Secondary Electron Blur Calculator
An absorbed EUV photon doesn't expose a point — it launches photo- and secondary electrons that travel a few nanometres before driving chemistry. Model that spread as a Gaussian and watch how it softens a line/space edge, drops contrast, and collapses the image log-slope.
How it works
Start from an idealised aerial/latent image of an equal line/space grating: intensity 1 inside a line, 0 in the space, with pitch = 2×half-pitch. Convolve it with a Gaussian point-spread function of width σ that lumps together photoelectron range, secondary-electron transport, and acid diffusion:
Two numbers summarise the damage. Image contrast (I_max − I_min)/(I_max + I_min) falls toward zero as σ approaches the half-pitch. NILS — the Normalized Image Log-Slope — measures how steeply intensity crosses the print threshold, scaled by the feature width:
NILS is the metric lithographers actually watch: a value of ~2 or more means the edge is steep enough to tolerate dose and focus variation, while NILS below ~1 means small process errors move the printed edge a long way — the feature is losing its process window. Push σ up relative to the half-pitch and you can watch a well-resolved grating slide into a flat, unresolvable smear.
What the model deliberately ignores
- The real PSF isn't Gaussian. Secondary-electron blur has an energy-dependent range distribution with heavier tails; a Gaussian is a convenient first approximation only.
- Optics. This starts from an ideal binary image; a real aerial image is already band-limited by the projection optics (finite NA) before any resist blur.
- Shot noise. This tool is deterministic — it shows the mean blurred image. Combine it with photon shot noise to see why blurred, low-count edges become stochastic defects.
Further reading
Secondary-electron and acid-blur modelling in EUV resists has a deep literature — e.g. the resist-mechanism work of Kozawa & Tagawa, and NILS/process-window treatments in standard lithography texts. Use those to anchor the σ you plug in here.
Method & numerics
The pattern is sampled at up to 0.1 nm resolution over three pitches with periodic wrap-around, convolved directly with a Gaussian kernel truncated at ±4σ and renormalised to unit area. Contrast and NILS are measured over the central pitch; the edge slope is a finite difference at the first threshold crossing. The grayscale strips show the ideal pattern (top) and blurred pattern (bottom), with dark = resist line.
contrast = (I_max − I_min) / (I_max + I_min) NILS ≈ | dI/dx | / I · w at I = threshold