh optimization approaches solve the three tasks sequentially, one by one at a time, to manage the run time complexity of the tasks at the expense of losing the quality of results. However, since the three tasks are tightly inter-related, simultaneously optimizing all three tasks is essential, if the run time is ever permitted, to synthesize an economical clock mesh network. In this dissertation, we propose an approach which is able to tackle the problem in an integrated fashion by combining the three tasks into an iterative framework of incremental updates and solving them simultaneously to find a globally optimal allocation of mesh resources while taking into account the clock skew tolerance constraints. The core parts of this dissertation are a precise analysis on the relation among the resource optimization tasks and an establishment of mechanism for effective and efficient integration of the tasks. In particular, to handle the run time problem, we propose a set of speed-up techniques i.e., modeling RC circuit for eliminating redundant matrix multiplications, exploiting sliding window scheme, and fast buffer sizing effect estimation, which are fitted into our context of fast clock skew estimation in mesh resource optimization as well as an invention of early decision policies. In summary, this dissertation presents the efficient design methodology for clock mesh synthesis with consideration on integration of three tasks and reduction of runtime complexity.Abstract i Contents iii List of Figures vi List of Tables x 1 Introduction 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Contributions of This Dissertation . . . . . . . . . . . . . . . . . . . 3 2 Background 5 2.1 Clock Distribution Network . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Clock Network Topologies . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Design Metrics of Clock Network . . . . . . . . . . . . . . . . . . . 7 2.4 The Effects of Variations on Clock Skew . . . . . . . . . . . . . . . . 9 3 Clock Mesh Synthesis Flow 12 3.1 Elements of Clock Mesh . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Conventional Clock Mesh Synthesis Overview . . . . . . . . . . . . . 13 3.3 Initial Grid Generation . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Mesh Buffer Placement and Sizing . . . . . . . . . . . . . . . . . . . 14 3.5 Clock Mesh Optimization . . . . . . . . . . . . . . . . . . . . . . . . 17 4 Integrated Resource Allocation and Binding in Clock Mesh Synthesis 19 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.3 Framework of Clock Mesh Optimization . . . . . . . . . . . . . . . . 26 4.3.1 Incremental Resource Updates . . . . . . . . . . . . . . . . . 29 4.3.2 Constraints for Variation Tolerance . . . . . . . . . . . . . . 34 4.3.3 Early Decision Policies . . . . . . . . . . . . . . . . . . . . . 38 4.3.4 Time Complexity Analysis . . . . . . . . . . . . . . . . . . . 39 4.4 Fast Clock Skew Estimation Techniques . . . . . . . . . . . . . . . . 40 4.4.1 Partially Reusing Matrix Multiplication for Incremental Updates 41 4.4.2 Adopting Sliding Window Scheme . . . . . . . . . . . . . . . 43 4.4.3 Adjusting Delay Caused by Buffer Resizing . . . . . . . . . . 44 4.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.5.1 Experimental Environments . . . . . . . . . . . . . . . . . . 46 4.5.2 Resource Requirement and Variation Tolerance Comparison . 48 4.5.3 Comparison with Clock Mesh Optimization using Worst Case Timing Analysis of Commercial Tool . . . . . . . . . . . . . 56 4.5.4 Analysis of the Effect of Proposed Techniques . . . . . . . . 58 4.5.5 Run Time Analysis . . . . . . . . . . . . . . . . . . . . . . . 61 4.5.6 Accuracy and Run Time of Fast Clock Skew Estimation . . . 63 4.5.7 Electromigration Analysis . . . . . . . . . . . . . . . . . . . 68 4.5.8 Run-time Analysis in Multi-thread Computing Environment . 70 4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5 Conclusion 74 Abstract in Korean 84Docto