Simulation of capacitively coupled RF discharge in argon

In this work, the axial profiles of the density of electrons and positive ions, the mean electron energy, the electric field strength, and the potential were obtained, both on average over the period and in dynamics. It was shown that argon discharges are dominated by ionization by electrons that ga...

Full description

Saved in:
Bibliographic Details
Published in:Problems of Atomic Science and Technology
Date:2023
Main Authors: Lisovskiy, V., Dudin, S., Shakhnazarian, A., Platonov, P., Yegorenkov, V.
Format: Article
Language:English
Published: Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2023
Subjects:
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/196190
Tags: Add Tag
No Tags, Be the first to tag this record!
Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Simulation of capacitively coupled RF discharge in argon / V. Lisovskiy, S. Dudin, A. Shakhnazarian, P. Platonov, V. Yegorenkov // Problems of Atomic Science and Technology. — 2023. — № 4. — С. 129-133. — Бібліогр.: 21 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
_version_ 1859648956966895616
author Lisovskiy, V.
Dudin, S.
Shakhnazarian, A.
Platonov, P.
Yegorenkov, V.
author_facet Lisovskiy, V.
Dudin, S.
Shakhnazarian, A.
Platonov, P.
Yegorenkov, V.
citation_txt Simulation of capacitively coupled RF discharge in argon / V. Lisovskiy, S. Dudin, A. Shakhnazarian, P. Platonov, V. Yegorenkov // Problems of Atomic Science and Technology. — 2023. — № 4. — С. 129-133. — Бібліогр.: 21 назв. — англ.
collection DSpace DC
container_title Problems of Atomic Science and Technology
description In this work, the axial profiles of the density of electrons and positive ions, the mean electron energy, the electric field strength, and the potential were obtained, both on average over the period and in dynamics. It was shown that argon discharges are dominated by ionization by electrons that gained energy by stochastic heating during the expansion of near-electrode sheaths. This ionization occurs in two pulses during one RF period. At low RF voltage between the electrodes, the role of Ohmic heating of electrons in the electric field in a quasi-neutral plasma increases, but the contribution of stochastic heating remains dominant. The time-averaged plasma potential was found to increase non-linearly with the RF voltage between the electrodes Urf. It is shown that at low Urf values (when the RF voltage approaches the discharge extinction curve), the average potential Φ can reach Urf due to the axial redistribution of the instantaneous potential in the gap between Отримано осьові профілі густини електронів та позитивних іонів, середньої енергії електронів, напруженості електричного поля та потенціалу як у середньому за період, так й їхню динаміку. Показано, що в розряді в аргоні переважає іонізація електронами, які набули енергії під час стохастичного нагріву при розши ренні приелектродних шарів. Ця іонізація відбувається двома імпульсами протягом одного ВЧ-періоду. При низькій ВЧ-напрузі між електродами зростає роль омічного нагріву електронів у електричному полі в квазінейтральній плазмі, але внесок стохастичного нагріву залишається домінуючим. З’ясовано, що середній за часом потенціал плазми Φ нелінійно зростає з ВЧ-напругою Urf між електродами. Показано, що при низьких значеннях Urf (при наближенні ВЧ-напругою до кривої згасання розряду) середній потенціал Φ може досягати Urf завдяки осьовому перерозподілу миттєвого потенціалу в проміжку між електродами.
