Thin Film Stack Designer

Design arbitrary multilayer thin-film coatings with full control over layer count, order, materials, and thickness. Visualize reflectance and transmittance spectra in real time.

Thin Film Stack Designer

Design multi-layer thin film coatings with arbitrary materials, order, and thickness. Add/remove/reorder layers freely. Supports 20+ materials.

Incident medium:AirSiO₂SiliconGePolymerGlass (BK7)

Substrate:AirSiO₂SiliconGePolymerGlass (BK7)

Preset:CustomBARL 4-layer (default)2-layer AR (MgF₂/TiO₂)Broadband AR (4-layer)HR Blue mirrorNIR-cut filter

Target:Blue (430-470nm)Green (510-560nm)Red (590-640nm)Visible (430-640nm)Full (380-780nm)

Layers (4)top → bottom (light direction)

1SiO₂Si₃N₄HfO₂TiO₂Al₂O₃MgF₂Ta₂O₅ZrO₂Nb₂O₅ZnSZnSeCaF₂ITOAlNSiCGePolymerTungsten

nm

2SiO₂Si₃N₄HfO₂TiO₂Al₂O₃MgF₂Ta₂O₅ZrO₂Nb₂O₅ZnSZnSeCaF₂ITOAlNSiCGePolymerTungsten

nm

3SiO₂Si₃N₄HfO₂TiO₂Al₂O₃MgF₂Ta₂O₅ZrO₂Nb₂O₅ZnSZnSeCaF₂ITOAlNSiCGePolymerTungsten

nm

4SiO₂Si₃N₄HfO₂TiO₂Al₂O₃MgF₂Ta₂O₅ZrO₂Nb₂O₅ZnSZnSeCaF₂ITOAlNSiCGePolymerTungsten

nm

Avg R in band:4.19%

Avg T in band:95.81%

Min R:0.88% @ 560 nm

Total thickness:80 nm

Stack cross-section:

Air

10

25

15

30

Silicon

SiO₂ HfO₂ Si₃N₄

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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Thin Film Optics · BARL Design recipe

Physics Notes

Thin-Film Anti-Reflection Theory

Plain-English Intuition

Anti-reflection layers work like timing control for echoes. A wave reflected from the top of a film can meet a wave reflected from the bottom of the film with opposite phase, canceling the return wave. But the cancellation only holds over a limited wavelength and angle range, so a CIS BARL stack is always a compromise between blue, green, red, angle, process limits, and absorption.

The BARL optimizer searches thin-film thicknesses that reduce reflection and parasitic loss before photons reach silicon. It is a constrained multilayer interference problem: each film changes phase, admittance, absorption, and therefore the color-channel QE tradeoff.

Assumptions

• All candidate BARL layers are planar, laterally infinite films evaluated with coherent thin-film optics.
• Material optical constants and thickness limits are treated as known inputs; process drift and roughness are not fitted here.
• The objective is optical: it balances reflection, useful silicon absorption, and parasitic absorption before electrical collection.

Outputs

• Recommended layer thicknesses, channel-weighted loss, reflectance trend, silicon absorption trend, and parasitic absorption warning signs.
• A first-pass coating design that should be rechecked with full TMM/RCWA once the surrounding pixel stack is fixed.

Validation Example

• For a single lossless quarter-wave layer with $n_1\approx\sqrt{n_0n_s}$, reflectance should dip near the design wavelength.
• If a proposed BARL increases silicon absorption while also increasing parasitic absorption strongly, inspect the energy budget before accepting it.

Core Equations

Bare-interface reflection

$$r_{0s}=\frac{n_0-n_s}{n_0+n_s}, \quad R_{0s}=|r_{0s}|^2$$

• \(r_{0s}\): Complex amplitude reflection coefficient between incident medium and substrate
• \(R_{0s}\): Bare-interface reflectance
• \(n_0,n_s\): Incident and substrate refractive indices

The optimizer is useful because polymer/oxide-to-silicon index contrast creates a large reflection penalty without a matching layer.

Quarter-wave phase target

$$\delta_1=\frac{2\pi n_1d_1}{\lambda_0}\approx\frac{\pi}{2}, \quad d_1\approx\frac{\lambda_0}{4n_1}$$

• \(\delta_1\): Phase thickness of a single anti-reflection layer
• \(d_1\): Physical thickness of the layer
• \(n_1\): Refractive index of the anti-reflection layer
• \(\lambda_0\): Design wavelength

Quarter-wave thickness is a seed, not the final answer, because CIS stacks are absorbing, broadband, and angle dependent.

