Silicon Absorption Depth

Visualize how photon absorption depth in silicon varies with wavelength using the Beer-Lambert law. Understand why pixel thickness is a critical design parameter for quantum efficiency.

Silicon Absorption Depth Visualizer

Explore how light penetration depth in silicon depends on wavelength using Beer-Lambert law.

Wavelength: 550 nm

Si Thickness: 3.0 um

Photodiode Depth: 2.0 um

Absorption coeff. alpha

6,397 cm^-1

Penetration depth delta

1.563 um

Absorbed in PD

72.2%

Absorbed in full Si

85.3%

Model scope

Use this browser tool for intuition, relative trends, and design-space exploration. Its local simplified model is not a substitute for RCWA/FDTD sign-off, silicon calibration, or vendor process data.

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Pixel Optical Effects · Quantum Efficiency

Physics Notes

Beer-Lambert Absorption in Silicon

Plain-English Intuition

Silicon swallows different colours at different depths. Blue light is absorbed within the first few hundred nanometres near the surface, while red and near-infrared photons sneak much deeper before being absorbed — sometimes deeper than the photodiode reaches. That is why thin BSI pixels often lose near-IR sensitivity.

Silicon absorption depends strongly on wavelength. Blue light is absorbed near the surface, while red and NIR photons penetrate much deeper.

Assumptions

Silicon absorption follows Beer-Lambert attenuation using wavelength-dependent absorption coefficient data.
The model treats silicon as a uniform slab and does not include surface texturing, interference, or carrier collection probability.
Absorbed photons are optical absorption events, not automatically collected electrons.

Outputs

Absorption coefficient, penetration depth, and absorbed fraction versus wavelength and silicon thickness.
A wavelength-regime map showing why blue absorbs near the surface and red/NIR requires thicker silicon.

Validation Example

At fixed thickness, blue absorption should be higher than red/NIR absorption for typical visible silicon data.
Increasing silicon thickness should help long wavelengths more than short wavelengths once blue absorption is already saturated.

Core Equations

Absorption coefficient

$$\alpha(\lambda) = \frac{4\pi k(\lambda)}{\lambda}$$

$\alpha$: Absorption coefficient ($1/\mu\text{m}$)
$k$: Extinction coefficient
$\lambda$: Incident wavelength

The extinction coefficient k is converted to an absorption coefficient.

Intensity decay

$$I(z, \lambda) = I_0 e^{-\alpha(\lambda)z}$$

$I(z)$: Intensity at depth $z$
$I_0$: Intensity at the surface ($z=0$)

This is the Beer-Lambert law for a uniform absorbing medium.

Absorbed fraction

$$A(d, \lambda) = 1 - e^{-\alpha(\lambda)d}$$

$A(d)$: Absorbed fraction within thickness $d$
$d$: Silicon physical thickness

This ignores front-surface reflection and interference.

Model Interpretation

Thin BSI pixels may collect visible light well but lose NIR photons.
DTI, backside texture, and reflectors can increase the effective path length.
Carrier collection depth is a separate electrical problem not included here.

Wavelength Regimes

Blue light has large $\alpha$, so it is absorbed near the surface and is sensitive to surface passivation and shallow collection.
Red and NIR light have smaller $\alpha$, so a thin silicon layer can transmit photons without useful absorption.
The absorption length $1/\alpha$ is a useful scale, but 63% absorption at one length is not the same as high QE.

Device Implications

Thicker silicon improves red/NIR absorption but may worsen crosstalk if carriers are generated far from the intended photodiode.
Backside reflectors or light trapping can convert escape transmission into another absorption opportunity.
Collection probability $\eta_{\text{cc}}(z)$ should be multiplied with the absorption profile for electrical QE.

Known Missing Physics

Beer-Lambert absorption ignores interference from upper films and coherent standing waves inside the stack.
The model does not include doping, temperature, strain, or free-carrier absorption changes in silicon.
It predicts where photons are absorbed, not whether generated carriers are collected.