Layout-aware statistical yield analysis – WDM transceiver

Fabrication process variability has a strong impact on the performance of photonics integrated circuits, and such an impact typically shows strong correlations across circuit layouts. In photonic circuit designs, an accurate circuit yield analysis should consider not only the statistical variations of circuit elements but also elements’ layout spatial correlations. In this example, we demonstrate INTERCONNECT’s capability to run layout-aware statistical yield analysis based on a 4-channel WDM transceiver design.

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Overview

Understand the simulation workflow and key results

In this design, four WDM carriers are combined off-chip and coupled to the transmitter chip through grating couplers. On the transmitter side, four cascaded ring modulators modulate the four WDM carriers at a speed of 20Gb/s, respectively. On the receiver side, the modulated WDM channels are dropped by ring filters, individually, and each optical channel is detected by a high-speed photodetector. This design is built with a CML that includes statistical models for ring modulators, waveguides, and grating couplers. The figures-of-merits for this design include the extinction ratios (ER) and bit-error rate (BER) for each WDM channel, as well as the tuning power consumption for ring modulators and filters.

Step 1: Nominal spectral response of ring modulators

First, this example will perform frequency domain analysis on the key transceiver components, i.e., ring modulators, to study their nominal resonant wavelengths. The same ring modulators are used in the receiver circuit as ring filters, except that they operate without electrical modulation.

Step 2: Monte Carlo analysis for individual ring modulators

Then, this example runs Monte Carlo analysis to study the spectral response of a ring modulator under manufacturing variations. Automated thermal tuning is applied to re-align the resonant wavelength with the target carrier wavelength before each simulation iteration.

Step 3: Nominal transient simulation for transceiver

Next, we will perform transient simulation on the 4-channel WDM transceiver to study its nominal performance. We consider a layout-driven flow for the transceiver design, where the circuit layout is designed in Tanner L-Edit Photonics using the GPIC iPDK, a generic photonic PDK. The circuit netlist is then extracted from L-Edit and imported into an INTERCONNECT test bench simulation file. We conduct a time domain simulation where the four modulators are driven by four individual non-return to zero (NRZ) signal based on a pseudo-random bit sequence (PRBS) at 20Gb/s. Eye Diagram Analyzers are used to obtain the eye diagrams of the received time signal at the receiver outputs.

Step 4: Yield analysis for transceiver

Finally, we will run Monte Carlo analysis to study the impact of manufacturing variability on transceiver’s figure-of-merits, predict the yield, and highlight the importance of spatial correlation on photonics circuit design.

Run and results

Instructions for running the model and discussion of key results

Step 1: Nominal spectral response of ring modulators

Ring nominal spectrum

The four ring modulators' radii are carefully designed to obtained nominal resonant wavelengths at 1552.52 nm, 1551.72 nm, 1550.92nm, and 1550.12 nm, respectively, which perfectly match the standard DWDM channel 31, channel 32, channel 33, and channel 34, respectively. In the transceiver design to be discussed in Step 3 and Step 4, these four DWDM channels are the optical carriers.

Note that there are two tuning schemas in the ring modulator model. One is electrical tuning for high-speed signal modulation; and the other is thermal tuning to align its resonant wavelength with a target .

Step 2: Monte Carlo analysis for individual ring modulators

Resonance wavelengths of a ring modulator/filter are sensitive to process variations, therefore in practice, a fabricated ring modulator/filter needs to be thermally tuned to re-align its operating wavelength to the target optical carrier wavelength.

Ring tuning voltage/power

The automation of the ring tuning process is done by the setup script in Root Element. In Root Element setup script tab, the following script reads ‘tuned_V’ from the step2_ring_Monte_Carlo_analysis_RM_1.json file and set this value to the DC source voltage before the simulation starts:

ProjectFileName = filebasename(currentfilename);
RM_1_tuning=jsonread(%local path% + "/" + ProjectFileName +"_RM_1.json");
setnamed("DC_1", "amplitude", RM_1_tuning.tuned_V);

The Root Element setup script is set to run always to make sure the DC source voltage is up to date with the current “resonant_wavelength” value of the ring modulator models.

It can be seen that the resonant wavelength of the ring modulator is perfectly tuned and stabilized to 1.55252e-6 m when statistical variations are applied.

Step 3: Nominal transient simulation for transceiver

Physical layout of the transceiver

The physical layout of transceiver is shown below:

The entire transceiver layout is split into two chips, i.e., a transmitter chip on the top and a receiver chip on the bottom, with a dicing line across in the middle. All the optical inputs and outputs (I/Os) are placed on the west edge of the chips, and they are spaced by a 127 um pitch for fiber array alignment. The RF pads for the transmitter and receiver are placed on the north edge and the south edge, respectively. All the DC pads are placed on the east edge. Such a configuration makes it convenient for wafer testing before dicing. The extracted circuit netlist, which includes the physical coordinates for all the circuit elements, is also attached in this example package for user’s reference (see file WDM_Tx_Rx_netlist.spi ).

