Timing–driven variation–aware synthesis of hybrid mesh/tree clock distribution networks

Clock skew variations adversely affect timing margins, limiting performance, reducing yield, and may also lead to functional faults. Non-tree clock distribution networks, such as meshes and crosslinks, are employed to reduce skew and also to mitigate skew variations. These networks, however, increase the dissipated power while consuming significant metal resources. Several methods have been proposed to trade off power and wires to reduce skew. In this paper, an efficient algorithm is presented to reduce clock skew variations while minimizing power dissipation and metal area overhead. With a combination of nonuniform meshes and unbuffered trees (UBT), a variation-tolerant hybrid clock distribution network is produced. Clock skew variations are selectively reduced based on circuit timing information generated by static timing analysis (STA). The skew variation reduction procedure is prioritized for critical timing paths, since these paths are more sensitive to skew variations. A framework for skew variation management is proposed. The algorithm has been implemented in a standard 65 nm cell library using standard EDA tools, and tested on several benchmark circuits. As compared to other nonuniform mesh construction methods that do not support managed skew tolerance, experimental results exhibit a 41% average reduction in metal area and a 43% average reduction in power dissipation. As compared to other methods that employ skew tolerance management techniques but do not use a hybrid clock topology, an 8% average reduction in metal area and a 9% average reduction in power dissipation are achieved.     

同步电路设计中CLOCK SKEW 的分析

Clock skew是数字集成电路设计中一个重要的因素。本文比较了在同步电路设计中0clock skew和非0clock skew时钟分布对电路性能的影响，分析了通过调整时钟树中CLOCK SKEW来改善电路性能的方法，从而说明非0clock skew时钟分布是如何提高同步电路运行的最大时钟频率的。     

Hierarchical distribution network for low skew and high variation-tolerant bufferless resonant clocking

We propose a hierarchical interconnection network with two-phase bufferless resonant clock distribution, which mixes the advantages of mesh and tree architectures.The problems of skew reduction and variation-tolerance in the mixed interconnection network are studied through a pipelined multiplier under a TSMC 65 nm standard CMOS process.The post-simulation results show that the hierarchical architecture reduces more than 75% and 65%of clock skew compared with pure mesh and pure H-tree networks,respectively.The maximum skew in the proposed clock distribution is less than 7 ps under imbalanced loading and PVT variations,which is no more than 1%of the clock cycle of about 760 ps.     

Fast thermal analysis for fixed-outline 3D floorplanning

Three dimensional integrated circuits (3D ICs) can alleviate the problem of interconnection, a critical problem in the nanoscale era, and are also promising for heterogeneous integration. However, the thermal challenge in industry is one of key obstacles to adopt the 3D ICs technology. Various thermal analysis models for 3D IC have been proposed in literature. However, the long simulation cycle makes runtime of thermal management inefficient during floorplanning phase. In this paper, we propose a fast thermal analysis method for fixed-outline 3D floorplanning. Before floorplanning, we simulate the thermal distribution of each block placed on different positions. Based on the simulated thermal profiles, bilinear interpolation is adopted to quickly estimate temperature during floorplanning. After the block planning, a heuristic method, which combines the shortest path and min-cost-max-flow, is presented for TSV allocation with minimization of chip temperature and wirelength. Compared with the superposition of thermal profiles method, the proposed thermal analysis method can reduce the peak temperature by 6.7% on average with short runtime for 3D fixed-outline floorplanning, which demonstrates the efficiency and effectiveness of the proposed thermal analysis method.     

低偏斜、高变化容忍的层次化无缓冲谐振时钟分布网络

无缓冲谐振时钟分布网络能够最小化同步系统的时钟功耗。但由于没有缓冲器,时钟网络的偏斜受到多方面因素的影响,例如时钟互连线寄生参数的差异,非平衡时钟负载以及工艺、电压温度变化。本文提出了一种层次化的两相无缓冲谐振时钟互连网络结构,将网格型和树型结构的各自优点相结合。在TSMC 65nm标准CMOS工艺下,通过一个流水线乘法器电路分析了该结构时钟网络的偏斜及变化容忍特性。版图后仿真结果表明,层次化时钟网络的偏斜分别比纯网格和纯H树结构时钟网络降低超过75%和65%,而且在非平衡时钟负载或工艺、电压温度变化的情况下,时钟网络偏斜最高小于7ps,不超过整个时钟周期（约760ps）的1%。     

