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The Force Needed to Move an Atom on a Surface

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Science  22 Feb 2008:
Vol. 319, Issue 5866, pp. 1066-1069
DOI: 10.1126/science.1150288

Abstract

Manipulation of individual atoms and molecules by scanning probe microscopy offers the ability of controlled assembly at the single-atom scale. However, the driving forces behind atomic manipulation have not yet been measured. We used an atomic force microscope to measure the vertical and lateral forces exerted on individual adsorbed atoms or molecules by the probe tip. We found that the force that it takes to move an atom depends strongly on the adsorbate and the surface. Our results indicate that for moving metal atoms on metal surfaces, the lateral force component plays the dominant role. Furthermore, measuring spatial maps of the forces during manipulation yielded the full potential energy landscape of the tip-sample interaction.

In 1990, Eigler and Schweizer (1) positioned single Xe atoms with atomic-scale precision on a Ni(110) surface using a scanning tunneling microscope (STM). This technique of atom manipulation has subsequently been used to build model physical systems—such as quantum-confined structures (2, 3), magnetic nanostructures (4, 5), and artificial molecules (6, 7)—one atom at a time. In the most common STM manipulation technique, the adsorbate follows the tip by hopping from one surface binding site to the next, because a partial chemical bond is formed between the apex atom of the tip and the adsorbed atom or molecule. Previous studies of the manipulation process with STM (8, 9) were highly revealing but could not determine the forces involved in manipulation. Recently, the atomic force microscope (AFM) has been used to manipulate atoms at semiconducting surfaces (10), even at room temperature (11, 12). Atom manipulation with an AFM is particularly promising, because it allows the direct measurement of the required forces.

In this work, we used an AFM to quantify the forces required to pull individual adsorbates along a surface. We find that moving cobalt (Co) on Pt(111) requires a lateral force of 210 pN and that this force is independent of the vertical force. The lateral force can vary substantially with the chemical nature of the underlying surface as it is only 17 pN for Co on Cu(111). For both surfaces, the force on the tip due to the Co atom is nearly spherically symmetric. In contrast, for manipulating a carbon monoxide (CO) molecule, the forces are more complex, deviating markedly from spherical symmetry.

We used a frequency modulated AFM (13) with the qPlus sensor design (14) operating in ultrahigh vacuum at a temperature of ∼5 K. A metal tip was mounted on an oscillating cantilever (resonance frequency f0 = 21,860 Hz) and used to probe the surface and move the adsorbates (Fig. 1A). The stiff cantilever (spring constant k0 ≈ 1800 Nm–1) allows stable, small amplitude oscillation (A = 30 pm) close to the surface. We monitored the shift of the oscillation frequency Δf, which for small A is roughly proportional to the vertical stiffness kz ≈ 2k0/f0 × Δf of the tip-sample junction (13). To allow comparisons with STM manipulation experiments, we also detected the tunneling conductance G between tip and surface (15).

Fig. 1.

Simultaneous AFM and STM measurements of individual adsorbates. (A) An atomically sharp metal tip is oscillating in z with an amplitude A = 30 pm over a flat metal surface on which an individual Co atom or CO molecule is adsorbed. The measured frequency shift of the cantilever from its natural resonance frequency is proportional to the vertical stiffness kz of the tip-sample interaction. A small bias voltage of 1 mV was applied between tip and sample to measure the tunneling current, which is proportional to the conductance G, given in units of the single-channel, spin-degenerate quantum of conductance G0 = 2e2/h = (12,906 ohm)–1, where e is the elementary charge and h is Planck's constant. The inset graph shows the tip motion z(t) between its closest distance (z') and farthest distance (z'+2A) from the sample. The ball models of the surfaces are scaled to match the dimensions of the images in the following panels. (B to E) Images measured at a constant height z' close to the threshold for adsorbate motion. (B) The tip-sample stiffness of a single Co atom on Pt(111). (C) Tip-sample conductance measured simultaneously for the same system as in (B). (D and E) Same as (B) and (C) for a single CO molecule on Cu(111). The colored curves in the panels are horizontal cross sections through the centers of the images.

Figure 1, B to E, shows constant-height images of a single Co atom on Pt(111) and a single CO molecule on Cu(111) with tip heights close to the threshold for atom manipulation. In these images, kz and G show circular symmetry, without any sign of the threefold substrate symmetry. The images obtained from Co on Pt(111) show a narrow dip in kz and a peak in G. In contrast, the images from a CO molecule on Cu(111) have a more complex structure: kz is flat around the central minimum, and G contains a central conductance peak within a broader conductance dip. For an asymmetric tip apex, kz often deviates from circular symmetry for CO (16). In these images, the change in stiffness due to the adsorbate is 17 Nm–1 on Co and 9 Nm–1 on CO, in the range of a metal-metal bond stiffness (10 to 100 Nm–1).

