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 is meant to be read in two passes. First, use the fast path and decision tables to find the few parameters you actually need. Then use the layer reference when you need the exact YAML field name.

Interactive Pixel Stack Builder

Adjust the thickness of each layer in a BSI pixel cross-section. Patterned layers show their z envelope separately from the actual microlens, color filter, grid, and DTI material.

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

Fast path: edit a pixel in five minutes

Do not start from a blank YAML file. Start from one of the known-good configs in configs/pixel/, change one physical idea at a time, and visualize the stack before launching a long solver run.

# Baseline 1.0 um BSI pixel
python scripts/run_simulation.py pixel=default_bsi_1um solver=torcwa source=wavelength_sweep

# Recent sample structures are listed in docs/guide/sample-pixels.md
python scripts/run_simulation.py pixel=sample_p0p56um_4x4ocl solver=torcwa

A practical edit loop looks like this:

1. Pick the closest starting file: default_bsi_1um.yaml for a generic Bayer pixel, or a sample_*.yaml file for a recent architecture.
2. Change only one family of parameters: pitch, microlens, CFA/grid, BARL, silicon/PD/DTI, or CRA shift.
3. Use the visual parameter map below to check whether the geometry still looks plausible.
4. Run a low-cost single-wavelength simulation.
5. Only after the geometry and one wavelength look sane, run a wavelength sweep or convergence study.

Mental model

A pixel config answers four questions:

Question	YAML block	First knob to inspect
How large is the repeated simulation tile?	pixel.pitch, pixel.unit_cell, pixel.bayer_map	pitch and unit_cell
How does light enter and focus?	layers.air, layers.microlens, layers.planarization	microlens height, radius_x/y, shift
Which color and isolation structure does each pixel see?	layers.color_filter, grid, bayer_map	CFA channel material/thickness/contact_angle, grid width, corner_radius
Where is light absorbed and collected?	layers.barl, layers.silicon, photodiode, dti	silicon thickness, PD size, DTI width/depth

For most studies, the highest-value parameters are pitch, microlens height, microlens radius_x/y, CRA shift.cra_deg, color-filter thickness, grid width, BARL layer thickness, silicon thickness, photodiode size, and DTI width/depth.

Which parameter should I change?

Goal	Change these first	Keep an eye on
Model a smaller or larger pixel	pitch, then scale microlens radius, grid width, PD size, and DTI width	Tiny features need finer RCWA/FDTD grids
Study corner shading or sensor-edge behavior	microlens.shift.mode: "auto_cra" and shift.cra_deg	CRA also changes source angle; do not compare to normal incidence blindly
Reduce optical crosstalk	Increase grid.width, enable/deepen dti, adjust PD footprint	More isolation can reduce fill factor or transmission
Improve peak QE	Tune microlens height/radius, BARL thicknesses, silicon thickness	A stack optimized for green may hurt blue or red
Compare Bayer, Quad Bayer, or 4x4 binning	unit_cell, bayer_map, color_filter.pattern, microlens.sharing	bayer_map dimensions must match unit_cell
Test fabrication-like rounded CFA corners	color_filter.grid.corner_radius	Radius is clamped by pitch and grid width
Make a faster debug run	Use a smaller unit_cell, simpler stack, lower solver order/grid	Do not treat debug results as converged physics

Coordinate system

COMPASS uses a right-handed coordinate system where light propagates downward through the stack. The compact sketch below is only for orientation; the detailed dimensional map is the next section.

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
• For photodiodes, position[0] and position[1] are lateral offsets from each pixel center. Most users should leave position unchanged and tune size first.

Parameter map (visual reference)

The diagram below labels every dimensional parameter directly on a 2D cross-section of the default 1.0 µm BSI pixel. Switch between XZ Cross-Section (vertical stack, layer thicknesses, DTI/photodiode depth) and XY Top View (in-plane pitch, microlens footprint, photodiode/DTI/grid widths). Hover any row in the legend to highlight that parameter on the diagram.

Hover a parameter row in the legend below to highlight it on the diagram. Dimensions follow the default 1.0 µm BSI pixel (configs/pixel/default_bsi_1um.yaml), including per-channel color-filter relief and metal-grid thickness.

	Parameter	Default	Meaning
	pixel.pitch	1.0 µm	In-plane pixel pitch (x and y)
	pixel.unit_cell	[2, 2]	Number of pixels in the periodic unit
	air.thickness	1.0 µm	Air gap above the microlens
	microlens.height	0.6 µm	Maximum lens sag (peak height)
	microlens.radius_x	0.48 µm	Lens semi-axis in x
	microlens.radius_y	0.48 µm	Lens semi-axis in y
	microlens.gap	0.00 µm	Gap between adjacent microlens bases
	microlens.shift.shift_x/y	0 (auto_cra)	Lateral lens offset (CRA correction)
	planarization.thickness	0.3 µm	Spacer thickness between ML and CF
	color_filter.{red,green,blue}.thickness	0.60-0.65 µm	Per-channel color-filter height above the CFA base
	color_filter.{red,green,blue}.contact_angle	62-72°	Sidewall taper above the metal-grid top
	color_filter.grid.width	0.05 µm	Metal grid line width at pixel borders
	color_filter.grid.thickness	0.47 µm	Metal grid height from the CFA base
	barl.layers[i].thickness	0.010-0.030 µm	Per-layer thickness of the AR stack
	silicon.thickness	3.0 µm	Total silicon substrate thickness
	silicon.dti.width	0.1 µm	Trench width at pixel boundaries
	silicon.dti.depth	3.0 µm	Trench depth from top of Si
	silicon.photodiode.size[dx,dy]	0.7 × 0.7 µm	PD lateral footprint per pixel
	silicon.photodiode.size[dz]	2.0 µm	PD depth (z extent inside Si)
	silicon.photodiode.position[z]	0.5 µm	PD center depth below top of Si

