Pixel Stack Configuration

The pixel structure is the central input to any COMPASS simulation. It is defined in a YAML file under the pixel: key and describes a Back-Side Illuminated (BSI) CMOS image sensor pixel as a vertical stack of optical layers. This page documents every parameter with its type, default value, and physical meaning.

Interactive Pixel Stack Builder

Adjust the thickness of each layer in a BSI pixel cross-section. The visualization shows the vertical stack with refractive indices and a scale bar.

Microlens height: 0.60 um

Planarization: 0.30 um

Color filter: 0.60 um

BARL total: 0.080 um

Silicon: 3.0 um

Show DTI trenches

Show metal grid

Total stack height:4.58 um

Coordinate system

COMPASS uses a right-handed coordinate system where light propagates downward through the stack.

Key conventions:

• All lengths are in micrometers (um)
• x, y: lateral (in-plane) directions
• z: vertical stack direction. Silicon sits at the bottom ($z_{\text{min}}$), air at the top ($z_{\text{max}}$)
• Light propagates in -z (from air toward silicon), consistent with BSI illumination
• The origin of the x-y plane is at the lower-left corner of the unit cell
• The position and size for photodiodes are relative to each pixel center

Top-level pixel parameters

pixel:
  pitch: 1.0          # Pixel pitch in um (both x and y)
  unit_cell: [2, 2]   # Number of pixels [rows, cols] in the unit cell
  bayer_map:           # Color channel assignment per pixel
    - ["R", "G"]
    - ["G", "B"]

Parameter	Type	Default	Description
pitch	float	1.0	Pixel pitch in um. Applied to both x and y.
unit_cell	[int, int]	[2, 2]	Pixels in the periodic unit cell [rows, cols].
bayer_map	list[list[str]]	[["R","G"],["G","B"]]	Color channel assignment. Maps to CFA materials.

The total simulation domain size is pitch * unit_cell[1] in x and pitch * unit_cell[0] in y. For a standard 2x2 Bayer pattern with 1.0 um pitch, the domain is 2.0 um x 2.0 um with periodic boundary conditions.

Layer stack

Layers are defined top-to-bottom under pixel.layers. The ordering of keys in the YAML dictionary determines the physical stacking order from top (air) to bottom (silicon).

pixel:
  layers:
    air:             # Superstrate (top)
    microlens:       # Curved focusing lens
    planarization:   # Flat dielectric spacer
    color_filter:    # Bayer CFA with optional metal grid
    barl:            # Bottom anti-reflection layers
    silicon:         # Photodiode substrate (bottom)

air

Simple dielectric layer above the microlens. This layer provides the medium from which light enters the pixel.

air:
  thickness: 1.0     # um
  material: "air"    # Material name from MaterialDB

Parameter	Type	Default	Description
thickness	float	1.0	Air gap above microlens in um.
material	str	"air"	Material name ($n=1.0$, $k=0.0$).

microlens

Curved focusing lens described by a superellipse profile. The microlens shape in 2D is defined as:

$$z(x,y)=h\cdot {(1-r(x,y{)}^2)}^{1/(2\alpha )}$$

where the normalized radial coordinate $r$ uses the superellipse norm:

$$r(x,y)={({\left|\frac{x-x_c}{R_x}\right|}^n+{\left|\frac{y-y_c}{R_y}\right|}^n)}^{1/n}$$

The parameter $n$ controls squareness ($n=2$ is a circle/ellipse, $n>2$ approaches a rectangle) and $\alpha$ controls curvature ($\alpha =1$ is spherical, $\alpha >1$ produces a flatter top).

microlens:
  enabled: true
  height: 0.6          # Lens sag height in um
  radius_x: 0.48       # Semi-axis in x (um)
  radius_y: 0.48       # Semi-axis in y (um)
  material: "polymer_n1p56"
  profile:
    type: "superellipse"
    n: 2.5              # Squareness parameter
    alpha: 1.0          # Curvature: 1=spherical, >1=flatter
  shift:
    mode: "auto_cra"    # none | manual | auto_cra
    cra_deg: 0.0        # Chief ray angle for auto shift
    shift_x: 0.0        # Manual x-offset (um)
    shift_y: 0.0        # Manual y-offset (um)
  gap: 0.0              # Gap between adjacent lenses (um)

