Noncontact Atomic Force Microscopy - Yale School of Engineering ...

P.I-31
Frequency Noise in Frequency Modulation Atomic Force Microscopy
Kei Kobayashi 1 , Hirofumi Yamada 2 , and Kazumi Matsushige 2
1 Innovative Collaboration Center, Kyoto University, Kyoto, Japan.
2 Department of Electronic Science and Engineering, Kyoto University, Kyoto, Japan.
Atomic force microscopy (AFM) using the frequency modulation (FM) detection method
has been widely used for atomic/molecular-scale investigations of various materials.
Recently, it has been shown that high-resolution imaging in liquids by the FM-AFM is
also possible by reducing the noise-equivalent displacement in the cantilever
displacement sensor and by oscillating the cantilever at a small amplitude, even with the
extremely reduced Q-factor due to the hydrodynamic interaction between the cantilever
and the liquid. However, it has not been clarified how the noise reduction of the
displacement sensor contributes to the reduction of the frequency noise in the FM-AFM
in low-Q environments. In this presentation, the contribution of the displacement sensor
noise to the frequency noise in the FM-AFM is analyzed in detail to show how it is
important to reduce the noise-equivalent displacement in the displacement sensor
especially in low-Q environments.
As a general equation for the frequency noise density of the oscillator, we have to
consider the contribution of the displacement sensor noise to the oscillator noise in
addition to the frequency noise of the high-Q cantilevers,
where N ds is the noise-equivalent displacement sensor noise density.
Figure 1: Schematics of the evolution of the displacement noise into the frequency noise without
and with the displacement sensor noise. The displacement noise spectrum of the cantilever around
the resonance frequency without the displacement sensor noise (a) and the corresponding
oscillator frequency noise (b). The total frequency noise considering the measurement noise
(dotted area in (b)) becomes constant as shown in (c). If there is non-zero displacement sensor
noise, it brings additional oscillator frequency noise and measurement noise as shown in (d).
Dark gray and black areas represent two levels (small and large) of additional displacement
sensor noise.
[1] K. Kobayashi, H. Yamada, and K. Matsushige, Rev. Sci. Instrum. accepted for publication (2009).
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