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Trench-Gate IGBT 2D
In this first half of a two-part example, a 2D model of a trench-gate IGBT is built, which will be extended to 3D in the second half. In general, it is the most efficient to start with a 2D model to make sure everything works as expected, before extending it to 3D. The Caughey-Thomas mobility model is combined with the Klaassen unified mobility model to account for velocity saturation and phonon, impurity, and carrier-carrier scattering. The contact resistance option of metal contact boundary conditions is used to implement the mixed-mode simulation with parasitic resistance at the collector and emitter as mentioned in the reference paper. The computed collector current density as a function of the collector voltage agrees reasonably well with the published result.
Introduction
In Ref. 1, Watanabe et al. studied the effect of three-dimensional current flow on the simulation result by comparing 2D and 3D models of trench-gate IGBTs. They found that the 3D model reveals a nonuniform current distribution in the third dimension in the high current regime, where the current in the MOS channel region is limited by the electron supply from the n+-emitter. This nonuniform current distribution explains the reason why while the 3D model agrees well with measured result, the 2D model is off by the factor of the ratio of the n+-emitter length to the total emitter length.
In this example, we start with the 2D model.
Model Definition
The model structure is detailed in Ref. 1, with additional details in Ref. 2.
Following the reference paper, the symmetry of the physics is used and only half of the cell is drawn in the geometry. Some thin regions are created under the gate and the emitter surface, in order to mesh those high-gradient regions with thin rectangles or isosceles trapezoids.
The Klaassen Unified Mobility Model and Caughey-Thomas Mobility Model are used. The band gap, effective density of states, and the band-gap narrowing reference concentration are modified according to Ref. 2. The Contact resistance option of metal contact boundary conditions is used to implement the mixed-mode simulation with parasitic resistance at the collector and emitter as mentioned in the reference paper.
See the comments in the section Modeling Instructions for more detailed discussions on the model construction, solution processes, and result visualization.
Results and Discussion
Figure 1 and Figure 2 show the collector current density as a function of the collector voltage, to be compared with Fig. 4(a) and (b) in Ref. 1. Reasonable agreement is seen.
Figure 1: Collector current density as a function of the collector voltage, log scale.
Figure 2: Collector current density as a function of the collector voltage, linear scale.
References
1. M. Watanabe and others, “Impact of three-dimensional current flow on accurate TCAD simulation for trench-gate IGBTs,” 31st International Symposium on Power Semiconductor Devices and ICs (ISPSD), pp. 311–314, 2019, doi: 10.1109/ISPSD.2019.8757640.
2. N. Shigyo and others, “Modeling and Simulation of Si IGBTs,” 2020 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), pp. 129–132, 2020, doi: 10.23919/SISPAD49475.2020.9241627.
Application Library path: Semiconductor_Module/Transistors/trench_gate_igbt_2d
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 Semiconductor>Semiconductor (semi).
3
Click Add.
4
Click  Study.
It is usually a good practice to start the first study with a Semiconductor Equilibrium study step, which is easier to converge and provides a good initial value for subsequent study steps.
5
In the Select Study tree, select Preset Studies for Selected Physics Interfaces>Semiconductor Equilibrium.
6
Click  Done.
Geometry 1
Set the length unit to a convenient one, in this model, micrometer.
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.
Enter the device model parameters for the "k=3" case in the reference paper. Hide most of the parameters that will not be used parametric sweeps (in the first Parameters node). Use a second Parameters node for the terminal voltages that may be swept.