基于BUFGMUX与DCM的FPGA时钟电路设计

与ASIC(专用集成电路)的时钟电路相比,基于FPGA(现场可编程门阵列)的时钟电路有其自身的特点。FPGA一般提供专用时钟资源搭建时钟电路,相应的综合工具也能够自动使用这些资源,但是针对门控时钟和时钟分频电路,如果直接使用综合工具自动处理的结果,会造成较大的时钟偏差。通过合理使用DCM(数字时钟管理单元)和BUFG-MUX(全局时钟选择缓冲器)等FPGA的特殊资源,手动搭建时钟电路,可以尽可能地减少时钟偏差对电路时序的影响。     

Design of Thermally Robust Clock Trees Using Dynamically Adaptive Clock Buffers

On-chip temperature gradient has emerged as a major design concern for high-performance integrated circuits for the current and future technology nodes. Clock skew is an undesirable phenomenon for synchronous digital circuits that is exacerbated by the temperature difference between various parts of the clock tree. The main aim of this paper is to provide intelligent solution for minimizing the temperature-dependent clock skew by designing dynamically adaptive circuit elements, particularly the clock buffers. Using an RLC model of the clock tree, we investigate the effect of on-chip temperature gradient on the clock skew for a number of temperature profiles that can arise in practice due to different architectures and applications. As an effective way of mitigating the variable clock skew, we present an adaptive circuit technique that senses the temperature of different parts of the clock tree and adjusts the driving strengths of the corresponding clock buffers dynamically to reduce the clock skew. Simulation results demonstrate that our adaptive technique is capable of reducing the skew by up to 92.4%, leading to much improved clock synchronization and design performance.      

Zero skew clock routing in X-architecture based on an improved greedy matching algorithm

As technology advances into nanometer territory, clock network layout plays an increasingly important role in determining circuit quality indicated by timing, power consumption, cost, power supply noise and tolerance to process variation. To alleviate the challenges to the existing routing algorithms due to the continuous increase of the problem size and the high-performance requirement, X-architecture has been proposed and applied to routing in that it can reduce wirelength and via counts, and thus improves the performance and routability compared with the conventional Manhattan routing. In this paper, we investigate zero skew clock routing using X-architecture based on an improved greedy matching algorithm (GMZSTX). The fitted Elmore delay model is employed to improve the accuracy over the Elmore delay model. The interactions among distance, delay balance and load balance are analyzed. Based on this analysis, an effective and efficient greedy matching scheme is suggested to reduce wire snaking and to get a more balanced clock tree. The proposed algorithm is simple and fast for practical applications. Experimental results on benchmark circuits show that our algorithm (GMZSTX) achieves a reduction of 8.15% in total wirelength, 30.19% in delay and 55.31% in CPU time on average compared with zero skew clock routing in the Manhattan plane (BB+DME-2, which means using the top-down balanced bipartition (BB) method [T.H. Chao, Y.C. Hsu, J.M. Ho, et al., Zero skew routing with minimum wirelength, IEEE Trans. Circuits Syst. II—Analog & Digital Signal Process 39 (11) (1992) 799–814] to generate the tree topology and using the Deferred-Merge Embedding (DME) algorithm [T.H. Chao, Y.C. Hsu, J.M. Ho, et al., Zero skew routing with minimum wirelength, IEEE Trans. Circuits Syst. II—Analog & Digital Signal Process 39 (11) (1992) 799–814] to embed the internal nodes), and reduces delay and CPU time by 17.44% and 62.21% on average over the BB+DME-4 method (which is similar to BB+DME-2, but routing in X-architecture). Our SPICE simulation further verifies the correctness of the resulting clock tree.     

Pattern-matching-based X-architecture zero-skew clock tree construction with X-Flip technique and via delay consideration

As IC fabrication technologies get into nanometer era, clock routing gradually dominates chip performance indicated by delay, cost, and power consumption. X-architecture can be applied for routing metal wires in diagonal and rectilinear directions to overcome the above challenges due to wirelength reduction. In this paper, we present a clock routing algorithm, called PMXF, to construct an X-architecture zero-skew clock tree with minimum delay. An X-pattern library is defined for simplifying the merging procedure of the DME approach, an X-Flip technique is proposed for reducing the wirelength between the paired points, and a wire sizing technique is applied for achieving zero skew. In terms of clock delay, wirelength, power consumption, and via count listed in the experimental results on benchmarks, the proposed PMXF algorithm can respectively achieve more reductions compared with other previous X-architecture clock routing algorithms.     

时钟延时及偏差最小化的缓冲器插入新算法

本文提出了以最小时钟延时和时钟偏差为目标的缓冲器插入新算法.基于Elmore延时模型,我们得到相邻缓冲器间的延时是缓冲器在时钟树中位置的凸函数.当缓冲器布局使所有缓冲器间延时函数具有相同导数值时,时钟延时达到最小;当所有源到各接收端点路径的延时函数值相等时,时钟偏差达到最小.对一棵给定的时钟树,我们在所有从源点到各接收端点路径上插入相同层数的缓冲器,通过优化缓冲器的位置实现时钟延时最小;通过调整缓冲器尺寸和增加缓冲器层数,实现时钟偏差最小.     

