Semiconductor Material Model
Use the Semiconductor Material Model to set the physical and transport properties of the semiconducting material. The following subnodes are available from the context menu (right-click the parent node) or from the Physics toolbar, Attributes menu.
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User-Defined Mobility Model
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Power Law Mobility Model (L)
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Arora Mobility Model (LI)
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Fletcher Mobility Model (C)
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Caughey–Thomas Mobility Model (E)
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Lombardi Surface Mobility Model (S)
See the theory in The Semiclassical Model.
Material Properties
For each of the following, the default is taken From material. For User defined enter a value or expression in the text field.
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Relative permittivity εr (dimensionless). For User defined, also select Isotropic, Diagonal, Symmetric, or Full.
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Band gap Eg,0 (SI unit: V). The band gap is the energy difference between the conduction and valence band at equilibrium (independent of doping). The input is actually the band gap energy divided by the elementary charge. Therefore it takes on the unit of electric potential, and its numerical value is the same as the band gap energy in eV. The default is 1.12 V.
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Electron affinity χ0 (SI unit: V). The electron affinity is the difference in energy between the vacuum level and the conduction band at equilibrium. The input is actually the electron affinity divided by the elementary charge. Therefore it takes on the unit of electric potential, and its numerical value is the same as the electron affinity in eV. The default is 4.05 V.
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Effective density of states, valence band Nv (SI unit: 1/m3). The default is 2.66·1019 1/cm3.
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Effective density of states, conduction band Nc (SI unit: 1/m3). The default is 2.86·1019 1/cm3.
Material Properties, Density-Gradient
This section appears only when one of the density-gradient formulation options are selected under the Discretization section.
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Electron effective mass, density-gradient meDG (SI unit: kg). The default is me_const.
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Hole effective mass, density-gradient mhDG (SI unit: kg). The default is me_const.
Semiconductor Equilibrium Study Settings
To display this section, which only applies for the Semiconductor Equilibrium study step, click the Show More Options button () and select Advanced Physics Options.
The default Equilibrium condition is Bias voltage, suitable for situations where there is a well-defined bias electric potential for the domain, for example, given by a metal contact. Enter a Bias voltage V0,bias (SI unit: V). The default is 0 V. All metal contacts attached to the domain will be set to the specified value of V0,bias for the Semiconductor Equilibrium study step.
The other option for Equilibrium condition is Total charge, suitable for situations where there is a well-defined total charge for the domain, for example, if the domain is insulated on all its exterior boundaries by dielectric material and/or thin insulator gate. Enter a Total charge Q0,tot (SI unit: C). The default is 0 C. In this case, the electric potential of the system still needs to be constrained, for example, by a Terminal or an Electric Potential boundary condition attached to a dielectric domain, or a Thin Insulator Gate boundary condition attached to the Semiconductor Material Model domain. If there are also metal contacts attached to the semiconductor domain, then the bias voltage on those contacts will be set to a value that is consistent with the specified total charge Q0,tot.
If there are two separate Semiconductor Material Model nodes, one assigned to each of two adjacent domains, then care must be taken when specifying the above settings, to ensure that the two domains are at the same equilibrium electric potential, for example, set the Bias voltage of the two domains to the same value.
Mobility Model
These settings determine the mobility values actually used by the Semiconductor interface. The defaults take constant values From material. For User defined manually define the electron and hole mobilities.
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Electron mobility μn (SI unit: m2/(V⋅s)).
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Hole mobility μp (SI unit: m2/(V⋅s)).
If mobility model subfeatures are added to the material model it is possible to select the output of these mobility models to be used as the mobility by changing the feature input from the appropriate model.
See the theory in Mobility Models.
Band Gap Narrowing
Band gap narrowing effects occur at high doping levels. To apply band gap narrowing, select an option from the Band gap narrowing list — None (the default), Slotboom, Jain–Roulston model, or User defined. Enter values or expressions for the following:
The Band Gap Narrowing theory section also describes these options.
Slotboom
This option applies Slotboom’s empirical model for the band gap narrowing. The model computes the band gap narrowing according to the equation:
where NI = Nd + Na and the other parameters are material properties. The fraction of the band gap narrowing taken up by the conduction band is defined directly as a material property by default.
For each of the following model properties the default takes values From material, or for User defined enter a different value or expression. There are additional options also available for each.
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Conduction band fraction α (dimensionless). The default is 0.5.
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Band gap narrowing reference energy Eref (SI unit: V). The default is 0.00692 V.
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Band gap narrowing reference concentration Nref (SI unit: 1/m3). The default is 1.3·1017 1/cm3.
Jain–Roulston Model
This option applies the physics-based model of Jain and Roulston for the band gap narrowing. Coefficients for the model are available for a wide range of III-V materials, as well as for silicon and germanium. The band gap narrowing is given by:
where An, Ap, Bn, Bp, Cn, and Cp are material properties (with the same units as the band gap) and Nref is a reference doping level (SI unit: 1/m3). The fraction of the band gap narrowing taken up by the conduction band is defined directly as a material property by default.
For each of the following properties the default takes values From material, or for User defined enter a different value or expression. There are additional options available for each.
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Conduction band fraction α (dimensionless). The default is 0.5.
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Jain–Roulston coefficient (n-type), A (An) (SI unit: V). The default is 10e-9 V.
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Jain–Roulston coefficient (n-type), B (Bn) (SI unit: V). The default is 3e-7 V.
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Jain–Roulston coefficient (n-type), C (Cn) (SI unit: V). The default is 10e-12 V.
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Jain–Roulston coefficient (p-type), A (Ap) (SI unit: V). The default is 10e-9 V.
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Jain–Roulston coefficient (p-type), B (Bp) (SI unit: V). The default is 3e-7 V.
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Jain–Roulston coefficient (p-type), C (Cp) (SI unit: V). The default is 10e-12 V.
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Band gap narrowing reference concentration Nref (SI unit: 1/m3). The default is 1.3·1017 1/cm3.
User Defined
Enter a value or expression for Band gap narrowing voltage ΔEg (SI unit: V). The default is 0 V, which represents the amount of band narrowing. Usually a function of the dopant concentrations should be specified.
Enter a value or expression for Conduction band fraction α (dimensionless). In general, the change in the band-gap energy can be taken up by a decrease in the conduction band energy and an increase in the valence band energy. The parameter α determines what fraction of the change is taken up by the conduction band. When band-gap narrowing is active Ec → Ec − αΔEg and Ec → Ec + (1 − α)ΔEg. The default value of α is 1.
Dopant Ionization
This section determines the ionization of the donors and acceptors. Specify the Dopant ionization — Complete ionization (the default) or Incomplete ionization. For Incomplete ionization, select an Ionization model — Standard (the default) or User defined.
For Standard enter values or expressions for the following:
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Relative donor energy (below conduction band) ΔEd (SI unit: V). The default is 0.05 V.
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Relative acceptor energy (above valence band) ΔEd (SI unit: V). The default is 0.05 V.
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Donor degeneracy factor gd (dimensionless). The default is 2.
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Acceptor degeneracy factor gd (dimensionless). The default is 4.
For User defined enter values or expressions for the following:
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Donor ionization fraction Nd+/Nd (dimensionless). The default is 1.
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Acceptor ionization fraction Na–/Na (dimensionless). The default is 1.
Incomplete ionization cannot be used together with the mobility models.
See the theory in Incomplete Ionization.