Kalman filter state estimation for a manufacturing system

Details Kalman filter state estimation for a manufacturing system Kalman filter state estimation for a manufacturing system

2002-07-31

2004-06-29

Rodriguez, Paul (Department: 2125)

Data processing: generic control systems or specific application

Specific application, apparatus or process

Product assembly or manufacturing

C700S029000, C700S044000, C700S052000, C702S188000

Reexamination Certificate

active

06757579

ABSTRACT:

BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates generally to the field of semiconductor device manufacturing and, more particularly, to a Kalman filter state estimation technique for monitoring a manufacturing system.
2. Description of the Related Art
It is typical in semiconductor manufacturing to see many different products being made by using a variety of process conditions on the same pieces of equipment. Because of the nature of the process conditions and the high cost of materials, it is very difficult and often impossible to obtain measurements of key process variables while the process is operating. Product wafers are run in batches on processing tools using recipes, which specify the parameters necessary to run the tool such as pressure, temperature, and processing time. Measurements are made after processing steps are completed to determine if batches meet their specifications. Run-to-run control methods use the measurement data available at the end of each run to determine better recipe settings for subsequent batches. This task is made more difficult by the fact that measurements are often confounded by several different possible sources of variation.
The manufacture of semiconductor devices is characterized by expensive equipment and raw materials being used to create microscopic features in a batch processing environment. In this environment, batches of wafers are subjected to a series of unit operations with the ultimate goal being to create functional parts. Throughout the operations, extreme processing conditions and features with a critical dimension being constructed are recurring themes. These conditions ultimately mean that it is difficult (and in many cases impossible) to measure important quality variables in situ. Variables of interest are typically measured after a batch has been processed. Unfortunately, it is typically not possible to go back and perform an operation again to correct a misprocessed batch. Therefore, effective process control is needed to ensure that every run goes according to plan.
Run-to-run control in semiconductor manufacturing is a type of batch control, where a batch may be as small as one wafer or as large as several lots of wafers. The standard output of a run-to-run controller is a process recipe. This recipe defines the set points for “low-level” controllers built into the processing tool. In this way, the run-to-run controller supervises the tool controller by specifying required values for process variables such as temperature, pressure, flow, and process time. The tool controller handles the actuations necessary to maintain these variables at the requested values. A typical run-to-run control setup includes a feedback loop where adjustments are made to the recipe parameters based on batch properties measured after processing. Typically, the job of the run-to-run controller is to ensure that each batch hits its inline targets. Inline targets refer to measurements that are taken while the wafers have only completed some of their processing steps. The inline targets are designed to provide guidelines for having functional parts at the end of the manufacturing line.
Run-to-run controllers for discrete parts manufacture have several inherent complications. Unlike a continuous process, where plant outputs can be blended together to make particular products, each part that is produced must meet all of its quality or performance objectives to function correctly. As a result, aggressive control laws must be chosen because the manufacturing constraints do not allow a series of off-target batches while the controller approaches the target. When the system model is able to make accurate predictions, the controller can be quite aggressive. This is because the stability of the controller is tied to the ability of the model to match the behavior of the real system. A controller that is too aggressive in the presence of model error and other uncertainties can actually exhibit poor performance and may lead to instability. This situation may arise because a controller makes process decisions based on assumptions about how its input changes will affect the process. The qualitative effects of small input changes are often easily understood and predicted in terms of the underlying physics of the system. On the other hand, larger, more dramatic changes can upset the process by introducing dynamics more quickly than the process can handle. With better understanding of the process, changes can be made more quickly and effectively.
The most aggressive controller that can be used is a plant inverse, or deadbeat controller. This controller attempts to immediately reject any measured incoming disturbances and set the controlled parameters for each batch exactly at their targets. The parameters may be determined by substituting the desired outputs into the process model and solving directly for the inputs. More conservative control actions can be obtained by imposing limits on how quickly input variables are allowed to change.
Because the process gain and other variables important to the manufacturing processes can change over time, a successful controller must adapt to changing process conditions. At the foundation of such an adaptive controller are system identification techniques. System identification techniques aim to determine a model with the same input-output characteristics and possibly the same natural model structure as the physical system under study. In many practical applications, it is not feasible to obtain an exact model form for the process under study. So, online system identification often takes the form of a parameter estimation problem. In this formulation, a form for the model is predetermined, and the model parameters are updated recursively from process data. Changing process conditions can be seen as a change in the estimated model parameters over time.
In microelectronics manufacturing, it is standard practice to apply statistical process control (SPC) techniques to the process outputs. SPC can also be applied to the outputs of a system under automated control. These outputs include not only the controlled outputs of the process but also the measured deviation of the real process from the prediction used by the controller. In general, the use of SPC techniques involves setting limits on the variables of interest and investigating the process when it strays outside the limits. As its name implies, statistical process control is heavily rooted in treating the process variables of interest as distributions. Several different statistics can be monitored to ensure that the process remains stationary. These techniques are designed to indicate whether a process is running in control or not, but decisions about what to do when the process goes out of control are left to engineers.
These SPC techniques can represent how well an automated controller is doing in terms of keeping the process running inside the control limits. When the limits are exceeded, either the process or the automatic controller must be adjusted. However, real processes and the disturbances to them change over time, so it is not necessarily true that all process variables of interest will remain stationary. In addition, there are many systems where all of the measurements important to control cannot be taken as frequently as desired. For these systems, it is possible that some measurements that would be outliers are not identified simply because they are not measured. In this context, static limits on process variables do not always make sense. The ideal solution is an automatic controller that can detect process changes and adjust itself to account for them. Such an automatic controller could adjust the process before the control limits on the quality outputs are even violated. This controller must recognize that the model it uses may become invalid, so it must always treat new measurement data as an opportunity to remodel the process.
To achieve adequate performance in an uncertain environment, the control system must react to pro

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