108 research outputs found
Virtual metrology for plasma etch processes.
Plasma processes can present dicult control challenges due to time-varying dynamics
and a lack of relevant and/or regular measurements. Virtual metrology (VM) is the
use of mathematical models with accessible measurements from an operating process to
estimate variables of interest. This thesis addresses the challenge of virtual metrology
for plasma processes, with a particular focus on semiconductor plasma etch.
Introductory material covering the essentials of plasma physics, plasma etching, plasma
measurement techniques, and black-box modelling techniques is rst presented for readers
not familiar with these subjects. A comprehensive literature review is then completed
to detail the state of the art in modelling and VM research for plasma etch processes.
To demonstrate the versatility of VM, a temperature monitoring system utilising a
state-space model and Luenberger observer is designed for the variable specic impulse
magnetoplasma rocket (VASIMR) engine, a plasma-based space propulsion system. The
temperature monitoring system uses optical emission spectroscopy (OES) measurements
from the VASIMR engine plasma to correct temperature estimates in the presence of
modelling error and inaccurate initial conditions. Temperature estimates within 2% of
the real values are achieved using this scheme.
An extensive examination of the implementation of a wafer-to-wafer VM scheme to estimate
plasma etch rate for an industrial plasma etch process is presented. The VM
models estimate etch rate using measurements from the processing tool and a plasma
impedance monitor (PIM). A selection of modelling techniques are considered for VM
modelling, and Gaussian process regression (GPR) is applied for the rst time for VM
of plasma etch rate. Models with global and local scope are compared, and modelling
schemes that attempt to cater for the etch process dynamics are proposed. GPR-based
windowed models produce the most accurate estimates, achieving mean absolute percentage
errors (MAPEs) of approximately 1:15%. The consistency of the results presented
suggests that this level of accuracy represents the best accuracy achievable for
the plasma etch system at the current frequency of metrology.
Finally, a real-time VM and model predictive control (MPC) scheme for control of
plasma electron density in an industrial etch chamber is designed and tested. The VM
scheme uses PIM measurements to estimate electron density in real time. A predictive
functional control (PFC) scheme is implemented to cater for a time delay in the VM
system. The controller achieves time constants of less than one second, no overshoot,
and excellent disturbance rejection properties. The PFC scheme is further expanded by
adapting the internal model in the controller in real time in response to changes in the
process operating point
Virtual metrology for plasma etch processes.
Plasma processes can present dicult control challenges due to time-varying dynamics
and a lack of relevant and/or regular measurements. Virtual metrology (VM) is the
use of mathematical models with accessible measurements from an operating process to
estimate variables of interest. This thesis addresses the challenge of virtual metrology
for plasma processes, with a particular focus on semiconductor plasma etch.
Introductory material covering the essentials of plasma physics, plasma etching, plasma
measurement techniques, and black-box modelling techniques is rst presented for readers
not familiar with these subjects. A comprehensive literature review is then completed
to detail the state of the art in modelling and VM research for plasma etch processes.
To demonstrate the versatility of VM, a temperature monitoring system utilising a
state-space model and Luenberger observer is designed for the variable specic impulse
magnetoplasma rocket (VASIMR) engine, a plasma-based space propulsion system. The
temperature monitoring system uses optical emission spectroscopy (OES) measurements
from the VASIMR engine plasma to correct temperature estimates in the presence of
modelling error and inaccurate initial conditions. Temperature estimates within 2% of
the real values are achieved using this scheme.
An extensive examination of the implementation of a wafer-to-wafer VM scheme to estimate
plasma etch rate for an industrial plasma etch process is presented. The VM
models estimate etch rate using measurements from the processing tool and a plasma
impedance monitor (PIM). A selection of modelling techniques are considered for VM
modelling, and Gaussian process regression (GPR) is applied for the rst time for VM
of plasma etch rate. Models with global and local scope are compared, and modelling
schemes that attempt to cater for the etch process dynamics are proposed. GPR-based
windowed models produce the most accurate estimates, achieving mean absolute percentage
errors (MAPEs) of approximately 1:15%. The consistency of the results presented
suggests that this level of accuracy represents the best accuracy achievable for
the plasma etch system at the current frequency of metrology.
