Simulating a 1550 nm InGaAs/InP PIN Photodiode

1. Introduction: InGaAs photodiodes and 1550 nm detection

A photodiode converts incident photons into an electrical current. For absorption to occur, the photon energy must be sufficient to excite an electron across the semiconductor bandgap. The photon energy at 1550 nm is approximately 0.80 eV:

\[ E_{\mathrm{ph}}=\frac{hc}{\lambda}\approx 0.80\ \mathrm{eV}. \]

Lattice-matched In_0.53Ga_0.47As has a room-temperature bandgap of approximately 0.74–0.75 eV, allowing it to absorb 1550 nm light. InP has a wider bandgap of approximately 1.34 eV and is therefore largely transparent at this wavelength. The InP layers can be used to form the junction and electrical contacts while the InGaAs layer acts as the optical absorber. These bandgap values are approximate reference values; the actual simulated band edges are determined by the material parameters selected in OghmaNano.

The p–i–n arrangement consists of a p-type layer, a nominally intrinsic absorber and an n-type layer. The low doping of the middle region enables much of the applied reverse bias to fall across the absorber, producing an electric field that transports photogenerated carriers towards the contacts.

2. Opening the preset simulation and understanding its structure

Begin by clicking New simulation in the File ribbon. Open the III–V / InGaAs demonstration category [CHECK THE EXACT PRESET CATEGORY], select InGaAs/InP PIN photodiode (1550 nm) [CHECK THE EXACT PRESET DISPLAY NAME], choose a destination folder and click Save. The complete device structure, optical input and electrical calculation are already configured: you do not need to build it from scratch. The following table explains the layers provided by the preset, starting from the illuminated side. Verify these nominal values against the final installed example.

Once the example opens, inspect the device in the Device structure tab (??). The layer editor lets you inspect the thickness and optical material of each layer. The doping editor and electrical parameter editor allow you to inspect the electrical properties. Do not alter the preset before running it for the first time.

The key electrical distinction is between the highly doped contact layers and the nominally intrinsic InGaAs absorber. The latter has no deliberately introduced doping in this example. Its electrostatic potential, carrier densities and recombination behaviour are obtained by solving the coupled semiconductor equations rather than by assigning a fixed electric field.

Set the material parameters for InP and InGaAs using the electrical material database. For an InGaAs alloy model, check the definition of the composition parameter: depending on the model, the variable x may describe the indium or the gallium fraction. The intended alloy here is In_0.53Ga_0.47As. Also check the electron affinity, bandgap, effective densities of states, mobilities and recombination parameters. In a heterojunction simulation these choices influence the band offsets and carrier extraction.

3. Running the preset and examining the J–V results

With the preset loaded, click the blue Run simulation button in the File ribbon, or press F9. The Terminal tab shows the progress of the optical and electrical calculations. OghmaNano first calculates the optical generation profile and then solves the device equations at the voltages in the configured J–V sweep. You can leave all parameters at their preset values for this first run.

At each applied voltage OghmaNano solves Poisson's equation together with the electron and hole drift–diffusion and continuity equations. The optical model supplies the spatially resolved photogeneration rate used by the electrical solver. For the underlying equations, see the drift–diffusion theory and optical transfer-matrix model. When the calculation finishes, select the Output tab and open the J–V data (typically jv.csv); the snapshots directory contains spatially resolved band and carrier profiles at successive voltages.

Start by examining the dark or illuminated J–V output, then compare the two conditions later in this tutorial. If the preset begins with illumination enabled, preserve those results before changing Light intensity (Suns) to zero and repeating the calculation in the dark.

4. Setting the 1550 nm illumination

The photodiode is illuminated with a light source centred on 1550 nm. A narrow-band spectrum is preferable to a broadband solar spectrum when examining a photodiode intended for a particular communication wavelength. We use a Gaussian laser spectrum with a nominal full width at half maximum (FWHM) of 2 nm and an integrated incident power density of 10 W m⁻². If your final simulation used a different linewidth or intensity, update these values before publication.

