Effect of total emitted electron velocity distribution function on the plasma sheath near a floating wall

Qing, Shaowei; Zhou, Huairong

doi:10.1063/1.5000507

Cited by 8 publications

(10 citation statements)

References 32 publications

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“…For secondary electrons, similarly one can consider its velocity distribution function, see Qing's work for details [41] . Note that when half Maxwellian distribution is selected, when its temperature 𝑇 𝑠𝑒 approaches 0, the solution converges to a fluid model solution, which utilizes energy conservation, flux conservation and secondary emission coefficient as shown in Eq.…”

Section: ⅲ Theoretical Analysesmentioning

confidence: 99%

Unveiling the role of dielectric trap states on capacitively coupled radio-frequency plasma discharge: dynamic charging behaviors

Zhang¹,

Sun²,

Volčokas³

et al. 2021

Plasma Sources Sci. Technol.

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The influence of charge trap states in the dielectric boundary material on capacitively coupled radio-frequency (RF) plasma discharge is investigated with theory and particle-in-cell/Monte Carlo collision simulation. It is found that the trap states of the wall material manipulated discharge properties mainly through the varying ion-induced secondary electron emission (SEE) coefficient in response to dynamic surface charges accumulated within the solid boundary. A comprehensive SEE model considering surface charging is established first, which incorporates the valence band electron distribution, electron trap density, and charge trapping through Auger neutralization and de-excitation. Theoretical analysis is carried out to reveal the effects of trap states on sheath solution, stability, plasma density and temperature, particle and power balance, etc. The theoretical work is supported by simulation results, showing the reduction of the mean RF sheath potential as charging-dependent emission coefficient increases. As the gas pressure increases, a shift of the maximum ionization rate from the bulk plasma center to the plasma-sheath interface is observed, which is also influenced by the trap states of the electrode material where the shift happens at a lower pressure with traps considered. In addition, charge traps are proven to be helpful for creating asymmetric plasma discharges with geometrically symmetric structures; such an effect is more pronounced in γ-mode discharges.

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Section: ⅲ Theoretical Analysesmentioning

confidence: 99%

Unveiling the role of dielectric trap states on capacitively coupled radio-frequency plasma discharge: dynamic charging behaviors

Zhang¹,

Sun²,

Volčokas³

et al. 2021

Plasma Sources Sci. Technol.

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show abstract

“…The choice of distribution function for emitted secondary electrons is not unique, and can influence particle as well as energy fluxes especially in the vicinity of boundaries [70,71]. Here it is chosen as half-Maxwellian, which was also adopted in several previous studies [63,69,72,73]:…”

Section: Kinetic Effects Of Ion-surface Interactionmentioning

confidence: 99%

Integrated modeling of plasma-dielectric interaction: kinetic boundary effects

Sun

Shu

et al. 2019

Plasma Sources Sci. Technol.

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Kinetic effects of plasma-dielectric interaction are studied theoretically with respect to the mechanisms of electron extraction from solids in response to ion and electron bombardment, coupled with plasma dynamics of a weakly emissive sheath. Emission coefficients of incident beams are first calculated by quantum mechanical as well as semi-classical approaches involving Auger neutralization, energy-dependent ejection due to primary beam, and reflection of lowenergy electrons, which are then incorporated into a 1D1V simulation and plasma kinetic theory. Presheath with sheath structures are derived using fluid and kinetic theory regarding ion-induced emission, respectively. The Bohm criterion considering surface emission is evaluated as well. For electron-induced emission, it is found that sheath potential is no longer collinear with plasma electron temperature in our integrated model. Additionally, reflection of low-energy electrons is justified to have a minor impact on the floating sheath for low temperature half-bounded plasma under low pressure. The combined effects of both incident ions and electrons in bounded plasma are analyzed with symmetrical/asymmetrical emission yields at two boundaries. It is then proved that wall potential is barely affected by bulk plasma influx if emission coefficients are symmetrical, while emission due to transiting beam can drastically modify the sheath solution. Electron reflection also becomes more influential if secondary electrons have low initial energy. Finally, we summarize different roles of ion and electron in sheath structure. It is shown that ioninduced emission mitigates sheath potential but cannot reach critical emission on contrast to that of electron flux.

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“…(2013, 2014) found that the critical SCL sheath has a solution if the temperature ratio of plasma electrons to emitted electrons is no less than unity. Qing & Hu (2017) found that different assumptions of the total emitted electron velocity distribution (EEVD) can significantly affect the range of average energy ratio of emitted electrons to primary electrons, in which the critical SCL sheath has a solution. This then indicates that the classic sheath may transit to an inverse sheath structure when the ratio is out of the range.…”

Section: Introductionmentioning

confidence: 99%

Stability of different plasma sheaths near a dielectric wall with secondary electron emission

et al. 2019

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The linear theory stability of different collisionless plasma sheath structures, including the classic sheath, inverse sheath and space-charge limited (SCL) sheath, is investigated as a typical eigenvalue problem. The three background plasma sheaths formed between a Maxwellian plasma source and a dielectric wall with a fully self-consistent secondary electron emission condition are solved by recent developed 1D3V (one-dimensional space and three-dimensional velocities), steady-state, collisionless kinetic sheath model, within a wide range of Maxwellian plasma electron temperature $T_{e}$ . Then, the eigenvalue equations of sheath plasma fluctuations through the three sheaths are numerically solved, and the corresponding damping and growth rates $\unicode[STIX]{x1D6FE}$ are found: (i) under the classic sheath structure (i.e. $T_{e}<T_{ec}$ (the first threshold)), there are three damping solutions (i.e. $\unicode[STIX]{x1D6FE}_{1}$ , $\unicode[STIX]{x1D6FE}_{2}$ and $\unicode[STIX]{x1D6FE}_{3}$ , $0>\unicode[STIX]{x1D6FE}_{1}>\unicode[STIX]{x1D6FE}_{2}>\unicode[STIX]{x1D6FE}_{3}$ ) for most cases, but there is only one growth-rate solution $\unicode[STIX]{x1D6FE}$ when $T_{e}\rightarrow T_{ec}$ due to the inhomogeneity of sheath being very weak; (ii) under the inverse sheath structure, which arises when $T_{e}>T_{ec}$ , there are no background ions in the sheath so that the fluctuations are stable; (iii) under the SCL sheath conditions (i.e. $T_{e}\geqslant T_{e\text{SCL}}$ , the second threshold), the obvious ion streaming through the sheath region again emerges and the three damping solutions are again found.

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Effect of total emitted electron velocity distribution function on the plasma sheath near a floating wall

Cited by 8 publications

References 32 publications

Unveiling the role of dielectric trap states on capacitively coupled radio-frequency plasma discharge: dynamic charging behaviors

Unveiling the role of dielectric trap states on capacitively coupled radio-frequency plasma discharge: dynamic charging behaviors

Integrated modeling of plasma-dielectric interaction: kinetic boundary effects

Stability of different plasma sheaths near a dielectric wall with secondary electron emission

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