Time-Series Modeling for Run-to-Run Control of an Area-Selective Atomic Layer Deposition Process

Matthew Tom¹, Sungil Yun¹, Henrik Wang¹, Feiyang Ou¹, Gerassimos Orkoulas³, and Panagiotis D. Christofides^1,2

1. Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA
2. Department of Electrical and Computer Engineering, University of California, Los Angeles, CA
3. Department of Chemical Engineering, Widener University, Chester, PA

During semiconductor fabrication, several procedures are employed to maintain the quality of the product, specifically the thin-film deposition rate, which is measured by sensitive metrological equipment, ex situ. However, the production of these semiconducting materials relies on stable operating conditions to promote ef­fective nanopatterning without time-consuming postprocessing steps, especially for bottom-up transistor stacking on wafers. Therefore, robust process control is necessary to monitor the changes in the processing environment while resisting the effects of disturbances, which are attributed to changes in the process input, genera­tion of byproducts, and equipment performance degradation with time. The application of statistical process control (SPC) methods has been widely used to mitigate process disturbances in order to retain the conformity of ultra-thin films and nanocoatings. In particular, run-to-run (R2R) control has been implemented in semi­conductor manufacturing processes as a model for process regulation and input adjustment according to the deviations between output variables and process-specified setpoint through various algorithms, including the exponentially weighted moving average (EWMA) [1,2]. Despite the robustness and reliability of R2R control strategy, it is not practical to perform output measurements and input modifications every batch from an industrial perspective due to ex situ monitoring. Additionally, even if in situ metrology systems are fully integrated, control might become unstable if inputs are modified too frequently in response to noises caused by measurement errors. One solution is to apply time-series fore­casting methods such as the autoregressive integrated moving average (ARIMA) method that employ a statistical predic­tion of the process through previously established data sets to perform input variable adjustment without requir­ing output measurements for each batch run [3,4]. Such an approach will en­able higher productivity while main­taining robust control within statistically significant limits.

This work will integrate an in silico, multiscale modeling approach from a previously developed area-selective atomic layer deposition (ASALD) process in a rotary spatial reactor configuration [5] in conjunction to a run-to-run controller that is characterized by the EWMA method. First, an elaborate multiscale data set for the output varia­ble, deposition rate, will be collected for a range of input operating conditions including the rotation speed of the reactor to construct an empirical, linear regression model of the data set. Next, an R2R controller will be integrated into the work by introducing a drift disturbance and a stochastic shift disturbance that reduces the rate of reaction and will be conducted through each batch run. Lastly, a time-series model will be developed from the prior R2R controller data, and tested to determine the optimal number of batch runs required before measurement is needed and a loss of control outside of operation bounds is observed.

References:

1. Moyne, J., Del Castillo, E., & Hurwitz, A.M., 2018. Run-to-run control in semiconductor manufacturing. CRC Press.
2. Del Castillo, E., 2002. Statistical process adjustment for quality control, Wiley-Interscience.
3. Montgomery, D. C., 2013. Introduction to statistical quality control, 7th ed., John Wiley & Sons.
4. Korabi, T. E., Graton, G., Adel, E. M. E, Ouladsine, M. & Pinaton, J., 2019. “Monitoring of a sampled process data under Run-to-Run control: application to a semiconductor process,” 2019 IEEE 15th International Conference on Automation Science and Engineering (CASE), Vancouver, BC, Canada.
5. Yun, S., Wang, H., Tom, M., Ou, F., Orkoulas, G., & Christofides P. D., 2023. “Multiscale CFD Modeling of Spatial Area-Selective Thermal Atomic Layer Deposition: Application to Reactor Design and Operating Condition Calculation,” Coatings, 13, 558.