X-Ray Photoelectron Spectroscopy for Determining Interface Dipoles of Self-Assembled Monolayers

In the current manuscript we assess to what extent X-ray photoelectron spectroscopy is a suitable tool for probing the dipoles formed at interfaces between self-assembled monolayers and metal substrates. To that aim, we perform dispersion-corrected, slab-type band-structure calculations on a number of biphenyl-based systems bonded to a Au(111) surface via different docking groups. In addition to changing the docking chemistry (and the associated interface dipoles), also the impacts of polar tail-group substituents and varying dipole densities are investigated. We find that for densely-packed monolayers the shifts of the peak positions of the simulated XP-spectra are a direct measure for the interface dipoles. In the absence of polar tail-group substituents they also directly correlate with adsorption-induced work-function changes. At reduced dipole-densities this correlation deteriorates, as work function measurements probe the difference between the Fermi-level of the substrate and the electrostatic energy far above the interface, while core level shifts are determined by the local electrostatic energy in the region of the atom from which the photoelectron is excited.


Computational Methodology
The structural and electronic properties of the metal-SAM interfaces were simulated by density functional theory, DFT, employing the all-electron, full potential FHI-aims code version 190715 [89][90][91][92][93] and periodic boundary conditions. The Perdew-Burke-Ernzerhof (PBE) [94,95] functional was used for describing exchange and correlation. Furthermore, long-range van der Waals interactions were accounted for by employing the surface version [96] of the Tkatchenko-Scheffler dispersion correction, [97] which was specifically parametrized for treating adsorbing molecules on metal substrates. The dispersion corrections between the Au atoms of the metal slab were turned off. All calculations were done with the so-called tight basis set for all atomic species (as supplied by FHIaims). A thorough description of the corresponding basis functions is included in the Supporting Information. Reciprocal space was sampled by a converged -centered 15×10×1 grid for the full coverage systems and by accordingly smaller sized grids for larger super cells. The change of the electron density was converged to 10 -5 eand the total energy to 10 -6 eV.
Interfaces were modelled employing the repeated-slab approach with the Au(111) substrate represented by five metal layers. The bottom three Au layers were kept fixed in all calculations to avoid spurious relaxations at the bottom surface. The periodic replicas of the slabs were quantummechanically and electrostatically decoupled by a vacuum gap of more than 20 Å and a selfconsistent dipole correction. [98,99] The geometries of the adsorbate molecules and the top two Aulayers in the full coverage unit cells were fully relaxed until the remaining forces on each atom were below 10 -3 eV/Å . The geometries of the other supercells considered here were directly derived from the full coverage unit cell by replicating it in x-and y-directions and removing all but one molecule from the resulting cell (see Supporting Information). These supercells were considered as model systems to study the impact of diluting the interfacial dipoles. Thus we fixed the remaining molecule in the geometry it adopts in the densely-packed layer, to prevent it from falling over. [100] The change of the work function () is defined as the difference of the calculated work functions at the bottom side of the Au(111)-slab (Au = 5.10 eV for all systems) and above the selfassembled monolayer. Furthermore, the work function change of VIa, i.e. the difference between the pristine Au(111) and the SAM moved 1 Å further away from its equilibrium adsorption distance, was defined as a reference point for all other calculations and amounts to ref = 0.11 eV.
The core-level binding energies were calculated using the initial state approach, relying on the Kohn-Sham eigenvalues of the respective orbitals. This approach does not provide absolute values 3 of 25 of the core-level binding energies, but yields relative shifts between different systems. [63,68,101-

