Computational Delay Models to Estimate the Delay of Floating Cubes in CMOS Circuits

The verification of the timing requirements of large VLSI circuits is generally performed by using simulation or timing analysis on each combinational block of the circuit. A key factor in timing analysis is the election of the delay model type. Pin-to-pin delay models are usually employed, but their application is limited in timing analysis when dealing with floating mode or complex gates. This paper does not introduce a delay model but a delay model type called Transistor Path Delay Model (TPDM). This new type of delay model is specially useful for timing analysis in floating mode, since it is not required to know the whole input sequence to apply it, and can manage complex CMOS gates. An algorithm to get upper bounds on the stabilization time of each gate output using TPDM is also introduced

Tabu Search Based Circuit Optimization

In this paper we address the problem of optimizing mixed CMOS/BiCMOS circuits. The problem is for- mulated as a constrained combinatorial optimization problem and solved using an tabu search algorithm. Only gates on the critical sensitizable paths are consid- ered for optimization. Such a strategy leads to sizable circuit speed improvement with minimum increase in the overall circuit capacitance. Compared to earlier approaches, the presented technique produces circuits with remarkable increase in speed (greater than 20%) for very small increase in overall circuit capacitance (less than 3%). Keywords: Tabu Search, Circuit Optimization, Search Algorithms, CMOS/BiCMOS, Mixed Technologies, Critical Path, False Path

Maximum and minimum sensitizable timing analysis using data dependent delays

Modern digital designs require high performance and low cost. In this scenario, timing analysis is an essential step for each phase of the integrated circuit design cycle. To minimize the design turn-around time, the ability to correctly predict the timing behavior of the chip is extremely important. This has resulted in a demand for techniques to perform an accurate timing analysis. A number of existing timing analysis approaches are available. Most of these are pessimistic in nature due because of some inherent inaccuracies in the modeling of the timing behavior of logic gates. Although some techniques use accurate gate delay models, they have only been used to calculate the longest sensitizable delay or the shortest topological path delay for the circuit. In this work, a procedure to and the shortest destabilizing delay, as well as the longest sensitizable delay of a static CMOS circuit is developed. This procedure is also able to determine the exact circuit path as well as the input vector transition for which the shortest destabilizing (or longest sensitizable) delay can be achieved. Over a number of examples, on an average, the minimum destabilizing delay results in an improvement of 24% as compared to the minimum static timing analysis approach. The maximum sensitizable timing analysis results in an improvement of 7% over sensitizable timing analysis with pin-to-output delays. Therefore, the results show that the pessismism in timing analysis can be considerably decreased by using data dependent gate delays for maximum as well as minimum sensitizable timing analysis

Optimization of power and delay in VLSI circuits using transistor sizing and input ordering

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.Includes bibliographical references (p. 85-88).by Chin Hwee Tan.M.S

Applications and implementation of neuro-connectionist architectures.

