Rest-period voltage relaxation in lithium-ion batteries is a non-invasive means to probe the battery's state of charge (SOC) and health without service interruption. However, to apply voltage relaxation as a reliable method for state estimation, an accurate on-board model is needed. The shape of the voltage relaxation depends on a multitude of factors, including the diffusivity and the initial Li concentration profile. By invoking the spherical-diffusion equation for an electrode particle, we solve it for the rest period with homogeneous boundary conditions of no flux at the center and surface. This leads to an analytical expression for the spatiotemporal evolution of Li concentration and, consequently, the SOC during the rest period. The solution is suitable for implementation on battery management systems as it calculates the equilibrium and the transient spatiotemporal profiles of SOC efficiently. The validation of the model predictions against the electrochemical-thermal model-generated data showed >95% accuracy.

Modeling lithium-ion batteries has been a challenging problem. One of the critical tasks among many is state estimation, as it enables researchers to design better battery management systems (BMS). Understanding important battery parameters allows researchers to monitor battery health, predict performance, and optimize battery operation. Traditionally, mathematical models using partial differential equations (PDEs) such as the pseudo two-dimensional model (P2D) have been widely used to estimate physical quantities within the battery. However, deployment of P2D for real-time prediction is limited by the high computational cost, instability of numerical techniques, and the requirement of specialized software. Recent studies have successfully applied various machine learning algorithms achieving high predictive accuracy in many cases. These algorithms, however, suffer from limitations on generalizability and high computation requirements, which limit their deployment. We investigate the applicability of symbolic regression(SR), a branch of symbolic AI techniques to the problem. The results demonstrate equivalent accuracy with P2D while offering orders of magnitude faster execution. As this study uses simulated P2D data, the findings should be interpreted as a proof-of-concept indicating that symbolic regression can yield interpretable, computationally efficient surrogates with promising BMS relevance.

Natural Graphite (NG) is a widely used anode material in lithium-ion batteries (LIBs), prized for its high theoretical capacity, excellent electrical conductivity and cost-effectiveness. However, its performance is strongly influenced by lithium diffusion through its layered structure, influencing the charging rates, cycle life, and overall efficiency. Thus, accurate estimation of lithium diffusivity in NG is crucial for understanding and optimizing its performance. Traditional methods, like Galvanostatic intermittent titration technique (GITT), often provide inaccurate diffusivity estimates due to non-linear dependence of the open-circuit potential (OCP) on the state of charge (SOC), and assumptions that oversimplify the diffusion process. The recently introduced method, DELVRT (Diffusivity Estimation from Long-term Voltage Relaxation Technique), offers a promising alternative. By harnessing the subtle dynamics of voltage relaxation during rest periods, dominantly influenced by solid-phase diffusion, DELVRT provides a more accurate and robust diffusivity estimation. In this study, DELVRT is used to measure the diffusivity of Lithium in NG as a function of the SOC, under various conditions, providing consistent, reliable estimates, independent of the current history. This is important towards robust state estimations for electrochemical models of LIBs and for NG to unlock its full potential as an anode material, enabling more efficient and reliable LIBs.

Accurate estimation of solid phase diffusivity, a rate-limiting step in Li-Ion batteries, is extremely important for battery management system (BMS) algorithms for precise state estimations and safe, stable battery operation. The present state-of-the-art diffusivity estimation methods give erroneous results, due to inherent limitations and invalid assumptions. Here, a new method is proposed, diffusivity estimation from long-term voltage relaxation technique (DELVRT), to estimate solid diffusivity using battery rest period voltage relaxation. As solid phase diffusion dominates rest period voltage relaxation, the derivation of the spatio-temporal evolution of the concentration profile is derived and used to demonstrate accurate estimation of diffusivity. For times greater than the diffusion time scale, the temporal voltage variation is directly proportional to the diffusivity, leading to an analytical expression for estimating diffusivity. The validation for this model is performed for various different conditions, with data generated using the Pseudo-2D electrochemical-thermal model. It is demonstrated that the diffusivity estimation using DELVRT is significantly more accurate compared to the widely used galvanostatic intermittent titration technique (GITT), especially where GITT performed poorly owing to high non-linearity in the open circuit potential-state of charge relationship of the active material.

