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MOSFET with Explicit Metal and Dielectric Domains
Introduction
This example is an adaptation of the DC Characteristics of a MOS Transistor (MOSFET) model (Application Library path Semiconductor_Module/Transistors/mosfet). In this adaptation the metallic and dielectric domains are modeled explicitly and not via an effective boundary condition. Therefore, for instance the potential profile inside the metal and inside the insulator can be observed. The coupling between the semiconductor and the metal is achieved by including an electric currents interface.
Model Definition
Figure 1 shows the model geometry composed of the semiconductor, metallic domains, namely, source, drain, and base, as well as the gate dielectric domain. The model uses the Semiconductor interface for the semiconductor and gate dielectric domains, and the Electric Currents interface to account for the metallic domains. The coupling between the two interfaces is achieved by defining the Normal Current Density under the Electric Currents interface and the Metal Contact under the Semiconductor interface.
Figure 1: Model geometry indicating different domains including explicit definition of metal and dielectric domains.
The procedure of the implementation is described in detail in the Modeling Instructions section.
Results and Discussion
Figure 2 shows the electric potential profile for the MOSFET with explicit metal and dielectric domains.
Figure 2: Electric potential profile of a MOSFET with explicit metal and dielectric domains.
Application Library path: Semiconductor_Module/Transistors/mosfet_with_explicit_metal_and_dielectric
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  2D.
2
In the Select Physics tree, select AC/DC > Electric Fields and Currents > Electric Currents (ec).
3
Click Add.
4
In the Select Physics tree, select Semiconductor > Semiconductor (semi).
5
Click Add.
6
Click  Study.
7
In the Select Study tree, select General Studies > Stationary.
8
Click  Done.
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
L
1e-6[m]
1E-6 m
Out-of-plane thickness
pdop
1e17[1/cm^3]
1E23 1/m³
p-doping
ndop
1e20[1/cm^3]
1E26 1/m³
n-doping
Geometry 1
1
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
2
In the Settings window for Geometry, locate the Units section.
3
From the Length unit list, choose µm.
Rectangle 1 (r1)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 3.
4
In the Height text field, type 0.7.
Polygon 1 (pol1)
1
In the Geometry toolbar, click  Polygon.
2
In the Settings window for Polygon, locate the Object Type section.
3
From the Type list, choose Closed curve.
4
Locate the Coordinates section. In the table, enter the following settings:
x (µm)
y (µm)
0
0.67
0
0.7
0.5
0.7
0.7
0.7
2.3
0.7
2.5
0.7
3
0.7
3
0.67
Rectangle 2 (r2)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 0.5.
4
In the Height text field, type 0.1.
5
Locate the Position section. In the y text field, type 0.7.
Rectangle 3 (r3)
1
Right-click Rectangle 2 (r2) and choose Duplicate.
2
In the Settings window for Rectangle, locate the Position section.
3
In the x text field, type 2.5.
Rectangle 4 (r4)
1
Right-click Rectangle 3 (r3) and choose Duplicate.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 1.6.
4
In the Height text field, type 30[nm].
5
Locate the Position section. In the x text field, type 0.7.
Rectangle 5 (r5)
1
Right-click Rectangle 4 (r4) and choose Duplicate.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 3.
4
In the Height text field, type 0.1.
5
Locate the Position section. In the x text field, type 0.
6
In the y text field, type -0.1.
Form Union (fin)
1
In the Model Builder window, click Form Union (fin).
2
In the Settings window for Form Union/Assembly, locate the Form Union/Assembly section.
3
From the Repair tolerance list, choose Absolute.
4
In the Absolute repair tolerance text field, type 3.0E-6.
Mesh Control Edges 1 (mce1)
1
In the Geometry toolbar, click  Virtual Operations and choose Mesh Control Edges.
2
Click the  Zoom Extents button in the Graphics toolbar.
3
On the object fin, select Boundary 6 only.
Add Material
1
In the Materials toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Semiconductors > Si - Silicon.
