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DOE/Opt has been used to generate optimal recipes for a plasma
enhanced chemical vapor deposition of silicon nitride (PECVD nitride)
process run on the Applied Materials Precision 5000 reactor (AMT5000).
As a part of the Microelectronics Manufacturing Science and Technology
(MMST) program our aim was to model (physically and empirically),
optimize, and adaptively control
the process to target [34][33].
We have used DOE/Opt to generate the initial
recipe for the process. Using the models of the PECVD nitride process,
the optimal equipment settings for the AMT5000 were generated to obtain
the desired outputs from the process.
The DOE/Opt setup for recipe generation is shown in
Fig. 9. The equipment controllables are specified
via the input table. The primary equipment controls on the AMT
5000 for the PECVD nitride by the nitrogen-silane-ammonia process are
the N
flow (
), SiH
flow (
), NH
flow (
),
pressure (
), rf power (
), and electrode gap (
). The
ranges are chosen by the process engineer based on his understanding
of the limitations of the equipment and validity of the process
models. The default values are the centers
of the hyperbox defined by the ranges. The quality characteristics of
interest include the film deposition rate (
), index of
refraction (
), stress (
), and thickness nonuniformity
(
). These responses, the corresponding desired values, and the
specification limits are indicated in the output table. The block
body contains the Tcl script used to encapsulate the
pre-existing PECVD nitride model program (invoked using the C
executable pecvd). The body script handles the conversion to
and from that expected by the pecvd program.
A Box-Wilson on a cube experimental
design was used to create full quadratic
response surface models. The run table
comprised 
rows, each of which corresponded to a point in the
input design space. For each of the rows the model was evaluated
and all four output values were obtained by executing the body. Once
the run table is filled, regression is used to generate full quadratic
response surface models
(consisting of 
coefficients) for each of the outputs in
terms of all six inputs. The generated RSM block files are linked to
the optimization problem via the ``rsm'' column in the output table.
A weighted sum of squares optimization is performed to determine the
optimal recipe for the process. The weights for the outputs are chosen
as the inverse of the standard errors of the models
(see [34] for rationale). For the PECVD nitride
process , , and are targets, whereas acts as a
constraint (the specific target and constraint values are shown in
Fig. 9). The objective function is specified to be a
weighted sum of squares of the difference between the model prediction
and the target. In one instance of recipe generation, all of the
inputs were allowed to vary for the optimization, optimal points were
found and verified, and the controller was initiated with the
generated initial recipe; the controller was subsequently able to
adjust the recipe to response to equipment shifts and
drifts [34]. A second instance of recipe generation is
described here, in which the process engineer wanted to generate an
optimal recipe where the was not changed from its value of
(either for the initial recipe or during control). Minimal
changes had to be made to the DOE/Opt block to generate the initial
recipe under the new constraint. The ``Vary'' button corresponding to
the in the input table was deselected (to toggle the
``vary'' value for the gap in Fig. 9). A new set
of starting points, without the variable , was then generated for
the optimizer. To minimize the probability of getting a solution at a
local minimum, multiple starting points are used for the optimization:
the nominal point and a 
point Latin hypercube design was used.
Corresponding to each of the starting points an optimal point was generated.
Two
distinct optima were found where the objective function values are relatively
small: for 
, 
, 
(with error 0.025) and
(with error 0.028).
Both of the optima are verified using the PECVD nitride model,
and the results are shown in Fig. 10.
Run #2
was chosen as the best recipe since it had a closer to target value
of by trading off a small amount on . The controller was
activated using the initial recipe generated by DOE/Opt. The
controller is presently in routine use [34].
Previous: Simulator Tuning
Up: Examples
Next: Design for Manufacturability
Previous Page: Simulator Tuning
Next Page: Design for Manufacturability