petch — technical evidence pack

~100×

faster on a matched 3-D via case (2.0 s vs 197 s, identical hardware, same etch depth)

0.19%

mask-opening error reproducing a published SiO₂ trench experiment (Krüger 2024)

I⁺ = I⁻

self-consistent surface charging, converged on every dielectric node — physics ViennaPS does not compute

0.073%

depth-rate agreement between 10 nm and 5 nm grids — the numbers hold under refinement

01The engine, end to end

One continuous calculation: energy–angle-resolved ion and neutral arrival → in-feature ballistic and diffuse transport → material-specific surface chemistry with finite, conserved surface state → mask erosion, passivation, and substrate etch → 3-D multi-material level-set motion, straight through pinch-off, enclosed-cavity formation, and reopening.

3-D cutaway via etch computed by petch — 60 s of process physics including mask overhang and profile bowing, rendered from the solver's own evolving surface.

trench etch animation — Trench etch to AR 9.3: the aspect-ratio-dependent transport starvation that governs deep-feature etching, emerging from first principles — not from a fitted rate-vs-depth curve.

02Speed, measured head-to-head

Same case, same hardware, same etch depth — petch against ViennaPS, the leading open-source profile simulator. Not projections: wall-clock recordings of both tools running.

Real-time race on a matched trench case: petch finishes in ~0.5 s while ViennaPS continues to ~25 s. Depth-matched comparison.

3-D via etch, side by side: ViennaPS 197 s, petch 2.0 s to the same depth (~100×). The extra horizontal sheet on the ViennaPS side is its exported buried mask/substrate interface — petch renders the true outer surface.

The full-physics certified operator (exact conservation ledgers, hard visibility, float64-certified ray transport at 5 nm) runs at ~7.8 s per step on a single consumer GPU today, profiled per-operator — and the same GPU-resident acceleration stack demonstrated above is scheduled onto it next.

03It reproduces a real published experiment

Krüger 2024: SiO₂ trench etch in fluorocarbon plasma, 60 s process, measured by SEM, driven by the paper's own measured reactor fluxes and ion energy–angle distributions. Two interpretable physical closures calibrated; everything else is physics.

The calibrated Krüger base case etching in time (trench array, periodic cell tiled ×3): mask erosion, sidewall passivation dynamics, and the deepening high-aspect-ratio trench, computed by the certified engine at 10 nm development fidelity. Scrub the timeline to any moment of the process.

Simulated base-case profile: mask necking, taper, and depth from the coupled transport–chemistry–motion chain. Fine-grained texture is grid-scale numerics; the shape is physics.

Observable	Experiment	petch	Error
Minimum mask opening	45.000 nm	45.085 nm	+0.19%
Etch depth	825.000 nm	853.219 nm	+3.42%

Driven end to end by the paper's measured reactor fluxes and ion energy–angle distributions — not tuned source shapes. The two calibrated closures are interpretable physics (a mask-film growth fraction and an oxide yield scale), and the same frozen pair carries forward unchanged into blind prediction.

04Charging: the physics that breaks HAR features

Electron shading charges deep features; the resulting in-feature field steers ions and produces notching, twisting, and profile distortion — the dominant failure modes of high-aspect-ratio dielectric etch. petch computes this self-consistently: field ↔ charged trajectories ↔ accumulated surface charge, converged until currents balance on every dielectric node, on the evolving profile.

charging validation — Charging floor-flux against the Hwang–Giapis microtrench experiment — untuned shape agreement — with the computed in-feature potential map.

charging notching — Causal demonstration: charging off → no notch. Charging on → the foot-of-sidewall notch appears, with the experimentally observed aspect-ratio trend (shape correlation r = 0.92).

Nozawa 3-D charging — The full 3-D engine solving the self-consistent potential on a real multi-line notching geometry (Nozawa 1995 layout): exact charge ledgers, converged current balance, charged transport through the evolving feature.

05Head to head with the open-source state of the art

ViennaPS is an excellent geometry engine — petch matches it exactly where it is strong, and carries the physics and guarantees it doesn't have.

	petch	ViennaPS
Self-consistent charging (fields, deflection, notching)	Converged I⁺=I⁻ on the evolving 3-D profile	Not computed — structurally blind to charging effects
Surface chemistry	Finite, conserved multi-material surface inventories (mask film, passivation, polymer) with exact ledgers	Parametrized rate/coverage models
Reactor boundary	Ingests measured energy–angle-resolved fluxes (checksummed) — predicts new conditions from their physics	Parametrized source distributions, retuned per condition
Reproducibility & audit	Bit-identical reruns, conservation receipts, checksummed provenance, freeze/reveal validation gates	No determinism or audit contract
Speed on matched cases	~50× (2-D trench), ~100× (3-D via), depth-matched, same hardware	Baseline
Geometric transport & topology	Parity — verified directly: ARDE transport agrees (0.727 vs 0.73 at AR 8.6) and pinch-off/reopen event times match ViennaLS within one grid cell. We benchmark against it because it's good.

06Breadth across chemistries and mechanisms

Developed against published wafer experiments spanning cryo SF₆/O₂ deep-trench ARDE, fluorocarbon SiO₂ trenches, charging microtrenches and notching, and Bosch cycling — one engine, one set of physics contracts.

de Boer ARDE — Aspect-ratio-dependent etch-rate collapse against the de Boer 2002 cryo-etch wafer data, including the deepest AR 40 point — the transport-starvation physics of deep features, captured across the full aspect-ratio range.

07Numbers that hold under refinement

Exact material conservation (zero residual, enforced every step), watertight topology-complete surface meshes, float64-certified ray transport, deterministic seeded sampling — bit-identical on re-run. And the observables converge: refine the grid 2× and the answers stay.

10 nm vs 5 nm refinement agreement on the observables (early-time depth-rate difference 0.073%) and the per-operator cost profile of a certified 5 nm step — the acceleration roadmap attacks each measured term.