**5. Sensing of dipole fields force in scanning tunneling and force microscopy experiments**

The electric field of dipoles localized at the atomic steps of metal surfaces due to the Smoluchowski effect were measured from the electrostatic force exerted on the biased tip of a scanning tunneling microscope. By varying the tip-sample bias the contribution of the step dipole was separated from changes in the force due to van der Waals and polarization forces. Combined with electrostatic calculations, the method was used to determine the local dipole moment in steps of different heights on Au(111) and on the 2-fold surface of an Al-Ni-Co decagonal quasicrystal.

#### **5.1 Background**

The different electronic structure of the atoms at steps and terraces of metal surfaces is thought to be responsible for their different (often-enhanced) chemical reactivity. Dipole moments are postulated to exist localized at the steps due to incomplete screening of the positive ion cores by conduction electrons, because the spatial variation of the charge density is limited by the Fermi wavelength. This is known as the Smoluchowski effect (Smoluchowski, 1941). Indirect support for this assumption is provided by work function () measurements. Besocke and Wagner found a decrease in proportional to the step density on Au(111) (Besocke & Wagner, 1973) and used this to estimate the average value of the step dipole. Similar results have been reported for Pt(111) and W(110) (Kral-Urban et al., 1977l; Besocke et al., 1977). Calculations using the jellium model (Ishida & Liebsch, 1992) predict that the localized step dipole increases with step height and screening length. Electronic structure calculations for the (111) and (100) microfacet steps on Al(111) produced very small dipole moments (Stumpf & Scheffler, 1996), indicating that the Smoluchowski effect alone is insufficient to fully describe the electronic structure of steps. It is therefore important that the presence and the magnitude of local dipole moments at steps be measured experimentally.

Scanning probe microscopy can be used to investigate the electronic structure of steps. Marchon *et al*. observed a reduction in the tunneling barrier at surface steps on sulfur-covered Re(0001) (Marchon et al., 1988) using scanning tunneling microscopy (STM). Later Jia *et al.* used this effect to calculate the step dipole for Au(111) and Cu(111) (Jia et al., 1998a; 1998b). Arai and Tomitori investigated step contrast as a function of tip bias on Si(111) (7x7) using dynamic atomic force microscopy (D-AFM) (Arai & Tomitori, 2000) and suggested that step dipoles could explain their observations. In contrast Guggisberg *et al.* investigated the same system using STM feedback combined with D-AFM force detection and concluded that the step dipole moments in Si(111)-(7x7) were negligible (Guggisberg et al., 2000). They attributed the D-AFM contrast effects to changes in the van der Waals and electrostatic polarization forces, which are reduced above and increased below the step edges relative to the flat terrace.

In this work we report measurements of the strength of the fields produced by the step dipoles through direct measurement of the electrostatic force they produce on biased tips. We use a combined STM-AFM system (Enachescu et al., 1998; Park et al., 2005b) with cantilevers that are made conductive by a ~30 nm coating of W2C. Relatively stiff cantilevers of 48 or 88 N/m were used to avoid jump-to-contact instabilities close to the surface. Attractive forces cause the cantilevers to bend toward the surface during imaging, as illustrated in Fig 27(a). Scanning is done at constant current as in standard STM mode, while forces are measured simultaneously from the cantilever deflection (Park et al., 2005c).

The force acting on the tip is the sum of van der Waals and electrostatic contributions. The former is independent of the applied bias. The electrostatic contributions are additive and can be written as (Jackson, 1975):

$$F = f(D \,/\ R)V^2 + g(D \,/\ R)PV + h(D \,/\ R)P^2 \tag{1}$$

where D is the tip-surface distance, R the tip radius and *f*, *g* and *h* are functions of the tip and sample geometry. P is the dipole moment, and *V* is the electrostatic potential difference between tip and sample. The first term in (1) represents the attractive force from polarization (i.e. image charges) induced by the applied voltage. The second term is due to surface dipoles *P* interacting with the biased tip, and is proportional to the bias. The last term is the force between the dipole *P* and its image on the tip. Of these contributions only the second term is linear with applied voltage, and provides an easy way to determine the net effect of the dipole field.

