| Summary: | Chemical vapor deposition (CVD) is an industrially important process to deposit crystalline and amorphous thin films on solid substrates. In situ sensing for CVD is necessary for process monitoring, fault detection, and process control. The challenge of in situ sensing lies in the prohibitive environment of the CVD process. Optical sensors such as the reflectometer and the ellipsometer are the most promising sensors because they can be installed outside of the deposition chamber, and are sensitive and easy to implement. However, the optical sensors do not measure film properties directly. Mathematical methods are needed to extract film properties from indirect optical measurements. Currently the most commonly used method is least squares fitting.
In this project, we systematically investigated in situ reflectometry data interpretation based on state estimation theory. Optical models for light reflection on both smooth and rough surfaces were studied. The model validation results indicated that the effective medium model is better than the scalar scattering model when the surface is microscopically rough. The analysis of the observability for the sensor models indicated that the linearized observability does not always guarantee the true observability of a nonlinear system.
We studied various state estimators such as batch least squares fitting (BLS), recursive least squares fitting (RLS), extended Kalman filter (EKF), and moving horizon estimation (MHE). It was shown that MHE is the general least-squares-based state estimation and BLS, RLS, and EKF are special cases of MHE. To reduce the computational requirement of MHE, a modified moving horizon estimator (mMHE) was developed which combines the advantage of the computational efficiency in RLS and the a priori estimate in MHE.
State estimators were compared in simulated film growth processes, including both process model mismatch and sensor model mismatch, and reflection of both single wavelength and dual wavelength. In the case of process model mismatch and reflection on a smooth surface, there exists an optimum horizon size for both RLS and mMHE, although mMHE is less sensitive to the horizon size and performs better than RLS at all horizon sizes. The estimate with dual wavelength is more accurate than that with single wavelength indicating that estimation improves with more independent measurements. In the case of reflection on a rough surface, RLS failed to give a reasonable estimate due to the strong correlation between roughness and the extinction coefficient. However, mMHE successfully estimated the extinction coefficient and surface roughness by using the a priori estimate. MHE is much more computationally intensive than mMHE and there is no significant improvement on the estimation results. In the case of sensor model mismatch, either state estimator gave a good result, although mMHE consistently gave a better estimate, especially at a shorter horizon size.
In order to test the state estimators in a real world environment, we built a cold-wall low-pressure chemical vapor deposition testbed with an in situ emissivity-correcting pyrometer. Fully automatic data-acquisition and instrument-control software was developed for the CVD testbed using LabVIEW. State estimators were compared using two experimental reflectance data sets acquired under different deposition conditions. The estimated film properties are compared with ex situ ellipsometry and AFM characterization results. In all cases, mMHE consistently yielded better estimates for processes under quite different deposition conditions. This indicated that mMHE is a useful and robust state estimator for in situ sensor data interpretation. By using the information from both the process and the sensor model, one can obtain a better estimate. A good feature of mMHE is that it provides such a versatile framework to organize all these useful information and gives a user the opportunity to interact with fitting and make wise decisions in the in situ sensor data interpretation.
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