Timing and Area Optimization for Standard-Cell VLSI Circuit Design

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / N00014-90-J-127

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

Clock Tree and Flip-flop Co-optimization for Reducing Power Consumption and Power/Ground Noise of Integrated Circuits and Systems

학위논문 (박사)-- 서울대학교 대학원 공과대학 전기·컴퓨터공학부, 2017. 8. 김태환.For very-large-scale integration (VLSI) circuits, the activation of all flip-flops that are used to store data is synchronized by clock signals delivered through clock networks. Due to very high frequency of clock signal switches, the dynamic power consumed on clock networks takes a considerable portion of the total power consumption of the circuits. In addition, the largest amount of power consumption in the clock networks comes from the flip-flops and the buffers that drive the flip-flops at the clock network boundary. In addition, the requirement of simultaneously activating all flip-flops for synchronous circuits induces a high peak power/ground noise (i.e., voltage drop) at the clock boundary. In this regards, this thesis addresses two new problems: the problem of reducing the clock power consumption at the clock network boundary, and the problem of reducing the peak current at the clock network boundary. Unlike the prior works which have considered the optimization of flip-flops and clock buffers separately, our approach takes into account the co-optimization of flip-flops and clock buffers. Precisely, we propose four different types of hardware component that can implement a set of flip-flops and their driving buffer as a single unit. The key idea for the derivation of the four types of clock boundary component is that one of the inverters in the driving buffer and one of the inverters in each flip-flop can be combined and removed without changing the functionality of the flip-flops. Consequently, we have a more freedom to select (i.e., allocate) clock boundary components that is able to reduce the power consumption or peak current under timing constraint. We have implemented our approach of clock boundary optimization under bounded clock skew constraint and tested it with ISCAS 89 benchmark circuits. The experimental results confirm that our approach is able to reduce the clock power consumption by 7.9∼10.2% and power/ground noise by 27.7%∼30.9% on average.Chapter 1 Introduction 1 1.1 Clock Signal 1 1.2 Metrics of Clock Design 2 1.3 Clock Network Topologies 4 1.4 Multibit Flip-flop 5 1.5 Simultaneous Switching Noise 6 1.6 Contributions of This Dissertation 6 Chapter 2 Clock Tree and Flip-flop Co-optimization for Reducing Power Consumption 8 2.1 Introduction 8 2.2 Types of Boundary Optimization 9 2.3 Analysis of Four Types of Flip-flop 12 2.3.1 Internal Power Comparison 12 2.3.2 Characterization of Power Consumption 14 2.4 Problem Formulation 15 2.5 The Proposed Algorithm 17 2.5.1 Independence Assumption 17 2.5.2 BoundaryMin Algorithm 17 2.6 Experimental Results 29 2.6.1 Experimental Setup 29 2.6.2 Clock Tree Boundary Optimization Results 33 2.6.3 Capacitance Analysis on Flip-flops 38 2.6.4 Slew and Skew Analysis 39 2.6.5 Window Width Analysis 39 2.7 Conclusions 41 Chapter 3 Clock Tree and Flip-flop Co-optimization for Reducing Power/Ground Noise 42 3.1 Introduction 42 3.2 Current Characteristic of Four Types of Flip-flop 45 3.3 Motivational Example 47 3.4 Problem Formulation 52 3.5 Proposed Algorithm 54 3.5.1 An Overview 54 3.5.2 Superposition of Current Flows 55 3.5.3 Formulation to Instance of MOSP Problem 57 3.5.4 Selecting Target Power Grid Points 59 3.5.5 Consideration of Reducing Power Consumption 62 3.6 Experimental Results 62 3.7 Summary 65 Chapter 4 Conclusion 68 4.1 Clock Buffer and Flip-flop Co-optimization for Reducing Power Consumption 68 4.2 Clock Buffer and Flip-flop Co-optimization for Reducing Power/Ground Noise 69 초록 78Docto

Physical Design of Optoelectronic System-on-a-Chip/Package Using Electrical and Optical Interconnects: CAD Tools and Algorithms

Current electrical systems are faced with the limitation in performance by the electrical interconnect technology determining overall processing speed. In addition, the electrical interconnects containing many long distance interconnects require high power to drive. One of the best ways to overcome these bottlenecks is through the use of optical interconnect to limit interconnect latency and power. This research explores new computer-aided design algorithms for developing optoelectronic systems. These algorithms focus on place and route problems using optical interconnections covering system-on-a-chip design as well as system-on-a-package design. In order to design optoelectronic systems, optical interconnection models are developed at first. The CAD algorithms include optical interconnection models and solve place and route problems for optoelectronic systems. The MCNC and GSRC benchmark circuits are used to evaluate these algorithms.Ph.D.Committee Chair: Abhijit Chatterjee; Committee Member: C. P. Wong; Committee Member: David E. Schimmel; Committee Member: John A. Buck; Committee Member: Madhavan Swaminatha

Clock routing for high performance microprocessor designs.

Tian, Haitong.Chinese abstract is on unnumbered page.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (p. 65-74).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivations --- p.1Chapter 1.2 --- Our Contributions --- p.2Chapter 1.3 --- Organization of the Thesis --- p.3Chapter 2 --- Background Study --- p.4Chapter 2.1 --- Traditional Clock Routing Problem --- p.4Chapter 2.2 --- Tree-Based Clock Routing Algorithms --- p.5Chapter 2.2.1 --- Clock Routing Using H-tree --- p.5Chapter 2.2.2 --- Method of Means and Medians(MMM) --- p.6Chapter 2.2.3 --- Geometric Matching Algorithm (GMA) --- p.8Chapter 2.2.4 --- Exact Zero-Skew Algorithm --- p.9Chapter 2.2.5 --- Deferred Merge Embedding (DME) --- p.10Chapter 2.2.6 --- Boundary Merging and Embedding (BME) Algorithm --- p.14Chapter 2.2.7 --- Planar Clock Routing Algorithm --- p.17Chapter 2.2.8 --- Useful-skew Tree Algorithm --- p.18Chapter 2.3 --- Non-Tree Clock Distribution Networks --- p.19Chapter 2.3.1 --- Grid (Mesh) Structure --- p.20Chapter 2.3.2 --- Spine Structure --- p.20Chapter 2.3.3 --- Hybrid Structure --- p.21Chapter 2.4 --- Post-grid Clock Routing Problem --- p.22Chapter 2.5 --- Limitations of the Previous Work --- p.24Chapter 3 --- Post-Grid Clock Routing Problem --- p.26Chapter 3.1 --- Introduction --- p.26Chapter 3.2 --- Problem Definition --- p.27Chapter 3.3 --- Our Approach --- p.30Chapter 3.3.1 --- Delay-driven Path Expansion Algorithm --- p.31Chapter 3.3.2 --- Pre-processing to Connect Critical ports --- p.34Chapter 3.3.3 --- Post-processing to Reduce Capacitance --- p.36Chapter 3.4 --- Experimental Results --- p.39Chapter 3.4.1 --- Experiment Setup --- p.39Chapter 3.4.2 --- Validations of the Delay and Slew Estimation --- p.39Chapter 3.4.3 --- Comparisons with the Tree Grow (TG) Approach --- p.41Chapter 3.4.4 --- Lowest Achievable Delays --- p.42Chapter 3.4.5 --- Simulation Results --- p.42Chapter 4 --- Non-tree Based Post-Grid Clock Routing Problem --- p.44Chapter 4.1 --- Introduction --- p.44Chapter 4.2 --- Handling Ports with Large Load Capacitances --- p.46Chapter 4.2.1 --- Problem Ports Identification --- p.47Chapter 4.2.2 --- Non-Tree Construction --- p.47Chapter 4.2.3 --- Wire Link Selection --- p.48Chapter 4.3 --- Path Expansion in Non-tree Algorithm --- p.51Chapter 4.4 --- Limitations of the Non-tree Algorithm --- p.51Chapter 4.5 --- Experimental Results --- p.51Chapter 4.5.1 --- Experiment Setup --- p.51Chapter 4.5.2 --- Validations of the Delay and Slew Estimation --- p.52Chapter 4.5.3 --- Lowest Achievable Delays --- p.53Chapter 4.5.4 --- Results on New Benchmarks --- p.53Chapter 4.5.5 --- Simulation Results --- p.55Chapter 5 --- Efficient Partitioning-based Extension --- p.57Chapter 5.1 --- Introduction --- p.57Chapter 5.2 --- Partition-based Extension --- p.58Chapter 5.3 --- Experimental Results --- p.61Chapter 5.3.1 --- Experiment Setup --- p.61Chapter 5.3.2 --- Running Time Improvement with Partitioning Technique --- p.61Chapter 6 --- Conclusion --- p.63Bibliography --- p.6

