Kobayashi Kei, Yamada Hirofumi, Matsushige Kazumi
Office of Society-Academia Collaboration for Innovation, Kyoto University, Katsura, Nishikyo, Kyoto 615-8520, Japan.
Rev Sci Instrum. 2011 Mar;82(3):033702. doi: 10.1063/1.3557416.
We recently reported the analysis of the frequency noise in the frequency modulation atomic force microscopy (FM-AFM) both in high-Q and low-Q environments [Rev. Sci. Instrum. 80, 043708 (2009)]. We showed in the paper that the oscillator noise, the frequency fluctuation of the oscillator, becomes prominent in the modulation frequency lower than f(0)∕2Q, where f(0) and Q are the resonance frequency and Q-factor. The magnitude of the oscillator noise is determined by the slope of the phase versus frequency curve of the cantilever at f(0). However, in actual FM-AFM in liquids, the phase versus frequency curve may not be always ideal because of the existence of various phase shifting elements (PSEs). For example, the spurious resonance peaks caused by the acoustic excitation and a band-pass filter in the self-oscillation loop increase the slope of the phase versus frequency curve. Due to those PSEs, the effective Q-factor is often increased from the intrinsic Q-factor of the cantilever. In this article, the frequency noise in the FM-AFM system with the PSEs in the self-oscillation loop is analyzed to show that the oscillator noise is reduced by the increase of the effective Q-factor. It is also shown that the oscillation frequency deviates from the resonance frequency due to the increase of the effective Q-factor, thereby causing the reduction in the frequency shift signal with the same factor. Therefore the increase of the effective Q-factor does not affect the signal-to-noise ratio in the frequency shift measurement, but it does affect the quantitativeness of the measured force in the FM-AFM. Furthermore, the reduction of the frequency noise and frequency shift by the increase of the effective Q-factor were confirmed by the experiments.
我们最近报道了对调频原子力显微镜（FM-AFM）在高Q值和低Q值环境下频率噪声的分析[《科学仪器评论》80, 043708 (2009)]。我们在论文中表明，振荡器噪声，即振荡器的频率波动，在调制频率低于f(0)∕2Q时变得显著，其中f(0)和Q分别是共振频率和Q因子。振荡器噪声的大小由悬臂梁在f(0)处的相位与频率曲线的斜率决定。然而，在实际的液体中的FM-AFM中，由于各种相移元件（PSE）的存在，相位与频率曲线可能并不总是理想的。例如，自振荡回路中的声激发和带通滤波器引起的虚假共振峰增加了相位与频率曲线的斜率。由于这些PSE，有效Q因子通常会从悬臂梁的固有Q因子增加。在本文中，对自振荡回路中存在PSE的FM-AFM系统的频率噪声进行了分析，结果表明有效Q因子的增加会降低振荡器噪声。还表明，由于有效Q因子的增加，振荡频率会偏离共振频率，从而导致频移信号以相同的因子减小。因此，有效Q因子的增加不会影响频移测量中的信噪比，但会影响FM-AFM中测量力的定量性。此外，通过实验证实了有效Q因子的增加会降低频率噪声和频移。