In the photolithographic process vital to semiconductor manufacturing, various types of defects appear during EUV pattering. Due to ever-shrinking pattern size, these defects are extremely small and cause false or missed detection during inspection. Specifically, the lack of defect-annotated quality data with good representation of smaller defects has prohibited deployment of deep learning based defect detection models in fabrication lines. To resolve the problem of data unavailability, we artificially generate scanning electron microscopy (SEM) images of line patterns with known distribution of defects and autonomously annotate them. We then employ state-of-the-art object detection models to investigate defect detection performance as a function of defect size, much smaller than the pitch width. We find that the real-time object detector YOLOv8 has the best mean average precision of 96% as compared to EfficientNet, 83%, and SSD, 77%, with the ability to detect smaller defects. We report the smallest defect size that can be detected reliably. When tested on real SEM data, the YOLOv8 model correctly detected 84.6% of Bridge defects and 78.3% of Break defects across all relevant instances. These promising results suggest that synthetic data can be used as an alternative to real-world data in order to develop robust machine-learning models.

To improve the cycle life of sodium-ion batteries, it is essential to understand the microscopic processes that lead to cell degradation. The mismatched response time of anode and cathode has profound but poorly understood impact on cycle life. In this work, we combine electrochemical and materials characterization along with electrochemical modeling to investigate the root cause of degradation in sodium-ion full cells made from Na4Fe3(PO4)(2)P2O7 (NFPP) cathodes and hard carbon (HC) anode. Our results pinpoint to the slow diffusion of Na in HC as the main cause of diffusional polarization that leads to cathode experiencing high local potentials and ultimately to active material loss over cycling. We demonstrate that by reducing the anode particle size, the diffusional timescales in anode can be matched with that of cathode to improve both extractable capacity as well as cycle life. These observations shed light on non-intuitive and intricate ways in which cathode and anode can interact with each other to cause degradation in Na-ion batteries and how microscopic understanding of these cause and effects can help design long lasting batteries.

Early detection of short circuits in battery-powered systems is critical in preventing potential catastrophic failures. However, nascent short-circuit signatures are extremely weak and challenging to detect using existing algorithms without compromising on prediction accuracy. Traditional physics-based approaches rely on hand-crafted models to establish relationships between battery operating parameters and short resistance, which limits their ability to capture all relevant details, resulting in sub-optimal accuracies. In this study, we present a machine learning-based approach that leverages rest period voltage data to detect short circuits. Our method employs a 1D convolutional neural network (CNN) classifier/estimator that extracts temporal dynamic features relevant to the short circuit prediction problem from both the long and short tails of the rest period voltage profile. The approach is validated using commercial battery data, generated at different conditions including temperatures, and short circuits of varying severities; with prediction accuracies greater than 90% even for soft shorts of 500 Omega. The key performance parameters of the 1D CNN model are compared against a physics-based short detection approach, demonstrating its superior performance and cost-effectiveness. Overall, our work represents a significant advancement in the field of short circuit detection in battery-powered systems, offering improved accuracy, efficiency, and cost-effectiveness.

Li-ion battery mishaps are primarily attributed to short circuits, which missed early detection. In this study, a method is introduced to address this issue by analyzing the voltage relaxation, after initiating a rest period. The voltage equilibration arising from solid-concentration profile relaxation is expressed by a double-exponential model, whose time constants, τ1 & τ2, capture the initial, rapid exponential contour and the long-term relaxation, respectively. By tracking τ2, which is very sensitive to small leakage currents, it is possible to detect a short early on and estimate the short resistance. This method, validated with experiments on commercial batteries induced with short circuits of varying extents, has >90% prediction accuracy and enables clear differentiation between different short severities, while factoring in the influence of temperature, state of charge (SOC), state of health (SOH), and idle currents. The method is applicable across different battery chemistries and form factors, offering precise and robust nascent-stage short detection-estimation for on-device implementation.