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.

XY top view: unit cell pitch, unit_cell, bayer_map

Layer stack

Layers live under pixel.layers. The examples list them in light-entry order for readability, but COMPASS recognizes the canonical layer keys and builds the physical BSI stack consistently: silicon at the bottom, then BARL, color filter, planarization, microlens, and air at the top. Add custom sub-layers inside barl.layers; do not invent arbitrary top-level layer names unless the geometry code supports them.

pixel:
  layers:
    air:             # Superstrate, light-entry side
    microlens:       # Curved focusing lens
    planarization:   # Flat dielectric spacer
    color_filter:    # Bayer CFA with optional metal grid
    barl:            # Bottom anti-reflection layers
    silicon:         # Photodiode substrate

Use this order in your YAML files because it matches the way people think about the optical path. Internally, the solver receives the corresponding bottom-to-top z stack.

air

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

XY top view: air uniform incident medium

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:

Start with the defaults unless the study is specifically about focusing. The most common safe edits are height, radius_x/y, and shift.cra_deg. If you reduce pitch, scale the radius and gap with it; a lens radius larger than roughly pitch / 2 will overlap neighboring lenses unless you are intentionally using multi-pixel OCL sharing.

XY top view: microlens radius, gap, sharing, CRA shift

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

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)
  sharing: 1            # 1 = per-pixel OCL, 2 = 2x2 OCL, 4 = 4x4 OCL

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.
sharing	int	1	Multi-pixel OCL grouping (see below).

Multi-pixel OCL sharing

sharing: N places one microlens over each $N\times N$ block of pixels (the lens straddles a Quad/Nona/Tetra² color group). When radius_x/radius_y are not set explicitly, they default to sharing * pitch / 2 so the lens fills the cluster.

sharing	Use case	Lens diameter (default)
1	Conventional per-pixel OCL	pitch
2	2×2 OCL / Quad PD (all-pixel PDAF)	2 × pitch
3	Nonacell shared lens (rare)	3 × pitch
4	4×4 super-cell OCL	4 × pitch

High-refractive-index microlens materials (polymer_hri_n1p70, polymer_hri_n1p85) are also registered for modelling recent flagship sub-µm pixels. See the Sample pixel structures guide.

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.

If you are not calibrating to a real cross-section, change this slowly. A planarization layer that is too thick can make the microlens focus too low; one that is too thin can make the CFA surface unrealistically close to the lens.

XY top view: planarization uniform spacer between lens and CFA

color_filter

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

This block controls both color selectivity and lateral optical isolation. For ordinary Bayer simulations, keep pattern: "bayer_rggb" and change the per-channel material fields only when you have custom material data. For crosstalk studies, the first knobs are grid enabled, width, thickness, and corner_radius.

For current BSI stacks, prefer the per-channel form below. Real color filters often rise above the metal grid and the red, green, and blue resists can have different heights. contact_angle controls the tapered protrusion above grid.thickness: 90 degrees is a vertical sidewall, while lower values make the top footprint smaller. The older thickness, materials, and grid.height fields still work as a legacy flat-slab fallback.

XY top view: color filter Bayer cells, metal grid, tapered top

color_filter:
  pattern: "bayer_rggb"
  red:
    material: "cf_red"
    thickness: 0.62
    contact_angle: 66.0
  green:
    material: "cf_green"
    thickness: 0.60
    contact_angle: 72.0
  blue:
    material: "cf_blue"
    thickness: 0.65
    contact_angle: 62.0
  grid:
    enabled: true
    width: 0.05          # Grid line width in um
    thickness: 0.47      # Grid thickness in um; usually lower than the CF
    material: "tungsten" # Metal grid material
    corner_radius: 0.0   # Optional: round CF corners by r (um). 0 = sharp.

Parameter	Type	Default	Description
thickness	float	0.6	Legacy flat color filter thickness in um. Used when per-channel thickness is absent.
pattern	str	"bayer_rggb"	CFA pattern name.
materials	dict	R/G/B mapping	Legacy color-key to material mapping.
red/green/blue.material	str	cf_*	Per-channel material name.
red/green/blue.thickness	float	thickness	Per-channel CF height in um.
red/green/blue.contact_angle	float	90.0	Sidewall angle in degrees for the protrusion above the grid.
grid.enabled	bool	true	Enable metal isolation grid.
grid.width	float	0.05	Grid line width in um.
grid.thickness	float	thickness	Metal grid height in um.
grid.height	float	0.6	Legacy alias for grid.thickness.
grid.material	str	"tungsten"	Grid material.
grid.corner_radius	float	0.0	Rounded-rectangle corner radius r (um), applied identically at all four corners of each CF cell. 0 keeps the sharp-cornered grid; values > 0 model each CF as a rounded rectangle and the grid as its complement. Auto-clamped to (pitch - grid.width) / 2.
n_slices	int	8 when tapered	Number of z-slices used to staircase a tapered CF surface.

Supported Bayer patterns:

Pattern	Same-color group	Super-pixel	Used by
bayer_rggb	1×1	2×2	Standard Bayer
bayer_grbg	1×1	2×2	Standard Bayer (GRBG variant)
bayer_gbrg	1×1	2×2	Standard Bayer (GBRG variant)
bayer_bggr	1×1	2×2	Standard Bayer (BGGR variant)
tetracell / quad_bayer	2×2	4×4	Quad Bayer (50 MP-class main cameras)
nonacell	3×3	6×6	9-cell binning (early 108 MP-class sensors)
tetra2cell / hexadeca	4×4	8×8	16-cell binning (200 MP-class sub-µm pixels)

The bayer_map at the top level determines which channel each pixel receives. R, G, and B resolve to the red, green, and blue channel blocks; custom material mappings can still use the legacy materials dictionary. 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 ($n\approx 4.0$).

XY top view: BARL full-area thin-film stack

Treat the BARL as a tunable thin-film recipe, not as a universal truth. The example stack is a reasonable starting point, but real products use vendor-specific material choices and thicknesses. When optimizing, change layer thicknesses in nanometer-scale increments and check the whole visible spectrum rather than a single wavelength.

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. The example above is one illustrative stack; the actual material set, layer count, and stacking order are vendor-specific recipes that vary widely (common ingredients include SiO2, Si3N4, HfO2, Al2O3, TiO2, Ta2O5). The general design strategy is to interleave higher- and lower-index dielectrics so that the index transition between filter and silicon becomes graded, with each layer tuned by 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).

This is where QE becomes collected signal. Silicon thickness controls the absorption path, photodiode.size controls the collection volume, and dti controls how strongly neighboring pixels are isolated. For a first pass, change photodiode.size before moving photodiode.position.

XY top view: silicon photodiode footprint and DTI grid

silicon:
  thickness: 3.0
  material: "silicon"
  photodiode:
    position: [0.0, 0.0, 0.5]   # PD center placement [x offset, y offset, z] in um
    size: [0.7, 0.7, 2.0]        # Photodiode extent [dx, dy, dz] in um
  dti:
    enabled: true
    mode: "fdti"                  # "fdti" or "bdti"
    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 center placement. x/y are lateral offsets from each pixel center; the z value controls vertical placement in silicon. Leave this at the default unless you are intentionally shifting the collection window.
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.mode	str	"fdti"	Trench direction model: "fdti" or "bdti".
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 strongest isolation in this simplified geometry.

Safe editing checklist

Before trusting a result, check the geometry against these simple rules:

Check	Why it matters
bayer_map shape matches unit_cell	A [4, 4] unit cell needs four rows and four columns in the map
Microlens radius is plausible	Per-pixel lenses usually stay just below pitch / 2; shared OCL lenses scale with sharing
Grid, DTI, and corner radius are not smaller than the simulation grid cell	Sub-grid features can disappear or converge slowly
BARL thicknesses are in realistic thin-film ranges	Typical values are tens of nanometers, written as 0.010 to 0.050 um
Silicon is thick enough for the wavelength range	Red/NIR light needs more silicon than blue light
PD size fits inside the pixel	photodiode.size[0] and [1] should usually be smaller than pitch
CRA shift is used consistently	If source CRA changes, update microlens.shift.cra_deg or intentionally set shift.mode: "none" for a no-compensation comparison

When something looks wrong, simplify the config first: disable the microlens, disable the metal grid, or use a single wavelength. Reintroduce features one at a time.

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:
      red: {material: "cf_red", thickness: 0.52, contact_angle: 66.0}
      green: {material: "cf_green", thickness: 0.50, contact_angle: 72.0}
      blue: {material: "cf_blue", thickness: 0.54, contact_angle: 62.0}
      grid: {width: 0.05, thickness: 0.39}
    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:
      red: {material: "cf_red", thickness: 0.83, contact_angle: 66.0}
      green: {material: "cf_green", thickness: 0.80, contact_angle: 72.0}
      blue: {material: "cf_blue", thickness: 0.86, contact_angle: 62.0}
      grid: {width: 0.06, thickness: 0.62}
    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:
      red: {material: "cf_red", thickness: 0.62}
      green: {material: "cf_green", thickness: 0.60}
      blue: {material: "cf_blue", thickness: 0.65}
    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