时钟网格与时钟树设计方法对比研究

基于片上偏差对芯片性能的影响,分析对比了时钟树设计与时钟网格设计,重点分析了时钟网格抗OCV影响的优点,并利用实际电路应用两种方法分别进行设计对比,通过结果分析,验证了理论分析的正确性,证明在抗OCV及时序优化时钟网格方法具有很大的优势。     

An efficient merging scheme for prescribed skew clock routing

In ultra-deep submicron very large-scale integration (VLSI) designs, clock network layout plays an increasingly important role on determining circuit quality indicated by timing, power consumption, cost, power-supply noise, and tolerance to process variations. In this brief, a new merging scheme is proposed for prescribed nonzero skew routings which are useful in reducing clock cycle time, suppressing power-supply noise, and improving tolerance to process variations. This technique is simple and easy to implement for practical applications. Experimental results on benchmark circuits with both buffered and unbuffered routings exhibit large improvement on wirelength and buffer cost compared with other existing works.     

Voltage Optimization of Power Delivery Networks through Power Bump and TSV Placement in 3D ICs

To reduce interconnect delay and power consumption while improving chip performance, a three‐dimensional integrated circuit (3D IC) has been developed with die‐stacking and through‐silicon via (TSV) techniques. The power supply problem is one of the essential challenges in 3D IC design because IR‐drop caused by insufficient supply voltage in a 3D chip reduces the chip performance. In particular, power bumps and TSVs are placed to minimize IR‐drop in a 3D power delivery network. In this paper, we propose a design methodology for 3D power delivery networks to minimize the number of power bumps and TSVs with optimum mesh structure and distribute voltage variation more uniformly by shifting the locations of power bumps and TSVs while satisfying IR‐drop constraint. Simulation results show that our method can reduce the voltage variation by 29.7% on average while reducing the number of power bumps and TSVs by 76.2% and 15.4%, respectively.     

ASIC后端设计中的时钟树综合

时钟树综合是当今集成电路设计中的重要环节,因此在FFT处理器芯片的版图设计过程中,为了达到良好的布局效果,采用时序驱动布局,同时限制了布局密度;为了使时钟偏移尽可能少,采用了时钟树自动综合和手动修改相结合的优化方法,并提出了关于时钟树约束文件的设置、buffer的选型及手动修改时钟树的策略,最终完成了FFT处理器芯片的时钟树综合并满足了设计要求。     

Measurement Scheme for One‐Way Delay Variation with Detection and Removal of Clock Skew

One‐way delay variation (OWDV) has become increasingly of interest to researchers as a way to evaluate network state and service quality, especially for real‐time and streaming services such as voice‐over‐Internet‐protocol (VoIP) and video. Many schemes for OWDV measurement require clock synchronization through the global‐positioning system (GPS) or network time protocol. In clock‐synchronized approaches, the accuracy of OWDV measurement depends on the accuracy of the clock synchronization. GPS provides highly accurate clock synchronization. However, the deployment of GPS on legacy network equipment might be slow and costly. This paper proposes a method for measuring OWDV that dispenses with clock synchronization. The clock synchronization problem is mainly caused by clock skew. The proposed approach is based on the measurement of inter‐packet delay and accumulated OWDV. This paper shows the performance of the proposed scheme via simulations and through experiments in a VoIP network. The presented simulation and measurement results indicate that clock skew can be efficiently measured and removed and that OWDV can be measured without requiring clock synchronization.     

Edge layer embedding algorithm for mitigating on-package variation in 3D clock tree synthesis

A 3D stacked IC is made of multiple dies possibly with heterogeneous process technologies. Therefore, the die-to-die variation between the stacked dies creates on-package variation in a 3D chip. In this paper, we analyze the effect of on-package variation on the 3D clock trees and address the problem of on-package variation aware layer embedding in 3D clock tree synthesis. The layer embedding problem is divided into two sub-problems: clock node embedding and clock edge embedding. While the clock node embedded problem has been intensively investigated by the previous 3D clock tree synthesis flows because the solution directly determines the TSV allocation, the clock edge embedding problem has not been fully addressed yet. We show in this work that a careful clock edge embedding can greatly reduce the impact of on-package variation on the 3D clock skew, thereby enhancing chip yield, and propose a two-step solution to the problem of on-package variation aware layer embedding of clock edges. Specifically, we formulate the edge embedding problem into a problem of maximizing the sharing of layers among the clock paths to minimize the impact of on-package variation globally and solve it efficiently, followed by applying a fine-grained refinement technique to balance the clock latency locally among the clock paths. From the experiments with Benchmark circuits, we confirm that compared to the results produced by the conventional on-package variation unaware layer embedding of clock edges, the proposed algorithm is able to improve the chip yield by 6.2–25.8% and 5.3–44.4% for 2-layered and 4-layered 3D designs, respectively.     

