Isentropic plasma sheath model for improved fidelity

Sahu, Rupali; Tropina, Albina; Miles, Richard B.

doi:10.1063/5.0084712

Cited by 3 publications

(4 citation statements)

References 26 publications

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“…However, the electron temperature gradient and to some extent the electron stress gradient are non-negligible even at the lowest pressures and become comparable to the largest terms at the highest neutral gas pressure (10 4 mTorr). Recent work has discussed modeling the electron temperature gradient term [26][27][28][29], and some discussion of how this may influence the plasma properties at the sheath edge is provided in section 4. 6.…”

Section: Resultsmentioning

confidence: 99%

“…It is known that electron temperature gradients exist in the presheath and sheath mainly due to the non-local kinetic effect of loss of high energy electrons (those above the sheath potential energy) to the wall [26,27]. Recent work has explored modified fluid models that attempt to account for this effect [27][28][29]. The accuracy of the isothermal assumption is assessed in sections 3 and 4.6, which also provide a discussion of how this aspect of the model might be improved.…”

Section: Fluid Modelmentioning

confidence: 99%

“…In recent works, attempts have been made to model this effect by replacing the isothermal assumption with an adiabatic assumption [d(n 1−γ e T e )/dx = 0]. This modifies Bohm's criterion by a factor of the polytropic index (γ) and the result depends on the electron temperature at the sheath edge (V i,se γT e,se /m i ), rather than in the bulk [27][28][29]. Following the method in [27], we found γ ≈ 1.1-1.3 depending on the pressure, which is lower than what others have found [27].…”

Section: Isothermal Electron Assumptionmentioning

confidence: 99%

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How sheath properties change with gas pressure: modeling and simulation

Beving

Hopkins

2022

Plasma Sources Sci. Technol.

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Particle-in-cell simulations are used to study how neutral pressure influences plasma properties at the sheath edge. The high rate of ion–neutral collisions at pressures above several mTorr are found to cause a decrease in the ion velocity at the sheath edge (collisional Bohm criterion), a decrease in the edge-to-center density ratio (h l factor), and an increase in the sheath width and sheath potential drop. A comparison with existing analytic models generally indicates favorable agreement, but with some distinctions. One is that models for the h l factor need to be made consistent with the collisional Bohm criterion. With this and similar corrections, a comprehensive fluid-based model of the plasma boundary transition is constructed that compares well with the simulation results.

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Section: Resultsmentioning

confidence: 99%

Section: Fluid Modelmentioning

confidence: 99%

Section: Isothermal Electron Assumptionmentioning

confidence: 99%

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How sheath properties change with gas pressure: modeling and simulation

Beving

Hopkins

2022

Plasma Sources Sci. Technol.

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“…Sahu et. al. propose to revisit the sheath boundary flux expressions and use an isentropic description of the sheath for improved fidelity [22,23]. However, it is still common to assume the ions thermalized with the neutrals (consequently a collisionless sheath).…”

Section: Introductionmentioning

confidence: 99%

Ion temperature profile importance in collisional sheath modelling

Mun

Muraglia

Agullo

et al. 2022

J. Phys.: Conf. Ser.

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A plasma fluid model is being developed for the simulation of a direct current plasma discharge simulation including the sheath regions. The code uses a second order centered finite difference scheme and time integration is done by strong stability preserving third order Runge-Kutta method. The separation of scalar and vectorial quantities in two different grids gives stable results. After validation by comparison with theoretical ion sheath profiles, a one dimensional direct current argon discharge was simulated and compared to 1D3v particle-in-cell simulation results. It is shown that the inclusion of a non constant ion temperature profile is mandatory in fluid models in order to recover correct increase of ion velocity in sheaths and thus to simulate direct current (DC) discharges where collisions are not negligible in the sheaths.

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Voltage waveform tailoring for high aspect ratio plasma etching of SiO2 using Ar/CF4/O2 mixtures: Consequences of ion and electron distributions on etch profiles

Krüger

Lee

Nam

et al. 2022

Journal of Vacuum Science &Amp; Technology A

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The quality of high aspect ratio (HAR) features etched into dielectrics for microelectronics fabrication using halogen containing low temperature plasmas strongly depends on the energy and angular distribution of the incident ions (IEAD) onto the wafer, as well as potentially that of the electrons (EEAD). Positive ions, accelerated to high energies by the sheath electric field, have narrow angular spreads and can penetrate deeply into HAR features. Electrons typically arrive at the wafer with nearly thermal energy and isotropic angular distributions and so do not directly penetrate deeply into features. These differences can lead to positive charging of the insides of the features that can slow etching rates and produce geometric defects such as twisting. In this work, we computationally investigated the plasma etching of HAR features into SiO2 using tailored voltage waveforms in a geometrically asymmetric capacitively coupled plasma sustained in an Ar/CF4/O2 mixture at 40 mTorr. The tailored waveform consisted of a sinusoidal wave and its higher harmonics with a fundamental frequency of 1 MHz. We found that some degree of control of the IEADs and EEADs is possible by adjusting the phase of higher harmonics φ through the resulting generation of electrical asymmetry and electric field reversal. However, the IEADs and EEADs cannot easily be separately controlled. The control of IEADs and EEADs is inherently linked. The highest quality feature was obtained with a phase angle φ = 0° as this value generated the largest (most negative) DC self-bias and largest electric field reversal for accelerating electrons into the feature. That said, the consequences of voltage waveform tailoring (VWT) on etched features are dominated by the change in the IEADs. Although VWT does produce EEADs with higher energy and narrower angular spread, the effect of these electrons on the feature compared to thermal electrons is not large. This smaller impact of VWT produced EEADs is attributed to thermal electrons being accelerated into the feature by electric fields produced by the positive in-feature charging.

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Isentropic plasma sheath model for improved fidelity

Cited by 3 publications

References 26 publications

How sheath properties change with gas pressure: modeling and simulation

How sheath properties change with gas pressure: modeling and simulation

Ion temperature profile importance in collisional sheath modelling

Voltage waveform tailoring for high aspect ratio plasma etching of SiO2 using Ar/CF4/O2 mixtures: Consequences of ion and electron distributions on etch profiles

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