An Elementary Model for Control of a Semiconductor Etching Process

Abstract

A dynamic model for the thermal chlorine etching of gallium arsenide is formulated and validated. The model consists of three ordinary differential equations. One models the chemical reaction between the chlorine gas and the gallium arsenide substrate being etched. The second equation, which is based on an inflow/outflow paradigm, models the dynamics of the pressure in the etching chamber. The third equation models the dynamics of a throttle valve which controls the chamber pressure. The entire model is based upon a combination of empirical and first principle physics-based reasoning, and is formulated using sophomore-level elementary chemistry, physics, and differential equations. Spectroscopic ellipsometry, a nondestructive optically based technique for real-time in-situ characterization of materials, is described. Offline and real-time ellipsometry measurements of sample thickness are used to identify or estimate otherwise unmeasurable parameters which appear in the model and to verify or validate our model via comparison with simulation results based upon the model. The use of the model in the design, implementation, and testing of a feedback control system for the etching process is discussed.