106]
We have also found it to provide a very good description of core-level shifts in SAMs. [21,22,48,49,64,65] In fact, when modelling the XP spectra of (partially) aromatic hydrocarbon SAMs bonded to Au substrates, we typically find that shifting the calculated spectra to higher binding energies by between 18.9 to 19.0 eV [22,49,107,108] yields an excellent correlation with experimental data. Therefore, throughout the manuscript work-function shifts relative to the peak position of the vacuum-level aligned system VIa are reported. The calculated value of that reference energy is -263.95 eV.
Another complication when employing the initial-state approach is that (in contrast to final-state approaches) [68,[109][110][111] it does not account for core-hole screening effects. Unfortunately, final-state approaches are not applicable to systems like the ones considered here, as in conjunction with periodic boundary conditions one would need unit cells comprising thousands of atoms in order to avoid spurious collective electrostatic effects due to periodic replicas of the core holes (and the compensation charges). [64,112] Therefore, we resorted to an a posteriori correction of screening by the metal substrate relying on an image charge model, which is explained in detail in the Supporting Information. [113,114] In passing we note that screening by the metal substrate has only a comparably minor impact on the spectra shown below, as we are dealing with rather extended, upright standing molecules, whose spectra are dominated by excitations of atoms, which are rather far away from the substrate. To account for the finite escape depth of the photoelectrons from lowerlying atoms, we scaled their contributions by an exponential attenuation function [115] setting the incident photon energy to 580 eV, as described in detail in the Supporting Information. To obtain the final spectra, the discrete peaks were convoluted with a Gaussian function with a variance of 0.3 eV.
For the analysis and visual representation of the data, Python was used in combination with NumPy [116] and matplotlib [117]. Ovito [118] was applied for generating the 3D view of the systems and for the 2D potential plot we used VESTA. [119] Finally, the figures were compiled with GIMP. [120]

Energetics of a metal-SAM interface
For understanding the correlation between XP spectra and interface dipoles, it is useful to first consider how interface dipoles impact the electronic properties of a system consisting of an inorganic substrate and a chemically bonded monolayer (formed by upright-standing molecules). For the sake of simplicity, in the following we will focus on metal substrates. In this way, further complications due to band-bending effects [35,64,121,122] in semiconducting substrates (and their modification by the adsorbate layer) can be avoided.

Figure 1: Schematics of the energy landscape of a metal-SAM interface and an XPS experiment
(disregarding the bias voltage applied between substrate and detector). The interface electronic structure is characterized by the work function, Φ, by the alignment of the frontier levels determining electron-and hole-injection barriers, EIB and HIB, and by the energetic positions of the core levels, here exemplarily denoted as EC1s. The shift of the electrostatic energy due to the interface dipole, ID, determines the changes in the injection barriers, DIB, and the core-level shifts, DEC1s. The work-function change, DΦ, is additionally influenced by the energetic shift due to the tail-group dipole, TD. Absorption of an X-ray photon with energy hν creates a photoelectron, which at the position of the detector has a with kinetic energy Ekin. Additional positive potentials (not included in the plot) applied to the detector relative to the substrate increase the measured kinetic energy of the photoelectron. The top panel sketches the metal-SAM interface, whose properties are determined by the interface-and the tail-group dipole. In passing we note that the actual situation can be further complicated, when additional dipoles are contained along the backbones of the molecules. [

15,17,19-22]
A schematic representation of the electronic structure of the metal-SAM interface is shown in Figure 1 for the case of a SAM in which an interface-dipole occurs (virtually all SAMs) and in which also a functional tail group is used bearing a tail-group dipole. Due to the superposition of the fields generated by the dipoles in the densely-packed monolayer (i.e., due to collective electrostatic effects), [27,31,40,42,45,46,64,123,124] steps in the electrostatic energy occur. The steps due to the interface dipole, ID, and due to the tail group dipole, TD, are indicated by vertical blue arrows. The sum of these two energy shifts causes the change in substrate work function due to monolayer adsorption, . Conversely, only the interface dipole is responsible for the change in injection barriers, IB, which determines the final electron-and hole-injection barriers, EIB and HIB, respectively. The core levels are shifted in line with the frontier levels. Consequently, the interface dipole should result in a shift of the positions of the core levels relative to the Fermi-level of the substrate, EC1s, that is equivalent to IB. This shift is directly translated into a modification of the kinetic energies of the electrons, Ekin, and, thus, in a shift of the XP spectra.
In this context it is important to stress that the above considerations disregard energetic shifts due to interfacial charge transfer processes, which could significantly modify the energies of strongly localized orbitals (i.e., the core levels). Indeed, for the atoms in a SAM that are in the immediate vicinity of the interface, this typically modify the core-level binding energies, [67][68][69]110,125,126] an effect that has also been observed for simulations on SAMs. [108] In experiments on extended, upright standing molecules it will, however, be inconsequential for the measured spectra, as the atoms in the immediate vicinity of the interface affected by these "chemical" shifts hardly contribute to the measured spectra. This is a consequence of the finite escape depth of the photoelectrons.
Finally, it should be mentioned that in the absence of an energetic shift due to a tail group dipole (or when comparing differently docked systems with identical tail-group dipoles), the above considerations imply that SAM-induced changes of the substrate work-function should directly correlate with shifts in core-level binding energies. Below, we will test under which circumstances such a situation is encountered at a metal-SAM interface.

