COMSOL 6.4 - Reverse Recovery of a PIN Diode

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Reverse Recovery of a PIN Diode

This tutorial simulates the turn-off transient (reverse recovery) of a simple PIN diode with an inductive load, loosely based on the book “Fundamentals of Power Semiconductor Devices” by B.J. Baliga (p. 256, 2008 edition; Ref. 1). Unlike the book, which assumes an initial constant current ramp rate followed by an abrupt bottoming out of the device voltage at the supplied reverse voltage, this model uses the circuit capability of COMSOL Multiphysics to simulate the inductive load with a flyback diode in a more realistic fashion. The resulting time evolutions of the current, voltages, and carrier concentrations compare well to those shown in the book (Figs. 5.42–5.45).

The PIN diode structure is an important building block for power electronic circuits. The process of switching the PIN rectifier from the on-state to the blocking state is referred to as the reverse recovery. The diode remains in the forward-biased mode for a short period of time after the applied voltage is switched, due to the large amount of stored charge carriers in the drift region during the on-state. This tutorial combines a simple 1D model of a PIN diode with a circuit of a voltage source, an inductive load, and a flyback diode to simulate the time evolutions of the current, voltages, and carrier concentrations.

Model Definition

The model simulates a diode of 80 μm length and 1 mm cross-section area. Important effects such as the Fletcher mobility model, Slotboom band gap narrowing, and Shockley–Read–Hall recombination are included. The device is grounded at the right endpoint and connected to the circuit at the left endpoint.

The circuit contains two voltage sources in parallel, but only one is activated at a time in the study steps. One voltage source is for the on-state and the other for the switching process.

The study step is used for the initial condition. Then the steady on-state is obtained by using a study step with the Auxiliary sweep, ramping the applied voltage from a small value up to the on-state voltage. Finally a study step is used to simulate the reverse recovery, first maintaining the applied voltage at the on-state value for 10 ns, then ramping it down to the reverse voltage in the next 10 ns, and then holding it there for the next 500 ns. The time axis is shifted so that at time = 0, the applied voltage has just been ramped down to the full reverse voltage.

Results and Discussion

Figure 1, Figure 2, and Figure 3 show the hole concentration at a few selected time points, the time evolution of the applied voltage and the device voltage, and the time evolution of the current, respectively. They exhibit the typical behavior as expected from the inductive load and the dissipation of the stored charge carriers in the drift region. The figures compare well with the corresponding figures in Ref. 1.

Figure 1: Hole concentration at a few selected time points.

Figure 2: Time evolution of the applied voltage and the device voltage.

Figure 3: Time evolution of the current.

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

Semiconductor_Module/Device_Building_Blocks/pin_reverse_recovery

Modeling Instructions

From the menu, choose .

In the window, click

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In the window, click

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In the tree, select > .

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In the tree, select > .

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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.

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

Build a simple 1D line interval of length 80 μm.

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

Create a ramp function for turning off the bias voltage.

Global Definitions

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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 checkbox.

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Click to expand the section. Select the checkbox.

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Select the checkbox.

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 the button in the window toolbar.

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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.

Add a mobility model to account for the carrier-carrier scattering effect.

Semiconductor Material Model 1

In the window, under > click .

Fletcher Mobility Model (C) 1

In the toolbar, click

and choose .

Note that the above step merely makes the mobility model available. To use it, we have to select it in the drop down menus in the Semiconductor Material Model node.

Semiconductor Material Model 1

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In the window, click .

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In the window for , locate the section.

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From the μn list, choose .

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From the μp list, choose .

Add band gap narrowing effect.

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Click to expand the section. From the list, choose .

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 .

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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 .

Add SRH recombination.

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].

Now set up the electrical circuit. The bidirectional coupling between the electrical circuit and the semiconductor model is done conveniently in two parts: 1) The current source within the electrical circuit is specified by the terminal current from the Semiconductor interface. 2) The voltage of the semiconductor metal contact is specified by the voltage of the current source using the built-in Terminal-Circuit connection function.

Electrical Circuit (cir)

In the window, under click .

