Statistical Interconnect Crosstalk Noise Model and Analysis for Process Variations

Crosstalk noise and transmission loss are two key elements in determining the performance of optical routers. We propose a universal method for crosstalk noise and transmission loss analysis for the N-port nonblocking optical router used in photonic networks-on-chip. Utilizing this method, we study the crosstalk noise and transmission loss for the five-, six-, seven-, and eight-port optical routers. We ascertain that the crosstalk noise and transmission loss are different for different input–output pairs. For the five-port optical router, the maximum crosstalk noise ranges from 0 to −7.07 dBm , and the transmission loss ranges from −9.05 to −0.51 dB . Furthermore, based on the crosstalk noise and transmission loss, we analyze optical signal-to-noise ratio (OSNR) and bit error ratio (BER) for the five-, six-, seven-, and eight-port nonblocking optical routers. As the number of ports increases, the minimum average OSNR decreases and the average BER increases. In addition, in order to present the performance of the routers more visually, a fiber-optic communications system is designed to simulate the transmission processes of the signals of the different paths of the routers in Optisystem. The results show that the power amplitude of the input signal is obviously higher than the corresponding output signal. With this method, we can easily evaluate the transmission loss, crosstalk noise, OSNR, and BER of high-radix nonblocking optical routers and conveniently study the performance of the N-port optical router.

With the rapid miniaturization of integrate circuit (IC) chip, wafer-level IC testing has become an important process in the semiconductor industry. The improvements of a vertical probe card allow the test to high speed and high-density devices with short probe length and fine pitch compared to conventional probe cards. Regradless these strength, signal degradation by crosstalk noise in probe card has arisen with smaller pad sizes, multi parallel testing, and increased signal input/output frequencies. Therefore, an analysis of crosstalk noise in probe card structure is necessary. In this paper, we propose a new probe card structure to reduce crosstalk noise by lowering the impedance of the ground return path. The proposed structure is analyzed in the frequency- and time-domains. It is designed with a 3D electromagnetic solver and the results are visualized through S-parameter curves up to 10 Gb/s and eye-diagrams at 1.6 Gb/s. To validate the effect, the original structure and the proposed structure are compared. Through frequecy - and time domain simulation results, we verified that the proposed structure successfully reduces the crosstalk noise.

The trends in technology scaling have made nanometer designs highly susceptible to reliability threats like soft errors and crosstalk noise while uncertainty in process parameters have made the physical realization of devices and interconnects unpredictable. The limitations in manufacturing processes and the impact of environmental noise poses a major threat to the signal quality, and hence the realization of reliable, low-power, high performance designs with acceptable parametric yields is a challenging problem. Most noise analysis and prevention techniques reported in the literature target single noise sources. However, reliability issues like crosstalk noise and radiation induced soft errors are deeply inter-related. Further, manufacturing variations have decreased the efficacy of online detection and correction schemes used for traditional noise optimization. In this work, we have proposed a methodology for simultaneous optimization of soft error rate(SER), crosstalk noise and power of circuits with delay constraints under process variations. Soft errors are modeled using a novel first order analysis model while crosstalk noise is modeled at the logic level using clustering based on Rent's exponent. The proposed multi-metric gate sizing methodology have been formulated into a mathematical program and has been efficiently solved. Experimental results on ISCAS'85 benchmark circuits indicate significant improvements in SER, crosstalk noise and timing yield compared to the corresponding constrained optimization problems.

