In this example, a PN depletion phase shifter for use in photonic integrated circuits is characterized, and its compact model is automatically generated using CML Compiler. The FDE and CHARGE solvers are used to characterize the phase shifter, and a compact model of the phase shifter is used in a simple circuit in INTERCONNECT. Performance metrics of the phase shifter such as capacitance, effective index perturbation, and loss are calculated. The effect of bias voltage on the signal phase shift in the circuit is also investigated.
Understand the simulation workflow and key results
The CHARGE and FDE solvers are used to characterize a phase shifter and to create a compact model for use in INTERCONNECT. The phase shifter compact model is then used to create a test circuit in INTERCONNECT.
The example assumes that the phase shifter structure is uniform along the light propagation direction so only a cross-section of the device must 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 phase shifter. The phase shifter element is then used to create a simple circuit to test its performance. A frequency domain simulation is then used to characterize the performance of the device.
Compact model generation with CML Compiler
To generate the compact model of the phase shifter with CML Compiler, simply skip compact model creation in Step 3 and provide the data extracted in Steps 1 to 2 to CML Compiler. The Parameter Extraction for CML Compiler section uses the 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 learn about the individual steps before moving to the Parameter Extraction for CML Compiler section.
Run and results
Instructions for running the model and discussion of key results
Step 1: Electrical simulation
- Open and run the phase shifter simulation file (.ldev) in CHARGE.
- 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
- Optionally run PN_phase_shifter_CHARGE.lsf file to obtain the capacitance of the device as a function of voltage
The figures above illustrate the electron distribution profile in log scale at the cross-section of the phase shifter for 0V (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 symmetric. 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 phase shifter and thus can be used in its circuit model to consider this effect. See the “Taking the model further” section for more details.
Step 2: Optical simulation
- Open the phase shifter simulation file in MODE.
- Import the charge distribution data (charge.mat) into the “np” grid attribute object.
- To find the mode properties at 0V bias, click the "run" button to open the Eigensolver Analysis window and then click "calculate modes".
- Select the fundamental mode and click 'Frequency Sweep' from the 'Frequency analysis' tab. Once the sweep is done, click the 'Export for INTERCONNECT' button from 'data export' option and save the parameters to ps_active_0.ldf.
- Run the “voltage” parameter sweep
- Once the sweep is done, run the script file PN_phase_shifter_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
- Optionally explore other properties of the device such as mode profiles by running a single wavelength modal analysis
The plots on the right show the change in real part of effective index (left) and the loss (right) of the phase shifter as a function of the applied voltage. The results show that a larger 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 phase shifter 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 phase shifter 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.
Step 3: Circuit simulation
- Open the phase shifter simulation file in INTERCONNECT.
- Import the 0V bias waveguide data in "ps_active_0.ldf" using the "WGD_1" MODE waveguide element and effective index data obtained from optical simulation in “neff_V.dat” using the “OM_1” optical modulator element.
- Run the parameter sweep.
- Visualize the "angle" result of the sweep which contains the phase data as a function of bias voltage.
The obtained phase results as a function of bias voltage are shown in the figure above. The shift in phase as the bias voltage varies is obvious from the plot. Here, the results show that for a length of 500um, the phase shift is about 0.2 rad at 4 volts bias voltage which indicates the Vπ.Lπ figure of merit of the phase shifter is about 0.03 V-m.
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.
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.
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.
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.
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.
Phase shifter data table
The data table of effective index vs. voltage for the phase shifter 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 MODE waveguide element 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 phase shifter (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 phase shift is needed. (CHARGE, FDE)
- Change the length of phase shifter to accommodate your own design. Note that when changing the length, it is important to update the 'length' property of both the phase shifter and waveguide components since the phase shifter is modeled as a combination of the optical modulator element which only contains index perturbation model and the MODE waveguide element which models unperturbed index for the waveguide (0V bias). (INTERCONNECT)
- Update the doping profile for the phase shifter. Generally, a heavily doped profile would result in more phase shift from the device 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)
Parameter Extraction for CML Compiler
Instructions for parameter extraction for CML Compiler for compact model generation
This section describes how to automatically run the device level simulations of the PN depletion phase shifter and extract the parameters for CML Compiler. Note that the simulation workflow is identical to the the one described at the beginning of this example. We use the workflow management object in the Finite Element IDE to run all the (device level) steps automatically. 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 .
- Open the PN_phase_shifter.ldev simulation file.
- Select and run the workflow object labeled parameter_extraction.
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 PN_phase_shifter_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 PN_phase_shifter.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 and script files, the simulation wavelength (for optical simulations), and the name and type (.mat or .json supported) of the data file.
step_1_electrical : This is a solver task that runs the Step 1 in the simulation workflow. It runs the CHARGE simulation in the PN_phase_shifter.ldev project file. The charge monitor named monitor_charge automatically saves the charge density data in a .mat file.
step_1_electrical_capacitance : This is a script task that runs the capacitance calculation from Step 1 in the simulation workflow. It uses the data obtained in the preceding task in the workflow to perform the calculation.
step_2_optical : This is a script task that runs the Step 2 in the simulation workflow. It uses Lumerical API to open MODE and load the PN_phase_shifter.lms project file. It then calculates the mode properties for both the unperturbed and perturbed waveguides in the phase shifter.
create_datafile : This is a script task that takes all the data from Step 1 to 2 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. properties of the passive portion of the phase shifter).
Passive and transition segments of the phase shifter
This example does not include the passive and transition segments of the phase shifter. However, for generation of the compact model using CML Compiler, data for these segments must be included. These data can be provided directly in the last step of the workflow management (create datafile) to be packaged along with the other simulation results. Here, the length of those segments is set to zero since we ignored those segments in the example.
The workflow above does not include the complete simulation of the electrical RC limited bandwidth since slab resistance calculation is also needed in addition to capacitance. However, for generation of the compact model using CML Compiler, electrical bandwidth data must be included. In this example, we have assumed that the slab resistance data is available from experimental measurements and have provided it directly in the last step of the workflow management (create datafile) to be packaged along with the other simulation results. See the section Taking the model further for more information about simulating the electrical bandwidth.
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 phase shifter, a time domain circuit simulation can be performed. The effect can be modeled by adding a low pass filter element to the electrical port of the phase shifter element. The cutoff frequency of the filter can be determined from the capacitance (and resistance) of the phase shifter obtained from electrical simulation or measurement.
- Modeling of the passive and transition segments of the phase shifter: The passive segment of the phase shifter usually includes a strip waveguide which can be modeled using a separate MODE simulation and its mode properties can be added in a separate waveguide element in INTERCONNECT compact model. The transition segments can also be modeled but usually considering their mode properties to be the average of active and passive segments is a good approximation.
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 documentation, examples and training material
- R. A. Soref and B. R. Bennett, SPIE Integr. Opt. Circuit Eng. 704, 32 (1987).