--- title: RF Electrode in a Microring Modulator jupyter: python3 ---
The microring resonator (MRR) is a key component in modern photonics design. In this notebook, we model the RF electrode in a silicon-on-insulator MRR, which carries the electrical signal responsible for optical modulation. In a full fidelity model, the MRR would require multiphysics coupling of thermal, charge, optical, and RF simulations. For this RF-only demonstration, we will approximate the reverse bias p-n junction, responsible for the optical phase modulation, with a lumped RC element. The focus will be on minimizing return loss within the operational bandwidth. ```{python} import gdstk import matplotlib.pyplot as plt import numpy as np import flex_rf.tidy3d as rf import flex_rf.web as web rf.config.logging.level = 'ERROR' ``` ## Building the Model ### Key Parameters and Materials The bandwidth of the simulation is 10-100 GHz. ```{python} # Frequency bandwidth f_min, f_max = (10e9, 100e9) f0 = (f_max + f_min) / 2 freqs = np.linspace(f_min, f_max, 101) # Dimensions len_inf = 1e5 bounds_electrode = (2.62, 3.02) bounds_oxide = (-3.017, 2.62) bounds_sub = (-len_inf, -3.017) TM = bounds_electrode[1] - bounds_electrode[0] # electrode thickness ``` The equivalent RC parameters of the reverse bias p-n junction can be estimated using a lumped circuit model. Details of the calculation are presented in section 2.2.3 of Ref [1]. ```{python} # Lumped electrical parameters C_lumped = 17.325e-15 # Farads R_lumped = 113.12 # Ohms Zref = 50 # Ohms, port reference impedance ``` The relevant materials are defined below. ```{python} # Mediums med_sub = rf.Medium(permittivity=12.3) # Si substrate med_oxide = rf.Medium(permittivity=4.2) # SiO2 med_metal = rf.LossyMetalMedium(conductivity=17, frequency_range=(f_min, f_max)) # Metal [S/um] ``` ### Geometry In lieu of building the electrode geometry from scratch, we will import a pre-constructed 2D shape from GDS. It is then extruded to the appropriate thickness. ```{python} # Load GDS and build metal electrode geometry gds_mrr = gdstk.read_gds("misc/mrr-electrode.gds") g_electrode = rf.Geometry.from_gds( gds_mrr["MRR"], gds_layer=12, gds_dtype=0, slab_bounds=bounds_electrode, axis=2 ) # Dielectric layers g_oxide = rf.Box.from_bounds( rmin=(-len_inf, -len_inf, bounds_oxide[0]), rmax=(len_inf, len_inf, bounds_oxide[1]) ) g_sub = rf.Box.from_bounds( rmin=(-len_inf, -len_inf, bounds_sub[0]), rmax=(len_inf, len_inf, bounds_sub[1]) ) ``` The geometries are combined with the corresponding mediums into `Structure` instances below. ```{python} # Structures str_sub = rf.Structure(geometry=g_sub, medium=med_sub) str_oxide = rf.Structure(geometry=g_oxide, medium=med_oxide) str_electrode = rf.Structure(geometry=g_electrode, medium=med_metal) structure_list = [str_sub, str_oxide, str_electrode] ``` ### Grid and Boundary The external boundaries of the simulation are terminated with Perfectly Matched Layers (PMLs) by default. We add some space padding around the electrode, although we do not expect it to radiate significantly. ```{python} # Simulation center and size sim_X0, sim_Y0, sim_Z0 = (30, -30, 0) sim_LX, sim_LY, sim_LZ = (450, 300, 400) ``` The grid should be able to resolve key features in the electrode, such as the gap and corners, for accurate results. To this end, we use the `LayerRefinementSpec` feature to automatically analyze the electrode geometry and generate an appropriately fine mesh. For added fidelity, we also define a `MeshOverrideStructure` around the microring region that constrains maximum grid size in the in-plane directions. ```{python} # Layer refinement lr1 = rf.LayerRefinementSpec.from_structures( structures=[str_electrode], corner_refinement=rf.GridRefinement(dl=1, num_cells=2), min_steps_along_axis=1, ) # Mesh override refine_box = rf.MeshOverrideStructure( geometry=rf.Box.from_bounds( rmin=(16.5, 1, bounds_electrode[0]), rmax=(43.5, 