Institute for Systems Research

In this paper, RtR control methods are generalized. The set-valued RtR controllers with ellipsoidapproximation are compared with other RtR controllers bysimulation according to the following criteria: A good RtR controller should be able to compensate for variousdisturbances, such as process drifts, process shifts (step disturbance)and model errors; moreover, it should beable to deal with limitations, bounds, cost requirement, multipletargets and time delays that are often encountered in realprocesses.

Preliminary results show the good performance of the set-valued RtRcontroller. Furthermore, this paper shows that it is insufficient to uselinear models to approximate nonlinear processes and it is necessary to developnonlinear model based RtR controllers.

A new approach, namely the set-valued RtR controller with ellipsoidapproximation, is proposed to estimate the process model from acompletely different point of view. Because the set-valued RtRcontroller identifies the process model in the feasible parameter setwhich is insensitive to noises, the controller is robust to theenvironment noises.Ellipsoid approximation can significantly reduce the computation load for the set-valued method.

In this paper, the Modified Optimal Volume Ellipsoid (MOVE) algorithm is used toestimate the process model in each run. Designof the corresponding controller and parameter selection of the controller are introduced.Simulation results showed that the controller is robust toenvironment noises and model errors.

By monitoring the resonant frequency of exhaust process gases, the depletion of WF6 resulting from the reduction by H2 was readily observed in the 0.5 Torr process for wafer temperatures ranging from 300 to 350 C. Despite WF6 depletion rates as low as 3-5%, in-situ wafer-state metrology was achieved with an error less than 6% over 17 processed wafers.

This in-situ metrology capability combined with accurate sensor response modeling suggests an effective approach for acoustic process sensing in order to achieve run-to-run process control of the deposited tungsten film thickness.

The DHOBE algorithm, for eachrecursion, returns an outer bounding ellipsoid of the estimated parameters. If the center of the ellipsoid each time istaken as the model coefficients, the explicit model update isimplemented which leads to a model-reference method. If we choose theworst-case point which maximizes the cost function in the set, then wecan apply the set-valued worst case approach. These two methods were compared with two other main RtRcontrol schemes: the Exponentially Weighted Moving Average (EWMA) methodand the Optimizing Adaptive Quality Controller (OAQC) method. Simulation results showed the superior performance of the RtRcontrollers based on the DHOBE algorithm. Furthermore this paper showedthat it is necessary to applynonlinear models to compensate for severe nonlinear processes.