Temperature sensing and control in multi-zone semiconductor thermal processing

Abstract

Resistance Temperature Detectors (RTD's) installed in a multi-zone bake-plate typically used for semiconductor thermal processing are subject to measurement bias. Data reconciliation (DR) techniques are extended so that RTD biases can be estimated online from process data. To handle frequently encountered non-normality in process data, a generalized T distribution (GT) based bias estimator is proposed. Equations are derived which relate variance of a bias estimator to sample size (number of wafer runs per estimation). These equations enable the computation of the sample size or the number of wafers needed by the bias estimator to achieve specified estimation variance. With this information, the precise number of wafers can be used and wastage can be prevented. Alternatively, these equations allow the calculation of the variance of the bias estimator and hence its precision if the number of wafers used is given.

The theoretical results on estimator analysis are verified experimentally. In the light of the equations derived, an efficient estimator can be selected. In the presence of outliers that are close to good data, the equations show that using GT, instead of normal distribution, to characterize process data gives rise to a more efficient estimator than Least Squares and Interquartile Test+Least Squares and therefore enables earlier remedial actions against RTD bias to save semiconductor wafers from sensing-related processing defects.

To fulfil the stringent requirement on temperature control of a multi-zone bake-plate, Multiplexed MPC (MMPC) with feedforward is demonstrated experimentally on a multi-zone bake-plate application. By distributing the control moves over one complete update cycle, MMPC can afford to work with higher sampling rate. It is shown to have the potential to make the bake-plate respond and recover faster than under conventional MPC when disturbance is induced by placement of a wafer and cannot be sufficiently compensated by feedforward.