#### **5.2 Experimental**

132 Atomic Force Microscopy – Imaging, Measuring and Manipulating Surfaces at the Atomic Scale

distance between the graphite layer and the underlying Pt substrate. The increased distance acts much like a tunneling barrier. In our measurements, we are able to measure current independently of topography, since the tip-sample contact is affected only by the mechanics of the system. The STM technique uses feedback on current to measure topography, so, for example, in the case of the blanketed Pt step, the STM tip would see the decrease in current and move closer to the sample to compensate. Thus, an STM image of a blanketed step would show a topographic step in the graphite layer with a width of 0.2 nm (i.e., typical STM resolution), while contact AFM indicates that the step width is many tens of nanometers. This width is the distance from the platinum step where the graphite layer begins to separate from the platinum substrate. Since the PCM technique is capable of separating mechanical and electrical measurements, it can offer additional insight into the

The STM images of Land et al. (Land et al., 1992a; 1992b) indicate that there is local conductivity modulation at both the lattice and the moiré periodicities. If we imagine the atoms in our AFM contact contributing to the contact current as a collection of STM tips, one for each atom, the total contact current would be the sum of the contribution of these tips. We would still expect to see both the lattice and the moiré periodicities in the resulting PCM image, although the magnitude of modulation relative to the average current would decrease. The modulation would sum to zero only in special, destructively interfering cases.

**5. Sensing of dipole fields force in scanning tunneling and force microscopy** 

The electric field of dipoles localized at the atomic steps of metal surfaces due to the Smoluchowski effect were measured from the electrostatic force exerted on the biased tip of a scanning tunneling microscope. By varying the tip-sample bias the contribution of the step dipole was separated from changes in the force due to van der Waals and polarization forces. Combined with electrostatic calculations, the method was used to determine the local dipole moment in steps of different heights on Au(111) and on the 2-fold surface of an Al-

The different electronic structure of the atoms at steps and terraces of metal surfaces is thought to be responsible for their different (often-enhanced) chemical reactivity. Dipole moments are postulated to exist localized at the steps due to incomplete screening of the positive ion cores by conduction electrons, because the spatial variation of the charge density is limited by the Fermi wavelength. This is known as the Smoluchowski effect (Smoluchowski, 1941). Indirect support for this assumption is provided by work function () measurements. Besocke and Wagner found a decrease in proportional to the step density on Au(111) (Besocke & Wagner, 1973) and used this to estimate the average value of the step dipole. Similar results have been reported for Pt(111) and W(110) (Kral-Urban et al., 1977l; Besocke et al., 1977). Calculations using the jellium model (Ishida & Liebsch, 1992) predict that the localized step dipole increases with step height and screening length. Electronic structure calculations for the (111) and (100) microfacet steps on Al(111) produced very small dipole moments (Stumpf & Scheffler, 1996), indicating that the Smoluchowski

electronic and tribological properties of surfaces.

This will be discussed in more detail in a future work.

**experiments** 

**5.1 Background** 

Ni-Co decagonal quasicrystal.

The measurements were carried out in ultra high vacuum with an optical deflection AFM. Several samples were used, including Pt(111), Au(111) and the two-fold surface of a Al74Ni10Co16 decagonal quasicrystal prepared by cutting the crystal parallel to the ten-fold axis. The growth and characterization of the Al-Ni-Co quasicrystal are outlined in detail elsewhere (Fisher et al., 1999). Due to the aperiodic nature of the atomic layering in the latter sample, steps of various heights were readily obtained on a single surface. The Pt single crystal and the quasicrystal (Park et al., 2004) samples were sputtered and annealed in UHV.

Nanoscale Effects of Friction, Adhesion and Electrical Conduction in AFM Experiments 135

Earlier studies of decagonal Al-Ni-Co quasicrystal surfaces (Kishida et al., 2002) indicate that the bulk structure consists of pairs of layers with 5-fold quasiperiodic structure stacked along the 10-fold direction with a periodicity of 0.4 nm. In our 2-fold surface this produces rows of atoms arranged periodically. The rows are separated by distances varying in an aperiodic manner and are parallel to the step edges. Most steps have heights of 0.5, 0.8 and 1.3 nm, although a few are observed also with 0.2 nm. The ratios of these heights follow the golden mean ( ~1.618), characteristic of their quasiperiodic nature. Fig. 28(a) shows a topographic profile perpendicular to the 10-fold axis, along with corresponding force profiles acquired at +1.2 and –1.2 V tip bias (at 100 pA tunneling current). Fig 28(b) shows similar topographic and force profiles across single and double-height steps on Au(111) at +3 and –3 V tip bias. Like in the Pt case, there is a reduction of the attractive force when the tip crosses over the steps (upward peaks in the force profile). While this reduction is present for both + and – bias, there is a noticeable difference between the two. The difference between forces at opposite biases eliminates all contributions except that from the second term in equation (1), which is purely due to the step dipole. We can immediately conclude that the positive end of the step dipole points up, consistent with a smaller attractive force at