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
W
16[um]
1.6E-5 m
Device width
S
1[um]
1E-6 m
Mesa width
DT
2[um]
2E-6 m
Trench depth
WT
0.33[um]
3.3E-7 m
Trench width
Wewin
0.16[um]
1.6E-7 m
Emitter contact window
Dp
1.4[um]
1.4E-6 m
p-base depth
Dn
0.13[um]
1.3E-7 m
n+ emitter depth
tOX
33[nm]
3.3E-8 m
Oxide thickness
Dnb
120[um]
1.2E-4 m
n-base depth
Ln
1.5[um]
1.5E-6 m
n+ emitter length
Lp
1.5[um]
1.5E-6 m
p+ emitter length
Nab
3.8e17[cm^-3]
3.8E23 1/m³
p-base peak doping
Ndb
8.5e13[cm^-3]
8.5E19 1/m³
n-base doping
Ndbf
9e15[cm^-3]
9E21 1/m³
n-buffer doping
Nac
3.7e18[cm^-3]
3.7E24 1/m³
p+ collector doping
Nae
1e20[cm^-3]
1E26 1/m³
p+ emitter doping
Nde
1e20[cm^-3]
1E26 1/m³
n+ emitter doping
tau0
10[us]
1E-5 s
Carrier lifetime
tnbf
5[um]
5E-6 m
n-buffer thickness
Dsub
10[um]
1E-5 m
p+ collector thickness
t0
Dp+Dnb+tnbf+Dsub
1.364E-4 m
Device thickness
d0
(Ln+Lp)/2
1.5E-6 m
Out-of-plan thickness
rhoCC
1.6e-4[ohm*cm^2]
1.6E-8 Ω·m²
p+ substrate equivalent resistivity
rhoCE
4.7e-6[ohm*cm^2]
4.7E-10 Ω·m²
Emitter contact resistivity
T0
300[K]
300 K
Lattice temperature
Eg0
1.1743[V]
1.1743 V
Band gap Shigyo
Nv_
(T0/300[K])^(3/2)*1.04e19[1/cm^3]
1.04E25 1/m³
Valence band DOS COMSOL
Nc_
(T0/300[K])^(3/2)*2.8e19[1/cm^3]
2.8E25 1/m³
Conduction band DOS COMSOL
ni0
1e10[cm^-3]
1E16 1/m³
Intrinsic carrier concentration
Nvcfac
sqrt(ni0^2/Nv_/Nc_/exp(-Eg0*e_const/T0/k_B_const))
4.2814
DOS factor to match ni
Nv0
Nvcfac*Nv_
4.4527E25 1/m³
Valence band DOS Shigyo
Nc0
Nvcfac*Nc_
1.1988E26 1/m³
Conduction band DOS Shigyo
Nref0
6.5e16[cm^-3]
6.5E22 1/m³
Band gap narrowing reference concentration Shigyo
4
Click to expand the Visibility section. Clear the Show in parameter selections check box.
Parameters 2
1
In the Home toolbar, click  Parameters and choose Add>Parameters.
2
In the Settings window for Parameters, locate the Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
Vc
0[V]
0 V
Collector voltage
Vg
5[V]
5 V
Gate voltage
Build the geometry. We will take advantage of the symmetry of the physics, so draw only half of the cell. Make the emitter contact window slightly wider to ensure good contact to both the n+ and p+ doped regions due to their 2D arrangement. Create thin regions under the gate and the emitter surface, in order to mesh those high-gradient regions with thin rectangles or isosceles trapezoids. Those regions can still be merged with the rest of the geometry by using Mesh Control Edges.
Geometry 1
Rectangle 1 - Device outline (half cell)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, type Rectangle 1 - Device outline (half cell) in the Label text field.
3
Locate the Size and Shape section. In the Width text field, type W/2.
4
In the Height text field, type t0.
5
Locate the Position section. In the y text field, type -t0.
6
Click to expand the Layers section. In the table, enter the following settings:
Layer name
Thickness (µm)
Layer 1
Dsub
Layer 2
tnbf
Rectangle 2 - Trench
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, type Rectangle 2 - Trench in the Label text field.
3
Locate the Size and Shape section. In the Width text field, type WT.
4
In the Height text field, type DT-WT/2.
5
Locate the Position section. In the x text field, type S/2.
6
In the y text field, type -(DT-WT/2).
