power spectral density analysis

PSD (Power Spectral Density) analysis is a frequency-domain technique for characterizing surface roughness — decomposing the surface height profile into its spectral components, revealing the contribution of each spatial frequency (wavelength) to the total roughness.

PSD Methodology

• FFT: Apply the Fast Fourier Transform to the surface height data — convert from spatial to frequency domain.
• PSD Function: $PSD(f) = |FFT(z(x))|^2 / L$ where $f$ is spatial frequency and $L$ is the scan length.
• 2D PSD: For 2D surface maps (AFM images), compute the 2D PSD and radially average for isotropic surfaces.
• Units: PSD is typically expressed in nm⁴ or nm²·µm² as a function of spatial frequency (µm⁻¹).

Why It Matters

• Multi-Scale: PSD reveals roughness contributions at every spatial wavelength — identify which frequencies dominate.
• Process Signatures: Different processes create roughness at different spatial frequencies — PSD is a process fingerprint.
• Stitching: Multiple measurement techniques (AFM, optical, scatterometry) can be stitched in PSD space to cover the full frequency range.

PSD Analysis is the fingerprint of surface roughness — revealing the spectral composition of surface texture for comprehensive roughness characterization.