In situ estimation of thin film growth rate, complex refractive index, and roughness during chemical vapor deposition using a modified moving horizon estimator

摘要

The primary method of estimating thin film properties from in situ reflectance measurements is the least squares fitting method. However, a state estimator offers a more rigorous approach to extract the quantities of interest from indirect measurements. The extended Kalman filter is a state estimator that has been applied previously in film deposition and etching processes. A modified moving horizon estimator was used here to estimate thin film growth rate, complex refractive index, and surface roughness in situ from a dual-wavelength reflectance measurement during a chemical vapor deposition process. Moving horizon estimation is a general framework, for which least squares fitting and the extended Kalman filter can be viewed as special cases. Predictions of the state estimates by the modified moving horizon estimator are compared with the predictions of the recursive least squares fitting method and the extended Kalman filter. The comparison of estimators is made first in simulations and then using experimental data. The simulation results indicate that the modified moving horizon estimator consistently yields more accurate estimates, by incorporating the prior estimates and error correlations in the optimization. The modified moving horizon estimator shows even more benefit in the experimental data, due to its enhanced robustness to nonideal behavior that is not included in the models.