Probing relaxations of atomic-scale junctions in the Pauli repulsion range

Clean metal as well as C60-terminated tips of an atomic force microscope probe the interaction with C60 molecules adsorbed on Cu(111) and Pb(111). The force measurements unveil a monotonic shift of the point of maximum attraction with the bias voltage. The conventional superposition of long-range van der Waals and electrostatic forces with short-range Pauli repulsion does not reproduce the shift. By phenomenologically including bias-dependent relaxations of the electrode geometry in the analytical expression for the short-range force the experimental data can qualitatively be described.


Introduction
The measurement of forces between atoms and molecules that are on the verge of forming a chemical bond belongs to the fascinating capabilities of an atomic force microscope (AFM). For instance, approaching the force sensor into the Pauli repulsion distance range where the orbital overlap between the atomic probe and a molecule is significant enables imaging of the molecular skeleton [1][2][3]. Another example is the manipulation of matter at the atomic scale, which involves the intentional movement of single atoms and molecules across a surface using the scanning probe. The required lateral forces were previously determined in AFM experiments [4].
Consequently, ample interest is directed towards atomic relaxations in junctions with ultimate dimensions and towards the underlying forces. Here, a combination of scanning tunnelling microscope (STM) and AFM experiments are presented that unravel an unexpected shift of the point of maximum attraction between two C 60 molecules with the bias voltage applied across the molecular junction. The prototypical junctions investigated consist of a C 60 -terminated metal tip and a C 60 molecule adsorbed on Cu(111). A similar shift is present for a clean metal tip and C 60 adsorbed on Pb(111). The superposition of long-range van der Waals and electrostatic attraction with short-range Pauli repulsion does not reproduce the monotonic variation of the contact point. A qualitative description of the experimental observations is achieved by phenomenologically considering voltagedependent relaxations of the electrode geometry.

Experiment
Distance-dependent force measurements were performed with a combined STM-AFM operated in ultrahigh vacuum (10 −9 Pa) and at low temperature (5.5 K). PtIr tips attached to the free prong of a quartz tuning fork, which is referred to as the qPlus configuration [40], with resonance frequency ≈29 kHz and quality factor ≈55 000 served as force probes. For measuring the tunnelling current a separate wire is connected to the tip, similar to previous assemblies [1,[41][42][43]. Simultaneous distance-dependent current and force data were acquired using a low gain (10 4 -10 6 V A -1 ) of the transimpedance amplifier. The entailed bandwidths of 500-200 kHz exceed the resonance frequency of the tuning fork and its higher harmonics. This setup and operation mode ensure the absence of cross-talk between the tunnelling current and the AFM signal [43].
Prior to the experiments the AFM tip had been prepared ex situ by focused ion beam milling to ensure a well defined macroscopic shape of the apex. In situ, the tips were prepared by field emission on and indentation into the substrate surfaces, which presumably led to coating of the tip with substrate material and microscopic changes of the tip apex. The tips were further prepared by the transfer of a single tip apex atom to the surface [10,11,16,19,20]. Such tips are particularly stable, give rise to submolecular contrast in STM images of C 60 and reliably show the signature of the Cu(111) Shockley surface state and the Bardeen-Cooper-Schrieffer energy gap of Pb(111) in spectra of the differential conductance (dI/dV ). Due to this in situ preparation protocol the tips are likely terminated by a pyramidal cluster, as previously demonstrated by calculations for Cu(111) [10] and Pb(111) [16]. Termination of the tip apex with a single C 60 molecule was routinely achieved by applying previously reported procedures [30,44]. The orientation of the tip apex molecule was determined by imaging atomic protrusions on the surface [30,45,46]. Cu(111) and Pb(111) surfaces were prepared by Ar + bombardment and annealing. C 60 molecules (purity: 99.95%) were sublimated from a heated Ta crucible onto the surfaces at room temperature. Ordered C 60 superstructures on Cu(111) were obtained after annealing the C 60 -covered surface at 400-500 K.
The vertical force, F, was calculated from the measured resonance frequency variation, Δf, using different deconvolution methods [47,48], which led to virtually identical results. Distance z=0 pm in force spectroscopy experiments is defined as the z position of the vertical force minimum at bias voltage V=0 V. Tunnelling (Contact) ranges span distances z<0 pm (z>0 pm). STM images of the sample surfaces were recorded in the constant-current mode with V applied to the sample and processed using WSXM [49]. Spectra of dI/dV were acquired by modulating the dc bias voltage with an ac signal (10 mV (root-mean-square), 500 Hz) and measuring the first harmonic of the current response with a lock-in amplifier.

