Metal Grid Effect

This recipe demonstrates how the tungsten metal grid between color filter sub-pixels affects QE and optical crosstalk.

Background

The metal grid sits between adjacent color filter elements. It provides optical isolation by blocking light from entering neighboring pixels through the color filter layer. However, it also:

• Reduces the effective aperture (less light enters each pixel)
• Can cause diffraction effects at the grid edges
• Absorbs some light (tungsten is lossy)

This recipe runs two simulations -- with and without the metal grid -- and compares the results.

BSI Pixel Cross-Section Anatomy

Click on any layer to highlight it and view a detailed description below. An animated light ray traces the optical path.

Click on a layer in the diagram to learn about its role in the pixel stack.

Setup

import copy
from compass.runners.single_run import SingleRunner
from compass.analysis.solver_comparison import SolverComparison
from compass.visualization.qe_plot import plot_qe_comparison, plot_crosstalk_heatmap
import matplotlib.pyplot as plt

base_config = {
    "pixel": {
        "pitch": 1.0,
        "unit_cell": [2, 2],
        "bayer_map": [["R", "G"], ["G", "B"]],
        "layers": {
            "air": {"thickness": 1.0, "material": "air"},
            "microlens": {
                "enabled": True, "height": 0.6,
                "radius_x": 0.48, "radius_y": 0.48,
                "material": "polymer_n1p56",
                "profile": {"type": "superellipse", "n": 2.5, "alpha": 1.0},
                "shift": {"mode": "none"},
            },
            "planarization": {"thickness": 0.3, "material": "sio2"},
            "color_filter": {
                "thickness": 0.6,
                "pattern": "bayer_rggb",
                "materials": {"R": "cf_red", "G": "cf_green", "B": "cf_blue"},
                "grid": {"enabled": True, "width": 0.05, "material": "tungsten"},
            },
            "barl": {
                "layers": [
                    {"thickness": 0.010, "material": "sio2"},
                    {"thickness": 0.025, "material": "hfo2"},
                ]
            },
            "silicon": {
                "thickness": 3.0, "material": "silicon",
                "photodiode": {"position": [0, 0, 0.5], "size": [0.7, 0.7, 2.0]},
                "dti": {"enabled": True, "width": 0.1, "material": "sio2"},
            },
        },
    },
    "solver": {
        "name": "torcwa", "type": "rcwa",
        "params": {"fourier_order": [11, 11]},
        "stability": {"precision_strategy": "mixed", "fourier_factorization": "li_inverse"},
    },
    "source": {
        "wavelength": {"mode": "sweep", "sweep": {"start": 0.40, "stop": 0.70, "step": 0.01}},
        "polarization": "unpolarized",
    },
    "compute": {"backend": "auto"},
}

Run: with metal grid

config_with_grid = copy.deepcopy(base_config)
config_with_grid["pixel"]["layers"]["color_filter"]["grid"]["enabled"] = True

result_with = SingleRunner.run(config_with_grid)
print("With grid: done")

Run: without metal grid

config_no_grid = copy.deepcopy(base_config)
config_no_grid["pixel"]["layers"]["color_filter"]["grid"]["enabled"] = False

result_without = SingleRunner.run(config_no_grid)
print("Without grid: done")

Compare QE spectra

fig, ax = plt.subplots(figsize=(10, 6))
plot_qe_comparison(
    results=[result_with, result_without],
    labels=["With grid", "No grid"],
    ax=ax,
)
ax.set_title("Metal Grid Effect on QE")
plt.tight_layout()
plt.savefig("metal_grid_qe_comparison.png", dpi=150)
plt.show()

Quantify the difference

comparison = SolverComparison(
    results=[result_with, result_without],
    labels=["with_grid", "no_grid"],
    reference_idx=0,
)
summary = comparison.summary()

for key, val in summary["max_qe_diff"].items():
    print(f"{key}: max |dQE| = {val:.4f}")

Compare crosstalk

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 6))

plot_crosstalk_heatmap(result_with, ax=ax1)
ax1.set_title("Crosstalk: With Grid")

plot_crosstalk_heatmap(result_without, ax=ax2)
ax2.set_title("Crosstalk: No Grid")

plt.tight_layout()
plt.savefig("metal_grid_crosstalk.png", dpi=150)
plt.show()

Interactive Pixel Crosstalk Heatmap

Explore how wavelength and pixel pitch affect optical crosstalk between neighboring pixels. The center pixel is illuminated; surrounding pixels show crosstalk intensity.

Wavelength: 550 nm

Pixel pitch: 1.00 um

Show Bayer overlay

Absorption Depth (Si):1.56 um

Nearest-neighbor Crosstalk:3.8%

Total Crosstalk:55.2%

Expected observations

1. QE reduction with grid: The metal grid slightly reduces peak QE (typically 2-5%) because it blocks some light and absorbs energy.
2. Crosstalk improvement: The grid significantly reduces optical crosstalk between adjacent pixels, especially for off-axis illumination.
3. Wavelength dependence: The grid effect is stronger at shorter wavelengths where diffraction effects are more pronounced relative to the grid width.

Grid width sweep

Study how grid width affects the QE/crosstalk trade-off:

import numpy as np

grid_widths = [0.0, 0.03, 0.05, 0.08, 0.10]
results_vs_width = []

for width in grid_widths:
    cfg = copy.deepcopy(base_config)
    cfg["pixel"]["layers"]["color_filter"]["grid"]["enabled"] = width > 0
    cfg["pixel"]["layers"]["color_filter"]["grid"]["width"] = width
    r = SingleRunner.run(cfg)
    results_vs_width.append(r)
    print(f"Grid width {width*1000:.0f} nm: done")

# Plot
fig, ax = plt.subplots(figsize=(10, 6))
plot_qe_comparison(
    results=results_vs_width,
    labels=[f"w={w*1000:.0f}nm" for w in grid_widths],
    ax=ax,
)
ax.set_title("QE vs Metal Grid Width")
plt.tight_layout()
plt.savefig("grid_width_sweep.png", dpi=150)