Home Search Collections Journals About Contact us My IOPscience Simulation of rarefied low pressure RF plasma flow around the sample This content has been downloaded from IOPscience Please scroll down to see the full text 2017 J Phys.: Conf Ser 789 012071 (http://iopscience.iop.org/1742-6596/789/1/012071) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 80.82.77.83 This content was downloaded on 01/03/2017 at 18:36 Please note that terms and conditions apply You may also be interested in: Measurement of Plasma Clotting Using Shear Horizontal Surface Acoustic Wave Sensor Tatsuya Nagayama, Jun Kondoh, Tomoko Oonishi et al Finite-element modelling of superconductors in over-critical regime with temperature dependent resistivity J Duron, F Grilli, L Antognazza et al Simulations of ion velocity distribution functions taking into account both elastic and charge exchange collisions Huihui Wang, Vladimir S Sukhomlinov, Igor D 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rarefied low pressure RF plasma flow around the sample V S Zheltukhin1, A Yu Shemakhin2 Kazan National Research Technological University, Kazan, Russia Kazan Federal University, Kazan, Russia Abstract The paper describes a mathematical model of the flow of radio frequency plasma at low pressure The hybrid mathematical model includes the Boltzmann equation for the neutral component of the RF plasma, the continuity and the thermal equations for the charged component Initial and boundary conditions for the corresponding equations are described The electron temperature in the calculations is 1-4 eV, atoms temperature in the plasma clot is (3-4) • 103 K, in the plasma jet is (3.2-10) • 102 K, the degree of ionization is 10-7-10-5, electron density is 1015-1019 m-3 For calculations plasma parameters is developed soft package on C++ program language, that uses the OpenFOAM library package Simulations for the vacuum chamber in the presence of a sample and the free jet flow were carried out Introduction RF plasma discharges at low pressures (P = 13, − 133 Pa) is used successfully for the modification of various materials: dielectric, conducting, semiconducting The plasma has the following properties: ionization degree is 10-7–10-5, electron density ne=1015–1019 м-3, electron temperature Te=1–4 эВ, temperature of atoms and ions in the plasma bunch Ta=(3-4)·103 К, in a plasma stream Ta=(3.210)·102 K [1,2,3,9] Mathematical model of low pressure RF plasmas stream The hybrid mathematical model, combining a kinetic model for the carrier gas and the continuous model for charged particles is developed The model includes: 1) the Boltzmann's transport equation for neutral atoms: f f f c F S ( f ), t r c (1) f( c, r, 0) f0 ( c, r), F -(1/ m a ) grad WT 2) the equation of the electron continuity: n e t ne div(Da gradn e va n e ) i n e , inlet neinlet , ne outlet 0, ne walls 0, (2) ne body 0, n e t 0 ne 3) the equation of the electron heating: Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI Published under licence by IOP Publishing Ltd IOP Publishing doi:10.1088/1742-6596/789/1/012071 LTP2016 IOP Conf Series: Journal of Physics: Conf Series 789 (2017) 012071 cp e Te T e div ( e grad T e kB neT e ve ) kB cn e (T e T a ) E i ne E I , t 2 inlet T einlet , T e outlet T eroom , T e walls T eroom , T e n 0, T e t 0 T e 0, (3) body 4) the equation of the metastable atoms: n m t nm div (Dm grad(n m )) Rn m n e , inlet ,outlet ,sides (4) 0 and closing equations: pa n a kBT a , va ( r, t ) c f (c, r, t )dc, ve va (Da / n e )grad n e (5) Here c and r are vectors of velocity and coordinates of atoms, f(c, r, t) are function of distribution of neutral atoms by velocities, f0 – Maxwell function of distribution by velocities, S(f) is collisions ~ integral, F is force, which influence on neutral atoms in elastic collision process, WT is energy, which transferred to atoms in elastic collision process , ne is density of electrons, Da is ambipolar diffusion coefficient, l e is coefficient of thermal conductivity of electron gas, ni is ionization frequency , c p is heat capacity of the electron gas, R is rate coefficient of step-wise ionization, n c is the frequency of elastic collisions of electrons with atoms and ions, s is plasma conductivity, E is the electric field vector, E=|E|, Ei is ionization potential, kB is Boltzmann constant, d = me /2ma, ma is atom mass, me is electron