Power Spectral Density (PSD)

Together with the line edge roughness (3*σ) or contact edge roughness (3*σ), two other important parameters, the correlation length (ξ) and the roughness exponent (H), can also be calculated from its power spectral density.

Power Spectral Density - PSD

 The graph on the left plots the PSD of left edges (the odd numbered edges).

 PSD - Left Edges PSD - Right Edges

Or both

PSD - Left and Right

 

The calculation

The power spectral frequency is defined as the square of the magnitude of the Fourier transform of the edge residuals.

PSDi (f) 
= ∫-∞∞∆xije-i2πfxdx2,

where,...

using Fast Fourier Transform (FFT)

 

(under construction)