Virtual metrology enabled early stage prediction for enhanced control of multi-stage fabrication processes

Semiconductor fabrication involves several sequential processing steps with the result that critical production variables are often affected by a superposition of affects over multiple steps. In this paper a Virtual Metrology (VM) system for early stage measurement of such variables is presented; the VM system seeks to express the contribution to the output variability that is due to a defined observable part of the production line. The outputs of the processed system may be used for process monitoring and control purposes. A second contribution of this work is the introduction of Elastic Nets, a regularization and variable selection technique for the modelling of highly-correlated datasets, as a technique for the development of VM models. Elastic Nets and the proposed VM system are illustrated using real data from a multi-stage etch process used in the fabrication of disk drive read/write heads. © 2013 IEEE.

MSC-clustering and forward stepwise regression for virtual metrology in highly correlated input spaces

Increasingly semiconductor manufacturers are exploring opportunities for virtual metrology (VM) enabled process monitoring and control as a means of reducing non-value added metrology and achieving ever more demanding wafer fabrication tolerances. However, developing robust, reliable and interpretable VM models can be very challenging due to the highly correlated input space often associated with the underpinning data sets. A particularly pertinent example is etch rate prediction of plasma etch processes from multichannel optical emission spectroscopy data. This paper proposes a novel input-clustering based forward stepwise regression methodology for VM model building in such highly correlated input spaces. Max Separation Clustering (MSC) is employed as a pre-processing step to identify a reduced srt of well-conditioned, representative variables that can then be used as inputs to state-of-the-art model building techniques such as Forward Selection Regression (FSR), Ridge regression, LASSO and Forward Selection Ridge Regression (FCRR). The methodology is validated on a benchmark semiconductor plasma etch dataset and the results obtained are compared with those achieved when the state-of-art approaches are applied directly to the data without the MSC pre-processing step. Significant performance improvements are observed when MSC is combined with FSR (13%) and FSRR (8.5%), but not with Ridge Regression (-1%) or LASSO (-32%). The optimal VM results are obtained using the MSC-FSR and MSC-FSRR generated models. © 2012 IEEE.

On Regression Methods for Virtual Metrology in Semiconductor Manufacturing

Virtual metrology (VM) aims to predict metrology values using sensor data from production equipment and physical metrology values of preceding samples. VM is a promising technology for the semiconductor manufacturing industry as it can reduce the frequency of in-line metrology operations and provide supportive information for other operations such as fault detection, predictive maintenance and run-to-run control. The prediction models for VM can be from a large variety of linear and nonlinear regression methods and the selection of a proper regression method for a specific VM problem is not straightforward, especially when the candidate predictor set is of high dimension, correlated and noisy. Using process data from a benchmark semiconductor manufacturing process, this paper evaluates the performance of four typical regression methods for VM: multiple linear regression (MLR), least absolute shrinkage and selection operator (LASSO), neural networks (NN) and Gaussian process regression (GPR). It is observed that GPR performs the best among the four methods and that, remarkably, the performance of linear regression approaches that of GPR as the subset of selected input variables is increased. The observed competitiveness of high-dimensional linear regression models, which does not hold true in general, is explained in the context of extreme learning machines and functional link neural networks.

Extreme learning machines for virtual metrology and etch rate prediction

Virtual metrology (VM) aims to predict metrology values using sensor data from production equipment and physical metrology values of preceding samples. VM is a promising technology for the semiconductor manufacturing industry as it can reduce the frequency of in-line metrology operations and provide supportive information for other operations such as fault detection, predictive maintenance and run-to-run control. Methods with minimal user intervention are required to perform VM in a real-time industrial process. In this paper we propose extreme learning machines (ELM) as a competitive alternative to popular methods like lasso and ridge regression for developing VM models. In addition, we propose a new way to choose the hidden layer weights of ELMs that leads to an improvement in its prediction performance.

A dynamic sampling methodology for plasma etch processes using Gaussian process regression

Plasma etch is a key process in modern semiconductor manufacturing facilities as it offers process simplification and yet greater dimensional tolerances compared to wet chemical etch technology. The main challenge of operating plasma etchers is to maintain a consistent etch rate spatially and temporally for a given wafer and for successive wafers processed in the same etch tool. Etch rate measurements require expensive metrology steps and therefore in general only limited sampling is performed. Furthermore, the results of measurements are not accessible in real-time, limiting the options for run-to-run control. This paper investigates a Virtual Metrology (VM) enabled Dynamic Sampling (DS) methodology as an alternative paradigm for balancing the need to reduce costly metrology with the need to measure more frequently and in a timely fashion to enable wafer-to-wafer control. Using a Gaussian Process Regression (GPR) VM model for etch rate estimation of a plasma etch process, the proposed dynamic sampling methodology is demonstrated and evaluated for a number of different predictive dynamic sampling rules. © 2013 IEEE.

Optimal wafer site selection using forward selection component analysis

Reducing wafer metrology continues to be a major target in semiconductor manufacturing efficiency initiatives due to it being a high cost, non-value added operation that impacts on cycle-time and throughput. However, metrology cannot be eliminated completely given the important role it plays in process monitoring and advanced process control. To achieve the required manufacturing precision, measurements are typically taken at multiple sites across a wafer. The selection of these sites is usually based on a priori knowledge of wafer failure patterns and spatial variability with additional sites added over time in response to process issues. As a result, it is often the case that in mature processes significant redundancy can exist in wafer measurement plans. This paper proposes a novel methodology based on Forward Selection Component Analysis (FSCA) for analyzing historical metrology data in order to determine the minimum set of wafer sites needed for process monitoring. The paper also introduces a virtual metrology (VM) based approach for reconstructing the complete wafer profile from the optimal sites identified by FSCA. The proposed methodology is tested and validated on a wafer manufacturing metrology dataset. © 2012 IEEE.