Results and discussion
In previous AFM experiments the tip-sample distance was varied and the resonance frequency change of the oscillating tuning fork simultaneously measured at a fixed bias voltage for various systems [44,[50][51][52][53][54][55]. The resulting force variation is of the Lennard-Jones (LJ) type that reflects the superposition of long-range van der Waals and electrostatic attraction and short-range Pauli repulsion. In particular, the force minimum signals the onset to chemical contact [44]. Additional forces have to be considered in the presence of magnetic materials [36,56], ionic crystals or polar molecules [57,58], and semiconducting surfaces [59].
The present experiments are in part motivated by a previous report on the voltage tuning of vibrational mode energies in single-molecule junctions [60]. A voltage-dependent shift of C 60 vibrational energies was observed in simultaneous transport and surface-enhanced Raman spectroscopy experiments and rationalized in terms of a bias-driven charging of the molecule [60]. Concomitantly with the charging intramolecular as well as molecule-electrode chemical bonds are modified, which has direct impact on bond strengths and, thus, on forces that are required to induce structural relaxations. Therefore, force spectroscopy has been applied here to C 60 junctions for a wide range of negative and positive bias voltages. Figure 1 presents an illustration of the STM-AFM junction used in the experiments. A C 60 molecule terminates a pyramidal tip apex and contacts a C 60 molecule adsorbed on the substrate surface. The distances introduced in figure 1 will be explained in the following. Figure 2 summarizes representative results obtained for a junction comprising a C 60 -terminated PtIr tip and C 60 adsorbed on a Cu(111) surface (figure 2(a)). In total, ten different tips were used for force measurements on ten C 60 molecules for each individual tip. STM images of C 60 -covered Cu(111) acquired with a C 60 -terminated tip show a hexagonal arrangement of the molecules in single-layer islands ( figure 2(b)). The trefoil-like submolecular pattern indicates a specific C 60 orientation, where a C hexagon is exposed to the vacuum. In accordance with previous observations [61] and calculations [62,63] these patterns are due to the next-to-lowest unoccupied molecular orbital. In addition, the STM data of figure 2(b) are compatible with a C 60 orientation at the tip apex that exposes a C hexagon to the sample surface [63]. The inset to figure 2(b) shows an STM image of Figure 1. Sketch of a C 60 -C 60 junction with definition of distances. Distance z=0 pm is defined as the point of maximum C 60 -C 60 attraction and referred to as z c . Intervals z<0 pm and z>0 pm define, respectively, tunnelling and contact ranges. For estimating van der Waals forces the C 60 -terminated tip is approximated as a metal sphere a distance ξ apart from a metal continuum (grey shaded area). Distance ξ m denotes the distance between point-like particles in the Lennard-Jones potential (see text). the tip apex that was obtained by scanning the C 60 -terminated tip across an atomic protrusion on Cu(111). The trefoil-like structural motif corroborates the C 60 hexagon orientation at the tip apex.
Δf (z) data (distance z is defined in figure 1) were recorded for C 60 molecules embedded in an island. To this end, after positioning the tip atop the center of an adsorbed C 60 molecule (asterisk in figure 2(b)) the feedback loop was disabled at the same current and sample voltage for all spectra, followed by the retraction of the tip to the same initial position and ramping the bias voltage to the desired value. Δf (z) in tunnelling and contact ranges was then acquired by applying a linear voltage ramp to the z piezoceramic actuator hosting the probe. Figure 2(c) shows a representative evolution of Δf for the indicated bias voltages. Surprisingly, the minimum of Δf depends on the bias voltage.
The resulting vertical force (figure 2(d)) resembles the evolution of LJ-type forces, which is in accordance with previous experimental reports [44,55]. The force trace exhibits a minimum at z c , which signals the onset to molecule-molecule contact. Obviously, z c depends on the bias voltage, which reflects the observed shift for Δf. The force at contact, F c ≈−280 pN at 0.15 V, is in agreement with findings reported previously for C 60 -C 60 contacts on Cu(111) [44].
