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P–N Diode Circuit
This model compares a full device level simulation with a lumped circuit model to simulate a half-wave rectifier.
Introduction
The p–n diode is of great importance in modern electronic applications. It is often used as a rectifier to convert alternative currents (AC) to direct currents (DC) by blocking either the positive or negative half of the AC wave. The present example simulates the transient behavior of a p–n diode used as the active component of a half-wave rectifier circuit –see Figure 1.
Figure 1: A basic half-wave rectifier circuit. An AC voltage source is connected to the anode of a p–n diode. The resistor represents the load of the circuit.
In this example, a full level device simulation is made by connecting a 2D meshed p–n junction to a circuit containing a sinusoidal source, a resistor, and a ground (the half-wave rectifier circuit is displayed in Figure 1). In order to validate the results, the outputs of the full device simulation are compared to the circuit response obtained using a large signal diode model (see the electrical circuit).
Model Definition
Figure 2 shows the modeled device cross section and doping profile. The diode has a width of 10 μm and a depth of 7 μm. The length of the diode has been set to 10 μm (not meshed). A Shockley–Read–Hall recombination is also added to the model in order to simulate the type of recombination usually observed in indirect band-gap semiconductor such as silicon, which is the material used in this example. The meshed diode is connected to the half wave circuit using an ohmic terminal. For the large signal diode model, the saturation current and ideality factor have been set to values fitting the I–V curve of the modeled diode.
Figure 2: Top: net doping concentration along the symmetry line (center of the diode cross section). Bottom: cross section of the simulated device. To save computation time, only half of the diode is meshed, that is, the right side delimited by the axis of symmetry (red dashed line).
If the entire time history is of interest, then the time-dependent study should use a physical solution as the initial condition. Usually, this is done by adding a Stationary study step before the time dependent study step. In addition, it is sometimes necessary to turn off the Consistent initialization under the Time Stepping section of the settings window for the Time-Dependent Solver node under the Solver Configurations tree structure.
For simplicity, this example model has omitted all the above steps.
For a more detailed discussion on setting up transient studies, see the blog post
  https://www.comsol.com/blogs/how-to-simulate-the-carrier-dynamics-in-semiconductor-devices/
and the two example models:
Forward Recovery of a PIN Diode (Application Library path Semiconductor_Module/Device_Building_Blocks/pin_forward_recovery)
Reverse Recovery of a PIN Diode (Application Library path Semiconductor_Module/Device_Building_Blocks/pin_reverse_recovery)
Results and Discussion
Figure 3 shows the output voltages obtained from both the full level simulation and large signal model. As expected from the reverse operation of a p–n diode, clipping occurs on the negative half of the wave in the diode.
Figure 3: Output voltages obtained from both the full level simulation and large signal model. Voltages have been monitored at the source, diode, and load ends.
Application Library path: Semiconductor_Module/Device_Building_Blocks/pn_diode_circuit
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
In the Select Physics tree, select AC/DC > Electrical Circuit (cir).
5
Click Add.
6
Click  Study.
7
In the Select Study tree, select General Studies > Time Dependent.
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
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file pn_diode_circuit_parameters.txt.
Geometry 1
1
In the Geometry toolbar, click  Sketch.
2
In the Model Builder window, click Geometry 1.
3
In the Settings window for Geometry, locate the Units section.
4
From the Length unit list, choose µm.
Rectangle 1 (r1)
1
In the Geometry toolbar, click  Rectangle.
2
In the Model Builder window, collapse the Geometry 1 node.
3
In the Model Builder window, click Rectangle 1 (r1).
4
In the Settings window for Rectangle, locate the Size and Shape section.
5
In the Width text field, type w_diode/2.
6
In the Height text field, type d_diode.
7
Locate the Position section. In the y text field, type -d_diode.
The doping profiles will be created in the Semiconductor interface. However, in order to have a finer mesh in the junction vicinities, it is wise to create geometry objects defining the doping regions in the semiconducting material.
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 w_anode/2+d_p.
4
In the Height text field, type d_p.
5
Locate the Position section. In the y text field, type -d_p.
Fillet 1 (fil1)
1
In the Geometry toolbar, click  Fillet.