Note that there are two operating schemas in this transceiver. For each ring modulator, its operating resonant wavelength is tuned to offset its carrier wavelength by 30 pm so as to optimize modulation efficiency. For each ring filter, its operating resonant wavelength is tuned to perfectly align with its carrier wavelength to filter out the channel modulated signal. The thermal tuning efficiency are the same for all the ring models, e.g., the amount of resonant wavelength shift per unit power is the same. The thermal tuning for wavelength alignment is automatic in this design and this will be discussed in detail in the following step.

Power spectrum and eye diagram

The plots generated by the script file step3_analyze_transceiver_nominal_performance.lsf are the power spectrum of the WDM system at the receiver end, and the four eye diagrams received at the four ring drop ports.

Step 4: Yield analysis for transceiver

This step runs the Monte Carlo analysis to study the impact of the manufacturing variability on the transceiver’s performance. Note that in each simulation iteration, ring modulators and filters are automatically tuned to their operating wavelength targets based on the approach described in Step 2.

Correlation for ring modulator tuning power

These two plots analyze the correlations of tuning power consumption between ring modulators. In this transceiver design, the 1 ^st and the 2 ^nd ring modulators are placed 200 um apart, and it is found that the difference of their power consumption confines in the range of ±2.2 mW. The 1 ^st and the 4 ^th ring modulators are placed 600 um apart, and it is found that the difference of their power consumption is up to ±5.9 mW. These results are good references for transceiver designers to implement smart tuning algorithm for aligning ring modulators'/filters' operating wavelengths with optical carriers’ wavelengths. For example, designers can start by tuning the first ring modulator, then with this tuning power found, and given the correlation of the tuning power between the first two ring modulators, the tuning power of the second ring modulator can be well estimated than chosen randomly, e.g., in a small tuning range of ±2.2 mW that is centered at the tuning power of the first ring modulator.

Extinction ratio yield analysis

Yield estimation is based on the ER of the four WDM channels, where the minimum acceptance is set to 2.7 dB. Running the analysis script step4_analyze_transceiver_Monte_Carlo_results.lsf prints the measured yield in INTERCONNECT Script Prompt window.

Important model settings

Description of important objects and settings used in this model

CML

This example requires the GPIC Compact Model Library (CML) to be installed before running the example files. The CML file GPIC.cml is provided with this example. See Install Compact Model Library page for detailed instructions. The statistical variation of the models is defined in the .lib file GPIC.lib which is associated with the CML.

Correlation

In Monte Carlo analysis, parameters can be correlated or uncorrelated. The correlation coefficients of the statistical parameters can be specified directly in the Monte Carlo analysis edit dialog window, under the “Correlations” tab.

It is also possible to specify spatial correlations between the elements’ statistical parameters in the .lib file by placing the parameters in correlation groups. The correlation coefficient between the parameters is then determined by the coordinates of the elements and the correlation length of the parameters’ correlation group. The correlation lengths can be seen in the “Value” column of the “Correlations” tab in the Monte Carlo analysis edit dialog window. In this example, correlation groups include ‘corr_delta_width’, ‘corr_delta_height’, and ‘corr_delta_ridge_height’, which apply spatial correlations for rib waveguide width variations, rib waveguide thickness variations, and ridge waveguide thickness variations, respectively. Correlation lengths for these three groups are 3 mm, 10 mm, and 3 mm, respectively. The calculated correlation coefficients between statistical parameters can be visualized by the ‘Preview’ column. Please refer to the Monte Carlo analysis with spatial correlations page for more information.

In this example, positions of elements are determined by the physical layout and are imported to INTERCONNECT through netlist. User can also change elements’ coordinates by setting their ‘x coordinate’ and ‘y coordinate’, and this will accordingly change their spatial correlations.

Variant

The statistical variants for the statistical models are defined in the .lib file. There are three types of variant defined in the file, namely the "nominal" variant, the "corner" variant and the "statistical" variant. When the file is loaded to the MC or Corner analysis object, the variant properties defined in the .lib file will be automatically imported. The "nominal" option is for the nominal values; the "corner" option is for the corner values and these two options are for the Corner analysis. The "statistical" option is for the model statistical values and this option is for the MC analysis.

Automated tuning and alignment

In the transceiver simulation, the script that automatically tunes the bias voltage for ring modulators and filters is defined in the Root Element using “Setup script”.

Updating the model with your parameters

Instructions for updating the model based on your device parameters

For this time domain simulation, users can set the simulation parameters such as:

• Set the wavelengths for the four channels.
• Add more channels for higher transmission efficiency.
• Set the bit rate.

Taking the model further

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

Other modulation and filter schema

This example uses the ring modulator and ring filters to mux and demux the DWDM signal. Users can use other types of modulators such as the Mach-Zehnder modulator to do the modulation, and can use other formats of filters as well.

Additional resources

Additional documentation, examples and training material

See also

• Ring Modulator
• INTERCONNECT Ring Modulator Model

• Wavelength division multiplexing

• Monte Carlo analysis utility
• Monte Carlo analysis with spatial correlation
• ONA frequency/time domain measurements
• Lumerical Compact Model Library

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