To explore the bias voltage dependence of the minimum of F, z c is plotted for bias voltages ranging from −0.8 to 1.1 V in figure 2(e). The scattering of the data in figure 2(e) may be attributed to the uncertainty of the lateral tip position above C 60 , which was previously estimated as ≈10% of the C 60 diameter [44]. A systematic analysis of a possible dependence of z c (V ) on the lateral tip position atop C 60 was not performed in this study. More remarkably, an essentially linear increase of z c from ≈−60 pm at −0.8 V to ≈95 pm at 1.1 V is observed giving rise to a slope of ∂ V z c ≈63 pm V -1 . A weak quadratic component of z c (V ) may be due to electrostatic forces (vide infra). Since the z c (V ) behaviour is dominated by the linear term, the linear variation shall be elucidated in the following. Figure 2(e) shows that the onset to contact is shifted by more than 150 pm towards larger z c . As will be discussed below, this shift does not reflect deformations of the C 60 cage since it exhibits a high mechanical stiffness [64]. Rather, relaxations of the tip-C 60 and C 60 -substrate distances are more likely. For different microtips that were obtained by in situ tip preparation z V c ¶ varied between 60 and 95 pm V -1 . Some tips gave rise to negligible z c shifts, i.e. z 0 V c ¶ » , which will be discussed at the end of the article.
It was further noticed that C 60 molecules that are differently hybridized with Cu(111) behaved similarly in force spectroscopy experiments. The different C 60 species are due to the coexistence of unreconstructed and reconstructed surface regions, which occur in the course of annealing the C 60 -covered surface [65]. In reconstructed regions, 7 Cu atoms are removed below each adsorbed C 60 molecule [65], which gives rise to a partial embedding of C 60 into the substrate surface and an enhanced coordination with Cu atoms compared to C 60 on unreconstructed Cu(111).
In order to explore whether the findings reported for C 60 -C 60 junctions (figure 2) are of general character, additional experiments were performed with clean PtIr tips and C 60 adsorbed on Pb(111) ( figure 3(a)), i.e. for markedly different junctions. C 60 molecules on Pb(111) arrange in a hexagonal array, as depicted in the STM image in figure 3(b). In addition to the molecular superstructure a moiré pattern is visible as the periodic modulation of the apparent height of C 60 molecules. For clarity the unit cell of the moiré lattice is indicated by the dashed lozenge. The moiré periodicity, 4.55±0.24 nm, is in agreement with one of the previously reported higher-order commensurate structures [66].
Bias-dependent force measurements were performed on individual C 60 molecules residing inside molecular islands, analogously to the aformentioned experiments for C 60  -. Therefore, the onset to contact is shifted by more than 100 pm towards the molecule in the probed V range, which is in accordance with the findings for C 60 -C 60 junctions ( figure 2). The monotonic shift of z c with V is remarkable since, as will be demonstrated next, it is not described by the superposition of long-range van der Waals and electrostatic together with short-range Pauli forces using conventional expressions for these forces. To see this, long-range and slowly varying van der Waals forces, F vdW , were derived from the interaction energy E vdW =−HR/(6ξ) (H: Hamaker constant) [67] between a metallic sphere of radius R and a semi-infinite metal, a distance ξ from the sphere ( figure 1). In addition, the attractive part of the LJ interaction energy, E 2 LJ m 12 m 6 e x x x x = -[( ) · ( ) ] (ε: depth of the LJ potential well), contributes to the van der Waals forces. The LJ interaction energy likewise contains the short-range repulsive part that is responsible for the Pauli force. E LJ considers the interaction of two point-like particles with equilibrium distance ξ m (figure 1). The point-like particle representing the C 60 molecule was positioned 0.7 nm above the metal surface, which corresponds to the molecular diameter. The electrostatic force, F el , between a spherical tip and a semi-infinite planar sample was inferred from the energy E R V V ln el 0 cp 2 pe x = -( ) (ε 0 : vacuum permittivity, V cp : contact voltage) [68]. V cp was extracted from the bias voltage evolution of the vertical force, F(V ) (not shown). In order to facilitate comparison with experimental data, a piezo displacement z is calculated from the electrode separation ξ via z c,0 x the distance at maximum attraction for V=0 V.