Circle 1 - Trench
1
In the Geometry toolbar, click  Circle.
2
In the Settings window for Circle, type Circle 1 - Trench in the Label text field.
3
Locate the Size and Shape section. In the Radius text field, type WT/2.
4
Locate the Position section. In the x text field, type S/2+WT/2.
5
In the y text field, type -(DT-WT/2).
Difference 1 - Device outline minus trench
1
In the Geometry toolbar, click  Booleans and Partitions and choose Difference.
2
In the Settings window for Difference, type Difference 1 - Device outline minus trench in the Label text field.
3
Select the object r1 only.
4
Locate the Difference section. Find the Objects to subtract subsection. Click to select the  Activate Selection toggle button.
5
Select the objects c1 and r2 only.
Point 1 - Emitter contact & doping boundary
1
In the Geometry toolbar, click  Point.
2
In the Settings window for Point, type Point 1 - Emitter contact & doping boundary in the Label text field.
3
Locate the Point section. In the x text field, type S/4-Wewin/1.5 S/4 S/4+Wewin/1.5.
4
In the y text field, type 0 0 0.
Rectangle 3 - Mesh help lines
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, type Rectangle 3 - Mesh help lines in the Label text field.
3
Locate the Size and Shape section. In the Width text field, type S/2.
4
In the Height text field, type Dn.
5
Locate the Position section. In the y text field, type -Dn.
Rectangle 4 - Mesh help lines
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, type Rectangle 4 - Mesh help lines in the Label text field.
3
Locate the Size and Shape section. In the Width text field, type 30[nm].
4
In the Height text field, type DT-WT/2.
5
Locate the Position section. In the x text field, type S/2-30[nm].
6
In the y text field, type -(DT-WT/2).
Rectangle 5- Mesh help lines
1
Right-click Rectangle 4 - Mesh help lines and choose Duplicate.
2
In the Settings window for Rectangle, type Rectangle 5- Mesh help lines in the Label text field.
3
Locate the Position section. In the x text field, type S/2+WT.
Circle 2 - Mesh help curves
1
In the Model Builder window, under Component 1 (comp1)>Geometry 1 right-click Circle 1 - Trench (c1) and choose Duplicate.
2
In the Settings window for Circle, type Circle 2 - Mesh help curves in the Label text field.
3
Locate the Object Type section. From the Type list, choose Curve.
4
Locate the Size and Shape section. In the Radius text field, type WT/2+30[nm].
5
In the Sector angle text field, type 180.
6
Locate the Rotation Angle section. In the Rotation text field, type 180.
Delete Entities 1 (del1)
1
In the Model Builder window, right-click Geometry 1 and choose Delete Entities.
2
On the object c2, select Boundaries 3 and 4 only.
Line Segment 1 - Mesh help line
1
In the Geometry toolbar, click  More Primitives and choose Line Segment.
2
In the Settings window for Line Segment, type Line Segment 1 - Mesh help line in the Label text field.
3
Locate the Starting Point section. From the Specify list, choose Coordinates.
4
In the y text field, type -DT*8.
5
Locate the Endpoint section. From the Specify list, choose Coordinates.
6
In the y text field, type -DT*8.
7
In the x text field, type W/2.
Mesh Control Edges 1 (mce1)
1
In the Geometry toolbar, click  Virtual Operations and choose Mesh Control Edges.
2
On the object fin, select Boundaries 8, 10, 15–18, 23, 25, 31, and 33 only.
3
In the Geometry toolbar, click  Build All.
Add the built-in silicon material. Some properties will be replaced in the physics settings according to the reference paper.
Add Material
1
In the Home 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 Add to Component in the window toolbar.
5
In the Home toolbar, click  Add Material to close the Add Material window.
Set up the physics. After creating the mobility subnodes, remember to select the desired mobility model in the Semiconductor Material Model parent node.
Semiconductor (semi)
1
In the Model Builder window, under Component 1 (comp1) click Semiconductor (semi).
