arXiv subjects

Victor Blanco

Publications and source records attributed to Victor Blanco.

15 recordsLinked to original sources

arXiv2025

Linear, nested, and quadratic ordered measures: Computation and incorporation into optimization problems

In this paper we address a unified mathematical optimization framework to compute a wide range of measures used in most operations research and data science contexts. The goal is to embed such metrics within general optimization models allowing their efficient computation. We assess the usefulness of this approach applying it to three different families of measures, namely linear, nested, and quadratic ordered measures. Computational results are reported showing the efficiency and accuracy of our methods as compared with standard implementations in numerical software packages. Finally, we illustrate this methodology by computing a number of optimal solutions with respect to different metrics on three well-known linear and combinatorial optimization problems: scenario analysis in linear programming, the traveling salesman and the weighted multicover set problem.

math.OC↗

arXiv2024

Scanning Electron Microscopy-based Automatic Defect Inspection for Semiconductor Manufacturing: A Systematic Review

In this review, automatic defect inspection algorithms that analyze Scanning Electron Microscopy (SEM) images for Semiconductor Manufacturing (SM) are identified, categorized, and discussed. This is a topic of critical importance for the SM industry as the continuous shrinking of device patterns has led to increasing defectivity and a greater prevalence of higher-resolution imaging tools such as SEM. Among others, these aspects threaten to increase costs due to increased inspection time-to-solution and decreased yield. Relevant research papers were systematically identified in four popular publication databases in January 2024. A total of 103 papers were selected after screening for novel contributions relating to automatic SEM image analysis algorithms for semiconductor defect inspection. These papers were then categorized based on the inspection tasks they addressed, their evaluation metrics, and the type of algorithms used. A notable finding from this categorization is that reference-based defect detection algorithms were the most popular algorithm type until 2020 when Deep Learning (DL)-based inspection algorithms became more popular, especially for defect classification. Furthermore, four broader research questions were discussed to come to the following conclusions: (i) the key components of inspection algorithms are set up, pre-processing, feature extraction, and final prediction; (ii) the maturity of the manufacturing process affects the data availability and required sensitivity of inspection algorithms; (iii) key challenges for these algorithms relate to the desiderata of minimizing time-to-solution which pushes for high imaging throughput, reducing manual input during algorithm setup, and higher processing throughput; and (iv) three promising directions for future work are suggested based on gaps in the reviewed literature that address key remaining limitations.

eess.IV↗

arXiv2024

Advancing SEM Based Nano-Scale Defect Analysis in Semiconductor Manufacturing for Advanced IC Nodes

In this research, we introduce a unified end-to-end Automated Defect Classification-Detection-Segmentation (ADCDS) framework for classifying, detecting, and segmenting multiple instances of semiconductor defects for advanced nodes. This framework consists of two modules: (a) a defect detection module, followed by (b) a defect segmentation module. The defect detection module employs Deformable DETR to aid in the classification and detection of nano-scale defects, while the segmentation module utilizes BoxSnake. BoxSnake facilitates box-supervised instance segmentation of nano-scale defects, supported by the former module. This simplifies the process by eliminating the laborious requirement for ground-truth pixel-wise mask annotation by human experts, which is typically associated with training conventional segmentation models. We have evaluated the performance of our ADCDS framework using two distinct process datasets from real wafers, as ADI and AEI, specifically focusing on Line-space patterns. We have demonstrated the applicability and significance of our proposed methodology, particularly in the nano-scale segmentation and generation of binary defect masks, using the challenging ADI SEM dataset where ground-truth pixelwise segmentation annotations were unavailable. Furthermore, we have presented a comparative analysis of our proposed framework against previous approaches to demonstrate its effectiveness. Our proposed framework achieved an overall mAP@IoU0.5 of 72.19 for detection and 78.86 for segmentation on the ADI dataset. Similarly, for the AEI dataset, these metrics were 90.38 for detection and 95.48 for segmentation. Thus, our proposed framework effectively fulfils the requirements of advanced defect analysis while addressing significant constraints.

cs.CV↗

arXiv2024

An Evaluation of Continual Learning for Advanced Node Semiconductor Defect Inspection