Parameter	Type	Default	Description
enabled	bool	true	Enable/disable microlens.
height	float	0.6	Maximum lens height (sag) in um.
radius_x	float	0.48	Semi-axis in x direction in um.
radius_y	float	0.48	Semi-axis in y direction in um.
material	str	"polymer_n1p56"	Lens material (Cauchy model, $n\approx 1.56$).
profile.type	str	"superellipse"	Profile model.
profile.n	float	2.5	Superellipse squareness. Higher = more square.
profile.alpha	float	1.0	Curvature control. 1.0 = spherical, >1 = flatter.
shift.mode	str	"auto_cra"	"none", "manual", or "auto_cra".
shift.cra_deg	float	0.0	Chief ray angle in degrees for auto shift.
gap	float	0.0	Inter-lens gap in um.

When shift.mode is "auto_cra", the microlens center is offset from the pixel center to accommodate off-axis chief ray angles at the image sensor edge. The shift is computed by tracing the chief ray through each layer below the microlens using Snell's law:

$$\mathrm{\Delta }x=\sum _i{h}_i\cdot \frac{\sin {\theta }_i}{\cos {\theta }_i},\sin {\theta }_i=\frac{n_{\text{air}}\cdot \sin {\theta }_{\text{CRA}}}{n_i}$$

where $h_i$ and $n_i$ are the thickness and refractive index of each layer (planarization, color filter, BARL, silicon to PD center). This accounts for refraction at each interface, improving accuracy over the simple $\tan ({\theta }_{\text{CRA}})$ approximation for CRA > 15° (Hwang & Kim, Sensors 2023, DOI: 10.3390/s23020702). The ref_wavelength parameter (default 0.55 um) controls which wavelength is used for the refractive index lookup.

planarization

Flat dielectric spacer between microlens and color filter.

planarization:
  thickness: 0.3
  material: "sio2"

Typically SiO2 or a polymer. This layer acts as the propagation medium between the microlens and the color filter. Adjust thickness to control where the microlens focuses light relative to the photodiode. The effective focal length of the microlens-planarization system determines optical crosstalk.

color_filter

Bayer CFA (Color Filter Array) with optional metal grid isolation.

color_filter:
  thickness: 0.6
  pattern: "bayer_rggb"
  materials:
    R: "cf_red"
    G: "cf_green"
    B: "cf_blue"
  grid:
    enabled: true
    width: 0.05          # Grid line width in um
    height: 0.6          # Grid height (usually = CFA thickness)
    material: "tungsten"  # Metal grid material

Parameter	Type	Default	Description
thickness	float	0.6	Color filter thickness in um.
pattern	str	"bayer_rggb"	CFA pattern name.
materials	dict	R/G/B mapping	Maps color keys to material names.
grid.enabled	bool	true	Enable metal isolation grid.
grid.width	float	0.05	Grid line width in um.
grid.height	float	0.6	Grid line height in um.
grid.material	str	"tungsten"	Grid material.

Supported Bayer patterns:

Pattern	Layout
bayer_rggb	Row 0: R G, Row 1: G B
bayer_grbg	Row 0: G R, Row 1: B G
bayer_gbrg	Row 0: G B, Row 1: R G
bayer_bggr	Row 0: B G, Row 1: G R

The bayer_map at the top level determines which material each pixel receives. The keys in materials must match the characters used in bayer_map. Custom patterns beyond standard Bayer (e.g., RGBW quad-pixel) can be defined by enlarging the unit_cell and bayer_map:

# 4x4 Quad-Bayer pattern
pixel:
  pitch: 0.7
  unit_cell: [4, 4]
  bayer_map:
    - ["R", "R", "G", "G"]
    - ["R", "R", "G", "G"]
    - ["G", "G", "B", "B"]
    - ["G", "G", "B", "B"]

barl (Bottom Anti-Reflection Layers)

Multi-layer dielectric stack for anti-reflection between the CFA and silicon. The purpose of the BARL is to minimize Fresnel reflection at the high-contrast interface between the color filter ($n\approx 1.55$) and silicon ($n\approx 4.0$).

barl:
  layers:
    - thickness: 0.010
      material: "sio2"
    - thickness: 0.025
      material: "hfo2"
    - thickness: 0.015
      material: "sio2"
    - thickness: 0.030
      material: "si3n4"