2
In the Settings window for Semiconductor, locate the Thickness section.
3
In the d text field, type d0.
4
Locate the Model Properties section. From the Carrier statistics list, choose Fermi-Dirac.
Semiconductor Material Model 1
In the Model Builder window, under Component 1 (comp1)>Semiconductor (semi) click Semiconductor Material Model 1.
Klaassen Unified Mobility Model (LIC) 1
In the Physics toolbar, click  Attributes and choose Klaassen Unified Mobility Model (LIC).
Semiconductor Material Model 1
In the Model Builder window, click Semiconductor Material Model 1.
Caughey-Thomas Mobility Model (E) 1
1
In the Physics toolbar, click  Attributes and choose Caughey-Thomas Mobility Model (E).
2
In the Settings window for Caughey-Thomas Mobility Model (E), locate the Input Mobilities section.
3
From the μn,in list, choose Electron mobility, Klaassen unified (semi/smm1/mmkl1).
4
From the μp,in list, choose Hole mobility, Klaassen unified (semi/smm1/mmkl1).
Semiconductor Material Model 1
1
In the Model Builder window, click Semiconductor Material Model 1.
2
In the Settings window for Semiconductor Material Model, locate the Model Input section.
3
In the T text field, type T0.
4
Locate the Material Properties section. From the Eg,0 list, choose User defined. In the associated text field, type Eg0.
5
From the Nv list, choose User defined. In the associated text field, type Nv0.
6
From the Nc list, choose User defined. In the associated text field, type Nc0.
7
Locate the Mobility Model section. From the μn list, choose Electron mobility, Caughey-Thomas (semi/smm1/mmct1).
8
From the μp list, choose Hole mobility, Caughey-Thomas (semi/smm1/mmct1).
9
Click to expand the Band Gap Narrowing section. From the Band gap narrowing list, choose Slotboom.
10
From the Nref list, choose User defined. In the associated text field, type Nref0.
Analytic Doping Model - n-base
1
In the Physics toolbar, click  Domains and choose Analytic Doping Model.
2
In the Settings window for Analytic Doping Model, type Analytic Doping Model - n-base in the Label text field.
3
Select Domain 3 only.
4
Locate the Impurity section. From the Impurity type list, choose Donor doping (n-type).
5
In the ND0 text field, type Ndb.
Analytic Doping Model - n-buffer
1
In the Physics toolbar, click  Domains and choose Analytic Doping Model.
2
In the Settings window for Analytic Doping Model, type Analytic Doping Model - n-buffer in the Label text field.
3
Select Domain 2 only.
4
Locate the Impurity section. From the Impurity type list, choose Donor doping (n-type).
5
In the ND0 text field, type Ndbf.
Analytic Doping Model - p+ collector
1
In the Physics toolbar, click  Domains and choose Analytic Doping Model.
2
In the Settings window for Analytic Doping Model, type Analytic Doping Model - p+ collector in the Label text field.
3
Select Domain 1 only.
4
Locate the Impurity section. In the NA0 text field, type Nac.
Geometric Doping Model - p-base
1
In the Physics toolbar, click  Domains and choose Geometric Doping Model.
2
In the Settings window for Geometric Doping Model, type Geometric Doping Model - p-base in the Label text field.
3
Select Domain 3 only.
4
Locate the Impurity section. In the NA0 text field, type Nab.
5
Locate the Profile section. In the dj text field, type Dp.
6
In the Nb text field, type Ndb.
Boundary Selection for Doping Profile 1
1
In the Model Builder window, expand the Geometric Doping Model - p-base node, then click Boundary Selection for Doping Profile 1.
2
Select Boundaries 7–10 and 13 only.
Geometric Doping Model - p+ emitter
1
In the Physics toolbar, click  Domains and choose Geometric Doping Model.
2
In the Settings window for Geometric Doping Model, type Geometric Doping Model - p+ emitter in the Label text field.
