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Microlens Process Shape Predictor ​

Estimate how lithographic layout, thermal reflow, and etch-transfer settings affect final CIS microlens gap, height, curvature, and 3D profile.

Microlens Process Shape Predictor

Explore how layout gap, reflow budget, and etch-transfer settings can move a CIS microlens toward a final gap, height, and profile.

Layout and resist
Thermal reflow
Etch transfer
Calibration coefficients

Use these multipliers when fitting the surrogate to AFM/SEM or DOE data. Keep them near 1.0 until measured profiles justify a process-specific correction.

Initial gap0.220 um
After reflow0.102 um
Final gap0.000 um
Final height0.538 um
ROC at vertex0.55 um
f-numberf/0.91
Fill factor91.0%
Height retention90%
Zero-gap etch18 s
Profile exponent2.24
Aspect ratio (WX:WY)1.00
Worst reflow gap0.102 um
Lens unit1x1
Lateral rate2.85 nm/s
Height-loss rate0.18%/s
zero-gap candidateover-etch margin
Section row:left-to-right cross-section through the 4x4 grid
1x11x11x11x1litho resist islandafter reflowafter etch transfer-2.2-1.10.01.12.20.00.20.40.60.8x (um)z (um)
Model note: This is a calibrated-by-user surrogate, not a foundry recipe. It combines volume-conserving reflow, parabolic/superellipse caps, and DOE-inspired etch trends: more etch time closes gap; polymerization mainly preserves height; mask thickness changes transfer robustness. Fit the calibration gains to measured gap, height, and profile data before making quantitative decisions.

Model scope

This browser tool is a surrogate process model, not a calibrated foundry recipe. Use it to reason about process direction, sensitivity, and failure modes. Replace the normalized coefficients with wafer metrology data before using it for quantitative process decisions.

What This Adds ​

Most existing COMPASS microlens tools start from an assumed lens geometry. This tool starts one step earlier:

  • Layout: pixel pitch, lithographic island width, aperture footprint shape, and a lens-unit layout selector for 1x1, 2x1, 1x2, 2x2 on-chip-lens groups (presets plus a custom 4x4 editor for heterogeneous die-level mixing of, e.g., 2x2 OCL with 1x1 fill).
  • Reflow: temperature/time as a normalized thermal budget that spreads the lens and changes height through volume conservation. Asymmetric (2x1 / 1x2) masks include a surface-tension correction that drives the long axis to spread less and the short axis to spread more, consistent with reflowed-photoresist observations.
  • Etch transfer: etch time closes residual lens gap; polymerization preserves height; mask thickness changes transfer robustness.
  • Calibration: reflow spread, volume retention, lateral etch, and vertical height-loss gains can be fitted to AFM/SEM or DOE data.
  • Inter-lens coupling for mixed layouts: per-edge proximity coupling (mass-flow asymmetry) and plasma microloading make the smaller lens bulge toward larger neighbors and leave a slightly larger residual gap on boundaries facing larger OCLs. Both effects vanish for uniform-size layouts (all 1x1 or all 2x2).
  • Outputs: final gap (worst of X/Y), height, aspect ratio (WX:WY), vertex radius of curvature, f-number, fill factor, zero-gap etch-time estimate, profile exponent, cross-section, top-down (XY) footprint view with per-side asymmetric outline and height heat-map for each lens group, 3D wireframe, and etch response curves.