0 20 40 60 x (nm)

2.5Å 5Å 5Å

8Å 8Å 2Å 13Å

=+1.2V

=-1.2V

Vt

Vt

8Å


Fig. 28. (a) Height and force profiles across steps for positive and negatively biased tip (I = 0.1nA) on the Al-Ni-Co quasicrystal surface showing steps of multiple heights (0.2, 0.5, 0.8 and 1.3 nm). (b) Height and force profile across steps on a Au(111) surface. Small relative peak shifts in the force profiles are caused by noise and thermal drift. Vt is the tip voltage


height (nm)



0

5Å

height (nm)

5

positive tip bias.

Fn (unit : 20nN)

attractive

repulsive

repulsive

attractive

with respect to the sample.

(a)

(b)

Vt

Vt =-3V

=+3V

Fn (unit: 5nN)

The Au sample was in the form of a thin film on glass, prepared in air by flame annealing and transferred to vacuum without further treatment. An average tip radius of 30-70 nm was determined by SEM imaging.

#### **5.3 Results and discussions**

Figure 27(b) and 27(d) shows the STM topography and force image of Pt(111) obtained simultaneously for a tip bias of –0.2 V. Fig 27(c) is a height and force profiles across the line in (b). The force, which is always attractive, increases by ~1.5 nN as the tip approaches the bottom of the step and decreases by ~4 nN after climbing over the step. When the attractive force increases, the STM current feedback loop retracts the base of the cantilever to keep the tunnel current, and hence the tip-sample distance, constant. The reduction of attractive force in the upper side of the steps is due to the reduction in the van der Waals and polarization part of the force (image charges), since in that position half of the surface (the lower terrace) is farther away from the tip. This is consistent with the results of Guggisberg (Guggisberg et al., 2000). By itself this result does not prove the existence of localized dipoles at the steps. For that we need to examine the changes in the force due to applied bias.

Fig. 27. (a) STM-AFM configuration using a conductive cantilever bending in response to forces. (b) 70 nm x 70 nm STM image of a Pt (111) surface (Vt = –0.2V, I=0.16nA). (c) Height and force profile across the steps. The force on the tip is more attractive at the bottom of the steps and less attractive at the top. (d) Force image simultaneously acquired with (b). Yellow and blue colors represent low and high attractive forces, respectively.

The Au sample was in the form of a thin film on glass, prepared in air by flame annealing and transferred to vacuum without further treatment. An average tip radius of 30-70 nm

Figure 27(b) and 27(d) shows the STM topography and force image of Pt(111) obtained simultaneously for a tip bias of –0.2 V. Fig 27(c) is a height and force profiles across the line in (b). The force, which is always attractive, increases by ~1.5 nN as the tip approaches the bottom of the step and decreases by ~4 nN after climbing over the step. When the attractive force increases, the STM current feedback loop retracts the base of the cantilever to keep the tunnel current, and hence the tip-sample distance, constant. The reduction of attractive force in the upper side of the steps is due to the reduction in the van der Waals and polarization part of the force (image charges), since in that position half of the surface (the lower terrace) is farther away from the tip. This is consistent with the results of Guggisberg (Guggisberg et al., 2000). By itself this result does not prove the existence of localized dipoles at the steps. For that we need to examine the changes in the

was determined by SEM imaging.

**5.3 Results and discussions** 

force due to applied bias.

(a)



(b) <sup>D</sup> h

(c) (d)

height

force

and blue colors represent low and high attractive forces, respectively.