Investigated Systems
To assess the possibility of probing bond dipoles by X-ray photoelectron spectroscopy, we simulated SAMs on Au (111) surfaces, as such systems have been studied extensively, [70,71,73,78,127] which qualifies them as prototypical model systems. As molecular backbones we chose biphenyls with two molecules per (3 × √3)rect surface unit cell arranged in a herringbone structure. [84] As docking groups we considered thiolates (system I), [70,71,73,78] methyl thiolates (system II), [70,71,73,78] pyridines (system III), [54,[128][129][130][131][132][133] isocyanides (system IV) [39,[133][134][135]] and cyanides (system V). For the sake of comparison, we also simulated an upright-standing biphenyl layer not bearing a dedicated docking group (system VI) which represents a metastable structure, as the equilibrium configuration for the biphenyl-Au interface would very likely be flat-lying molecules. Due to different interfacial charge rearrangements and intrinsic dipole moments associated with the docking groups in these six systems, we expect distinct variations of the respective interface dipoles. Notably, in system VI, the only reason for an interface dipole would be Pauli-pushback. [47,136,137] To eliminate also that effect and to generate an essentially dipolefree interface, we also considered a system with the biphenyl layer shifted by 1 Å further away from the substrate (system VIa). In passing we note that increasing the distance from the substrate by yet another 1 Å does not change the spectrum (see Supporting Information). The electronic structure of system VIa is essentially identical to what is obtained when assuming vacuum-level alignment between a Au(111) surface and a free-standing biphenyl monolayer (the calculated work-function reduction is on the order of 0.1 eV; for further information see Supporting Information). Additionally, we considered two systems bearing electron accepting (system VII) and electron donating (system VIII) tail-group substituents. These are known to change the work function without affecting the alignment of the frontier levels. [27]

Energetic shifts due to variations in the interface dipole
In Figure 3, we show the core-level binding energies and XP spectra of systems I, III, V, and VIa as prototypical examples for the impact of the docking groups on the core-level binding energies. In the following, the "vacuum level alignment" system VIa is used as energy reference for the workfunction as well as for the core-level binding energies (for the absolute values of the reference energies see Methods section). This directly yields EC1s and  (i.e, the quantities shown in Figure 1). As far as the systems not displayed in Figure 3 are concerned, the data points for II essentially coincide with those of I and (apart from chemical shifts for the carbon atoms directly bonded to nitrogen atoms) the binding energies of III and V are also similar. System VI is similar to VIa with binding energies shifted to higher values by 0.34 eV. The corresponding data can be seen in the Supporting Information, where we show a (somewhat busy) plot analogous to Figure 3 containing values for all investigated systems. Compared to System VIa, the core-level binding energies in all chemically bonded SAMs are shifted to higher (more negative) binding energies by several eV. The effect is largest for III, for which the shift amounts to 2.8 eV (see black arrow). Even between docked systems, the peak positions vary by 1.6 eV with the smallest value (-265.2 eV) for the methyl thiolate and the largest (-266.8 eV) for the pyridine. This is exactly the situation one would expect according to Figure 1 for varying interface dipoles as a consequence of collective electrostatic effects. [31,40,45,46,64] Superimposed on these electrostatic shifts of the XPS peaks, one can also identify the chemical shifts due to the differently bonded carbon atoms (cf. Figure 2a). For example, the carbon atoms connecting the two benzene rings are shifted by ~0.5 eV relative to the other carbon atoms of the rings. Also the carbon atoms attached to the docking groups are chemically shifted, resulting in distinct variations of the binding energies. This is, however, rather inconsequential for the positions and shapes of the XP spectra as a consequence of the finite escape depth of the photoelectrons. This is well visible, for example, for the isocyanide-docked SAM (system IV), where the lowest carbon atoms are shifted by ~2 eV relative to the ones in the rings. The latter still rather exclusively determine the position of the peak in the corresponding XP spectrum. Provided that the primary core-level shifts are truly a consequence of collective electrostatic effects caused by interface dipoles they should directly correlate with the SAM-induced changes in the work function for systems I to VIa. To test that, we plotted  as a function of EC1s for all investigated SAMs in Figure 4. Indeed, the data for all SAMs without polar tail group substituents align perfectly along a straight line with a slope of 1 passing through the origin. This supports the assessment that in these systems core-level shifts and work-function changes have the same origin (namely the interface dipole). In passing we note that the dipole due to the terminal C-H bond of the biphenyl cancels out for the evolution of  vs. EC1s (at least for similar coverages and tilt angles), as the non-interacting biphenyl monolayer is used as the reference for both quantities.

