Atomic resolution with high-eigenmode tapping mode atomic force microscopy

Atomic surface structure imaging is instrumental for the understanding of surface-related phenomena. Here, we show that conventional tapping mode atomic force microscopy with high cantilever eigenmodes and subnanometer amplitudes allow routine atomic imaging at atmospheric pressures. We identify the reasons for failure of atomic resolution imaging employing low eigenmodes. Strong tip-surface interactions cause significant differences between the oscillatory behaviors of the inclination of the cantilever as detected by conventional instruments and of the vertical position of the tip, which prevents correct functioning of instrumental feedback control loops. However, high effective spring constants of high eigenmodes make it possible to overcome the problem. Furthermore, the combination of high effective elastic constants of high cantilever eigenmodes with the high flexibility of the cantilever substantially enhances the imaging stability, thereby universally allowing atomic imaging of solid surfaces in gaseous environments and at elevated temperatures. Demonstrated imaging examples include single sulfur vacancies at the surface of ${\mathrm{MoS}}_2$ crystals imaged at temperatures ranging from room temperature to 250°C and potassium ions on hydrophilic and highly adhesive muscovite mica surfaces. Moreover, the high imaging stability allows knocking atoms off the ${\mathrm{MoS}}_2$ surface by hard tapping, indicating the potential for ultrahigh resolution lithography.

Figure 1

Distance dependencies of (a) average tip-surface forces, (b) normalized deflection amplitudes, and (c) phase shifts between excitation and cantilever deflection. The data were recorded with a generic tapping mode cantilever (NSC15) excited at frequencies matching its first (black/gray curves), second (magenta/light magenta), and third (blue/light blue curves) eigenmodes of a freely oscillating cantilever. The tip was first approaching (black/magenta/blue curves) and then retracting (gray/light magenta/light blue curves) from the ${\mathrm{MoS}}_2$ surface. The data were taken without active feedback control loops, i.e., excitation frequency and excitation amplitude remained constant. (d) First, (e) second, and (f) third eigenmode resonance curves taken with the same cantilever. The black and red curves show the amplitudes and phases, respectively. The green dashed line shows the fits with the solution for the driven damped harmonic oscillator. (c) As evident in the phase signal, the first mode goes out of resonance as the tip approaches the sample, while the third eigenmode excitation remains near resonance. The soft/hard tapping bar in (a) and (b) shows roughly the third eigenmode amplitude setpoints used to produce images shown in Figs. 5 and 6 in soft tapping and to knock off atoms in hard tapping. The “soft” imaging is achieved at $\sim 0$ force. The two vertical dotted lines in (a)–(c) are guides for the eye, illustrating the oscillation amplitude of $\sim 0.8\mathrm{nm}$.

Figure 2

The distance dependences of (a) average forces, (b) frequency shifts, (c) excitation powers, and (d) normalized amplitudes for first (black/gray curves), second (magenta/light magenta curves), third eigenmodes (blue/light blue curves). The color coding is the same as in Fig. 1. Two feedback control loops were on: The first feedback control loop kept the excitation frequency on resonance by keeping the phase shift $\sim {90}^{\circ }$, the second feedback control loop kept the amplitude constant by adjusting the excitation power. Such feedback control loops are typically employed in the frequency modulation (FM) atomic force microscopy (AFM). The frequency shift near the surface reduces from >70 kHz to a few kilohertz from first to third eigenmode. Additionally, excitation power required to keep the inclination amplitude reaches hardware saturation for the first eigenmode. We discuss that it is a sort of an instrumental artifact (see discussion)—for strong tip-surface interactions, with the inclination amplitude not being useful as a feedback parameter. These results make it evident that the cantilever oscillation when excited at its third eigenmode is more stable than at its first eigenmode.

Figure 3

Sketch of the model of an atomic force microscopy (AFM) clamped spring-coupled cantilever with a uniform cross-section.

Figure 4

We explain the instability of the first eigenmode cantilever deflection amplitudes with the shift of the eigenfrequency out of the resonance with the excitation due to tip-surface interactions (see also discussion). The shift out of the resonance is influenced by the changes in the shape of the oscillating cantilever. (a) Model calculations reveal that the cantilever inclination amplitudes ($A_{\alpha }^n$) in the $n\mathrm{th}$ mode at the end of a rectangular cantilever undergo a transition from being in phase to being out of phase with the tip oscillation ($A_z^n$), as the tip-surface interactions $\left(k^{*}\right)$ increase. Thus, neither phase nor cantilever inclination amplitude in the first eigenmode should be used as the feedback parameter for the strong tip-surface interactions. The large effective spring constant of the third eigenmode renders the detected cantilever amplitudes to be more stable. The sketch in (b) schematically illustrates the transition from in-phase to out-of-phase oscillations of tip position and cantilever inclination driven in resonance with its first eigenmode.

Figure 5

High-resolution atomic force microscopy (AFM) images using higher eigenmodes on various surfaces. (a) Phase image of the cleavage plane of a natural ${\mathrm{MoS}}_2$ crystal. The dashed rectangle highlights the area, which was subsequently tapped harder (Supplemental Material [41]); the inset (full rectangle) shows the same area after hard tapping. A few atoms were knocked off from the highlighted area. The white arrows highlight three atomic defects, which exist before and after the hard tapping; the red arrows highlight four newly created defects. A movie of knocking off the atoms is provided in the Supplemental Material [41]. (b) Phase image of a graphite surface. The white sketch in the figure the atomic scale honeycomb structure of graphene. (c) Phase image of an arachidic acid layer on a graphite surface. Inset shows height image taken simultaneously. The white sketch shows to scale the structure of an arachidic acid monolayer; the yellow dashed parallelogram shows the unit cell (adapted from Ref. [42]); the sketch was positioned to visually match the imaged pattern. (d) Height image of a ${\mathrm{MoS}}_2$ monolayer on an amorphous quartz substrate revealing defects and domain boundaries. Inset shows the fast Fourier transform (FFT) of the image, revealing a few domains. One of the domains is highlighted with white circles in the FFT and with lines in the topography image, respectively.

Figure 6

(a) and (b) Two subsequently acquired phase images of muscovite mica in dry nitrogen. The images were cropped from larger images, corrected for thermal drift using the mica unit cell as a reference. Inset shows the fast Fourier transform (FFT) of the respective image; the white arrows highlight the mica unit cell frequencies. The black arrows show the slow scan directions.