by H.S. Ng.Thesis (M.Phil.)--Chinese University of Hong Kong, 1996.Includes bibliographical references (leaves 91-97).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Introduction --- p.1Chapter 1.2 --- Neuro-connectionist Network --- p.2Chapter 2 --- Related Works --- p.5Chapter 2.1 --- Introduction --- p.5Chapter 2.1.1 --- Kruskal's Algorithm --- p.5Chapter 2.1.2 --- Prim's algorithm --- p.6Chapter 2.1.3 --- Sollin's algorithm --- p.7Chapter 2.1.4 --- Bellman-Ford algorithm --- p.8Chapter 2.1.5 --- Floyd-Warshall algorithm --- p.9Chapter 3 --- Binary Relation Inference Network and Path Problems --- p.11Chapter 3.1 --- Introduction --- p.11Chapter 3.2 --- Topology --- p.12Chapter 3.3 --- Network structure --- p.13Chapter 3.3.1 --- Single-destination BRIN architecture --- p.14Chapter 3.3.2 --- Comparison between all-pair BRIN and single-destination BRIN --- p.18Chapter 3.4 --- Path Problems and BRIN Solution --- p.18Chapter 3.4.1 --- Minimax path problems --- p.18Chapter 3.4.2 --- BRIN solution --- p.19Chapter 4 --- Analog and Voltage-mode Approach --- p.22Chapter 4.1 --- Introduction --- p.22Chapter 4.2 --- Analog implementation --- p.24Chapter 4.3 --- Voltage-mode approach --- p.26Chapter 4.3.1 --- The site function --- p.26Chapter 4.3.2 --- The unit function --- p.28Chapter 4.3.3 --- The computational unit --- p.28Chapter 4.4 --- Conclusion --- p.29Chapter 5 --- Current-mode Approach --- p.32Chapter 5.1 --- Introduction --- p.32Chapter 5.2 --- Current-mode approach for analog VLSI Implementation --- p.33Chapter 5.2.1 --- Site and Unit output function --- p.33Chapter 5.2.2 --- Computational unit --- p.34Chapter 5.2.3 --- A complete network --- p.35Chapter 5.3 --- Conclusion --- p.37Chapter 6 --- Neural Network Compensation for Optimization Circuit --- p.40Chapter 6.1 --- Introduction --- p.40Chapter 6.2 --- A Neuro-connectionist Architecture for error correction --- p.41Chapter 6.2.1 --- Linear Relationship --- p.42Chapter 6.2.2 --- Output Deviation of Computational Unit --- p.44Chapter 6.3 --- Experimental Results --- p.46Chapter 6.3.1 --- Training Phase --- p.46Chapter 6.3.2 --- Generalization Phase --- p.48Chapter 6.4 --- Conclusion --- p.50Chapter 7 --- Precision-limited Analog Neural Network Compensation --- p.51Chapter 7.1 --- Introduction --- p.51Chapter 7.2 --- Analog Neural Network hardware --- p.53Chapter 7.3 --- Integration of analog neural network compensation of connectionist net- work for general path problems --- p.54Chapter 7.4 --- Experimental Results --- p.55Chapter 7.4.1 --- Convergence time --- p.56Chapter 7.4.2 --- The accuracy of the system --- p.57Chapter 7.5 --- Conclusion --- p.58Chapter 8 --- Transitive Closure Problems --- p.60Chapter 8.1 --- Introduction --- p.60Chapter 8.2 --- Different ways of implementation of BRIN for transitive closure --- p.61Chapter 8.2.1 --- Digital Implementation --- p.61Chapter 8.2.2 --- Analog Implementation --- p.61Chapter 8.3 --- Transitive Closure Problem --- p.63Chapter 8.3.1 --- A special case of maximum spanning tree problem --- p.64Chapter 8.3.2 --- Analog approach solution for transitive closure problem --- p.65Chapter 8.3.3 --- Current-mode approach solution for transitive closure problem --- p.67Chapter 8.4 --- Comparisons between the different forms of implementation of BRIN for transitive closure --- p.71Chapter 8.4.1 --- Convergence Time --- p.71Chapter 8.4.2 --- Circuit complexity --- p.72Chapter 8.5 --- Discussion --- p.73Chapter 9 --- Critical path problems --- p.74Chapter 9.1 --- Introduction --- p.74Chapter 9.2 --- Problem statement and single-destination BRIN solution --- p.75Chapter 9.3 --- Analog implementation --- p.76Chapter 9.3.1 --- Separated building block --- p.78Chapter 9.3.2 --- Combined building block --- p.79Chapter 9.4 --- Current-mode approach --- p.80Chapter 9.4.1 --- "Site function, unit output function and a completed network" --- p.80Chapter 9.5 --- Conclusion --- p.83Chapter 10 --- Conclusions --- p.85Chapter 10.1 --- Summary of Achievements --- p.85Chapter 10.2 --- Future development --- p.88Chapter 10.2.1 --- Application for financial problems --- p.88Chapter 10.2.2 --- Fabrication of VLSI Implementation --- p.88Chapter 10.2.3 --- Actual prototyping of Analog Integrated Circuits for critical path and transitive closure problems --- p.89Chapter 10.2.4 --- Other implementation platform --- p.89Chapter 10.2.5 --- On-line update of routing table inside the router for network com- munication using BRIN --- p.89Chapter 10.2.6 --- Other BRIN's applications --- p.90Bibliography --- p.9

