Experimental investigations of electron heating dynamics and ion energy distributions in capacitive discharges driven by customized voltage waveforms

Berger, Birk; Brandt, Steven; Franek, James B.; Schüngel, Edmund; Koepke, M. E.; Mussenbrock, Thomas; Schulze, Julian

doi:10.1063/1.4937403

Cited by 23 publications

(27 citation statements)

References 89 publications

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“…In the following, we describe the derivation of the voltage drop across and the width of the grounded electrode sheath, because the IEDFs at the grounded electrode will be discussed in the results section; the properties of the powered electrode sheath can be determined in a similar procedure. The underlying model has been used in several studies of multi‐frequency plasmas before . A central assumption is that the total net charge within the entire discharge volume,

Q_{t o t}

, is purely located in the two sheaths, that is,

Q_{t o t} {= Q}_{s p} true(t true) + Q_{s g} true(t true)

, and that it is constant in time .…”

Section: Model Simulation and Experimentsmentioning

confidence: 99%

“…An analytical treatment would not be possible, if the cubic correction was included. The time dependent normalized charge in the grounded electrode sheath is found as

q_{s g} true(t true) = q_{t o t} - q_{s p} true(t true) = \frac{q_{t o t} - \sqrt{ϵ q_{t o t}^{2} - true(1 - ϵ true) \frac{η + ϕ_{\sim} true(t true)}{ϕ_{t o t}}}}{1 - ϵ} .

…”

Section: Model Simulation and Experimentsmentioning

confidence: 99%

“…Here, all charges are normalized by

Q_{0} {= A}_{p} \sqrt{2 e ϵ_{0} {true \overset{n}{true}}_{s p} ϕ_{t o t}}

with

A_{p}

being the surface area of the powered electrode and

{true \bar{n}}_{s p}

being the mean ion density in the powered electrode sheath region, that is,

q_{t o t} {= Q}_{t o t} {/ Q}_{0}

q_{s p} {= Q}_{s p} {/ Q}_{0}

, and

q_{s g} {= Q}_{s g} {/ Q}_{0}

η

and

ϕ_{\sim} true(t true)

are the DC self‐bias and the applied voltage,

ϕ_{t o t}

is the applied voltage amplitude . The symmetry of the discharge is taken into account in the model via the symmetry parameter

ϵ = true| \frac{ϕ_{s g}^{m a x}}{ϕ_{s p}^{m a x}} true|,

that is, as the absolute value of the ratio of the maximum voltage drops across the grounded and powered electrode sheaths.…”

Section: Model Simulation and Experimentsmentioning

confidence: 99%

“…The symmetry of the discharge is taken into account in the model via the symmetry parameter

ϵ = true| \frac{ϕ_{s g}^{m a x}}{ϕ_{s p}^{m a x}} true|,

that is, as the absolute value of the ratio of the maximum voltage drops across the grounded and powered electrode sheaths. Both the symmetry parameter and the total charge can easily be determined from the DC self‐bias,

η

, and from the global extrema of the applied voltage waveform,

ϕ_{\sim, \max}

and

ϕ_{\sim, \min}

, via

ϵ = - true(η + ϕ_{\sim, \max} true) / true(η + ϕ_{\sim, \min} true)

and

q_{t o t} = \sqrt{true(ϕ_{\sim, \max} - ϕ_{\sim, \min} true) / true[ϕ_{t o t} (1 + ϵ) false]}

. The time dependent voltage drop across the grounded electrode sheath is then

ϕ_{s g} true(t true) = ϵ ϕ_{t o t} {[q_{s g} (t)]}^{2} .

…”

Section: Model Simulation and Experimentsmentioning

confidence: 99%

“…Therefore, a geometrical asymmetry is present in the experiment. Further details on the experimental setup and discharge configuration can be found in a recent paper . The discharge is operated in argon at 5 Pa pressure.…”

Section: Model Simulation and Experimentsmentioning

confidence: 99%

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A Simple Model for Ion Flux‐Energy Distribution Functions in Capacitively Coupled Radio‐Frequency Plasmas Driven by Arbitrary Voltage Waveforms

Schüngel

Schulze

2016

Plasma Processes & Polymers

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The ion flux‐energy distribution function (IFEDF) is of crucial importance for surface processing applications of capacitively coupled radio‐frequency (CCRF) plasmas. Here, we propose a model that allows for the determination of the IFEDF in such plasmas for various gases and pressures in both symmetric and asymmetric configurations. A simplified ion density profile and a quadratic charge voltage relation for the plasma sheaths are assumed in the model, of which the performance is evaluated for single‐ as well as multi‐frequency voltage waveforms. The IFEDFs predicted by this model are compared to those obtained from PIC/MCC simulations and retarding field energy analyzer measurements. Furthermore, the development of the IFEDF shape and the ion dynamics in the plasma sheath region are discussed in detail based on the spatially and temporally resolved model data.

