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Probing rough surfaces: Markovian versus non-Markovian processes

Fazeli, S. M ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1088/1367-2630/10/8/083020
  3. Publisher: 2008
  4. Abstract:
  5. We demonstrate that Markov processes play a fundamental role in probing rough surfaces and characterizing their topography. The surface topography obtained by a probe, as in the atomic force microscopy (AFM) technique, is based on the probe-surface interactions. When the size of the probe tip is comparable with the height of the surface fluctuation, the surface image can be aberrated from its origin. Due to the tip effect, there is a crossover in the structure function of the surface. For scales smaller than the Markov length -the minimum length scale over which a process is Markovian - the stochastic function that describes a rough surface is non-Markovian, whereas for length scales larger than the Markov length, the surface may be described by a Markov process. Synthetic rough surfaces generated by fractional Guassian noise (FGN), as well as the rough surface of V2O5, obtained by AFM, confirm this. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft
  6. Keywords:
  7. Atomic force microscopy ; Engineering geology ; Imaging techniques ; Learning systems ; Markov processes ; Microscopic examination ; Scanning probe microscopy ; Surface measurement ; Surface structure ; Length scaling ; Markovian ; Non-Markovian ; Non-Markovian processes ; Probe tips ; Rough surfaces ; Structure functions ; Surface fluctuations ; Surface imaging ; Surface interactions ; Surface topography
  8. Source: New Journal of Physics ; Volume 10 , August , 2008 ; 13672630 (ISSN)
  9. URL: https://iopscience.iop.org/article/10.1088/1367-2630/10/8/083020