Fig. 27. (a) STM-AFM configuration using a conductive cantilever bending in response to forces. (b) 70 nm x 70 nm STM image of a Pt (111) surface (Vt = –0.2V, I=0.16nA). (c) Height and force profile across the steps. The force on the tip is more attractive at the bottom of the steps and less attractive at the top. (d) Force image simultaneously acquired with (b). Yellow

height (nm)

(b)

4Å

0

2

4

force (nN)

More attractive

Less attractive

6

8

10

R

Earlier studies of decagonal Al-Ni-Co quasicrystal surfaces (Kishida et al., 2002) indicate that the bulk structure consists of pairs of layers with 5-fold quasiperiodic structure stacked along the 10-fold direction with a periodicity of 0.4 nm. In our 2-fold surface this produces rows of atoms arranged periodically. The rows are separated by distances varying in an aperiodic manner and are parallel to the step edges. Most steps have heights of 0.5, 0.8 and 1.3 nm, although a few are observed also with 0.2 nm. The ratios of these heights follow the golden mean ( ~1.618), characteristic of their quasiperiodic nature. Fig. 28(a) shows a topographic profile perpendicular to the 10-fold axis, along with corresponding force profiles acquired at +1.2 and –1.2 V tip bias (at 100 pA tunneling current). Fig 28(b) shows similar topographic and force profiles across single and double-height steps on Au(111) at +3 and –3 V tip bias. Like in the Pt case, there is a reduction of the attractive force when the tip crosses over the steps (upward peaks in the force profile). While this reduction is present for both + and – bias, there is a noticeable difference between the two. The difference between forces at opposite biases eliminates all contributions except that from the second term in equation (1), which is purely due to the step dipole. We can immediately conclude that the positive end of the step dipole points up, consistent with a smaller attractive force at positive tip bias.

Fig. 28. (a) Height and force profiles across steps for positive and negatively biased tip (I = 0.1nA) on the Al-Ni-Co quasicrystal surface showing steps of multiple heights (0.2, 0.5, 0.8 and 1.3 nm). (b) Height and force profile across steps on a Au(111) surface. Small relative peak shifts in the force profiles are caused by noise and thermal drift. Vt is the tip voltage with respect to the sample.

Nanoscale Effects of Friction, Adhesion and Electrical Conduction in AFM Experiments 137

suitable choice of positions, a relatively small number of point charges (less than 10) can reproduce the potential over the surface of the sphere within ~1%. In this method the relative positions of the point charges and dipoles within the tip are fixed; only the magnitudes of the

For the present geometry, six point charges were distributed along the surface normal between the center and the sphere boundary, plus two symmetrical pairs of point dipoles located off-axis in the plane defined by the surface normal and the line dipole *P*. Once the effective charges were determined, the tip-sample forces were calculated as the sum of the forces between the point charges *qi*, *pi*, their image charges *qi*', *pi*' below the surface plane, and the fixed line dipole *P*. The field distribution calculated using these parameters is

Step height (nm)

0.5 1.0 1.5

sample

Fig. 30. (a) Difference in the force experienced by the tip at the steps for positive and

negative bias, per unit applied volt [nN/V]. Open symbols correspond to steps on Al-Ni-Co quasicrystal surface. Filled symbols to steps on Au(111). The lines are calculations for 1 Debye and 0.45 Debye per step atom respectively; by definition they pass through the origin. The error bar is associated with the noise level of force measurement. (b) Electric field distribution calculated using the GICM in the tip-sample region with a permanent

**R=70nm**

**R=30n<sup>m</sup>**

tip

0.5nm

charges are changed as the tip-sample geometry is changed.

(a)

2f *d*-Al-Ni-Co

Au (111)

shown in Fig. 30(b).

0

b

dipole

dipole close to the tip apex. (R=30 nm, D=0.5 nm).

1

2

(Force)/[2(Volt)] (nN/V)

3

4

Approach curves (force and current versus distance at fixed bias) were used to determine an STM tip-sample distance of 0.5 0.1 nm during tunneling as shown in Fig. 29. Tunnel current vs. voltage curves for all samples showed a metallic character, with no significant dependence on bias polarity, so there is no change in the tip-sample distance under STM feedback when polarity is reversed. Force *vs* voltage curves over flat terraces reveal a small tip-sample contact potential difference of 0.14 V for the quasicrystal and 0.20 V for gold. This contact potential difference is negligible compared with the applied bias and cannot account for the polarity-dependent force contrast at step edges.

The tip radius can be extracted from the force-distance curves as described in previous work (Sacha et al., 2005) that shows that the effective tip radius is given by R= 36A/V2, where A is the slope in the plot of electrostatic force F, versus 1/D, F is in nanonewton, 1/D in nm–1, V in volts, and R in nm, as shown in the inset of Fig. 29.

