This example has been updated. Find the latest version at Travelling Wave Mach-Zehnder Modulator.

In this section, we will use MODE eigenmode analysis to extract the RF characteristics of the TWM. The project tw_modulator_RF.lms contains the setup for the coplanar transmission line, as described in Fig. 1 of ref. [1]. To model the material properties of the aluminum layers, a conductive material model is used. A conductive model is also used for the silicon substrate, with the resistivity set to 750 ohm-cm, corresponding to the value reported for the silicon wafer. The sheet resistance of the partially etched silicon is modeled with a 2D rectangle object and a "RLC" material model. The resistivity is set to 0.8 ohm-cm for both the n-type and p-type silicon, corresponding to a resistance of 1.6 ohm-cm for the TWM. The same RLC material model was used to model the junction capacitance, with C set to 0.20 fF/um, corresponding the junction capacitance for the PN junction (see Electrical Simulation) at V = 0.63.

For the solver region, the background index is set to 2 (silicon oxide permittivity at DC). PMC boundaries are used for the top and bottom simulation boundaries, and symmetry is applied in the x direction to reduce the simulation region by a factor of 2.

Open the Eigensolver Analysis window by clicking on the "Run" button, and calculate the modes. Here, a guess effective index of 3 is used to located the desired mode efficiently. For cases where the wavelength is much larger than the key feature sizes, it is important to make sure that the simulation region is large enough such that the E and H fields have decayed sufficiently at the edges of the simulation region. Plotting the E and H field profiles on a log scale is a good way to make sure that the simulation region is sufficiently large. For this example, the simulation spans have been set to 10000um. Note that the time it takes to calculate the mode is not affected by the simulation span since the number of grid cells used for the mode calculation does not change. The figures below shows the E field profile in linear and log scale.

The effective index and loss of this mode can be extracted from the mode list. For the TWM mode at 10 GHz we have a microwave index of 3.38+0.77i (13 dB/cm).

The characteristic impedance of the RF mode can be calculated using the equation Z0=P/(I*conj(I). P is the power carried by the mode which can be calculated by integrating the normal component of the Poynting vector over the area of the mode,

And I is the current carried by the strip which can be calculated by integrating the H fields around a loop around the conductor

The characteristic impedance calculated using this method is returned as a result of the FDE solver, with the current integral specified under the "Impedance" tab. For this example, the current integral is defined to be the right half of the simulation region, enclosing one of the conductors.

The script tw_modualtor_RF_sweep.lsf can be used to track the impedance as a function of frequency and generate the following plots: