Multi-Zone Thermal Processing in Semiconductor Manufacturing: Bias Estimation

Temperature uniformities within a wafer and from wafer to wafer have significant impact on the smallest feature size or critical dimension of integrated circuits. These are important issues with stringent specifications. To obtain temperature uniformity, a wafer is heated by multiple independently controlled heating elements simultaneously. The accuracy of temperature sensing is hence an important issue. In this paper, sensor bias is estimated for the difficult problem where measurement outliers are close to good data such that they cannot be separated easily. Equations are derived to predict the variance of the estimates from sample size. This information enables the selection of an efficient estimator. Sensor bias estimation efficiency translates into earlier bias removal and less faulty wafers. The theory is verified experimentally in a multi-zone thermal system for semiconductor wafer processing.