2
On the object r2, select Point 2 only.
It might be easier to select the correct point by using the Selection List window. To open this window, in the Home toolbar click Windows and choose Selection List. (If you are running the cross-platform desktop, you find Windows in the main menu.)
3
In the Settings window for Fillet, locate the Radius section.
4
In the Radius text field, type d_p.
Point 1 (pt1)
1
In the Geometry toolbar, click  Point.
2
In the Settings window for Point, locate the Point section.
3
In the x text field, type w_anode/2.
4
Click  Build All Objects.
Load the semiconductor material properties for silicon.
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.
Semiconductor (semi)
Analytic Doping Model 1
1
In the Physics toolbar, click  Domains and choose Analytic Doping Model.
2
In the Settings window for Analytic Doping Model, locate the Domain Selection section.
3
From the Selection list, choose All domains.
4
Locate the Impurity section. From the Impurity type list, choose Donor doping (n-type).
5
In the ND0 text field, type Nd_back.
Analytic Doping Model 2
1
In the Physics toolbar, click  Domains and choose Analytic Doping Model.
2
In the Settings window for Analytic Doping Model, locate the Domain Selection section.
3
From the Selection list, choose All domains.
4
Locate the Distribution section. From the list, choose Box.
5
Locate the Uniform Region section. Specify the r0 vector as
0[um]
X
-d_diode
Y
6
In the W text field, type w_diode/2.
7
Locate the Impurity section. From the Impurity type list, choose Donor doping (n-type).
8
In the ND0 text field, type Nd_max.
9
Locate the Profile section. From the Nb list, choose Donor concentration (semi/adm1).
Analytic Doping Model 3
1
In the Physics toolbar, click  Domains and choose Analytic Doping Model.
2
In the Settings window for Analytic Doping Model, locate the Domain Selection section.
3
From the Selection list, choose All domains.
4
Locate the Distribution section. From the list, choose Box.
5
Locate the Uniform Region section. In the W text field, type w_anode/2.
6
In the D text field, type d_p.
7
Locate the Impurity section. In the NA0 text field, type Na_max.
8
Locate the Profile section. From the Nb list, choose Donor concentration (semi/adm1).
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.
Metal Contact 1
1
In the Physics toolbar, click  Boundaries and choose Metal Contact.
2
Select Boundary 5 only.
3
In the Settings window for Metal Contact, locate the Terminal section.
4
From the Terminal type list, choose Circuit (current).
Metal Contact 2
1
In the Physics toolbar, click  Boundaries and choose Metal Contact.
2
Select Boundary 2 only.
Electrical Circuit (cir)
Resistor 1 (R1)
1
In the Electrical Circuit toolbar, click  Resistor.
Use a 100 kOhm load resistor to limit the current in the circuit.
2
In the Settings window for Resistor, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
1
n
0
4
Locate the Device Parameters section. In the R text field, type 100[kohm].
Voltage Source 1 (V1)
1
In the Electrical Circuit toolbar, click  Voltage Source.
2
In the Settings window for Voltage Source, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
2
n
0
4
Locate the Device Parameters section. From the Source type list, choose Sine source.
5
In the vsrc text field, type Vac.
6
In the f text field, type f.
External I vs. U 1 (IvsU1)
1
In the Electrical Circuit toolbar, click  External I vs. U.
2
In the Settings window for External I vs. U, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p
2
n
1
4
Locate the External Device section. From the V list, choose Terminal voltage (semi/mc1).
By adding another circuit model, you can compare our coupled model with a full circuit model (using a large-signal diode model).
Add Physics
1
In the Home toolbar, click  Add Physics to open the Add Physics window.
2
Go to the Add Physics window.
3
In the tree, select AC/DC > Electrical Circuit (cir).
4
Click the Add to Component 1 button in the window toolbar.
5
In the Home toolbar, click  Add Physics to close the Add Physics window.
Electrical Circuit 2 (cir2)
Voltage Source 1 (V1)
1
In the Electrical Circuit toolbar, click  Voltage Source.
2
In the Settings window for Voltage Source, type V2 in the Name text field.
3
Locate the Node Connections section. In the table, enter the following settings:
Label
Node names
p
1
n
0
4
Locate the Device Parameters section. From the Source type list, choose Sine source.
