Abstract
Radio frequency (RF) power coupling in inductively coupled plasmas is investigated numerically using a self-consistent fluid model. Hydrogen discharges are simulated at pressures from 0.3–10 Pa and at RF powers of around 1 kW. At the low excitation frequency of 1 MHz a high magnetic RF field of around 30 G is generated by the RF coil, meaning that discharges at low pressures are in the nonlinear skin effect regime. Therefore, a description of the RF power coupling by simple collisional Joule heating is not appropriate. Moreover, models that account for collisionless heating by means of a stochastic collision frequency or as diffusion of the RF current density (as is state of the art for discharges operated in the anomalous skin effect regime at higher frequencies of e.g. 13.56 MHz) are incapable of describing the RF power coupling in the nonlinear skin effect regime properly. This is due to their total neglect or simplified treatment of the RF Lorentz force. Instead, this work demonstrates that the RF power coupling mechanism for discharges operating at low RF in the nonlinear skin effect regime can be described by an electron momentum balance retaining the nonlinear RF Lorentz force as well as electron inertia and advection. The crucial role of the RF Lorentz force in generating the RF plasma current density and thus in shaping the plasma parameter profiles is validated successfully with experimentally obtained electrical and spatially resolved plasma parameters for pressures as low as 0.5 Pa. Below this pressure the results obtained from the model and the ones from the experiment diverge. Most likely this is caused by a sudden change in the electron distribution function at the lowest pressures.
Highlights
Introduction ce an us criInductively coupled plasmas (ICPs) operated in hydrogen are widely used in the plasma processing industry and in fusion science because of their favorable properties such as easy setting up and low maintenance requirements, as well as good control over the plasma parameters [1, 2].In these ICPs typically only a certain fraction of the Radio frequency (RF) generator output power- called RF power transfer efficiency η - is absorbed by the plasma
Coil geometry, gas pressure, and on the plasma parameters, in particular their spatial profiles; most importantly on those of the electrons, since they are directly heated by the electric component of the RF field
An approach for including collisionless heating in spatially resolved fluid models was proposed by Hagelaar [20], where diffusion of the RF current density caused by thermal motion of the electrons is described by an effective viscosity coefficient μeff that is incorporated in the RF component of the electron momentum balance
Summary
The measurement techniques for the RF power transfer efficiency are shown together with the lines of sight for the determination of the plasma parameters via a collisional radiative model [29, 30]. A helical copper RF coil with 5 windings is connected via a matching network to an RF generator that produces output powers of up to 1 kW at a radio frequency of 1 MHz. A constant inflow of 5 sccm of molecular hydrogen is maintained and by changing the speed of the vacuum pump the pressure can be varied between 0.3 and 10 Pa. The experimental setup is equipped with several diagnostic devices for determination of electrical and plasma parameters. By shifting the OES line-of-sight in the z direction, axial plasma parameter profiles are obtained, where each point of the profile is radially line-of-sight averaged
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