Deep learning-based semiconductor defect inspection has gained traction in recent years, offering a powerful and versatile approach that provides high accuracy, adaptability, and efficiency in detecting and classifying nano-scale defects. However, semiconductor manufacturing processes are continually evolving, leading to the emergence of new types of defects over time. This presents a significant challenge for conventional supervised defect detectors, as they may suffer from catastrophic forgetting when trained on new defect datasets, potentially compromising performance on previously learned tasks. An alternative approach involves the constant storage of previously trained datasets alongside pre-trained model versions, which can be utilized for (re-)training from scratch or fine-tuning whenever encountering a new defect dataset. However, adhering to such a storage template is impractical in terms of size, particularly when considering High-Volume Manufacturing (HVM). Additionally, semiconductor defect datasets, especially those encompassing stochastic defects, are often limited and expensive to obtain, thus lacking sufficient representation of the entire universal set of defectivity. This work introduces a task-agnostic, meta-learning approach aimed at addressing this challenge, which enables the incremental addition of new defect classes and scales to create a more robust and generalized model for semiconductor defect inspection. We have benchmarked our approach using real resist-wafer SEM (Scanning Electron Microscopy) datasets for two process steps, ADI and AEI, demonstrating its superior performance compared to conventional supervised training methods.

cs.CV↗

arXiv2024

Addressing Class Imbalance and Data Limitations in Advanced Node Semiconductor Defect Inspection: A Generative Approach for SEM Images

Precision in identifying nanometer-scale device-killer defects is crucial in both semiconductor research and development as well as in production processes. The effectiveness of existing ML-based approaches in this context is largely limited by the scarcity of data, as the production of real semiconductor wafer data for training these models involves high financial and time costs. Moreover, the existing simulation methods fall short of replicating images with identical noise characteristics, surface roughness and stochastic variations at advanced nodes. We propose a method for generating synthetic semiconductor SEM images using a diffusion model within a limited data regime. In contrast to images generated through conventional simulation methods, SEM images generated through our proposed DL method closely resemble real SEM images, replicating their noise characteristics and surface roughness adaptively. Our main contributions, which are validated on three different real semiconductor datasets, are: i) proposing a patch-based generative framework utilizing DDPM to create SEM images with intended defect classes, addressing challenges related to class-imbalance and data insufficiency, ii) demonstrating generated synthetic images closely resemble real SEM images acquired from the tool, preserving all imaging conditions and metrology characteristics without any metadata supervision, iii) demonstrating a defect detector trained on generated defect dataset, either independently or combined with a limited real dataset, can achieve similar or improved performance on real wafer SEM images during validation/testing compared to exclusive training on a real defect dataset, iv) demonstrating the ability of the proposed approach to transfer defect types, critical dimensions, and imaging conditions from one specified CD/Pitch and metrology specifications to another, thereby highlighting its versatility.

cs.CV↗

arXiv2024

Towards Improved Semiconductor Defect Inspection for high-NA EUVL based on SEMI-SuperYOLO-NAS

Due to potential pitch reduction, the semiconductor industry is adopting High-NA EUVL technology. However, its low depth of focus presents challenges for High Volume Manufacturing. To address this, suppliers are exploring thinner photoresists and new underlayers/hardmasks. These may suffer from poor SNR, complicating defect detection. Vision-based ML algorithms offer a promising solution for semiconductor defect inspection. However, developing a robust ML model across various image resolutions without explicit training remains a challenge for nano-scale defect inspection. This research's goal is to propose a scale-invariant ADCD framework capable to upscale images, addressing this issue. We propose an improvised ADCD framework as SEMI-SuperYOLO-NAS, which builds upon the baseline YOLO-NAS architecture. This framework integrates a SR assisted branch to aid in learning HR features by the defect detection backbone, particularly for detecting nano-scale defect instances from LR images. Additionally, the SR-assisted branch can recursively generate upscaled images from their corresponding downscaled counterparts, enabling defect detection inference across various image resolutions without requiring explicit training. Moreover, we investigate improved data augmentation strategy aimed at generating diverse and realistic training datasets to enhance model performance. We have evaluated our proposed approach using two original FAB datasets obtained from two distinct processes and captured using two different imaging tools. Finally, we demonstrate zero-shot inference for our model on a new, originating from a process condition distinct from the training dataset and possessing different Pitch characteristics. Experimental validation demonstrates that our proposed ADCD framework aids in increasing the throughput of imaging tools for defect inspection by reducing the required image pixel resolutions.

cs.CV↗

arXiv2023

Applying Machine Learning Models on Metrology Data for Predicting Device Electrical Performance

