Moving horizon estimation for in situ monitoring of chemical vapor deposition process

A moving horizon estimation (MHE) technique was used to estimate thin film growth rate, thickness, and high temperature optical constants in situ from a normal reflectance measurement. The advantage of MHE over the virtual interface (VI) method is that it does not require the assumption of constant film growth rate and optical properties, and this allows in situ monitoring of more general dynamic film growth processes. MHE and VI methods were applied to a simulated film growth process in which film growth rate and extinction coefficient are changing with time. The result indicated that MHE gave a better estimate by capturing the change of film growth rate and extinction coefficient, while VI method only gave an averaged growth rate and extinction coefficient. The MHE and VI methods were also compared in an experimental CVD testbed where a polycrystalline yttria thin film was deposited on a silicon substrate by MOCVD. Although these two methods gave roughly the same estimate of film properties at the end point, MHE additionally estimated the dynamic change of film properties during the deposition. Finally the connection between the MHE and VI method was discussed and it was shown that a finite horizon implementation of VI is a special case of MHE when certain weighting matrices are discarded.