Virtual Instruments in Dimensional Metrology

During the last five years, in order to improve understanding of content related to "Coordinate Metrology", the Laboratorio de Metrología y Metrotecnia (LMM) from the Polytechnic University of Madrid offers its PhD students, as a course work, the construction of a virtual instrument. This virtual instrument simulates the imaging of a part to be measured by optical dimensional metrology instruments (microscopes, profile projectors, vision machines). The LMM provides students with images similar to those they would obtain with real instrumentation for the instrument adjustment and calibration process. Working with these images, students should determine the adjustment parameters of the virtual instrument. Once these parameters are set, the student can perform the proper calibration of the virtual instrument. Beyond this process, the instrument is already able to perform traceable measurement. In order to do that, LMM offers students some images of parts. Students should perform some measurements using those images and estimate the corresponding uncertainties.

Desarrollo de un Laboratorio Virtual para la realización de e-comparisons en los ensayos de aislamiento acústico de fachadas según UNE-EN ISO 140-5

Actualmente son una práctica común los procesos de normalización de métodos de ensayo y acreditación de laboratorios, ya que permiten una evaluación de los procedimientos llevados a cabo por profesionales de un sector tecnológico y además permiten asegurar unos mínimos de calidad en los resultados finales. En el caso de los laboratorios de acústica, para conseguir y mantener la acreditación de un laboratorio es necesario participar activamente en ejercicios de intercomparación, utilizados para asegurar la calidad de los métodos empleados. El inconveniente de estos ensayos es el gran coste que suponen para los laboratorios, siendo en ocasiones inasumible por estos teniendo que renunciar a la acreditación. Este Proyecto Fin de Grado se centrará en el desarrollo de un Laboratorio Virtual implementado mediante una herramienta software que servirá para realizar ejercicios de intercomparación no presenciales, ampliando de ese modo el concepto e-comparison y abriendo las bases a que en un futuro este tipo de ejercicios no presenciales puedan llegar a sustituir a los llevados a cabo actualmente. En el informe primero se hará una pequeña introducción, donde se expondrá la evolución y la importancia de los procedimientos de calidad acústica en la sociedad actual. A continuación se comentará las normativas internacionales en las que se soportará el proyecto, la norma ISO 145-5, así como los métodos matemáticos utilizados en su implementación, los métodos estadísticos de propagación de incertidumbres especificados por la JCGM (Joint Committee for Guides in Metrology). Después, se hablará sobre la estructura del proyecto, tanto del tipo de programación utilizada en su desarrollo como la metodología de cálculo utilizada para conseguir que todas las funcionalidades requeridas en este tipo de ensayo estén correctamente implementadas. Posteriormente se llevará a cabo una validación estadística basada en la comparación de unos datos generados por el programa, procesados utilizando la simulación de Montecarlo, y unos cálculos analíticos, que permita comprobar que el programa funciona tal y como se ha previsto en la fase de estudio teórico. También se realizará una prueba del programa, similar a la que efectuaría un técnico de laboratorio, en la que se evaluará la incertidumbre de la medida calculándola mediante el método tradicional, pudiendo comparar los datos obtenidos con los que deberían obtenerse. Por último, se comentarán las conclusiones obtenidas con el desarrollo y pruebas del Laboratorio Virtual, y se propondrán nuevas líneas de investigación futuras relacionadas con el concepto e-comparison y la implementación de mejoras al Laboratorio Virtual. ABSTRACT. Nowadays it is common practise to make procedures to normalise trials methods standards and laboratory accreditations, as they allow for the evaluation of the procedures made by professionals from a particular technological sector in addition to ensuring a minimum quality in the results. In order for an acoustics laboratory to achieve and maintain the accreditation it is necessary to actively participate in the intercomparison exercises, since these are used to assure the quality of the methods used by the technicians. Unfortunately, the high cost of these trials is unaffordable for many laboratories, which then have to renounce to having the accreditation. This Final Project is focused on the development of a Virtual Laboratory implemented by a software tool that it will be used for making non-attendance intercomparison trials, widening the concept of e-comparison and opening the possibility for using this type of non-attendance trials instead of the current ones. First, as a short introduction, I show the evolution and the importance today of acoustic quality procedures. Second, I will discuss the international standards, such as ISO 145-5, as well the mathematic and statistical methods of uncertainty propagation specified by the Joint Committee for Guides in Metrology, that are used in the Project. Third, I speak about the structure of the Project, as well as the programming language structure and the methodology used to get the different features needed in this acoustic trial. Later, a statistical validation will be carried out, based on comparison of data generated by the program, processed using a Montecarlo simulation, and analytical calculations to verify that the program works as planned in the theoretical study. There will also be a test of the program, similar to one that a laboratory technician would carry out, by which the uncertainty in the measurement will be compared to a traditional calculation method so as to compare the results. Finally, the conclusions obtained with the development and testing of the Virtual Laboratory will be discussed, new research paths related to e-comparison definition and the improvements for the Laboratory will be proposed.