Literature Basis ​

  • Ristoiu et al., A DOE study of plasma etched microlens shape for CMOS image sensors, SPIE 2020. This is the closest direct CIS process reference: reflowed microlenses are plasma transferred, and gap/height evolution is modeled versus mask thickness, polymerizing gas flow, and etch time. DOI: 10.1117/12.2551857
  • Baillie and Gendler, Zero-space microlenses for CMOS image sensors: optical modeling and lithographic process development, SPIE 2004. This motivates the layout-gap and zero-space problem: too little lithographic space risks merging during melt/reflow, while residual space reduces fill factor. DOI: 10.1117/12.533453
  • Jin, Liu, and Yang, Design, characterization and evaluation of high performance 2.8 μm pitch zero space microlens, Optics Communications, 2011. This connects zero-space microlens geometry to AFM characterization and silicon-level sensitivity/crosstalk tests. DOI: 10.1016/j.optcom.2010.11.073
  • Tan, Goh, and Kim, Microfabrication of Microlens by Timed-Development-and-Thermal-Reflow, Micromachines, 2020. This supports the parabolic/superellipse profile framing and shows how aperture geometry, development time, diameter, thickness, radius of curvature, and focal length can be regression-modeled. DOI: 10.3390/mi11030277
  • Choi et al., Profile control of asymmetric reflowed microlens for CMOS image sensors, Microelectronic Engineering (2014). This is the basis for the long-axis-shrinks / short-axis-grows surface-tension correction used here for 2x1 and 1x2 lens units: asymmetric reflowed photoresist evolves toward an isotropic equilibrium shape, so the post-reflow X gap and Y gap end up unequal even when the as-printed boundary gap is identical.
  • Y. Oike et al. (Sony Semiconductor Solutions), All-pixel phase-detection autofocus pixel architectures with 2x1 on-chip lens (Dual Pixel CMOS Image Sensor), ISSCC / IEEE Journal of Solid-State Circuits. The 2x1 OCL footprint shares one shaped lens across two adjacent photodiodes; the lens long axis is the PDAF separation direction. Motivates the All 2x1 (Sony 2PD) preset.
  • J. Park et al. (Samsung), A 1/2.55-inch 1.0 μm-pixel 64-Mpixel CMOS image sensor with Tetracell color filter array, ISSCC. Same-color 2x2 sub-pixels share one 2x2 OCL for low-light binning; the boundary against adjacent (different-color) 2x2 cells is the merger-risk surface. Motivates the All 2x2 (Tetracell OCL) preset.
  • Lee et al., Covered Microlens Structure for Quad Color Filter Array of CMOS Image Sensor, Current Optics and Photonics, 2023. Directly studies a mixed-size lens layout (one covered microlens over four sub-pixels) and shows that the surrounding lens geometry materially changes optical efficiency — empirical motivation for the per-side proximity coupling in the Top view. URL: https://opg.optica.org/copp/abstract.cfm?uri=copp-7-5-485
  • Mogab, The Loading Effect in Plasma Etching, J. Electrochem. Soc., 1977. Classical reference for the plasma etch loading effect: lateral etch rate drops in dense pattern regions due to local etchant depletion. Drives the microloading term that widens the residual gap on boundaries adjacent to larger OCLs. DOI: 10.1149/1.2133486
  • Gottscho, Jurgensen, and Vitkavage, Microscopic uniformity in plasma etching, J. Vac. Sci. Technol. B, 1992. Foundational ARDE / microloading reference connecting per-feature etch-rate variation to local pattern density and aspect ratio; basis for the per-edge density score used to set inter-OCL gap asymmetry.
  • Sony / Samsung / OmniVision on-chip-lens design-rule patents (e.g., US8941766, US11765476, US12022217, US12069384) explicitly widen the bottom of OCLs adjacent to smaller neighbors and shift them per local CRA — empirical confirmation of the per-side coupling we approximate.

WARNING

The public papers do not expose a universal CIS recipe. The simulator therefore preserves the directional relationships from the literature and makes the coefficients explicit enough to replace later with DOE or AFM/SEM data.

Related tools

Microlens Ray Trace · MLA Array Visualizer · Microlens & CRA recipe

Physics Notes

Layout-to-Etch Microlens Shape Model

Plain-English Intuition

Start with a printed resist island. Heating lets surface tension round it into a lens cap, so a wider cap usually means a lower cap if the same material volume is spread out. Plasma etch then transfers that cap into the target layer: longer etch can remove the valley between lenses, but it can also flatten the lens. The useful process window is therefore a compromise between zero gap, enough height, acceptable curvature, and no lens merger.

This page treats microlens formation as a three-stage surrogate: lithographic resist volume, volume-conserving thermal reflow, and plasma etch transfer that closes residual gap while eroding height. The goal is not a foundry recipe, but a transparent model that can later be fitted to AFM/SEM metrology.

