In this example, we will study the performance of an electrically tunable contra-directional coupler (CDC) using CHARGE (electrical simulation) and MODE (optical simulation).
Theory
To calculate the effect of the change in the carrier density on the waveguide loss and effective index, a MODE simulation will be run. 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 formula, please visit the section on Charge to index conversion.
Simulation Setup
The dual wave-guide structure of the CDC can be set up in CHARGE. Open the pin_cdc.ldev file in CHARGE. The dimensions of the waveguides reflect the structures in the referenced paper by W. Shi et al.. The component is fabricated in an SOI process, where a thin layer of silicon is formed epitaxially on a buried oxide. The silicon is then etched back to pattern the waveguide structures. The peak doping concentrations and dimensions of the doping profile in the referenced paper are used to define the PIN structure in the layout for the electrical model. The doping profile is approximated using an analytic model.
Cross-section of the simulation region in CHARGE.
In the referenced device, a grating is formed by etching holes in the central region separating the waveguides. In the electrical simulation, a 2D cross-section is chosen such that it will not intersect the grating holes, ensuring electrical continuity between the contacts. Heavily doped wells are implanted beneath the contacts in the experimental component, therefore ohmic contacts are used in the electrical simulation. In the optical simulation, the grating will be treated as a weak perturbation, and the modes in the two arms will be simulated in the same cross-section as the electrical simulation.
The layout for the optical simulation mirrors that of the electrical simulation. Open the pin_cdc.lms file in MODE. The charge monitor in CHARGE will save the n and p distributions into a matlab data file named cdc_charge.mat. This data can then be exported into MODE.
To calculate the effective index of each waveguide as a function of the applied voltage, a parameter sweep is used. Users with multi-processor computers or access to concurrent computing resources (e.g. a compute cluster) can take advantage of these extra processors by configuring the resources in MODE to utilize all available cores during the parameter sweep. The results of the parameter sweep (the effective mode of each index as a function of voltage) can be plotted using the voltageMODEsweep_cdc.lsf script file provided.
Results and Discussion
CHARGE (Electrical Simulation)
Thin-Film Silicon Properties and IV Response
The CDC is a thin-film silicon device, with a large surface area to volume ratio relative to a traditional planar structure. Consequently, surface and bulk recombination effects will influence the electrical behaviour. Two material models for silicon are included in the project file: the standard (bulk) model, and "Si (Silicon) thin-film," with a reduced carrier lifetime for the bulk trap-assisted recombination model, and a surface recombination velocity of 10cm/s for the Si-SiO2 interface. For further details on defining the semiconductor material properties, please consult the reference on the electrical materials. The effect of the increased recombination is clearly visible in the IV response when the device is operated in forward bias. At low bias voltages, the recombination current is dominant. This technique can be used to establish an estimate of the material properties, and the two results are illustrated in the IV response below.
IV response for thin-film (blue) and bulk silicon (green) electrical material models.
To generate this plot,
- Run the simulation in the unmodified project file
- Right click on the "CHARGE" and choose "Visualize" "anode" to plot the IV response. Do not close the visualizer window.
- Return to the main window, and switch back to layout mode by clicking the "Layout" button
- Change the material for the silicon structures (left and right waveguides, slab) to "Si (Silicon)" and re-run the simulation.
- Again, right-click on the "CHARGE" and chose "Add to visualizer 1" "anode"
- Choose a log scale to compare the two curves while only keeping total current (I) attributes in the visualizer.
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Note: Once the I-V plot is created, change the material for the silicon structure back to Si (Silicon) thin film. |
Note that as the carrier lifetimes decrease and the surface recombination velocity is increased, the current at low bias voltages increases. Using the thin-film model for the silicon, the IV response can be compared to the experimental data. The simulation will over-predict the current when parasitic impedances are ignored. Open and run the script compare_iv.lsf to generate the curve on the left below. To generate the curve on the right, with a 50-ohm parasitic impedance, open the anode boundary condition edit window and change the rse ( series resistance) from 0 to 50 ohms and run the simulation again. You will notice much better agreement between the simulation and measured results. When plotting the graph for the case with the 50-ohm impedance, enable the last line of the script file to save the I-V data in a .mat file. This data will used later while plotting optical results from MODE simulation.
Simulated (blue) and measured (green) IV response with no parasitic (probe) impedance.
Simulated (blue) and measured (green) IV response with 50-ohm parasitic (probe) impedance.
Extracting Carrier Concentrations
The carrier concentrations can be visualized following a simulation by choosing "visualizecharge" in the CHARGE object context menu, and navigating to the the electron (n) or hole (p) concentrations. An image plot with log scaling will reveal the distribution of carriers. The result is parameterized by the bias voltage, and by expanding the "Parameters" group, the result can be viewed at different bias voltages. In the figures below, the injection of electrons into the waveguide region is clearly visible under forward bias (V = 0.5V) conditions.
The electron concentration (log scale) at V = 0 V.
The electron concentration (log scale) at V = 0.5 V.
The carrier concentrations can be collected from the simulation and exported in a format suitable for MODE. Open the script file extractDeltaCharge_cdc.lsf in the script file editor and run the script to export the carrier density data. Make sure all the provided associated files are downloaded and exist in current working directory. The script will generate a data file for each region of the simulation: the left and right waveguides and the slab.
MODE Optical Simulation
Open the pin_cdc.lms file in MODE. 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. [1]. For a more detailed description of this grid attribute and the formula, please visit the section on Charge to index conversion.
The eigenmode solver can then be run for that voltage. To sweep the range of applied bias voltages, a parameter sweep is used. Choose the parameter sweep "bias voltage" and click Run. The results of the parameter sweep can be plotted using the voltageSweepMODE_cdc.lsf script file provided. The change in the index can also be used to tune the resonance wavelength:
$$\Delta \lambda \approx \lambda_{0}\left(\frac{\Delta n_{e f f .1}+\Delta n_{e f f .2}}{n_{e f f .1}+n_{e f f .2}}\right)$$
Open and run this script file. The following plots should be generated from the script:
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Note: In order to create the last plot above, the current versus voltage data must be saved from CHARGE using the compare_iv.lsf script file as mentioned in the previous section.
Reference
Wei Shi, Xu Wang, Charlie Lin, Han Yun, Yang Liu, Tom Baehr-Jones, Michael Hochberg, Nicolas A. F. Jaeger, and Lukas Chrostowski, "Electrically Tunable Resonant Filters in Phase-Shifted Contra-Directional Couplers", 2012 IEEE 9th International Conference on Group IV Photonics (GFP), San Diego, CA, Aug. 2012.