Line Edge Roughness (LER) Analysis

Stochastic Effects & Power Spectral Density

2.8 nm
Total LER (3σ)
45 nm
Correlation Length (ξ)
0.85
Roughness Exponent (α)
3.9 nm
Line Width Roughness
Key Physics Equations:
LER = 3σ of edge position distribution
LWR² = LER_left² + LER_right² (uncorrelated edges)
PSD(f) = σ²ξ / [1 + (2πfξ)²]^((α+1)/2)
Shot Noise LER ∝ 1/√(dose × area)
Acid Diffusion LER ∝ √(2Dt) where D=diffusion, t=PEB time

Roughness Parameters

σ LER (nm) 2.5
Correlation Length ξ (nm) 50
Roughness Exponent α 0.8
Photon Shot Noise (nm) 1.5
Acid Diffusion (nm) 1.0
Measurement Length (μm) 2.0
Sampling Interval (nm) 5
PEB Time (s) 90

1. Line Edge Profile with Roughness

2. LER Distribution Histogram

3. Power Spectral Density (PSD)

4. Autocorrelation Function

5. LER vs Measurement Length

6. LER Budget Breakdown

7. Height-Height Correlation Function

3D Rough Edge Visualization