To make sure that the actual device will work as expected, it is often necessary to consider imperfections that can result from the fabrication process. To do this, we first set up a nested parameter sweep to track change in FSR as a function of the waveguide height and width (assuming fabrication error of ±10nm). The following figure shows the map of the FSR vs waveguide height and width:
Then, in the yield analysis, we can define the target range for the FSR. Once the
simulations finishes running, the log at the bottom of the "Yield analysis status" window will show the calculated yield percentage which corresponds to the percentage of trials that falll within the specified yield estimate range. One can also plot the FSR histogram as shown below. (Note that even though we are only considering the FSR in this example, it is very straightforward to extend this analysis to take into account other properties such as the shift in the resonance peaks, the Q factors ... etc using the same methodology.)
The parameter sweep and yield analysis shown in this example required more than 100 simulations. More simulations will be necessary if we want to change more parameters.
This is another reason to consider using the Propagator instead of running 3D FDTD simulations.
7.2 Modeling instructions
This page contains 3 independent sections. The first section (Parameter extraction)
describes how to setup the mode expansion monitors for parameter extraction. If you prefer to skip this section,the completed simulation files are provided on the first page of the tutorial. The second section describes how to use the S parameter results from the first section in a circuit level simulation in INTERCONNECT. The final section shows how to track the effect of fabrication errors on the free spectral range (FSR) of the ring resonator by performing yield analysis.
In this topic
We will start with the file ring_resonator.lms from Ring resonator (design and initial simulation) .
Open the ring_resonator.lms file and run the simulation.
Before adding the mode expansion monitor, please read the following page on the calculations behind mode expansion monitors: User Guide -> Using Mode Expansion Monitors.
Add a mode expansion monitor by pressing on the arrow on the Monitors button
and select the Mode expansion monitor from the pull-down menu. Set the properties according to the following table. (Note that you can add mode expansion monitors in layout or analysis mode, so it is not necessary to switchtolayout if the simulation has already been ran.)
tab property value
name expansion
Geometry monitor type 2D X-normal
x (µm) -4.2
y (µm) 3.6
y span (µm) 3
z (um) 0
z span (um) 2
We have positioned this monitor directly in front of the MODE source, and we will use the fundamental mode of the top waveguide to expand the field at the 4 ports of the ring resonator.
In the Mode expansion tab, select the fundamental mode for "Mode calculation". You can use the Visualize Mode Data button to study the field profile for this mode.
In the "Monitors for expansion table", select the 4 power monitors we have set up at the 4 ports of the Ring Resonator as follows:
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Plot results
Once the mode expansion monitor has been defined, you will see the list of results in the Result VIew panel. Multi-select the modal expansion results and select "Calculate". Once the calculations are complete, one can plot the results in the Visualizer.
Note that when the Visualizer first opens up, you will see a list of all the attributes of all the results. One can use the "Remove" button on the right side of the attribute panel to remove any unwanted attributes, keeping only the relevant ones. For a complete description of all the results from the mode expansion monitors, please refer to User Guide -> Using Mode Expansion Monitors.
S parameter calculations
In ring_resonator2.lms, the model analysis group in the provided pre-made simulation file has been set up to calculate the S parameters. Since the expansion monitor
automatically returns the expansion coefficients for the forward and backward propagating light (a and b), we can calculate the S parameters very straightforwardly. The calculations can be found in the script under the Analysis tab of the "model" group, this script will also export the S parameter results into a .txt file, which can be imported directly by
INTERCONNECT.
As shown in the figures above, the Results View will automatically show the S parameters result returned by the model analysis group. One can then visualize this result by right-clicking on "S" and selecting Visualize.
Yield analysis
To test how our design is affected by fabrication errors, we can use either a parameter sweep or an yield analysis project.
In ring_resonator2_yield.lms, a "FSR" analysis group has been added, which will return the FSR by finding the peaks in the transmission spectrum of the "through" monitor.
We will track the change in the FSR as a function of the waveguide width and height, assuming a fabrication error of ±10nm.
Parameter sweep
A nested parameter sweep project has been set up to track the change in FSR as a function of the width of the waveguide (from 0.39 to 0.41 microns) and the height of the waveguide (from 0.17 to 0.19 microns). Once the sweep is complete, one can plot the map of the FSR as a function of the waveguide height and width to see how the result deviates from the original design as a result of this ±10nm fabrication error.
Yield analysis
An yield analysis project has also been set up to vary the width of the waveguide based on a Gaussian distribution centered at 0.4 microns, with a standard deviation of 0.01 microns.
Once this is run, we will be able to see whether the FSR falls within our target specification range of 27nm to 27.5nm.