We can derive the force to move an atom from the measurement of kz as a function of both vertical and lateral tip position. Figure 2 shows “line scans” obtained by moving the tip parallel to the surface at constant height, passing over the top of an isolated Co atom on Pt(111). These scans were repeated at progressively smaller tip heights until the Co atom hopped to a neighboring adsorption site, as illustrated in Fig. 2A. The direction of these scans corresponds to the direction of easiest motion on this substrate: It connects two neighboring threefold hollow adsorption sites. Figure 2, C and D, shows that both G and |kz| increased as the tip height was decreased. At the smallest tip height and at a lateral position about halfway to the adjacent binding site, a sudden jump occurred in both kz and G. At this tip position, the Co atom reproducibly hopped from its initial binding site to the next and was imaged again at its new position by the continuing line scan. In contrast, the atom reliably remained at its initial binding site when the tip was only 5 pm farther from the surface.

Fig. 2.

Measuring the force to move Co on Pt(111). (A) Schematic top view of the Pt(111) surface atoms (gray) and the adsorbed Co atom (red). In the following panels, constant-height line scans in the direction of easiest adsorbate motion (x direction) were taken at successively reduced tip-sample separations until the Co atom hopped to the adjacent adsorption site [red circle in (A)]. The scan speed was ∼0.5 nm/s. (B) The force F* between tip apex and the Co atom can be divided into the lateral force Fx and the vertical force Fz*. The total vertical force Fz is the sum of Fz* and the background force FB. (C and D) Simultaneously measured conductance G and stiffness kz (circles and gray lines). Note that these values are time-averaged over the cantilever oscillation between z = z' and z = z' + 2A. We label selected line scans with the closest approach z' during the oscillation (15). (E to G) Tip-sample interaction energy U, vertical force Fz, and lateral force Fx extracted from the stiffness kz data in (D). Selected line scans are labeled with the tip height z; here, the oscillation amplitude has been deconvolved from the curves. The red arrows in (C) to (G) indicate the hop of the Co atom to the neighboring binding site. Colored lines in (C), (F), and (G) are fits with the s-wave model.

The vertical force Fz was determined by integrating kz along z. The frequency shift, and therefore kz, is an average of the tip-surface interaction over one oscillation cycle of the tip. This vertical blurring in all data was removed when computing Fz from kz, by means of a deconvolution process (17).

We interpret Fz as the sum of two components: a background force FB and the force Fz* due to the presence of the adsorbate (Fig. 2B). The background force is in large part due to long-range (van der Waals) forces (18) and increases as the tip approaches the surface but does not depend on the lateral position. The vertical force Fz* due to the adsorbate grows rapidly (Fig. 2F and fig. S3B), doubling in magnitude as z is changed by only 15 pm near the move threshold, indicating the short-range nature of this force.

We found the tip-sample interaction force to be nondissipative as long as the adsorbate did not hop to a new binding site (19). In this nondissipative range of tip positions, we calculated the tip-sample interaction potential U (Fig. 2E) by integration of Fz along z (20). The lateral force Fx was then calculated by differentiation of U in the x direction (Fig. 2G). This technique allowed us to determine forces in any direction, even though the cantilever only senses the vertical stiffness. The lateral force was zero with the tip placed above the adsorbate, grew as the tip was moved laterally until a maximum was reached, and vanished far from the adsorbate.

This procedure allows us to determine the force that it takes to move a single Co atom across a Pt(111) surface. At the point where the atom hopped, we found a lateral force Fx = 210 ± 30 pN (21). This force varied by only ±5% between different tips (22). At the same time, Fz* = –1.4 ± 0.2 nN was much larger than the lateral force and was nearly half as large as the bond-breaking force of 4 nN for a Pt point contact (23). To understand the interplay between the vertical and horizontal force components, we decreased z below the threshold height for hopping and continued to measure the forces. We found that the lateral force to move the atom remained constant, whereas the vertical force varied by a large factor (figs. S1 and S2). For the range of heights measured, Fz* at the point where the Co atom hopped varied from –0.45 nN (with the tip laterally far from the atom) to –3.0 nN (with the tip nearly above the atom). These results suggest that the lateral force is the key for the manipulation of metal adsorbates on flat metal surfaces. This insensitivity to Fz* is in contrast to the mechanism determined for moving Si atoms on Si(111) (12). There, it was found that the vertical force plays a dominant role by causing a reduction of the energy barrier between two adsorption sites as a result of relaxation of the Si adsorbate and surface.

The force that is required to move an atom strongly depends on the supporting substrate. Much smaller forces were sufficient to manipulate Co atoms on Cu(111) (fig. S3). Here, the required lateral force was only 17 ± 3 pN, even though Cu and Pt are both face-centered cubic (fcc) crystals and the Co atom binds at a three-fold hollow site on both surfaces. This indicates that the nature of the chemical bonding plays a strong role. For Cu, the bonding is dominated by hybridization of the electronic states of the Co adsorbate with the 4s metal band, which shows no discernible direction dependence. In contrast, extra bonding occurs on Pt resulting from its partially filled and strongly directional 5d bonds (24), which apparently increase the forces necessary for manipulation.

To explore the spatial symmetry of the tip-adsorbate force, we modeled it as depending only on the tip-adsorbate distance [for details, see the supporting online material (SOM) text]. For this model, which is similar to the one suggested by Braun and Hla (25), the distance dependence of the force was derived from Fz* measured at x = 0 (fig. S4). Despite the simplicity of this model, it agrees well with Co on Pt(111), as shown in Fig. 2, and with Co on Cu(111), as shown in fig. S3. This observed spherical symmetry of the force between the Co adsorbate and the tip apex suggests that the interaction occurs primarily via s-wave orbitals in both the tip-apex atom and the Co atom.

The manipulation forces for Co and a small molecule (CO) differed dramatically even though both adsorbates move on Cu(111) at a similar tunneling conductance in STM experiments (8). We found that the lateral manipulation force for CO molecules (160 ± 30 pN) is an order of magnitude larger than that for Co atoms (Fig. 3 and fig. S3). More importantly, the spatial dependence of the forces was markedly different. For example, Fz* at closest tip-sample approach before hopping was almost independent of the lateral tip position around the center of the molecule and became repulsive at x ≈ ±300 pm (Fig. 3). This dependence is in contrast to the s-wave nature of the forces that we found for metal adsorbates.

Fig. 3.

Vertical and lateral forces for manipulating CO on Cu(111). Vertical (A) and lateral (B) force components when moving the tip over a CO molecule on Cu(111) for different tip heights z. The x direction corresponds to the easiest adsorbate motion from an on-top binding site to an adjacent one via a bridge site. The blue arrows mark a repulsive force Fz* = FzFB of up to 20 pN between tip and molecule (see inset). At z = 80 pm, the molecule hopped between neighboring binding sites (red arrows). The green line in (B) is a linear fit to the lateral force with a slope of 1.2 N/m.

At small tip heights, the adsorbate follows the tip from binding site to binding site (8, 9). Under these conditions, maps of the forces and the tip-sample interaction potential can be constructed by combining kz images obtained at various tip heights both above and below the manipulation threshold (26). Figure 4A shows this interaction potential for Co manipulated on Cu(111). The most stable adsorption sites are the fcc hollow sites (9), which appear as minima in the potential map. The neighboring hexagonal close-packed (hcp) sites have a slightly higher potential energy. We note that the Co atom can only be stabilized on this binding site when the tip is in close proximity (9). The fcc and hcp sites were separated by a potential barrier of 35 ± 5 meV, whereas the highest potential of 160 ± 30 meV occurred when the tip was placed above an on-top site of the surface. In contrast, in the potential landscape of Co on Pt(111), the barrier is 200 ± 30 meV and the two types of threefold hollow sites are essentially indistinguishable (fig. S5E). The potential landscape for an adsorbed CO molecule (Fig. 4B) clearly reflects the different symmetry of the binding site. In this case, we found that the bridge site had the lowest barrier (70 ± 10 meV) between two on-top binding sites.

Fig. 4.

Tip-adsorbate energy landscape during manipulation. Two-dimensional potential landscapes of the tip-sample interaction energies during controlled manipulation of Co (A) and CO (B) on Cu(111). The energy scales of the color-coded images are shifted so that U = 0 at the preferred adsorption site for Co (fcc hollow site) and CO (on-top site). The underlying Cu(111) lattice is superimposed as a ball-and-stick model. The size of each image is 550 × 480 pm2. (For more details, see fig. S5.)

For all three systems, the measured potential barrier height for positioning the tip between two neighboring adsorption sites is in close agreement with the diffusion barrier for adsorbate motion as determined by density functional theory [37 meV for Co on Cu(111)] (27) and experiments performed without the presence of a probe tip [75 meV for CO on Cu(111) (28) and 200 ± 10 meV for Co on Pt(111) (29)]. Although diffusion experiments detect the lowest barrier of the adsorbate-surface potential landscape without the presence of a tip, our measurements determine the potential for moving the tip resulting from all interactions among tip, surface, and adsorbate.

The present method for measuring the full tip-sample potential landscape and the forces necessary to manipulate atoms and molecules in arbitrary directions provides important information about the manipulation process without relying on advanced simulations such as density functional theory. It could give additional impetus to the exploration of atomic-scale friction and atom and molecule diffusion on surfaces and offer a deeper insight into controlled bottom-up assembly mechanisms. A systematic investigation of the manipulation forces on different surface-adsorbate combinations is now possible, and the driving mechanism to create future nanoscale devices can be explored in a quantitative manner.

Supporting Online Material

www.sciencemag.org/cgi/content/full/319/5866/1066/DC1

SOM Text

Figs. S1 to S5

References and Notes

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