![\"MIM\"](\"img/all_dielectric.png\")
\n",
"\n",
"You can find related content in [MIM resonator](https://www.flexcompute.com/tidy3d/examples/notebooks/MIMResonator/), [Dielectric metasurface absorber](https://www.flexcompute.com/tidy3d/examples/notebooks/DielectricMetasurfaceAbsorber/), and [CMOS RGB image sensor](https://www.flexcompute.com/tidy3d/examples/notebooks/CMOSRGBSensor/).\n",
"\n",
"If you are new to the finite-difference time-domain (FDTD) method, we highly recommend going through our [FDTD101](https://www.flexcompute.com/fdtd101/) tutorials. FDTD simulations can diverge due to various reasons. If you run into any simulation divergence issues, please follow the steps outlined in our [troubleshooting guide](https://www.flexcompute.com/tidy3d/examples/notebooks/DivergedFDTDSimulation/) to resolve it. \n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First we will include all the libraries needed to run the notebook and also include the `Design` plugin as `tdd`."
]
},
{
"cell_type": "code",
"execution_count": 1,
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"execution": {
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"source": [
"# Standard python imports.\n",
"import matplotlib.pylab as plt\n",
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"# Import regular tidy3d.\n",
"import tidy3d as td\n",
"import tidy3d.plugins.design as tdd\n",
"from scipy.signal import find_peaks"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulation Set Up\n",
"\n",
"The device geometry is comprised of a periodic pattern of dielectric multilayer stacks. Each unit cell consists of a 60 nm thick $SiO_{3}N_{4}$ layer, a 140 nm thick $TiO_{2}$ spacer layer, and a 100 nm thick $SiO_{2}$ capping layer. The thin film multilayer was built by successive material depositions into a silica substrate. Below, we will define the device geometric parameters."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"execution": {
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"outputs": [],
"source": [
"period = 0.35 # Unit cell period (um).\n",
"gap = 0.15 # Gap between adjacent unit cells (um).\n",
"sio2_thick = 0.10 # SiO2 dielectric thin film thickness (um).\n",
"tio2_thick = 0.14 # TiO2 dielectric thin film thickness (um).\n",
"si3n4_thick = 0.06 # Si3N4 dielectric thin film thickness (um).\n",
"sub_thick = 0.6 # SiO2 substrate thickness (um).\n",
"air_thick = 1.0 # Upper air layer thickness (um)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Material definition."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:33:50.717302Z",
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"source": [
"n_sio2 = 1.45 # SiO2 refractive index.\n",
"n_tio2 = 2.41 # TiO2 refractive index.\n",
"n_si3n4 = 2.00 # Si3N4 refractive index.\n",
"\n",
"mat_sio2 = td.Medium(permittivity=n_sio2**2) # SiO2.\n",
"mat_tio2 = td.Medium(permittivity=n_tio2**2) # TiO2.\n",
"mat_si3n4 = td.Medium(permittivity=n_si3n4**2) # Si3N4.\n",
"mat_air = td.Medium(permittivity=1) # Air."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we define the wavelength, frequencies, and other simulation parameters."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:33:50.721842Z",
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"source": [
"wl_min = 0.400 # Minimum simulation wavelength (um).\n",
"wl_max = 0.700 # Maximum simulation wavelength (um).\n",
"n_wl = 151 # Number of wavelength points within the simulation bandwidth.\n",
"wl_res = np.asarray([0.63, 0.52, 0.45]) # Resonance wavelengths of RGB pixels.\n",
"run_time = 2e-12 # Simulation run time (s).\n",
"\n",
"wl_c = (wl_min + wl_max) / 2 # Central simulation wavelength (um).\n",
"wl_range = np.linspace(wl_min, wl_max, n_wl) # Simulation wavelength range (um).\n",
"freq_c = td.C_0 / wl_c # Central simulation frequency (Hz).\n",
"freq_range = td.C_0 / wl_range # Simulation frequency range (Hz).\n",
