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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 . 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  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 . 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 .