The effects of electron energy distribution function on the plasma sheath structure in the presence of charged nanoparticles

Abstract

The effects of the electron energy distribution function (EEDF) on the structure of a dusty plasma sheath are investigated. Here, it is assumed that the electrons obey a Druyvesteyn-type distribution with a parameter $x$ controlling the shape of the EEDF. The Druyvesteyn-like distribution tends to a Maxwellian distribution as $x$ varies from 2 to 1. Using the orbital motion limited theory, the incident electron current on the dust is evaluated for a given $x$ . The results of numerical simulations are compared with those of a Maxwellian distribution. It was found that the sheath dynamics depends strongly on the magnitude of $x$ . The sheath thickness increases monotonically with increasing $x$ . However, the absolute dust charge decreases and, as a result, the accelerating ion drag force is weakened and thus the dust number density is enhanced. For a plasma with a Druyvesteyn-like distribution, the Bohm speed is a function of $x$ and increases with increasing $x$ .

Anti-oxidant copper layer by remote mode N2 plasma for low temperature copper–copper bonding

“…As the electron temperature along with the plasma density greatly affects the electron energy distribution function (EEDF), we can infer the chemical reactions occurring in the plasma through the EEDF. If we assume that the EEDF follows the Maxwell distribution, the equation can be written as 32 , 37 , 38 where is the electron energy and is the electron density, which is considered to be equal to the plasma density. Figure 5 shows the constructed EEDF and it demonstrates the electron energy distributions with the electron temperature and the plasma mode.…”

Dust particle charging process in a radio frequency sheath of plasma containing kappa distribution electrons

“…In a large variety of plasma applications, such as plasma processing and controlled fusion research, the dust particles mainly result from plasma-wall interactions and then enter the bulk plasma region across the sheath, which causes contamination in the plasma processing of integrated circuits and safety problems in fusion devices Krasheninnikov, Smirnov & Rudakov 2011;Pustylnik et al 2021). On the other hand, fine dust probes can be used to study plasma-sheath characteristics since the dust particles immersed in the plasma become charged by the action of electron and ion fluxes (Samarian & James 2001;Beadles, Wang & Horanyi 2017).…”

“…The RF sheath of plasma containing non-Maxwellian electrons has been investigated recently (Ou, An & Men 2019;Ou & Huang 2020) and it is found that the supra-thermal electrons can modify the spatio-temporal variation of the plasma profile in the sheath region; such an effect of the non-Maxwellian electrons on the dust particle charge can be expected. According to the results of dust particles in a static sheath of non-Maxwellian plasma (Foroutan & Akhoundi 2012;Ou, Zhao & Lin 2018;El Ghani, Driouch & Chatei 2019;Khalilpour & Foroutan 2020;Zhao et al 2020), it has been shown that the non-Maxwellian electrons can modify the profile of the dust particle when the dust components are relatively dense (Foroutan & Akhoundi 2012;El Ghani et al 2019;Khalilpour & Foroutan 2020), while they can change the dust particle charging process and levitation when the dust density is very low (Ou et al 2018;Zhao et al 2020). Since the charge number of the dust particle in an RF sheath depends strongly on the RF field (Bacharis et al 2010), the dust particle charging process in the non-Maxwellian electron RF sheath is more complex than in the static sheath.…”

“…Based on the Whipple approximation (Whipple 1981) and the neglect of the plasma screening, the dust particle charge can be calculated from the Debye-Hückel potential. For some applications, such as in a fusion plasma, however, the dust particle size limit no longer holds because the dust particle size can be up to tens of microns (Krasheninnikov et al 2011;Zhang et al 2021) while the local Debye length is relatively small due to the high plasma density. As a result, the Whipple approximation is only applicable in a limited range of dust size and the effect of the plasma screening on the dust particle charging must be taken into account.…”

Ion energy distribution in a radio frequency sheath of plasma with Kappa electron velocity distribution

“…The presence of energetic electrons makes the electron distribution non-equilibrium and some deviation from the Maxwellian. Related to the problem of the sheath formation in non-stationary plasmas, some authors attempted to include the effects of a non-Maxwellian distribution function by the sum of two distributions consisting of a thermal Maxwellian background F I G U R E 1 The geometry of the radio frequency (RF) sheath model and the corresponding schematic diagram of the equivalent circuit for the RF sheath model and a small super-thermal population, [10][11][12] a q-non-extensive electron distribution, or Kappa distribution. [13][14][15][16] For plasmas described by a Kappa distribution, it has been shown [14] that the Debye length is always smaller than the shielding distance in a Maxwellian plasma.…”