4
Click the Add to Component button in the window toolbar.
5
In the Materials toolbar, click  Add Material to close the Add Material window.
Materials
Si - Silicon (mat1)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
Click  Clear Selection.
3
Select Domain 2 only.
Metal
1
In the Model Builder window, right-click Materials and choose Blank Material.
2
In the Settings window for Material, type Metal in the Label text field.
3
Select Domains 1, 3, and 5 only.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Electric conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
1e7
S/m
Basic
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
1
1
Basic
Oxide
1
Right-click Materials and choose Blank Material.
2
In the Settings window for Material, type Oxide in the Label text field.
3
Select Domain 4 only.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
4.5
1
Basic
Electric Currents (ec)
1
In the Model Builder window, under Component 1 (comp1) click Electric Currents (ec).
2
Select Domains 1, 3, and 5 only.
3
In the Settings window for Electric Currents, locate the Thickness section.
4
In the d text field, type L.
Normal Current Density 1 - Ground left
1
In the Physics toolbar, click  Boundaries and choose Normal Current Density.
2
In the Settings window for Normal Current Density, type Normal Current Density 1 - Ground left in the Label text field.
3
Select Boundary 6 only.
4
Locate the Normal Current Density section. In the Jn text field, type semi.nJ.
Normal Current Density 2 - Drain
1
Right-click Normal Current Density 1 - Ground left and choose Duplicate.
2
In the Settings window for Normal Current Density, type Normal Current Density 2 - Drain in the Label text field.
3
Locate the Boundary Selection section. Click  Clear Selection.
4
Select Boundary 16 only.
Normal Current Density 3 - Ground bottom
1
Right-click Normal Current Density 2 - Drain and choose Duplicate.
2
In the Settings window for Normal Current Density, type Normal Current Density 3 - Ground bottom in the Label text field.
3
Locate the Boundary Selection section. Click  Clear Selection.
4
Select Boundary 4 only.
Ground left
1
In the Physics toolbar, click  Boundaries and choose Electric Potential.
2
In the Settings window for Electric Potential, type Ground left in the Label text field.
3
Select Boundary 7 only.
Ground bottom
1
Right-click Ground left and choose Duplicate.
2
In the Settings window for Electric Potential, type Ground bottom in the Label text field.
3
Locate the Boundary Selection section. Click  Clear Selection.
4
Select Boundary 2 only.
Drain
1
Right-click Ground bottom and choose Duplicate.
2
In the Settings window for Electric Potential, type Drain in the Label text field.
3
Locate the Boundary Selection section. Click  Clear Selection.
4
Select Boundary 17 only.
5
Locate the Electric Potential section. In the V0 text field, type 1.
Semiconductor (semi)
1
In the Model Builder window, under Component 1 (comp1) click Semiconductor (semi).
2
Select Domains 2 and 4 only.
3
In the Settings window for Semiconductor, locate the Thickness section.
4
In the d text field, type L.
Charge Conservation 1
1
In the Physics toolbar, click  Domains and choose Charge Conservation.
2
Select Domain 4 only.
Gate
1
In the Physics toolbar, click  Boundaries and choose Terminal.
2
In the Settings window for Terminal, type Gate in the Label text field.
3
Select Boundary 12 only.
4
Locate the Terminal section. In the Φc text field, type 4.1[V].
5
From the Terminal type list, choose Voltage.
6
In the V0 text field, type 2.
Metal Contact 1 - Ground left
1
In the Physics toolbar, click  Boundaries and choose Metal Contact.
2
In the Settings window for Metal Contact, type Metal Contact 1 - Ground left in the Label text field.
3
Select Boundary 6 only.
4
Locate the Terminal section. In the V0 text field, type V.
Metal Contact 2 - Drain
1
Right-click Metal Contact 1 - Ground left and choose Duplicate.
2
In the Settings window for Metal Contact, type Metal Contact 2 - Drain in the Label text field.
3
Locate the Boundary Selection section. Click  Clear Selection.
