Drift Diffusion Model
The Drift Diffusion Model adds the equations for electron transport in a plasma. Specify expressions for the electron diffusivity, mobility, electron energy diffusivity and electron energy mobility. There are also model inputs for the electric potential and collisional power loss.
Model Inputs
This section contain fields and values that are inputs to expressions that define material properties. If such user-defined property groups are added, the model inputs are listed here.
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Electric potential V (SI unit: V). Used to compute the electric field which results in migration of the electrons.
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Collisional power loss Sen (SI unit: W/m3). Represents the energy loss due to elastic and inelastic collisions.
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When the Use Reduced Electron Transport Properties check box is selected, choose Neutral number density Nn (SI unit: 1/m3) to compute the electron transport.
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When the Compute Tensor Electron Transport Properties check box is selected, choose Magnetic flux density B (SI unit: T) to compute the tensor form of the electron transport properties when a static magnetic field is present.
The electric potential typically comes from an Electrostatics interface and the collisional power loss is typically defined by The Heavy Species Transport Interface.
Electron Density and Energy
This section is not available if the Compute Tensor Electron Transport Properties check box is selected.
For all other choices, select an option from the Electron transport properties list — Specify Mobility Only (the default), Specify All, or Use Lookup Tables.
The other transport properties are computed using Einstein’s relation, see Tensor Transport Properties for more details.
Specify Mobility Only
When no check boxes, or the Include Thermal Diffusion or Mean Electron Energy check boxes are selected, and if Specify mobility only is selected, enter a value or expression for the Electron mobility μe (SI unit: m2/(V·s)). Select Isotropic, Diagonal, Symmetric or Anisotropic based on the model. The electron diffusivity, energy mobility and energy diffusivity are automatically computed using Einstein’s relation for a Maxwellian EEDF:
(4-1)
If the Use Reduced Electron Transport Properties check box is selected, enter the Reduced electron mobility μeNn (SI unit: 1/(V·m·s)). The actual electron mobility is then computed by dividing the reduced electron mobility by the neutral number density. The electron diffusivity, energy mobility and energy diffusivity are then computed as in Equation 4-1.
Specify All
For Specify all enter values or expressions for all of the properties, which can be either scalars or tensors. The appropriate values for the transport properties can be computed with The Boltzmann Equation, Two-Term Approximation Interface. For all of the properties, select Isotropic, Diagonal, Symmetric or Anisotropic from the list based on the model, then enter values or expressions for all of these properties:
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Electron mobility μe (SI unit: m2/(V·s))
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Electron diffusivity De (SI unit: m2/s)
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Electron energy diffusivity Den (SI unit: m2/s)
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Electron energy mobility μen (SI unit: m2/(V·s))
If the Use Reduced Electron Transport Properties check box is selected, then enter:
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Reduced electron mobility μeNn (SI unit: 1/(V·m·s))
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Reduced electron diffusivity DeNn (SI unit: 1/(m·s))
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Reduced electron energy diffusivity DenNn (SI unit: 1/(m·s))
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Reduced electron energy diffusivity μenNn (SI unit: 1/(V·m·s))
Use Lookup Tables
For Use lookup tables enter or load a lookup table with the transport properties as listed above versus mean electron energy (eV).
If the Use Reduced Electron Transport Properties check box is selected, the appropriate values for the transport properties can be computed with The Boltzmann Equation, Two-Term Approximation Interface and written out to a text file. The text file can then be loaded in for each electron transport property.
Mean electron energy specification
This section is available when the Mean electron energy is set to Local field approximation. Select how to provide the relation between the reduce electric field and the mean electron energy from the Specify using list — Expression or Use lookup table.
DC Electron Mobility
This section is available if the Compute Tensor Electron Transport Properties check box is selected. Enter a value for the DC electron mobility, μdc (SI unit: m2/(V·s)).
The section is also available when both the Compute Tensor Electron Transport Properties and the Use Reduced Electron Transport Properties check boxes are chosen. Then enter a value or expression for the Reduced DC electron mobility, μdcNn (SI unit: 1/(V·m·s)).