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Fig. 12 shows the DOE/Opt problem formulation for
optimizing a gate oxidation process. The set up is analogous to that
described in the previous section. The input table consists of
six variables. There are two process parameters: time of gate
oxidation (
), and temperature of gate oxidation
(
). Associated with each of the process parameters are the
mean and the standard deviation for the disturbances, denoted by the
prefixes 
and 
. The means and the standard deviations for
the disturbances, which are assumed to be independent and normally
distributed, can be determined by tuning FABRICS to the fabrication
line for which the process is to be optimized [42]. In
using DOE/Opt we have explicitly specified the means and standard
deviations of the disturbances corresponding to and
, and do not vary the standard deviations (i.e. they are
fixed at their tuned values). The output table consists of five
parameters. These correspond to the mean of the gate oxide thickness
(
), standard deviation of the gate oxide thickness
(
), signal-to-noise ratio of the gate oxide thickness
(
) defined as the ratio of the mean to the standard
deviation, mean of Monte Carlo parametric yield for the gate oxide
thickness (
), and the standard deviation of Monte
Carlo parametric yield for the gate oxide thickness
(
). The standard deviation is used to determine the
confidence interval on the yield based on the Monte Carlo sampling.
Yield calculation is based on whether the resulting responses fall
within a region of acceptability; the limits for the acceptability of
the gate oxide thickness are specified using the DOE/Opt coefficients
table.