Performance Analysis of Takagi–Sugeno Fuzzy Model For Run-to-run Control with Stochastic Metrology Delay

In the semiconductor manufacturing process, measurements can not always be performed online. It will cause the metrology delay. The delay will affect the stability, performance and reliability of the process. Generally the metrology delay is stochastic, so it is difficult to model such semiconductor manufacturing processes. This paper present a novel modeling approach —- Takagi–Sugeno(T-S) model to handle the different metrology delay. This approach does not require the knowledge of exact values of the stochastic delays. And, it can addresses situations involving all possible delays. On basis of the T-S model and exponentially weighted moving average (EWMA) disturbance estimation algorithm, the mean and the variance of the output are derived. Some numerical examples are provided to prove the validity of the T-S model.