3
Select Domain 3 only.
4
Locate the Impurity section. In the NA0 text field, type Nae.
5
Locate the Profile section. In the dj text field, type Dn.
6
In the Nb text field, type Ndb.
Boundary Selection for Doping Profile 1
1
In the Model Builder window, expand the Geometric Doping Model - p+ emitter node, then click Boundary Selection for Doping Profile 1.
2
Select Boundaries 7 and 8 only.
Geometric Doping Model - n+ emitter
1
In the Physics toolbar, click  Domains and choose Geometric Doping Model.
2
In the Settings window for Geometric Doping Model, type Geometric Doping Model - n+ emitter in the Label text field.
3
Select Domain 3 only.
4
Locate the Impurity section. From the Impurity type list, choose Donor doping (n-type).
5
In the ND0 text field, type Nde.
6
Locate the Profile section. In the dj text field, type Dn.
7
In the Nb text field, type Ndb.
Boundary Selection for Doping Profile 1
1
In the Model Builder window, expand the Geometric Doping Model - n+ emitter node, then click Boundary Selection for Doping Profile 1.
2
Select Boundaries 9 and 10 only.
Trap-Assisted Recombination 1
1
In the Physics toolbar, click  Domains and choose Trap-Assisted Recombination.
2
In the Settings window for Trap-Assisted Recombination, locate the Domain Selection section.
3
From the Selection list, choose All domains.
4
Locate the Shockley-Read-Hall Recombination section. From the τn list, choose User defined. In the associated text field, type tau0.
5
From the τp list, choose User defined. In the associated text field, type tau0.
Metal Contact - Emitter
1
In the Physics toolbar, click  Boundaries and choose Metal Contact.
2
In the Settings window for Metal Contact, type Metal Contact - Emitter in the Label text field.
3
Select Boundaries 8 and 9 only.
4
Locate the Terminal section. In the Terminal name text field, type E.
5
Select the Contact resistance check box.
6
In the ρc text field, type rhoCE.
Metal Contact - Collector
1
In the Physics toolbar, click  Boundaries and choose Metal Contact.
2
In the Settings window for Metal Contact, type Metal Contact - Collector in the Label text field.
3
Select Boundary 2 only.
4
Locate the Terminal section. In the Terminal name text field, type C.
5
In the V0 text field, type Vc.
6
Select the Contact resistance check box.
7
In the ρc text field, type rhoCC.
Thin Insulator Gate 1
1
In the Physics toolbar, click  Boundaries and choose Thin Insulator Gate.
2
Select Boundaries 11 and 12 only.
3
In the Settings window for Thin Insulator Gate, locate the Terminal section.
4
In the Terminal name text field, type G.
5
In the V0 text field, type Vg.
6
Locate the Gate Contact section. In the εins text field, type 3.9.
7
In the dins text field, type tOX.
Create the mesh. To reduce computation time, a relatively coarse mesh is used in this example.
Mesh 1
Edge 1 - Metal contact
1
In the Mesh toolbar, click  Edge.
2
In the Settings window for Edge, type Edge 1 - Metal contact in the Label text field.
3
Select Boundaries 8 and 9 only.
4
Click to expand the Control Entities section. Clear the Smooth across removed control entities check box.
Distribution 1
1
Right-click Edge 1 - Metal contact and choose Distribution.
2
In the Settings window for Distribution, locate the Distribution section.
3
From the Distribution type list, choose Predefined.
4
In the Number of elements text field, type 4.
5
In the Element ratio text field, type 4.
6
Select the Symmetric distribution check box.
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
Click the Custom button.
4
Locate the Element Size Parameters section. In the Maximum element size text field, type 9.1.
5
In the Minimum element size text field, type 0.04.
6
In the Maximum element growth rate text field, type 1.25.
7
In the Curvature factor text field, type 0.35.
8
In the Resolution of narrow regions text field, type 1.1.