External U vs. I 1 (UvsI1)

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In the toolbar, click

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In the window for , locate the section.

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In the table, enter the following settings:


Label	Node names
n	0

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Locate the section. From the I list, choose .

Add the load inductor and a generic flyback diode.

Inductor 1 (L1)

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In the toolbar, click

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In the window for , locate the section.

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In the table, enter the following settings:


Label	Node names
n	1

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Locate the section. In the L text field, type L0.

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In the toolbar, click

.

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In the window for , locate the section.

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In the table, enter the following settings:


Label	Node names
p	2
n	1

Add two voltage sources, one for the initial steady state and the other for the time-dependent study.

Voltage Source 1 (V1)

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In the toolbar, click

.

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In the window for , locate the section.

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In the table, enter the following settings:


Label	Node names
p	2
n	0

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Locate the section. In the vsrc text field, type V0.

Voltage Source 2 (V2)

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In the toolbar, click

.

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In the window for , locate the section.

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In the table, enter the following settings:


Label	Node names
p	2
n	0

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Locate the section. In the vsrc text field, type Von+(Voff-Von)*rm1((t+10[ns])/10[ns]).

The voltage ramp is shifted 10 ns earlier so that at time = 0, the applied voltage is just ramped down to the full reverse voltage, Voff.

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 column of the table, under , clear the checkbox for .

Add a stationary study step to ramp the applied voltage from a small value up to the on-state voltage Von.

Step 2: Stationary

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In the toolbar, click

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In the window for , locate the section.

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Select the checkbox.

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In the tree, select > > .

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Click to expand the section. Select the checkbox.

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In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
V0 (Applied DC voltage)	0.1 0.3 0.5 0.7 Von	V

Add a time dependent study step using the 2nd voltage source to start the applied voltage at the on state voltage Von for 10 ns, ramp it down to the reverse voltage Voff in the next 10 ns, and keep it at Voff for 500 ns afterward. Set the tolerance to 1e-5 for better accuracy.

Step 3: Time Dependent

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In the toolbar, click

.

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In the window for , locate the section.

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Select the checkbox.

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In the tree, select > > .

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Locate the section. From the list, choose .

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In the text field, type range(-20,1,0) range(10,10,500).

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From the list, choose .

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In the text field, type 1e-5.

For study steps 2 and 3, where the solution from the previous study step is used as the initial condition, we can use scaling of the dependent variables to obtain better error estimate and better convergence.

Solution 1 (sol1)

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In the toolbar, click

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In the window, expand the node, then click .

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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 window, under > > click .

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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 toolbar, click

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Plot the hole concentration at a few selected time points to see its evolution.

Net Dopant Concentration (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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From the list, choose .

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In the toolbar, click

.

Hole 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 Hole Concentration in the text field.

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Locate the section. From the list, choose .

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In the text field, type 1 range(26,5,46) 48 49.

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Locate the section. Clear the checkbox.

Set the axis limits to the range of interest.

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Locate the section. Select the checkbox.

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In the text field, type 89.

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In the text field, type -2e15.

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In the text field, type 1e17.

Electron Concentration

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In the window, expand the node.

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Right-click and choose .

Hole Concentration

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In the window for , click to expand the section.

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From the list, choose .

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In the toolbar, click

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Plot the time evolution of the applied voltage and the device voltage.

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In the toolbar, click

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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
cir.v_2	V	Voltage at node 2 (applied)
cir.v_1	V	Voltage at node 1 (PIN diode)

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In the toolbar, click

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Plot the time evolution of the current.

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In the toolbar, click

.

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In the window for , type I(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.I0_2	A	Terminal current

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In the toolbar, click

.

Combine the voltage and current plots using 2 y-axes for the model thumbnail.

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In the window, right-click and choose .

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

In the window, under > right-click and choose .

In the window, right-click and choose .

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In the window for , click to expand the section.

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From the list, choose .

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Locate the section.

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Select the checkbox. In the associated text field, type Applied and device voltage (V).

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Select the checkbox.

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In the table, select the checkbox for .

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Locate the section. From the list, choose .

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In the toolbar, click

.