Applications and implementation of neuro-connectionist architectures.

by H.S. Ng.Thesis (M.Phil.)--Chinese University of Hong Kong, 1996.Includes bibliographical references (leaves 91-97).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Introduction --- p.1Chapter 1.2 --- Neuro-connectionist Network --- p.2Chapter 2 --- Related Works --- p.5Chapter 2.1 --- Introduction --- p.5Chapter 2.1.1 --- Kruskal's Algorithm --- p.5Chapter 2.1.2 --- Prim's algorithm --- p.6Chapter 2.1.3 --- Sollin's algorithm --- p.7Chapter 2.1.4 --- Bellman-Ford algorithm --- p.8Chapter 2.1.5 --- Floyd-Warshall algorithm --- p.9Chapter 3 --- Binary Relation Inference Network and Path Problems --- p.11Chapter 3.1 --- Introduction --- p.11Chapter 3.2 --- Topology --- p.12Chapter 3.3 --- Network structure --- p.13Chapter 3.3.1 --- Single-destination BRIN architecture --- p.14Chapter 3.3.2 --- Comparison between all-pair BRIN and single-destination BRIN --- p.18Chapter 3.4 --- Path Problems and BRIN Solution --- p.18Chapter 3.4.1 --- Minimax path problems --- p.18Chapter 3.4.2 --- BRIN solution --- p.19Chapter 4 --- Analog and Voltage-mode Approach --- p.22Chapter 4.1 --- Introduction --- p.22Chapter 4.2 --- Analog implementation --- p.24Chapter 4.3 --- Voltage-mode approach --- p.26Chapter 4.3.1 --- The site function --- p.26Chapter 4.3.2 --- The unit function --- p.28Chapter 4.3.3 --- The computational unit --- p.28Chapter 4.4 --- Conclusion --- p.29Chapter 5 --- Current-mode Approach --- p.32Chapter 5.1 --- Introduction --- p.32Chapter 5.2 --- Current-mode approach for analog VLSI Implementation --- p.33Chapter 5.2.1 --- Site and Unit output function --- p.33Chapter 5.2.2 --- Computational unit --- p.34Chapter 5.2.3 --- A complete network --- p.35Chapter 5.3 --- Conclusion --- p.37Chapter 6 --- Neural Network Compensation for Optimization Circuit --- p.40Chapter 6.1 --- Introduction --- p.40Chapter 6.2 --- A Neuro-connectionist Architecture for error correction --- p.41Chapter 6.2.1 --- Linear Relationship --- p.42Chapter 6.2.2 --- Output Deviation of Computational Unit --- p.44Chapter 6.3 --- Experimental Results --- p.46Chapter 6.3.1 --- Training Phase --- p.46Chapter 6.3.2 --- Generalization Phase --- p.48Chapter 6.4 --- Conclusion --- p.50Chapter 7 --- Precision-limited Analog Neural Network Compensation --- p.51Chapter 7.1 --- Introduction --- p.51Chapter 7.2 --- Analog Neural Network hardware --- p.53Chapter 7.3 --- Integration of analog neural network compensation of connectionist net- work for general path problems --- p.54Chapter 7.4 --- Experimental Results --- p.55Chapter 7.4.1 --- Convergence time --- p.56Chapter 7.4.2 --- The accuracy of the system --- p.57Chapter 7.5 --- Conclusion --- p.58Chapter 8 --- Transitive Closure Problems --- p.60Chapter 8.1 --- Introduction --- p.60Chapter 8.2 --- Different ways of implementation of BRIN for transitive closure --- p.61Chapter 8.2.1 --- Digital Implementation --- p.61Chapter 8.2.2 --- Analog Implementation --- p.61Chapter 8.3 --- Transitive Closure Problem --- p.63Chapter 8.3.1 --- A special case of maximum spanning tree problem --- p.64Chapter 8.3.2 --- Analog approach solution for transitive closure problem --- p.65Chapter 8.3.3 --- Current-mode approach solution for transitive closure problem --- p.67Chapter 8.4 --- Comparisons between the different forms of implementation of BRIN for transitive closure --- p.71Chapter 8.4.1 --- Convergence Time --- p.71Chapter 8.4.2 --- Circuit complexity --- p.72Chapter 8.5 --- Discussion --- p.73Chapter 9 --- Critical path problems --- p.74Chapter 9.1 --- Introduction --- p.74Chapter 9.2 --- Problem statement and single-destination BRIN solution --- p.75Chapter 9.3 --- Analog implementation --- p.76Chapter 9.3.1 --- Separated building block --- p.78Chapter 9.3.2 --- Combined building block --- p.79Chapter 9.4 --- Current-mode approach --- p.80Chapter 9.4.1 --- "Site function, unit output function and a completed network" --- p.80Chapter 9.5 --- Conclusion --- p.83Chapter 10 --- Conclusions --- p.85Chapter 10.1 --- Summary of Achievements --- p.85Chapter 10.2 --- Future development --- p.88Chapter 10.2.1 --- Application for financial problems --- p.88Chapter 10.2.2 --- Fabrication of VLSI Implementation --- p.88Chapter 10.2.3 --- Actual prototyping of Analog Integrated Circuits for critical path and transitive closure problems --- p.89Chapter 10.2.4 --- Other implementation platform --- p.89Chapter 10.2.5 --- On-line update of routing table inside the router for network com- munication using BRIN --- p.89Chapter 10.2.6 --- Other BRIN's applications --- p.90Bibliography --- p.9

