PN Diode

1. Overview

In this worked example, a simple symmetrical PN junction is modelled and analysed to illustrate the fundamental workflow of diode simulation in the Aquarius TCAD environment. The device structure consists of a uniformly doped silicon p-region and n-region, each with equal doping concentrations. The device cross-sectional area and region lengths are specified, and ideal ohmic contacts are applied at the anode and cathode.

An analytical IV characteristic is derived using the Shockley diode equation, which requires evaluation of the reverse saturation current ($I_s$) from fundamental semiconductor transport relations. This involves calculating minority carrier diffusion coefficients and diffusion lengths based on carrier mobility and lifetime, together with the intrinsic carrier concentration of silicon.

The analytical model provides a baseline for expected diode behaviour, including exponential forward conduction and saturation in reverse bias. This worked example demonstrates both the physics behind diode operation and the practical steps required to set up and validate a PN diode simulation in the Aquarius TCAD environment, serving as a foundation for more advanced semiconductor devices.

2. Parameters

Parameter	Symbol	Value	Unit	Description
Length	$L1$	$1 \times 10^{-4}$	cm	Length of the P-type region in the Y dimension.
Length	$L2$	$1 \times 10^{-4}$	cm	Length of the P-type region in the Y dimension.
Width	$W$	$2 \times 10^{-5}$	cm	Width of the device in the X dimension
Depth	$D$	$1 \times 10^{-4}$	cm	Thickness of the device in the Z dimension
Acceptor Doping	$N_A$	$1 \times 10^{-16}$	cm-3	Acceptor concentration in the P-type region.
Donor Doping	$N_D$	$1 \times 10^{-16}$	cm-3	Donor concentration in the N-type region.
Temperature	$T$	$300$	K	Temperature of the diode.
Electron Minority Carrier Lifetime	$\tau_n$	$1 \times 10^{-5}$	s	Average time an electron exists as a minority carrier in the P region before recombination.
Hole Minority Carrier Lifetime	$\tau_p$	$1 \times 10^{-5}$	s	Average time a hole exists as a minority carrier in the N region before recombination.
Electron Mobility	$\mu_n$	$1360$	cm2/Vs	Indicates how easily electrons move under an electric field.
Hole Mobility	$\mu_p$	$495$	cm2/Vs	Indicates how easily holes move under an electric field.

3. Analytical Model

3.1. Ideal Diode Equation

For an ideal diode, the current–voltage relation is given by:

$$I = I_s \left( e^{\tfrac{qV}{kT}} - 1 \right)$$

Where:

• $I$ = Diode current (A)
• $I_s$ = Reverse saturation current (A)
• $V$ = Applied bias voltage (V)
• $q$ = Elementary charge (C)
• $k$ = Boltzmann constant (J/K)
• $T$ = Absolute temperature (K)

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In forward bias ($V>0$) the current rises exponentially with voltage, in reverse bias ($V<0$) the current saturates at $I_s$. No resistance is included, therefore the exponential law holds across the full bias range.

3.2. Reverse Saturation Current

The reverse saturation current arises from minority carrier diffusion across the junction and is given by:

$$I_s = q A \left( \frac{D_p n_i^2}{L_p N_D} + \frac{D_n n_i^2}{L_n N_A} \right)$$

Where:

• $q$ = Elementary charge (C)
• $A$ = Cross-sectional area (cm²)
• $D_p$ = Hole diffusion coefficient (cm²/s)
• $D_n$ = Electron diffusion coefficient (cm²/s)
• $L_p$ = Hole diffusion length (cm²/s)
• $L_n$ = Electron diffusion length (cm²/s)
• $N_A$ = Acceptor concentration (cm⁻³)
• $N_D$ = Donor concentration (cm⁻³)
• $n_i$ = Intrinsic carrier concentration (cm⁻³)
• $T$ = Absolute temperature (K)

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$D_p$ and $D_n$ are related to carrier mobilities:

$$D = \mu \frac{kT}{q}$$

$L = \sqrt{D \tau}$, where $\tau$ is the minority carrier lifetime.

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The ideal diode IV characteristic is shown below.

