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

Schüngel, Edmund; Schulze, Julian

doi:10.1002/ppap.201600117

Cited by 15 publications

(26 citation statements)

References 62 publications

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“…By computing ion trajectories, the energy of the ions upon the arrival at the electrodes as well as the ion transit time can be obtained for ions starting from arbitrary positions. Based on these, the structure of the IFEDFs was successfully explained in [72] for various discharge conditions. Here, we make use of the same model and carry out calculations to explain the characteristic changes of the IFEDFs as an effect of varying φ 2 in classical DF discharges operated in oxygen.…”

Section: Classical Dual-frequency Excitationmentioning

confidence: 99%

Ion energy and angular distributions in low-pressure capacitive oxygen RF discharges driven by tailored voltage waveforms

Derzsi

Vass

Schulze

et al. 2018

Plasma Sources Sci. Technol.

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We investigate the energy and angular distributions of the ions reaching the electrodes in low-pressure, capacitively coupled oxygen radio-frequency discharges. These distributions, as well as the possibilities of the independent control of the ion flux and the ion energy are analysed for different types of excitation: single-and classical dual-frequency, as well as valleys-and sawtooth-type waveforms. The studies are based on kinetic, particle-based simulations that reveal the physics of these discharges in great details. The conditions cover weakly collisional to highly collisional domains of ion transport via the electrode sheaths. Analytical models are also applied to understand the features of the energy and angular distribution functions.

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Section: Classical Dual-frequency Excitationmentioning

confidence: 99%

Ion energy and angular distributions in low-pressure capacitive oxygen RF discharges driven by tailored voltage waveforms

Derzsi

Vass

Schulze

et al. 2018

Plasma Sources Sci. Technol.

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“…These observations hold for f HF = 20 MHz as well, the mean energy of the ions increases only slightly with V LF and the flux-energy distributions shown in figure 14(b) are rather similar at any V LF , except for the disappearance of the peak created by charge transfer collisions [138]. We recall that the origin of these peaks is that ions that have undergone charge transfer collisions at times of a low sheath voltage can accumulate in certain spatial regions and get accelerated again when the sheath voltage reaches an appreciable value [139]. The periodicity of the decay and rise of the sheath electric field under single-frequency excitation can this way synchronize the motion of many ions, forming peaks in F (ε).…”

Section: Case 1: P = 20 Pamentioning

confidence: 76%

“…The IFEDF exhibits a series of peaks, characteristics for ion transport through the sheaths in the presence of charge-exchange collisions [138,139].…”

Section: Quantitymentioning

confidence: 99%

eduPIC: an introductory particle based code for radio-frequency plasma simulation

Donko,

Derzsi,

Vass

et al. 2021

Preprint

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Particle based simulations are indispensable tools for numerical studies of charged particle swarms and low-temperature plasma sources. The main advantage of such approaches is that they do not require any assumptions regarding the shape of the particle Velocity/Energy Distribution Function (VDF/EDF), but provide these basic quantities of kinetic theory as a result of the computations. Additionally, they can provide, e.g., transport coefficients, under arbitrary time and space dependence of the electric/magnetic fields. For the self-consistent description of various plasma sources operated in the low-pressure (nonlocal, kinetic) regime, the Particle-In-Cell simulation approach, combined with the Monte Carlo treatment of collision processes (PIC/MCC), has become an important tool during the past decades. In particular, for Radio-Frequency (RF) Capacitively Coupled Plasma (CCP) systems PIC/MCC is perhaps the primary simulation tool these days. This approach is able to describe discharges over a wide range of operating conditions, and has largely contributed to the understanding of the physics of CCPs operating in various gases and their mixtures, in chambers with simple and complicated geometries, driven by single-and multi-frequency (tailored) waveforms. PIC/MCC simulation codes have been developed and maintained by many research groups, some of these codes are available to the community as freeware resources. While this computational approach has already been present for a number of decades, the rapid evolution of the computing infrastructure makes it increasingly more popular and accessible, as simulations of simple systems can be executed now on personal computers or laptops. During the past few years we have experienced an increasing interest in lectures and courses dealing with the basics of particle simulations, including the PIC/MCC technique. In a response to this, this paper (i) provides a tutorial on the physical basis and the algorithms of the PIC/MCC technique and (ii) presents a basic (spatially one-dimensional) electrostatic PIC/MCC simulation code, whose source is made freely available in various programming languages. We share the code in C/C++ versions, as well as in a version written in Rust, which is a rapidly emerging computational language. Our code intends to be a "starting tool" for those who are interested in learning the details of the PIC/MCC technique and would like to develop the "skeleton" code further, for their research purposes. Following the description of the physical basis and the algorithms used in the code, a few examples of results obtained with this code for single-and dual-frequency CCPs in argon are also given.

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“…Low‐pressure capacitively coupled plasma (CCP) has been widely used in a variety of plasma processing applications in semiconductor industry, such as etching, deposition, and many other surface treatment technics . CCP is commonly generated by applying radio‐frequency (rf) voltage or current to electrodes immersed in plasma, which creates high voltage capacitive sheath between the electrode and plasma bulk.…”

Section: Introductionmentioning

confidence: 99%

On the role of secondary electron emission in capacitively coupled radio‐frequency plasma sheath: A theoretical ground

Sun

et al. 2019

Plasma Processes & Polymers

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We propose a theoretical ground for emissive capacitively coupled radio-frequency (rf) plasma sheath under low pressure. The rf sheath is assumed to be collisionless and oscillates with external source. A known sinusoidal voltage instead of current is taken as prerequisite to derive sheath dynamics. Kinetic studies are performed to determine mean wall potential as a function of secondary emission coefficient and applied voltage amplitude, with which the complete mean direct current sheath is resolved. Analytical analyses under homogeneous model and numerical analyses under inhomogeneous model are conducted to deduce real-time sheath properties including space potential, sheath capacitance, and stochastic heating. Obtained results are validated by a continuum kinetic simulation without ionization. The influences of collisionality and ionization induced by secondary electrons are elucidated with a particle-in-cell simulation, which further formalizes proposed theories and inspires future works. K E Y W O R D S capacitively coupled plasma, kinetic theory, modeling, secondary electron emission, surfaces

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

Cited by 15 publications

References 62 publications

Ion energy and angular distributions in low-pressure capacitive oxygen RF discharges driven by tailored voltage waveforms

Ion energy and angular distributions in low-pressure capacitive oxygen RF discharges driven by tailored voltage waveforms

eduPIC: an introductory particle based code for radio-frequency plasma simulation

On the role of secondary electron emission in capacitively coupled radio‐frequency plasma sheath: A theoretical ground

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