This study uses the spatial features of defects on the wafers to examine the detection and control of process variation in semiconductor fabrication. It applies spatial stochastic process to semiconductor yield modeling and the extrinsic reliabil- ity estimation model. New yield models of integrated circuits based on the spatial point process are established. The defect density which varies according to location on the wafer is modeled by the spatial nonhomogeneous Poisson process. And, in order to capture the variations in defect patterns between wafers, a random coeff- cient model and model-based clustering are applied. Model-based clustering is also applied to the fabrication process control for detecting these defect clusters that are generated by assignable causes. An extrinsic reliability model using defect data and a statistical defect growth model are developed based on the new yield model.

For the past four decades, Moore's law has been the most important benchmark in microelectronic circuits. Continuous improvement in lithographic technology has key enabler for growth in transistor density. In recent times, the wavelength of the light source has not kept its pace in scaling. Consequently, modern devices have feature sizes that are smaller than the wavelength of light source used currently in lithography. Printability in sub-wavelength lithography is one of the contemporary research issues. Some of the printability issues arise from optical defocus, lens aberration, wafer tilting, isotropic etching and resist thickness variation. Many of such sources lead to line width variation in today's layouts. In this work we propose to simulate such lithographic variation and estimate their impact on current devices and interconnects. We also propose to model such effects and aim to provide measures at the design level to mitigate these problems. Variations arising out of lithography process also impact yield and performance. We plan to study the impact of sub-wavelength lithography on yield and provide solutions for its measure, and directed pattern developement and testing.

abstract: Yield is a key process performance characteristic in the capital-intensive semiconductor fabrication process. In an industry where machines cost millions of dollars and cycle times are a number of months, predicting and optimizing yield are critical to process improvement, customer satisfaction, and financial success. Semiconductor yield modeling is essential to identifying processing issues, improving quality, and meeting customer demand in the industry. However, the complicated fabrication process, the massive amount of data collected, and the number of models available make yield modeling a complex and challenging task. This work presents modeling strategies to forecast yield using generalized linear models (GLMs) based on defect metrology data. The research is divided into three main parts. First, the data integration and aggregation necessary for model building are described, and GLMs are constructed for yield forecasting. This technique yields results at both the die and the wafer levels, outperforms existing models found in the literature based on prediction errors, and identifies significant factors that can drive process improvement. This method also allows the nested structure of the process to be considered in the model, improving predictive capabilities and violating fewer assumptions. To account for the random sampling typically used in fabrication, the work is extended by using generalized linear mixed models (GLMMs) and a larger dataset to show the differences between batch-specific and population-averaged models in this application and how they compare to GLMs. These results show some additional improvements in forecasting abilities under certain conditions and show the differences between the significant effects identified in the GLM and GLMM models. The effects of link functions and sample size are also examined at the die and wafer levels. The third part of this research describes a methodology for integrating classification and regression trees (CART) with GLMs. This technique uses the terminal nodes identified in the classification tree to add predictors to a GLM. This method enables the model to consider important interaction terms in a simpler way than with the GLM alone, and provides valuable insight into the fabrication process through the combination of the tree structure and the statistical analysis of the GLM. / Dissertation/Thesis / Ph.D. Industrial Engineering 2011

<p>In the Central Hardwood Region, the quantity and quality of hardwood timber critically depend on forest management decisions made by private landowners, since they hold the largest share of woodlands, some of which are plantations. These plantations are in a unique and critical position to provide much-needed hardwood resources. However, there is a lack of research and tools enabling rigorous assessments of profitability of long-term investments in hardwood plantations. Partially due to this, the majority of these privately held plantations remain unmanaged.</p> <p>This study aims at providing scientific evidence and tools to help promote forest management on hardwood plantations held by private landowners. To this end, I demonstrate in Chapter 1 an economic-modeling approach that minimizes establishment costs while ensuring free-to-grow status by year 5, and crown closure by year 10. Using temperate hardwoods such as black walnut and red oak as focal species, I find a black walnut plantation can attain crown closure in year six at the lowest cost ($4,540/ha) with 6 feet x 7 feet spacing, herbicide application for the first year, and fencing. For red oak, the minimum-cost option ($5,371/ ha) which achieves crown closure in year 10 requires a planting density of 6 feet x 7 feet, herbicide application for the first three years, and fencing. Modelling uncertainty in growth and mortality in a stochastic counterpart shifts optimal solutions to denser plantings for black walnut; planting more trees is, thus, risk mitigative. Based upon these research outcomes, I identify the tradeoffs between efficacy of treatments towards establishment success viz a viz their relative costs which serve as a solid foundation for the assessment of subsequent management strategies.</p> <p>Next, in chapter 2, I first calibrate growth, yield, and crown-width models for black walnut trees with existing and new tree measurements on selected Hardwood Tree Improvement and Regeneration Center (HTIRC) plots. Using spatial information on trees, I develop an individual tree level thinning model and simulate their post-thinning growth and yield. Significant predictors of annual diameter growth between years 10 to 18 include the initial tree DBH, forest edge effects, distance-dependent neighborhood competition, and tree age. Significant edge effects exist up to 3 rows and 3 trees from the non-forested edge. A tree on the perimeter rows grows 0.30 cm (0.12in.) in DBH more per year than the interior trees, between years 10 to 18. Next, I dovetail my results from the spatially explicit thinning model with the USFS Forest Vegetation Simulator (FVS) to understand the impacts of different scenarios of planting densities, site productivities, thinning treatments, and expected yields (as percentage of the total volume) of veneer sawlogs to quantify the growth and profitability from the mid-rotation until the final harvest. To support the attendant financial analyses, I incorporate risk into these projections by simulating stochastic windthrows based on certain assumptions. My projections suggest that, without the threat of windthrow damage, the net present day value (NPV) could exceed $4,900 per acre on the highest quality sites (SI =100) and high densities at planting (6 feet x 6 feet), assuming 10% or more of final volume was veneer and using a 3% discount rate. In contrast, under simulations of probable windthrow disturbances from mid-rotation to final harvest, the chances that standing timber value at harvest exceeds $5,000 per acre are 43.13% for a 96- and 90-year rotation and increase to 45.48% for 75 and further to 56.04% for 60.</p>