Finally, a real-time VM and model predictive control (MPC) scheme for control of
plasma electron density in an industrial etch chamber is designed and tested. The VM
scheme uses PIM measurements to estimate electron density in real time. A predictive
functional control (PFC) scheme is implemented to cater for a time delay in the VM
system. The controller achieves time constants of less than one second, no overshoot,
and excellent disturbance rejection properties. The PFC scheme is further expanded by
adapting the internal model in the controller in real time in response to changes in the
process operating point
Global and Local Virtual Metrology Models for a Plasma Etch Process
Virtual metrology (VM) is the estimation of metrology
variables that may be expensive or difficult to measure using
readily available process information. This paper investigates the
application of global and local VM schemes to a data set recorded
from an industrial plasma etch chamber. Windowed VM models
are shown to be the most accurate local VM scheme, capable
of producing useful estimates of plasma etch rates over multiple
chamber maintenance events and many thousands of wafers. Partial
least-squares regression, artificial neural networks, and Gaussian
process regression are investigated as candidate modeling
techniques, with windowed Gaussian process regression models
providing the most accurate results for the data set investigated
Computational Intelligence Techniques for OES Data Analysis
Semiconductor manufacturers are forced by market demand to continually
deliver lower cost and faster devices. This results in complex industrial processes
that, with continuous evolution, aim to improve quality and reduce
costs. Plasma etching processes have been identified as a critical part of the
production of semiconductor devices. It is therefore important to have good
control over plasma etching but this is a challenging task due to the complex
physics involved.
Optical Emission Spectroscopy (OES) measurements can be collected
non-intrusively during wafer processing and are being used more and more
in semiconductor manufacturing as they provide real time plasma chemical
information. However, the use of OES measurements is challenging due to
its complexity, high dimension and the presence of many redundant variables.
The development of advanced analysis algorithms for virtual metrology,
anomaly detection and variables selection is fundamental in order to
effectively use OES measurements in a production process.
This thesis focuses on computational intelligence techniques for OES data
analysis in semiconductor manufacturing presenting both theoretical results
and industrial application studies. To begin with, a spectrum alignment
algorithm is developed to align OES measurements from different sensors.
Then supervised variables selection algorithms are developed. These are defined
as improved versions of the LASSO estimator with the view to selecting
a more stable set of variables and better prediction performance in virtual
metrology applications. After this, the focus of the thesis moves to the unsupervised
variables selection problem. The Forward Selection Component
Analysis (FSCA) algorithm is improved with the introduction of computationally
efficient implementations and different refinement procedures. Nonlinear
extensions of FSCA are also proposed. Finally, the fundamental topic
of anomaly detection is investigated and an unsupervised variables selection
algorithm tailored to anomaly detection is developed. In addition, it is shown
how OES data can be effectively used for semi-supervised anomaly detection
in a semiconductor manufacturing process.