Despite having a high theoretical capacity, silicon-based anodes fall short in providing practical and cycle-stable specific capacity close to the theoretical potential. The main challenge, namely particle pulverization and loss of mechanical integrity due to a large volume expansion, is commonly addressed by nano-structuring and blending with graphite in a Si/C composite anode. However, a maximum Si content of 15% in Si/C composite anodes has been realized, leaving scope for much improvement. Herein we discuss and theoretically benchmark a new strategy to increase Si content and achievable specific capacity by limiting anode utilization to minimize degradation. Through careful consideration to differential rates of lithiation of Si and C, particle fracture, and electrode swelling limit, our physical analysis suggests that this strategy could provide specific capacities of greater than 1100 Ah/Kg while eliminating degradation. These benchmarks are arrived at though a comprehensive analysis of lithiation of Si and C on an individual component level and the associated propensity for Si particle fracture as well as reduction in electrode porosity due to volume expansion and arriving at safe lithiation limits for a given set of electrode parameters under consideration. Since this safe range of operation is dependent on particle size, we show that we can optimize the Si% in Si/C to achieve maximum utilizable specific capacity for a given particle size.

Lithium-ion batteries are typically modelled using the pseudo-2-dimensional (P2D) model, where a set of partial differential equations describing transport and electrochemical reactions are solved numerically to obtain battery state information. To improve computational efficiency and enable on-board implementation for state-estimation, reduced order models are developed, where one such model reduction technique includes using a profile approximation for solving solid phase diffusion inside electrode particles. While greatly reducing model complexity, the profile approximation also leads to reduced accuracy, especially at low characteristic diffusion lengths. We address this issue by developing an improved model, which recognizes the existence of a penetration depth and the solution is obtained by dividing the particle into diffusion-free core and a shell corresponding to the penetration depth. The time-scale for the diffusion front to reach the particle centre depends on the diffusivity and particle radius. A similarity solution for this period, leads to an expression for the State of charge (SOC) in the spatio-temporal domain. The predictions are compared to that from the benchmark P2D and experimental data, revealing accuracies >99%, while adding no computational cost. This improved model is particularly useful under high C-rate or low temperature operation, where the characteristic diffusion lengths are low.

A new metric to detect, classify and estimate the severity of short circuits in batteries is introduced in this work. State-of-the-art techniques mostly focus on the detection part and not much work is done on appropriately quantifying its severity. Barring accidental events, a majority of the short circuits have a long incubation period, where the short resistance continually decreases, to a point of thermal runaway. Thus, apart from detecting the short during its inception, a metric to track the severity, map it against a predetermined threshold to flag a potential catastrophe would be of great practical utility. A short fatigue metric (SFM) is proposed, based on the charge/discharge hysteresis, to classify short circuits into soft and hard. The SFM, which is more sensitive than other short-specific battery signatures, provides a fluid classification of short circuits, with continuous values, as a function of the short leakage current, ranging from 0 (no-fault cell) to 1 (hard cell), where 0.1 is defined as the soft-hard transition point. With emulated, persistent short circuit experiments on commercial batteries, the SFM is verified, to show that it is a useful metric to detect short especially in its early stages, classify and accurately estimate its severity.

