Run-to-Run Controller for BSTO Thin Film Manufacturing

In run-to-run control, the values of the nominal operating set-points (called recipe variables) are adjusted after one run of the process based on measurements of wafer properties before processing the next wafer. Either the reactor-scale CFD-ACE model or an empirical model based on actual data that relates the manipulated inputs (precursor flow) to the outputs (deposition thickness and stoichiometry) may be used to generate the static model for the run-to-run controller design.

The model is run after varying each precursor concentration (i.e., input or recipe variable) while keeping the others unchanged at their nominal values. Alternatively, actual experiments may be performed using the reactor to determine this input-ouput model. For small variations, a single perturbation from the nominal value per recipe variable is sufficient to create the model. For larger variations, non-linear behavior may need to be taken into account by calculating deposition thickness and uniformity for multiple values of each input. Because the precursors are present in very small quantities in a dilute state, the outputs (thickness and uniformity) are linear in terms of the precursors (although they are non-linear function of the temperatures).

The resulting static map relating the recipe variable set-points (inputs) to the corresponding sets of measured performance parameters (outputs) is called the response surface, and is represented by a m x n matrix with m being the number of outputs and n the number of recipe variables. In this case, it is a 3X3 matrix. Inversion of this matrix is the key to run-to-run control. The theoretical details can be found here.

In most cases, the target region may be reached after one cycle of iterations. The ternary figure below shows a run-to-run example where the target (desired) region is shown as a quadrilateral. In this case, due to some large perturbation, the stoichiometry at the center of the current wafer is very far away from the desired region. It is seen in the figure below that this starting point is in a barium-rich region of the diagram. However, use of the run-to-run controller results in the convergence in sixteen simulated iterations. The converged inputs were used in the full reactor-scale model and were shown to produce outputs very close to that predicted by the low-order sensitivity model.

Figure 1. Ternary diagram showing sixteen run-to-run iterations from the starting point to the target operating point. The starting and target points are shown using filled square and bullet symbols respectively, while the individual iterations are shown as unfilled circles. The desired operating area is shown as a quadrilateral.

The implication of this result is significant because it indicates that it is possible to speed up the run-to-run control by performing the iterations on a virtual reactor in simulation, and performing experiments only to test the accuracy of the converged values of thickness and stoichiometry. The use of model-based simulations for run-to-run control significantly reduces the cost associated with the use of actual wafers and increases throughput while improving reproducibility. Even if the run-to-run control cannot provide the desired stoichiometry after the first set of iterations, the new starting point as determined from the experiments will be much closer to the target region than would otherwise be possible.