The Transport of Charge Carriers Interface
The Transport of Charge Carriers (tcc) interface (), found under the Electric Discharge branch (), is used to solve the number density of one or multiple charge carriers. The charge carriers can be charged species such as electrons, ions, and neutral species like molecules and their excited states. Transport and reactions of charge carriers can be handled with this interface. The driving forces for transport can be drift when coupled to an electromagnetic field, convection when coupled to a flow field, and diffusion.
The interface supports simulation of charge transport in 1D, 2D, and 3D as well as for axisymmetric components in 1D and 2D. Stationary; time dependent; and frequency dependent, perturbation study types are available for the interface.
Settings
The Label is the default physics interface name.
The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.
The default Name (for the first physics interface in the model) is tcc.
Domain Selection
If any part of the model geometry should not partake in the transport model, remove that part from the selection list.
Out-of-Plane Thickness
For 2D component and 1D axisymmetric components, the Out-of-plane thickness dz (default value: 1 cm) defines a parameter for the thickness of the geometry perpendicular to the two-dimensional cross section. Only constant thickness is supported. The value of this parameter is used, among other things, to automatically calculate the electric current flowing across the boundary.
Cross-Sectional Area
For 1D components, enter a Cross-sectional area Ac to define a parameter for the area of the geometry perpendicular to the 1D component. Only constant area is supported. The value of this parameter is used, among other things, to automatically calculate the electric current flowing across the boundary. The default is 1 cm2.
Transport Mechanisms
Use the checkboxes available to control transport mechanisms. There are four types of mechanisms that can be freely combined:
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Electric field drift, which is selected by default, considers the drift of charged species in an electric field.
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Magnetic field drift, which considers the drift of charged species in a magnetic field.
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Convection, which models the background fluid flow where all species drift with the flow field.
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Diffusion, which is selected by default.
Consistent Stabilization
To display this section, click the Show More Options button () and select Stabilization. By default, the Streamline diffusion checkbox is selected. The streamline diffusion stabilization does not change the original equation but adds the diffusion in the weak form and it vanishes once the original equation is converged. Use it when the transport equation is drift or convection-dominated. See more details in Numerical Stabilization in the COMSOL Multiphysics Reference Manual.
If the Streamline diffusion checkbox is selected, the Include time steps effect on stabilization time scale checkbox will become visible. Enabling this checkbox will account for the time steps’ effect on the stabilization time scale in time-dependent studies.
Inconsistent Stabilization
To display this section, click the Show More Options button () and select Stabilization. By default, the Isotropic diffusion checkbox is not selected, because this type of stabilization adds artificial diffusion and affects the accuracy of the original problem. However, this option can be used to get a good initial guess for underresolved problems. To add isotropic diffusion, select the Isotropic diffusion checkbox. The field for the Tuning parameter δid then becomes available. The default value is 0.1; increase or decrease the value of δid to increase or decrease the amount of isotropic diffusion. See more details in Numerical Stabilization in the COMSOL Multiphysics Reference Manual.
Discretization
Use this section to change the discretization of the transport equations. Two formulations, Finite element, log formulation (linear shape function) (the default) and Finite element, log formulation (quadratic shape function), are available.
To display all settings available in this section, click the Show More Options button () and select Advanced Physics Options.
The Compute boundary fluxes checkbox is activated by default so that COMSOL Multiphysics computes predefined accurate boundary flux variables. When this option is selected, the solver computes variables storing accurate boundary fluxes from each boundary into the adjacent domain.
If the checkbox is cleared, the COMSOL Multiphysics software instead computes the flux variables from the dependent variables using extrapolation, which is less accurate in postprocessing results but does not create extra dependent variables on the boundaries for the fluxes.
The flux variable affected in the interface is ntflux_c (where c is the carrier name). This is the normal total flux and corresponds to all flux contributions (drift, convection, and diffusion).
Also the Apply smoothing to boundary fluxes checkbox is available if the previous checkbox is selected. The smoothing can provide a more well-behaved flux value close to singularities.
For details about the boundary fluxes settings, see Computing Accurate Fluxes in the COMSOL Multiphysics Reference Manual.
The Value type when using splitting of complex variables setting should in most pure mass transfer problems be set to Real, which is the default. It makes sure that the dependent variable does not get affected by small imaginary contributions, which can occur, for example, when combining a Time Dependent or Stationary study with a frequency-domain study. For more information, see Splitting Complex-Valued Variables in the COMSOL Multiphysics Reference Manual.
Dependent Variables
The dependent variables are named as Charge carriers n by default. The names must be unique with respect to all other dependent variables in the component.
Add or remove charge carriers in the model and also change the names accordingly. Enter the Number of charge carriers. Use the Add Charge Carrier () and Remove Charge Carrier () buttons as needed.
You can access the number density of a carrier c either as n_c or through the physics scope variable name.n_c where name is the physics interface name, as described earlier. Note that for Finite element, log formulation, the actual dependent variable is the natural logarithm of the number density divided by one per cubic centimeter, which is named as name.logn_c and defined as log(n_c/(1 cm−3)).