Implementation of Nonthreaded Estimation for Run-to-Run Control of High Mix Semiconductor Manufacturing

Semiconductor processing consists of many different unit operations that are combined in a sequence to create the finished product. Many of these unit operations utilize run to run control in order to keep the process within the required manufacturing constraints. Typically, the difference, or bias, between the desired and actual result of processing a particular wafer is affected by not only the particular product being produced, but the prior processing path. Each possible effect is called a context category, and the particular context items relevant for a wafer is called a thread. Because of frequent changes and updates in semiconductor products as well as a large number of product lines, run to run control must deal with a high-mix environment of products, and a large number of threads. Previously, several authors have discussed a method of describing the bias for a particular thread as a sum of context item biases and using a Kalman Filter to estimate these biases. However, two issues with previous implementations have been the observability of the state realization of the bias model, and the computational cost of the Kalman filter. In this paper, we introduce a model formulation that does not require model reduction or the specification of special reference threads, thus easily allowing new threads to be added and old threads removed. In addition, we describe how the problem structure allows the information form of the Kalman filter to be much more computationally efficient. Simulation results illustrate the proposed method.