103 research outputs found
The effect of ambipolar electric fields on the electron heating in capacitive RF plasmas
We investigate the electron heating dynamics in electropositive argon and
helium capacitively coupled RF discharges driven at 13.56 MHz by Particle in
Cell simulations and by an analytical model. The model allows to calculate the
electric field outside the electrode sheaths, space and time resolved within
the RF period. Electrons are found to be heated by strong ambipolar electric
fields outside the sheath during the phase of sheath expansion in addition to
classical sheath expansion heating. By tracing individual electrons we also
show that ionization is primarily caused by electrons that collide with the
expanding sheath edge multiple times during one phase of sheath expansion due
to backscattering towards the sheath by collisions. A synergistic combination
of these different heating events during one phase of sheath expansion is
required to accelerate an electron to energies above the threshold for
ionization. The ambipolar electric field outside the sheath is found to be time
modulated due to a time modulation of the electron mean energy caused by the
presence of sheath expansion heating only during one half of the RF period at a
given electrode. This time modulation results in more electron heating than
cooling inside the region of high electric field outside the sheath on time
average. If an electric field reversal is present during sheath collapse, this
time modulation and, thus, the asymmetry between the phases of sheath expansion
and collapse will be enhanced. We propose that the ambipolar electron heating
should be included in models describing electron heating in capacitive RF
plasmas
Customized ion flux-energy distribution functions in capacitively coupled plasmas by voltage waveform tailoring
We propose a method to generate a single peak at a distinct energy in the ion
flux-energy distribution function (IDF) at the electrode surfaces in
capacitively coupled plasmas. The technique is based on the tailoring of the
driving voltage waveform, i.e. adjusting the phases and amplitudes of the
applied harmonics, to optimize the accumulation of ions created by charge
exchange collisions and their subsequent acceleration by the sheath electric
field. The position of the peak (i.e. the ion energy) and the flux of the ions
within the peak of the IDF can be controlled in a wide domain by tuning the
parameters of the applied RF voltage waveform, allowing optimization of various
applications where surface reactions are induced at particular ion energies
Kinetic simulation of the sheath dynamics in the intermediate radio-frequency regime
The dynamics of temporally modulated plasma boundary sheaths is studied in
the intermediate radio frequency regime where the applied radio frequency and
the ion plasma frequency are comparable. Two kinetic simulation codes are
employed and their results are compared. The first code is a realization of the
well-known scheme, Particle-In-Cell with Monte Carlo collisions (PIC/MCC) and
simulates the entire discharge, a planar radio frequency capacitively coupled
plasma (RF-CCP) with an additional heating source. The second code is based on
the recently published scheme Ensemble-in-Spacetime (EST); it resolves only the
sheath and requires the time resolved voltage across and the ion flux into the
sheath as input. Ion inertia causes a temporal asymmetry (hysteresis) of the
sheath charge-voltage relation; also other ion transit time effects are found.
The two codes are in good agreement, both with respect to the spatial and
temporal dynamics of the sheath and with respect to the ion energy
distributions at the electrodes. It is concluded that the EST scheme may serve
as an efficient post-processor for fluid or global simulations and for
measurements: It can rapidly and accurately calculate ion distribution
functions even when no genuine kinetic information is available
Effects of fast atoms and energy-dependent secondary electron emission yields in PIC/MCC simulations of capacitively coupled plasmas
In most PIC/MCC simulations of radio frequency capacitively coupled plasmas
(CCPs) several simplifications are made: (i) fast neutrals are not traced, (ii)
heavy particle induced excitation and ionization are neglected, (iii) secondary
electron emission from boundary surfaces due to neutral particle impact is not
taken into account, and (iv) the secondary electron emission coefficient is
assumed to be constant, i.e. independent of the incident particle energy and
the surface conditions. Here we question the validity of these simplifications
under conditions typical for plasma processing applications. We study the
effects of including fast neutrals and using realistic energy-dependent
secondary electron emission coefficients for ions and fast neutrals in
simulations of CCPs operated in argon at 13.56 MHz and at neutral gas pressures
between 3 Pa and 100 Pa. We find a strong increase of the plasma density and
the ion flux to the electrodes under most conditions, if these processes are
included realistically in the simulation. The sheath widths are found to be
significantly smaller and the simulation is found to diverge at high pressures
for high voltage amplitudes in qualitative agreement with experimental
findings. By switching individual processes on and off in the simulation we
identify their individual effects on the ionization dynamics and plasma
parameters. We conclude that fast neutrals and energy-dependent secondary
electron emission coefficients must be included in simulations of CCPs in order
to yield realistic results
Kinetic Interpretation of Resonance Phenomena in Low Pressure Capacitively Coupled Radio Frequency Plasmas
The kinetic origin of resonance phenomena in capacitively coupled radio
frequency plasmas is discovered based on particle-based numerical simulations.
