2D particle-in-cell simulations of geometrically asymmetric low-pressure capacitive RF plasmas driven by tailored voltage waveforms

Abstract

The effects of the simultaneous presence of two different types of plasma asymmetry, viz, geometric and electrical, on low-pressure capacitively coupled argon discharges are studied by 2D3V graphics-processing-unit-based particle-in-cell/Monte Carlo simulations. The geometric asymmetry originates from the different powered vs grounded electrode surface areas, while the electrical asymmetry is established by applying peaks/valleys and sawtooth-up/-down driving voltage waveforms. While in geometrically symmetric discharges, the {peaks ↔ valleys} and the {sawtooth-down ↔ sawtooth-up} switching of the waveforms is equivalent to exchanging the powered and grounded electrodes, this transformation is violated when the geometric symmetry is broken. Under such conditions, the plasma characteristics and the DC self-bias generation behave differently, compared to the geometrically symmetric case. This leads to different sheath dynamics and, therefore, strongly influences the electron power absorption dynamics. For identical peak-to-peak voltages, the plasma density obtained for such tailored voltage waveforms is found to be higher compared to the classical single-frequency waveform case. Reduced plasma densities are found in the valleys- and sawtooth-down waveform cases, compared to the peaks- and sawtooth-up waveforms. By including realistic energy and material-dependent secondary electron emission (SEE) coefficients in the simulations, the electron-induced SEE is found to be reduced in the valleys- and sawtooth-down waveform cases, which explains the behaviour of the plasma density. Using such tailored waveforms in geometrically asymmetric discharges is also found to lead to the formation of different charged particle energy distributions at the boundary surfaces, compared to those in geometrically symmetric plasma sources.

Global simulation of plasma series resonance effect in radio frequency capacitively coupled Ar/O2 plasma

“…Thus, with the superposition effects of the increasing difference between the 125203-6 two electrode areas and the Gaussian waveform with a positive amplitude, the asymmetry of the discharge increases with the formation of a higher negative DC self bias. Wang et al [7] found from their particle simulation results that a thicker sheath would be formed at the powered electrode due to the strong negative DC self-bias, which can lead to fast sheath expansion and excitation of strong PSR oscillations. From our results, with the enhancement of the superposition of electrical and geometrical asymmetry, the absolute value of the negative DC self-bias voltage really becomes larger, as shown in Fig.…”

“…As shown in Fig. 14(a), owing to the destructive superposition between the electrical asymmetry and geometrical asymmetry, the DC self bias is positive [7] and decreases as A d decreases, so the sheath becomes thinner and expands slowly, leading to the weakening of PSR oscillation and the decreasing of the resonance frequency. Figure 14(b) shows that with the decrease of the driving electrode area, the sheath capacitance lessens very slightly, but the bulk inductance increases a lot and gradually becomes the main reason for the resonance frequency decreasing, while the electrical asymmetry and geometrical asymmetry suppress each other.…”

“…The geometric asymmetry effect (GAE) can significantly affect the power absorption dynamics and the distributions of charged particles, and thus influencing the quality and efficiency of etching or deposition. Moreover, for the electrical asymmetry effect (EAE), it was first proposed by driving a fundamental frequency and its second harmonic in a geometrically symmetric chamber, [5] and then was extended by applying peaks/valleys, sawtooth-up/-down, or Gaussian-type driving voltage waveforms even in geometrically asymmetric CCPs, [6,7] to have higher possibility of controlling not only ion properties but also electron power absorption and plasma density. At low-pressure CCPs, the RF sheath exhibits a similar charge-voltage characteristic of strong nonlinearity to an capacitance, while the bulk plasma has inductive and resistive properties, when taking into account the electron inertia and the power dissipation caused by collisions of electrons with neutrals and momentum transfer from the oscillating sheath edge, respectively.…”

Electron heating dynamics and plasma parameters control in capacitively coupled plasma

“…简单化学反应的氩气CCP放电, 一维(one dimensional, 1D)模拟大约需要1-2天 [17,58] , 柱坐标小 腔室(10 cm腔室半径, 2 cm电极间距)、低密度 (10 15 -10 16 m -3 )的串行二维(two dimensional, 2D) 模拟需要1-2周 [18] , 针对略大一些腔室结构(12 cm 腔室半径, 6.7 cm电极间距), 基于GPU的2D并 行PIC/MCC模拟同样需要10天左右 [19,59] 等 [3,59] 开发的基于GPU的2D PIC/MCC模型等.…”

Self-bias voltage formation and charged particle dynamics in multi-frequency capacitively coupled plasmas

“…The primary computational tool for these investigations has been the Particle-in-Cell/Monte Carlo Collisions (PIC/MCC) simulation. [55][56][57][58] This particle based approach is fully capable to capture kinetic effects, 59 therefore is well suited for the description of plasma sources operated at low pressures where non-local particle transport [60][61][62][63] appears. An analytical model 27 based on the voltage balance of the discharge has aided the understanding of the observations.…”