Design and test for timing uncertainty in VLSI circuits.

由於特徵尺寸不斷縮小，集成電路在生產過程中的工藝偏差在運行環境中溫度和電壓等參數的波動以及在使用過程中的老化等效應越來越嚴重，導致芯片的時序行為出現很大的不確定性。多數情況下，芯片的關鍵路徑會不時出現時序錯誤。加入更多的時序餘量不是一種很好的解決方案，因為這種保守的設計方法會抵消工藝進步帶來的性能上的好處。這就為設計一個時序可靠的系統提出了極大的挑戰，其中的一些關鍵問題包括：(一)如何有效地分配有限的功率預算去優化那些正爆炸式增加的關鍵路徑的時序性能；(二)如何產生能夠捕捉準確的最壞情況時延的高品質測試向量；(三)為了能夠取得更好的功耗和性能上的平衡，我們將不得不允許芯片在使用過程中出現一些頻率很低的時序錯誤。隨之而來的問題是如何做到在線的檢錯和糾錯。為了解決上述問題，我們首先發明了一種新的技術用於識別所謂的虛假路徑，該方法使我們能夠發現比傳統方法更多的虛假路徑。當將所提取的虛假路徑集成到靜態時序分析工具里以後，我們可以得到更為準確的時序分析結果，同時也能節省本來用於優化這些路徑的成本。接著，考慮到現有的延時自動向量生成(ATPG) 方法會產生功能模式下無法出現的測試向量，這種向量可能會造成測試過程中在被激活的路徑周圍出現過多(或過少)的電源噪聲(PSN) ，從而導致測試過度或者測試不足情況。為此，我們提出了一種新的偽功能ATPG工具。通過同時考慮功能約束以及電路的物理佈局信息，我們使用類似ATPG 的算法產生狀態跳變使其能最大化已激活的路徑周圍的PSN影響。最後，基於近似電路的原理，我們提出了一種新的在線原位校正技術，即InTimeFix，用於糾正時序錯誤。由於實現近似電路的綜合僅需要簡單的電路結構分析，因此該技術能夠很容易的擴展到大型電路設計上去。With technology scaling, integrated circuits (ICs) suffer from increasing process, voltage, and temperature (PVT) variations and aging effects. In most cases, these reliability threats manifest themselves as timing errors on speed-paths (i.e., critical or near-critical paths) of the circuit. Embedding a large design guard band to prevent timing errors to occur is not an attractive solution, since this conservative design methodology diminishes the benefit of technology scaling. This creates several challenges on build a reliable systems, and the key problems include (i) how to optimize circuit’s timing performance with limited power budget for explosively increased potential speed-paths; (ii) how to generate high quality delay test pattern to capture ICs’ accurate worst-case delay; (iii) to have better power and performance tradeoff, we have to accept some infrequent timing errors in circuit’s the usage phase. Therefore, the question is how to achieve online timing error resilience.To address the above issues, we first develop a novel technique to identify so-called false paths, which facilitate us to find much more false paths than conventional methods. By integrating our identified false paths into static timing analysis tool, we are able to achieve more accurate timing information and also save the cost used to optimize false paths. Then, due to the fact that existing delay automated test pattern generation (ATPG) methods may generate test patterns that are functionally-unreachable, and such patterns may incur excessive (or limited) power supply noise (PSN) on sensitized paths in test mode, thus leading to over-testing or under-testing of the circuits, we propose a novel pseudo-functional ATPG tool. By taking both circuit layout information and functional constrains into account, we use ATPG like algorithm to justify transitions that pose the maximized functional PSN effects on sensitized critical paths. Finally, we propose a novel in-situ correction technique to mask timing errors, namely InTimeFix, by introducing redundant approximation circuit with more timing slack for speed-paths into the design. The synthesis of the approximation circuit relies on simple structural analysis of the original circuit, which is easily scalable to large IC designs.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Yuan, Feng.Thesis (Ph.D.)