Vertical photodetector

This example describes a complete multiphysics (optical, electrical) simulation of a vertical Ge-Si photodetector, ending with a compact model circuit simulation in INTERCONNECT. It also provides an automated workflow to run the device-level simulations and collect data for CML Compiler for compact model generation. Key results such as dark and photocurrents, responsivity, bandwidth, and eye diagram are calculated. Two methods of bandwidth calculation, small-signal AC and transient + FFT are described and compared in the appendix, as well as photodetector length optimization using EME and power absorption calculation. Links to other types of photodetectors, such as lateral and uni-travelling carriers can be found in the additional resources.

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Overview

Understand the simulation workflow and key results

This example is taken from T.-Y Liow et al.[1], where a Ge-on-Si vertical photodetector illuminated at 1.55 um wavelength is fed from a Si waveguide into a Ge absorption layer through a taper. This input light signal generates electron-hole pairs in Ge, which are subsequently separated under internal electric fields in the photodetector and flow towards electrical contacts forming charge current. FDTD is used to characterize the optical performance of the detector, while CHARGE is used to obtain the electric performance. Parameters from these simulations are imported into a compact model in INTERCONNECT to perform a photonic circuit simulation and obtain an eye diagram.

Step 1:

A detailed electromagnetic simulation using 3D FDTD with a mode source at 1.55 um wavelength calculates the field propagation through the taper and into the detector. The field distribution inside the Ge layer is used to calculate the absorption profile and optical generation rate. The optical generation rate is then imported into CHARGE to perform the electrical simulations. Single-frequency simulations are appropriate for narrowband devices where the mode profiles are relatively constant over the wavelength range of operation.

Step 2:

The CHARGE solver is run in steady-state and small-signal AC mode to obtain current, responsivity, and bandwidth.

In steady state, the imported generation is first disabled to obtain dark current and then enabled for photocurrent and responsivity. Since the photodetector is relatively uniform along its length, the 3D optical generation rate from FDTD is averaged along the length, which allows doing 2D CHARGE simulations, significantly reducing simulation time; values obtained for dark current and responsivity is used in step 3 for the circuit simulation.

The bandwidth of the photodetector is calculated by running a CHARGE small-signal AC simulation with an optical source having both DC and AC components. The 3dB bandwidth will be imported into the compact model in step 3 for circuit simulation with INTERCONNECT.

The recombination parameters used in this step are calibrated in order to fit the calculated dark current to the dark current in the publication; the method is described later, in the "Updating the model with your parameters" section.

Step 3:

Using simulation results from previous steps, we create a compact model of the photodetector in INTERCONNECT and perform circuit simulations. Eye diagrams at different data rates are calculated.

Further details such as compact model generation, length optimization, and transient simulation are provided later in this article, after the "Run and results" section.

Run and results

Instructions for running the model and discussion of key results

Step 1: Absorption and generation rate

In this structure, germanium is the absorbing layer. That's why the analysis group that performs the generation calculation (the yellow box) encompasses germanium (shown on left). On the right, we can see a visualization of generation at an arbitrary cross-section along propagation direction (x). The 3D generation data is averaged along the detector's length before it is imported for the 2D CHARGE simulation.

Step 2: Current, responsivity, and bandwidth

A. Steady-state simulation:

Side view of the structure simulated in CHARGE

Photocurrent                                                                            Responsivity

The results indicate a responsivity of 0.95 A/W at -1 V reverse bias, which agrees well with the publication.

B. Small signal AC optical bandwidth:

In this approach, a small-signal perturbation is added to the DC optical generation rate and the small-signal response (photocurrent) of the photodetector is recorded as a function of the frequency of the small-signal.

In this step, the high field mobility in germanium is turned on and convergence settings are adjusted to improve the convergence stability. Additionally, the scale factor of imported data is modified so the DC current approximates the peak impulse current in publication (about 0.1 mA).

The bandwidth is found to be around 4 GHz at -1 V reverse bias, agreeing well with the publication.

Step 3: Compact model and circuit simulation

This INTERCONNECT project represents a photonic circuit consisting of a CW laser source with 0.12 mW power and 1.55 um wavelength, whose amplitude is modulated according to a random series of bits, driving a photodetector with 0.95 A/W responsivity, 4 GHz bandwidth, and 0.34 uA dark current. The finite bandwidth of the photodetector is modeled by including an RC low pass filter with the cut-off frequency equal to the bandwidth.