The spectrum can be generated with the Python script described in the Optical Spectra Database documentation. Copy the resulting spectrum directory into your local optical spectra database and select it as the illumination source. Check that the light-source intensity multiplier is set as intended; multiplying the source intensity will change the incident optical power without altering its wavelength distribution.

OghmaNano must also sample the laser line adequately on its optical wavelength mesh. A mesh covering many hundreds of nanometres with only a small number of points can miss a 2 nm-wide emission peak. For a narrow laser line, select a wavelength interval and sampling density fine enough to resolve the peak and any important absorption features. Wider FP or ASE spectra may require a correspondingly wider interval.

5. Examining the optical generation profile

The optical properties of the two semiconductors determine where the incident photons are absorbed. At 1550 nm the wide-bandgap InP layers are expected to absorb comparatively little light, whereas the InGaAs layer produces electron–hole pairs. The spatial generation rate G(x) is the number of electron–hole pairs generated per unit volume per unit time. For a single wavelength, it can be related to the local absorbed optical power density by

\[ G(x,\lambda)=\frac{\alpha(\lambda)I(x,\lambda)}{hc/\lambda}, \]

where \(\alpha\) is the optical absorption coefficient and \(I\) is the local optical irradiance in the material. The full model evaluates the optical field through the layer stack and calculates absorption from the wavelength-dependent optical constants.

?? shows the calculated generation rate across the device. The large increase at the entrance to InGaAs and the much smaller generation in the InP regions are consistent with their differing bandgaps. The oscillations within the absorber are a consequence of interference between optical waves propagating through and reflecting within the multilayer structure. For a refractive index near 3.5, an interference feature in intensity has a characteristic spatial period of approximately \(\lambda/(2n)\), or about 220 nm at 1550 nm.

The envelope of the generation rate generally falls across the absorber as the incident light is absorbed. Its detailed shape depends on the optical constants, layer thicknesses and reflections, so it should not be interpreted as a simple exponential without considering the optical interference.

6. Energy bands at 0 V in the dark

To examine equilibrium, select the Optical ribbon, set Light intensity (Suns) to zero, rerun the preset, and open the snapshots folder from the Output tab. Use the snapshot slider to select 0 V in the dark. At thermal equilibrium the electron and hole quasi-Fermi levels coincide, forming one spatially constant Fermi level. The conduction- and valence-band edges are not flat, however, because a built-in electrostatic potential forms between the doped layers.

The bandgap is visibly smaller in InGaAs than in InP. At the InP/InGaAs interfaces, discontinuities in the conduction- and valence-band edges represent heterojunction band offsets. The precise size of each offset depends on the bandgaps and electron affinities used by the electrical material model.

Across the nominally intrinsic absorber, both band edges slope as a consequence of the built-in electric field. The field is related to the gradient of the electrostatic potential, \(F=-d\phi/dx\). Since the band edges follow that potential, an approximately linear band-edge profile indicates an approximately uniform field over that region. This field can collect photogenerated carriers even when no external voltage is applied.

7. Applying −2 V reverse bias

Restore the 1550 nm illumination, rerun the simulation, and use the snapshots viewer slider to select approximately −2 V. Photodiodes are commonly operated under reverse bias. Applying a negative voltage across the junction increases the magnitude of the electric field in the depleted absorber and drives electrons and holes towards opposite sides of the device. In this example we examine the band diagram at −2 V under illumination.

Compared with the 0 V equilibrium result, the conduction- and valence-band edges have a stronger slope across InGaAs. Under illumination the electron and hole quasi-Fermi levels need not coincide: carrier generation and extraction drive the device away from thermal equilibrium. Their spatial gradients are related to the flow of electron and hole current. Sharp changes in a quasi-Fermi level close to an interface can also indicate a significant transport resistance or extraction barrier, which should be evaluated alongside the carrier densities and current profiles.