应对3DIC测试挑战的ATE解决方案Advantest V93000准备就绪

三维集成电路(3DIC)的出现需要具备自动测试设备开发能力才能解决这些结构带来的挑战。在符合以下条件的解决方案中找到了这种能力:提供多时钟域、每个3DIC层粒状硬件移植、以及功能强大的测试语言来控制此硬件和协作软件开发环境;在这种环境下,各层的测试开发团队可紧密合作,为迅速生产做好准备。Advantest引进了每个引脚时钟域、多端口硬件、并发测试框架、协议感知以及smarTest程序管理器,可有效解决3DIC的测试挑战。它们可使生产解决方案达到开发团队所需的粒度。     

Legitimate Skew Clock Routing with Buffer Insertion

In this paper, we propose a new quick and effective legitimate skew clock routing with buffer insertion algorithm. We analyze the optimal buffer position in the clock path, and conclude the sufficient condition and heuristic condition for buffer insertion in clock net. During the routing process, this algorithm integrates buffer insertion and node merging together, and performs them in parallel. Compared with the method of buffer insertion after zero skew clock routing, our method improves the maximal clock delay by at least 48%. Compared with legitimate skew clock routing algorithm with no buffer, this algorithm further decreases the total wire length and gets reductions from 42 to 82% in maximal clock delay. The experimental results show that our algorithm is quick and effective. Xinjie Wei received his B.Sc. degree in Computer Science from the PLA Nanjing Institute of Communications Engineering in 1993, and got M.S. degree in Computer Science from Xidian University in 1998. He is currently pursuing the Ph.D. degree at Tsinghua University. His research interests include computer network security, neural network and design automation for VLSI circuits and systems. And the major research attention is focused on VLSI physical design. Yici Cai received BSc degree in Electronic Engineering from Tsinghua University in 1983 and received in and MS degree in Computer Science & Technology from Tsinghua University in 1986, She has been an associate professor in the Department of Computer Science & Technology, Tsinghua University. Beijing, China. Her research interests include VLSI layout theory and algorithms. Meng Zhao has been an researcher in Semiconductor Industry Association of Beijing. She received her Bachelor of Engineering degree in Electronical Engineering from Tsinghua University, China, in 2000. She received her Master of Science degree in Computer Science from Tsinghua University, China, in 2003. Her research interests include VLSI design and CAD, Electronical material and device, VLSI verification and so on. Xianlong Hong graduated from Tsinghua University, Beijing, China in 1964. Since 1988, he has been a professor in the Department of Computer Science Technology, Tsinghua University. His research interests include VLSI layout algorithms and DA systems. He is the fellow of IEEE and the Senior Member of Chinese Institute of Electronics.     

Integrated Placement and Skew Optimization for Rotary Clocking

The clock distribution network is a key component of any synchronous VLSI design. High power dissipation and pressure volume temperature-induced variations in clock skew have started playing an increasingly important role in limiting the performance of the clock network. Rotary clocking is a novel technique which employs unterminated rings formed by differential transmission lines to save power and reduce skew variability. Despite its appealing advantages, rotary clocking requires flip-flop locations to match predesigned clock skew on rotary clock rings. This requirement poses a difficult chicken-and-egg problem which prevents its wide application. In this paper, we propose an integrated placement and skew scheduling methodology to break this hurdle, making rotary clocking compatible with practical design flows. A network flow based flip-flop assignment algorithm and a cost-driven skew optimization algorithm are developed. We also present an integer linear programming formulation that minimizes maximum capacitance loaded at any of the rotary rings, thereby maximizing the operating frequency. Experimental results on benchmark circuits show that our method can reduce the tapping cost (measured as the total length of the wire segments connecting the rotary rings to the clock sinks) for rotary clocking by 33%-53%     

A 64-b quad-issue CMOS RISC microprocessor

The HP-PA8000 is a 180-MHz quad-issue custom VLSI implementation of the HP-PA 2.0 64-b architecture delivering 11.84 SPECint95 and 20.18 SPECfp95 with 3.8 million transistors integrated on a 17.68 mm×19.1 mm die in a 3.3-V, 0.5-μm CMOS process. Specialized clock circuits and extensive use of dynamic logic are key factors in this microprocessor's performance. Attention to clock analysis and distribution resulted in a 170 ps clock skew between any two clock nodes. This microprocessor utilizes a 56-entry instruction reorder buffer (IRE), register renaming, and dual functional units to fully exploit instruction level parallelism