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Mach-Zehnder Modulator

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Characterize a SOI waveguide modulator for use in a Mach-Zehnder Interferometer (MZI). The FDE and CHARGE solvers are used to characterize the modulator. A compact model of the waveguide modulator is then used in a MZI circuit in INTERCONNECT. Performance metrics of the modulator such as capacitance, effective index perturbation, and loss are calculated. The effect of modulation on the performance of the interferometer circuit is also investigated.

Related: Travelling Wave Modulator, Ring Modulator

Files and Required Solvers

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Contents

Overview

Run and results

Important model settings

Updating the model with your parameters

Taking the model further

Convergence

Additional resources

Overview

Understand the simulation workflow and key results

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The CHARGE and FDE solvers are used to characterize a waveguide modulator and to create a compact model in INTERCONNECT.  The waveguide modulator compact model is then used to create a Mach-Zehender modulator in INTERCONNECT.  

The example assumes that the modulator structure is uniform along the light propagation direction so only a cross-section of the waveguide modulator needs to be simulated.

Step 1: Electrical simulation

Calculate the spatial carrier concentration as a function of applied voltage. Optionally, from the carrier concentration, we can estimate the device capacitance.  

Step 2: Optical simulation

The carrier concentration obtained from electrical simulation changes the refractive index of the waveguide. This makes the effective index of the waveguide modes voltage dependent.

Step 3: Circuit simulation

The change in effective index as a function of applied voltage is used to create a compact model of the waveguide modulator.  The waveguide modulator elements are then used to create a MZI.  A frequency domain simulation is then used to characterize the performance of the MZI (eg. the transmission spectrum).

Run and results

Instructions for running the model and discussion of key results

Step 1: Electrical simulation

1.Open and run the MZI simulation file in DEVICE.

2.Right click on the charge monitor and visualize charge results. Make sure the charge data is exported to a file named charge.mat in the same location as the simulation file

3.Optionally run MZI_DEVICE.lsf file to obtain the capacitance of the device as a function of voltage

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Figures on the right illustrate the electron distribution profile in log scale at the cross-section of the waveguide modulator for oV (left) and -4V (right) bias voltage applied to the device. It can be seen from the figures that with no bias voltage applied, the charge distribution at the cross-section of the waveguide is rather symmetric where as by applying a reverse bias that is strong enough, the electrons are partially pushed out of the waveguide (to the left) as a result of the widening of the depletion region across the pn junction causing a rather dramatic change in charge distribution across the waveguide.

 

This change in charge distribution and depletion region width will change the junction capacitance as depicted in the C-V plot of the device. As expected, the contribution of electrons and holes to the junction capacitance is very similar and is reduced as a higher reverse bias voltage is applied due to the widening of the depletion region. The amount of capacitance will affect the operation speed (bandwidth) of the modulator and thus can be used in its circuit model to consider this effect. See “taking the model further” section for more details.

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Step 2: Optical simulation

1.Open the MZI simulation file in MODE Solutions.

2.Import the charge distribution data (charge.mat) into the “np” grid attribute object.

3.Run the “voltage” parameter sweep

4.Once the sweep is done, run the script file MZI_MODE.lsf to plot and export the change in effective index and loss as a function of bias voltage. Make sure the data is exported to a file named neff_V.dat

5.Optionally explore other properties of the device such as mode profiles by running a single wavelength modal analysis

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The plots on the above right show the change in real part of effective index (left) and the loss (right) of the modulator as a function of the applied voltage. The results show that a larger modulator reverse bias results in a higher effective index perturbation and lower loss. This is expected since the depletion of free carriers from the junction (waveguide) as a result of reverse bias application should reduce the amount of light absorption along the waveguide. A higher index perturbation will result in lowering the required length of the MZI circuit to achieve a π phase shift thanks to the extra phase shift provided by this perturbation.

 

The mode profile for the fundamental TE mode of the modulator’s waveguide at a -4V applied bias voltage for the wavelength of 1.55 um is shown on the right. It is obvious that the mode is well confined within the waveguide and thus overlaps significantly with the carrier distribution within the waveguide which can affect the effective index of the mode in a noticeable manner.