Moore Law states that transistor density will double every two years, which is sustained until today due to continuous multi-directional innovations, such as extreme ultraviolet lithography, novel patterning techniques etc., leading the semiconductor industry towards 3nm node and beyond. For any patterning scheme, the most important metric to evaluate the quality of printed patterns is EPE, with overlay being its largest contribution. Overlay errors can lead to fatal failures of IC devices such as short circuits or broken connections in terms of P2P electrical contacts. Therefore, it is essential to develop effective overlay analysis and control techniques to ensure good functionality of fabricated semiconductor devices. In this work we have used an imec N14 BEOL process flow using LELE patterning technique to print metal layers with minimum pitch of 48nm with 193i lithography. FF structures are decomposed into two mask layers (M1A and M1B) and then the LELE flow is carried out to make the final patterns. Since a single M1 layer is decomposed into two masks, control of overlay between the two masks is critical. The goal of this work is of two-fold as, (a) to quantify the impact of overlay on capacitance and (b) to see if we can predict the final capacitance measurements with selected machine learning models at an early stage. To do so, scatterometry spectra are collected on these electrical test structures at (a)post litho, (b)post TiN hardmask etch, and (c)post Cu plating and CMP. Critical Dimension and overlay measurements for line-space pattern are done with SEM post litho, post etch and post Cu CMP. Various machine learning models are applied to do the capacitance prediction with multiple metrology inputs at different steps of wafer processing. Finally, we demonstrate that by using appropriate machine learning models we are able to do better prediction of electrical results.

eess.SP↗

arXiv2023

Improved Defect Detection and Classification Method for Advanced IC Nodes by Using Slicing Aided Hyper Inference with Refinement Strategy

In semiconductor manufacturing, lithography has often been the manufacturing step defining the smallest possible pattern dimensions. In recent years, progress has been made towards high-NA (Numerical Aperture) EUVL (Extreme-Ultraviolet-Lithography) paradigm, which promises to advance pattern shrinking (2 nm node and beyond). However, a significant increase in stochastic defects and the complexity of defect detection becomes more pronounced with high-NA. Present defect inspection techniques (both non-machine learning and machine learning based), fail to achieve satisfactory performance at high-NA dimensions. In this work, we investigate the use of the Slicing Aided Hyper Inference (SAHI) framework for improving upon current techniques. Using SAHI, inference is performed on size-increased slices of the SEM images. This leads to the object detector's receptive field being more effective in capturing small defect instances. First, the performance on previously investigated semiconductor datasets is benchmarked across various configurations, and the SAHI approach is demonstrated to substantially enhance the detection of small defects, by approx. 2x. Afterwards, we also demonstrated application of SAHI leads to flawless detection rates on a new test dataset, with scenarios not encountered during training, whereas previous trained models failed. Finally, we formulate an extension of SAHI that does not significantly reduce true-positive predictions while eliminating false-positive predictions.

cs.CV↗

arXiv2023

Automated Semiconductor Defect Inspection in Scanning Electron Microscope Images: a Systematic Review

A growing need exists for efficient and accurate methods for detecting defects in semiconductor materials and devices. These defects can have a detrimental impact on the efficiency of the manufacturing process, because they cause critical failures and wafer-yield limitations. As nodes and patterns get smaller, even high-resolution imaging techniques such as Scanning Electron Microscopy (SEM) produce noisy images due to operating close to sensitivity levels and due to varying physical properties of different underlayers or resist materials. This inherent noise is one of the main challenges for defect inspection. One promising approach is the use of machine learning algorithms, which can be trained to accurately classify and locate defects in semiconductor samples. Recently, convolutional neural networks have proved to be particularly useful in this regard. This systematic review provides a comprehensive overview of the state of automated semiconductor defect inspection on SEM images, including the most recent innovations and developments. 38 publications were selected on this topic, indexed in IEEE Xplore and SPIE databases. For each of these, the application, methodology, dataset, results, limitations and future work were summarized. A comprehensive overview and analysis of their methods is provided. Finally, promising avenues for future work in the field of SEM-based defect inspection are suggested.

cs.CV↗

arXiv2023

Polyhedral geometry and combinatorics of an autocatalytic ecosystem

Developing a mathematical understanding of autocatalysis in reaction networks has both theoretical and practical implications. We review definitions of autocatalytic networks and prove some properties for minimal autocatalytic subnetworks (MASs). We show that it is possible to classify MASs in equivalence classes, and develop mathematical results about their behavior. We also provide linear-programming algorithms to exhaustively enumerate them and a scheme to visualize their polyhedral geometry and combinatorics. We then define cluster chemical reaction networks, a framework for coarse-graining real chemical reactions with positive integer conservation laws. We find that the size of the list of minimal autocatalytic subnetworks in a maximally connected cluster chemical reaction network with one conservation law grows exponentially in the number of species. We end our discussion with open questions concerning an ecosystem of autocatalytic subnetworks and multidisciplinary opportunities for future investigation.