first_indexed 2025-12-07T13:31:03Z
format Article
fulltext ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. № 4(146) 129 https://doi.org/10.46813/2023-146-129 SIMULATION OF CAPACITIVELY COUPLED RF DISCHARGE IN ARGON V. Lisovskiy, S. Dudin, A. Shakhnazarian, P. Platonov, V. Yegorenkov V.N. Karazin Kharkiv National University, Kharkiv, Ukraine E-mail: lisovskiy@yahoo.com In this work, the axial profiles of the density of electrons and positive ions, the mean electron energy, the electric field strength, and the potential were obtained, both on average over the period and in dynamics. It was shown that argon discharges are dominated by ionization by electrons that gained energy by stochastic heating during the ex- pansion of near-electrode sheaths. This ionization occurs in two pulses during one RF period. At low RF voltage between the electrodes, the role of Ohmic heating of electrons in the electric field in a quasi-neutral plasma increas- es, but the contribution of stochastic heating remains dominant. The time-averaged plasma potential was found to increase non-linearly with the RF voltage between the electrodes Urf. It is shown that at low Urf values (when the RF voltage approaches the discharge extinction curve), the average potential F can reach Urf due to the axial redistribu- tion of the instantaneous potential in the gap between the electrodes. PACS: 52.80.Hc INTRODUCTION Radio-frequency capacitive discharge in gases is widely used in many plasma technologies. With its help, various materials are sputtered, various films are depos- ited (both metal and dielectric), semiconductor materials are etched during the production of microchips, gas dis- charge lasers are pumped, and the surfaces of techno- logical and research chambers are cleaned (from centi- meter size to the scale of large tokamaks and stellara- tors), etc. Therefore, considerable attention is paid to both experimental and theoretical research of its proper- ties. Usually, either the external parameters of the RF capacitive discharge (for example, the current-voltage characteristics) or the time-averaged plasma parameters are measured experimentally [1 - 7]. But in order to understand exactly how the processes of birth and loss of charged particles take place, and what the dynamics of the internal parameters of the plasma look like, nu- merical modeling is frequently used [2, 7 - 9]. The purpose of this work was to carry out numerical modeling of the parameters of a radio-frequency capaci- tive discharge in argon using the SIGLO-rf hydrody- namic code. Plasma parameters averaged over the RF period were determined, and their changes with time were investigated. The mechanisms of ionization, the time and place within the discharge, where and when they occur, have been clarified. 1. DESCRIPTION OF SIGLO-RF CODE SIGLO-rf is fluid code, which is the 1D user- friendly simulation software of capacitively coupled RF discharges. It was developed by JP Boeuf and LC Pitch- ford at the University of Toulouse and is based on the same physics as in [10, 11]. SIGLO-rf numerically solves the continuity, momen- tum, and energy equations for electrons, the discontinui- ty and momentum equations for positive ions, and Pois- son's equation for the electric field. In the axial profiles shown in the next section, the left electrode is grounded, and RF voltage Urf oscillating with a frequency of 13.56 MHz is applied to the right electrode. The distance between the electrodes is fixed and is 2 cm. The gas pressure is 1 Torr. Calculations were made for argon. Accordingly, the necessary information was entered into the file with gas parameters. The dependences of electron mobility, aver- age electron energy, and ionization coefficient (the first Townsend coefficient a/p) on the reduced electric field E/p for gas temperature T = 300 K were preliminary cal- culated using the Bolsig+ code [12]. At the same time, cross-sections of electron collisions with argon atoms were used, given in the LXCat database (www.lxcat.net) [13], where cross-sections from the Phelps set [14] were selected. In addition, for argon, the mobilities of positive Ar+ ions in Ar, given in the review [15], were used. Ion- electron recombination was neglected due to the very small value of the coefficient for this process [16]. 