- boundaryThe list of boundary IDs from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundary IDs from the mesh where this object applies
- emission_coeffsThe species dependent secondary electron emission coefficients for this boundary
C++ Type:std::vector<std::string>
Controllable:No
Description:The species dependent secondary electron emission coefficients for this boundary
- ionsA list of ion densities in log form
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:A list of ion densities in log form
- position_unitsUnits of position.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Units of position.
- potential_unitsThe potential units.
C++ Type:std::string
Controllable:No
Description:The potential units.
- rThe reflection coefficient
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The reflection coefficient
- variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on
FieldEmissionBC
The electron flux boundary condition due to field emission (Based on Forbes (2006) and Forbes (2008))
Overview
FieldEmissionBC
is an outflow boundary condition that assumes the electron current density is defined by field emission.
Using a Fowler-Nordheim calculation for the field emission, the electron current density is defined as
Where is the electron current density, is the first Fowler–Nordheim constant, is the local work function, is the local field, is the second Fowler–Nordheim constant, is a correction factor that depends on the scaled barrier field (), is the normal vector of the boundary, is the field enhancement factor, and is the potential. is defined such that the outflow is only defined when the drift velocity is direct towards the wall and zero otherwise. With the electron current density, the outward electron flux is defined as
Where is the outflow normal to the boundary, is the mobility coefficient of the ions, indicates the advection behavior ( for positively charged species and for negatively charged species), is the ion density, is the diffusion coefficient of ions, is the elemental charge, and is the ion induced secondary electron emission coefficient. is defined as the fraction of particles reflected by the surface.
When converting the density to log form and applying a scaling factor of the mesh and voltage, the strong form is given by
Where is the molar density of the species in log form, is Avogadro's number, is the scaling factor of the potential, and is the scaling factor of the mesh.
Example Input File Syntax
[BCs]
[FieldEmission_left]
type = FieldEmissionBC
variable = em
boundary = 'left'
ip = Arp
mean_en = mean_en
r = 0
position_units = ${dom0Scale}
[]
[]
(test/tests/field_emission/field_emission.i)Input Parameters
- displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
- field_property_namefield_solver_interface_propertyName of the solver interface material property.
Default:field_solver_interface_property
C++ Type:std::string
Controllable:No
Description:Name of the solver interface material property.
- relaxFalseUse relaxation for emission.
Default:False
C++ Type:bool
Controllable:No
Description:Use relaxation for emission.
- tau1e-09The time constant for ramping the boundary condition.
Default:1e-09
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The time constant for ramping the boundary condition.
Optional Parameters
- absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
- extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
- extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
- matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Controllable:No
Description:The tag for the matrices this Kernel should fill
- vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Controllable:No
Description:The tag for the vectors this Kernel should fill
Contribution To Tagged Field Data Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
- diag_save_inThe name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
- enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
- implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
- save_inThe name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
- seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
- skip_execution_outside_variable_domainFalseWhether to skip execution of this boundary condition when the variable it applies to is not defined on the boundary. This can facilitate setups with moving variable domains and fixed boundaries. Note that the FEProblem boundary-restricted integrity checks will also need to be turned off if using this option
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip execution of this boundary condition when the variable it applies to is not defined on the boundary. This can facilitate setups with moving variable domains and fixed boundaries. Note that the FEProblem boundary-restricted integrity checks will also need to be turned off if using this option
- use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Advanced Parameters
- prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
- use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Material Property Retrieval Parameters
Input Files
References
- Richard G Forbes.
Simple good approximations for the special elliptic functions in standard fowler-nordheim tunneling theory for a schottky-nordheim barrier.
Applied physics letters, 2006.
doi:10.1063/1.2354582.[BibTeX]
- Richard G Forbes.
Physics of generalized fowler-nordheim-type equations.
Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena, 26(2):788–793, 2008.
doi:10.1116/1.2827505.[BibTeX]