Single-layer cancellation condition

$$r_{01}+r_{1s}e^{2i\delta_1}\approx0, \quad n_1\approx\sqrt{n_0n_s}\;\text{(lossless normal-incidence limit)}$$

• \(r_{01},r_{1s}\): Fresnel reflection amplitudes at the two interfaces of the layer
• \(e^{2i\delta_1}\): Round-trip phase factor inside the layer
• \(\sqrt{n_0n_s}\): Ideal matching index for a lossless single layer

Real BARL material choices rarely hit the ideal index, so multiple layers and numerical search are used.

Oblique-incidence admittance

$$\eta_j^{(s)}=\tilde{n}_j\cos\theta_j, \quad \eta_j^{(p)}=\frac{\tilde{n}_j}{\cos\theta_j}$$

• \(\eta_j^{(s)},\eta_j^{(p)}\): Layer optical admittance for s and p polarization
• \(\tilde{n}_j\): Complex refractive index of layer $j$
• \(\theta_j\): Internal propagation angle

A coating optimized at normal incidence may fail at high CRA because s and p admittances diverge.

Optimization objective

$$\mathcal{L}=\sum_{c\in\{R,G,B\}}w_c\left\langle R_c(\lambda,\theta)+\gamma A_{\text{parasitic},c}(\lambda,\theta)\right\rangle_{\lambda\in\Omega_c}$$

• \(\mathcal{L}\): Weighted loss minimized by the optimizer
• \(w_c\): Channel weight for color $c$
• \(\Omega_c\): Wavelength band of interest for channel $c$
• \(\gamma\): Penalty weight for parasitic non-silicon absorption

In practice, the best stack minimizes reflection without moving too much power into lossy BARL or color-filter absorption.

QE improvement budget

$$\Delta A_{\text{Si}}\approx-\Delta R-\Delta T_{\text{escape}}-\Delta A_{\text{parasitic}}$$

• \(\Delta A_{\text{Si}}\): Change in useful silicon absorption
• \(\Delta R\): Change in reflected power
• \(\Delta T_{\text{escape}}\): Change in power transmitted past the active silicon region
• \(\Delta A_{\text{parasitic}}\): Change in absorption outside the photodiode silicon

A lower reflectance curve is only valuable if the saved photons are redirected into silicon absorption.

Model Interpretation

• The optimum depends on incident medium, silicon optical constants, color-filter absorption, angle, polarization, and allowed process materials.
• A stack optimized for green peak QE can hurt blue, red, or off-axis response because phase cancellation is narrowband.
• BARL optimization should be judged by silicon absorption and total color-channel balance, not reflectance alone.

Tuning Workflow

• Start from quarter-wave thickness near the target band, then sweep thickness around that seed because real stacks are absorbing and multilayered.
• Check $R$, $T$, parasitic absorption, and $A_{\text{Si}}$ together; a reflectance minimum alone can be misleading.
• Re-run the candidate at oblique incidence and both polarizations before treating it as a camera-edge solution.

Process Constraints

• Allowed materials, minimum thickness, etch selectivity, stress, thermal budget, and contamination rules usually restrict the mathematical optimum.
• The same BARL stack may behave differently under different color-filter refractive-index and absorption spectra.
• Thickness tolerance should be checked because narrow interference minima can be fragile to wafer non-uniformity.

Known Missing Physics

• The optimizer is a planar-film model; it does not include microlens focusing, metal-grid diffraction, DTI, roughness scattering, or color-filter relief.
• It treats optical constants as known inputs; process drift in $n,k$ can move the optimum.
• For sub-wavelength lateral features, validate BARL candidates with RCWA/FDTD after TMM screening.

References

• Macleod, Thin-Film Optical Filters, 5th ed., CRC Press, 2017 — Thin-film coating design, characteristic matrices, and anti-reflection stack interpretation.
• Born & Wolf, Principles of Optics, 7th ed., Cambridge University Press, 1999 — Background for Fresnel coefficients, polarization, and coherent interference.
• Green, "Self-consistent optical parameters of intrinsic silicon at 300 K", Solar Energy Materials and Solar Cells, 2008 — Silicon optical constants used when judging whether saved photons are absorbed usefully.