"freq_bw = 0.5 * (freq_range[0] - freq_range[-1]) # Source bandwidth (Hz).\n",
"freq_res = td.C_0 / wl_res # Resonance frequencies (Hz).\n",
"\n",
"size_z = (\n",
" sub_thick + si3n4_thick + tio2_thick + sio2_thick + air_thick\n",
") # Simulation size in the z-direction (um)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The next function defines the device unit cell. Here, we will define the dielectric stack structure, a plane wave source, and include a flux monitor to calculate the reflectance. The function accepts the unit cell `period` as an input parameter and returns a `Simulation` object. We will use it later as a pre-processing function to run the parameter sweep."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:33:50.727233Z",
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"source": [
"def build_sim(period: float = period) -> td.Simulation:\n",
" \"\"\"Builds the device simulation and returns a simulation object.\n",
" Parameters:\n",
" period: float\n",
" Device unit cell period (um).\n",
" Returns:\n",
" sim: tidy3d.Simulation\n",
" FDTD simulation object.\n",
" \"\"\"\n",
"\n",
" _inf = 10\n",
"\n",
" # Dielectric stack width (um).\n",
" width = period - gap\n",
"\n",
" # Simulation size.\n",
" size_x = period\n",
" size_y = period\n",
"\n",
" # Substrate.\n",
" substrate = td.Structure(\n",
" geometry=td.Box.from_bounds(\n",
" rmin=(-_inf, -_inf, -_inf), rmax=(_inf, _inf, -size_z / 2 + sub_thick)\n",
" ),\n",
" medium=mat_sio2,\n",
" )\n",
"\n",
" # Si3N4 layer.\n",
" si3n4_layer = td.Structure(\n",
" geometry=td.Box.from_bounds(\n",
" rmin=(-width / 2, -width / 2, -size_z / 2 + sub_thick),\n",
" rmax=(width / 2, width / 2, -size_z / 2 + sub_thick + si3n4_thick),\n",
" ),\n",
" medium=mat_si3n4,\n",
" )\n",
"\n",
" # TiO2 layer.\n",
" tio2_layer = td.Structure(\n",
" geometry=td.Box.from_bounds(\n",
" rmin=(-width / 2, -width / 2, -size_z / 2 + sub_thick + si3n4_thick),\n",
" rmax=(\n",
" width / 2,\n",
" width / 2,\n",
" -size_z / 2 + sub_thick + si3n4_thick + tio2_thick,\n",
" ),\n",
" ),\n",
" medium=mat_tio2,\n",
" )\n",
"\n",
" # SiO2 layer.\n",
" sio2_layer = td.Structure(\n",
" geometry=td.Box.from_bounds(\n",
" rmin=(\n",
" -width / 2,\n",
" -width / 2,\n",
" -size_z / 2 + sub_thick + si3n4_thick + tio2_thick,\n",
" ),\n",
" rmax=(\n",
" width / 2,\n",
" width / 2,\n",
" -size_z / 2 + sub_thick + si3n4_thick + tio2_thick + sio2_thick,\n",
" ),\n",
" ),\n",
" medium=mat_sio2,\n",
" )\n",
"\n",
" # Plane wave excitation source.\n",
" plane_wave = td.PlaneWave(\n",
" source_time=td.GaussianPulse(freq0=freq_c, fwidth=freq_bw),\n",
" size=(td.inf, td.inf, 0),\n",
" center=(0, 0, size_z / 2 - wl_c / 2),\n",
" direction=\"-\",\n",
" pol_angle=0,\n",
" angle_theta=0,\n",
" )\n",
"\n",
" # Flux monitor to measure the reflectance.\n",
" ref_monitor = td.FluxMonitor(\n",
" center=(0, 0, size_z / 2 - wl_c / 4),\n",
" size=(td.inf, td.inf, 0),\n",
" freqs=freq_range,\n",
" name=\"R\",\n",
" )\n",
"\n",
" # Simulation\n",
" sim = td.Simulation(\n",
" size=(size_x, size_y, size_z),\n",
" center=(0, 0, 0),\n",
" grid_spec=td.GridSpec.auto(min_steps_per_wvl=40, wavelength=(wl_min + wl_max) / 2),\n",
" structures=[substrate, si3n4_layer, tio2_layer, sio2_layer],\n",
" sources=[plane_wave],\n",
" monitors=[ref_monitor],\n",
" run_time=run_time,\n",
" boundary_spec=td.BoundarySpec(\n",
" x=td.Boundary.periodic(), y=td.Boundary.periodic(), z=td.Boundary.pml()\n",
" ),\n",
" symmetry=(-1, 1, 0),\n",
" medium=mat_air,\n",
" )\n",
" return sim"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Before running any simulation, we will visually inspect the simulation setup."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"execution": {
"iopub.execute_input": "2025-05-15T10:33:50.735034Z",
"iopub.status.busy": "2025-05-15T10:33:50.734752Z",