Assumptions

  • The resist island is represented by pitch, mask width, thickness, and a footprint-shape exponent; local corner rounding and stochastic CD variation are not solved.
  • Reflow is volume constrained and monotonic with a normalized temperature/time budget; the coefficients are user-calibrated surrogate parameters.
  • Etch transfer is split into lateral gap closure and vertical height loss, following the DOE variables exposed by the CIS plasma-etch literature.
  • Lens units can be 1x1, 2x1, 1x2, or 2x2 cells with a constant boundary-gap convention (the boundary gap from the slider applies between adjacent lens units regardless of unit size). Heterogeneous mixtures within a die are supported through a 4x4 grid editor; only rectangular 1x1/2x1/1x2/2x2 groupings are physically meaningful.
  • For 2x1 and 1x2 lens units the reflow model adds a surface-tension correction so the long axis spreads less and the short axis spreads more, mirroring the equilibrium-shape behavior reported for asymmetric reflowed photoresist.

Outputs

  • Initial gap, post-reflow gap, final gap (worst of X/Y), final height, aspect ratio (WX:WY), fill factor, vertex radius, f-number proxy, profile exponent, and zero-gap etch-time estimate, all computed for the representative lens unit (e.g., 2x2 OCL when present).
  • Cross-section view through one row of lens units, top-down (XY) view with per-group mask/reflow/final footprints rendered as superellipses and a viridis height heat-map, 3D surface wireframe, and etch-time response curves for gap and height retention.

Validation Example

  • At fixed reflow settings, increasing etch time should reduce $g_f$ while reducing height retention; if metrology shows the opposite, refit the lateral and vertical etch gains separately.
  • At fixed etch settings, a larger reflow spread gain should reduce residual gap but also lower height through volume conservation.

Core Equations

Lithographic starting gap
$$g_0 = \max(0, p - w_m)$$
  • \(g_0\): Initial space between neighboring resist islands
  • \(p\): Pixel pitch or microlens array pitch
  • \(w_m\): Lithographic mask island width after clamping to allowed pitch limits

A small layout gap helps optical fill factor but increases the chance that resist islands touch or merge during reflow.

Normalized reflow budget
$$B_r = c_T \hat{T} + c_t \hat{t}, \quad \hat{T}=\frac{T_r-T_{\min}}{T_{\max}-T_{\min}}, \quad \hat{t}=\frac{\log(1+t_r/t_0)}{\log(1+t_{\max}/t_0)}$$
  • \(B_r\): Dimensionless reflow budget used by the simulator
  • \(T_r\): Reflow temperature
  • \(t_r\): Reflow time
  • \(c_T, c_t\): Temperature and time weights; defaults encode a directional surrogate, not universal kinetics

The logarithmic time term makes early reflow changes stronger than late soak changes, matching the qualitative behavior of many resist reflow processes.

Reflow spread and residual gap
$$\Delta_r = G_r B_r(k_0+k_h h_0+k_g g_0), \quad w_r=\min(1.04p, w_m+2\Delta_r), \quad g_r=\max(0,p-w_r)$$
  • \(\Delta_r\): Lateral spread per side during reflow
  • \(G_r\): User calibration multiplier for reflow spread gain
  • \(h_0\): Initial resist thickness
  • \(w_r\): Post-reflow lens footprint width
  • \(g_r\): Gap after reflow but before etch transfer

The constants are intentionally exposed as surrogate coefficients: a real process should replace them with DOE-fitted values.

Anisotropic spread for 2x1 / 1x2 lens units
$$\Delta_{r,x}=\Delta_{r,x}^{0}-\tau, \quad \Delta_{r,y}=\Delta_{r,y}^{0}+\tau, \quad \tau=k_{\sigma}B_r\,\frac{w_{m,x}-w_{m,y}}{w_{m,x}+w_{m,y}}\,\overline{\Delta_r^{0}}$$
  • \(\Delta_{r,x},\Delta_{r,y}\): Per-axis reflow spreads after the surface-tension correction
  • \(\Delta_{r,x}^{0},\Delta_{r,y}^{0}\): Gap-driven base spreads computed independently in X and Y from the same surrogate as the 1x1 case
  • \(w_{m,x},w_{m,y}\): Mask island width in X and Y for the lens unit (constant boundary gap: w_{m,x}=W_x\cdot p-g_b, w_{m,y}=W_y\cdot p-g_b for a W_x \times W_y unit)
  • \(k_{\sigma}\): Surface-tension correction strength (0 for 1x1 and 2x2; non-zero only when mask is asymmetric)

Asymmetric reflowed photoresist relaxes toward an isotropic equilibrium shape, so the long axis grows less and the short axis grows more than the isotropic prediction. For symmetric units (1x1, 2x2) the correction vanishes and the model reduces to the previous formula.