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Q_{t o t}

, is purely located in the two sheaths, that is,

Q_{t o t} {= Q}_{s p} true(t true) + Q_{s g} true(t true)

, and that it is constant in time .…”

Section: Model Simulation and Experimentsmentioning

confidence: 99%

“…An analytical treatment would not be possible, if the cubic correction was included. The time dependent normalized charge in the grounded electrode sheath is found as

q_{s g} true(t true) = q_{t o t} - q_{s p} true(t true) = \frac{q_{t o t} - \sqrt{ϵ q_{t o t}^{2} - true(1 - ϵ true) \frac{η + ϕ_{\sim} true(t true)}{ϕ_{t o t}}}}{1 - ϵ} .

…”

Section: Model Simulation and Experimentsmentioning

confidence: 99%

“…Here, all charges are normalized by

Q_{0} {= A}_{p} \sqrt{2 e ϵ_{0} {true \overset{n}{true}}_{s p} ϕ_{t o t}}

with

A_{p}

being the surface area of the powered electrode and

{true \bar{n}}_{s p}

being the mean ion density in the powered electrode sheath region, that is,

q_{t o t} {= Q}_{t o t} {/ Q}_{0}

q_{s p} {= Q}_{s p} {/ Q}_{0}

, and

q_{s g} {= Q}_{s g} {/ Q}_{0}

η

and

ϕ_{\sim} true(t true)

are the DC self‐bias and the applied voltage,

ϕ_{t o t}

is the applied voltage amplitude . The symmetry of the discharge is taken into account in the model via the symmetry parameter

ϵ = true| \frac{ϕ_{s g}^{m a x}}{ϕ_{s p}^{m a x}} true|,

that is, as the absolute value of the ratio of the maximum voltage drops across the grounded and powered electrode sheaths.…”

Section: Model Simulation and Experimentsmentioning

confidence: 99%

“…The symmetry of the discharge is taken into account in the model via the symmetry parameter

ϵ = true| \frac{ϕ_{s g}^{m a x}}{ϕ_{s p}^{m a x}} true|,

η

, and from the global extrema of the applied voltage waveform,

ϕ_{\sim, \max}

and

ϕ_{\sim, \min}

, via

ϵ = - true(η + ϕ_{\sim, \max} true) / true(η + ϕ_{\sim, \min} true)

and

q_{t o t} = \sqrt{true(ϕ_{\sim, \max} - ϕ_{\sim, \min} true) / true[ϕ_{t o t} (1 + ϵ) false]}

. The time dependent voltage drop across the grounded electrode sheath is then

ϕ_{s g} true(t true) = ϵ ϕ_{t o t} {[q_{s g} (t)]}^{2} .

…”

Section: Model Simulation and Experimentsmentioning

confidence: 99%

Section: Model Simulation and Experimentsmentioning

confidence: 99%

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A Simple Model for Ion Flux‐Energy Distribution Functions in Capacitively Coupled Radio‐Frequency Plasmas Driven by Arbitrary Voltage Waveforms

Schüngel

Schulze

2016

Plasma Processes & Polymers

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Numerical Study of the Effect of Applied Voltage on Simultaneous Modes of Electron Heating in RF Capacitive Discharges

Missaoui

Elkaouini

Chatei

2020

Lecture Notes in Electrical Engineering

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Enhanced power coupling efficiency in inductive discharges with RF substrate bias driven at consecutive harmonics with adjustable phase

Berger

Steinberger

Schüngel³

et al. 2017

Applied Physics Letters

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Inductive discharges with radio-frequency (RF) substrate bias are frequently used for various technological applications. We operate such a hybrid discharge with a phase-locked RF substrate bias at twice the frequency of the inductive coupling with fixed but adjustable phase between both RF sources in neon at low pressures of a few Pa. The ion flux to the substrate is found to be a function of this relative phase in the H-mode at constant RF powers as long as some residual capacitive coupling of the planar coil is present. For distinct choices of the phase, Phase Resolved Optical Emission Spectroscopy measurements show that energetic beam electrons generated by the expanding boundary sheaths (i) are well confined, (ii) are accelerated efficiently, and (iii) propagate vertically through the inductive skin layer at the times of maximum azimuthal induced electric field within the fundamental RF period. This enhances the inductive stochastic electron heating, the power coupling efficiency, and finally the ion flux.

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Experimental investigations of electron heating dynamics and ion energy distributions in capacitive discharges driven by customized voltage waveforms

Cited by 23 publications

References 89 publications

A Simple Model for Ion Flux‐Energy Distribution Functions in Capacitively Coupled Radio‐Frequency Plasmas Driven by Arbitrary Voltage Waveforms

A Simple Model for Ion Flux‐Energy Distribution Functions in Capacitively Coupled Radio‐Frequency Plasmas Driven by Arbitrary Voltage Waveforms

Numerical Study of the Effect of Applied Voltage on Simultaneous Modes of Electron Heating in RF Capacitive Discharges

Enhanced power coupling efficiency in inductive discharges with RF substrate bias driven at consecutive harmonics with adjustable phase

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