2. EXPERIMENTAL RESULTS RF capacitive discharge consists of three regions, a quasi-neutral plasma and two sheaths of space charge, which are actually transition parts between the plasma and the electrode walls limiting it. Quasi-neutral plasma and near-electrode sheaths differ greatly in terms of parameters. At the same time, it is necessary to consider not only the average parameters of the discharge over the RF period but also to take into account that these parameters also change over time due to the harmonic change of the RF voltage on the right (potential) elec- trode. Therefore, below we will present the average pro- files of plasma parameters for the RF period, and for some of them, we will find out their dynamics. The time-averaged axial profiles of electron density Ne and positive ion density Np are shown in Fig. 1. It can be seen from the figure that the quasi-neutrality condi- tion is fulfilled in the plasma volume, that is, the densi- ties of electrons and positive ions are equal to each oth- er, and the corresponding parts of the curves in the fig- ure coincide. The near-electrode sheaths are dominated by posi- tive ions, and the electron density here is much lower than the ion density. That is, here we observe a violation of the condition of quasi-neutrality. From the plasma to the boundary of the sheaths, positive ions and electrons move in the mode of ambipolar diffusion, so their densi- ties in the plasma are the same. 130 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. № 4(146) Fig. 1. Time-averaged axial profiles of the density of electrons and positive ions But after reaching the limit of the plasma region, positive ions are accelerated to the electrodes by a strong electric field averaged over time, the voltage of which increases approximately according to a linear law when approaching the electrodes (Fig. 2). In a quasi- neutral plasma, this field is small (approximately units V/cm and increases to 20 V/cm at the boundary of the sheaths) but it is zero only in the center of the discharge gap. In the considered case, the average electric field strength near the electrode surface approaches 1400 V/cm. As a result of the oscillations of the electrons in the instantaneous radio-frequency electric field, some of them enter the electrodes. Therefore, there are more positive ions than electrons in the discharge gap. Thanks to this, the plasma has a positive potential in relation to the electrodes. Let us recall that the left electrode is grounded, and the potential of the right electrode chang- es according to the harmonic law and is also zero on average during the RF period. Therefore, positive ions are accelerated by this electric field averaged over the RF period from the plasma to the electrodes, due to which the RF capacitive discharge has found wide ap- plication in many plasma technologies. Fig. 2. Time-averaged axial profiles of potential and electric field strength The value of the average plasma potential depends on the RF voltage applied to the electrodes, the pressure, and the type of gas. For argon gas at 1 Torr pressure and 500 V RF voltage, the average plasma potential (for the center of the discharge) is about 230 V (see Fig. 2). Now let's consider the time-averaged axial profiles of the mean electron energy, which are shown in Fig. 3. From the figure, one can see that the mean electron en- ergy in the plasma reaches up to approximately 6 eV, however, in the space charge sheaths, it quickly de- creases down to 1 eV near the electrodes. But here, it should be taken into account that electrons alternately fill the near-electrode sheaths, and during certain parts of the RF period they are not present near the electrodes at all, and, accordingly, their average energy is consid- ered zero in this case. Fig. 3 also shows the time-averaged axial profile of the ionization rate. From its unit of measurement, cm -3 s -1 , it is clear that this value is equal to the product of the electron density and the ionization frequency ni·Ne and is the term of the electron and ion balance equation, which describes the rate of ionization birth of charged particles in 1 cm 3 per 1 s at a certain point in the discharge gap. The maximum values of the ioniza- tion rate appear near the boundaries of the near- electrode sheaths and indicate the presence of enhanced electron heating in these areas. A much lower ionization rate is observed in the central part of the discharge gap. We will consider the processes of electron heating be- low. Now let's pay attention to the time dependences of the axial profiles of the plasma parameters. First, let's consider the profiles of the plasma potential for several moments of time during one-half of the RF period (Fig. 4). At the initial moment, when the high-amplitude RF voltage is applied to the right electrode, almost the entire potential drop is concentrated on the left near- electrode sheaths, because the left electrode plays the role of an instantaneous cathode. In the left sheaths, the electric field strength is maximum, and the right sheaths has practically collapsed. A flow of electrons enters the right electrode, which is limited by a small voltage drop near the electrode. Fig. 3. Time-averaged axial profiles of average electron energy and ionization rate Fig. 4. Axial profiles of potential for different parts of RF period for voltage between the electrodes of 500 V ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. № 4(146) 131 Then, over time, the voltage drop on the left sheaths decreases with the simultaneous narrowing of the thick- ness of the left sheaths. At the right electrode, the volt- age decreases first to zero, and then further to a negative amplitude value. Throughout this half-period, the thick- ness of the right sheaths increases. This