Characterizing Turbulence and Wave Dynamics Under Rotation: Enhancing Semiconductor Processes through CFD Analysis and High-Speed Imaging
Authors: Belmiloud Naser 
Published: December 2024

Introduction
In semiconductor manufacturing, precision in wafer processing is crucial for advancing device technology. The spinning system, essential for wafer cleaning and etching, significantly impacts device quality by facilitating dynamic air-liquid interactions, affecting surface chemistry. This study utilizes Computational Fluid Dynamics (CFD) and high-speed camera analysis to explore turbulence and wave dynamics, confronting Fast Fourier Transform (FFT) analysis against the Kolmogorov cascade to improve manufacturing outcomes by understanding these dynamics more thoroughly.
Experimental Setup
Our approach integrates high-speed imaging with advanced CFD simulations to capture and analyze the wave phenomena in spinning liquid films. High-speed cameras are strategically positioned to provide comprehensive side and top views, enabling detailed observation of wave formation and interaction with the air. Concurrently, CFD simulations offer a granular view of the fluid dynamics, focusing on the generation and propagation of turbulence within the liquid film. The application of FFT analysis to CFD data allows us to delve into the turbulent wave dynamics, specifically investigating the energy cascade, per the Kolmogorov theory [1]. This methodology not only deepens our understanding of wave behavior but also highlight its potential impacts on key factors defining the exchange kinetics of the liquid-air interface.
Discussion
For a single wafer, a gas molecule, characterized by a diffusion coefficient D, will diffuse through the liquid film of thickness h to reach the wafer surface in a time approximated by t ~ h²/D. Specifically for oxygen, (D~2×10⁻⁹ m²/s) and 100µm thin film, the process takes about 5 seconds, while the coverage of the liquid takes less than 0.5s so an order of magnitude lower [2]. The Peclet number (Pe), defined by Pe=Uh/D, represents the advection to diffusion ratio. Here, Pe~10-4 >> 1 indicating advection dominance. This suggests wave and hydrodynamics (laminar vs. turbulence) primarily transport air into the liquid. Near the wafer edge, where the flow speeds up and the liquid film thins out, gas molecules reach the wafer faster than at its center.
Advection rates are higher on wavy surfaces due to complex streamlines shaped by the undulating contours of the interface. This will enhance mixing transport, while the increased surface area boosts heat and mass exchange. Depending on wave celerity, recirculation atop the waves further boost local mixing [3,4].
In Figure 1, the FFT analysis indicates that turbulent dynamics align with the Kolmogorov cascade, highlighting a spectrum of energy dissipation that could significantly impact oxygen diffusion and heat transfer. These findings suggest that the wave-induced turbulence could be leveraged to optimize the distribution of reactive species and thermal management during the spinning process. It highlights that the energy is injected by the swirling and concentric waves near the center of the wafer.
In Figure 2, the Iribaren number, a dimensionless metric for classifying wave breaking patterns [5], is extracted from the liquid thickness distribution on wafer. It compares the slope steepness to the wave steepness, predicting whether waves will spill, plunge, or surge. Spilling waves, associated with low Iribarren numbers below 0.5 as found in our study, gently dissipate energy over wide areas. These spilling waves dissipate energy over long distances, breaking into smaller wavelets and introducing turbulence showing complex interactions between wave dynamics and the wafer.
Figure 3 shows the dynamics of spilling waves with concentric waves collapsing towards the edge using a high-speed camera. This phenomenon is observed in a side view of a centrally dispensed fluid on a rotating wafer. The captured speed range is notably high, exceeding 50 km/h. The size and number of waves are affected by the rotation speed. A wave will collapse faster at high rpm because of a thinner film and higher centrifugal forces.
Conclusion
This research reveals the relationship between wave dynamics in spinning liquid films and their potential impact on semiconductor manufacturing efficiency. The synergy of high-speed imaging, CFD analysis, and FFT insights not only enhances our understanding of fluid dynamics but also paves the way for optimizing wafer cleaning and etching techniques. This study lays the groundwork for future technological advancements, promising to elevate the precision, efficiency, and quality of semiconductor production.
References:
[1] A. N. Kolmogorov, Journal of Fluid Mechanics, 13(1), 82-85,(1962)
[2] N. Belmiloud, M. Sato, & Y. Okuno, Solid State Phenomena, 346, 231-235,(2023).
[3] D. Flagiello, A. Parisi, A. Lancia, & F. Di Natale, ChemEngineering, 5(3), 43, (2021).
[4] U. Farooq, J. Stafford, C. Petit, & O. K. Matar, Physical Review E, 102(4), 043106, (2020).
[5] S. I. Okazaki, & T. Sunamura, Journal of Coastal Research, 559-564, (1991).

Figure 1