Accurate detection and classification of wafer defects constitute an important component in semiconductor manufacturing. It provides interpretable information to find the possible root causes of defects and to take actions for quality management and yield improvement. Traditional approach to classify wafer defects, performed manually by experienced engineers using computer-aided tools, is time-consuming and can be low in accuracy. Hence, automated detection of wafer defects using deep learning approaches has attracted considerable attention to improve the performance of detection process. However, a majority of these works have focused on defect classification and have ignored defect localization which is equally important in determining how specific process steps can lead to defects in certain locations. To address this, we evaluate the state-of-the-art You Only Look Once (YOLO) architecture to accurately locate and classify wafer map defects. Experimental results obtained on 19200 wafer maps show that YOLOv3 and YOLOv4, the variants of YOLO architecture, can achieve >94% of classification accuracy in real-time. For comparison, other architectures, namely ResNet50 and DenseNet121 are also evaluated for wafer defect classification and they give accuracies 89% and 92% respectively, however, without localization abilities. We find that the object detection methods are very useful in locating and classifying defects on semiconductor wafers.

Early detection of internal short circuits (ISC) in Lithium-Ion Batteries (LIBs) is crucial for avoiding potential catastrophes. State-of-the art health monitoring methods fall short in terms of their ability to detect early-stage short circuits and in terms of ease of implementation. We report a unique internal-short circuit detection method, capable of detecting early-stage short circuits. A set of electrochemically curated pulse current probes, activated at predetermined states of charge (SOC), accurately determine the short-induced leakage current by comparing with an on-board physics based electrochemical-thermal reduced order model, that considers characteristic non-linear behaviour of LIBs. These specially designed diagnostic probes act as a ‘treadmill’ test, which detect soft short and estimates the soft short resistance accurately. Importantly, we demonstrate its ability to detect, estimate both internal short and ageing-related battery degradation, even when both are present. Proof-of-concept experiments on commercial batteries show our method's ability to detect soft short (up to 200Ω) and ageing extents (>90%) with >98% accuracy. Anchored in underlying electrochemical processes of the battery, we provide a detailed analysis on how and why this method is uniquely positioned as an accurate, practically implementable health and safety monitoring algorithm on a battery management system.

Roughness-induced resistivity variation of thin metal films is conveniently described by the Fuchs–Sondheimer model, where the phenomenological parameter p is used to quantify the extent of specular scattering at surfaces. However, p is a lumped parameter and does not include microscopic information that characterizes roughness, viz., auto-correlation function, root-mean-square height, and correlation length. In this work, we extract these roughness parameters for Cu films of thickness ranging from 31 nm to 95 nm. We find that the roughness–roughness correlation function is an exponential with a characteristic correlation length that increases monotonically with the film thickness. Using this, we predict the roughness parameter-dependent specularity coefficient, which has an implicit thickness dependency. This alters the resistivity scaling compared to the prevailing model of resistivity scaling, where p is assumed to be a constant.

The maximum extractable power from lithium-ion batteries is a crucial performance metric both in terms of safety assessment and to plan prudent corrective action to avoid sudden power loss/shutdown. However, precise estimation of state of power remains a challenge because of the highly non-linear behaviour of batteries that are further aggravated at extremities of temperature as well as battery state of charge. To address this issue, we present the current limit estimate (CLE), which is determined using a robust electrochemical-thermal reduced order model, as a function of the pulse duration, depth of discharge, pre-set voltage cut-off and importantly the temperature. The CLE calculated from the model is experimentally validated using commercial mobile phone cells. With cell temperatures varying from 0 ?C to 65 ?C and full range of depths of discharge, the model gives a prediction accuracy of more than 98%. The model is computationally efficient and compact enough to be implemented on battery management systems for on-board, real time state of power estimation. Further, key insights on what limits power capability of a battery are drawn through an analysis of contributions of different kinetic and transport processes to the cell resistance as a function of temperature and depth of discharge.

