Multidimensional hydrodynamic plasma-wall model for collisional plasma discharges with and without magnetic-field effects (original) (raw)

Two-dimensional Fluid Model of DC and RF Plasma Discharges in Magnetic Field

36th AIAA Plasmadynamics and Lasers Conference, 2005

The hydrodynamic equations of continuity and momentum for electrons and ions along with the electrostatic field equation are solved numerically using a self-consistent finite-element algorithm in the low-pressure, high frequency regime. The plasma formation over a flat plate is investigated for three different cases. The twodimensional numerical algorithm is first benchmarked with published literature for plasma formed between symmetric electrodes in nitrogen gas. Discharge characteristics of plasma for an electrode-insulator configuration are then analyzed under steady and transient conditions using argon as a working gas. The effect of magnetic field on electric potential and charge difference is studied for an infinitesimally thin electrode. The magnetic field distorts the stream-wise distribution because of strong y-momentum vĂ—B coupling. Finally, the shape effects of insulator-conductor edge for an electrode of finite thickness have been compared using a 90 o shoulder and a 45 o chamfer. The 90 o chamfer displays a stronger body force created due to plasma in the downward and forward directions.

Hydrodynamic Model of Plasma-Sheath for RF Discharges with and without Collision

43rd AIAA Aerospace Sciences Meeting and Exhibit, 2005

We present a numerical model for two-species bounded plasma discharge with a time varying potential at 0.1 torr pressure in collisional and collisionless regimes. The plasma-wall problem is modeled using hydrodynamic equations coupled with the Poisson equation. The model is based on a robust finite element algorithm utilized to overcome the stiffness of the plasma-wall equations. Appropriate flux boundary conditions with directions are imposed at both electrodes. Typical discharge characteristics including electron gas flooding at electrode, sheath heating, sheath evolution with time and electric double layer are predicted. The spatial and temporal evolution of charge density, electric field and total current are documented. Numerical limitations are also highlighted from the theoretical derivation of algorithm amplification factor and phase velocity.

Two-dimensional fluid simulation of electronegative discharge plasmas

IEEE Conference Record - Abstracts. 1996 IEEE International Conference on Plasma Science

For radio-frequency discharges of electronegative gases, one-dimensional equilibrium equations for plasma variables are formulated and the scaling formulae of the plasma variables are derived in terms of the control parameters. The control parameters consist of three parameters: p (pressure), lp (halfsystem length), and P (power) or ne (electron density). The classifications of the operating regions are performed according to the prevailing particle-loss mechanism (recombination-loss-dominated or ion-flux-loss-dominated) and according to the main heating mechanism (ohmic-heating-dominated or stochastic-heating-dominated). The variations of the charged particle densities with pressure and absorbed power are estimated and compared with the results of a particle-in-cell simulation.

Finite element modeling of a two-fluid RF plasma discharge

2005

The design and understanding of plasma and its bounding sheath requires an effective modeling technique that is both adaptable to arbitrary geometry and time accurate. We present a finite-element-based model for two-fluid plasma. The continuity and momentum equations for electrons and ions are solved simultaneously with the Poisson equation, using an efficient subgrid-embedded algorithm. The model does not involve any conventional patching techniques at the plasma-sheath interface. The solutions are interpreted using the speed of ionization as one key parameter determining collisional sheath behavior. Numerical limitations are also analyzed from the theoretical derivation of solution amplification factor and phase velocity.

Modelling of discharges and non-thermal plasmas—applications to plasma processing

1993

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.

Modeling low pressure collisional plasma sheath with space-charge effect

Physics of Plasmas, 2003

The present work develops a computationally efficient one-dimensional subgrid embedded finite element formulation for plasma-sheath dynamics. The model incorporates space-charge effect throughout the whole plasma and the sheath region using multifluid equations. Secondary electron emission is not considered. A third-order temperature dependent polynomial is used to self-consistently calculate the rate of ionization in the plasma dynamic equations. The applications include dc and rf sheath inside a glow discharge tube where the noble gas is immobile, and a partially ionized plasma sheath inside an electric propulsion thruster channel in which the gas flows. The electron and ion number densities of the numerical solution decrease in the sheath region as expected. The ion velocity and electron temperature profiles also exhibit the expected behavior. The computed sheath potential compares well with the available experimental data.

Fluid modeling of electron heating in low-pressure, high-frequency capacitively coupled plasma discharges

Fluid modeling approaches encounter several shortcomings when used for simulation of capacitively coupled plasma discharges, especially under low-pressure and high-frequency conditions. For example, fluid models fail to accurately predict important features such as the collisionless electron heating and the electron temperature profiles in these discharges. We improve the classical fluid modeling approach to include the full electron momentum equation instead of the approximate drift-diffusion and a nonlocal collisionless electron heat flux terms instead of the Fourier heat flux form. A one-dimensional form of the fluid model is used in our studies. Improved predictions of the collisionless electron heating effect, charged species densities, and sheath electron temperature profiles are shown. Also accurate prediction of discharge impedance characteristics in the low-pressure, high-frequency regime are demonstrated.

A computational investigation of the effects of varying discharge geometry for an inductively coupled plasma

IEEE Transactions on Plasma Science, 2000

In this paper, a numerical investigation of ionization and density profiles in a low pressure inductively coupled plasma (ICP) discharge is presented. ICP reactors have in recent years become a popular choice for semiconductor processing. To ensure high yields, it is important to optimize process uniformity. Off-axis ionization can result in the hollowing of the density profile of the plasma.

Magnetic field effects on gas discharge plasmas

Physics of Plasmas, 2006

A study of the fluid model for cylindrical weakly ionized quasineutral plasmas in an axial magnetic field is presented. The model takes into account ionization, ion and electron inertia, as well as frictional forces for ions and electrons. The behavior of the plasma parameters for arbitrary magnitudes of the magnetic field, arbitrary gas pressure, and plasma size is presented, making the model applicable for a wide range of discharge conditions. A magnetic field parameter is introduced, which specifies a parameter range for the magnetic field, gas pressure, and plasma size where the Boltzmann equilibrium with the ambipolar field for the electron distribution is satisfied. In addition, a parametric relation for the magnetic field, gas pressure, and plasma size is obtained, which separates the region of weak magnetic field effects from the region of strong magnetic field effects. For strongly magnetized plasmas, an asymptotic solution with nonzero plasma density at the plasma boundary...