mass, Rvk is radius of the cylindrical vacuum chamber, Lvk is length, Rrk is the radius of the plasma torch outlet, subscripts inlet, outlet, body, walls devoted parameter value on inlet and outlet of the chamber, on the walls of the sample, and the vacuum chamber, respectively, W T = т E cdV dt , dV is volume element, E c = k n T T a B c e e is energy of elastic collisions transport Coefficients Da, n i , l e are functions of electron temperature Te Numerical method and program Bird’s method [6] is modified by introducing the area heat source power WT A three-step iterative process is constructed for solving the problem (1) - (5) Software package that allows to find the spatial distribution of the main plasma flow characteristics is developed OpenFOAM [10] library environment is used by the software program under the Linux operating system Calculations of low pressure RF plasma flow characteristics The gas-dynamic characteristics of low pressure RF plasma undisturbed flow as well as stream with overflowing sample in the vacuum chamber of Rvk=0,2 m, Lvk=0,5 m and Rgk=0,012 m, on the center of the base plate is carried out A cylindrical sample of radius Rb=0,03 m and a height Lb=0.02 m located in the plasma jet at a distance Ltb=0,02 m Flow input parameters are the following: the plasma forming gas is argon, gas flow rate G=0,12–0,24 g/s, pressure Pinlet = 35–85 Pa, the temperature T inlet = 400–600 K, the degree of ionization δi=10-4 The initial pressure in the vacuum chamber LTP2016 IOP Conf Series: Journal of Physics: Conf Series 789 (2017) 012071 IOP Publishing doi:10.1088/1742-6596/789/1/012071 P0 =3,5–8,5 Pa Distributions of temperature, velocity, and pressure of carrier gas as well as electron temperature and density are obtained Figure Pressure (left side) and neutral’s velocity (right side) distributions Figure Electron density (left side) and neutral’s temperature (right side) distributions Figure illustrates the velocity and pressure contour lines of neutral gas It can be noted that the pressure increases near the sample because of stream stagnation Pressure is straightening around 30 Pa in the area behind the sample Figure shows electron density and temperature of carrier gas contour lines The maximum value of electron density equal to 9·1017 1/m3 in the region of the inlet hole The density goes down to zero near the boundaries, because of electron-ion recombination Overheating of neutral atoms is found on the jet edge The temperature maximum is 650 - 670 K in this area The reason is abrupt deceleration of stream atoms on statical atoms in chamber Neuman’s conditions is laid on the sample surface and LTP2016 IOP Conf Series: Journal of Physics: Conf Series 789 (2017) 012071 IOP Publishing doi:10.1088/1742-6596/789/1/012071 thus the temperature behind the sample is about 370 K The temperature in the jet middle is in range of 550 – 650 K The calculations results are in satisfactory agreement with experimental data [1,5,9] Acknowledgments The work was supported by RFBR (grant № 16-31-60081, theoretical part) and the Ministry of Education of the Russian Federation (the basic part of the state task number 2196, the experimental part of the work) References [1] Abdullin I S, Zheltukhin V S, Sagbiyev I R and Shayekhov M F 2007 Modifikaciya Nanosloev v Vysokochastotnoj Plazme Ponizhennogo Davleniya (Kazan: Izdatel’stvo Kazanskogo Tekhnologicheskogo Universiteta) [2] Khubatkhuzin A A, Abdullin I S, Gatina E B, Zheltukhin V S and Shemakhin A Y 2012 Vestn Kazan Tekhnol Univ 15 72 [3] Khubatkhuzin A A, Abdullin I S, Bashkirtsev A A and Gatina E B 2012 Vestn Kazan Tekhnol Univ 15 71 [4] Dulov V G and Lukyanov G A 1984 Gazodinamika Processov Istecheniya (Moscow: Nauka) [5] Mitchner M and Kruger C H 1973 Partially Ionized Gases (New York: John Wiley and Sons) [6] Bird G A 1976 Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press: Oxford) [7] Zheltukhin V S and Shemakhin A Y 2011 Uch Zap Kazan Univ., Ser Fiz.-Mat Nauki 135 [8] Zheltukhin V S and Shemakhin A Y 2014 Math Model Comput Simul 101 [9] Abdullin I S, Zheltukhin V S, Khubatkhuzin A A and Shemakhin A Y 2014 Matematicheskoe Modelirovanie Gazodinamiki Strujnykh Techenij Vysokochastotnoj Plazmy Ponizhennogo Davleniya (Kazan: Izdatel’stvo Kazanskogo Tekhnologicheskogo Universiteta) [10] OpenFOAM OpenFOAM Foundation Free Open Source CFD 2011–2016 http://www.openfoam.org