EUV Aerial Image Formation

Hopkins partially coherent imaging model for EUV lithography at 13.5nm wavelength with numerical aperture and coherence control

8.1 nm
Resolution (k₁λ/NA)
45 nm
Depth of Focus
2.45
NILS
78%
Image Contrast

Imaging Parameters

13.5 nm13.5 nm
0.250.33
0.30.6
20 nm40 nm
0.30.5
-100 nm0 nm
0.250.3
ConventionalConventional

Hopkins Partially Coherent Imaging

I(x) = ∫∫ TCC(f,g) · |H(f)|² · |H(g)|² · exp[i·2π(f-g)x] df dg

TCC(f,g) = ∫∫ S(fx,fy) · P(fx-f,fy) · P*(fx-g,fy) dfx dfy

Resolution: R = k₁·λ/NA
DOF: DOF = k₂·λ/NA²
NILS = (1/pitch) · (dI/dx)max / Ith

Aerial Image Intensity

Frequency Domain (Pupil)

Contrast vs Pitch

Depth of Focus Analysis

2D Aerial Image Heatmap

3D Intensity Distribution

NILS vs NA