Royal Institute of Technology (KTH), Section for Nanostructure Physics, Albanova University Center, SE-106 91 Stockholm, Sweden.
Beilstein J Nanotechnol. 2013;4:45-56. doi: 10.3762/bjnano.4.5. Epub 2013 Jan 21.
Intermodulation atomic force microscopy (ImAFM) is a mode of dynamic atomic force microscopy that probes the nonlinear tip-surface force by measurement of the mixing of multiple modes in a frequency comb. A high-quality factor cantilever resonance and a suitable drive comb will result in tip motion described by a narrow-band frequency comb. We show, by a separation of time scales, that such motion is equivalent to rapid oscillations at the cantilever resonance with a slow amplitude and phase or frequency modulation. With this time-domain perspective, we analyze single oscillation cycles in ImAFM to extract the Fourier components of the tip-surface force that are in-phase with the tip motion (F(I)) and quadrature to the motion (F(Q)). Traditionally, these force components have been considered as a function of the static-probe height only. Here we show that F(I) and F(Q) actually depend on both static-probe height and oscillation amplitude. We demonstrate on simulated data how to reconstruct the amplitude dependence of F(I) and F(Q) from a single ImAFM measurement. Furthermore, we introduce ImAFM approach measurements with which we reconstruct the full amplitude and probe-height dependence of the force components F(I) and F(Q), providing deeper insight into the tip-surface interaction. We demonstrate the capabilities of ImAFM approach measurements on a polystyrene polymer surface.
内调制原子力显微镜（ImAFM）是一种动态原子力显微镜模式，通过测量频率梳中多个模式的混合来探测非线性针尖-表面力。高质量因数的悬臂梁共振和合适的驱动梳将导致针尖运动由窄带频率梳描述。我们通过时间尺度的分离表明，这种运动等效于悬臂梁共振的快速振荡，具有缓慢的幅度和相位或频率调制。通过这种时域视角，我们分析了 ImAFM 中的单个振荡周期，以提取与针尖运动同相的针尖-表面力的傅里叶分量（F(I)）和正交于运动的分量（F(Q)）。传统上，这些力分量被认为仅取决于静态探针高度。在这里，我们表明 F(I)和 F(Q)实际上取决于静态探针高度和振荡幅度。我们在模拟数据上演示了如何从单个 ImAFM 测量中重建 F(I)和 F(Q)的幅度依赖性。此外，我们引入了 ImAFM 方法测量，通过该方法我们重建了力分量 F(I)和 F(Q)的全幅度和探针高度依赖性，从而更深入地了解针尖-表面相互作用。我们在聚苯乙烯聚合物表面上演示了 ImAFM 方法测量的能力。
