Gaussian process regression for virtual metrology of microchip quality and the resulting strategic sampling scheme

Manufacturing of integrated circuits involves many sequential processes, often ex- ecuted to nanoscale tolerances, and the yield depends on the often unmeasured quality of intermediate steps. In the high-throughput industry of fabricating microelectronics on semi-conducting wafers, scheduling measurements of product quality before the electrical test of the complete IC can be expensive. We therefore seek to predict metrics of product quality based on sensor readings describing the environment within the relevant tool during the processing of each wafer, or to apply the concept of virtual metrology (VM) to monitor these intermediate steps. We model the data using Gaussian process regression (GPR), adapted to simultaneously learn the nonlinear dynamics that govern the quality characteristic, as well as their operating space, expressed by a linear embedding of the sensor traces’ features. Such Bayesian models predict a distribution for the target metric, such as a critical dimension, so one may assess the model’s credibility through its predictive uncertainty. Assuming measurements of the quality characteristic of interest are budgeted, we seek to hasten convergence of the GPR model to a credible form through an active sampling scheme, whereby the predictive uncertainty informs which wafer’s quality to measure next. We evaluate this convergence when predicting and updating online, as if in a factory, using a large dataset for plasma-enhanced chemical vapor deposition (PECVD), with measured thicknesses for ~32,000 wafers. By approximately optimizing the information extracted from this seemingly repetitive data describing a tightly controlled process, GPR achieves ~10% greater accuracy on average than a baseline linear model based on partial least squares (PLS). In a derivative study, we seek to discern the degree of drift in the process over the several months the data spans. We express this drift by how unusual the relevant features, as embedded by the GPR model, appear as the in- puts compensate for degrading conditions. This method detects the onset of consistently unusual behavior that extends to a bimodal thickness fault, anticipating its flagging by as much as two days.Mechanical Engineerin

Discrete distributions when modeling the disability severity score of motor victims

Many European states apply score systems to evaluate the disability severity of non-fatal motor victims under the law of third-party liability. The score is a non-negative integer with an upper bound at 100 that increases with severity. It may be automatically converted into financial terms and thus also reflects the compensation cost for disability. In this paper, discrete regression models are applied to analyze the factors that influence the disability severity score of victims. Standard and zero-altered regression models are compared from two perspectives: an interpretation of the data generating process and the level of statistical fit. The results have implications for traffic safety policy decisions aimed at reducing accident severity. An application using data from Spain is provided.Hurdle discrete data models, zero-inflated distribution, generalized method of moments, personal injuries, disability rating scale. JEL classification:-

Forecasting overhead distribution line failures using weather data and gradient-boosted location, scale, and shape models

Overhead distribution lines play a vital role in distributing electricity, however, their freestanding nature makes them vulnerable to extreme weather conditions and resultant disruption of supply. The current UK regulation of power networks means preemptive mitigation of disruptions avoids financial penalties for distribution companies, making accurate fault predictions of direct financial importance. Here we present predictive models developed for a UK network based on gradient-boosted location, scale, and shape models, providing spatio-temporal predictions of faults based on forecast weather conditions. The models presented are based on (a) tree base learners or (b) penalised smooth and linear base learners -- leading to a Generalised Additive Model (GAM) structure, with the latter category of models providing best performance in terms of out-of-sample log-likelihood. The models are fitted to fifteen years of fault and weather data and are shown to provide good accuracy over multi-day forecast windows, giving tangible support to power restoration.Comment: 25 pages, 7 figures, based on the MSc dissertation of the primary author submitted for the MSc degree in Applied Statistics and Datamining at the University of St Andrews in 2021 -- under the supervision of the co-autho

An Empirical Validation of Object-Oriented Design Metrics for Fault Prediction

Object-oriented design has become a dominant method in software industry and many design metrics of object-oriented programs have been proposed for quality prediction, but there is no well-accepted statement on how significant those metrics are. In this study, empirical analysis is carried out to validate object-oriented design metrics for defects estimation. Approach: The Chidamber and Kemerer metrics suite is adopted to estimate the number of defects in the programs, which are extracted from a public NASA data set. The techniques involved are statistical analysis and neuro-fuzzy approach. Results: The results indicate that SLOC, WMC, CBO and RFC are reliable metrics for defect estimation. Overall, SLOC imposes most significant impact on the number of defects. Conclusions/Recommendations: The design metrics are closely related to the number of defects in OO classes, but we can not jump to a conclusion by using one analysis technique. We recommend using neuro-fuzzy approach together with statistical techniques to reveal the relationship between metrics and dependent variables, and the correlations among those metrics also have to be considered

Yield and Reliability Analysis for Nanoelectronics

As technology has continued to advance and more break-through emerge, semiconductor devices with dimensions in nanometers have entered into all spheres of our lives. Accordingly, high reliability and high yield are very much a central concern to guarantee the advancement and utilization of nanoelectronic products. However, there appear to be some major challenges related to nanoelectronics in regard to the field of reliability: identification of the failure mechanisms, enhancement of the low yields of nano products, and management of the scarcity and secrecy of available data [34]. Therefore, this dissertation investigates four issues related to the yield and reliability of nanoelectronics. Yield and reliability of nanoelectronics are affected by defects generated in the manufacturing processes. An automatic method using model-based clustering has been developed to detect the defect clusters and identify their patterns where the distribution of the clustered defects is modeled by a new mixture distribution of multivariate normal distributions and principal curves. The new mixture model is capable of modeling defect clusters with amorphous, curvilinear, and linear patterns. We evaluate the proposed method using both simulated and experimental data and promising results have been obtained. Yield is one of the most important performance indexes for measuring the success of nano fabrication and manufacturing. Accurate yield estimation and prediction is essential for evaluating productivity and estimating production cost. This research studies advanced yield modeling approaches which consider the spatial variations of defects or defect counts. Results from real wafer map data show that the new yield models provide significant improvement in yield estimation compared to the traditional Poisson model and negative binomial model. The ultra-thin SiO2 is a major factor limiting the scaling of semiconductor devices. High-k gate dielectric materials such as HfO2 will replace SiO2 in future generations of MOS devices. This study investigates the two-step breakdown mechanisms and breakdown sequences of double-layered high-k gate stacks by monitoring the relaxation of the dielectric films. The hazard rate is a widely used metric for measuring the reliability of electronic products. This dissertation studies the hazard rate function of gate dielectrics breakdown. A physically feasible failure time distribution is used to model the time-to-breakdown data and a Bayesian approach is adopted in the statistical analysis