Joint Simulation of Mach-Zehnder Electro-Optic Modulator Using Macondo and Nuwa TCAD Software

   Mach-Zehnder modulator (MZM) is an optoelectronic device that utilizes phase modulation to achieve intensity modulation. MZM splits the input optical wave into two equal beams using a beam splitter, propagates them through optical channels made of electro-optic materials, and controls their refractive indices by adjusting the externally applied electric field strength, thereby altering the phase of the optical waves. At the end of the optical channels, the two beams interfere with each other, modulating the intensity of the optical signal. With the advancement of optical interconnection and high-speed optical communication, carrier-depletion MZMs have gained significant attention due to their high modulation speed and low insertion loss. They are widely used in fiber optic communication, optical interconnects, and optical computing, playing a crucial role in data centers, 5G communication, and high-performance computing networks.

Figure 1. Schematic diagram of the carrier-depletion MZM device structure and phase shifter structure^[1]

  This study focuses on the core component of the traveling-wave Mach-Zehnder modulator (TW-MZM)—the traveling-wave phase shifter, analyzing its internal working principles in depth. Figure 1 illustrates the structure of a carrier-depletion MZM and its phase shifter. Through optoelectronic co-simulation, the process of applying a reverse bias voltage to a PN junction to change the depletion region's carrier concentration, thereby altering the waveguide refractive index and precisely controlling the optical phase, is simulated.

1. Co-simulation process for the electro-optic modulator

   This section introduces the simulation steps for the electro-optic modulator. Figure 2 illustrates the co-simulation workflow for the MZM. First, Nuwa TCAD software is used to simulate the electrical characteristics of the semiconductor device under different bias voltages, obtaining the carrier distribution. The results are then imported into Macondo software for photonic simulations, calculating the effective refractive index under different voltage conditions. By processing the effective refractive index difference, key MZM parameters such as phase shift and modulation efficiency are obtained.

Figure 2. Co-simulation workflow for the electro-optic modulator

2. Device structure and doping distribution

   The cross-sectional structure of the traveling-wave phase shifter in the TW-MZM device is shown in Figure 3. Aluminum (Al) electrodes are placed on both sides of the ridge waveguide, and the silicon (Si) waveguide adopts a Gaussian doping profile. The device structure used in this simulation is referenced from literature [2].

Figure 3. Cross-sectional structure of the traveling-wave phase shifter in TW-MZM

  Table 1 lists the structural and material parameters of the MZM device.

Table 1. Structural and material parameters of the MZM device

  The relationship between carrier concentration and the refractive index of Si material at a wavelength of 1550 nm is based on 2011 experimental data fitted to the following equations:

$$\mathrm{\Delta }n(\text{ at }1550\mathrm{n}\mathrm{m})=-5.4\times 10^{-22}\mathrm{\Delta }{N}^{1.011}-1.53\times 10^{-18}\mathrm{\Delta }{P}^{0.838}\backslash Delta\; n(\backslash text\; \{\; at\; \}\; 1550\; \backslash mathrm\{~nm\})=-5.4\; \backslash times\; 10^\{-22\}\; \backslash Delta\; N^\{1.011\}-1.53\; \backslash times\; 10^\{-18\}\; \backslash Delta\; P^\{0.838\}$$

$$\mathrm{\Delta }\alpha (\text{ at }1550\mathrm{n}\mathrm{m})=8.88\times 10^{-21}\mathrm{\Delta }{N}^{1.167}+5.84\times 10^{-20}\mathrm{\Delta }{P}^{1.109}\backslash Delta\; \backslash alpha(\backslash text\; \{\; at\; \}\; 1550\; \backslash mathrm\{~nm\})=8.88\; \backslash times\; 10^\{-21\}\; \backslash Delta\; N^\{1.167\}+5.84\; \backslash times\; 10^\{-20\}\; \backslash Delta\; P^\{1.109\}$$

  Table 2 records the doping distribution of the MZM device.

Table 2. Doping distribution of the MZM device

  The device structure and net doping distribution modeled in Nuwa TCAD is shown in Figure 4.

Figure 4. Device structure and doping distribution modeled in Nuwa TCAD

3. Key metrics of MZM

3.1 Phase shift

The phase shift (Δφ) refers to the change in the optical signal phase relative to the unmodulated state during modulation. Phase shift affects optical transmission characteristics, leading to variations in signal delay.

The phase shift in an MZM modulator when an external modulation is applied is given by:

$$\mathrm{\Delta }\varphi =\mathrm{\Delta }\beta \cdot L\backslash Delta\; \backslash phi\; =\; \backslash Delta\; \backslash beta\; \backslash cdot\; L$$

where L is the modulation arm length and Δβ is the propagation constant:

$$\mathrm{\Delta }\beta =k_0\cdot \mathrm{\Delta }{n}_{\text{eff }}=\frac{2\pi \mathrm{\Delta }{n}_{\text{eff }}}{\lambda }\backslash Delta\; \backslash beta\; =\; k\_\{0\}\; \backslash cdot\; \backslash Delta\; n\_\{\backslash text\; \{eff\; \}\}\; =\; \backslash frac\{2\; \backslash pi\; \backslash Delta\; n\_\{\backslash text\; \{eff\; \}\}\}\{\backslash lambda\}$$

where k₀ is the phase constant.

