Image Sensor Optics

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This page describes the optical structure of a backside-illuminated (BSI) CMOS image sensor pixel, which is the primary simulation target of COMPASS.

BSI pixel architecture

In a BSI pixel, light enters through the silicon backside (opposite to the wiring side). The pixel stack, from top (light-entry side) to bottom, consists of:

              Incident light
                   |
                   v
    +---------------------------------+
    |             Air                  |
    +---------------------------------+
    |          Microlens               |   Focuses light into pixel center
    +---------------------------------+
    |       Planarization (SiO2)       |   Uniform dielectric
    +---------------------------------+
    |  Color Filter (Bayer pattern)    |   Wavelength-selective absorption
    |  + Metal Grid (W)               |   Optical isolation between pixels
    +---------------------------------+
    |   BARL (anti-reflection stack)   |   Minimizes reflection at CF/Si
    +---------------------------------+
    |         Silicon                  |   Absorbs photons, generates e-h pairs
    |   [Photodiode regions]           |   Collects charge
    |   [DTI trenches]                 |   Prevents optical/electrical crosstalk
    +---------------------------------+

Interactive BSI Pixel Stack Cross-Section

Click on any layer to view its material properties and role in the pixel stack.

Click a layer in the stack diagram to see its properties.

Microlens

The microlens is a curved polymer structure that focuses incoming light toward the center of the pixel. In COMPASS, microlenses are modeled as superellipse profiles:

$$h(x,y)=H{(1-{\left|\frac{x-c_x}{r_x}\right|}^n-{\left|\frac{y-c_y}{r_y}\right|}^n)}^{1/\alpha }$$

Parameters:

• $H$: lens height (typical: 0.4-0.8 um)
• $r_x,r_y$: semi-axes (typical: slightly less than half the pitch)
• $n$: squareness parameter (2.0 = ellipse, higher = more square)
• $\alpha$: curvature control

The microlens center can be shifted to account for the Chief Ray Angle (CRA) -- the angle at which light arrives from the camera lens. Pixels at the edge of the image sensor receive light at a larger CRA, so their microlenses must be shifted to maintain good light collection.

Color filter array

The color filter array (CFA) selectively absorbs light to create color sensitivity. The most common pattern is the Bayer RGGB arrangement:

  +---+---+
  | R | G |
  +---+---+
  | G | B |
  +---+---+

Each color filter material has a wavelength-dependent complex refractive index with absorption ($k>0$) outside its passband and low absorption within the passband. The filters absorb unwanted wavelengths while transmitting the target color.

Interactive Bayer Pattern Viewer

Explore different color filter array (CFA) patterns. Click a pixel to see its details.

Pattern:RGGB (standard Bayer)GRBGBGGRGBRGQuad-Bayer (2x2 OCL)

Pattern

RGGB

Unit Cell Size

2x2

Green Ratio

50%

Description

Most common Bayer pattern. Two green pixels per unit cell provide higher luminance resolution, mimicking human vision sensitivity.

The metal grid between color filter sub-pixels (typically tungsten, 40-80 nm wide) provides optical isolation, preventing light from leaking between adjacent color channels.

BARL: Bottom Anti-Reflection Layer

The BARL is a thin multi-layer dielectric stack at the interface between the color filter and silicon. Its purpose is to minimize reflection at this high-contrast interface.

Without BARL, the reflection at a color-filter/silicon interface ($n\approx 1.55$ to $n\approx 4.0$) is:

$$R={\left(\frac{n_{\text{Si}}-n_{\text{CF}}}{n_{\text{Si}}+n_{\text{CF}}}\right)}^2\approx 20\mathrm{\%}$$

A well-designed BARL stack (e.g., SiO2/HfO2/Si3N4) can reduce this to under 5% across the visible spectrum.

Silicon and photodiode

Silicon is the absorbing medium where photon-to-electron conversion occurs. The absorption depth depends strongly on wavelength:

Wavelength	Color	Absorption depth in Si
400 nm	Violet	~0.1 um
450 nm	Blue	~0.4 um
550 nm	Green	~1.7 um
650 nm	Red	~3.3 um
800 nm	NIR	~10 um

This means blue light is absorbed near the surface while red/NIR light requires several micrometers of silicon. Typical BSI pixel silicon thickness is 2-4 um.

The photodiode occupies a defined region within the silicon. Only photons absorbed within the photodiode volume contribute to the photocurrent. COMPASS models this by integrating the absorbed power within the photodiode bounding box.

Deep Trench Isolation (DTI)

DTI is a vertical trench filled with a low-index material (typically SiO2, $n\approx 1.46$) that optically isolates adjacent pixels within the silicon. The large index contrast between silicon ($n\approx 3.5-4.0$) and SiO2 causes total internal reflection at the trench walls, preventing light from crossing into neighboring pixels.

DTI is critical for:

• Reducing optical crosstalk
• Improving color fidelity
• Maintaining MTF (modulation transfer function)

Optical phenomena in BSI pixels

Effect	Mechanism	Impact on QE
Thin-film interference	Multi-beam interference in BARL/planarization	Spectral ripple
Diffraction	Sub-wavelength metal grid	Angle-dependent light redistribution
Waveguide modes	DTI creates a silicon waveguide	Traps light, can enhance or degrade QE
Microlens focusing	Refraction	Concentrates light in pixel center
Optical crosstalk	Light leaking to adjacent pixels	Reduces color accuracy
Total internal reflection	High-index Si / low-index surroundings	Traps light, increases effective path length

All of these effects are captured automatically by the full-wave EM solvers (RCWA, FDTD) in COMPASS.