Per-side neighbor coupling for mixed lens-unit layouts
$$\sigma_s = \frac{A_N - A_G}{A_N + A_G}, \quad \delta\Delta_{r,s} = k_m\,B_r\,\sigma_s, \quad \delta g_s = k_\ell\,v_{\ell,0}\,t_e\,\rho_s, \quad \rho_s = \max\!\Big(0,\tfrac{A_G + A_N - 2}{6}\Big)$$
  • \(\sigma_s\): Per-side shape-asymmetry parameter: positive when the neighbor on side s is larger than this group, zero for same-size or grid edge
  • \(A_G, A_N\): Cell areas (1, 2 or 4) of this group and its neighbor on side s; grid-edge neighbor is treated as A=1
  • \(\delta\Delta_{r,s}\): Extra lateral reflow spread on side s, scaled by mass-flow coefficient k_m and thermal budget B_r; bulges the lens edge toward larger neighbors
  • \(\delta g_s\): Extra residual gap on side s from plasma microloading: dense neighborhoods deplete etchant locally and reduce lateral closure
  • \(\rho_s\): Local pattern-density score for side s, normalized so two 1x1 cells give 0 and two 2x2 OCLs give 1
  • \(k_m, k_\ell\): User-tunable proximity-coupling and microloading gains; setting either to 0 recovers the independent-lens model

Both effects vanish for uniform-size layouts (all 1x1 or all 2x2). For mixed layouts (e.g., 1x1 next to 2x2 OCL), the smaller lens bulges toward the larger neighbor (Choi et al.; Stanford E241 survey), while the gap on that boundary stays slightly larger than the gap on a 1x1–1x1 boundary because of microloading (Mogab 1977; Gottscho 1992). Sony, Samsung, and OmniVision OCL design-rule patents document this empirically.

Volume-constrained reflow height
$$V_0 \approx A_m h_0, \quad V_r \approx C_{\text{cap}} A_r h_r, \quad h_r \approx \frac{G_v\eta_v A_m h_0}{C_{\text{cap}}A_r}$$
  • \(V_0, V_r\): Resist volume before and after reflow
  • \(A_m, A_r\): Mask island area and reflowed lens footprint area
  • \(C_{\text{cap}}\): Shape factor for the cap profile; a parabolic cap has a different value from a spherical cap
  • \(G_v\): User calibration multiplier for effective volume retention
  • \(\eta_v\): Effective volume retention after reflow
  • \(h_r\): Reflowed lens height before etch transfer

This is the key physical constraint: if the footprint grows faster than volume, lens height must drop.

Etch-transfer gap closure and height loss
$$g_f=\max(0,g_r-2G_{\ell}v_{\ell,0}t_e), \quad h_f=h_r(1-L_e), \quad L_e=\operatorname{clip}(G_z v_{z,0} t_e,0,L_{\max}), \quad t_{zg}=\frac{g_r}{2G_{\ell}v_{\ell,0}}$$
  • \(g_f\): Final gap after etch transfer
  • \(h_f\): Final transferred lens height
  • \(G_{\ell},G_z\): User calibration multipliers for lateral etch closure and vertical height loss
  • \(v_{\ell,0},v_{z,0}\): Base lateral closure and vertical flattening rates from the normalized surrogate
  • \(t_e\): Etch time
  • \(t_{zg}\): Estimated etch time needed to reach zero gap before clipping

In this surrogate, polymerizing gas increases lateral gap closure and reduces height loss; mask thickness changes transfer robustness; the four gains expose the DOE fitting knobs.

Final 3D surface profile
$$\rho=\left[\left|\frac{x}{a}\right|^n+\left|\frac{y}{a}\right|^n\right]^{1/n}, \quad z(x,y)=h_f\max(0,1-\rho^q)$$
  • \(\rho\): Normalized superellipse radius
  • \(a\): Final half-width or aperture radius of the lens footprint
  • \(n\): Footprint exponent: 2 is circular, larger values approach rounded-square or square footprints
  • \(q\): Profile exponent controlling edge steepness and cap flatness

This links the 2D layout aperture to the 3D height field used in the wireframe view.