Thus, the phase shift induced by external voltage modulation in the MZM structure is:

$$\mathrm{\Delta }\varphi =\frac{2\pi \mathrm{\Delta }{n}_{\text{eff }}\cdot L}{\lambda }\backslash Delta\; \backslash phi\; =\; \backslash frac\{2\; \backslash pi\; \backslash Delta\; n\_\{\backslash text\; \{eff\; \}\}\backslash cdot\; L\}\{\backslash lambda\}$$

3.2 Modulation efficiency

$V_{\pi }LV\_\{\backslash pi\}\; L$ is an important metric for evaluating the modulation efficiency of an MZM. A smaller $V_{\pi }LV\_\{\backslash pi\}\; L$ indicates higher modulation efficiency.

Half-wave voltage ($V_{\pi }V\_\{\backslash pi\}$) refers to the voltage applied to the modulator that results in a phase change of $\pi \{\backslash pi\}$. A lower half-wave voltage indicates higher electro-optic modulation efficiency.

The modulation efficiency metric is obtained by calculating the difference in effective refractive index:

$$\begin{array}{cccc}& {\displaystyle \mathrm{\Delta }\varphi =\frac{2\pi \mathrm{\Delta }{n}_{eff}L}{{\lambda }_0}\to \mathrm{\Delta }{n}_{eff}\left(V_{\pi }\right)=\frac{{\lambda }_0}{2L_{\pi }}}& & \end{array}\backslash begin\{equation\}\; \backslash Delta\; \backslash phi=\backslash frac\{\; 2\; \backslash pi\backslash Delta\; n\_\{e\; f\; f\}\; L\}\{\backslash lambda\_\{0\}\}\; \backslash rightarrow\; \backslash Delta\; n\_\{e\; f\; f\}\backslash left(V\_\{\{\backslash pi\}\}\backslash right)=\backslash frac\{\backslash lambda\_\{0\}\}\{2\; L\_\{\backslash pi\}\}\; \backslash end\{equation\}$$

3.3 Optical loss

Optical loss refers to the loss of optical power during signal transmission in the modulator. Lower optical loss indicates higher signal transmission efficiency.

$$\begin{array}{cccc}& {\displaystyle loss=-20{\log }_{10}(e^{-2\pi \kappa \mathrm{/}{\lambda }_0})}& & \end{array}\backslash begin\{equation\}\; loss=-20\backslash log\_\{10\}(e^\{-2\backslash pi\; \backslash kappa\; /\backslash lambda\; \_0\}\; )\; \backslash end\{equation\}$$

In practical applications, the optical loss of an MZM is also influenced by various other factors, such as device design, material properties, operating temperature, and the polarization state of the optical signal. This formula provides a theoretical reference for calculating the optical loss of an MZM device, but further validation and adjustments are required in real-world applications.

4. Results of optoelectronic co-simulation

  First, Nuwa TCAD software is used to simulate the carrier distribution characteristics under different cathode voltages ranging from -0.5V to 4V. The corresponding electron and hole concentration distributions at different operating voltages are obtained, as shown in Figure 5.

Figure 5. Electron concentration distribution under different voltages

  Next, the carrier distribution data for different voltages is imported into Macondo. Using the grid mapping function in Macondo software, the structured mesh carrier distribution from the TCAD solver is associated with the refractive index perturbation of the structured mesh, obtaining the effective refractive index and waveguide propagation loss after carrier-induced refractive index changes.

Figure 6. Unstructured mesh and Yee grid mapping for calculating the effective refractive index of a 1550nm ridge waveguide

  Finally, using the equations provided in Section 3 on MZM key metrics, the phase shift $\varphi \backslash phi$, modulation efficiency $V_{\pi }LV\_\{\backslash pi\}L$, and waveguide propagation loss $LossLoss$ under different voltages are computed. The results are shown in Figures 7 and 8.

Figure 7. Computed phase shift and modulation efficiency characteristics

Figure 8. Computed waveguide propagation loss characteristics

5. Conclusion

  This study focuses on the optoelectronic co-simulation of the traveling-wave phase shifter in TW-MZM using Nuwa TCAD and Macondo software. By analyzing the refractive index variations induced by carrier distribution across the waveguide cross-section under different voltages, the phase shift $\varphi \backslash phi$, modulation efficiency $V_{\pi }LV\_\{\backslash pi\}L$, and waveguide propagation loss $lossloss$ of the traveling-wave phase shifter were computed.

  This study presents a standard co-simulation case for a modulator type. The co-simulation methodology outlined in this study can be referenced to simulate and optimize other modulators, including electro-optic, thermo-optic, and acousto-optic modulators. In future work, a link simulation tool will be integrated to simulate the transmission spectrum and eye diagram of the TW-MZM.

References

[1] Rosa, María Félix, et al. "Design of a carrier-depletion Mach-Zehnder modulator in 250 nm silicon-on-insulator technology." Advances in Radio Science: ARS 15 (2017): 269.
[2] Baehr-Jones, Tom, et al. "Ultralow drive voltage silicon traveling-wave modulator." Optics express 20.11 (2012): 12014-12020.
[3] Nedeljkovic, M, Soref. "Free-Carrier Electrorefraction and Electroabsorption Modulation Predictions for Silicon Over the 1–14 μm Infrared Wavelength Range." IEEE Photonics Journal, 2011.