Edge 2 - Emitter surface
1
In the Mesh toolbar, click  Edge.
2
In the Settings window for Edge, type Edge 2 - Emitter surface in the Label text field.
3
Select Boundary 7 only.
4
Locate the Control Entities section. Clear the Smooth across removed control entities check box.
Distribution 1
1
Right-click Edge 2 - Emitter surface and choose Distribution.
2
In the Settings window for Distribution, locate the Distribution section.
3
From the Distribution type list, choose Predefined.
4
In the Number of elements text field, type 3.
5
In the Element ratio text field, type 6.
6
Select the Reverse direction check box.
Edge 3 - Emitter surface
1
In the Mesh toolbar, click  Edge.
2
In the Settings window for Edge, type Edge 3 - Emitter surface in the Label text field.
3
Select Boundary 10 only.
4
Locate the Control Entities section. Clear the Smooth across removed control entities check box.
Distribution 1
1
Right-click Edge 3 - Emitter surface and choose Distribution.
2
In the Settings window for Distribution, locate the Distribution section.
3
From the Distribution type list, choose Predefined.
4
In the Element ratio text field, type 3.
5
Select the Symmetric distribution check box.
Copy Edge 1
1
In the Model Builder window, right-click Mesh 1 and choose Copying Operations>Copy Edge.
2
Select Boundaries 7–10 only.
3
In the Settings window for Copy Edge, locate the Destination Boundaries section.
4
Click to select the  Activate Selection toggle button.
5
Select Boundary 26 only.
6
Click to expand the Control Entities section. Clear the Smooth across removed control entities check box.
Mapped 1 - Emitter depth
1
In the Mesh toolbar, click  Mapped.
2
In the Settings window for Mapped, type Mapped 1 - Emitter depth in the Label text field.
3
Locate the Domain Selection section. From the Geometric entity level list, choose Domain.
4
Select Domain 9 only.
5
Click to expand the Control Entities section. Clear the Smooth across removed control entities check box.
6
Click to expand the Reduce Element Skewness section. Select the Adjust edge mesh check box.
Distribution 1
1
Right-click Mapped 1 - Emitter depth and choose Distribution.
2
Select Boundaries 18 and 29 only.
3
In the Settings window for Distribution, locate the Distribution section.
4
From the Distribution type list, choose Predefined.
5
In the Element ratio text field, type 3.
6
Select the Reverse direction check box.
7
Click the  Zoom to Selection button in the Graphics toolbar.
8
Click  Build Selected.
Mapped 2 - Gate depth
1
In the Mesh toolbar, click  Mapped.
2
In the Settings window for Mapped, type Mapped 2 - Gate depth in the Label text field.
3
Locate the Domain Selection section. From the Geometric entity level list, choose Domain.
4
Select Domains 5–8 only.
5
Locate the Control Entities section. Clear the Smooth across removed control entities check box.
6
Locate the Reduce Element Skewness section. Select the Adjust edge mesh check box.
Distribution 1 - Left depth
1
Right-click Mapped 2 - Gate depth and choose Distribution.
2
In the Settings window for Distribution, type Distribution 1 - Left depth in the Label text field.
3
Select Boundaries 19, 28, and 30 only.
4
Locate the Distribution section. From the Distribution type list, choose Predefined.
5
In the Element ratio text field, type 10.
6
Select the Reverse direction check box.
Distribution 2 - Right depth
1
In the Model Builder window, right-click Mapped 2 - Gate depth and choose Distribution.
2
In the Settings window for Distribution, type Distribution 2 - Right depth in the Label text field.
3
Select Boundaries 13 and 31 only.
4
Locate the Distribution section. From the Distribution type list, choose Predefined.
5
In the Element ratio text field, type 10.
Distribution 3 - Left surface
1
Right-click Mapped 2 - Gate depth and choose Distribution.
2
In the Settings window for Distribution, type Distribution 3 - Left surface in the Label text field.