4. Simulation using Aquarius

4.1. Creating the Device Model

To create a resistor device model in Aquarius, follow the steps below.

4.1.1. Launch Editor

• Launch the Device Editor. (see resistor example) for details.

4.1.2. Define Device Geometry

• In the Menu Bar, click the rectangle button , alternatively , select Define → Region → Rectangle.
• Position the cursor on the canvas to draw a rectangular shape:
  • Left-click to start drawing.
  • Left-click again to finish the shape.

• After drawing the rectangle, the Exact Coordinates dialog will open automatically:
  • Set the First Vertex to (-0.1, 1.0).
  • Set the Second Vertex to (0.1, 2.0).
  • Click OK to confirm.

• The Region Properties dialog will then open:
  • Set the region Name to P.
  • Set the region Material to Si (Silicon).
  • Set the Acceptor Doping to 1E+16
  • Click OK to confirm.

• Repeat process above, again but this time define the region with the following parameters:
  • First Vertex = (-0.1, 1.0).
  • Second Vertex = (0.1, 0.0).
  • Name = N.
  • Donor Doping = 1E+16.
  • Select a colour for the N region. It is recommended to use a different colour from the P region for clear differentiation.

4.1.3. Define Device Contacts

With the device geometry and material properties defined, the next step is to specify electrical contacts to allow the device to be connected to a circuit for simulation. In this example, the top and bottom edges will be used to define the device contacts. A and K, respectively, with the default contact parameters applied.

Define two contacts, Anode A on the top of the device and Cathode K on the bottom as can been seen in the image above.

• Define the first contact (A):

  1. From the menu, select Define → Contact.
  2. Move the cursor over the left geometric edge. When the edge highlights in green and the cursor changes to indicate a selectable element, Left-click to select it.
  3. Right-click anywhere to open the Contact Properties dialog. Use this dialog to set the contact's properties.
  4. In the General section, set Name to A, leave all other properties at their default values.
  5. Click OK.

• Define the second contact (B), repeat steps 1–5 above, but instead:

  1. Select the bottom geometric edge.
  2. In the Contact Properties window, set Name to K and Colour to green.
  3. Click OK.

tip

For more detailed instructions on defining contacts, click here.

4.1.4. Defining the Mesh

In order to discretise the problem, the finite element method (FEM) is used. This triangulation is formed of triangular elements of varying sizes. Aquarius includes meshing algorithms that allow the user to specify a finer mesh near areas of interest and a coarser mesh elsewhere to optimise computational efficiency.

For a PN junction, the junction itself is the key region of interest; therefore, a finer mesh is specified in this area to accurately capture the strong variations in potential and carrier concentration.

• In the Menu Bar, select Mesh → Generate Finite Element Mesh Model.

The Mesh Properties window will appear.

• Set the refinement parameters as follows:

  Mesh Quality Options

  • Max Element Edge Length (Hint): 0.5 µm
  • Minimum Angle: 30°

  Metallurgical Junction Refinement

  • Distance to Junction: 0.3 µm
  • Minimum Edge Length (Hint): 0.02 µm
  • Maximum Edge Length (Hint): 0.1 µm

  Oxide Interface Refinement parameters are not required as there is not oxide in this device.

• Click OK to generate the mesh with specified settings.

info

These parameters ensure that Aquarius automatically generates a quality triangular mesh, finely resolving the PN junction while maintaining a coarser mesh in less critical regions. This approach achieves high numerical accuracy without excessive computational cost.

The generated mesh will be displayed.

4.1.5. Save the Device Model

• In the Menu Bar, select File → Save As.... The Save dialog will open.
• Navigate to the folder you wish to save the device in.
• Specify the filename (e.g. pn_diode.sdm).
• Click Save to store the device model.

The Diode is now ready to be added to a circuit.

4.2. Steady State Simulation

4.2.1. Simulation Setup

A circuit must be created before simulation can begin. A device (the diode), a DC Voltage Source and a Ground will be added to the circuit editor and connected together.

• Launch the Circuit Editor. (see resistor example) for details.

