A Modified Moving Horizon Estimator for <i>In Situ</i> Sensing of a Chemical Vapor Deposition Process

Abstract

A modified moving horizon estimator (mMHE) was developed to estimate thin film thickness, growth rate, and refractive indices <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> from a dual-wavelength reflectance measurement during chemical vapor deposition. In this application, mMHE combines the advantage of high speed of the recursive least squares estimator (RLS) and the accuracy of the moving horizon estimator (MHE). A simulated deposition process with drifting growth rate was used as a benchmark to compare the performance of RLS, MHE, mMHE, and the extended Kalman filter (EKF). The results indicate that mMHE yields more accurate estimates than RLS by incorporating <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> estimates in the optimization function. Improved accuracy of mMHE over EKF was obtained due to the horizon of data used at each time step. In addition, mMHE provided similar accuracy to MHE for short horizons, and it was much faster than MHE. RLS, MHE, mMHE, and EKF were also compared on an experimental chemical vapor deposition system where a yttrium oxide thin film was deposited on a silicon substrate. The <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ex situ</i> ellipsometry characterization indicated that a more accurate and robust estimate was obtained by MHE and mMHE, compared to the RLS and EKF estimates.