Fig. 29. Force and current-distance curves measured on Au(111) at a tip bias of –3V. Before contact the electrostatic force bends the tip towards the surface. This attraction is used to calculate the tip radius (inset), from the slope of F vs. 1/D, yielding R =30 nm.

Results from measurements using the polarity-dependent component of the force (i.e., the difference between forces at V+ and V– bias, divided by 2|V|) at steps of various heights are shown in figure 30(a). As can be seen, the experimental points follow a straight line. To determine the magnitude of the step dipole moment, we compute the electrostatic force using the *Generalized Image Charge Method* (GICM) program (Mesa et al., 1996; Gómez-Moñivas et al., 2001), a variational method for solving electrostatic problems that is particularly efficient for problems with high symmetry. The tip is modeled by a sphere of radius R, which is an equipotential surface produced by a series of point charges *qi* and dipoles *pi* at fixed positions *rj* within the sphere. The magnitudes of the charges are adjusted to reproduce the boundary conditions of a constant potential *V* at radius R, and the sample surface at ground. With a

Approach curves (force and current versus distance at fixed bias) were used to determine an STM tip-sample distance of 0.5 0.1 nm during tunneling as shown in Fig. 29. Tunnel current vs. voltage curves for all samples showed a metallic character, with no significant dependence on bias polarity, so there is no change in the tip-sample distance under STM feedback when polarity is reversed. Force *vs* voltage curves over flat terraces reveal a small tip-sample contact potential difference of 0.14 V for the quasicrystal and 0.20 V for gold. This contact potential difference is negligible compared with the applied bias and cannot account

The tip radius can be extracted from the force-distance curves as described in previous work (Sacha et al., 2005) that shows that the effective tip radius is given by R= 36A/V2, where A is the slope in the plot of electrostatic force F, versus 1/D, F is in nanonewton, 1/D in nm–1, V

current force


calculate the tip radius (inset), from the slope of F vs. 1/D, yielding R =30 nm.

0123 1/D(1/nm)

Vertical displacement of piezo (nm)

Fig. 29. Force and current-distance curves measured on Au(111) at a tip bias of –3V. Before contact the electrostatic force bends the tip towards the surface. This attraction is used to

Results from measurements using the polarity-dependent component of the force (i.e., the difference between forces at V+ and V– bias, divided by 2|V|) at steps of various heights are shown in figure 30(a). As can be seen, the experimental points follow a straight line. To determine the magnitude of the step dipole moment, we compute the electrostatic force using the *Generalized Image Charge Method* (GICM) program (Mesa et al., 1996; Gómez-Moñivas et al., 2001), a variational method for solving electrostatic problems that is particularly efficient for problems with high symmetry. The tip is modeled by a sphere of radius R, which is an equipotential surface produced by a series of point charges *qi* and dipoles *pi* at fixed positions *rj* within the sphere. The magnitudes of the charges are adjusted to reproduce the boundary conditions of a constant potential *V* at radius R, and the sample surface at ground. With a

**D**





current (nA)

0

0.5

1

for the polarity-dependent force contrast at step edges.

in volts, and R in nm, as shown in the inset of Fig. 29.



Fn(nN)



normal force (nN)

0

10

20

suitable choice of positions, a relatively small number of point charges (less than 10) can reproduce the potential over the surface of the sphere within ~1%. In this method the relative positions of the point charges and dipoles within the tip are fixed; only the magnitudes of the charges are changed as the tip-sample geometry is changed.

For the present geometry, six point charges were distributed along the surface normal between the center and the sphere boundary, plus two symmetrical pairs of point dipoles located off-axis in the plane defined by the surface normal and the line dipole *P*. Once the effective charges were determined, the tip-sample forces were calculated as the sum of the forces between the point charges *qi*, *pi*, their image charges *qi*', *pi*' below the surface plane, and the fixed line dipole *P*. The field distribution calculated using these parameters is shown in Fig. 30(b).

Fig. 30. (a) Difference in the force experienced by the tip at the steps for positive and negative bias, per unit applied volt [nN/V]. Open symbols correspond to steps on Al-Ni-Co quasicrystal surface. Filled symbols to steps on Au(111). The lines are calculations for 1 Debye and 0.45 Debye per step atom respectively; by definition they pass through the origin. The error bar is associated with the noise level of force measurement. (b) Electric field distribution calculated using the GICM in the tip-sample region with a permanent dipole close to the tip apex. (R=30 nm, D=0.5 nm).