The analysis of the spatio-temporal distributions of plasma parameters such as
the densities of hot and cold electrons, as well as the conduction and
displacement currents reveals the mechanism of the formation of multiple
electron beams during sheath expansion. The interplay between highly energetic
beam electrons and low energetic bulk electrons is identified as the physical
origin of the excitation of harmonics in the current
Simulation benchmarks for low-pressure plasmas: capacitive discharges
Benchmarking is generally accepted as an important element in demonstrating the correctness of computer simulations. In the modern sense, a benchmark is a computer simulation result that has evidence of correctness, is accompanied by estimates of relevant errors, and which can thus be used as a basis for judging the accuracy and efficiency of other codes. In this paper, we present four benchmark cases related to capacitively coupled discharges. These benchmarks prescribe all relevant physical and numerical parameters. We have simulated the benchmark conditions using five independently developed particle-in-cell codes. We show that the results of these simulations are statistically indistinguishable, within bounds of uncertainty that we define. We therefore claim that the results of these simulations represent strong benchmarks, that can be used as a basis for evaluating the accuracy of other codes. These other codes could include other approaches than particle-in-cell simulations, where benchmarking could examine not just implementation accuracy and efficiency, but also the fidelity of different physical models, such as moment or hybrid models. We discuss an example of this kind in an appendix. Of course, the methodology that we have developed can also be readily extended to a suite of benchmarks with coverage of a wider range of physical and chemical phenomena
Experimental benchmark of kinetic simulations of capacitively coupled plasmas in molecular gases
International audienceWe discuss the origin of uncertainties in the results of numerical simulations of low-temperature plasma sources, focusing on capacitively coupled plasmas. These sources can be operated in various gases/gas mixtures, over a wide domain of excitation frequency, voltage, and gas pressure. At low pressures, the non-equilibrium character of the charged particle transport prevails and particle-based simulations become the primary tools for their numerical description. The particle-in-cell method, complemented with Monte Carlo type description of collision processes, is a well-established approach for this purpose. Codes based on this technique have been developed by several authors/groups, and have been benchmarked with each other in some cases. Such benchmarking demonstrates the correctness of the codes, but the underlying physical model remains unvalidated. This is a key point, as this model should ideally account for all important plasma chemical reactions as well as for the plasma-surface interaction via including specific surface reaction coefficients (electron yields, sticking coefficients, etc). In order to test the models rigorously, comparison with experimental ?benchmark data? is necessary. Examples will be given regarding the studies of electron power absorption modes in O 2 , and CF 4 ?Ar discharges, as well as on the effect of modifications of the parameters of certain elementary processes on the computed discharge characteristics in O 2 capacitively coupled plasmas
The effect of the driving frequency on the confinement of beam electrons and plasma density in low pressure capacitive discharges
The effect of changing the driving frequency on the plasma density and the
electron dynamics in a capacitive radio-frequency argon plasma operated at low
pressures of a few Pa is investigated by Particle in Cell/Monte Carlo
Collisions simulations and analytical modeling. In contrast to previous
assumptions the plasma density does not follow a quadratic dependence on the
driving frequency in this non-local collisionless regime. Instead, a step-like
increase at a distinct driving frequency is observed. Based on the analytical
power balance model, in combination with a detailed analysis of the electron
kinetics, the density jump is found to be caused by an electron heating mode
transition from the classical -mode into a low density resonant heating
mode characterized by the generation of two energetic electron beams at each
electrode per sheath expansion phase. These electron beams propagate through
the bulk without collisions and interact with the opposing sheath. In the low
density mode, the second beam is found to hit the opposing sheath during its
collapse. Consequently, a high number of energetic electrons is lost at the
electrodes resulting in a poor confinement of beam electrons in contrast to the
classical -mode observed at higher driving frequencies. Based on the
analytical model this modulated confinement quality and the related modulation
of the energy lost per electron lost at the electrodes is demonstrated to cause
the step-like change of the plasma density. The effects of a variation of the
electrode gap, the neutral gas pressure, the electron sticking and secondary
electron emission coefficients of the electrodes on this step-like increase of
the plasma density are analyzed based on the simulation results
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