The C 60 -C 60 interaction was modelled by the LJ potential owing to its significantly better agreement with experimental data than obtained for the Girifalco potential [69]. Indeed, using the Girifalco potential that was originally conceived for the interaction between two free C 60 molecules gives rise to considerable deviations from experimental data. Most likely, the C 60 -tip and C 60 -surface hybridization and concomitant charge transfer render the Girifalco potential a less appropriate description of the metallic C 60 -C 60 contact presented here. A better agreement between force data and the Girifalco picture was previously reported for C 60 -terminated tips and C 60 adsorbed on Si(111) [70], which hints at the nearly free-molecule character on a semiconductor surface. Moreover, z c (V ) is similar for C 60 -terminated tips (figure 2(e)) and metal tips (figure 3(e)) that are presumably terminated by a single atom, which corroborates the deviation of C 60 adsorbed to the metal tip from its freemolecule state and further justifies the use of the LJ potential.
The modelling of the C 60 molecule as a metallic sphere in the expression of van der Waals and electrostatic interactions certainly represents an approximation. The metallic or dielectric nature of a C 60 molecule was debated in several works with contradictory conclusions [71][72][73]. In the present case, the metal-sphere approximation is appropriate since F(V ) recorded for a wide range of tip-surface distances covering tunnelling to contact exhibits parabolic behaviour, which is expected for the electrostatic force between a metal sphere and a semi-infinite metal. The similar behaviour of z c (V ) for C 60 -terminated tips and metal PtIr tips (vide supra) further supports the metallic character of the C 60 tip.
Forces due to permanent and induced molecular dipoles were not considered since their contribution to the total force F is negligible. In simulations based on density functional theory (not shown), C 60 was adsorbed with a C hexagon on a 4-layer Cu(111) slab modelling the substrate and on a triangular Cu cluster adsorbed to a 4-layer Cu(111) slab serving as a tip. Permanent dipoles due to charge transfer processes were calculated as ≈1.5 D (1 D=1 Debye=3.3356·10 −30 Cm) for C 60 adsorbed on Cu(111) and ≈1.8 D for C 60 on the tip at a distance between the facing C hexagons of 0.6 nm. Near contact, i.e. at a mutual C hexagon distance of 0.25 nm, the dipoles decreased to ≈1.2 D for C 60 on Cu(111) and to ≈1.3 D for C 60 on the tip due to reorganization of the accumulated charge at chemical-bond distances. Considering the molecules as point dipoles at distances 0.6 nm and 0.25 nm led to dipole-dipole forces of, respectively, 4·10 −3 nN and 3·10 −3 nN, which are two orders of magnitude lower than the measured total force. The induced dipole at 1 V may be estimated by using the experimentally determined polarizability of isolated C 60 (0.076 5 nm 3 ) [74], which yields an electric dipole moment of ≈0.2 D being even lower than the permanent dipole. Dipole moments of metal tips, which are relevant to the PtIr-C 60 contacts, were previously demonstrated to be on the order of several Debyes below 10 D [75,76]. Therefore, resulting dipole-dipole forces are still much smaller than the total force.
The superposition, F tot =F vdW +F el +F LJ , is plotted as a function of z in figure 4(a) for 0.6 V and in figure 4(b) for −0.6 V. F tot was calculated for bias voltages between −1.5 and 1.5 V leading to the z c evolution presented in figure 4(c). Table 1 summarizes the parameters used for the simulations in figures 4 and 5. z c depends weakly and in a non-monotonic way on V deviating from the experimentally observed evolution (figures 2(e), 3(e)). The close-up view of z c (V ) in figure 4(d) shows a parabola-like behaviour with a minimum at ≈0.2 V, which reflects the response to the electrostatic force that is proportional to V V cp 2 -( ) with measured V cp ≈0.2 V. Consequently, the superposition F vdW +F el +F LJ using conventional expressions for the individual forces fails in describing bias-dependent force data.
