WKB Tunneling Model, Electrons
This subnode is available when the option WKB tunneling model is selected for a heterojunction or Schottky contact. Add this subnode to compute the contribution to the electron current density from tunneling, using the WKB approximation.
Potential barrier domain selection
Select a domain adjacent to the boundary selection of this subnode, where the potential barrier is located and electrons tunnel across the domain.
When drawing the geometry for the device model, consider adding a thin layer of domain adjacent to the heterojunction or Schottky contact, where you plan to use the WKB tunneling feature.
Opposite Boundary Selection
Select a boundary on the opposite side of the Potential Barrier Domain Selection from the boundary selection of this subnode. These two boundary selections are each at the upstream and downstream of the electric field line. In other words, if an electron tunnel into the boundary selection of the subnode, it emerges out of the Opposite Boundary Selection.
WKB Tunneling Model, Electrons
In this section, enter the electron effective mass and one or more coordinates depending on the space dimension of the model.
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For Effective mass, enter the electron effective mass m (SI unit: kg). The default is the free electron mass me_const.
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For Field line coordinate, enter an appropriate variable flc (SI unit: m) that is (approximately) proportional to the arc length along the electric field line across the potential barrier domain selection. The default is the first coordinate of the global coordinate system. The variable should be valid within the potential barrier domain selection and its isosurfaces should be approximately parallel to the equipotential surfaces in the domain.
In general a Curvilinear Coordinates physics interface can be used to compute the (approximated) electric field line coordinate, or each of the boundary coordinates below. See the Application Libraries example Semiconductor_Module/Verification_Examples/heterojunction_tunneling
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For 2D and 3D components, enter Boundary coordinate bndc (SI unit: m). The default is the second coordinate of the global coordinate system. See below for more details.
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For 2D axisymmetry and 3D components, enter Boundary coordinate 2 bndc2 (SI unit: m). The default is the Z coordinate of the global coordinate system. For this input and the input for bndc above, enter an appropriate variable that can be used to form the boundary coordinate system of the boundary selection of the subnode. The variable should be valid within the potential barrier domain selection and its isosurfaces should be approximately parallel to the electric field lines in the domain.
For the formulation used in the WKB Tunneling Model subnodes, see the theory section WKB Tunneling Model.