Case Studies on Clock Gating and Local Routign for VLSI Clock Mesh

The clock is the important synchronizing element in all synchronous digital systems. The difference in the clock arrival time between sink points is called the clock skew. This uncertainty in arrival times will limit operating frequency and might cause functional errors. Various clock routing techniques can be broadly categorized into 'balanced tree' and 'fixed mesh' methods. The skew and delay using the balanced tree method is higher compared to the fixed mesh method. Although fixed mesh inherently uses more wire length, the redundancy created by loops in a mesh structure reduces undesired delay variations. The fixed mesh method uses a single mesh over the entire chip but it is hard to introduce clock gating in a single clock mesh. This thesis deals with the introduction of 'reconfigurability' by using control structures like transmission gates between sub-clock meshes, thus enabling clock gating in clock mesh. By using the optimum value of size for PMOS and NMOS of transmission gate (SZF) and optimum number of transmission gates between sub-clock meshes (NTG) for 4x4 reconfigurable mesh, the average of the maximum skew for all benchmarks is reduced by 18.12 percent compared to clock mesh structure when no transmission gates are used between the sub-clock meshes (reconfigurable mesh with NTG =0). Further, the research deals with a ‘modified zero skew method' to connect synchronous flip-flops or sink points in the circuit to the clock grids of clock mesh. The wire length reduction algorithms can be applied to reduce the wire length used for a local clock distribution network. The modified version of ‘zero skew method’ of local clock routing which is based on Elmore delay balancing aims at minimizing wire length for the given bounded skew of CDN using clock mesh and H-tree. The results of ‘modified zero skew method' (HC_MZSK) show average local wire length reduction of 17.75 percent for all ISPD benchmarks compared to direct connection method. The maximum skew is small for HC_MZSK in most of the test cases compared to other methods of connections like direct connections and modified AHHK. Thus, HC_MZSK for local routing reduces the wire length and maximum skew

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

Power Reduction Techniques in Clock Distribution Networks with Emphasis on LC Resonant Clocking

In this thesis we propose a set of independent techniques in the overall concept of LC resonant clocking where each technique reduces power consumption and improve system performance. Low-power design is becoming a crucial design objective due to the growing demand on portable applications and the increasing difficulties in cooling and heat removal. The clock distribution network delivers the clock signal which acts as a reference to all sequential elements in the synchronous system. The clock distribution network consumes a considerable amount of power in synchronous digital systems. Resonant clocking is an emerging promising technique to reduce the power of the clock network. The inductor used in resonant clocking enables the conversion of the electric energy stored on the clock capacitance to magnetic energy in the inductor and vice versa. In this thesis, the concept of the slack in the clock skew has been extended for an LC fully-resonant clock distribution network. This extra slack in comparison to standard clock distribution networks can be used to reduce routing complexity, achieve reduction in wire elongation, total wire length, and power consumption. Simulation results illustrate that by utilizing the proposed approach, an average reduction of 53% in the number of wire elongations and 11% reduction in total wire length can be achieved. A dual-edge clocking scheme introduced in the literature to enable the operation of the flip-flop at the rising- and falling edges of the clock has been modified. The interval by which the charging elements in the flip-flop are being switched-on was reduced causing a reduction in power consumption. Simulating the flip-flop in STMicroelectronics 90-nm technology shows correct functionality of the Sense Amplifier flip-flop with a resonant clock signal of 500 MHz and a throughput of 1 GHz under process, voltage, and temperature (PVT) variations. Modeling the resonant system with the proposed flip-flop illustrates that dual-edge compared to single-edge triggering can achieve up to 58% reduction in power consumption when the clock capacitance is the dominating factor. The application of low-swing clocking to LC resonant clock distribution network has been investigated on-chip. The proposed low-swing resonant clocking scheme operates with one voltage supply and does not require an additional supply voltage. The Differential Conditional Capturing flip-flop introduced in the literature was modified to operate with a low-swing sinusoidal clock. Low-swing resonant clocking achieved around 5.8% reduction in total power with 5.7% area overhead. Modeling the clock network with the proposed flip-flop illustrates that low-swing clocking can achieve up to 58% reduction in the power consumption of the resonant clock. An analytical approach was introduced to estimate the required driver strength in the clock generator. Using the proposed approach early in the design stage reduces area and power overhead by eliminating the need for programmable switches in the driving circuit