3
Select Boundaries 20 and 27 only.
4
Locate the Distribution section. From the Distribution type list, choose Predefined.
5
In the Number of elements text field, type 20.
6
In the Element ratio text field, type 3.
7
Select the Symmetric distribution check box.
Distribution 4 - Right surface
1
Right-click Mapped 2 - Gate depth and choose Distribution.
2
In the Settings window for Distribution, type Distribution 4 - Right surface in the Label text field.
3
Select Boundaries 22 and 32 only.
4
Locate the Distribution section. From the Distribution type list, choose Predefined.
5
In the Number of elements text field, type 6.
6
In the Element ratio text field, type 4.
Distribution 5 - Bottom surface
1
Right-click Mapped 2 - Gate depth and choose Distribution.
2
In the Settings window for Distribution, type Distribution 5 - Bottom surface in the Label text field.
3
Select Boundaries 12, 21, 33, and 34 only.
4
Locate the Distribution section. From the Distribution type list, choose Predefined.
5
In the Number of elements text field, type 8.
6
Click the  Zoom to Selection button in the Graphics toolbar.
7
Click  Build Selected.
Free Triangular 1
1
In the Mesh toolbar, click  Free Triangular.
2
In the Settings window for Free Triangular, locate the Domain Selection section.
3
From the Geometric entity level list, choose Domain.
4
Select Domain 4 only.
5
Click to expand the Control Entities section. Clear the Smooth across removed control entities check box.
6
Click the  Zoom to Selection button in the Graphics toolbar.
7
Click  Build Selected.
Copy Edge 2
1
In the Model Builder window, right-click Mesh 1 and choose Copying Operations>Copy Edge.
2
Select Boundary 25 only.
3
In the Settings window for Copy Edge, locate the Destination Boundaries section.
4
Click to select the  Activate Selection toggle button.
5
Select Boundaries 2, 4, and 6 only.
6
Locate the Control Entities section. Clear the Smooth across removed control entities check box.
Mapped 3
1
In the Mesh toolbar, click  Mapped.
2
In the Settings window for Mapped, locate the Control Entities section.
3
Clear the Smooth across removed control entities check box.
4
Locate the Reduce Element Skewness section. Select the Adjust edge mesh check box.
Distribution 1 - n-base
1
Right-click Mapped 3 and choose Distribution.
2
In the Settings window for Distribution, type Distribution 1 - n-base in the Label text field.
3
Select Boundaries 5 and 24 only.
4
Locate the Distribution section. From the Distribution type list, choose Predefined.
5
In the Number of elements text field, type 10.
6
In the Element ratio text field, type 5.
7
Select the Symmetric distribution check box.
Distribution 2 - n-buffer
1
In the Model Builder window, right-click Mapped 3 and choose Distribution.
2
In the Settings window for Distribution, type Distribution 2 - n-buffer in the Label text field.
3
Select Boundaries 3 and 15 only.
4
Locate the Distribution section. From the Distribution type list, choose Predefined.
5
In the Element ratio text field, type 10.
Distribution 3 - p+ collector
1
Right-click Mapped 3 and choose Distribution.
2
In the Settings window for Distribution, type Distribution 3 - p+ collector in the Label text field.
3
Select Boundaries 1 and 14 only.
4
Locate the Distribution section. From the Distribution type list, choose Predefined.
5
In the Number of elements text field, type 3.
6
In the Element ratio text field, type 30.
7
Select the Reverse direction check box.
8
Click  Build All.
Add a Stationary study step to sweep the collector voltage from 0 to 5 V. For this second study step, use initial value based scaling and manual scaling for better error estimate.
Study 1
Stationary
1
In the Study toolbar, click  Study Steps and choose Stationary>Stationary.
2
In the Settings window for Stationary, click to expand the Study Extensions section.
3
Select the Auxiliary sweep check box.
4
Click  Add.
