Ad. Marrs, Sequential Bayesian estimation for tracking the composition of growing silicon-germanium alloys, P ROY SOC A, 457(2009), 2001, pp. 1137-1151
Citations number
11
Categorie Soggetti
Multidisciplinary
Journal title
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
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 att
empts to use in situ ellipsometry for composition estimation are overcome,
namely the lack of continuity in estimates produced using iterative nonline
ar 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 filterin
g 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 p
roblems. The results demonstrate that, using a particle filter, estimation
of semiconductor composition can be performed in 'real time', yielding resu
lts 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 appa
ratus 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-li
ne to be cleaned.