The Potential of 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 (XPS) 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 an Au(111) surface via di ﬀ erent docking groups. In addition to changing the docking chemistry (and the associated interface dipoles), the impacts of polar tail group substituents and varying dipole densities are also 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 di ﬀ erence 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.

Changes in core level binding energies can be probed by X-ray photoelectron spectroscopy (XPS) [66][67][68][69][70], which is one of the default techniques for characterizing SAMs, used, for example, for analyzing the quality of self-assembled monolayers and to verify bonding [67,[71][72][73][74][75][76][77][78][79][80][81][82]. In this paper we will argue that the electrostatic core level shifts make XPS an ideally suited tool for probing interface dipoles. For supporting that claim, we will use state of the art quantum-mechanical simulations to determine core level shifts encountered in biphenyl-based SAMs attached to an Au (111) substrate by a variety of chemically different docking groups. To the best of our knowledge, a corresponding set of experimental XPS data with systematically varied docking groups and consistent film structures and morphologies does not exist yet. Nevertheless, first steps in that direction have been undertaken and biphenyl-based SAMs on various metallic substrates have been studied, albeit with a clear focus on thiol docking groups [60,73,[81][82][83][84][85][86][87][88][89]. We, however, do not consider this to be an all too serious problem for a study focusing on the conceptual physical aspects that allow a determination of interface dipoles by XPS. Moreover, we have high confidence in the employed computational approach, which is described in the following section. This confidence is based on the fact that in the past we have performed several joint theoretical and experimental studies on aliphatic [63,64] and aromatic [22,48,49] SAMs bonded to the substrate by thiol and dithiocarbamate [90] groups, for which we observed an excellent agreement between measured and simulated core level shifts.
In the present study we will show that core level spectroscopy is not only useful for measuring chemical shifts or to explore the role of dipoles contained in the adsorbates. Rather, it can also be used as a tool for systematically determining the "interface dipole" at the interface between a substrate and an adsorbate.

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 [91][92][93][94][95] (see also aimsclub.fhi-berlin.mpg.de) and periodic boundary conditions. The Perdew-Burke-Ernzerhof (PBE) [96,97] functional was used for describing exchange and correlation. Furthermore, long-range van der Waals interactions were accounted for by employing the surface version [98] of the Tkatchenko-Scheffler dispersion correction [99], which was specifically parameterized for treating adsorbing molecules on metal substrates. The dispersion correction between the Au atoms of the metal slab was turned off. All calculations were done with the so-called tight basis set for all atomic species (as supplied by FHI-aims). A thorough description of the corresponding basis functions is included in the Supplementary Materials. Reciprocal space was sampled by a converged Γ-centered 15 × 10 × 1 grid for the full coverage systems and by accordingly smaller sized grids for larger super cells. The change of the volume-integrated electron density was converged to 10 −5 e − and the total energy to 10 −6 eV.
Interfaces were modeled 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 quantum-mechanically and electrostatically decoupled by a vacuum gap of more than 20 Å and a self-consistent dipole correction [100,101]. The geometries of the adsorbate molecules and the top two Au-layers 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 xand y-directions and removing all but one molecule from the resulting cell (see Supplementary Materials). 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 [102].
The change of the work function was obtained from the difference of the calculated work functions at the bottom side of the Au(111)-slab (Φ Au = 5.10 eV for all systems) and above the self-assembled monolayer. Furthermore, the work function change of the nominally non-interacting system, i.e., the SAM without a docking group moved 1 Å away from the substrate compared to its equilibrium adsorption distance (see Section 3.2), was defined as a reference point relative to which the work function changes (∆Φ) for all other systems are reported. The difference between lower and upper slab work function for the reference system amounts to δΦ 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 of the core level binding energies, but yields relative shifts between different systems [65,68,[103][104][105][106][107][108]. We have also found it to provide a very good description of core level shifts in SAMs [21,22,48,49,63,64]. In fact, when modeling the X-ray photoelectron (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 [22,49,90,109] yields an excellent correlation with experimental data. Therefore, throughout the manuscript (like for the work functions) core level shifts are reported relative to the nominally non-interacting reference system consisting of a SAM without the docking group moved 1 Å away from the substrate compared to its equilibrium adsorption distance (see Section 3.2). The calculated value of that reference energy was −263.95 eV.
Another complication when employing the initial-state approach is that (in contrast to final-state approaches) [68,70,110,111] 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 of thousands of atoms in order to avoid spurious collective electrostatic effects due to periodic replicas of the core holes (and the compensation charges) [63,112]. 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 Supplementary Materials [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 lower-lying 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 Supplementary Materials. To obtain the final spectra, the discrete peaks were convoluted with a Gaussian function with a variance of 0.3 eV. A flowchart summarizing the simulation procedure can be found in the Supplementary Materials. Furthermore, for the sake of reproducibility, we also provide all FHI-aims input and output files for all simulations contained in this manuscript. The data set has been uploaded to the NOMAD database and can be accessed and downloaded via the doi: 10.17172/NOMAD/2020.08.13-1.
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 [35,63,121,122] in semiconducting substrates (and their modification by the adsorbate layer) can be avoided.
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) [27,31,40,42,45,46,63,123,124], 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, ∆Φ. 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, ∆E C1s , that is equivalent to ∆IB. This shift is directly translated into a modification of the kinetic energies of the electrons, E kin , 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, such a charge transfer typically modifies the core level binding energies [68,69,125,126], which has also been observed for simulations on SAMs [90]. In experiments on extended, upright standing molecules it will, however, be often inconsequential for the measured spectra, as the atoms in the immediate vicinity of the interface mostly affected by these "chemical" shifts hardly contribute to the measured spectra, especially when using primary photon energies of a few hundred eV in synchrotron measurements. This is a consequence of the finite escape depth of the photoelectrons. The situation changes for experiments with typical lab sources with primary photon energies of, e.g., 1253.6 eV (Mg-Kα) and 1486.6 eV (Al-Kα), for which the attenuation length can be larger than the typical thickness of SAMs. Thus, for properly resolving the electrostatic shifts discussed her, the said synchrotron experiments are preferable (also because of the often higher energy resolution).
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.
∆Φ. 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. Figure 1. Schematics of the energy landscape of a metal-self-assembled monolayer (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 Figure 1. Schematics of the energy landscape of a metal-self-assembled monolayer (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 E C1s . The shift of the electrostatic energy due to the interface dipole, ID, determines the changes in the injection barriers, ∆IB, and the core level shifts, ∆E C1s . The work function change, ∆Φ, 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 kinetic energy of E kin . 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, e.g., when additional dipoles are contained along the backbones of the molecules [15,17,[19][20][21][22].