5
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
Vc (Collector voltage)
range(0,0.1,1.2) range(1.5,0.5,5)
V
6
In the Study toolbar, click  Get Initial Value.
Solver Configurations
In the Model Builder window, expand the Study 1>Solver Configurations node.
Solution 1 (sol1)
1
In the Model Builder window, expand the Study 1>Solver Configurations>Solution 1 (sol1) node, then click Dependent Variables 2.
2
In the Settings window for Dependent Variables, locate the Scaling section.
3
From the Method list, choose Initial value based.
4
In the Model Builder window, expand the Study 1>Solver Configurations>Solution 1 (sol1)>Dependent Variables 2 node, then click Voltage drop across contact (comp1.semi.V_dae).
5
In the Settings window for Field, locate the Scaling section.
6
From the Method list, choose Manual.
7
In the Study toolbar, click  Compute.
Plot the Jc-Vc curve in log and linear scales to compare with Fig. 4(a) and (b) in the reference paper.
Results
J-V (log) - Fig.4(a)
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type J-V (log) - Fig.4(a) in the Label text field.
3
Locate the Axis section. Select the Manual axis limits check box.
4
In the x minimum text field, type 0.
5
In the x maximum text field, type 5.
6
In the y minimum text field, type 10.
7
In the y maximum text field, type 3000.
8
Select the y-axis log scale check box.
9
Locate the Legend section. From the Position list, choose Lower right.
Global 1 - 2D
1
Right-click J-V (log) - Fig.4(a) and choose Global.
2
In the Settings window for Global, type Global 1 - 2D in the Label text field.
3
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
semi.J0_C
A/cm^2
2D
4
In the J-V (log) - Fig.4(a) toolbar, click  Plot.
J-V (linear) - Fig.4(b)
1
In the Model Builder window, right-click J-V (log) - Fig.4(a) and choose Duplicate.
2
In the Settings window for 1D Plot Group, type J-V (linear) - Fig.4(b) in the Label text field.
3
Locate the Axis section. In the x maximum text field, type 3.
4
In the y minimum text field, type -20.
5
In the y maximum text field, type 700.
6
Clear the y-axis log scale check box.
7
In the J-V (linear) - Fig.4(b) toolbar, click  Plot.
Finally plot the electron and hole current streamlines on top of the electron concentration as the model thumbnail.
Electron Concentration & Current Streamlines
1
In the Model Builder window, under Results click Electron Concentration (semi).
2
In the Settings window for 2D Plot Group, type Electron Concentration & Current Streamlines in the Label text field.
3
Locate the Plot Settings section. Click  Go to Source.
Definitions
Axis
1
In the Model Builder window, expand the View 1 node, then click Axis.
2
In the Settings window for Axis, locate the Axis section.
3
In the x minimum text field, type -0.1.
4
In the x maximum text field, type 0.6.
5
In the y minimum text field, type -0.8.
6
In the y maximum text field, type 0.05.
7
Click  Update.
Results
Streamline 1 - Electron current
1
In the Model Builder window, right-click Electron Concentration & Current Streamlines and choose Streamline.
2
In the Settings window for Streamline, type Streamline 1 - Electron current in the Label text field.
3
Click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Semiconductor>Currents and charge>Electron current>semi.JnX,semi.JnY - Electron current density.
4
Locate the Streamline Positioning section. In the Number text field, type 10.
5
Select Boundary 9 only.
Streamline 2 - Hole current
1
Right-click Electron Concentration & Current Streamlines and choose Streamline.
2
In the Settings window for Streamline, type Streamline 2 - Hole current in the Label text field.
3
Click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Semiconductor>Currents and charge>Hole current>semi.JpX,semi.JpY - Hole current density.
4
Locate the Streamline Positioning section. In the Number text field, type 10.
5
Select Boundary 8 only.
6
Locate the Coloring and Style section. Find the Point style subsection. From the Color list, choose White.
7
In the Electron Concentration & Current Streamlines toolbar, click  Plot.