In this paper, statistical models for the efficient analysis of interconnect delay and crosstalk noise in the presence of back-end process variations are developed. The proposed models enable closed-form computation of means and variances of interconnect-delay, crosstalk-noise peak, and coupling-induced-delay change for given magnitudes of variation in relevant process parameters, such as linewidth, metal thickness, metal spacing, and interlayer dielectric (ILD) thickness. The proposed approach is based on the observation that if the variations in different physical dimensions are assumed to be independent normal random variables, then the interconnect behavior also tends to have a Gaussian distribution. In the proposed statistical models, delay and noise are expressed directly as functions of changes in physical parameters. This formulation allows us to preserve all correlations and can be very useful in evaluating delay and noise sensitivities due to changes in various physical dimensions. For interconnect-delay computation, the authors express the resistance and capacitance of a line as a linear function of random variables and then use these to compute circuit moments. They show that ignoring higher order terms in the resulting variational moments does not result in a loss of accuracy. Finally, these variability-aware moments are used in known closed-form delay and slew metrics to compute interconnect-delay probability density functions (pdfs). Similarly for coupling noise and dynamic-delay analysis, the authors rely on the linearity (Gaussian) assumption, allowing us to truncate nonlinear terms and express noise and dynamic-delay pdfs as linear functions of variations in relevant geometric dimensions. They compare their approach to SPICE-based Monte Carlo simulations and report the error in mean and standard deviation of interconnect delay to be 1% and 4% on average, respectively

With the continuous increase in the size and complexity of machine learning models, the need for specialized hardware to efficiently run such models is rapidly growing. To address such a need, silicon-photonic-based neural network (SP-NN) accelerators have recently emerged as a promising alternative to electronic accelerators due to their lower latency and higher energy efficiency. Not only can SP-NNs alleviate the fan-in and fan-out problem with linear algebra processors, their operational bandwidth can match that of the photodetection rate (typically <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\approx$</tex-math></inline-formula> 100 GHz), which is at least over an order of magnitude faster than electronic counterparts that are restricted to a clock rate of a few GHz. Unfortunately, the underlying silicon photonic devices in SP-NNs suffer from inherent optical losses and crosstalk noise originating from fabrication imperfections and undesired optical couplings, the impact of which accumulates as the network scales up. Consequently, the inferencing accuracy in an SP-NN can be affected by such inefficiencies—e.g., can drop to below 10%—the impact of which is yet to be fully studied. In this paper, we comprehensively model the optical loss and crosstalk noise using a bottom-up approach, from the device to the system level, in coherent SP-NNs built using Mach–Zehnder interferometer (MZI) devices. The proposed models can be applied to any SP-NN architecture with different configurations to analyze the effect of loss and crosstalk. Such an analysis is important where there are inferencing accuracy and scalability requirements to meet when designing an SP-NN. Using the proposed analytical framework, we show a catastrophic inferencing accuracy drop of up to 84% for SP-NNs of different scales with three known MZI mesh configurations (i.e., Reck, Clements, and Diamond) due to accumulated optical loss and crosstalk noise.

Recently, progress in the high‐density wiring technique on a printed circuit board (PCB) has been remarkable. Thus the problem of malfunctions due to crosstalk noise occurring on the signal line must be addressed. The authors have been developing the noise estimation system for PCB named NESSY and a program to calculate the capacitance of multiconductor system (CALCAP). In NESSY, the wiring pattern is divided into small segments, which comprise the equivalent element circuit. The partial capacitance of the printed pattern is calculated by solving the integral equation and using the image method in CALCAP. The crosstalk analysis of equivalent circuit was made by the circuit simulation program.Among the results of this analysis, crosstalk noise using the partial element equivalent circuit (PEEC) agrees quite well with the measurement. The crosstalk noise should be anticipated by the close coupling theory in the case of frequently used wiring (both the width of signal line and line spacing are less than 1 mm). The crosstalk noise voltage was relatively large in the case of impedance mismatching. The far end crosstalk noise, previously neglected in most cases, becomes especially large.