4
Select Boundary 16 only.
Metal Contact 3 - Ground bottom
1
Right-click Metal Contact 2 - Drain and choose Duplicate.
2
In the Settings window for Metal Contact, type Metal Contact 3 - Ground bottom in the Label text field.
3
Locate the Boundary Selection section. Click  Clear Selection.
4
Select Boundary 4 only.
Analytic Doping Model 1
1
In the Physics toolbar, click  Domains and choose Analytic Doping Model.
2
Select Domain 2 only.
3
In the Settings window for Analytic Doping Model, locate the Impurity section.
4
In the NA0 text field, type pdop.
Analytic Doping Model 2
1
Right-click Analytic Doping Model 1 and choose Duplicate.
2
In the Settings window for Analytic Doping Model, locate the Distribution section.
3
From the list, choose Box.
4
Locate the Impurity section. From the Impurity type list, choose Donor doping (n-type).
5
In the ND0 text field, type ndop.
6
Locate the Uniform Region section. Specify the r0 vector as
0.6[um]
Y
7
In the W text field, type 0.6[um].
8
In the D text field, type 0.1[um].
9
Locate the Profile section. Select the Specify different length scales for each direction checkbox.
10
Specify the dj vector as
0.2[um]
X
0.25[um]
Y
11
From the Nb list, choose Acceptor concentration (semi/adm1).
Analytic Doping Model 3
1
Right-click Analytic Doping Model 2 and choose Duplicate.
2
In the Settings window for Analytic Doping Model, locate the Uniform Region section.
3
Specify the r0 vector as
2.4[um]
X
Trap-Assisted Recombination 1
1
In the Physics toolbar, click  Domains and choose Trap-Assisted Recombination.
2
Select Domain 2 only.
Mesh 1
1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
2
In the Settings window for Mesh, locate the Sequence Type section.
3
From the list, choose User-controlled mesh.
Size
1
In the Model Builder window, under Component 1 (comp1) > Mesh 1 click Size.
2
In the Settings window for Size, locate the Element Size section.
3
From the Predefined list, choose Finer.
4
Click to expand the Element Size Parameters section.
Mapped 1
1
In the Mesh toolbar, click  Mapped.
2
Drag and drop below Size.
3
In the Settings window for Mapped, locate the Domain Selection section.
4
From the Geometric entity level list, choose Domain.
5
Select Domain 6 only.
Distribution 1
1
Right-click Mapped 1 and choose Distribution.
2
In the Settings window for Distribution, locate the Boundary Selection section.
3
Click  Paste Selection.
4
In the Paste Selection dialog, type 21 in the Selection text field.
5
Click OK.
6
In the Settings window for Distribution, locate the Distribution section.
7
From the Distribution type list, choose Predefined.
8
In the Number of elements text field, type 10.
9
In the Element ratio text field, type 5.
10
From the Growth rate list, choose Exponential.
11
Select the Reverse direction checkbox.
Distribution 2
1
In the Model Builder window, right-click Mapped 1 and choose Distribution.
2
In the Settings window for Distribution, locate the Boundary Selection section.
3
Click  Paste Selection.
4
In the Paste Selection dialog, type 23 in the Selection text field.
5
Click OK.
6
In the Settings window for Distribution, locate the Distribution section.
7
In the Number of elements text field, type 400.
Size 1
1
In the Model Builder window, under Component 1 (comp1) > Mesh 1 click Size 1.
2
In the Settings window for Size, locate the Element Size section.
3
From the Predefined list, choose Fine.
Size 2
1
In the Model Builder window, click Size 2.
2
In the Settings window for Size, locate the Element Size section.
3
From the Predefined list, choose Finer.
4
Click  Build All.
Study 1
In the Study toolbar, click  Compute.
Results
Surface 1
1
In the Model Builder window, expand the Electron Concentration (semi) node, then click Surface 1.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type semi.log10N.
4
Locate the Coloring and Style section. From the Color table list, choose Rainbow.
