【正文】 The fabwide control framework proposed here also draws analogy from the MPC framework,but the focus is optimized control of electrical parameters of the devices. The Etest data are used to update the device model parameters based on mismatch between the Etest data and the model. After parameter estimation is performed, the estimated parameters are sent to a fabwide optimizer,which distributes targets to lowerlevel controllers that regulate steps within the manufacturing model updated with the new set of model parameters is used for EPC control. 3. Run to run control algorithms In recent years, runtorun (R2R) control technology has received tremendous interest in semiconductor manufacturing. Moyne and Hurwitz (Moyne et al. [34]) define the runtorun control as ??a form of discrete process and machine control in which the product recipe with respect to a particular process is modified ex situ, ., between machine ?runs‘, so as to minimize process drift, shift, and variability‘‘. In order to modify the recipe to address the process drift, shift and other variability, the current tool and wafer states need to be estimated. One class of widely used runtorun controllers is based on the exponentially weighted moving average (EWMA) statistics to estimate process disturbances. The EWMA has been used for a long time for quality monitoring purposes [9]. Its use as a basis for runtorun control is relatively recent [40]. For a time series of easurement {x[n],x[n1], . . .}, where n denotes the run number, the EWMA is given in the following recursive formula: X[n]=wx[n1]+(1w)x[n] One of the most effective manipulated variables in R2R control is the processing time within a processing step such as etch time, exposure time, and planarization time. The controlled variables in this case are typically the extent to which the process develops under the processing time, such as depth of etch and critical dimensions. This multiplicative model does not fit into the typical linear state space model presented earlier, but it can be converted to the linear state space model with process and measurement noise by simply taking the logarithm. Therefore, all the control algorithms presented earlier in this paper are applicable to time control. 4. Fault detection and diagnosis Processing tool data such as temperatures, pressures, and gas flow rates will be used to monitor recipes applied to single wafers or batches of wafers. Some typical processing operations include plasma etching, thin film deposition, rapid thermal annealing, ion implantation, and chemical mechanical planarization. At most processing steps, sensors collect data for each wafer or batch of wafers that are processed on the tool. This data can be in the form of realtime data for a recipe, summary statistics available at the end of each run, or data from more advanced sensor platforms such as optical emission spectroscopy. Data based fault detection and diagnosis has been successfully developed and applied in other industries (., [30,49]). These data driven fault detection techniques are based on multivariate statistical analysis such as principal ponent analysis (PCA) and partial least squares (PLS) and are related to statistical quality control methods [26]. A recent review of these process monitoring methods is given in [36]. While the batch nature of semiconductor manufacturing provides plenty of opportunities for applying multiway process monitoring [35], many forms of semiconductor metrology data are naturally organized in three dimensions. One such case is CD metrology, where the three dimensions are wafer, site, and parameter. Batch data are also monly available from processing tools, which exhibits the dimensions of batch, time, and parameter (Fig. 2). Multiway PCA has been successfully applied for batch process monitoring across many different industries. In the field of semiconductor manufacturing, Yue et al. [52] demonstrated the concept of unfolding data by applying multiway PCA to optical emission spectra for plasma etchers. For metrology and processing tool monitoring, the data can be unfolded by site or time (every row represents one site on a wafer or time instant in a batch) or by wafer (every row represents one wafer). In this work, wafer level fault detection and identification is desired, so the latter has been chosen as the more appropriate unfolding method (Fig. 4). However, as will be discussed later, the advantages of analyzing data by site or time can be realized simply by implementing the multiblock approach. . Metrology data monitoring While processing operations build the structures, metrology operations characterize them. Some examples of metrology measurements include development inspection critical dimension (DICD), final inspection critical dimension (FICD), and film thickness. Metrology measurements are normally taken at several locations on the semiconductor wafers, oftentimes for multiple features at the same site (., top and bottom DICD). Fault detection and identification applied to sitelevel metrology data is intended to validate whether the structures built on the semiconductor wafers hit their targets and do so uniformly across the wafer surfaces. As an example, we use PCA to perform fault detection and identification on DICD data from Advanced Micro Devices‘ Fab25 in Austin, Texas. The DICD is the width of the pattern in the photoresist after the photoresist has been developed and before the next trim step. As shown in Fig. 3, isotropy in development results in a small difference between the top of the photoresist and the bottom. The data set consists of 700 wafers, where both the top and bottom of the resist are measured at nine sites on each wafer. While Fig. 6 grouped all 9 sites together for each of the two parameters, the Fig. 7 contributions tak