Abstract
Q-controlled atomic force microscopy utilizes an oscillating probe with an adjustable quality factor, which is done by adding a variable damping interaction to the probe. While the Q-control can enhance the probe sensitivity by increasing the Q-factor, the applied interaction increases the noise of the probe motion as well. Thus, the signal-to-noise ratio (SNR) associated with the probe sensitivity varies accordingly. Here, we analytically derive the noise spectral density of the tip motion, and theoretically investigate the SNR in Q-controlled atomic force microscopy. We show that both the overall tip-motion signal and the noise monotonically increase with the effective Q-factor under control, whereas the SNR exhibits a global minimum near the original Q value and asymptotically scales as the square root of the effective Q-factor. Therefore, in general, the Qcontrol technique can be used to alter the quality factor, the magnitudes of signal and noise, and the probe sensitivity in amplitude-modulation atomic force microscopy.
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References
B. Anczykowski, J. P. Cleveland, D. Krüger, V. Elings and H. Fuchs, Appl. Phys. A: Mater. Sci. Process. 66, S885 (1998).
R. Garćia and R. Perez, Surf. Sci. Rep. 47, 197 (2002).
M. Heyde, M. Sterrer, H-P. Rust and H-J. Freund, Appl. Phys. Lett. 87, 083104 (2005).
J. Tamayo, A. D. L. Humphris and M. J. Miles, Appl. Phys. Lett. 77, 582 (2000).
T. Sulchek et al., Appl. Phys. Lett. 76, 1473 (2000).
H. Hlscher and U. D. Schwarz, Int. J. Nonlinear Mech. 42, 608 (2007).
J. Tamayo, A. D. L. Humphris, R. J. Owen and M. J. Miles, Biophys. J. 81, 526 (2001).
S. Gao, L. F. Chi, S. Lenhert, B. Anczykowski, C. M. Niemeyer, M. Adler and H. Fuchs, Chem. Phys. Chem. 6, 384 (2001).
T. R. Rodriguez and R. Garcia, Appl. Phys. Lett. 82, 4821 (2003).
J. Jahng, M. Lee, H. Noh, Y. Seo and W. Jhe, Appl. Phys. Lett. 91, 023103 (2007).
M. Lee, J. G. Hwang, J. Jahng, Q. Kim, H. Noh, S. An and W. Jhe, J. Appl. Phy. 120, 074503 (2016).
J. Kim, B. Sung, B. I. Kim and W. Jhe, J. Appl. Phys. 114, 054302 (2013).
P. D. Ashby, Appl. Phys. Lett. 91, 254102 (2007).
J. Jahng, M. Lee, C. Stambaugh, W. Bak and W. Jhe, Phys. Rev. A 84, 022318 (2011).
M. Poggio, C. L. Degen, H. J. Mamin and D. Rugar, Phys. Rev. Lett. 99, 017201 (2007).
J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Grblacher, M. Aspelmeyer and O. Painter, Nature 478, 89 (2011).
N. Wax, Noise and stochastic processes (Dover Publications, New York, 1964).
T. R. Albrecht, P. Grtter, D. Horne and D. Rugar, J. Appl. Phys. 69, 668 (1991).
M. Lee and W. Jhe, Phys. Rev. Lett. 97, 036104 (2006).
M. Lee, B. Kim, J. Kim and W. Jhe, Nat. Commun. 6, 7359 (2015).
J. Comtet et al., Nat. Mater. 16, 634 (2017).
T. K. Shim et al., J. Korean Phys. Soc. 48, 1476 (2006).
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Lee, M., An, S. & Jhe, W. Analytical Study of Noise Spectral Density in Q-controlled Atomic Force Microscopy. Journal of the Korean Physical Society 72, 384–389 (2018). https://doi.org/10.3938/jkps.72.384
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DOI: https://doi.org/10.3938/jkps.72.384