2.5 Gbits/s                                   10 Gbits/s                                       25 Gbits/s

Important model settings

Description of important objects and settings used in this model

Step 1: FDTD simulation of absorption and optical generation rate

Ge absorption : At 1.55 um most of the optical absorption is in the Ge layer on top of Si, while Si absorption can be neglected. The region where the optical generation rate is calculated can be limited to Ge layer.

Mode source : Only the fundamental mode is considered, which is calculated at the central frequency of the injected pulse at 1.55 um. The mode profile at other frequencies of the injected pulse is assumed constant, which is a good approximation for narrowband inputs.

Ge absorption layer length : While this length is reported to be 100 um in the publication, it is limited in the simulation to 50 um to minimize the simulation time. This is a good approximation as most of the light gets absorbed in the first 50 um (refer to Detector length optimization section in the Appendix).

Boundary conditions : y min boundary is set to anti-symmetric according to the symmetry rules of the fundamental TE mode. This will reduce the simulation region by a factor of two.

Generation rate analysis group : This object calculates the absorption and generation rate according to a theory described in the appendix. The optical source input power is normalized to 1 W, by setting the source intensity parameter to be equal to 1/(source area), where the source plane is normal to x-direction and from the source object it can be seen to be 15 um2.

Step 2: CHARGE simulation of the dark current

Trap recombination (Rsrh) : The fitting of this parameter enables a good match of simulated and experimental dark currents. It is a reasonable assumption that this parameter will be process-dependent and may need tweaking.

Surface recombination at Ge-SiO2 interface : The surface recombination velocity, as well as its temperature dependence at the Ge-SiO2 interface, are the other two parameters that are expected to play an important role in the dark current and whose values may be subject to some uncertainty.

Doping : Doping is an important parameter that determines the internal electric field, which in turn determines the electron-hole separation dynamics and current flow. Therefore, it is important to create doping objects to resemble the doping profile in the real device as accurately as possible. This is especially important in devices with very high internal fields.

Surface recombination at other boundaries : Every interface has, to at least some extent, traps that lead to increased dark current, so it is important to include surface recombination objects at Si-Metal, Ge-Metal, and Si-Ge interfaces, with some reasonable values.

Photodetector length : Since CHARGE simulation is 2D the length of the device should be specified in the field ‘norm length’ in the ‘CHARGE’ edit window.

Optical generation rate : The generation rate object calculated with FDTD is set for 1 W input power. Here, it is important to properly set the ‘scale factor’ in the ‘gen’ object to represent the actual power used in the publication. Input power of 1.2 mW has been used, which corresponds to ~1 mA of short circuit current (i.e. current for zero bias) reported in the paper.

When calculating the bandwidth, the scaling factor is adjusted to match the reported peak impulse response in the paper (0.1 mA); 0.12 mW input power was used which is 10 times smaller than the value used in the steady-state simulation.

High field mobility model : The photodetector bandwidth will depend on how fast generated electron-hole pairs can be separated under the internal electric field and how fast they will reach contacts. For this reason, it is important to turn on the high-field mobility model (i.e. velocity saturation) in material properties to avoid overestimating the bandwidth. In this example, we turned on the high field mobility model in Ge layer only as the electric field is highest there.

Small signal AC parameters : In order to calculate the 3dB bandwidth we need to define the proper frequency range and number of points. This can be done in the CHARGE edit window under the Small signal AC tab. Usually, log scale for frequency has to be used to accommodate large frequency ranges. Small signal perturbation value will not have an impact on bandwidth because the current response is linear in perturbation and the amplitude will be cancelled when taking the ratio of currents to find the 3dB drop.

Step 3: INTERCONNECT simulation of the photodetector eye diagram

Circuit simulation in INTERCONNECT is done using an amplitude-modulated CW laser source and assuming -1 V reverse bias of the photodetector. Since the bandwidth due to the amplitude modulation is much smaller than the optical frequency, using single frequency parameters for responsivity is a good approximation.

Bit rate : Random sequence of bits drives the amplitude modulation of the CW laser source. This quantity should be set at the root element so that it can be reused in all the elements that need to know about it, which are in this case the PRBS generator and the eye diagram analyzer. To set the bit rate at these lower-level elements set their bitrate expression field to %bitrate%.

Photodetector dark current and response : The photodetector circuit element accepts the responsivity parameter as a constant or as a frequency-dependent table. In this simulation, we use the responsivity that has been calculated in CHARGE for a single frequency (1.55 um) and photodetector bias -1 V. Dark current is also set as a constant at -1 V bias.