The wider-bandgap InP regions can introduce heterojunction barriers. These do not by themselves imply poor device operation, but their magnitudes should be realistic and the simulated electron and hole currents should remain consistent through the device.

8. Comparing dark and illuminated J–V characteristics

Run a J–V simulation over the reverse- and low-forward-bias range. The supplied starter model was configured for a sweep from −2.0 V to +0.2 V; use the actual sweep range from your final simulation if this has changed. First run the simulation with the light source disabled to obtain the dark current, and then repeat with the 1550 nm source enabled.

The dark characteristic is expected to be strongly rectifying. At sufficiently small forward bias there is little injection current, while at larger forward bias the current can rise rapidly. Under reverse bias, an idealised drift–diffusion model may predict a very small dark current. In real InGaAs photodiodes, bulk generation–recombination, surface leakage and field-assisted processes can make the reverse dark current larger. The predicted current therefore depends on which physical loss mechanisms are included.

Under illumination, absorbed photons create electron–hole pairs. Once collection becomes efficient, the reverse-bias photocurrent should be relatively insensitive to further increases in reverse voltage. A substantial voltage dependence may instead indicate incomplete collection, recombination losses or transport barriers. The photocurrent density is obtained by subtracting the dark result from the illuminated result at the same applied voltage:

\[ J_{\mathrm{ph}}(V)=J_{\mathrm{light}}(V)-J_{\mathrm{dark}}(V). \]

The sign of \(J_{\mathrm{ph}}\) depends on the current convention. For the responsivity calculation below, we use its magnitude.

9. Calculating photodiode responsivity

The responsivity describes how much photocurrent is produced by a given incident optical power. Using current density \(J_{\mathrm{ph}}\) and incident power density \(P_{\mathrm{in}}\), the responsivity is

\[ R(\lambda)=\frac{|J_{\mathrm{ph}}|}{P_{\mathrm{in}}}\qquad [\mathrm{A/W}]. \]

Here \(P_{\mathrm{in}}\) is the incident optical power per unit device area, not the absorbed power. Consequently, the calculated responsivity includes reflection and incomplete absorption as well as electrical collection losses. At a single wavelength, the maximum external responsivity corresponding to one collected electron per incident photon is

\[ R_{\mathrm{ideal}}=\frac{q\lambda}{hc}\approx 1.25\ \mathrm{A/W}\quad \text{at }1550\ \mathrm{nm}. \]

For example, with an incident irradiance of 10 W m⁻² and an actual responsivity of 1.0 A/W, the expected photocurrent density is 10 A m⁻², equivalent to 1.0 mA cm⁻². This is an illustration, not a measured result from this simulation.

There is a second useful consistency check. Integrating the optical generation rate through the device gives the maximum current density that could be collected if every generated electron–hole pair contributed to the current:

\[ |J_{\mathrm{gen}}|=q\int G(x)\,dx. \]

Compare \(|J_{\mathrm{gen}}|\) with the simulated photocurrent under sufficient reverse bias. A smaller extracted current can indicate recombination or incomplete extraction, although the comparison also requires consistent optical and electrical geometries and the same incident illumination.

10. Further investigations

Once the reference photodiode is working, changing one parameter at a time can help identify which parts of the device control its response.

11. Summary and what you have learned

This tutorial has demonstrated how OghmaNano can combine an optical transfer-matrix calculation with drift–diffusion transport to model an InGaAs/InP PIN photodiode. The wide-bandgap InP layers allow 1550 nm light to reach the InGaAs absorber, optical interference shapes the spatial generation profile, and the junction field separates and collects photogenerated carriers. By comparing dark and illuminated J–V curves, the photocurrent and responsivity can be obtained from the same device model.

For information about importing and generating custom laser spectra, see the Optical Spectra Database documentation.