High-speed atomic force microscope imaging: Adaptive multiloop mode

In this paper, an imaging mode (called the adaptive multiloop mode) of atomic force microscope (AFM) is proposed to substantially increase the speed of tapping mode (TM) imaging while preserving the advantages of TM imaging over contact mode (CM) imaging. Due to its superior image quality and less sample disturbances over CM imaging, particularly for soft materials such as polymers, TM imaging is currently the most widely used imaging technique. The speed of TM imaging, however, is substantially (over an order of magnitude) lower than that of CM imaging, becoming the major bottleneck of this technique. Increasing the speed of TM imaging is challenging as a stable probe tapping on the sample surface must be maintained to preserve the image quality, whereas the probe tapping is rather sensitive to the sample topography variation. As a result, the increase of imaging speed can quickly lead to loss of the probe-sample contact and/or annihilation of the probe tapping, resulting in image distortion and/or sample deformation. The proposed adaptive multiloop mode (AMLM) imaging overcomes these limitations of TM imaging through the following three efforts integrated together: First, it is proposed to account for the variation of the TM deflection when quantifying the sample topography; second, an inner-outer feedback control loop to regulate the TM deflection is added on top of the tapping-feedback control loop to improve the sample topography tracking; and, third, an online iterative feedforward controller is augmented to the whole control system to further enhance the topography tracking, where the next-line sample topography is predicted and utilized to reduce the tracking error. The added feedback regulation of the TM deflection ensures the probe-sample interaction force remains near the minimum for maintaining a stable probe-sample interaction. The proposed AMLM imaging is tested and demonstrated by imaging a poly(tert-butyl acrylate) sample in experiments. The experimental results demonstrate that the image quality achieved by using the proposed AMLM imaging at a scan rate of 25 Hz and over a large-size imaging (50 $\mu \text{m}\times 25$ $\mu$m) is at the same level of that obtained using TM imaging at 1 Hz, while the probe-sample interaction force is noticeably reduced from that achieved using TM imaging at 2.5 Hz.

Figure 1

Schematic block diagram of the rms-$z$-feedback control in conventional TM imaging.

Figure 2

A schematic plot of probe-sample interaction distance vs the probe sample interaction force.

Figure 3

Height difference between two points on the sample surface during TM imaging.

Figure 4

Schematic block diagram of the proposed AMLM imaging.

Figure 5

$d_{\text{TM}}$ vs $A_{\mathrm{def}}/A_{\mathrm{free}}$.

Figure 6

Sample topography images (scan area, 50 $\mu \text{m}\times 25$ $\mu$m; scan direction, 50 $\mu$m) obtained by using the TM imaging at the scan rate of (a1) 1 Hz and (b1) 2.5 Hz; the corresponding TM deflection measured at (a2) 1 Hz and (b2) 2.5 Hz; and the corresponding sample topography quantified using Eq. (4) at (a3) 1 Hz and (b3) 2.5 Hz.

Figure 7

Comparison of the cross sections at the same scan line of the three images as marked out in Figs. 6(a1), 6(a3), and 6(b3).

Figure 8

Top-view plot (i.e., image) of the $z$-piezo displacement obtained using (a) the proposed AMLM-imaging technique at a scan rate of 25 Hz and (b) TM imaging at a scan rate of 2.5 Hz, respectively.

Figure 9

Comparison of the $z$-piezo displacement profile at the same cross-section location as marked out in Figs. 8, 8(b), and 6(a3).

Figure 10

Phase images obtained using (a) the proposed AMLM-imaging technique at a scan rate of 25 Hz and (b) TM imaging at a scan rate of 2.5 Hz, respectively.

Figure 11

Comparison of the averaged probe-sample interaction force (i.e., the TM deflection) (a1) by using AMLM imaging at 25 Hz to (a2) that by using TM imaging at 2.5 Hz, and (b1), (b2) the images of the corresponding tapping-amplitude ratio ($A_{\mathrm{def}}/A_{\mathrm{free}}$), and the comparisons of (c1) the averaged force and (c2) the tapping-amplitude ratio at the cross section location marked in (a1) to (b2).

Figure 12

Comparison of the topography image obtained (a) using the proposed AMLM-imaging technique at the scan rate of 25 Hz to (b) the TM image at 1 Hz and (c) comparison of the corresponding topography profile cross sections.

Figure 13

Comparison of the sample topography error obtained using the proposed AMLM imaging at 25 Hz to those obtained by using TM imaging at 1 and 2.5 Hz [with respect to the sample topography at the 1 Hz TM scan quantified via Eq. (4)].

Figure 14

The sample topography image obtained using the proposed AMLM imaging at (a1) 40 Hz and (a2) the zoomed-in image, and images of the corresponding (b1) averaged force and (b2) the tapping-amplitude ratio ($A_{\mathrm{def}}/A_{\mathrm{free}}$), respectively.