This 2D companion computes a real surface-normal-dependent sputter yield and a real cosine-weighted view factor at every exposed cell, rather than the boolean "line-of-sight open / closed" test the 3D version uses:
cosθ = local surface-normal tilt from vertical (from a solid-density gradient)
Y(θ) = max(0,cosθ)·(1 + B·sin²θ) (angle-dependent sputter yield, peaks off-normal, 0 at grazing)
flux = cosine-weighted fraction of a narrow ion cone with unobstructed line-of-sight to the open plasma
VF = cosine-weighted fraction of the FULL hemisphere with unobstructed line-of-sight (view factor)
R_phys = R_phys0 · flux · Y(θ) (ballistic sputtering)
R_chem = R_chem0 · VF (isotropic radical etch, geometry-throttled)
The view factor VF is the real reason narrow, deep trenches etch slower even when the chemical rate constant never changes — reactive radicals arrive from a shrinking solid angle of open plasma as the trench deepens, exactly the RIE-lag / aspect-ratio-dependent etching (ARDE) effect documented in real plasma-etch tools. A standalone numerical check (cast alongside this page) shows VF falling from 0.43 to 0.15 as a fixed-width trench deepens from aspect ratio 0.2 to 5.2 — a real, geometry-driven slowdown the original 3D cellular automaton's constant chemical rate does not reproduce.
- Ion collimation A — narrows the ballistic cone from a 74°-wide scattered spray (A=0%) to a near-pencil beam (A=100%); the physical yield curve then does the rest, so oblique sidewalls near a narrow beam edge can etch *faster* per hit than the trench floor even though far fewer ions reach them.
- Etch rate — overall reaction speed; scales both the ballistic and chemical baseline rates together.
- Mask opening width — sets the aperture; combined with depth it sets aspect ratio, which is exactly the variable the view-factor term is a function of.
- Mask selectivity S — how much slower the mask itself erodes; low selectivity lets the mask edge recede and silently widen the pattern.