Curvature, focal length, and f-number proxy
$$R_{\text{vtx}}\approx\frac{a^2+h_f^2}{2h_f}, \quad f\approx\frac{R_{\text{vtx}}}{n_{\ell}-1}, \quad N\approx\frac{f}{2a}$$
  • \(R_{\text{vtx}}\): Vertex radius of curvature estimated from a spherical-cap approximation
  • \(f\): Thin-lens focal length proxy
  • \(n_{\ell}\): Microlens refractive index
  • \(N\): Microlens f-number proxy

The optical numbers are screening metrics only; diffraction, finite stack thickness, and CRA shift require ray tracing or EM simulation.

Model Interpretation

  • The model separates layout-limited gap, reflow-limited spread/height, and etch-limited transfer loss so each failure mode is visible.
  • Zero gap is not automatically good: over-reflow can merge lenses, while over-etch can erase sag and weaken focusing.
  • The browser result should be interpreted as a process-window map before calibration, not as a released process recipe.

How To Calibrate This Surrogate

  • Measure $g_f$, $h_f$, footprint width, and profile exponent from AFM/SEM across a DOE grid of mask thickness, polymerizing gas flow, and etch time.
  • Fit the reflow coefficients first using pre-etch or short-etch samples, then fit $v_{\ell}$ and $v_z$ from etch-time sweeps.
  • Validate the optical proxy by comparing predicted $R_{\text{vtx}}$, $N$, and fill factor against ray-trace collection or silicon-level QE/crosstalk data.

What The References Contribute

  • Ristoiu et al. motivates the DOE variables used here: mask thickness, polymerizing gas, and etch time as drivers of final microlens gap and height.
  • Baillie and Gendler frame the zero-space problem: residual space reduces optical fill factor, but insufficient lithographic space can cause reflow merger.
  • Jin, Liu, and Yang connect zero-space microlens geometry to AFM characterization and sensor-level sensitivity/crosstalk tests.
  • Tan, Goh, and Kim support the aperture-geometry and regression view of thermal-reflow microlens fabrication.
  • Choi et al. ground the surface-tension correction applied to 2x1 and 1x2 lens units: asymmetric reflowed resist evolves toward an isotropic equilibrium, so X and Y spread differently even when the as-printed boundary gap is identical.
  • Sony 2x1 on-chip-lens (Dual Pixel) work motivates the All 2x1 (Sony 2PD) preset: one elongated lens shared across two adjacent photodiodes for all-pixel phase-detection autofocus.
  • Samsung Tetracell ISSCC work motivates the All 2x2 (Tetracell OCL) preset: same-color 2x2 sub-pixels share one 2x2 OCL for low-light binning, and the boundary against the adjacent (different-color) 2x2 cell is the merger-risk surface.
  • Lee et al. (Covered Microlens) directly study how a single large microlens sits over multiple smaller pixels in a Quad-CFA layout and how the surrounding lens geometry changes optical efficiency, supporting the per-side coupling and asymmetric footprint visualisation in the Top view.
  • Mogab (loading effect) and Gottscho et al. (microscopic uniformity in plasma etching) ground the microloading term: dense neighborhoods deplete etchant and slow lateral closure, so boundaries adjacent to larger OCLs end up with slightly larger residual gap than boundaries between two 1x1 cells.
  • Sony/Samsung/OmniVision OCL design-rule patents (US8941766, US11765476, US12022217, US12069384, …) explicitly widen the bottom of OCLs adjacent to smaller neighbors and shift them per local CRA, empirically confirming the per-side coupling our surrogate models.

Known Missing Physics

  • The model does not solve surface-tension fluid dynamics, resist viscosity, contact-angle pinning, or plasma sheath chemistry. Inter-lens coupling is captured only as an effective surrogate (sigma + density), not by solving Young–Laplace flow between adjacent islands.
  • It does not include color-filter topography, wafer-edge non-uniformity, or lens shift for CRA compensation.
  • Use this page to choose DOE regions; use measured profiles plus optical simulation before making device-performance claims.

References