The developed algorithms open up opportunities for the effective use of
OES data for advanced process control. All the developed methodologies
require minimal user intervention and provide easy to interpret models. This
makes them practical for engineers to use during production for process monitoring
and for in-line detection and diagnosis of process issues, thereby resulting
in an overall improvement in production performance
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Fault Classification of Nonlinear Small Sample Data through Feature Sub-Space Neighbor Vote
The fault classification of a small sample of high dimension is challenging, especially for a nonlinear and non-Gaussian manufacturing process. In this paper, a similarity-based feature selection and sub-space neighbor vote method is proposed to solve this problem. To capture the dynamics, nonlinearity, and non-Gaussianity in the irregular time series data, high order spectral features, and fractal dimension features are extracted, selected, and stacked in a regular matrix. To address the problem of a small sample, all labeled fault data are used for similarity decisions for a specific fault type. The distances between the new data and all fault types are calculated in their feature subspaces. The new data are classified to the nearest fault type by majority probability voting of the distances. Meanwhile, the selected features, from respective measured variables, indicate the cause of the fault. The proposed method is evaluated on a publicly available benchmark of a real semiconductor etching dataset. It is demonstrated that by using the high order spectral features and fractal dimensionality features, the proposed method can achieve more than 84% fault recognition accuracy. The resulting feature subspace can be used to match any new fault data to the fingerprint feature subspace of each fault type, and hence can pinpoint the root cause of a fault in a manufacturing process
Development of dynamic model and control techniques for microelectromechanical gyroscopes
In this thesis we investigate the effects of stiffness, damping and temperature on the performance of a MEMS vibratory gyroscope. The stiffness and damping parameters are chosen because they can be appropriately designed to synchronize the drive and sense mode resonance to enhance the sensitivity and stability of MEMS gyroscope. Our results show that increasing the drive axis stiffness from its tuned value by 50%, reduces the sense mode magnitude by ~27% and augments the resonance frequency by ~21%. The stiffness and damping are mildly sensitive to typical variations in operating temperature. The stiffness decreases by 0.30%, while the damping increases by 3.81% from their initial values, when the temperature is raised from -40 to 60C. Doubling the drive mode damping from its tuned value reduces the oscillation magnitude by 10%, but ~0.20% change in the resonance frequency. The predicted effects of stiffness, damping and temperature can be utilized to design a gyroscope for the desired operating condition
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Thermal behaviour model identification for three different office buildings
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The thermal behaviour was investigated of three offices positioned in three buildings built in different periods, one academic institute built in 1920 and two modem commercial buildings in London. The buildings chosen for this study are the
Rockefeller Building, which is part of University College London (UCL), Portman House in Oxford Street and the Visa Building in Paddington. Due to the lack of specific information related to the structure of the buildings such as windows, doors, building dimensions and other information that would allow the use of physical models, in this project black-box linear and non-linear mathematical models were used. Data relating to room temperature, hot and chilled water temperature, air flow and temperature from air handling units and outside temperature were collected for one year, from the actual building management systems (BMSs) installed in these buildings. The main assumption of the model development in the three buildings was that although occupancy, computers, printers etc cause an additional internal heat gain, their impact is in part indirectly included in the model. The primary objective of the analysis was to identify the inputs (independent variables) that gave good models for the prediction of room temperature for a certain period. Consequently, the process of input selection and period of validity in obtaining models that give good thermal prediction (within the same period) were the key points in season subdivision. The first part of the analysis applied the following linear parametric mathematical models to the three office buildings selected: Box Jenkins (BJ), autoregressivem oving averagew ith exogenousi nput (ARMAX) and output error (OE) structure. The project then deals with non-linear mathematical models. The same inputs selected and assumptions made with linear analysis were used to build, in turn, models with feedforward backpropagation (FFBP), non-linear autoregressive mathematical models with parallel arrangement (NARX) and series-parallel arrangement (NARXSP). The research presented in this project is related to developing models for three real offices positioned in three different buildings whereas previous researchers have applied these models mainly to experimental rooms and HVAC plants, with the purpose of fault detection and diagnostics. Furthermore, in the past, research on thermal model development has been related to one office or HVAC plant, and for a limited period of time (a few weeks or months). In contrast, this study undertakes an overall analysis of thermal model development for three offices and for a period of one year, where the process of input selection is given priority to obtain good models. Thus, previous studies have not utilized these two types of models for such a long period of data collection nor related them to three different buildings.