Each entry is a {thickness, material} pair. Layers are ordered top-to-bottom. Typical BARL stacks use alternating high/low refractive index materials (SiO2/HfO2 or SiO2/Si3N4) to create a graded index transition. The optimal thickness for each sub-layer follows the quarter-wave condition:

$$t=\frac{{\lambda }_0}{4n}$$

where ${\lambda }_0$ is the target wavelength and $n$ is the layer refractive index.

silicon

Absorbing substrate containing photodiode regions and DTI (Deep Trench Isolation).

silicon:
  thickness: 3.0
  material: "silicon"
  photodiode:
    position: [0.0, 0.0, 0.5]   # Offset from pixel center [x, y, z] in um
    size: [0.7, 0.7, 2.0]        # Photodiode extent [dx, dy, dz] in um
  dti:
    enabled: true
    width: 0.1                    # Trench width in um
    depth: 3.0                    # Trench depth in um (from top of silicon)
    material: "sio2"              # Fill material

Parameter	Type	Default	Description
thickness	float	3.0	Total silicon thickness in um.
material	str	"silicon"	Substrate material.
photodiode.position	[float, float, float]	[0, 0, 0.5]	PD offset from pixel center (x, y, z) in um.
photodiode.size	[float, float, float]	[0.7, 0.7, 2.0]	PD extent (dx, dy, dz) in um.
dti.enabled	bool	true	Enable deep trench isolation.
dti.width	float	0.1	DTI trench width in um.
dti.depth	float	3.0	DTI depth in um (from top of Si).
dti.material	str	"sio2"	DTI fill material.

DTI trenches are placed at pixel boundaries in the silicon layer. They serve as optical barriers that reduce crosstalk by reflecting light back into the intended pixel. Full-depth DTI (depth == thickness) provides the best isolation.

Example configurations

Small pixel (0.8 um)

pixel:
  pitch: 0.8
  unit_cell: [2, 2]
  layers:
    air: {thickness: 1.0, material: "air"}
    microlens:
      height: 0.5
      radius_x: 0.38
      radius_y: 0.38
    planarization: {thickness: 0.25, material: "sio2"}
    color_filter:
      thickness: 0.5
      grid: {width: 0.05, height: 0.5}
    barl:
      layers:
        - {thickness: 0.010, material: "sio2"}
        - {thickness: 0.020, material: "hfo2"}
    silicon:
      thickness: 2.5
      photodiode:
        size: [0.55, 0.55, 1.6]
      dti: {depth: 2.5}
  bayer_map:
    - ["R", "G"]
    - ["G", "B"]

Large pixel (1.4 um) with thicker CFA

pixel:
  pitch: 1.4
  unit_cell: [2, 2]
  layers:
    air: {thickness: 1.0, material: "air"}
    microlens:
      height: 0.8
      radius_x: 0.65
      radius_y: 0.65
      profile: {n: 3.0, alpha: 1.2}
    planarization: {thickness: 0.4, material: "sio2"}
    color_filter:
      thickness: 0.8
      grid: {width: 0.06, height: 0.8}
    barl:
      layers:
        - {thickness: 0.010, material: "sio2"}
        - {thickness: 0.025, material: "hfo2"}
        - {thickness: 0.015, material: "sio2"}
        - {thickness: 0.030, material: "si3n4"}
    silicon:
      thickness: 3.5
      photodiode:
        size: [1.0, 1.0, 2.5]
      dti: {depth: 3.5}
  bayer_map:
    - ["R", "G"]
    - ["G", "B"]

No microlens (flat top)

Disable the microlens to simulate a bare pixel without focusing optics:

pixel:
  pitch: 1.0
  unit_cell: [2, 2]
  layers:
    air: {thickness: 1.0, material: "air"}
    microlens:
      enabled: false
    planarization: {thickness: 0.3, material: "sio2"}
    color_filter:
      thickness: 0.6
    silicon:
      thickness: 3.0

Loading a pixel config in Python

from pathlib import Path
from omegaconf import OmegaConf
from compass.core.config_schema import CompassConfig

# Load from YAML
raw = OmegaConf.load("configs/pixel/default_bsi_1um.yaml")
config = CompassConfig(**OmegaConf.to_container(raw, resolve=True))

# Inspect
print(f"Pitch: {config.pixel.pitch} um")
print(f"Unit cell: {config.pixel.unit_cell}")
print(f"Bayer map: {config.pixel.bayer_map}")

Next steps

• Material Database -- understand and extend the materials used in each layer
• Choosing a Solver -- select the right solver for your pixel structure
• Visualization -- plot the pixel stack to verify your configuration