(170g) Real-Time Adaptive Model Predictive Control Framework of Plasma Process

Plasma process is one of the most critical process in semiconductor manufacturing. Since it determines the dimension of entire processes, it has a decisive effect on the performance of devices. With the continually evolving process technologies that require high quality constraint, semiconductor industry has been imperatively considering real-time control over current run-to-run based control.

They have been to use recipe that is terminology indicating optimal process inputs which produce maximal yields. The recipe is obtained from several experiments by trial-and-error and is applied to consecutive processes with run-to-run adjustment. However, even with this recipe, the process may not reproduce the desired results especially when the required dimension gets smaller. This is because the process is essentially driven by the plasma formed by the recipe and can be disturbed by external factors. Thus, it is necessary to implement a real-time cascade control to include the plasma as a control variable [1] and to reject the disturbance fast.

The biggest obstacle to real-time control is the nature of the plasma. Plasma is generated by applying power at nearly vacuum pressure of 1.3 Pa (0.00001 bar). Hence this sparse system of multi-physics can be intrinsically affected even if there are small disturbances. The key considerations in controlling such systems are: the use of sensors that do not affect the system, the control of highly nonlinear system, and the way to dealt with inter- and intra- system variability.

In this work, we used optical emission spectroscope (OES), since it is not only having no concern about invasiveness toward process, but also a default plasma diagnostic tool for every plasma etcher in production line. We calibrated it with Langmuir probe and calculated the core plasma variables such as electron density and electron temperature from the intensity data [2,3].

To cope with nonlinearities in system gain, the response surface was piecewise linearized and structured as a linear parameter varying (LPV) system [4,5]. The other system dynamic parameters related to time were identified through the design of experiment, since the dynamics is very fast nearly as the minimal sampling rate.

Inter- and intra- system variability are known to be caused by the difference in equipment/recipes, discrete events between unit processes, and history of precedent processes. Due to the nature of the semi-batch process, the process is more likely to be exposed to these effects than other conventional processes. Therefore, deterioration of control performance coming from the model-plant-mismatch is inevitable. Even in the case of process drift, it is difficult to model it because the information is distributed over multiple nonlinear signals. Therefore, we utilized recurrent neural network (RNN) to track process state variables and drawn initial values for operating condition.

Consequently, an adaptive model predictive control (AMPC) is constructed. The objective function was formulated with a mixed-integer quadratic programming (MIQP) since only integer inputs are applicable to the equipment as a practical restriction. The developed controller was implemented on the field equipment with 100ms of sampling rate and proved it can enhance the reproducibility of process results. This novel framework is expected to deal with the major challenges in real-time control of plasma systems.

[1] Ringwood, J. V., Lynn, S., Bacelli, G., Ma, B., Ragnoli, E., & McLoone, S. (2010). Estimation and control in semiconductor etch: Practice and possibilities. IEEE Transactions on Semiconductor Manufacturing, 23(1), 87-98.

[2] Boffard, J. B., Lin, C. C., & DeJoseph Jr., C. A. (2004). Application of excitation cross sections to optical plasma diagnostics. J. Phys. D: Appl. Phys. 37, R143-R161.

[3] Zhu, X.-M., Pu, Y.-K., (2010). Optical emission spectroscopy in low-temperature plasmas containing argon and nitrogen: determination of the electron temperature and density by the line-ratio method. J. Phys. D: Appl. Phys. 43, 403001.

[4] Keville, B., Zhang, Y., Gaman, C., Holohan, A. M., Daniels, S., & Turner, M. M. (2013). Real-time control of electron density in a capacitively coupled plasma. Journal of Vacuum Science & Technology A, 31(3), 031302.

[5] White, A. P., Zhu, G., & Choi, J. (2013). Linear parameter-varying control for engineering applications. New York: Springer.