Influence of Different Tail Groups on the XP-spectra
This raises the question, what would happen if the SAM-forming molecules were substituted with tail-groups bearing dipoles significantly different from the terminal C-H bond of a phenyl ring. According to Figure 1, this should (significantly) modify the work-function shift, while leaving the core-level binding energies essentially unchanged, with the exception of chemical shifts experienced by carbon atoms in or directly bonded to the substituents. To test that hypothesis, we simulated systems VII and VIII containing -CN and -NH2 tail groups. As far as the simulated core-level binding energies are concerned, we find them to be very similar for all three systems (I, VII, and VIII), as shown in Figure 5. Concerning the chemically shifted C1s binding energies of the uppermost carbon atoms, for system VII the shift of the top carbon atoms in the phenylene and the carbons in the -CN groups go in opposite directions. Thus their impacts on the XP spectrum essentially cancel. As a consequence, the peak position of the C1s XP spectra of I and VII are virtually the same. Also in VIII the shift of the peak remains comparably small (amounting to only 0.19 eV), as there only the topmost carbon atoms in the two molecules per unit cell are affected by the presence of the amine. This means Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 19 July 2020 doi:10.20944/preprints202007.0406.v1 that for all systems considered in the present study, the position of the peak in the C1s spectrum is a valid measure for the interface dipole. As shown in Figure 4, in sharp contrast to the core-level spectra, the work-function changes for VII and VIII differ significantly from that of I (by 3.63 eV for VII and by -1.30 eV for VIII). This is again fully consistent with the model described in section 2. Figure 5. (a) Simulated shifts of carbon 1s orbital energies, DEC1s, as a function of the escape depth of the electrons for the equally docked systems I, VII, and VIII; (b) corresponding XP-spectra generated from the calculated energy levels. As the substituents significantly impact the extent of the SAMs above the top ring, but its volume density is rather low, the topmost carbon atom of the benzene ring was chosen as the origin of the x-axis. In this way, the axis is consistent with the xaxis of Figure 4 and the carbon rings are aligned at essentially the same positions. The large number of data points for each system is a consequence of the two inequivalent molecules per unit cell.