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Step 3: Circuit simulation

1.Open the MZI simulation file in INTERCONNECT.

2.Import the effective index data obtained from optical simulation in “neff_V.dat” using the “OM_1” and "OM_2" modulator elements.

3.Run the simulation

4.Visualize the transmission (gain) of the MZI circuit obtained by the Optical Network Analyzer object

5.Optionally change the modulation voltage applied to the modulator and observe the change in the transmission spectra.

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The obtained transmission spectra reveals that the transmission notches of the MZI circuit can be shifted depending on the amount of applied bias voltage to the modulator which is stemming from the fact that the phase shift across the upper arm of the MZI circuit (which contains the modulator) can be modulated and thus the wavelengths at which the interference between the upper and lower arms happens can be varied. Here, the results show that for a length of 1cm, the Vπ for the modulator is at around 2.5V since this is the voltage the causes the transmission notch to shift for the amount of half of the free spectral range (FSR). The same amount of shift can be achieved by applying the same voltage to either of the MZI arms.

Important model settings

Description of important objects and settings used in this model

Simulation region orientation

For both electrical and optical simulations, the simulation region orientation should be identical (in this example Y-normal is chosen which means the simulation in done in XZ plane). This is a requirement for successful and hassle-free data transfer from electrical to optical simulation since the imported data in optical simulation will end up on the same plane as the structure.

Charge monitor data settings

To obtain the junction capacitance, the total charge across the junction is required. Therefore, “integrate total charge” should be enabled for the charge monitor. In addition, in order to export the charge distribution profile to the optical simulation, the “save data” option of the charge monitor should be enabled and a file name needs to be specified. The file containing the data will be located in the same location as the simulation file after the simulation is run.

Bias voltage

In order to apply a reverse bias to the junction, a negative voltage can be applied to the “drain” contact of the device using an electrical boundary condition. To sweep over a range of bias, the sweep type can be chosen as “range” and the range and number bias points can be adjusted accordingly.

Np density grid attribute

An np density grid attribute object in MODE will take the carrier density information and calculate the corresponding changes in the real and imaginary parts of refractive index of the material according to a formulation in a work by Soref et al. For a more detailed description of this grid attribute and the index perturbation model used, please visit the Additional Resources section.

Simulation region span

In order to improve the performance of the optical simulation, the optical simulation region can have a smaller span than that of the electrical simulation. For example, the contacts can be left out as the charge distribution in the area close to the contact is of no optical importance since the optical modes are majorly confined within the waveguide.

Boundary conditions

Since the optical modes are well confined within the waveguide, metal boundary conditions are physically correct to use and offer a far better simulation performance than PML boundary conditions.

Mesh size

Since the charge data imported from electrical simulation is located on a finite-element mesh where as the optical simulation is performed on a rectilinear mesh, an interpolation is necessary to use the imported data. An adequately refined mesh will ensure the accuracy of this interpolation. To maintain the simulation performance, the mesh can be locally refined around the areas of great importance (waveguide and the slab) as opposed to the entire simulation area. This can be accomplished through mesh override objects and since the simulation is on XZ plane, only mesh refinement in X and Z directions is necessary.  

Parameter sweep

Since the simulation requires the effective index and mode calculations at various bias voltages, a parameter sweep is defined. This will sweep the “V_drain_index” parameter of the np density grid attribute as each index corresponds to a bias voltage within the imported data of the grid attribute object.  The “neff” dataset returned by the FDE solver object is chosen as the result for the parameter sweep which can be used to obtain the effective index perturbation resulting from the voltage sweep.

ONA orthogonal identifier

Since the effective index data extracted from optical simulation were for the fundamental TE mode, the orthogonal identifier of the ONA should be set to 1, which is equivalent to TE, in order for the entire circuit to operate in TE mode.

Modulator data table

The data table of effective index vs. voltage for the modulator should be loaded from file and thus the measurement type should be set to “effective index”.