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{
"data": {
"text/html": [
"\n",
" \n",
" \n",
" "
],
"text/plain": [
"18:55:58 CEST Running 11 Simulations \n", "\n" ], "text/plain": [ "\u001b[2;36m18:55:58 CEST\u001b[0m\u001b[2;36m \u001b[0mRunning \u001b[1;36m11\u001b[0m Simulations \n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "results = design_space.run(fn=build_sim, fn_post=fn_post, verbose=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Design Results\n", "\n", "To analyze the design results we will create a `dataframe` using the `to_dataframe()` method. This dataframe shows the sweep parameter `period` as well as the post-processing function results. As one can see, we can return single values like `Peak Reflectance` and `Peak Wavelength`, or higher dimensional datasets such as `FluxMonitor` dataset included in the `Reflectance` column." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2025-05-15T10:34:39.122198Z", "iopub.status.busy": "2025-05-15T10:34:39.122083Z", "iopub.status.idle": "2025-05-15T10:34:39.143538Z", "shell.execute_reply": "2025-05-15T10:34:39.143295Z" } }, "outputs": [ { "data": { "text/html": [ "
| \n", " | period | \n", "Reflectance | \n", "Peak Reflectance | \n", "Peak Wavelength | \n", "
|---|---|---|---|---|
| 0 | \n", "0.30 | \n", "attrs={} type='FluxData' monitor=FluxMonitor(a... | \n", "1.000444 | \n", "0.444 | \n", "
| 1 | \n", "0.31 | \n", "attrs={} type='FluxData' monitor=FluxMonitor(a... | \n", "0.999349 | \n", "0.464 | \n", "
| 2 | \n", "0.32 | \n", "attrs={} type='FluxData' monitor=FluxMonitor(a... | \n", "0.995011 | \n", "0.482 | \n", "
| 3 | \n", "0.33 | \n", "attrs={} type='FluxData' monitor=FluxMonitor(a... | \n", "1.000225 | \n", "0.502 | \n", "
| 4 | \n", "0.34 | \n", "attrs={} type='FluxData' monitor=FluxMonitor(a... | \n", "0.999426 | \n", "0.520 | \n", "
| 5 | \n", "0.35 | \n", "attrs={} type='FluxData' monitor=FluxMonitor(a... | \n", "0.998759 | \n", "0.538 | \n", "
| 6 | \n", "0.36 | \n", "attrs={} type='FluxData' monitor=FluxMonitor(a... | \n", "0.996279 | \n", "0.556 | \n", "
| 7 | \n", "0.37 | \n", "attrs={} type='FluxData' monitor=FluxMonitor(a... | \n", "0.998858 | \n", "0.572 | \n", "
| 8 | \n", "0.38 | \n", "attrs={} type='FluxData' monitor=FluxMonitor(a... | \n", "0.995181 | \n", "0.588 | \n", "
| 9 | \n", "0.39 | \n", "attrs={} type='FluxData' monitor=FluxMonitor(a... | \n", "0.996786 | \n", "0.606 | \n", "
| 10 | \n", "0.40 | \n", "attrs={} type='FluxData' monitor=FluxMonitor(a... | \n", "0.998408 | \n", "0.622 | \n", "
| \n", " | 0.3 | \n", "0.31 | \n", "0.32 | \n", "0.33 | \n", "0.34 | \n", "0.35 | \n", "0.36 | \n", "0.37 | \n", "0.38 | \n", "0.39 | \n", "0.4 | \n", "
|---|---|---|---|---|---|---|---|---|---|---|---|
| Wavelength | \n", "\n", " | \n", " | \n", " | \n", " | \n", " | \n", " | \n", " | \n", " | \n", " | \n", " | \n", " |
| 0.400 | \n", "0.025456 | \n", "0.009510 | \n", "0.004938 | \n", "0.005282 | \n", "0.004005 | \n", "0.003507 | \n", "0.004259 | \n", "0.005932 | \n", "0.008572 | \n", "0.113618 | \n", "0.013770 | \n", "
| 0.402 | \n", "0.027709 | \n", "0.010223 | \n", "0.004895 | \n", "0.005223 | \n", "0.004197 | \n", "0.003309 | \n", "0.003622 | \n", "0.004812 | \n", "0.006518 | \n", "0.351169 | \n", "0.009320 | \n", "
| 0.404 | \n", "0.030227 | \n", "0.010899 | \n", "0.004978 | \n", "0.005099 | \n", "0.004489 | \n", "0.003276 | \n", "0.003190 | \n", "0.003936 | \n", "0.005147 | \n", "0.210617 | \n", "0.012160 | \n", "
| 0.406 | \n", "0.033060 | \n", "0.011776 | \n", "0.005201 | \n", "0.004925 | \n", "0.004768 | \n", "0.003431 | \n", "0.002945 | \n", "0.003295 | \n", "0.004023 | \n", "0.047286 | \n", "0.016562 | \n", "
| 0.408 | \n", "0.036279 | \n", "0.012768 | \n", "0.005291 | \n", "0.004728 | \n", "0.005067 | \n", "0.003669 | \n", "0.002865 | \n", "0.002836 | \n", "0.003128 | \n", "0.014790 | \n", "0.025667 | \n", "