Fluid modeling of electron heating in low-pressure, high-frequency capacitively coupled plasma discharges (original) (raw)
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We present an overview of models of low pressure, non-thermal gas discharges as commonly used in plasma processing. Significant progress has been made in the past decade towards the goal of a self-consistent model of the electrical properties of discharges, whether d.c., r.f. or microwave discharges. These models are based on solutions of the charged particle transport equations coupled with Poisson's equation for the electric field, and provide the space and time distribution of charged particle densities, current densities and electric field or potential. Some of the most sophisticated models also provide the electron and ion velocity distribution functions in the discharge at any point in space or time. It is now possible to describe reasonably accurately the physical properties of a discharge (including the plasma, the electrode regions and the walls) for two-dimensional cylindrical geometries, even for complex electrode configurations involving e.g. a hollow cathode or anode. A survey of the available models is presented here and we illustrate the current state ofthe art by results from one-and two-dimensional models ofd.c., r.f. and transient discharges.
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A self-consistent particle-in-cell simulation study is performed to investigate the effect of driving frequency on the electric field non-linearity, electron heating mechanism and electron energy distribution function (EEDF) in a low pressure symmetric capacitively coupled plasma (CCP) discharge at a constant electron plasma frequency. The driving frequency is varied from 27.12 MHz to 100 MHz for a discharge gap of 3.2 cm in argon at a gas pressure of 1 Pa. The simulation results provide insight of higher harmonic generations in a CCP system for a constant electron response time. The spatio-temporal evolution and spatial time averaged electron heating is presented for different driving frequencies. The simulation results predict that the electric field non-linearity increases with a rise in driving frequency along with a concurrent increase in higher harmonic contents. In addition to the electron heating and cooling near to the sheath edge a positive <J.E> is observed in to th...
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Numerical calculations by using a self-consistent model of the collisional sheath for the capacitively coupled RF discharge are our target. The results indicated that, at high pressure, the ohmic heating is usually the dominant heating mechanism in the discharge. The power dissipated in the sheath is calculated and compared with the measured data. Moreover, we indicated that, when the gas pressure is increased, the calculated dissipated power is decreased also while the measured input RF power is increased. Furthermore the sheath thickness of the capacitively coupled discharge is calculated and in the same order of the electron oscillation amplitude in the RF field, while the ionization mean free path is shorter than it.
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The Darwin approximation is investigated for its possible use in simulation of electromagnetic effects in large size, high frequency capacitively coupled discharges. The approximation is utilized within the framework of two different fluid models which are applied to typical cases showing pronounced standing wave and skin effects. With the first model it is demonstrated that Darwin approximation is valid for treatment of such effects in the range of parameters under consideration. The second approach, a reduced nonlinear Darwin approximation-based model, shows that the electromagnetic phenomena persist in a more realistic setting. The Darwin approximation offers a simple and efficient way of carrying out electromagnetic simulations as it removes the Courant condition plaguing explicit electromagnetic algorithms and can be implemented as a straightforward modification of electrostatic algorithms. The algorithm described here avoids iterative schemes needed for the divergence cleaning and represents a fast and efficient solver, which can be used in fluid and kinetic models for self-consistent description of technical plasmas exhibiting certain electromagnetic activity.
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ABSTRACT Benchmarking is generally accepted as an important element in demonstrating the correctness of computer simulations. In the modern sense, a benchmark is a computer simulation result that has evidence of correctness, is accompanied by estimates of relevant errors, and which can thus be used as a basis for judging the accuracy and efficiency of other codes. In this paper, we present four benchmark cases related to capacitively coupled discharges. These benchmarks prescribe all relevant physical and numerical parameters. We have simulated the benchmark conditions using five independently developed particle-in-cell codes. We show that the results of these simulations are statistically indistinguishable, within bounds of uncertainty that we define. We, therefore, claim that the results of these simulations represent strong benchmarks, which can be used as a basis for evaluating the accuracy of other codes. These other codes could include other approaches than particle-in-cell simulations, where benchmarking could examine not just implementation accuracy and efficiency, but also the fidelity of different physical models, such as moment or hybrid models. We discuss an example of this kind in the Appendix. Of course, the methodology that we have developed can also be readily extended to a suite of benchmarks with coverage of a wider range of physical and chemical phenomena. V C 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4775084\]
Physics of Plasmas, 2005
A numerical model for two-species plasma involving electrons and ions at pressure of 0.1 torr is presented here. The plasma-wall problem is modeled using one-and two-dimensional hydrodynamic equations coupled with Poisson equation. The model utilizes a finite-element algorithm to overcome the stiffness of the resulting plasma-wall equations. The one-dimensional result gives insight into the discharge characteristics including net charge density, electric field, and temporal space-charge sheath evolution. In two dimensions, the plasma formation over a flat plate is investigated for three different cases. The numerical algorithm is first benchmarked with published literature for plasma formed between symmetric electrodes in nitrogen gas. The characteristics of plasma are then analyzed for an infinitesimally thin electrode under dc and rf potentials in the presence of applied magnetic field using argon as a working gas. The magnetic field distorts the streamwise distribution because of a large y-momentum V ϫ B coupling. Finally, the shape effects of the insulator-conductor edge for an electrode with finite thickness have been compared using a 90°shoulder and a 45°chamfer. The 90°chamfer displays a stronger body force created due to plasma in the downward and forward directions.
On electron heating in a low pressure capacitively coupled oxygen discharge
Journal of Applied Physics, 2017
We use the one-dimensional object-oriented particle-in-cell Monte Carlo collision code oopd1 to explore the charged particle densities, the electronegativity, the electron energy probability function, and the electron heating mechanism in a single frequency capacitively coupled oxygen discharge, when the applied voltage amplitude is varied. We explore discharges operated at 10 mTorr, where electron heating within the plasma bulk (the electronegative core) dominates, and at 50 mTorr, where sheath heating dominates. At 10 mTorr, the discharge is operated in a combined drift-ambipolar and α-mode, and at 50 mTorr, it is operated in the pure α-mode. At 10 mTorr, the effective electron temperature is high and increases with increased driving voltage amplitude, while at 50 mTorr, the effective electron temperature is much lower, in particular, within the electronegative core, where it is roughly 0.2–0.3 eV, and varies only a little with the voltage amplitude.