Monte–Carlo evaluation of bias and variance in hurst exponents computed from power spectral analysis of atomic force microscopy topographic images

2021 ◽  
pp. 152092
Author(s):  
Robert Chrostowski ◽  
Zixuan Li ◽  
James Smith ◽  
Filippo Mangolini
Keyword(s):  
Atomic Force Microscopy ◽  
Monte Carlo ◽  
Spectral Analysis ◽  
Power Spectral Analysis ◽  
Force Microscopy ◽  
Atomic Force ◽  
Power Spectral ◽  
Monte Carlo Evaluation ◽  
Hurst Exponents

scholarly journals Determining cantilever stiffness from thermal noise

2013 ◽  
Vol 4 ◽  
pp. 227-233 ◽  
Author(s):  
Jannis Lübbe ◽  
Matthias Temmen ◽  
Philipp Rahe ◽  
Angelika Kühnle ◽  
Michael Reichling
Keyword(s):  
Atomic Force Microscopy ◽  
Spectral Analysis ◽  
Thermal Noise ◽  
Oscillation Mode ◽  
Thermal Bath ◽  
Frequency Range ◽  
Force Microscopy ◽  
Experimental Systems ◽  
Atomic Force ◽  
Power Spectral

We critically discuss the extraction of intrinsic cantilever properties, namely eigenfrequency f n , quality factor Q n and specifically the stiffness k n of the nth cantilever oscillation mode from thermal noise by an analysis of the power spectral density of displacement fluctuations of the cantilever in contact with a thermal bath. The practical applicability of this approach is demonstrated for several cantilevers with eigenfrequencies ranging from 50 kHz to 2 MHz. As such an analysis requires a sophisticated spectral analysis, we introduce a new method to determine k n from a spectral analysis of the demodulated oscillation signal of the excited cantilever that can be performed in the frequency range of 10 Hz to 1 kHz regardless of the eigenfrequency of the cantilever. We demonstrate that the latter method is in particular useful for noncontact atomic force microscopy (NC-AFM) where the required simple instrumentation for spectral analysis is available in most experimental systems.

AFM Methodology for the Measurement of Silicon Wafer Microroughness

1996 ◽  
Vol 440 ◽  
Author(s):  
A.G. Gilicinski ◽  
S.E. Beck ◽  
R.M. Rynders ◽  
D.A. Moniot
Keyword(s):  
Atomic Force Microscopy ◽  
Spectral Density ◽  
Silicon Wafer ◽  
Power Spectral Density ◽  
Cutoff Frequency ◽  
Force Microscopy ◽  
Atomic Force ◽  
Experimental Solution ◽  
Power Spectral ◽  
Afm Probe

AbstractDespite the growing use of atomic force microscopy (AFM) for the measurement of silicon wafer microroughness, no generally accepted method has been developed to deal with issues around accuracy and reproducibility. We review problems that affect these AFM studies and demonstrate the effect of probe tip size on AFM microroughness data. Without knowledge of AFM probe tip geometry, it is impossible to quantitatively compare Ra or RMS microroughness data between different measurements. An experimental solution is to characterize tip sizes during imaging and compare data taken with similar size tips. While this will significantly improve quantitation, it is restrictive in that data taken with different size tips cannot be easily compared. We propose a solution to this problem in the use of power spectral density (PSD) to evaluate microroughness with a “cutoff frequency” at the lateral wavelength where tip effects begin to affect the accuracy of the microroughness measurement. An example of this approach is described

Spectral Analysis of Irregular Roughness Artifacts Measured by Atomic Force Microscopy and Laser Scanning Microscopy

2014 ◽  
Vol 20 (6) ◽  
pp. 1682-1691 ◽  
Author(s):  
Yuhang Chen ◽  
Tingting Luo ◽  
Chengfu Ma ◽  
Wenhao Huang ◽  
Sitian Gao
Keyword(s):  
Atomic Force Microscopy ◽  
Spectral Analysis ◽  
Template Matching ◽  
Laser Scanning ◽  
Laser Scanning Microscopy ◽  
Scanning Microscopy ◽  
Height Distribution ◽  
Force Microscopy ◽  
Atomic Force ◽  
Autocorrelation Length

AbstractAtomic force microscopy (AFM) and laser scanning microscopy (LSM) measurements on a series of specially designed roughness artifacts were performed and the results characterized by spectral analysis. As demonstrated by comparisons, both AFM and LSM can image the complex structures with high resolution and fidelity. When the surface autocorrelation length increases from 200 to 500 nm, the cumulative power spectral density spectra of the design, AFM and LSM data reach a better agreement with each other. The critical wavelength of AFM characterization is smaller than that of LSM, and the gap between the measured and designed critical wavelengths is reduced with an increase in the surface autocorrelation length. Topography measurements of surfaces with a near zero or negatively skewed height distribution were determined to be accurate. However, obvious discrepancies were found for surfaces with a positive skewness owing to more severe dilations of either the solid tip of the AFM or the laser tip of the LSM. Further surface parameter evaluation and template matching analysis verified that the main distortions in AFM measurements are tip dilations while those in LSM are generally larger and more complex.

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