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.

Efficient Marginal Likelihood Computation for Gaussian Process Regression

In a Bayesian learning setting, the posterior distribution of a predictive model arises from a trade-off between its prior distribution and the conditional likelihood of observed data. Such distribution functions usually rely on additional hyperparameters which need to be tuned in order to achieve optimum predictive performance; this operation can be efficiently performed in an Empirical Bayes fashion by maximizing the posterior marginal likelihood of the observed data. Since the score function of this optimization problem is in general characterized by the presence of local optima, it is necessary to resort to global optimization strategies, which require a large number of function evaluations. Given that the evaluation is usually computationally intensive and badly scaled with respect to the dataset size, the maximum number of observations that can be treated simultaneously is quite limited. In this paper, we consider the case of hyperparameter tuning in Gaussian process regression. A straightforward implementation of the posterior log-likelihood for this model requires O(N^3) operations for every iteration of the optimization procedure, where N is the number of examples in the input dataset. We derive a novel set of identities that allow, after an initial overhead of O(N^3), the evaluation of the score function, as well as the Jacobian and Hessian matrices, in O(N) operations. We prove how the proposed identities, that follow from the eigendecomposition of the kernel matrix, yield a reduction of several orders of magnitude in the computation time for the hyperparameter optimization problem. Notably, the proposed solution provides computational advantages even with respect to state of the art approximations that rely on sparse kernel matrices.

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.

Space-Constrained Massive MIMO: Hitting the Wall of Favorable Propagation

The recent development of the massive multiple-input multiple-output (MIMO) paradigm, has been extensively based on the pursuit of favorable propagation: in the asymptotic limit, the channel vectors become nearly orthogonal and interuser interference tends to zero [1]. In this context, previous studies
have considered fixed inter-antenna distance, which implies an increasing array aperture as the number of elements increases. Here, we focus on a practical, space-constrained topology, where an increase in the number of antenna elements in a fixed total space imposes an inversely proportional decrease in the inter-antenna distance. Our analysis shows that, contrary to existing studies, inter-user interference does not vanish in the massive MIMO regime, thereby creating a saturation effect on the achievable rate.

A Significance-Driven Programming Framework for Energy-Constrained Approximate Computing

Approximate execution is a viable technique for energy-con\-strained environments, provided that applications have the mechanisms to produce outputs of the highest possible quality within the given energy budget.
We introduce a framework for energy-constrained execution with controlled and graceful quality loss. A simple programming model allows users to express the relative importance of computations for the quality of the end result, as well as minimum quality requirements. The significance-aware runtime system uses an application-specific analytical energy model to identify the degree of concurrency and approximation that maximizes quality while meeting user-specified energy constraints. Evaluation on a dual-socket 8-core server shows that the proposed
framework predicts the optimal configuration with high accuracy, enabling energy-constrained executions that result in significantly higher quality compared to loop perforation, a compiler approximation technique.

Impact of electric vehicles on a carbon constrained power system—a post 2020 case study

Electric vehicles (EVs) offer great potential to move from fossil fuel dependency in transport once some of the technical barriers related to battery reliability and grid integration are resolved. The European Union has set a target to achieve a 10% reduction in greenhouse gas emissions by 2020 relative to 2005 levels. This target is binding in all the European Union member states. If electric vehicle issues are overcome then the challenge is to use as much renewable energy as possible to achieve this target. In this paper, the impacts of electric vehicle charged in the all-Ireland single wholesale electricity market after the 2020 deadline passes is investigated using a power system dispatch model. For the purpose of this work it is assumed that a 10% electric vehicle target in the Republic of Ireland is not achieved, but instead 8% is reached by 2025 considering the slow market uptake of electric vehicles. Our experimental study shows that the increasing penetration of EVs could contribute to approach the target of the EU and Ireland government on emissions reduction, regardless of different charging scenarios. Furthermore, among various charging scenarios, the off-peak charging is the best approach, contributing 2.07% to the target of 10% reduction of Greenhouse gas emissions by 2025.

Constrained Multi-Objective Aerofoil Design Using a Multi-Level Optimisation Strategy

A novel approach for the multi-objective design optimisation of aerofoil profiles is presented. The proposed method aims to exploit the relative strengths of global and local optimisation algorithms, whilst using surrogate models to limit the number of computationally expensive CFD simulations required. The local search stage utilises a re-parameterisation scheme that increases the flexibility of the geometry description by iteratively increasing the number of design variables, enabling superior designs to be generated with minimal user intervention. Capability of the algorithm is demonstrated via the conceptual design of aerofoil sections for use on a lightweight laminar flow business jet. The design case is formulated to account for take-off performance while reducing sensitivity to leading edge contamination. The algorithm successfully manipulates boundary layer transition location to provide a potential set of aerofoils that represent the trade-offs between drag at cruise and climb conditions in the presence of a challenging constraint set. Variations in the underlying flow physics between Pareto-optimal aerofoils are examined to aid understanding of the mechanisms that drive the trade-offs in objective functions.

Forward and backward least angle regression for nonlinear system identification

A forward and backward least angle regression (LAR) algorithm is proposed to construct the nonlinear autoregressive model with exogenous inputs (NARX) that is widely used to describe a large class of nonlinear dynamic systems. The main objective of this paper is to improve model sparsity and generalization performance of the original forward LAR algorithm. This is achieved by introducing a replacement scheme using an additional backward LAR stage. The backward stage replaces insignificant model terms selected by forward LAR with more significant ones, leading to an improved model in terms of the model compactness and performance. A numerical example to construct four types of NARX models, namely polynomials, radial basis function (RBF) networks, neuro fuzzy and wavelet networks, is presented to illustrate the effectiveness of the proposed technique in comparison with some popular methods.

