Plasma Modeling
There are three methods typically employed to model plasmas: kinetic, fluid approximation, and hybrid. All methods essentially involve solving an appropriate transport equation along with Maxwell’s equations.
Physics Guide
The complexity of plasma modeling lies in the fact that it combines elements of reaction engineering, statistical physics, fluid mechanics, physical kinetics, heat transfer, mass transfer, and electromagnetics. The net result is a true multiphysics problem involving complicated coupling between the different physics. The module is designed to simplify the process of setting up a self-consistent model of a low-temperature plasma.
The physics interfaces include all the necessary tools to model plasma discharges, beginning with a Boltzmann Equation, Two-Term Approximation solver that computes the electron transport properties and source coefficients from a set of electron impact collision cross sections. This interface makes it possible to determine many of the interesting characteristics of a discharge by providing input properties such as the electric field and the electron impact reactions that make up the plasma chemistry, without solving a space-dependent problem.
For space-dependent models, the reactions and species which make up the plasma chemistry are conveniently managed in the Model Builder. When the fluid velocity and gas temperature are of interest, there are physics interfaces available for laminar flow and heat transfer. There are several options available when coupling the charged species transport to the electromagnetic fields.
Physics Interface List by Space Dimension and Preset Study Type
 
AC/DC
stationary; frequency domain; time dependent; frequency domain; eigenfrequency
stationary; time dependent; stationary source sweep
Fluid Flow
Single-Phase Flow
Plasma
Nonisothermal Plasma Flow
Equilibrium Discharges
Species Transport
1 This physics interface is included with the core COMSOL package but has added functionality for this module.
2 Requires the addition of the AC/DC Module.
3 Requires the addition of the RF Module.
4 This physics interface is a predefined multiphysics coupling that automatically adds all the physics interfaces and coupling features required.
AC/DC Interfaces
The AC/DC Branch chapter describes the two physics interfaces available with this module under the AC/DC branch of the Model Wizard. Many of the plasma interfaces already solve Poisson’s equation, and volume and surface charges are automatically accounted for. This means that the Electrostatics interface will rarely need to be used.
Fluid Flow Interfaces
The Fluid Flow Branch describes the Laminar Flow interface, which has a few additional features available for this module compared to the basic license.
Boltzmann Equation, Two-Term Approximation Interface
The Boltzmann Equation, Two-Term Approximation interface computes the electron energy distribution function (EEDF) from a set of collision cross sections for some mean discharge conditions. The interface can be used as a preprocessing stage before solving a full space dependent model. The main purpose of this interface is to compute electron source coefficients and transport properties.
Drift Diffusion Interface
The Drift Diffusion interface is used to compute the electron density and mean electron energy for any type of plasma. A wide range of boundary conditions are available to handle secondary emission, thermionic emission, and wall losses. This interface rarely needs to be used by itself as it makes up part of the application specific interfaces described later.
charge transport
The Charge Transport interface computes the density of charge carriers in a background gas under the assumption that the transport is dominated by migration. This is typically only used as part of the Corona Discharge multiphysics interface (see below).
The Heavy Species Interface
The Heavy Species Transport interface solves a mass balance equation for all nonelectron species. This includes charged, neutral, and electronically excited species. The interface also allows you to add electron impact reactions, chemical reactions, surface reactions, volumetric species, and surface species via the Model Builder. This interface rarely needs to be used by itself as it makes up part of the application specific interfaces described later.
Application Specific Interfaces
The Plasma Module provides four application specific multiphysics interfaces for modeling the most common types of discharge.
Plasma
The Plasma interface can be used to model positive columns, DBD discharges, glow discharges, and corona discharges. The complicated coupling between the electron transport, heavy species transport, and electrostatic field is handled automatically by the software. Furthermore, the secondary emission flux from ion bombardment on an electrode is automatically computed and used in the boundary condition for electrons.
Plasma, Time Periodic
The Plasma, Time Periodic interface can be used to model capacitively coupled plasmas. Instead of solving the problem in the time domain, the periodic steady-state solution is computed. This avoids having to solve for tens or hundreds of thousands of RF cycles, which is typically how long it takes before the plasma reaches the periodic steady-state solution. This approach maintains all the nonlinearity of the model while dramatically reducing computation time. The physics interface accomplishes this by attaching an extra dimension to the underlying mathematical equations representing one RF cycle, and enforcing periodic boundary conditions in the aforementioned extra dimension.
