Sequential Bayesian estimation for tracking the composition of growing silicon-germanium alloys

A new method for the real-time inference of semiconductor composition from in situ spectroscopic ellipsometry measurements is presented. Treating the problem as one of dynamic state estimation, the limitations of previous attempts to use in situ ellipsometry for composition estimation are overcome, namely the lack of continuity in estimates produced using iterative nonlinear model-fitting methods or the linear/Gaussian approximations necessary to use standard filtering algorithms such as the extended Kalman filter. The innovative approach presented here is to use recent advances in sequential Bayesian inference, which have lead to the development of particle filtering techniques. The particle filter removes the need for gross approximations to the measurement and system-evolution models and assumptions of Gaussian noise, enabling sequential inference to be performed on the most complex problems. The results demonstrate that, using a particle filter, estimation of semiconductor composition can be performed in 'real time', yielding results comparable with those obtained using off-line characterization methods such as secondary ion mass spectroscopy. In addition, by taking a multiple model approach, inferences can be made regarding the dominant growth regime. In a commercial fabrication environment the gradual contamination of apparatus over a period of time would lead to a degradation in growth quality. The ability to infer growth regime introduces the possibility of monitoring growth quality and identifying when the apparatus needs to be taken off-line to be cleaned.