Coverage Dependence
As a last aspect it should be addressed to what extent the above conclusions hold for less densely packed polar layers at the interface. [42,113] To assess that, in a gedankenexperiment we constructed hypothetical low-coverage systems with upright-standing molecules (for details see Methods section and Supporting Information). Based on the Helmholtz solution to the Poisson equation, one would expect a linear dependence of the dipole density and, thus, of  and EC1s on coverage. The actual coverage-dependence of  and EC1s is shown in Figure 6 for the same systems that had already been considered in Figure 3. Interestingly, one observes that  changes much more strongly at low than at high coverages. This is a consequence of depolarization effects. These strongly reduce the interface dipoles at high coverages. [138][139][140][141][142][143][144][145][146] Therefore, work-function changes at full coverages are strongly reduced compared to what one would expect based on the dipoles associated with the adsorption of a single molecule. [147]  Another observation in Figure 6 is that the coverage-dependence of the core-level binding energies (circles full line) is much weaker than that of  (squares and dotted line). This is particularly obvious for system VI, for which there is almost no change of EC1s with coverage, while the work function still changes by ~0.5 eV. Qualitatively, the behavior is, however, the same for all studied systems, as shown in Figure 7. There, one sees that the energy range covered by the  values is significantly larger than that for EC1s. As a result, the slope of the linear fit to the dependence of  on EC1s (black lines in Figure 7) significantly decreases with decreasing coverage. The main consequence of this observation is that at low dipole densities (in contrast to the fullcoverage case, see above) EC1s is no longer a direct measure for the interface dipole. This can be explained by the different degrees of locality with which  and EC1s probe the electronic structure of the interface: [48,146,148] The value of  is determined by the energy difference between the Fermi level and the vacuum level far above the surface, i.e., in the far field. Conversely, core-level binding energies probe the electrostatic energy in the immediate vicinity of the atom whose core electron is excited. 47 The latter is comparably close to the interface dipole at the bond between the molecule and the substrate. Thus, the shift in the electrostatic energy due to the dipole is still relevant, even if it is strongly reduced due to the drop of the shift with the inverse of the third power of the distance between atom and dipole. This is illustrated in Figure 8, where we show the change in electrostatic energy due to the formation of the bond between the pyridine-docked SAM and the metal substrate. consequently, Figure 8 does not actually reflect the impact of the entire interface dipole, but only of the part resulting from the bond dipole. This quantity, can, however, be calculated conveniently by subtracting the electrostatic energies of the sub-systems from that of the bonded interface, which is not possible for the full interface dipole. It is also well suited to qualitatively illustrate the difference between the local and the far-field situation, even if one cannot expect quantitative agreement with the data from Figures 6 and 7, which are still determined by the entire interface dipole. For the full coverage system in the bottom panel of Figure 8, the main drop in electrostatic energy occurs at the immediate metal-pyridine interface and the electrostatic energy in the region of the top ring is essentially the same as far above the sample (despite a minor potential variation at the distance of the topmost C-H bond). Conversely, at 1/16 coverage the far-field electrostatic energy far above the interface (relevant for the work function) is several tenths of an eV higher than in the region of the upper carbon atoms (determining the position of the XPS peak).

Conclusions
In the present contribution it is shown that X-ray photoelectron spectroscopy is a suitable tool for determining interface dipoles in densely-packed self-assembled monolayers. This is shown via simulations on a number of biphenyl-based monolayers bonded to a Au(111)-substrate by a broad range of different docking groups. The varying interface dipoles in these systems result in shifts of the core-level binding energies by more than one eV, concomitantly shifting also the associated XP spectra. For SAMs not bearing polar tail groups the electrostatically triggered core-level shifts directly correlate with SAM-induced work-function changes. This correlation is broken, when work functions are further modified by polar tail-group substituents. Nevertheless, even in these cases the XP spectra are a direct measure for the interface dipoles. The situation changes, when the dipole density at the interface is reduced. Then core-level binding energies are still determined by the local electrostatic energy at the atoms from which the photoelectrons are excited. This energy is, however, no longer directly representative of the magnitude of the interface dipole, as it is strongly influenced, for example, by the distance of the excited atom from the location of the dipole. As a result, also the direct equivalence between core-level shifts and work-function changes is lost at reduced coverages, even though XPS still is suited for probing the local electrostatic energy (at least as long as chemical shifts, e.g., due to interfacial charge transfer are not superimposed on the electrostatic ones).
Supplementary Materials: Additional information on the computational methodology, additional computational results and views of unit cells and supercells are available online at www.mdpi.com/xxx/s1.
Author Contributions: Thomas Taucher has performed all calculations, analyzed the results, compiled most figures, and wrote a first draft of the manuscript. Egbert Zojer, guided and supervised the research, contributed to the analysis of the data, compiled Figure 1, and revised the manuscript.

Conflicts of Interest:
The authors declare no conflict of interest.