Photodetector bandwidth : The easiest way to include a finite bandwidth of the photodetector in INTERCONNECT is by adding a low pass RC filter element, connecting it to the output of the photodetector element, and set its cutoff frequency to the value of the 3dB bandwidth calculated in CHARGE.

CW laser frequency : This frequency should correspond to the optical source frequency in FDTD (1.55 um).

Updating the model with your parameters

Instructions for updating the model based on your device parameters

When updating the model to match your parameters, it is important to remember that multiple solvers and simulation files are involved. Changes must be made consistently in all the files. Some key parameters are listed below:

Photodetector geometry :

• Change the photodetector length or width in steps FDTD and CHARGE. Rerun step 1 and import a new optical generation rate into CHARGE. Re-run step 2 to obtain the updated results, then set the new values for dark current, responsivity, and bandwidth in INTERCONNECT before running step 3. In CHARGE you have the possibility of sweeping recombination parameters to fit dark current again.
• Change the taper length in step 1 and rerun. Import new optical generation rate into step 2 and rerun. Update the responsivity and bandwidth parameters in step 3 and rerun.

Optical source frequency : Change the source frequency in FDTD and rerun all the steps. You would be importing a new optical generation rate in CHARGE and updating responsivity, bandwidth, and source frequency in INTERCONNECT.

Material : Update the material in your FDTD and CHARGE simulation. Again, you would need to re-run all the steps and update the generation rate in CHARGE and dark current, responsivity, and bandwidth in INTERCONNECT. In CHARGE you can perform the recombination parameter sweep to fit the dark current.

Doping profile : Change the doping profile in CHARGE simulations in step 2. Rerun step 2 with possibly different sweep recombination parameters or with fixed parameters and rerun to get the dark current and set the same recombination rate parameters if changed. Re-run step 2 and update the dark current, responsivity, and bandwidth in INTERCONNECT (step 3).

Photodetector reverse bias : Change bias in CHARGE and re-run. Update the dark current, responsivity, and bandwidth parameters in step 3 at the new reverse bias and rerun.

Parameter Extraction for CML Compiler

Instructions for extracting parameters for CML Compiler

To generate the compact model of the photodetector with CML Compiler, provide the data extracted in Steps 1 and 2 to CML Compiler. The Parameter extraction for the CML Compiler section uses workflow management to automatically go through all the device-level steps and extract the data for CML Compiler in the required format. Advanced users already familiar with this example can proceed to this section directly. If you are new to this example, we strongly recommend going through the preceding sections and learning about the individual steps before moving to the Parameter extraction for the CML Compiler section.

The simulation workflow here is identical to the one described at the beginning of this example except that the bandwidth calculation in Step 2.B is done using transient simulation instead of small-signal ac (for information about the transient simulation see Appendix: Step 2.B using transient simulation).

Once the parameters are extracted in the required format, they can be used in CML Compiler to generate the compact model. Note that the running of the CML Compiler is beyond the scope of this example. For more information about CML Compiler visit the product page .

Some important considerations for running the workflow object:

• The Lumerical API must be configured beforehand. For Windows users the configuration is done automatically during installation of the software; however, for Linux and Mac users some additional steps are required, as explained here .
• The workflow creates a subfolder with the name vpd_CHARGE_parameter_extraction and copies all the project and script files inside it. The workflow only runs the project and script files in this subfolder and all the original project and script files in the parent folder remain unchanged (except for the vpd_CHARGE.ldev file which will contain the results from the workflow).
• The data file generated by the workflow will be saved in the parent folder along with the original project and script files.

The different components of the workflow object are described below:

parameter_extraction : This is the workflow object that drives all the device-level simulations and extracts the data. It contains user-defined parameters such as the names of the different project files, the simulation wavelength (for optical simulations), and the name and type (.mat or .json supported) of the data file.

step_1_FDTD : This is a script task that runs the Step 1 in the simulation workflow. It uses Lumerical API to open FDTD and loads the vpd_FDTD.fsp project file and runs the simulation. Once the simulation finishes it runs the generation analysis group to calculate the optical generation rate.

step_2_dark_current : This step contains a script task to set up the simulation for a bias sweep, followed by a solver task to run the CHARGE simulation. Once simulation finishes it records the current at the anode contact which is the dark current of the photodetector.

step_3_photocurrent : This step contains two script tasks and a solver task. The 'setup' script task sets up the simulation by enabling the optical generation (gen) object and by loading the generation data saved by FDTD.  The solver task then runs the CHARGE simulation and records the anode current (photocurrent). The 'analyze' script task then calculates the responsivity from the photocurrent.

step_4_optical_BW : This step also contains two script tasks and a solver task. The 'setup' script tasks set up a transient simulation for bandwidth calculation. The solver task then runs the simulation and finally the 'analyze' script task calculates the 3dB cutoff frequency of the photodetector.

create_datafile : This is a script task that takes all the data from Step 1 to 4 and combines them to create the data file. Any additional data required by the CML Compiler besides the simulations results are provided in this step as part of the script (e.g. saturation power and thermal noise).