half-period ends with the reverse situation in relation to the initially con- sidered zero time moment, namely, the left near- electrode sheaths has collapsed, and the left electrode receives a flow of electrons (which is regulated by a small voltage drop near its surface). Fig. 5. Axial density profiles of positive ions and electrons for different parts of the period for RF voltage between electrodes of 500 V The dynamics of the electron density profile for the same moments of time are shown in Fig. 5. The positive ion density profile practically does not change with time, because the frequency of the RF field of 13.56 MHz applied to the electrodes is too high for them. Ions are heavy inert particles, in a discharge they react only to constant (or time-averaged) and low- frequency (less than 1 MHz) electric fields. Light elec- trons, in the presence of sufficiently frequent collisions with gas molecules, are able to sense changes in the electric field almost without inertia. At the initial mo- ment (t/T = 0), electrons are pushed out of the left near- electrode sheaths and, having filled the right sheaths, enter the right electrode (instantaneous anode). At the same time, we note that the electron density profile in the right sheaths practically coincides with the profile of the density of positive ions, with the exception of a nar- row region near the very surface of the right electrode. That is, it can be said that quasi-neutral plasma almost completely fills the right sheaths at the initial moment of time. Later, as shown in Fig. 4, the voltage on the right electrode decreases. The plasma potential also de- creases, but more slowly than the voltage on the right electrode, so the voltage drop on the right sheaths in- creases. This leads to the fact that the thickness of the right sheaths increases. Electrons, which initially almost completely filled the right sheaths, are now pushed from the right electrode back into the plasma because the potential of this electrode is now more negative in rela- tion to the plasma. This ejection increases the electron energy and is called stochastic heating [17 - 20]. This stochastic heating led to an increase in the ionization rate near the boundaries of the near-electrode sheaths on the time-averaged axial profiles (see Fig. 3). Fig. 6 shows in which places and when exactly sto- chastic heating occurs in the RF capacitive discharge. The first peak of the ionization rate (it is located on the right in the figure) occurs when electrons are pushed out of the right near-electrode sheaths. The stochastic heat- ing itself affects the ionization rate both in the right sheaths and outside it in the region of quasi-neutral plasma near the sheaths boundary. At the same time, electrons fill the left sheaths. After the potential on the right electrode reaches the maximum negative value, the voltage on the left sheaths begins to increase. This in- crease in voltage pushes electrons out of the left sheaths, and as a result of stochastic heating, we observe a spike in the ionization rate, which is on the left in Fig. 6. Fig. 6. Spatio-temporal dependence of ionization rate for RF voltage between electrodes of 500 V Let's note one more important feature of RF capaci- tive discharge, which occurs in any gas, namely, the balance of positive and negative charges arriving on the surface of each of the electrodes. Fig. 7 shows the cur- rent densities of positive ions and electrons that reach the surface of the left electrode during one RF period. It can be seen from the figure that the flow of positive ions is maximal at the beginning and at the end of the RF period (corresponding to the amplitude of positive RF voltage on the right electrode). Fig. 7. Time dependence of the current density of positive ions and electrons on the left electrode for RF voltage between the electrodes of 500 V In the middle of the period, the ion flow decreases, but not to zero. That is, during the entire RF period, positive ions arrive on the surface of the left electrode. Electrons also arrive at the same electrode but in the form of a short burst with a maximum when the RF voltage on the right electrode reaches the negative am- plitude value. Therefore, for the stable burning of the discharge, it is necessary that the balance of positive and negative charges be fulfilled, that is, the number of elec- trons that entered the left electrode during the burst
id nasplib_isofts_kiev_ua-123456789-196190
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1562-6016
language English
last_indexed 2025-12-07T13:31:03Z
publishDate 2023
publisher Національний науковий центр «Харківський фізико-технічний інститут» НАН України
record_format dspace
spelling Lisovskiy, V.
Dudin, S.
Shakhnazarian, A.
Platonov, P.
Yegorenkov, V.
2023-12-11T12:35:45Z
2023-12-11T12:35:45Z
2023
Simulation of capacitively coupled RF discharge in argon / V. Lisovskiy, S. Dudin, A. Shakhnazarian, P. Platonov, V. Yegorenkov // Problems of Atomic Science and Technology. — 2023. — № 4. — С. 129-133. — Бібліогр.: 21 назв. — англ.