Unperturbed indices and loss

The effective and group index and loss values of the unperturbed waveguide (obtained from the optical simulation for 0V bias) should be added to the waveguide models in the circuit.

Updating the model with your parameters

Instructions for updating the model based on your device parameters

Change the dimensions (geometry) of the modulator (e.g. waveguide) based on your own design. The example assumes that a 450nm silicon layer on a thick silicon dioxide (oxide) layer. The waveguide is 500nm wide, and the remaining silicon is etched back 400nm to leave a waveguide 400nm thick and 500nm wide, which sits on a 50nm silicon pad. (CHARGE, FDE)

Modify the bias voltage range to accommodate your own design based on how much modulation (phase shift) is needed.  (CHARGE, FDE)

Change the length (or the length difference) of the two arms of the MZI circuit to accommodate your own design. Note that when changing the arm length, it is important to update the 'length' property of both the modulator and waveguide components since the modulator is modelled as the active part of the arm and only contains index perturbation model for the waveguide. (INTERCONNECT)

Update the doping profile for the modulator. Generally, a heavily doped profile would result in more phase shift from the modulator but more loss due to free carrier absorption.  (CHARGE)

Choose the material(s) of your choice. Pay attention that depending on the material, a different charge to index conversion model might be needed.   (CHARGE, FDE)

Use your own design operation wavelength. Note that the built-in Soref and Bennett model used for index perturbation only supports two communication wavelengths (1550 and 1310 nm). The model coefficients for other wavelengths need to be defined by the user. Alternatively, the less accurate Drude model can be used which supports a wide range of wavelengths.   (FDE, INTERCONNECT)

Taking the model further

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

Bandwidth limitation effect: To simulate the effect of limited bandwidth on the response of the modulator, a time domain circuit simulation can be performed. The effect can be modeled by adding a low pass filter element to the modulation port of the modulator element. The cutoff frequency of the filter can be determined from the capacitance (and resistance) of the modulator obtained from electrical simulation.

More accurate modeling of the passive portion of the MZI circuit: The example considers the passive and active portion of the bottom arm of the MZI to have the same properties for simplification purpose by including only one waveguide element for both portions in the circuit. A more accurate model should consider one 100um long waveguide element for the passive portion (which is usually undoped) and one 10000um long waveguide element for the active section with different properties such as effective index, group index and loss for each portion.

Realistic Y-branch element: The INTERCONNECT MZI circuit currently uses idealized Y-branch elements. These could be replaced with Y-branch elements that more closely match the performance of your device.

Convergence

Tips for ensuring that your model is giving accurate results

The default settings of the example provide a reasonable balance between accuracy and simulation time.  The following changes may provide higher accuracy, at the expense of longer simulation time and more required memory:  

 

Electrical simulation: Since the charge distribution is the ultimate output of the electrical simulation, an adequately refined mesh is essential to ensure accurate representation of data. This can be verified by looking at the electron and hole capacitance values (Cn and Cp) returned by the simulation. A reasonably refined mesh will make sure these values are as close as possible. Local mesh refinement around the waveguide is recommended as this is the area where charge distribution overlaps with confined optical modes.

 

Optical simulation: A converged electrical simulation is a requirement for the convergence in optical simulation. This means that a convergence for the electrical simulation should be reached first and then the charge distribution from the converged electrical simulation should be imported into the optical simulation for further convergence testing. Since the index perturbation will be calculated on a rectilinear mesh and the imported charge data is located on a finite-element mesh, an interpolation is necessary which demands an adequately refined optical mesh to ensure accurate interpolation. Generally, a mesh grid size of equal or less than that of the electrical simulation is recommended for the optical simulation to reach convergence.

Additional resources

Additional documentation, examples and training material

Related publication: R. A. Soref and B. R. Bennett, SPIE Integr. Opt. Circuit Eng. 704, 32 (1987).

Charge to index conversion

Related Lumerical University courses

Course_FDE100 Course_CT100 Course_INT100

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