Inductively Coupled Plasma
The Inductively Coupled Plasma interface can be used to model discharges sustained through induction currents. These discharges typically operate in the MHz frequency range. Inductively coupled plasmas (ICP) are important in plasma processing and plasma sources because the plasma density can be considerably higher than in capacitively coupled discharges. Inductively coupled plasmas are also attractive from the modeling perspective because they are relatively straightforward to model, due to the fact that the induction currents can be solved for in the frequency domain. This means that the RF cycle applied to the driving coil does not need to be explicitly resolved when solving. As such, the quasi steady-state solution is reached in relatively few time steps.
Inductively Coupled Plasma with RF bias
The Inductively Coupled Plasma with Rf Bias interface can be used to model discharges sustained through induction currents and that have a periodic RF biased electrode. This interface uses the Plasma, Time Periodic interface to solve the periodic steady state for the RF bias. The inductive currents are solved in the frequency domain as in the Inductively Coupled Plasma interface. This type of discharges are interesting because the plasma density and the ions flux at a surface can be controlled somewhat independently.
Microwave Plasma
The Microwave Plasma interface can be used to model discharges which are sustained through heating of electrons due to electromagnetic waves. These discharges typically operate in the GHz frequency range. Wave–heated discharges usually fall into one of two categories: discharges with no external DC magnetic field and discharges with a high intensity static magnetic field. If a suitably high DC magnetic field is present then electron cyclotron resonance (ECR) can occur where electrons continually gain energy from the electric field over 1 RF period. Modeling microwave plasmas involves solving equations for the electron density, mean electron energy, heavy species, the electrostatic potential, and the high frequency electric field. The high frequency electric field is computed in the frequency domain and losses are introduced via a complex plasma conductivity.
Nonisothermal Plasma Flow
The Nonisothermal Plasma Flow interface couples existent plasma interfaces with Laminar Flow and Heat Transfer in Fluids interfaces. Use these interfaces when there are important fluid velocities and when the background gas temperature depends strongly on the operation conditions.
Equilibrium Discharges, Out-of-Plane Currents
The Equilibrium Discharges, Out-of-plane Currents multiphysics interface, available in 2D and 2D axisymmetric, is used to study equilibrium discharges in a magnetohydrodynamics (MHD) framework where the currents are out-of-plane. This multiphysics interface adds three single physics interfaces: Magnetic Fields, Heat Transfer in Fluids, and Laminar Flow, together with several multiphysics coupling features. The multiphysics couplings add the MHD coupling between the Magnetic Fields and the Laminar Flow interfaces. The multiphysics couplings also add heating and cooling of the equilibrium plasma by enthalpy transport, Joule heating and radiation loss.
Equilibrium Discharges, In-Plane Currents
The Equilibrium Discharges, in-plane Currents multiphysics interface, available in 2D and 2D axisymmetric, is used to study equilibrium discharges in a magnetohydrodynamics (MHD) framework where the currents are in-plane. This multiphysics interface adds three single physics interfaces: Magnetic and Electric Fields, Heat Transfer in Fluids, and Laminar Flow, together with several multiphysics coupling features. The multiphysics couplings add the MHD coupling between the Magnetic and Electric Fields and the Laminar Flow interfaces. The multiphysics couplings also add heating and cooling of the equilibrium plasma by enthalpy transport, Joule heating and radiation loss as well as special boundary conditions to model the ion and electron heating at the plasma boundaries.
Equilibrium Discharges
The Equilibrium Discharges multiphysics interface, available in 3D, is used to study equilibrium discharges in a magnetohydrodynamics (MHD) framework. This multiphysics interface adds three single physics interfaces: Magnetic and Electric Fields, Heat Transfer in Fluids, and Laminar Flow, together with several multiphysics coupling features. The multiphysics couplings add the MHD coupling between the Magnetic and Electric Fields and the Laminar Flow interfaces. The multiphysics couplings also add heating and cooling of the equilibrium plasma by enthalpy transport, Joule heating, and radiation loss as well as special boundary conditions to model the ion and electron heating at the plasma boundaries.
Corona Discharge
The Corona Discharge interface employs a simplified charge transport model combined with electrostatics to approximate the charge density and electrostatic field in stationary corona discharges. This model does not include the ionization layer of corona discharges, instead utilizing an approximate boundary condition. Additionally, electron dynamics are not solved in this approach.
electrical breakdown detection
The Electrical Breakdown Detection interfaces uses an approximate method to determine if electrical breakdown will occur in a given design by integrating Townsend growth coefficients along electric field lines.
Limitations of the Plasma Module
The Plasma module cannot model plasmas that are not collisional enough for the fluid-type equations used to be valid. For reactors with characteristic dimensions of 10 cm the lower possible pressure would be 20 mTorr.