Nanoscale Effects of Friction, Adhesion and Electrical Conduction in AFM Experiments 139

The clean Pt(111) surface could be imaged in STM mode with cantilevers stiff enough to avoid the jump-to-contact instability. When such a surface is brought into contact with a clean tip, strong bonds are formed that cause rupture of the contact in the bulk part of the tip and/or substrate upon separation. Sliding is strongly impeded in this case and always

With passivated tips, low adhesion energy contacts (~1 J/m2) are formed. The friction properties of such contacts depend on whether additional adsorbate layers are also present on the Pt surface. Passivated areas of the surface give rise to low friction and sigmoid-type I-V characteristics, typical of poorly conductive or semiconducting materials. Clean Pt areas

Clean Pt can be imaged in contact mode with passivated tips and gives rise to atomic lattice stick-slip friction with the Pt(111) lattice periodicity. This is the first time that a chemically active metal surface has been imaged in UHV in AFM contact-mode, revealing stick-slip with atomic lattice periodicity, and indicates that the passivating layer on the WC tip is bound strongly enough to the tip that material is not transferred to the active Pt even in

The results indicate that even in ultrahigh vacuum conditions, transfer of low-conductivity, passivating material can easily occur in nano-scale contacts. This demonstrates that detailed studies of third-body processes at the nanoscale are accessible with this AFM-STM multifunctional approach. The presence of these species substantially effects friction and adhesion. These results are relevant to the understanding of transfer film formation and its influence on the structural evolution and tribology of interfaces, whose inelastic properties

We presented the first results of the combination of PCM and AFM techniques, in which current images, obtained on contacts many nanometers in diameter produced by very high loads (up to 5 GPa), reveal the atomic scale periodicity of the substrate. This surprising observation indicates that, even after averaging over many contact points of atomic

We also showed that PCM is capable of measuring variations in local conductivity with a lateral resolution that is similar to the corresponding AFM resolution. Moreover, the technique is capable of separating mechanical and electrical contributions to the measured current. We were able to determine that local conductivity variations arise from different sources, namely, moiré superstructure and the conductivity to the underlying substrate.

We favor point-contact current imaging of lattice resolution as an explanation for many of the STM images on graphite presented in the past, especially in the first decade of STM experiments. In these experiments, it is likely that the tip was in contact with the surface, as in PCM, which explains the weak dependence of "tunneling" current as a function of tip

Point contact current imaging, in conjunction with simultaneous friction and topographic imaging, should be an important tool in current efforts to understand the atomic origin of friction. We are currently applying these techniques to study the tribological behavior of

leads to severe cantilever deformations and distorted force-displacement curves.

conditions where substantial energy dissipation takes place during friction.

are only beginning to be probed and understood at the nanometer scale.

dimension, the lattice periodicity does not average out.

distance.

surfaces.

produce Ohmic contact characteristics.

The radii of the tips used for the Au and Al-Ni-Co samples derived from the forcedistance curves was found to be 30 11 nm, and 70 30 nm respectively. Calculations performed for several values of tip radius and for 0.5 nm for D, are shown in figure 30(a) as a function of step height and step dipole moment (Park et al., 2005a). As we can see the data (difference in the force at + and – bias per unit applied volt) fit well the lines corresponding to step dipole values of 1.6 Debye/nm or 0.45 Debye/step atom for Au(111) monoatomic steps (Park et al., 2005a) with the tip radius of 30 nm, and 2.5 Debye/nm or 1.0 Debye/step atom for the smallest (0.2 nm) quasicrystal steps with the tip radius of 70 nm. We can conclude that the dipole moment scales proportionally to step height, at least for steps up to 1.5 nm.

The dipole moment obtained for Au(111) is ~3 times larger than the value of 0.16 Debye/atom obtained by Jia *et al.* (Jia et al., 1998a; 1998b) from STM barrier height measurements and ~2 times larger than the 0.20 to 0.27 Debye/atom obtained by Besocke *et al.* (Besocke & Wagner, 1973) from work-function measurements on stepped Au(111). Bartels *et al.* (Bartels et al., 2003) obtained 0.33 Debye/atom for Cu(111) steps from STM spectroscopy of localized states at step edges. Apart from systematic and statistical errors in the measurements, the discrepancy could be related to the very different methods used, tunneling barrier in one case and average work function in another as compared to direct measurement of the dipole force field in the present work.
