Minimum time control of conductive heating systems for microelectronics processing

Abstract

A minimum time control scheme is designed to improve repeatability by minimizing the loading effects induced by the common processing condition of placement of a semiconductor wafer at ambient temperature on a large thermal-mass bake plate at processing temperature. The minimum time control strategy provides an optimal solution for minimizing the worst case deviation from a nominal temperature set-point during the load disturbance condition. This results in a predictive controller that performs a predetermined heating sequence prior to the arrival of the wafer as part of the resulting feedforward/feedback strategy to eliminate the load disturbance. The controller is easy to design and implement and makes it more suitable for online implementation such as automatic online tuning of a feedforward controller. Experimental results depict an order-of-magnitude improvement in the settling time and the integral-square temperature error between the optimal predictive controller and a feedback controller for a typical load disturbance.