Modeling and analysis of crosstalk induced effects in graphene-carbon nanotube composite interconnects

Praise for Signal Integrity Effects in Custom IC and ASIC Designs For the first time, this book is taking a closer look at the signal integrity problems faced by both high-performance and cost-performance applications, digital and mixed-signal integrated circuits. --Alina Deutsch, Research Staff Member, T.J. Watson Research Center, International Business Machines book surveys the latest literature on electrical integrity analysis and design and is, therefore, an invaluable resource for anyone designing systems-on-a-chip. --Kenneth L. Shepard, Professor, Columbia University book offers a tutorial guide to IC designers who want to move to the next level of chip design by unlocking the secrets of signal integrity. --Jake Buurma, Senior Vice President, Worldwide Research & Development, Cadence Design Systems, Inc. collection of papers...is the most comprehensive syllabus of important results for researchers and designers on the topic. I highly recommend to read it and to pay attention to the messages given by the papers of the collection. --Alberto Sangiovanni-Vincentelli, Professor, University of California Berkeley The editor has gathered together a collection of papers, both tutorial and advanced, that address a broad range of interconnect problems. --Jacob White, Professor, Massachusetts Institute of Technology Signal Integrity Effects in Custom IC and ASIC Designs compiles recent expert research papers in state-of-the-art IC (Integrated Circuits) design. It offers a detailed focus on all the major topics in understanding and modeling real-world IC signal integrity issues for CAD and IC design engineers, as well as graduate engineering students. Practical, in-depth discussion of interconnect effects, inductance effects, power grid and distribution noise, and substrate noise and coupling is included. This specialized coverage provides the knowledge necessary to overcome serious problems in new, more complicated IC designs, such as:Wired and wireless communications ICs Large custom analog mixed-signal ICs ASIC designs from 0.12 microns and above Integrated custom IC blocks in ASIC (Applications-Specific Integrated Circuit) designs

Statistical static timing analysis (SSTA) tools have mostly addressed the process variations of devices and lumped interconnect RC effects. This paper provides an overview of interconnect process variations of capacitive coupling and its effect on crosstalk delay and noise. The correlations among parallel plate, lateral and total capacitance is shown. Correlations between resistance and capacitance are illustrated to enable development of a simple and efficient model for delay and noise analysis. Experimental results are shown to validate the assumptions on the linearity of sensitivity of delay and noise to process variations. A methodology to account for process variations in crosstalk delay and noise is proposed.

In integrated circuit (IC) design for advanced manufacturing processes, iterative improvement processes are an approach commonly used for improving design quality, particularly for low-energy, high-frequency circuits. Layout-dependent effects (LDEs) affect IC design and fabrication, resulting in differences in circuit functionality and performance in presimulation versus postsimulation. These differences can greatly increase the length of design iteration cycles. Foundries have attempted to accelerate the iterative design process by providing process design kit libraries to IC designers. However, these kits can neither fully mitigate the negative affect of LDEs on design for manufacturability (DFM) nor eliminate the difference between presimulation and postsimulation results. To address this problem, this study proposed a novel algorithm-based design process in which an IC designer can use layout parasitic extraction to extract the DFM parameters of all components in a circuit prior to the routing process; these parameters include netlists that describe the internal connectivity of components as well as their interconnectivity with other components. Accordingly, the IC designer can determine the effects of DFM parameters on the circuit and modify them in advance if necessary. When the LDEs generated by device placement have been confirmed to not affect circuit properties, physical verification of the routing of metal wires in the IC layout can be performed. In this verification, postsimulations only need to focus on problems regarding the wire loading and timing effects of metal routing. The proposed design process is useful for mitigating LDEs in IC design and considerably reduces the time required for iterative improvement processes. Specifically, this study provides a method of enhancing design iteration cycles and provides guidelines for analyzing factors that hinder IC device functionality and performance. In sum, various problems can be resolved by separately extracting the DFM parameters associated with LDEs and parasitic parameters associated with routing.