4.2.1.1. Add the Device

• Select the Device from the tool bar and drag and drop it onto the circuit editor.
• Set the device Properties:
  • Click Get .sdm File, select the device file that you created in the previous steps and click OK.
  • Ensure Scaling Factor (cm) is set to 0.0001. Which sets the device depth to 1μm depth.
  • Click OK to close the Device Properties.

note

Note: The device can be rotated by Left-clicking on it to select it and then using CTRL + R to rotate it by 90°.

tip

For more detailed instructions on Adding Components, click here.

4.2.1.2. Add a Source and Ground

• Select the DC Voltage Source from the tool bar by Dragging and Dropping it onto the circuit editor.
• Select the Ground from the tool bar by Dragging and Dropping it onto the circuit editor.
• Connect the components together as they are in the image below.

tip

For more detailed instructions on Wiring Circuits, click here.

4.2.1.3. Set Source Properties

• Double-click on the DC Voltage Source to open its properties.
• Click Add Range to open the Add Range Properties and set to the values below:
  • Start Voltage (V) = 0
  • End Voltage (V) = 0.8
  • Step (V) = 0.01
  • Click OK to set the range.
• Click OK to set the DC Voltage Source Properties.

tip

For more detailed instructions on Steady State (DC) Sources, click here.

4.2.1.4. Save the Solution File

Save the simulation at this point.

• In the Menu Bar, select File → Save As.... The Save dialog will open.
• Navigate to the folder you wish to save the solution file. The solution file should be saved in the same directory as the device file.
• Specify the filename (e.g. pn_diode_iv.sol).
• Click Save to store the solution file.

4.2.2. Run Simulation

To run the Steady State Simulation press the blue run button, alternatively in the menu use Simulation → Steady State.

tip

For more detailed instructions on Running a Simulations, click here.

The simulation will begin and the Simulation Status will appear on the screen. Wait until the simulation has completed at which point Simulation Stopped will appear in the bottom left of the status window and the text "Aquarius simulator completed execution." will be show in the screen.

tip

For more detailed instructions on the Simulation Status output, click here.

4.3. Simulation Results

4.3.1. Visualising the Results

Next results visualiser will be used to understand the output of the simulation. On the start page Click Open Results Visualiser (the third option). The application will ask the user to select a .res results file. The name of the .res file will be the same as the .sol which has just run (e.g. pn_diode_iv.res). Then the Results Visualiser will open with the selected results file loaded.

• Click External Plot at the top of the results visualiser.
• Set External Plot Settings:
  • The file should match your results file name.
  • X Axis Contact = DEV1.A
  • X Axis Variable = Voltage
  • Y Axis Contact = DEV1.A
  • X Axis Variable = Total Current
• Click New Plot to generate a graph showing Total Current (A) at terminal A of DEV1 (the diode's name) versus the Voltage (V) at the same terminal.

4.3.2. Analysing Results

Once the IV characteristic is plotted, you can export the data as a CSV file.

• Click Export Data to save the plot data in .csv format.

When the file dialog appears, enter a filename (e.g., pn_diode_iv.csv) and click Save. Now with the csv file exported it is possible to overlay the aquarius simulation result and the analytical ideal diode equation.

Between 0 V and ~ 0.7 V, the Aquarius Simulation Result matches the Ideal Diode Equation. When the voltage applied to the anode increases above the built-in potential, the series resistance in the diode starts to control the current flow. This resistance – arising from the P region, N region, and depletion region – is not included in the ideal diode model, so the simulated current increases at a slower rate, causing the deviation at higher voltages.

5. Conclusion

This example demonstrated the setup and simulation of a silicon PN junction diode in Aquarius. The simulated IV curve matched the analytical ideal diode behaviour up to about 0.7 V, confirming correct model implementation. At higher voltages, deviations due to series resistance became evident. Overall, the example validates Aquarius for accurate diode simulation and provides a foundation for more advanced device studies.

6. Downloads

File	Description	Download
pn_diode.sdm	PN diode device model.	Download
pn_diode_iv.sol	Solution file to generate the IV characteristic for pn_diode.sdm.	Download