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 [71,72,74,79,127], 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 [85]. As docking groups we considered thiolates (system I) [71,72,74,79], methyl thiolates (system II) [71,72,74,79], pyridines (system III) [54,[128][129][130][131][132][133], isocyanides (system IV) [39,[133][134][135]] and cyanides (system V). The structures of all investigated systems can be seen in Figure 2. Furthermore, 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 dipole-free 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 Supplementary Materials). The electronic structure of system VIa is essentially identical to what is obtained when assuming vacuum-level alignment between an 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 Supplementary Material). 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].
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 21 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 was used as an energy reference for the work function as well as for the core level binding energies (for the absolute values of the reference energies see the Methods Section). This directly yields ∆E C1s and ∆Φ (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 Supplementary Materials, 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 electronvolts. 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 [31,40,45,46,63].
In passing we note that, to the best of our knowledge, there is no systematic experimental study of docking group induced shifts in a series of well-ordered monolayers, but there are examples comparing thiols and isocyanides: Zangmeister et al. compared 4,4 -ethynylphenyl-1-benzenethiols on polycrystalline Au bonded either by thiols or by isocyanides and for the isocyanide-docked SAMs they observed a C1s peak at 0.6 eV higher binding energy than for the thiol case [138]. There is also indirect evidence that such shifts occur in other types of SAMs: when comparing thiolate and isocyanide bonded acene SAMs, Kim et al. measured a distinctly larger ionization energy of the isocyanide-bonded system with the shift between the valence orbitals amounting to 0.7 eV [139]. Unfortunately, they did not report corresponding C1s core level spectra, but, as discussed above, the shifts of valence and core levels have the same physical origin. Overall, the results in [138,139] are well in line with the data for systems I and IV in Figure 3, where the somewhat larger shift in the simulations is presumably due to assumed perfect ordering of the SAMs.
Superimposed on the electrostatic shifts of the XPS peaks, one can also identify the chemical shifts due to the differently bonded carbon atoms (cf. Figure 3a). 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. Additionally, 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 ∆Φ as a function of ∆E C1s 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 ∆Φ vs. ