Image correction for atomic force microscopy images with functionalized tips

It has been demonstrated that atomic force microscopy imaging with CO-functionalized tips provides unprecedented resolution, yet it is subject to strong image distortions. Here we propose a method to correct for these distortions. The lateral force acting on the tip apex is calculated from three-dimensional maps of the frequency shift signal. Assuming a linear relationship between lateral distortion and force, atomic force microscopy images could be deskewed for different substrate systems.

Figure 1

Pentacene adsorbed on (a) bare Cu(111) and (b) NaCl/Cu(111) was imaged by recording the frequency shift $\Delta f$ at a constant height of $z=0$. Dots indicate the positions of carbon atoms in the known geometry of pentacene. In comparison, one realizes that the molecule's geometric structure appears distorted. This effect is attributed to a bending of the CO due to forces acting on it. The distortions are considerably larger on the NaCl substrate as compared to the case of adsorption on the bare copper. In the right part of the image in the top panel there is a CO molecule on the surface.

Figure 2

Component of the lateral force between tip and sample above an individual pentacene molecule along the high-symmetry directions of the molecule at $z=0$. The lateral force of pentacene (and CO) on clean Cu(111) [(a) and (c)] and pentacene on NaCl [(b) and (d)] are shown with respect to the short and long axes of the molecule (directions as indicated by the arrows). The main contribution is a force pointing towards the center of the molecule. In order to reflect mainly the lateral forces acting on the CO molecule of the functionized tip, the integration of $\Delta f$ has been limited to $z_{\text{lim}}=3.95$ Å. On the NaCl substrate, the lateral force is considerably larger compared to the Cu substrate.

Figure 3

(a) Schematic illustration of the geometry and definition of $z$ and $z_{\text{lim}}$. (b) The coordinates of the positions at which one would expect the carbon atoms of pentacene on Cu(111) in the distorted AFM images are indicated by white dots, their positions according to the known structure of pentacene by yellow crosses. The dash-dotted line in (c) shows the averaged absolute lateral gradient of each image. This is a relative measure of the corrugation in each image. The solid line represents the same quantity multiplied with ${\zeta }_i$ and is a measure of the relative contribution of each image to the resulting lateral force at $z=0$. The best fit of the scaling constant $\alpha$ is displayed in (d) as a function of the upper limit of integration $z_{\text{lim}}$. The corresponding residual displacement of carbon atoms in the corrected image is shown in (e). A selected subset of $\Delta f$ images in (f) shows that the largest contribution to the lateral forces arises from the “bathtub” like depression in these images. Scale bars are 10 Å.

Figure 4

(a) $\Delta f$ image of pentacene on Cu(111) at $z\simeq 1$ Å, showing a characteristic bathtub feature. Its lateral derivatives along the short and long molecular axes are shown in panels (b) and (c), respectively (directions as indicated by the arrows). These images closely resemble the lateral forces shown in Fig. 2, establishing the direct relation between the bathtub feature and lateral forces. Scale bar is 10 Å.

Figure 5

Original and deskewed images of individual pentacene molecules at $z=0$. In (a) and (c) the original images of pentacene adsorbed on Cu(111) and on NaCl/Cu(111) are shown for easy reference (same as in Fig. 1). These images are deskewed by means of the lateral force shown in Fig. 2 and are displayed in (b) and (d).