q-bio.MN↗

arXiv2014

Continuous Location under Refraction

In this paper we address the problem of locating a new facility on a $d$-dimensional space when the distance measure ($\ell_p$- or polyhedral-norms) is different at each one of the sides of a given hyperplane $\mathcal{H}$. We relate this problem with the physical phenomenon of refraction, and extends it to any finite dimension space and different distances at each one of the sides of any hyperplane. An application to this problem is the location of a facility within or outside an urban area where different distance measures must be used. We provide a new second order cone programming formulation, based on the $\ell_p$-norm representation given in \cite{BPE2014} that allows to solve, exactly, the problem in any finite dimension space with semidefinite programming tools. We also extend the problem to the case where the hyperplane is considered as a rapid transit media (a different third norm is also considered over $\mathcal{H}$) that allows the demand to travel faster through $\mathcal{H}$ to reach the new facility. Extensive computational experiments run in Gurobi are reported in order to show the effectiveness of the approach.

math.OC↗

arXiv2009

Computing the number of numerical semigroups using generating functions

This paper presents a new methodology to count the number of numerical semigroups of given genus or Frobenius number. We apply generating function tools to the bounded polyhedron that classifies the semigroups with given genus (or Frobenius number) and multiplicity. First, we give theoretical results about the polynomial-time complexity of counting the number of these semigroups. We also illustrate the methodology analyzing the cases of multiplicity 3 and 4 where some formulas for the number of numerical semigroups for any genus and Frobenius number are obtained.

math.CO↗

arXiv2009

On the complexity of some fuzzy integer programs

Fuzzy optimization deals with the problem of determining 'optimal'solutions of an optimization problem when some of the elements that appear in the problem are not precise. In real situations it is usual to have information, in systems under consideration, that is not exact. Thisimprecision can be modeled in a fuzzy environment. Zadeh (1965) analyzed systems of logic that permit truth values between zero and one instead of the classical binary true-false logic. In this framework, satisfying a certain condition means to evaluate how close are the elements involved to the complete satisfaction. Then, each element in a 'fuzzy set' is coupled with a value in [0,1] that represents the membership level to the set. In linear programming some or all the elements that describe a problem may be considered fuzzy: objective function, right-hand side vector or constraint matrix, the notion of optimality (ordering over the feasible solutions), the level of satisfaction of the constraints, etc. Moreover, in integer programs, the integrality constraints may be seen as fuzzy constraints. Here, we present new complexity results about linear integer programming where some of its elements are considered fuzzy using previous results on short generating functions for solving multiobjective integer programs.

math.OC↗

arXiv2008

Partial Gröbner bases for multiobjective integer linear optimization

In this paper we present a new methodology for solving multiobjective integer linear programs using tools from algebraic geometry. We introduce the concept of partial Gröbner basis for a family of multiobjective programs where the right-hand side varies. This new structure extends the notion of Gröbner basis for the single objective case, to the case of multiple objectives, i.e., a partial ordering instead of a total ordering over the feasible vectors. The main property of these bases is that the partial reduction of the integer elements in the kernel of the constraint matrix by the different blocks of the basis is zero. It allows us to prove that this new construction is a test family for a family of multiobjective programs. An algorithm 'à la Buchberger' is developed to compute partial Gröbner bases and two different approaches are derived, using this methodology, for computing the entire set of efficient solutions of any multiobjective integer linear problem (MOILP). Some examples illustrate the application of the algorithms and computational experiments are reported on several families of problems.

math.OC↗

arXiv2008

Short Rational Generating Functions For Multiobjective Linear Integer Programming

This paper presents algorithms for solving multiobjective integer programming problems. The algorithm uses Barvinok's rational functions of the polytope that defines the feasible region and provides as output the entire set of nondominated solutions for the problem. Theoretical complexity results on the algorithm are provided in the paper. Specifically, we prove that encoding the entire set of nondominated solutions of the problem is polynomially doable, when the dimension of the decision space is fixed. In addition, we provide polynomial delay algorithms for enumerating this set. An implementation of the algorithm shows that it is useful for solving multiobjective integer linear programs.

math.OC↗