1562-6016
PACS: 52.80.Hc
DOI: https://doi.org/10.46813/2023-146-129
https://nasplib.isofts.kiev.ua/handle/123456789/196190
In this work, the axial profiles of the density of electrons and positive ions, the mean electron energy, the electric field strength, and the potential were obtained, both on average over the period and in dynamics. It was shown that argon discharges are dominated by ionization by electrons that gained energy by stochastic heating during the expansion of near-electrode sheaths. This ionization occurs in two pulses during one RF period. At low RF voltage between the electrodes, the role of Ohmic heating of electrons in the electric field in a quasi-neutral plasma increases, but the contribution of stochastic heating remains dominant. The time-averaged plasma potential was found to increase non-linearly with the RF voltage between the electrodes Urf. It is shown that at low Urf values (when the RF voltage approaches the discharge extinction curve), the average potential Φ can reach Urf due to the axial redistribution of the instantaneous potential in the gap between
Отримано осьові профілі густини електронів та позитивних іонів, середньої енергії електронів, напруженості електричного поля та потенціалу як у середньому за період, так й їхню динаміку. Показано, що в розряді в аргоні переважає іонізація електронами, які набули енергії під час стохастичного нагріву при розши ренні приелектродних шарів. Ця іонізація відбувається двома імпульсами протягом одного ВЧ-періоду. При низькій ВЧ-напрузі між електродами зростає роль омічного нагріву електронів у електричному полі в квазінейтральній плазмі, але внесок стохастичного нагріву залишається домінуючим. З’ясовано, що середній за часом потенціал плазми Φ нелінійно зростає з ВЧ-напругою Urf між електродами. Показано, що при низьких значеннях Urf (при наближенні ВЧ-напругою до кривої згасання розряду) середній потенціал Φ може досягати Urf завдяки осьовому перерозподілу миттєвого потенціалу в проміжку між електродами.
This work was supported by the National Research Foundation of Ukraine in the framework of the project 2021.01/0204.
en
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
Problems of Atomic Science and Technology
Gas discharge, plasma-beam discharge and their applications
Simulation of capacitively coupled RF discharge in argon
Моделювання ВЧ ємнісного розряду в аргоні
Article
published earlier
spellingShingle Simulation of capacitively coupled RF discharge in argon
Lisovskiy, V.
Dudin, S.
Shakhnazarian, A.
Platonov, P.
Yegorenkov, V.
Gas discharge, plasma-beam discharge and their applications
title Simulation of capacitively coupled RF discharge in argon
title_alt Моделювання ВЧ ємнісного розряду в аргоні
title_full Simulation of capacitively coupled RF discharge in argon
title_fullStr Simulation of capacitively coupled RF discharge in argon
title_full_unstemmed Simulation of capacitively coupled RF discharge in argon
title_short Simulation of capacitively coupled RF discharge in argon
title_sort simulation of capacitively coupled rf discharge in argon
topic Gas discharge, plasma-beam discharge and their applications
topic_facet Gas discharge, plasma-beam discharge and their applications
url https://nasplib.isofts.kiev.ua/handle/123456789/196190
work_keys_str_mv AT lisovskiyv simulationofcapacitivelycoupledrfdischargeinargon
AT dudins simulationofcapacitivelycoupledrfdischargeinargon
AT shakhnazariana simulationofcapacitivelycoupledrfdischargeinargon
AT platonovp simulationofcapacitivelycoupledrfdischargeinargon
AT yegorenkovv simulationofcapacitivelycoupledrfdischargeinargon
AT lisovskiyv modelûvannâvčêmnísnogorozrâduvargoní
AT dudins modelûvannâvčêmnísnogorozrâduvargoní
AT shakhnazariana modelûvannâvčêmnísnogorozrâduvargoní
AT platonovp modelûvannâvčêmnísnogorozrâduvargoní
AT yegorenkovv modelûvannâvčêmnísnogorozrâduvargoní