Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands.
Ultramicroscopy. 2013 Dec;135:113-20. doi: 10.1016/j.ultramic.2013.07.008. Epub 2013 Jul 19.
Experiments in Heterodyne Force Microscopy (HFM) show the possibility to image deeply buried nanoparticles below a surface. However, the contrast mechanism and the motion of the cantilever, which detects the subsurface signal, are not yet understood. We present a numerical study of the cantilever motion in different HFM modes using realistic tip-sample interactions. The results provide information on the sensitivity to the heterodyne signal. The parameters in our calculations are chosen as closely as possible to the situation in real experiments to enable (future) comparisons based on our predictions. In HFM both the tip and the sample are excited at slightly different ultrasonic frequencies such that a difference frequency is generated that can contain subsurface information. We calculate the amplitude and phase of the difference frequency generated by the motion of the cantilever. The amplitude shows a local maximum in the attractive Van-der-Waals regime and an even higher plateau in the repulsive regime. The phase shifts 180° or 90°, depending on the mode of operation. Finally, we observe oscillations in both the amplitude and the phase of the difference frequency, which are caused by a shift of the resonance frequency of the cantilever and an involved transient behavior.
外差力显微镜（HFM）实验表明，有可能对埋在表面以下的纳米粒子进行成像。然而，检测亚表面信号的悬臂梁的对比机制和运动尚不清楚。我们使用现实的尖端-样品相互作用，对不同 HFM 模式下的悬臂梁运动进行了数值研究。结果提供了有关对异频信号灵敏度的信息。我们计算中的参数尽可能接近实际实验中的情况，以便能够根据我们的预测进行（未来）比较。在 HFM 中，尖端和样品都以略不同的超声波频率激发，从而产生可以包含亚表面信息的差频。我们计算了由悬臂梁运动产生的差频的幅度和相位。在吸引力范德华（Van-der-Waals）范围内，幅度显示出局部最大值，在排斥范围内，幅度显示出更高的平台。相位根据操作模式而变化 180°或 90°。最后，我们观察到差频的幅度和相位都发生了振荡，这是由于悬臂梁的共振频率的偏移和涉及的瞬态行为引起的。
