Simulation of nanoparticle coagulation in radio-frequency capacitively coupled C ₂ H ₂ discharges

Abstract

A self-consistent fluid model is employed to investigate the coagulation stage of nanoparticle formation, growth, charging, and transport in a radio-frequency capacitively coupled parallel-plate acetylene (C 2 H 2 ) discharge. In our simulation, the distribution of neutral species across the electrode gap is determined by mass continuity, momentum balance, and energy balance equations. Since a thermal gradient in the gas temperature induced by the flow of the neutral gas, a careful study of the thermophoretic force on the spatial distribution of the nanoparticle density profiles is indispensable. In the present paper, we mainly focus on the influences of the gas flow rate, voltage, and gas pressure on the spatial distribution of the nanoparticle density. It appears that the resulting density profile of the 10-nm particles experiences a significant shift towards the upper showerhead electrode once the neutral equations are applied, and a serious shift is observed when increasing the gas flow rate. Thus, the flow of neutral gas can strongly influence the spatial distribution of the particles in the plasma.

Modeling of the nanoparticle coagulation in pulsed radio-frequency capacitively coupled C 2 H 2 discharges

“…Moreover, since the gas flow is taken 075204-4 into account, a gas temperature gradient is presented in the discharge, which will make the gas molecules transfer more momentum from the hotter area of the plasma to the cooler area, and then a local maximum is created in front of the upper electrode. [21] However, in this work, we observe that by varying duty ratio, the peak of nanoparticle density gradually flow to the upper electrode. This is due to the fact that the negative ion density (H 2 CC − ) can diffuse to the wall in the pulseoff time, which is the main initial particle for the nanoparticle formation.…”

“…Previous work [21] has shown that gas flow has a great effect on the nanoparticle density spatial distribution. Hence, in Section 2, the neutral gas equations including the density, flux, and energy balances are taken into account and the mechanisms for particle formation are also elaborated.…”

Discharge dynamics, plasma kinetics and gas flow effect in argon–acetylene discharges

“…For most cases, the only factors that vary very rapidly in the expression of S s-e are the rate constant that depends on T e and the electron density. The expression of the time-averaged value of S s-e over one RF period may be written: (10) Taking into account the discussion above, the expression of time-averaged continuity equations of long characteristic-time (LCT) species may be written as:…”

“…Capacitively coupled RF (CCRF) discharges in hydrocarbon (HC) containing mixtures have been the subject of interest for many decades [1], [2], [3]. These discharges were indeed used fairly early for the deposition of a variety of (multi-)functional carbon, i.e., Diamond-Like-carbon(DLC) [4] or TaC [5], and hydrogen-carbon coatings (aC:H) [6] with applications in a large number of fields such as tribology [7], diffusion barriers [8], anti-corrosion coatings [9], adhesion-enhancement [6], nanocomposites elaboration [10], biomedical [11], just to cite few examples. Although the carbon deposits elaborated by HC-containing discharges enable reaching a large number of functionalities, the physical properties and functional characteristics of the deposits are usually highly sensitive to the process characteristics.…”

Fluid simulation of inductively coupled Ar/O 2 plasmas: Comparisons with experiment

“…Zhao et al [15] used a hybrid model to investigate the Ar/CF 4 gas ratio effects on the Si etch rate and profile uniformity in ICPs, revealing that the etching property is better at higher Ar/CF 4 gas ratios. Liu et al [16] used a fluid model to investigate influences of the gas flow rate, the radio frequency source voltage, and the pressure on the formation of dust particles in RF CCP acetylene (C 2 H 2 ) discharge, and they found that the gas flow rate is an important parameter for the particle growth mechanism. Moreover, some experimental research has also been done.…”