Finally, model development and then validation were pursued utilizing the same week, different weeks and different days (where the first part of the data in each case was used for model estimation and the following part for model validation). This was one within the period that the models gave good results for the prediction of room temperature. The best mathematical models (linear and non-linear) that predict the room temperature, in terms of the inputs selected, has been determined for each season. The procedures for how to choose the best models are based on the following techniques: final prediction error (FPE for linear models), mean squared error (mse for non-linear models), and model fits and errors between measurements and simulated model output. Overall, the results related for the prediction of room temperature with non-linear models, are better than those obtained with linear models, as a result of comparison between models' errors, FPE and mse obtained with linear and non-linear models.Funding was obtained from the Brunel University Department of Mechanical Engineering
Statistical Methods for Semiconductor Manufacturing
In this thesis techniques for non-parametric modeling, machine learning, filtering and prediction and run-to-run control for semiconductor manufacturing are described.
In particular, algorithms have been developed for two major applications area:
- Virtual Metrology (VM) systems;
- Predictive Maintenance (PdM) systems.
Both technologies have proliferated in the past recent years in the semiconductor industries, called fabs, in order to increment productivity and decrease costs.
VM systems aim of predicting quantities on the wafer, the main and basic product of the semiconductor industry, that may be physically measurable or not. These quantities are usually ’costly’ to be measured in economic or temporal terms: the prediction is based on process variables and/or logistic information on the production that, instead,
are always available and that can be used for modeling without further costs.
PdM systems, on the other hand, aim at predicting when a maintenance action has to be performed. This approach to maintenance management, based like VM on statistical
methods and on the availability of process/logistic data, is in contrast with other classical approaches:
- Run-to-Failure (R2F), where there are no interventions performed on the machine/process until a new breaking or specification violation happens in the production;
- Preventive Maintenance (PvM), where the maintenances are scheduled in advance based on temporal intervals or on production iterations.
Both aforementioned approaches are not optimal, because they do not assure that breakings and wasting of wafers will not happen and, in the case of PvM, they may lead to unnecessary maintenances without completely exploiting the lifetime of the machine or of the process.
The main goal of this thesis is to prove through several applications and feasibility studies that the use of statistical modeling algorithms and control systems can improve the efficiency, yield and profits of a manufacturing environment like the semiconductor
one, where lots of data are recorded and can be employed to build mathematical models.
We present several original contributions, both in the form of applications and methods.
The introduction of this thesis will be an overview on the semiconductor fabrication process: the most common practices on Advanced Process Control (APC) systems
and the major issues for engineers and statisticians working in this area will be presented.
Furthermore we will illustrate the methods and mathematical models used in the applications.
We will then discuss in details the following applications:
- A VM system for the estimation of the thickness deposited on the wafer by the Chemical Vapor Deposition (CVD) process, that exploits Fault Detection and Classification (FDC) data is presented. In this tool a new clustering algorithm based on Information Theory (IT) elements have been proposed. In addition, the Least Angle Regression (LARS) algorithm has been applied for the first time to VM problems.
- A new VM module for multi-step (CVD, Etching and Litography) line is proposed, where Multi-Task Learning techniques have been employed.
- A new Machine Learning algorithm based on Kernel Methods for the estimation of scalar outputs from time series inputs is illustrated.
- Run-to-Run control algorithms that employ both the presence of physical measures and statistical ones (coming from a VM system) is shown; this tool is based on IT elements.
- A PdM module based on filtering and prediction techniques (Kalman Filter, Monte Carlo methods) is developed for the prediction of maintenance interventions in the Epitaxy process.
- A PdM system based on Elastic Nets for the maintenance predictions in Ion Implantation tool is described.
Several of the aforementioned works have been developed in collaborations with major European semiconductor companies in the framework of the European project UE FP7 IMPROVE (Implementing Manufacturing science solutions to increase equiPment pROductiVity and fab pErformance); such collaborations will be specified during the thesis, underlying the practical aspects of the implementation of the proposed technologies in a real industrial environment
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