High-performance digital circuits are facing increasingly severe signal integrity problems due to crosstalk noise and therefore the state-of-the-art static timing analysis (STA) methods consider crosstalk-induced delay variation. Current noise-aware STA methods compute noise-induced delay uncertainty for each net independently and annotate appropriate delay changes of nets onto data paths and associated clock paths to determine timing violations. Since delay changes in individual nets contribute cumulatively to delay changes of paths, even small amounts of pessimism in noise computation of nets can add up to produce large timing violations for paths, which may be unrealistic. Unlike glitch noise analysis where noise often attenuates during propagation, quality of delay noise analysis is severely affected by any pessimism in noise estimation and can unnecessarily cost valuable silicon and design resources for fixing unreal violations. In this paper, we propose a method to reduce pessimism in noise-aware STA by considering signal correlations of all nets associated with an entire timing path simultaneously, in a path-based approach. We first present an exact algorithm based on the branch-and-bound technique and then extend it with several heuristic techniques so that very large industrial designs can be analyzed efficiently. These techniques, which are implemented in an industrial crosstalk noise analysis tool, show as much as 75% reduction in the computed path delay variations.

Computer-aided design (CAD) tools play a critical role in optimizing integrated circuit (IC) designs, especially as the complexity and scale of ICs continue to grow. This paper introduces a via-aware parallel layer assignment algorithm to address the key challenges of routing and layer assignment in large-scale IC designs. The algorithm utilizes parallel processing techniques to divide the IC layout into distinct regions, improving load balancing and reducing routing congestion. Additionally, the via-aware strategy minimizes the number of vias used during layer assignment, significantly lowering manufacturing costs. Experimental data show that this method reduces runtime by approximately 22% and via count by 15% compared to traditional algorithms. Notably, when handling complex test cases, the algorithm demonstrates a substantial increase in efficiency, with a runtime speedup ratio of 2.16 and a via count reduction of 11.60% in most test cases. These results indicate that the proposed algorithm is highly effective in optimizing IC design for large-scale applications, with significant practical value.

The reliability variation simulation methodology for advanced integrated circuit (IC) design is presented from an Electronic Design Automation (EDA) perspective. Reliability effects, such as hot carrier injection (HCI) and bias temperature instability (BTI), continue to be one of major concerns when devices scale down to smaller sizes. Reliability variability, considering process variation (PV) and aging variation (AV), is becoming critical for circuit reliability and yield. In this paper, we present and compare various reliability variability methodologies that incorporate process and aging variations for circuit simulation. Additionally, the correlation between PV and AV is analyzed. Finally, two representative circuits (ring oscillator and SRAM) are demonstrated with the reliability variation-aware simulation.

In this paper, we focus on hardware Trojans inserted into IC (Integrated Circuit) chips during IC design. We propose a hardware Trojan detection technique which is based on the chip temperature characterization by using SOM neural network. This method can achieve a high detection rate for Trojans without gold First, we use a tool called HotSpot to get the steady-state heatmap from running IC. Then, we make use of 2DPCA (Dimensional Principal Component Analysis) to extract the features of the heatmap profile and feed them into a SOM (Self Organizing Map) neural network. Finally, the SOM neural network automatically distinguishes Trojan-free chips from Trojaninfected chips. The experimental results show that our method can achieve high detection rate, with 20% chip PV (Process Variability), for all centralized Trojans which are located at different positions.

To address the performance bottleneck in metal-based interconnects, hybrid optical network-on-chip (HONoC) has emerged as a new alternative. However, as the size of the HONoC grows, insertion loss and crosstalk noise increase, leading to excessive laser source output power and performance degradation. Therefore, we propose a low-power scalable HONoC architecture by incorporating semiconductor optical amplifiers (SOAs). An SOA placement algorithm is developed considering insertion loss and crosstalk noise. Furthermore, we establish a worst-case crosstalk noise model of SOA-enabled HONoC and induce optimized SOA gains with respect to power consumption and performance, respectively. Extensive simulations for worst-case signal-to-noise ratio (SNR) and power consumption are conducted under various traffic patterns and different network sizes. Simulation results show that the proposed SOA-enabled HONoC architecture and the associated algorithm help sustain the performance as network size increases without additional laser source power.