5
From the Scale list, choose Linear.
6
In the Electron Concentration (semi) toolbar, click  Plot.
Surface 1
1
In the Model Builder window, expand the Hole Concentration (semi) node, then click Surface 1.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type semi.log10P.
4
Locate the Coloring and Style section. From the Color table list, choose Rainbow.
5
From the Scale list, choose Linear.
6
In the Hole Concentration (semi) toolbar, click  Plot.
Study 1/Solution 1 (2) (sol1)
1
In the Model Builder window, expand the Results > Datasets node.
2
Right-click Results > Datasets > Study 1/Solution 1 (sol1) and choose Duplicate.
Selection
1
In the Results toolbar, click  Attributes and choose Selection.
2
In the Settings window for Selection, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Domain.
4
Select Domains 1–3 and 5 only.
Extrusion 2D 1
1
In the Results toolbar, click  More Datasets and choose Extrusion 2D.
2
In the Settings window for Extrusion 2D, locate the Data section.
3
From the Dataset list, choose Study 1/Solution 1 (2) (sol1).
Study 1/Solution 1 (3) (sol1)
In the Model Builder window, under Results > Datasets right-click Study 1/Solution 1 (2) (sol1) and choose Duplicate.
Selection
1
In the Model Builder window, expand the Study 1/Solution 1 (3) (sol1) node, then click Selection.
2
In the Settings window for Selection, locate the Geometric Entity Selection section.
3
Click  Clear Selection.
4
Select Domain 4 only.
Extrusion 2D 2
1
In the Model Builder window, under Results > Datasets right-click Extrusion 2D 1 and choose Duplicate.
2
In the Settings window for Extrusion 2D, locate the Data section.
3
From the Dataset list, choose Study 1/Solution 1 (3) (sol1).
3D representation
1
In the Results toolbar, click  3D Plot Group.
2
In the Settings window for 3D Plot Group, type 3D representation in the Label text field.
3
Click to expand the Title section. From the Title type list, choose None.
Surface 1
1
Right-click 3D representation and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type 1.
4
Locate the Data section. From the Dataset list, choose Extrusion 2D 1.
Material Appearance 1
1
Right-click Surface 1 and choose Material Appearance.
2
In the Settings window for Material Appearance, locate the Appearance section.
3
From the Appearance list, choose Custom.
4
From the Material type list, choose Custom.
5
Set the Metallic value to 0.3.
6
Click the  Zoom Extents button in the Graphics toolbar.
Surface 2
1
In the Model Builder window, right-click 3D representation and choose Surface.
2
In the Settings window for Surface, locate the Data section.
3
From the Dataset list, choose Extrusion 2D 1.
4
Locate the Expression section. In the Expression text field, type V2.
5
Locate the Coloring and Style section. From the Color table list, choose GrayBody.
Surface 3
1
Right-click 3D representation and choose Surface.
2
In the Settings window for Surface, locate the Data section.
3
From the Dataset list, choose Extrusion 2D 2.
4
Locate the Expression section. In the Expression text field, type 1.
Material Appearance 1
1
Right-click Surface 3 and choose Material Appearance.
2
In the Settings window for Material Appearance, locate the Appearance section.
3
From the Appearance list, choose Custom.
4
From the Material type list, choose Sand.
5
Click the  Show Legends button in the Graphics toolbar.
6
Click the  Show Grid button in the Graphics toolbar.
7
In the Model Builder window, expand the Results > Views node.
Camera
1
In the Model Builder window, expand the Results > Views > View 3D 2 node, then click Camera.
2
In the Settings window for Camera, locate the Position section.
3
In the x text field, type 11.
4
In the y text field, type 8.
5
In the z text field, type 13.
6
Locate the Up Vector section. In the x text field, type -0.15.
7
In the y text field, type 1.
8
In the z text field, type -0.25.
9
Click  Update.
3D representation
1
In the Model Builder window, under Results click 3D representation.
2
In the 3D representation toolbar, click  Plot.