Analyzing atomic force microscopy images using spectral methods

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Abstract
Various statistical quantities (such as average, peak-to-valley, and root-mean-square roughness) have been applied to characterize surface topography. However, they provide only vertical information. Because spectral analysis provides both lateral and longitudinal information, it is a more informative measurement than all these commonly used statistical quantities. Unfortunately, a standard method to calculate power spectral density (PSD) is not available. For example, the dimensions of PSD are often denoted as either (length)3 or (length)4. This may lead to confusion when utilizing spectral analysis to study surface morphology. In this paper, we will first compare the definitions of PSD commonly used by various authors. Using silicon surface roughness measurements as examples, we will demonstrate the advantages of spectral methods on atomic force microscopic (AFM) image analysis. In this context, we study the effects of typical AFM imaging distortions such as image bow, drift, tip-shape effects, and acoustic noise. As a result, we will provide a procedure to obtain accurate and reproducible AFM measurements.