--Chinese University of Hong Kong, 2012.Includes bibliographical references (leaves 88-100).Abstract also in Chinese.Abstract --- p.iAcknowledgement --- p.ivChapter 1 --- Introduction --- p.1Chapter 1.1 --- Challenges to Solve Timing Uncertainty Problem --- p.2Chapter 1.2 --- Contributions and Thesis Outline --- p.5Chapter 2 --- Background --- p.7Chapter 2.1 --- Sources of Timing Uncertainty --- p.7Chapter 2.1.1 --- Process Variation --- p.7Chapter 2.1.2 --- Runtime Environment Fluctuation --- p.9Chapter 2.1.3 --- Aging Effect --- p.10Chapter 2.2 --- Technical Flow to Solve Timing Uncertainty Problem --- p.10Chapter 2.3 --- False Path --- p.12Chapter 2.3.1 --- Path Sensitization Criteria --- p.12Chapter 2.3.2 --- False Path Aware Timing Analysis --- p.13Chapter 2.4 --- Manufacturing Testing --- p.14Chapter 2.4.1 --- Functional Testing vs. Structural Testing --- p.14Chapter 2.4.2 --- Scan-Based DfT --- p.15Chapter 2.4.3 --- Pseudo-Functional Testing --- p.17Chapter 2.5 --- Timing Error Tolerance --- p.19Chapter 2.5.1 --- Timing Error Detection --- p.19Chapter 2.5.2 --- Timing Error Recover --- p.20Chapter 3 --- Timing-Independent False Path Identification --- p.23Chapter 3.1 --- Introduction --- p.23Chapter 3.2 --- Preliminaries and Motivation --- p.26Chapter 3.2.1 --- Motivation --- p.27Chapter 3.3 --- False Path Examination Considering Illegal States --- p.28Chapter 3.3.1 --- Path Sensitization Criterion --- p.28Chapter 3.3.2 --- Path-Aware Illegal State Identification --- p.30Chapter 3.3.3 --- Proposed Examination Procedure --- p.31Chapter 3.4 --- False Path Identification --- p.32Chapter 3.4.1 --- Overall Flow --- p.34Chapter 3.4.2 --- Static Implication Learning --- p.35Chapter 3.4.3 --- Suspicious Node Extraction --- p.36Chapter 3.4.4 --- S-Frontier Propagation --- p.37Chapter 3.5 --- Experimental Results --- p.38Chapter 3.6 --- Conclusion and Future Work --- p.42Chapter 4 --- PSN Aware Pseudo-Functional Delay Testing --- p.43Chapter 4.1 --- Introduction --- p.43Chapter 4.2 --- Preliminaries and Motivation --- p.45Chapter 4.2.1 --- Motivation --- p.46Chapter 4.3 --- Proposed Methodology --- p.48Chapter 4.4 --- Maximizing PSN Effects under Functional Constraints --- p.50Chapter 4.4.1 --- Pseudo-Functional Relevant Transitions Generation --- p.51Chapter 4.5 --- Experimental Results --- p.59Chapter 4.5.1 --- Experimental Setup --- p.59Chapter 4.5.2 --- Results and Discussion --- p.60Chapter 4.6 --- Conclusion --- p.64Chapter 5 --- In-Situ Timing Error Masking in Logic Circuits --- p.65Chapter 5.1 --- Introduction --- p.65Chapter 5.2 --- Prior Work and Motivation --- p.67Chapter 5.3 --- In-Situ Timing Error Masking with Approximate Logic --- p.69Chapter 5.3.1 --- Equivalent Circuit Construction with Approximate Logic --- p.70Chapter 5.3.2 --- Timing Error Masking with Approximate Logic --- p.72Chapter 5.4 --- Cost-Efficient Synthesis for InTimeFix --- p.75Chapter 5.4.1 --- Overall Flow --- p.76Chapter 5.4.2 --- Prime Critical Segment Extraction --- p.77Chapter 5.4.3 --- Prime Critical Segment Merging --- p.79Chapter 5.5 --- Experimental Results --- p.81Chapter 5.5.1 --- Experimental Setup --- p.81Chapter 5.5.2 --- Results and Discussion --- p.82Chapter 5.6 --- Conclusion --- p.85Chapter 6 --- Conclusion and Future Work --- p.86Bibliography --- p.10