Battery packs are often designed with multiple battery cells configured in series and/or parallel combinations to meet the energy and/or power requirements of target applications. Modeling of these battery packs is very complex, computationally challenging and requires extending a single cell model to multi-cell models including electrical connections between cells. Also, the cell-to-cell variations of capacity, resistance, and temperature in the pack are vital in the battery pack design and battery management system development. Therefore, a robust modeling platform with in-built physics and fully coupled models both at the cell and the pack level is developed. The modeling framework consists of Simplified Electrochemical and lumped Thermal Model (SEM-T) at the cell level and Equivalent-Circuit Model (ECM) for Ohmic calculations and natural Convective Thermal Model (CTM) for thermal distribution at the pack level. A 7S4P battery pack with 21700 NCA cylindrical cells is considered in this study and the model is validated with the experimental data sets at different c-rates and temperatures. The developed model is able to successfully predict the pack voltage, capacities, and temperatures. The proposed model is computationally efficient and can be easily adopted for on-board implementation in battery management system for safe and reliable operations.

The development of inexpensive and large-capacity energy storage solutions is critical to support future electric grids for grid stability as well as to solve the intermittency of renewable generation. As the cost of stored energy per cycle is a primary concern as compared to the energy density in these applications, low cost and easy-to-produce battery active materials are intensely explored. In this pursuit, hydroxyphosphate-based materials have also been studied where tavorite LiFePO4OH has grasped attention. Though the material exhibits lower redox potential and thus offers lower energy density, it is still very attractive for stationary (grid) storage applications as it consists of earth-abundant elements. To evaluate the performance characteristics of this system, we establish an electrochemical reduced-order model and validate it against experiments. Based on this model, the effects of cell design parameters, electrode thickness, active material loading, and particle size, on battery performance, including the trade-off between energy and power capabilities were investigated by generating Ragone plots. While it was found that all three parameters have a significant effect on energy and power capabilities, a cathode particle of >2 mu m would affect the power capability adversely because of the slow solid-state diffusion. Furthermore, the energy efficiency of the system was evaluated to be >82.5%, making it very attractive for stationary applications from the cost per unit energy stored perspective. These results highlight the commercial viability of hydroxyphosphate battery chemistry.

We investigate using the Boltzmann transport equation the electrical resistivity of atomically smooth single-crystal Cu(111) and Cu(001) films with thickness 1-45 nm. Our transport calculations show that, in the absence of grain-boundary scattering and surface perturbations, the resistivity of Cu films of thickness comparable to the electron mean free path (40 nm for bulk copper) is close to the bulk resistivity. The resistivity increases trivially for sub-40-nm-thick films. These single-crystal Cu films show an intrinsic limit of resistivity. A steep increase in resistivity observed for ultrathin films is due to enhanced finite-size effects. We explain the cause of increase in resistivity by investigating the electronic structure at the Fermi level.

Next generation of Battery Management Systems (BMS) are moving towards implementing electrochemical models for Li-ion cell and pack state estimation modules, for better accuracy at a wide range of operating conditions. To enable this, the knowledge of geometric, kinetic and transport parameters used in electrochemical model of the cell become crucial for operation and performance of the BMS. However, most of these parameters are proprietary and are not provided by the battery supplier. Thus it becomes important for the BMS developer to obtain these properties for any new given cell in a quick, cost effective and non-destructive manner. Here, we propose development of an approach which uses Electrochemical Impedance Spectroscopy (EIS) and purpose designed cycling data from any given cell, in conjunction with a suite of electrochemical models, to estimate parameters of the cell. The sensitivities of the models to these parameters are established using Monte Carlo Simulation and the p-value calculation method. Then individual parameters are estimated using the models to which they show higher sensitivity. We call this mapping of parameters to responses of the cell as 'Characteristic Response Isolation'. A Particle Swarm based optimization scheme with Kalman correction is applied to estimate the parameters. It is seen that the use of multiple responses to estimate different sets of parameters leads to higher accuracy, lesser computation time compared to using only voltage error minimization. The results obtained through simulation show low error in the estimated parameters and good matching of the voltage and current profile. The same approach applied on data generated for commercial cell shows good accuracy in voltage estimation in normal operating regime.