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Control of Electron Energy Distribution Functions by Current Waveform Tailoring in Inductively Coupled Radio Frequency Plasmas

Zhaoyu Chen, Zili Chen, Yu Wang, Jonas Giesekus, Wei Jiang, Yonghua Ding, Donghui Xia, Ya Zhang, Julian Schulze

TL;DR

This work introduces Current Waveform Tailoring (CWT) as a method to electrically control the Electron Energy Probability Function ($EEPF$) and plasma chemistry in inductively coupled plasmas (ICPs). Using 2D PIC/MCC simulations, the coil current is constructed from harmonics up to the 4th order with a tunable parameter $m$, enabling non-sinusoidal, sawtooth-like waveforms that break the standard temporal symmetry. The study shows that such waveform tailoring shifts energy absorption between inductive and capacitive channels, reshapes the high-energy tail of the $EEPF$, and lowers the excitation-to-ionization ratio, thereby influencing radical and ion production. Importantly, these effects can be realized on existing ICP platforms by upgrading the external power supply with multi-frequency impedance matching, offering a practical route to enhanced plasma process control in reactive-gas environments.

Abstract

Based on two-dimensional particle-in-cell simulations a novel approach towards Electron Energy Probability Function (EEPF) and plasma chemistry control by Current Waveform Tailoring (CWT) in the coil of inductively coupled discharges is proposed. Varying the shape of this current waveform provides electrical control of the dynamics of the electric field in the plasma. Using sawtooth instead of sinusoidal waveforms allows breaking and controlling the temporal symmetry of the electric field dynamics. In this way CWT allows controlling the EEPF, the ionization-to-excitation rate ratio, and the plasma chemistry.

Control of Electron Energy Distribution Functions by Current Waveform Tailoring in Inductively Coupled Radio Frequency Plasmas

TL;DR

This work introduces Current Waveform Tailoring (CWT) as a method to electrically control the Electron Energy Probability Function () and plasma chemistry in inductively coupled plasmas (ICPs). Using 2D PIC/MCC simulations, the coil current is constructed from harmonics up to the 4th order with a tunable parameter , enabling non-sinusoidal, sawtooth-like waveforms that break the standard temporal symmetry. The study shows that such waveform tailoring shifts energy absorption between inductive and capacitive channels, reshapes the high-energy tail of the , and lowers the excitation-to-ionization ratio, thereby influencing radical and ion production. Importantly, these effects can be realized on existing ICP platforms by upgrading the external power supply with multi-frequency impedance matching, offering a practical route to enhanced plasma process control in reactive-gas environments.

Abstract

Based on two-dimensional particle-in-cell simulations a novel approach towards Electron Energy Probability Function (EEPF) and plasma chemistry control by Current Waveform Tailoring (CWT) in the coil of inductively coupled discharges is proposed. Varying the shape of this current waveform provides electrical control of the dynamics of the electric field in the plasma. Using sawtooth instead of sinusoidal waveforms allows breaking and controlling the temporal symmetry of the electric field dynamics. In this way CWT allows controlling the EEPF, the ionization-to-excitation rate ratio, and the plasma chemistry.
Paper Structure (4 sections, 3 equations, 5 figures, 2 tables)

This paper contains 4 sections, 3 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Computational model
  3. Results
  4. Conclusions

Figures (5)

  • Figure 1: (a) 2D axisymmetric simulation domain showing the reactor geometry. Region 1 represents a $1 \times 1$ cm$^2$ square centered at $(r, z) = (4, 5)$ cm used for data analysis. (b) Coil current and (c) corresponding coil voltage waveforms for the reference single frequency case (SF) and tailored coil current waveforms characterized by different m-values (equ. 1).
  • Figure 2: Spatial distributions of the (a, c, e) electron density, $n_e$, and (b, d, f) electric potential, $\varphi$, averaged over one fundamental RF period.
  • Figure 3: Spatiotemporal evolution of electron dynamics at $R = 3$ cm over one fundamental RF period. The rows show: (a)–(c) azimuthal inductive heating rate $E_{\theta} \cdot J_{\theta e}$; (d)–(f) axial heating rate $E_{z} \cdot J_{z e}$; and (g)–(i) number density of high-energy electrons with energy $\ge 16~\mathrm{eV}$. The sampling windows for the EEPF are denoted by Time 1 and Time 2.
  • Figure 4: Direction-resolved EEPF in the sheath region 1, indicated in Fig. 1, and averaged over the phase intervals time 1 and 2, as indicated in Fig. 3. (a)(c) Azimuthal component ($v_\theta$), predominantly driven by the inductive field. (b)(d) Axial component ($v_z$), primarily governed by sheath dynamics.
  • Figure 5: Temporal evolution of the spatially averaged (a) excitation rate per electron and (b) ionization rate per electron over one fundamental RF period.