Multiscale Computational Fluid Dynamics: Methodology and Application to Film Microstructure Control in PECVD

Plasma enhanced chemical vapor deposition (PECVD) remains a popular technique for the manufacture of silicon thin films used in the microelectronics and photovoltaic industries [1]-[2]. Over the past decade, there have been significant strides in the multiscale modeling of the silicon deposition process in an effort to better understand and improve product manufacturing [3]-[4]. Nonetheless, these models typically rely on simplified Navier-Stokes and continuity equations and therefore cannot accurately predict the composition and dynamics of the deposition species of interest throughout the PECVD reactor gas-phase. Integrating computational fluid dynamics modeling with microscopic simulation techniques within a parallel computation environment is an important research challenge.

Motivated by the above considerations, a novel, multiscale modeling strategy is developed which allows for the concurrent simulation of both the macroscopic gas phase and the microscopic surface interactions that contribute to thin film growth, and is applied to a common manufacturing problem of drift in the thin film product thickness caused by fouling during the conditioning phase of reactor operation [5]. In a previous publication, a detailed kinetic Monte Carlo (kMC) algorithm was developed which has been shown to accurately reproduce thin film growth rates and surface morphologies at four distinct locations across the wafer surface [3]. In this work, we propose the addition of a computational fluid dynamics (CFD) model that can account for the complex geometry of the PECVD reactor allowing for the prediction of accurate plasma flow fields and chemistry which are required within the microscopic kMC domain. Furthermore, parallel computation is introduced through the use of the message passing interface (MPI) framework, which has made possible the simultaneous simulation of numerous reactor zones with far increased lattice dimensions. Specifically, the parallel-plate PECVD reactor of interest in this work is divided into ten discrete, radial zones, each of which interacts with both of their neighboring zones, as well as the process gas (i.e., plasma) flowing over the wafer surface. Although open-loop simulations reveal significant variability in the film thickness across the wafer surface and between successive batch deposition sequences [6], the multiscale model developed in this work demonstrates that through the use of a carefully designed exponentially weighted moving average (EWMA) algorithm, the offset in the product thickness can be reduced to <1% within 10 batches of reactor operation. Additionally, the run-to-run control strategy is shown to recover the desired product thickness (i.e., return to the thin film thickness set-point of 300 nm) in the presence of disturbances in the plasma quality caused by fluctuations in the radio frequency (RF) power and feed gas composition.

[1] Reif R. Plasma enhanced chemical vapor deposition of thin films for microelectronics processing. Noyes Park Ridge. 1990.

[2] Shah A, Torres P, Tscharner R, Wyrsch N, Keppner H. Photovoltaic technology: the case for thin-film solar cells. Science. 1999;285:692-698.

[3] Crose M, Kwon JSI, Nayhouse M, Ni D, Christofides PD. Multiscale modeling and operation of PECVD of thin film solar cells. Chemical Engineering Science. 2015;136:50-61.

[4] Christofides PD and A. Armaou. Control and optimization of multiscale process systems. Computers and Chemical Engineering. 2006;30:1670-1686.

[5] Gabriel O, Kirner S, Klick M, Stannowski B, Schlatmann R. Plasma monitoring and PECVD process control in thin film silicon-based solar cell manufacturing. EPJ Photovoltaics. 2014;55202:1–9.

[6] Crose M, Kwon JSI, Tran A, Christofides PD. Multiscale modeling and run-to-run control of PECVD of thin film solar cells. Renewable Energy. 2016; submitted.