Recently, the research group led by Associate Professor Fu Yangyang from the Department of Electrical Engineering and Applied Electronics (EEA) at Tsinghua University made significant progress in the study of radio-frequency (RF) plasma similarity and scaling laws. Their findings, titled "Demonstration of Similarity Laws and Scaling Networks for Radio-Frequency Plasmas," were published in the high-impact journal Physical Review Letters (PRL). The paper's authors include Yang Dong, a doctoral student in the 2020 cohort at Tsinghua University (first author), Professor John P. Verboncoeur from Michigan State University (IEEE Vice President and IEEE Fellow), and Associate Professor Fu Yangyang, who is the corresponding author.

High-end semiconductor manufacturing equipment has become a strategic focal point in global technological competition. Plasma technology is widely used in semiconductor processing, including photolithography, etching, thin film deposition, ion implantation, and cleaning, with its total technical assembly accounting for over a third of the integrated circuit industry. Plasma technology has evolved into a critical core technology supporting national strategic initiatives, digital economy development, and information industry security. Low-pressure RF discharge is extensively employed to generate large-size plasma sources used in etching and is a core technology for key semiconductor equipment such as plasma etchers. With the ongoing development of semiconductor manufacturing processes, the generation of large, uniform, and stable RF plasma sources has become a key prerequisite for advancing etching technologies. Understanding the multi-parameter coupling and control laws of large-size RF plasmas has become a frontier topic jointly explored by academia and industry.

Inspired by the concepts of "symmetry" and "scale invariance" in physics, Fu Yangyang's research group proposed and developed an RF discharge similarity theory that considers low-pressure non-local effects. This theory was experimentally verified for the first time using phase-resolved optical emission spectroscopy (PROES), demonstrating the existence of RF discharge similarity. The mathematical rigor of similarity discharge theory was further explained through first-principles particle simulations and the Boltzmann kinetic equation.

Based on this similarity theory, the researchers identified the experimental parameters and control conditions for low-pressure RF similarity discharges. The discharge chamber and diagnostic system are shown in Figure 1. By adjusting the discharge pressure (p), electrode dimensions (spacing d, radius R), and RF source frequency (f), two geometrically similar RF discharge systems with proportional sizes were designed. By combining electrical and optical diagnostic techniques, the excitation rate and light intensity distribution of RF discharges were confirmed to satisfy similarity invariance.

Figure 1. RF discharge diagnostic system and design of similarity RF discharge parameters

Figure 2 demonstrates the spatiotemporal evolution of excitation rates under pressure, scale, and frequency adjustments in RF discharges, covering the initial state (000), similarity state (111), and six transitional states. The experimental results show a high degree of consistency with simulation results, not only confirming the scale invariance between the initial and similarity states but also revealing the comprehensive state transition laws from the initial state to the similarity state.

Figure 2. Spatiotemporal evolution of RF discharge excitation rates under different parameter adjustments

Based on the above research, the group further proposed a parameter network scaling method (see Figure 3). Using experimental and simulation data, they constructed a scaling network for discharge parameters, which exhibited good consistency. By adjusting three control parameters, 12 parameter scaling laws were established across 8 state nodes. As more control parameters are introduced, the number of states can be expanded to identify more scaling laws. With the current parameter scaling laws, the network scaling method provides a theoretical basis for optimizing parameters of large-size RF plasma sources for etching and opens new avenues for the development of advanced plasma etching equipment and technologies.

Figure 3. Construction of RF discharge network scaling method based on similarity theory

The research results, titled "Demonstration of Similarity Laws and Scaling Networks for Radio Frequency Plasmas," were published in the academic journal Physical Review Letters (PRL). The first author of the paper is Yang Dong, a doctoral student from EEA at Tsinghua University, and the corresponding author is Associate Professor Fu Yangyang. During the research period, the group engaged in extensive discussions with experts from the Weizmann Physics Center in Hungary, Professor Zoltán Donkó, Princeton Plasma Physics Laboratory's Professor Igor Kaganovich, and Dr. Alexander V. Khrabrov. This research work was supported by the National Natural Science Foundation of China’s Original Exploration Program (grant number: 52250051), Tsinghua University’s Academic Promotion Program, and independent research projects.

Corresponding Author’s Profile: Fu Yangyang is an Associate Professor, Special Researcher, and PhD supervisor at EEA. He is also the Deputy Director of the Institute of High Voltage and Insulation Technology and the Director of the Gas Discharge and Plasma Laboratory. His main research directions include gas breakdown and insulation, low-pressure RF discharge, high-pressure pulsed discharge, laser-sustained plasma, micro-discharge devices, and applications. He serves as an associate editor for High Voltage, a guest editor for journals such as IEEE Transactions on Plasma Science and Frontiers in Physics, a senior member of IEEE, a senior member of the Chinese Electrical Engineering Society, and a youth member of the Plasma Committee of the Chinese Electrical Engineering Society. He was selected for the National High-Level Overseas Talent Recruitment Program (Youth Program). As a project leader, he has overseen over ten research projects, including National Natural Science Foundation Original Exploration Program, Tsinghua University’s independent innovation projects, and industrial collaborations. He has won the Ministry of Education's Award for Excellence in Scientific Research in Higher Education, the IEEE International Conference on Plasma Science (ICOPS) Best Paper Award, and the 2024 IEEE Nuclear and Plasma Science Society Early Achievement Award. He has served as a session chair at various international conferences, including IEEE ICOPS, PPPS, CIEEC, and IWM. He has published over 80 papers in journals such as PRL (2) and APL (11), authored more than 100 conference papers and abstracts, and holds a US patent (as the first inventor). He has delivered two keynote speeches and over 30 invited talks at academic conferences. He has guided students who have won academic awards, including Best Paper Awards at international conferences like IEEE ICOPS and ICPSA.

Paper Link:

D. Yang, J. P. Verboncoeur, Y. Fu, “Demonstration of Similarity Laws and Scaling Networks for Radio-Frequency Plasmas,” Physical Review Letters 134, 045301 (2025)

DOI: 10.1103/PhysRevLett.134.045301

Related Papers:

D. Yang, H. Wang, B. Zheng, X. Zou, X. Wang, and Y. Fu, "Application of similarity laws to dual-frequency capacitively coupled radio frequency plasmas with electrical asymmetry effect," Plasma Sources Science and Technology 31, 115002 (2022)

D. Yang, H. Wang, B. Zheng, X. Zou, X. Wang, and Y. Fu, "Scale-invariant resonance characteristics in magnetized capacitive radio frequency plasmas," Physics of Plasmas 30, 063510 (2023)

Y. Fu, H. Wang, and X. Wang, "Similarity theory and scaling laws for low-temperature plasma discharges: a comprehensive review," Reviews of Modern Plasma Physics 7, 10 (2023)

Y. Fu, H. Wang, B. Zheng, P. Zhang, Q. H. Fan, X. Wang, and J. P. Verboncoeur, "Generalizing similarity theory for radio frequency discharge plasmas across nonlinear transition regimes," Physical Review Applied 16, 054016 (2021)

Y. Fu, B. Zheng, D.-Q. Wen, P. Zhang, Q. H. Fan, and J. P. Verboncoeur, "Similarity law and frequency scaling in low-pressure capacitive radio frequency plasmas," Applied Physics Letters 117, 204101 (2020)