One-dimensional autocorrelation and power spectrum density functions of irregular regions

Scanning probe microscopy (SPM) can be effectively used for evaluation of nanoscale roughness of surfaces obtained by different technological processes. Spectral properties of surface roughness can be evaluated using algorithms based on Fast Fourier Transform (FFT). For data that are not rectangular, this approach, however fails. In this paper we describe a modification of SPM data evaluation algorithms enabling to use FFT based approach even for irregular and non-continuous data. This opens novel possibilities in analysis of local surface roughness in many fields, e.g. on nanoparticles, semiconductor structures or any other nanostructured samples prepared using nanotechnology methods. Together with theoretical description of proposed method we present benchmarks for its performance and typical results of its application on different samples.

► 1D autocorrelation and height–height correlation functions of irregular regions.
► They are calculated using FFT with complexity comparable to rectangular regions.
► RMS and autocorrelation length of roughness stable with respect to excluded data.