In this example, we will study the performance of a PIN Mach-Zehnder modulator using CHARGE (electrical simulation) and MODE (optical simulation).
The PIN MZ creates a change in refractive index by injecting charge into a quasi-intrinsic (lightly doped) region in the waveguide. A PIN junction is formed by doping the arms of the slab adjacent to the waveguide. N-type (donor) dopants are applied to one side of the device, and p-type (acceptor) dopants to the other, giving rise the built-in potential of the junction. A cross section of the doping profile is shown in the figure below. Open the file pin_mz.ldev and run it. After the simulation is run, type the following line of script into the script prompt to run the plotDopingProfile.lsf script file and generate the following figure:
Strongly doped implants are formed beneath the contacts (x < -3.6um and x > 3.6um) to form an ohmic contact interface.
1D doping profile of the p-i-n structure
You can then, visualize the carrier distribution, by right clicking on the "CHARGE" object, selecting "visualize" and then clicking "charge". The carrier distribution in the silicon illustrates the charge response to the applied bias. The PIN MZ operates in a forward bias mode, where the amount of charge transported (and consequently, the current) increase exponentially with the applied voltage. Note that in the plots shown below, the axes have been scaled to make the plots square. This can be done from the chart settings option of the visualizer.
V = 0 V
V = 0.5 V
V = 1 V
Simulation Setup and Analysis
IV Response and Carrier Extraction with CHARGE
Using the thin-film model for the silicon, the IV response can be calculated. Open the pin_mz.ldev project. To view the material properties, expand the Materials group and select the “Si (Silicon) thin film” material charge transport properties. This material is used for the waveguide rib and thin-film silicon slab. The carrier lifetime has been reduced, and a surface recombination model is applied between the silicon and the surrounding oxide. The file is set up to apply a voltage sweep from 0.5 V to 1.2 V in 21 steps. After running the simulation, the current response can be plotted by choosing "Visualize anode" from the CHARGE object context menu.
The charge monitor (monitor_wg) is set up so that it will automatically save the n and p distributions into "pin_charge.mat" file to be exported to MODE later.
Effective Index Simulation with MODE
Open the pin_mz.lms file in MODE. An np density grid attribute object in MODE (np) 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. The "np" object in the project file is already loaded with charge data from CHARGE. Alternatively the new data from "pin_charge.mat" can be loaded into the "np" object from its property editor.
Next the eigenmode solver can be run to calculate the optical mode at different voltages. To sweep the range of applied bias voltages, a parameter sweep is used. Choose the parameter sweep "voltage" and click Run. (Please note that the sweep will take a while to sweep over all 21 bias points). The results of the parameter sweep can be plotted using the voltageMODEsweep_mzi.lsf script file provided. Open and run this script file. The following plots should be generated from the script. The figure on the left shows the change in effective index of the optical mode with respect to applied bias and the figure on the right plots the propagation loss [dB/cm] in the waveguide due to material absorption as a function of bias voltage.
Change in refractive index versus bias voltage
Loss versus bias voltage
In addition, the modulation response is calculated by assuming a modulation length of 700 micron for demonstration purpose.
Transmission versus bias voltage
Based on this calculation, it is straightforward to determine the key modulation parameters (note that more accurate values can be determined by including more bias voltages in the analysis).
For more details on the modulation response calculation, please visit the section on Modulation Response.
Effect of Joule Heating on Modulator Performance
The p-i-n Mach-Zehnder modulator is operated in forward bias mode. At an operating voltage of more than 1 V, a significant amount of current will flow through the device which will contribute to Joule heating. The heating will increase the temperature of the waveguide which will increase the effective index of the optical mode. This will work against the index modulation due to charge injection and the performance of the modulator will be degraded. To properly model the performance of the modulator, a self-consistent electro-thermal simulation is necessary. This can be easily done in the CHARGE solver by using the "coupled" mode. In the "coupled" mode, the CHARGE solver couples internally with the HEAT solver and performs a self-consistent eletro-thermal simulation. In the following portion of this example, we will look into the effect of Joule heating on the p-i-n modulator performance.
Open the pin_mz.ldev project file in CHARGE. Open the property editor for the CHARGE solver object and select the "coupled" option for the "temperature dependence." Enable the temperature monitor to capture the temperature profile of the waveguide. The monitor is set up to save the temperature data in "pin_temp.mat" file. Run the simulation to save the charge and temperature profiles in .mat files. The current can be viewed from the solver region as discussed earlier. In the figure below (top), the current from the isothermal simulation is plotted as well for reference. It can be seen that the change in current is very small. However, the temperature plot from the monitor below (bottom) shows that the temperature in the waveguide rises by almost 2 K at a bias voltage of 1.2 V.
Current from electro-thermal simulation
Temperature profile of the pin modulator
Open the pin_mz.lms file in MODE. Load the new charge data from "pin_charge.mat" file into the "np" object. Next enable the temperature grid attribute (temperature) and load the temperature data from the "pin_temp.mat" file. Run the "voltage" sweep again. Once the sweep is run, use the voltageMODEsweep_mzi.lsf script file to plot the modulator optical properties again. In the following plots, the previous plots without Joule heating are superimposed on the new plots for comparison.
Effective index versus bias voltage with Joule heating
Loss versus bias voltage with Joule heating
Transmission versus bias voltage with Joule heating
The plot on the left shows that as expected, the effect of the rise in temperature reduces the variation in effective index with applied bias. The plot in the middle shows that the loss in the modulation remains almost the same as the loss in the waveguide is not affected by the small change in temperature (in fact the material model we used for silicon did not have any variation to the imaginary part of the refractive index due to temperature. Only variations in the real part of the index was modeled). Finally the plot on the right shows that the value of V_pi changes by almost 0.1 V due to the affect of Joule heating. The extinction ration and insertion loss remains unaffected by Joule heating.