In identifying possible origins for the observed bias voltage dependence of z c several scenarios were excluded. First, C 60 is a non-polar molecule with a high polarizability [74,79]. Therefore, the electric field across the C 60 -C 60 junction polarizes the molecules giving rise to induced dipole moments. However, dipole-dipole forces are negligible in the present setup (vide supra). Second, variations in Δf (z) may be induced by high sample resistances on the order of 100 MΩ [59]. For the presented C 60 -C 60 (PtIr-C 60 ) contacts a resistance of ≈600 kΩ (≈60 kΩ) was measured, which is nearly 3 (4) orders of magnitude lower than the resistances relevant to appreciable Δf [59]. Therefore, this scenario is excluded as well. Third, electron wind forces that are due to    [81]. The linear shift of z c with V is not compatible with this complicated energy dependence and, hence, cannot be rationalized in terms of electron wind. In the following, junction relaxations depending on the bias voltage are considered. To this end, a biasdependent electrode separation, ξ+α V, is phenomenologically included in the LJ interaction energy. This suggestion is motivated by a previous density functional theory (DFT) study that revealed new equilibrium positions and orientations of C 60 in an external electric field [82]. DFT also demonstrated the linear dependence of the distance between a negatively charged oxygen atom and the supporting graphene sheet on the external electric field [83]. In addition, it was shown on theoretical grounds that a current flowing across nanometresized objects induces the non-equilibrium population of electronic states with a concomitant weakening of intramolecular bonds that leads to a deformation of the molecular object [60,84,85]. Figure 5 summarizes the calculated results considering voltage-dependent relaxations in F LJ . In contrast to the assumption of a rigid junction geometry (figure 4) the position of the force minimum, z c (squares in figures 5(a), (b)), varies considerably with the bias voltage ( figure 5(c)). Using α=30 pm V -1 leads to a monotonic evolution of z c with V ( figure 5(c)) in a distance range comparable with the experimental observations (figures 2(e), 3(e)). A linear component with slope ≈63 pm V -1 dominates the monotonic increase of z c with V.
The suggested bias-dependent relaxations may intuitively be understood by considering charge transfer processes. It was previously shown that adsorption of C 60 on Cu and Pb surfaces leads to electron transfer from the substrate to the molecule [65,[86][87][88][89]. Therefore, in PtIr-C 60 junctions the negatively charged C 60 adsorbed on Pb(111) is attracted to (repelled from) the positively (negatively) charged sample at positive (negative) bias voltage. This simple picture is consistent with the bias voltage evolution of z c in these junctions.
In the case of C 60 -terminated tips the aforementioned picture does not directly hold, in the following sense. Assuming similarly charged C 60 molecules at the tip and on the surface as well as taking into account smaller tip-C 60 than C 60 -substrate interactions [44] would lead to similar z c at negative and positive bias voltage, which is not in agreement with the observation (figure 2(e)). Therefore, the assumption of similarly charged C 60 molecules may not be applicable. The comparison of dI/dV spectra of C 60 -terminated tips with non-zero ( z 0 V c ¶ > , figure 6(a)) and negligible ( z 0 V c ¶ » , figure 6(b)) z c variations helps clarify this issue. Spectroscopic features appearing at negative bias voltage correspond to unoccupied states of C 60 at the tip. In particular, the lowest unoccupied molecular orbital (LUMO) is more than 1 eV below the Fermi energy (E F , V=0 V) for C 60 -terminated tips with z 0 V c ¶ > ( figure 6(a)). In contrast, C 60 -terminated tips with the LUMO spectroscopic signature much closer to E F (figure 6(b)) exhibit a weak shift ( z 0 V c ¶ » ) at most. The vicinity of the C 60 LUMO to E F is a measure for the extent of the charge transfer between the molecule and the metal substrate it is adsorbed on [90]. In particular, C 60 tips with z 0 V c ¶ > ( z 0 V c ¶ » ) represent C 60 molecules that received a comparatively low (high) amount of charge from the metal tip. Therefore, C 60 molecules at the tip with z 0 V c ¶ > (figure 6(a)) are less susceptible to the electric field in the junctions and behave in a similar manner as observed for the clean PtIr tip. C 60 molecules subject to larger charge transfer (figure 6(b)) exhibit a stronger displacement in the electric field and give rise to a reduced z c shift. The larger charge transfer may be related to C 60 adsorption at rather blunt tip regions, which involves more tip atoms than in the case of sharper tips.

Conclusions
The point of maximum attraction in single-molecule contacts has been explored by distance-dependent force measurements and is subject to the bias voltage across the junction. Structural relaxations of the electrode atomic geometry induced by the electric field between tip and sample acting on partially charged molecules can account for the experimental observations. The presented findings are relevant to chemical reactions in external fields at the single-molecule level.