| Manufacturing lines are formed by several unit process steps whose individual purposes are to bring about a predetermined transformation to the product part by subjecting it to the processing step. The quality of each individual step is determined by the product variables that are modified during the processing transformation. In general, product variables are not directly measurable in situ as the product part is being processed. However, it is often possible to install sensors that measure some of the critical parameters of the process referred to as process variables. In this case, the resulting combination of process sensors and estimation algorithms provide a very powerful tool for process control, diagnostics, and preventive maintenance. However, the relationship between the process variables and the product variables is affected by many uncertain factors that may change from one run of the process to the next. These uncertainties include process variations, and variations in the incoming product. One of the difficulties in designing a system able to estimate the product variables is that one needs to ensure good estimation performance across an envelope of runs of the process.; The main focus of this dissertation is the analysis and design of algorithms for estimating product variables by measuring process variables during manufacturing processes. We give a rigorous mathematical formulation of the qualitative problem of designing an estimator for this problem using a collection of data that captures the process envelope. Within this framework, we define notions of optimality and consistency. Using an important result from statistical learning theory, we obtain a set of sufficient conditions that guarantees convergence of the design procedure to the optimal estimator when the training set is sufficiently large.; We apply the algorithms resulting from this study to the area of microelectronics manufacturing. In particular, we obtain novel algorithms for real-time thickness estimation of semiconductor wafers using in situ spectroscopic ellipsometry. |