5
In the vsrc text field, type Vac.
6
In the f text field, type f.
Use the diode large scale model with the following parameters.
Diode 1 (D1)
1
In the Electrical Circuit toolbar, click  Diode.
2
In the Settings window for Diode, type D2 in the Name text field.
3
Locate the Node Connections section. In the table, enter the following settings:
Label
Node names
p
1
n
2
4
Locate the Model Parameters section. In the IS text field, type I0.
5
In the N text field, type eta.
Resistor 1 (R1)
1
In the Electrical Circuit toolbar, click  Resistor.
2
In the Settings window for Resistor, type R2 in the Name text field.
3
Locate the Node Connections section. In the table, enter the following settings:
Label
Node names
p
2
n
0
4
Locate the Device Parameters section. In the R text field, type 100[kohm].
Study 1
Step 1: Time Dependent
1
In the Model Builder window, under Study 1 click Step 1: Time Dependent.
2
In the Settings window for Time Dependent, locate the Study Settings section.
3
Click  Range.
4
In the Range dialog, type tmax/50 in the Step text field.
5
In the Stop text field, type tmax.
6
Click Replace.
7
In the Settings window for Time Dependent, locate the Physics and Variables Selection section.
8
In the Solve for column of the table, under Component 1 (comp1), clear the checkbox for Electrical Circuit 2 (cir2).
Solution 1 (sol1)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 1 (sol1) node, then click Time-Dependent Solver 1.
3
In the Settings window for Time-Dependent Solver, click to expand the Time Stepping section.
4
From the Steps taken by solver list, choose Manual.
5
In the Time step text field, type tmax/100.
6
In the Study toolbar, click  Compute.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select General Studies > Time Dependent.
4
Click the Add Study button in the window toolbar.
5
In the Home toolbar, click  Add Study to close the Add Study window.
Study 2
Step 1: Time Dependent
1
In the Settings window for Time Dependent, locate the Study Settings section.
2
Click  Range.
3
In the Range dialog, type tmax/100 in the Step text field.
4
In the Stop text field, type tmax.
5
Click Replace.
6
In the Settings window for Time Dependent, locate the Study Settings section.
7
From the Tolerance list, choose User controlled.
8
In the Relative tolerance text field, type 0.001.
9
Locate the Physics and Variables Selection section. In the Solve for column of the table, under Component 1 (comp1), clear the checkboxes for Semiconductor (semi) and Electrical Circuit (cir).
10
In the Study toolbar, click  Compute.
Results
Voltage probes
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type Voltage probes in the Label text field.
3
Locate the Data section. From the Dataset list, choose None.
4
Click to expand the Title section. From the Title type list, choose None.
5
Locate the Plot Settings section.
6
Select the x-axis label checkbox. In the associated text field, type time (s).
7
Select the y-axis label checkbox. In the associated text field, type Voltage (V).
8
Locate the Legend section. From the Position list, choose Lower right.
Global 1
1
Right-click Voltage probes and choose Global.
2
In the Settings window for Global, locate the Data section.
3
From the Dataset list, choose Study 1/Solution 1 (sol1).
4
Click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1) > Electrical Circuit > Devices > V1 > cir.V1.v - Voltage across device V1 - V.
5
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
cir.V1.v
V
Voltage across device V1
cir.IvsU1.v
V
Voltage across device External I Vs. U 1
cir.R1.v
V
Voltage across device R1
6
Click to expand the Coloring and Style section. Find the Line markers subsection. From the Marker list, choose Cycle.
7
From the Positioning list, choose Interpolated.
Global 2
1
In the Model Builder window, right-click Voltage probes and choose Global.
2
In the Settings window for Global, locate the Data section.
3
From the Dataset list, choose Study 2/Solution 2 (sol2).
4
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
cir2.V2.v
V
Voltage across device V2
cir2.D2.v
V
Voltage across device D2
cir2.R2.v
V
Voltage across device R2
5
Locate the Coloring and Style section. Find the Line markers subsection. From the Marker list, choose Cycle.
6
From the Positioning list, choose Interpolated.
7
In the Voltage probes toolbar, click  Plot.