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Forward Recovery of a PIN Diode
This tutorial simulates the turn-on transient (forward recovery) of a simple PIN diode, based on the book “Fundamentals of Power Semiconductor Devices” by B.J. Baliga (p. 242, 2008 edition; Ref. 1). The diode is current driven with a constant ramp rate of 1·109, 2·109, and 1·1010 A/(cm2·s) and a steady state current density of 100 A/cm2. The resulting time evolution of the device voltage and electron concentration compare well to those shown in the book (Figs. 5.30–5.31). For a more sophisticated example including band gap narrowing, carrier–carrier scattering, and external load circuit elements, see the tutorial Reverse Recovery of a PIN Diode.
Introduction
The PIN diode structure is an important building block for power electronic circuits. The process of switching the PIN rectifier from the off-state to the on-state is referred to as the forward recovery. During the turn-on time interval with a specified current input, the device voltage shows an initial spike, due to the amount of time required to accumulate extra charge carriers in the drift region for the diode to be fully turned on. This tutorial follows the approach in Ref. 1, where an idealized linearly ramped-on current input (with a specified max on-current) is used. For a more sophisticate example that uses the circuit capability of COMSOL Multiphysics to simulate the inductive load with a flyback diode in a more realistic fashion, see the tutorial Reverse Recovery of a PIN Diode That tutorial also includes band gap narrowing and carrier–carrier scattering effects.
Model Definition
The model simulates a diode of 80 μm length and 1 mm cross-section area. The background n-doping is 5·1013/cm3 and the peak n- and p-doping at the exterior boundaries is 1·1019/cm3. Shockley–Read–Hall recombination is included. The device is grounded at the right endpoint and current driven from the left endpoint.
A Ramp function with a Cutoff is used to specify the linear current ramp up to the max on-current.
The Semiconductor Equilibrium study step is used for the initial condition. Then a Time Dependent study step is used to simulate the forward recovery, with an Auxiliary sweep to study a few different current ramp rates.
Results and Discussion
Figure 1 and Figure 2 show the time evolution of the device voltage and the electron concentration at a few selected time points, respectively. They exhibit the typical behavior as expected from the initial accumulation of extra charge carriers in the drift region. The figures compare well with the corresponding figures in Ref. 1.
Figure 1: Time evolution of the device voltage.
Figure 2: Time evolution of the electron concentration.
Reference
1. B.J. Baliga, Fundamentals of Power Semiconductor Devices, 2008 ed., Springer, pp. 242–243.
Application Library path: Semiconductor_Module/Device_Building_Blocks/pin_forward_recovery
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  1D.
2
In the Select Physics tree, select Semiconductor > Semiconductor (semi).
3
Click Add.
4
Click  Study.
The Semiconductor Equilibrium study can be used to obtain a good initial condition.
5
In the Select Study tree, select Preset Studies for Selected Physics Interfaces > Semiconductor Equilibrium.
6
Click  Done.
Geometry 1
The Model Wizard exits and starts the COMSOL Desktop at the Geometry node. We can set the length scale here right away.
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.
Import global parameters from a text file.
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 pin_forward_recovery_parameters.txt.
Build a simple 1D line interval of length 80 μm.
Geometry 1
Interval 1 (i1)
1
In the Model Builder window, under Component 1 (comp1) right-click Geometry 1 and choose Interval.
2
In the Settings window for Interval, locate the Interval section.
3
In the table, enter the following settings:
Coordinates (µm)
0
80
Add silicon material.
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 the Add to Component button in the window toolbar.
5
In the Home toolbar, click  Add Material to close the Add Material window.
Materials
Si - Silicon (mat1)
Enter the cross-section area for the 1D model.
Semiconductor (semi)
1
In the Model Builder window, under Component 1 (comp1) click Semiconductor (semi).
2
In the Settings window for Semiconductor, locate the Cross-Section Area section.
3
In the A text field, type area.
Set up doping - first the background doping.
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 5e13[1/cm^3].
Then the P and N doping.
Geometric Doping Model 1
1
In the Physics toolbar, click  Domains and choose Geometric Doping Model.
2
In the Settings window for Geometric Doping Model, locate the Domain Selection section.
3
From the Selection list, choose All domains.
4
Locate the Impurity section. In the NA0 text field, type 1e19[1/cm^3].
5
Locate the Profile section. In the dj text field, type 10[um].