Application-specific Design and Optimization for Ultra-Low-Power Embedded Systems

University of Minnesota Ph.D. dissertation. August 2019. Major: Electrical/Computer Engineering. Advisor: John Sartori. 1 computer file (PDF); xii, 101 pages.The last few decades have seen a tremendous amount of innovation in computer system design to the point where electronic devices have become very inexpensive. This has brought us on the verge of a new paradigm in computing where there will be hundreds of devices in a person’s environment, ranging from mobile phones to smart home devices to wearables to implantables, all interconnected. This paradigm, called the Internet of Things (IoT), brings new challenges in terms of power, cost, and security. For example, power and energy have become critical design constraints that not only affect the lifetime of an ultra-low-power (ULP) system, but also its size and weight. While many conventional techniques exist that are aimed at energy reduction or that improve energy efficiency, they do so at the cost of performance. As such, their impact is limited in circumstances where energy is very constrained or where significant degradation of performance or functionality is unacceptable. Focusing on the opposing demands to increase both energy efficiency and performance simultaneously in a world where Moore’s law scaling is decelerating, one of the underlying themes of this work has been to identify novel insights that enable new pathways to energy efficiency in computing systems while avoiding the conventional tradeoff that simply sacrifices performance and functionality for energy efficiency. To this end, this work proposes a method to analyze the behavior of an application on the gate-level netlist of a processor for all possible inputs using a novel symbolic hardware-software co-analysis methdology. Using this methodology several techniques have been proposed to optimize a given processor-application pair for power, area and security

Accurate statistical circuit simulation in the presence of statistical variability

Semiconductor device performance variation due to the granular nature of charge and matter has become a key problem in the semiconductor industry. The main sources of this ‘statistical’ variability include random discrete dopants (RDD), line edge roughness (LER) and metal gate granularity (MGG). These variability sources have been studied extensively, however a methodology has not been developed to accurately represent this variability at a circuit and system level. In order to accurately represent statistical variability in real devices the GSS simulation toolchain was utilised to simulate 10,000 20/22nm n- and p-channel transistors including RDD, LER and MGG variability sources. A statistical compact modelling methodology was developed which accurately captured the behaviour of the simulated transistors, and produced compact model parameter distributions suitable for advanced compact model generation strategies like PCA and NPM. The resultant compact model libraries were then utilised to evaluate the impact of statistical variability on SRAM design, and to quantitatively evaluate the difference between accurate compact model generation using NPM with the Gaussian VT methodology. Over 5 million dynamic write simulations were performed, and showed that at advanced technology nodes, statistical variability cannot be accurately represented using Gaussian VT . The results also show that accurate modelling techniques can help reduced design margins by elimiating some of the pessimism of standard variability modelling approaches