Steps to use the data file and build a Photodetector - Lumfoundry Template – Ansys Optics element compact model using CML Compiler are :

Taking the model further

Information and tips for users that want to further customize the model

There are other photodetector examples in the Photonic Integrated Circuits > Photodetectors section that give details about simulating other important types of photodetectors. These examples focus on some of the important steps, mainly FDTD and CHARGE simulations (with some exceptions). The users can refer to those examples to find out how to simulate those steps for other types of photodetectors:

• Germanium-on-Silicon Lateral Photodetector : An example of a lateral p-i-n photodetector.
• InP/InGaAs Uni-Traveling Carrier Photodetector : An example of a uni-travelling carrier photodetector optimized for high speed.

Additional resources

Additional documentation, examples and training material

Related publications

1. T.-Y Liow et al., “Silicon Modulators and Germanium Photodetectors on SOI: Monolithic Integration, Compatibility and Performance Optimization”, IEEE Journal of Selected Topics in Quantum Electronics, Vol. 16, No.1 (2010)

See also

• Germanium-on-Silicon Lateral Photodetector
• InP/InGaAs Uni-Traveling Carrier Photodetector :

Related Ansys Innovation Courses

Appendix

Additional background information and theory

Dark current fitting

The CHARGE solver can be first used to calibrate the material properties in order to fit the calculated dark current to the dark current in the publication. This step does not require the generation rate data from FDTD. The dark current is sensitive to bulk and surface recombination rate material parameters. For this, run a parameter sweep over the Ge bulk recombination lifetime, surface recombination velocity at Ge/SiO2 interface, and the order of temperature dependency for surface recombination (eta). Once the recombination rates are optimized for a good fit of dark current values at different temperatures, they will be imported into steps 2.A (photocurrent) and 2.B (bandwidth) and the dark current will be imported into the compact model for circuit simulation in INTERCONNECT in step 3.

As an example, the steps below are provided, which demonstrates the fitting done in this article to match the dark current to that reported in the publication:

Detector length optimization

It is important to determine the optimum device dimension, such as device length, since it may affect its performance, for example its ability to absorb light. However, such calculations (e.g. absorption vs. device length), can be time consuming when using FDTD. A length sweep of this VPD device can be done efficiently using the EME solver. The VPD structure is divided into several EME cell groups. Since the Ge structure has a uniform cross-section along the propagation axis, it is ideal to use the EME solver to sweep the length. In port 1, the fundamental TE mode is injected. Light is then coupled from the silicon waveguide to the Ge structure, and therefore light is absorbed. In this example, an analysis group is used to calculate the absorption.

The taper is not included in the structure and the waveguide is assumed to be constant in width that is equal to the wider end of the taper. This is an approximation because the taper will cause the transmission to higher modes of such a wide waveguide, while we only consider the fundamental mode. However, it is a good approximation, since around 80% of the power still remains in the fundamental mode after transmission through the taper.

Open vpd_absorption_length_optimization.lms with MODE and run the simulation to find the modes. Once the simulation is run, we can re-use the calculated eigenmodes and the overlap results for propagation and return absorption as a function of device length. An absorption vs device length plot can be generated using [[vpd_absorption_length_optimization.lsf]]. It is expected to observe a larger absorption as the device length increases. We can see that most of the light is absorbed in the first 50 um of the photodetector.

EME convergence testing: It is also important to check results convergence for the EME simulations. The number of eigenmodes used in the simulation is usually a critical parameter. In the plot below, the absorption of a 50 um long Ge VPD starts to converge when more than 70 modes are used in the EME simulations. Use [[vpd_mode_convergence.lsf]] to generate the plot.

The number of modes used in the EME calculations also affects the E-field profile. When more modes are used, we can observe that the field profiles can converge and become more comparable to the FDTD results. For devices that support a lot of modes, it is recommended to check results convergence with respect to the number of modes.