6
From the Nb list, choose Donor concentration (semi/adm1).
Boundary Selection for Doping Profile 1
1
In the Model Builder window, expand the Geometric Doping Model 1 node, then click Boundary Selection for Doping Profile 1.
2
Select Boundary 1 only.
Geometric Doping Model 2
1
In the Physics toolbar, click  Domains and choose Geometric Doping Model.
2
In the Settings window for Geometric 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 1e19[1/cm^3].
6
Locate the Profile section. In the dj text field, type 10[um].
7
From the Nb list, choose Donor concentration (semi/adm1).
Boundary Selection for Doping Profile 1
1
In the Model Builder window, expand the Geometric Doping Model 2 node, then click Boundary Selection for Doping Profile 1.
2
Select Boundary 2 only.
Add ohmic contacts.
Metal Contact 1
1
In the Physics toolbar, click  Boundaries and choose Metal Contact.
2
Select Boundary 2 only.
Metal Contact 2
1
In the Physics toolbar, click  Boundaries and choose Metal Contact.
2
Select Boundary 1 only.
3
In the Settings window for Metal Contact, locate the Terminal section.
4
From the Terminal type list, choose Current.
5
In the I0 text field, type J_on*area*rm1(t/t_on).
The ramp function rm1 is not yet defined and turns the expression to yellow colored. Let us define it now.
Definitions
Ramp 1 (rm1)
1
In the Definitions toolbar, click  More Functions and choose Ramp.
2
In the Settings window for Ramp, locate the Parameters section.
3
Select the Cutoff checkbox.
Add SRH recombination.
Semiconductor (semi)
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 1[us].
5
From the τp list, choose User defined. In the associated text field, type 1[us].
Study 1
Step 1: Semiconductor Equilibrium
Add a time dependent study step with Auxiliary sweep, to simulate a few different current ramp rates.
Step 2: Time Dependent
1
In the Study toolbar, click  Time Dependent.
2
In the Settings window for Time Dependent, locate the Study Settings section.
3
From the Time unit list, choose ns.
4
In the Output times text field, type range(0,1,99).
5
From the Tolerance list, choose User controlled.
6
In the Relative tolerance text field, type 1e-5.
7
Click to expand the Study Extensions section. Select the Auxiliary sweep checkbox.
8
Click  Add.
9
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
dJdt (Desired current density ramp rate)
1e9 2e9 1e10
A/cm^2/s
10
In the Study toolbar, click  Compute.
Plot the time evolution of the device voltage, to see the different amount of spiking for the different current ramp rates.
Results
Net Dopant Concentration (semi)
1
In the Model Builder window, under Results click Net Dopant Concentration (semi).
2
In the Settings window for 1D Plot Group, locate the Data section.
3
From the Parameter selection (dJdt) list, choose First.
4
From the Time selection list, choose First.
5
In the Net Dopant Concentration (semi) toolbar, click  Plot.
V(t)
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type V(t) in the Label text field.
Global 1
1
Right-click V(t) and choose Global.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
semi.V0_2
V
Terminal voltage
4
In the V(t) toolbar, click  Plot.
Plot the electron concentration at a few selected time points, to see the initial buildup of the charge carriers in the drift region.
Electron Concentration
1
In the Model Builder window, right-click Carrier Concentrations (semi) and choose Duplicate.
2
Click the  y-Axis Log Scale button in the Graphics toolbar.
3
In the Settings window for 1D Plot Group, type Electron Concentration in the Label text field.
4
Locate the Data section. From the Parameter selection (dJdt) list, choose Last.
5
From the Time selection list, choose Manual.
6
In the Time indices (1-100) text field, type 3 7 10 15.
7
Locate the Plot Settings section. Clear the y-axis label checkbox.
8
Locate the Axis section. Select the Manual axis limits checkbox.
9
In the x maximum text field, type 31.
10
In the y minimum text field, type -2e14.
11
In the y maximum text field, type 1e16.
1
In the Model Builder window, expand the Electron Concentration node, then click Electron Concentration.
2
In the Settings window for Line Graph, click to expand the Legends section.
3
From the Legends list, choose Automatic.
Hole Concentration
In the Model Builder window, right-click Hole Concentration and choose Delete.
Electron Concentration
1
In the Model Builder window, under Results click Electron Concentration.
2
In the Electron Concentration toolbar, click  Plot.