Forward Recovery of a PIN Diode

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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.

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. is included. The device is grounded at the right endpoint and current driven from the left endpoint.

A function with a is used to specify the linear current ramp up to the max on-current. The interface is used to mark the abrupt change in the slope of the applied current at the end of the current ramp, so that the time-dependent solver can take appropriate actions.

The study step is used for the initial condition. Then a study step is used to simulate the forward recovery, with an 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.

1. B.J. Baliga, Fundamentals of Power Semiconductor Devices, 2008 ed., Springer, pp. 242–243.

Semiconductor_Module/Device_Building_Blocks/pin_forward_recovery

Modeling Instructions

From the menu, choose .

In the window, click

.

1

In the window, click

.

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In the tree, select .

3

Add an interface to capture the abrupt change in the slope of the applied voltage.

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In the tree, select .

5

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The study can be used to obtain a good initial condition.

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In the tree, select .

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The Model Wizard exits and starts the COMSOL Desktop at the Geometry node. We can set the length scale here right away.

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

Import global parameters from a text file.

Global Definitions

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In the window, under click .

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In the window for , locate the section.

3

.

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Browse to the model’s Application Libraries folder and double-click the file pin_forward_recovery.txt.

Build a simple 1D line interval of 80 um long.

Interval 1 (i1)

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In the window, under right-click and choose .

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In the window for , locate the section.

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In the table, enter the following settings:


Coordinates (µm)
0
80

Add silicon material.

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In the toolbar, click

to open the window.

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Go to the window.

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In the tree, select .

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Click in the window toolbar.

5

In the toolbar, click

to close the window.

Si - Silicon (mat1)

Enter the cross-section area for the 1D model.

Semiconductor (semi)

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In the window, under click .

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In the window for , locate the section.

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In the A text field, type area.

Set up doping - first the background doping.

Analytic Doping Model 1

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. From the list, choose .

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In the ND0 text field, type 5e13[1/cm^3].

Then the P and N doping.

Geometric Doping Model 1

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the NA0 text field, type 1e19[1/cm^3].

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Locate the section. In the dj text field, type 10[um].

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From the Nb list, choose .

Boundary Selection for Doping Profile 1

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In the window, expand the node, then click .

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Select Boundary 1 only.

Geometric Doping Model 2

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

4

Locate the section. From the list, choose .

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In the ND0 text field, type 1e19[1/cm^3].

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Locate the section. In the dj text field, type 10[um].

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From the Nb list, choose .

Boundary Selection for Doping Profile 1

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In the window, expand the node, then click .

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Select Boundary 2 only.

Add ohmic contacts.

Metal Contact 1

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In the toolbar, click

and choose .

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Select Boundary 2 only.

Metal Contact 2

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In the toolbar, click

and choose .

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Select Boundary 1 only.

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In the window for , locate the section.

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From the list, choose .

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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.

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In the toolbar, click

and choose .

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In the window for , locate the section.

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Select the check box.

Add SRH recombination.

Semiconductor (semi)

Trap-Assisted Recombination 1

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. From the τn list, choose . In the associated text field, type 1[us].

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From the τp list, choose . In the associated text field, type 1[us].

Add an event to mark the end of the applied current ramp, so that the time-dependent solver can take appropriate actions.

In the window, under click .

Explicit Event 1

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In the toolbar, click

and choose .

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In the window for , locate the section.

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In the ti text field, type t_on.

Exclude the Events interface from the initial study step.

Step 1: Semiconductor Equilibrium

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In the window, under click .

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In the window for , locate the section.

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In the table, clear the check box for .

Add a time dependent study step with Auxiliary sweep, to simulate a few different current ramp rates.

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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In the text field, type range(0,1,99).

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From the list, choose .

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In the text field, type 1e-5.

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Click to expand the section. Select the check box.

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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

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In the toolbar, click

.

Plot the time evolution of the device voltage, to see the different amount of spiking for the different current ramp rates.

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In the toolbar, click

and choose .

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In the window for , type V(t) in the text field.

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Right-click and choose .

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In the window for , locate the section.

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In the table, enter the following settings:


Expression	Unit	Description
semi.V0_2	V	Terminal voltage

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In the toolbar, click

.

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

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In the window, right-click and choose .

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button in the toolbar.

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In the window for , type Electron Concentration in the text field.

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Locate the section. From the list, choose .

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From the list, choose .

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In the text field, type 3 7 10 15.

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Locate the section. Clear the check box.

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Locate the section. Select the check box.

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In the text field, type 31.

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In the text field, type -2e14.

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In the text field, type 1e16.

Electron Concentration

1

In the window, click .

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In the window for , click to expand the section.

3

From the list, choose .

Hole Concentration

In the window, right-click and choose .

Electron Concentration

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In the window, click .

2

In the toolbar, click

.