The significance of interconnector counter-trading in a security constrained electricity market

Throughout the European Union there is an increasing amount of wind generation being dispatched-down due to the binding of power system operating constraints from high levels of wind generation. This paper examines the impact a system non-synchronous penetration limit has on the dispatch-down of wind and quantifies the significance of interconnector counter-trading to the priority dispatching of wind power. A fully coupled economic dispatch and security constrained unit commitment model of the Single Electricity Market of the Republic of Ireland and Northern Ireland and the British Electricity Trading and Transmission Arrangement was used in this study. The key finding was interconnector counter-trading reduces the impact the system non-synchronous penetration limit has on the dispatch-down of wind. The capability to counter-trade on the interconnectors and an increase in system non-synchronous penetration limit from 50% to 55% reduces the dispatch-down of wind by 311 GW h and decreases total electricity payments to the consumer by €1.72/MW h. In terms of the European Union electricity market integration, the results show the importance of developing individual electricity markets that allow system operators to counter-trade on interconnectors to ensure the priority dispatch of the increasing levels of wind generation.

Supervised Aggregative Feature Extraction for Big Data Time Series Regression

In many applications, and especially those where batch processes are involved, a target scalar output of interest is often dependent on one or more time series of data. With the exponential growth in data logging in modern industries such time series are increasingly available for statistical modeling in soft sensing applications. In order to exploit time series data for predictive modelling, it is necessary to summarise the information they contain as a set of features to use as model regressors. Typically this is done in an unsupervised fashion using simple techniques such as computing statistical moments, principal components or wavelet decompositions, often leading to significant information loss and hence suboptimal predictive models. In this paper, a functional learning paradigm is exploited in a supervised fashion to derive continuous, smooth estimates of time series data (yielding aggregated local information), while simultaneously estimating a continuous shape function yielding optimal predictions. The proposed Supervised Aggregative Feature Extraction (SAFE) methodology can be extended to support nonlinear predictive models by embedding the functional learning framework in a Reproducing Kernel Hilbert Spaces setting. SAFE has a number of attractive features including closed form solution and the ability to explicitly incorporate first and second order derivative information. Using simulation studies and a practical semiconductor manufacturing case study we highlight the strengths of the new methodology with respect to standard unsupervised feature extraction approaches.

LD Score regression distinguishes confounding from polygenicity in genome-wide association studies

Both polygenicity (many small genetic effects) and confounding biases, such as cryptic relatedness and population stratification, can yield an inflated distribution of test statistics in genome-wide association studies (GWAS). However, current methods cannot distinguish between inflation from a true polygenic signal and bias. We have developed an approach, LD Score regression, that quantifies the contribution of each by examining the relationship between test statistics and linkage disequilibrium (LD). The LD Score regression intercept can be used to estimate a more powerful and accurate correction factor than genomic control. We find strong evidence that polygenicity accounts for the majority of the inflation in test statistics in many GWAS of large sample size.

Participation of Smallholders in Agroforestry Agri-Environmental Scheme: A lesson from the rural Mount Kenya region

The likelihood of smallholder farmers not participating in agroforestry agri-environmental schemes and payments for ecosystem services (PES) may be due to limited farmland endowment and formal credit constraints. These deficits may lead to an ‘exclusive club’ of successful farmers, which are not necessarily poor, enjoying the benefits of agri-environmental schemes and PES although agrienvironmental schemes and PES have been devised as a means of fostering rural sustainable development and improving the livelihood of poor smallholder farmers. Smallholder farmers in parts of rural Kenya continue to enroll in ‘The International Small Group Tree Planting Programme’ (TIST), an agri-environmental scheme, promoting agroforestry, carbon sequestration and conservation agriculture (CA). The question remains if these farmers are really poor? This study examines factors that determine the participation of smallholder farmers in TIST in parts of rural Kenya. We use survey data compiled in 2013 on 210 randomly selected smallholder farmers from Embu, Meru and Nanyuki communities; the sample consists of TIST and non-TIST members. A random utility model and logit regression were used to test a set of non-monetary and monetary factors that influence participation in the TIST. The utility function is conceptualized to give non-monetary factors, particularly the common medium of communication in rural areas – formal and informal – a central role. Furthermore, we investigate other factors (incl. credit accessibility and interest rate) that reveal the nature of farmers participating in TIST. The findings suggest that spread of information via formal and informal networks is a major driver of participation in the TIST program. Furthermore, variables such credit constrains, age and labour supply positively correlate with TIST participation, while for education the opposite is true. It is important to mention that these correlations, although somewhat consistent, were all found to be weak. The results indicate that participation in the TIST program is not influenced by farm size; therefore we argue that the TIST scheme is NOT an ‘exclusive club’ comprising wealthy and successful farmers. Older farmers’ being more likely to join the TIST is an argument for their long- rather than widely assumed short-term planning horizon and a new contribution to the literature. Given the importance of poverty alleviation and climate smart agriculture in developing countries, sustainable policy should strengthening the social and human capital as well as informal networks in rural areas. Extension services should effectively communicate benefits to less educated and credit constrained farmers.