Calculating power absorption

As light is incident on the Germanium layer, it gets absorbed. The absorption per unit volume can be calculated from the divergence of the Poynting vector,

$$P_{abs}=-0.5\textrm{real}\left(\vec{\nabla}\cdot\vec{P} \right)$$

It is possible to calculate the absorption directly from this formula (see the Divergence of Poynting vector section), but divergence calculations tend to be very sensitive to numerical problems. Fortunately, there is a more numerically stable form. It can be shown that the above formula is equivalent to

$$P_{abs}=0.5 \textrm{real}\left(i\omega\vec{E}\cdot\vec{D}^* \right)$$

With a little more work, we get the desired result

$$P_{abs}=-0.5\omega\left|{E} \right|^2\textrm{imag}\left(\varepsilon \right)$$

To calculate the absorption as a function of space and frequency, we only need to know the electric field intensity and the imaginary part of the permittivity.  Both quantities are easy to measure in an FDTD simulation. The number of absorbed photons per unit volume can then be calculated by dividing this value by the energy per photon:

$$g=\frac{P_{abs}}{\hbar\omega}=\frac{-0.5\left|E \right|^2\textrm{imag}\left(\varepsilon \right)}{\hbar}$$

The absorbed photons will generate electron-hole pairs which will be separated out of the depletion region by the electric field and produce a flow of current.

Step 2.B using transient simulation

The bandwidth in step 2.B can also be calculated by running a transient simulation and performing a Fourier transform of the impulse current response. For this purpose, a global shutter is used to simulate turning on of the optical generation rate:

# Turn on high field mobility model in Ge
matname = 'materials::Ge (Germanium) thin film::Ge (Germanium) thin film';
setnamed(matname,'electronic.l.mun.high field.active model','monotonic');
setnamed(matname,'electronic.l.mun.high field.driving field','grad Phi');

# Make convergence more stable when high field mobility model is turned on
setnamed('CHARGE','global iteration limit',100);
setnamed('CHARGE','gradient mixing','fast');
setnamed('CHARGE','use default update limits',false);
setnamed('CHARGE','dds max update',1);
setnamed('CHARGE','poisson max update',1);

# Set transient simulation and optical source shutter
setnamed('CHARGE','solver mode','transient');
setnamed('CHARGE','transient min time step',100e-15); #s
setnamed('CHARGE','transient max time step',5e-12); #s
setnamed('CHARGE','shutter mode','step on');
setnamed('CHARGE','shutter ton',1e-12); #s
setnamed('CHARGE','shutter tslew',2e-12); #s
setnamed('CHARGE','shutter slew function','log');
setnamed('CHARGE','shutter slew cutoff',1e-6);

# Enable the optical generation rate object and set scale factor so that the
# step on current is approximately equal to the peak impulse current in the
# publication of around 0.1 mA. This object should already have data file imported
setnamed('CHARGE::gen','enabled',true);
setnamed('CHARGE::gen','scale factor',1.2e-4);

#Set transient reverse bias
setnamed('CHARGE::boundary conditions::anode','bc mode','transient');
t=[0,500e-12]; #s
V=[-1,-1]; #V
setnamed('CHARGE::boundary conditions::anode','transient voltage time steps',t);
setnamed('CHARGE::boundary conditions::anode','transient voltage table',V);

Transient vs. small-signal AC bandwidth simulation

Transient simulation is fully nonlinear and it can capture all the effects of a large signal. Small signal simulation is based on explicit linearization of drift-diffusion equations around the DC operating point, so any nonlinear effects arising from the presence of a large signal will be missed. Small signal AC simulation is more accurate for smaller signal as shown in the figures below (optical source power for the left-hand side figure is 1.2e-4 W and for the right-hand side figure is 1.2e-5 W):

Bandwidth calculated from a transient simulation will be sensitive to the following parameters:

• Time step size -- even if the transient simulation converges nonlinear drift-diffusion equations successfully at each time step, the users may want to perform a result convergence test with respect to the time step size, by limiting the global min and max time step values in CHARGE’s edit window under Transient tab (the most stringent test would be to set max and min to the same small value). Sometimes smaller time steps will be required to get a more accurate and stable result for the bandwidth.
• Total simulation time -- it must be long enough for the device to reach a steady state.
• Shutter slew time -- it should be small enough so that the shutter bandwidth is larger than the device bandwidth.

The user must ensure that the bandwidth value is converged with respect to these parameters. Also, transient simulations, being more numerically complex, are usually more difficult to converge than steady-state simulations.

Transient simulation usually takes longer because one nonlinear equation needs to be solved for each time step for each steady-state bias. Small signal simulation just needs a steady-state solution for each bias.

When a transient simulation is used to calculate the bandwidth, the user needs to perform a Fourier transform as a post-process, while small-signal simulation directly produces frequency domain data.