Simulation of Low-Pressure Inductively Coupled Plasma with Displacement Potential and Gas Flow

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Abstract

The dependence of the parameters of low-pressure inductively coupled argon plasma (13.3–113 Pa) and field frequency of 13.5٦ MHz at the coil on the potential applied to the electrode and on gas flow rate up to 4000 sccm is numerically studied. The model is developed in the COMSOL Multiphysics environment and verified with experimental data, as well as over the Knudsen number. As a result of a numerical experiment, it is revealed as follows: when the displacement potential increases linearly, the density of charged particles increases exponentially and a slight increase in the electron temperature is observed; when the gas flow rate increases linearly, the density of charged particles increases exponentially, the density of excited states has an extremum at 2000 sccm, and the gas and electron temperature increases linearly.

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About the authors

A. Yu. Shemakhin

Kazan (Volga Region) Federal University

Author for correspondence.
Email: shemakhin@gmail.com
Russian Federation, Kazan

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Supplementary files

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2. Fig. 1. Schematic of the setup, boundary markings and geometry of the computational domain of the two-dimensional axisymmetric model. The dimensions are given in mm, argon supply is from the lower end of the tube, constant pressure is set at the upper end (boundary condition of gas pumping). The violet lines schematically depict a plasma clot

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3. Fig. 2. Block diagram of the numerical model. The basic equations are given in blocks, each block takes a certain set of variables as input and outputs the results of calculations in the form of the following variables. The arrows indicate transitions from one block of equations to another

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4. Fig. 3. Distribution area (a), distribution of the potential field strength Ep,z along the discharge tube at different values of the bias potential φ at the upper boundary (b)

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5. Fig. 4. Distribution region (a), dependence of the electron temperature at the discharge tube outlet on the bias potential φ at the upper boundary (b)

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6. Fig. 5. Spatial distribution of mean electron energy at gas flow rate G = 2000 sccm (a), G = 3000 sccm (b), G = 8000 sccm (c)

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7. Fig. 6. Debye number to discharge chamber diameter ratio at gas flow rate G = 2000 sccm (a), G = 3000 sccm (b), G = 8000 sccm (c)

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8. Fig. 7. Knudsen number Kn in the flowless regime at p = 13 Pa (a), p = 26 Pa (b), p = 53 Pa (c)

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9. Fig. 8. Knudsen number Kn at p = 9.65 Pa (a), p = 53 Pa (b) and a flow rate of 8000 sccm

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10. Fig. 9. Spatial distribution of pressure p (a), velocity modulus v (b) and gas temperature (c) at gas flow rate G = 2000 sccm

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11. Fig. 10. Distribution region (a); dependence of the concentration of electrons, excited states and ions at the discharge tube outlet ne,m,i:outlet on the gas flow rate G (b). The graphs of the concentration of electrons ne and ions ni are superimposed on each other, so that the dependence of ni is poorly visible in the figure; the temperature of electrons and the temperature of neutral particles as a function of the gas flow rate G (c)

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12. Fig. 11. Distribution area (a); dependence of the concentrations of electrons nez (b), excited states nmz (c) and neutral argon atoms niz (d) along the discharge tube (a) on the gas flow rate G

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