Modeling and simulation of thermal chlorine etching of gallium arsenide with application to real-time feedback control

Abstract

A dynamic model for the simulation of thermal chlorine etching of gallium arsenide is developed. The primary motivation for the development of the simulation is the design and testing of real time adaptive feedback controllers which rely upon in-situ optical measurements of etch depth obtained via spectroscopic ellipsometry. The basis for the model is an empirically derived relationship between etch rate, chlorine pressure, and substrate temperature. The chlorine pressure in the chamber is regulated by a throttle valve which determines the effective pumping rate of a turbo-molecular pump which is used to evacuate chlorine pressure dynamics and a second-order damped harmonic oscillator with zero-order hold valve position command inputs is used to model the dynamics of the throttle valve. An output equation is used to model the fact that ellipsometry based etch depth and chamber pressure can be observed at discrete time intervals. Unmeasurable parameters which appear in the model are identified, and the model is validated using experimental data. An adaptive linear-quadratic Gaussian based controller based on our model which forces etching to precede at a desired rate while estimating the often difficult to measure substrate temperature is designed and then tested using our simulation.