27, bounds_electrode[1]) ), dl=(1, 1, None), ) ``` The overall grid specification is defined below. The rest of the simulation grid is automatically generated based on the shortest wavelength. ```{python} # Grid specification grid_spec = rf.GridSpec.auto( min_steps_per_wvl=15, wavelength=rf.C_0 / f_max, layer_refinement_specs=[lr1], override_structures=[refine_box], ) ``` ### Monitors We define a field monitor just below the electrode plane for visualization purposes. ```{python} # Field Monitor mon_1 = rf.FieldMonitor( center=(sim_X0, sim_Y0, bounds_electrode[0]), size=(len_inf, len_inf, 0), freqs=[f_min, f0, f_max], name="field in-plane", ) monitor_list = [mon_1] ``` ### Lumped Ports and Elements We will use lumped ports and elements in this model since the structure is extremely sub-wavelength. ```{python} # Lumped port LP1 = rf.LumpedPort( center=(30, -85, bounds_electrode[1]), size=(60, 10, 0), voltage_axis=1, name="LP1", impedance=Zref, ) ``` The equivalent RC circuit representing the p-n junction is defined below. ```{python} # Define equivalent RC series circuit resistor = rf.LumpedCircuitComponent(element_type='R', node_plus='0', node_minus='1', value=R_lumped) cap = rf.LumpedCircuitComponent(element_type='C', node_plus='1', node_minus='2', value=C_lumped) circuit = rf.CircuitImpedanceModel( components=[resistor, cap], port_node_plus='0', port_node_minus='2' ) ``` ```{python} # Define lumped element using the RC circuit LE1 = rf.LinearLumpedElement( center=(30, 24.795, bounds_electrode[1]), size=(2, 2.2, 0), voltage_axis=1, network=circuit, name="LumpedRC", ) ``` ### Simulation and TerminalComponentModeler The simulation and `TerminalComponentModeler` instances are defined below. ```{python} sim = rf.Simulation( center=(sim_X0, sim_Y0, sim_Z0), size=(sim_LX, sim_LY, sim_LZ), grid_spec=grid_spec, structures=structure_list, monitors=monitor_list, lumped_elements=[LE1], run_time=1e-10, ) tcm = rf.TerminalComponentModeler( simulation=sim, ports=[LP1], freqs=freqs, ) ``` ### Visualization Before running the simulation, let us visualize the geometry and grid. The lumped port (green) and lumped RC element (blue) are also depicted below. ```{python} # Metal electrode plane fig, ax = plt.subplots(1, 2, figsize=(10, 3), tight_layout=True) tcm.simulation.plot_grid(z=bounds_electrode[1], ax=ax[0]) tcm.plot_sim(z=bounds_electrode[1], ax=ax[0], monitor_alpha=0, hlim=(-150, 210), vlim=(-125, 50)) tcm.simulation.plot_grid(z=bounds_electrode[0], ax=ax[1]) tcm.plot_sim(z=bounds_electrode[1], ax=ax[1], monitor_alpha=0, hlim=(15, 45), vlim=(0, 30)) plt.show() ``` We can also use the 3D viewer. ```{python} sim.plot_3d() ``` ## Running the Simulation The simulation is executed below. ```{python} #| scrolled: true tcm_data = web.run(tcm, task_name="microring_electrode", path="data/microring_electrode.hdf5", verbose=False) ``` ## Results ### S-parameter We extract and plot S11 below. ```{python} # Extract S11 smat = tcm_data.smatrix() S11 = np.conjugate(smat.data.squeeze()) ``` The return loss (RL) is shown below. From the RL plot, we observe that the electrode has a -3 dB bandwidth of up to 55 GHz. ```{python} # Plot return loss fig, ax = plt.subplots(figsize=(10, 4), tight_layout=True) ax.plot(freqs / 1e9, 20 * np.log10(np.abs(S11))) ax.set_title("Return Loss (dB)") ax.set_ylabel("dB") ax.set_xlabel("f (GHz)") ax.grid() plt.show() ``` ### Field profile We extract the field monitor data and plot the in-plane field magnitude at the center frequency below. ```{python} # Extract monitor data sim_data = tcm_data.data["LP1"] # Plot field monitor data fig, ax = plt.subplots(figsize=(10, 5), tight_layout=True) f_plot = f0 sim_data.plot_field("field in-plane", field_name="E", val="abs", f=f_plot, ax=ax) ax.set_xlim(-150, 210) ax.set_ylim(-150, 80) plt.show() ``` ## Reference [1] Wang, Zhao. "Silicon micro-ring resonator modulator for inter/intra-data centre applications." PhD diss., 2017.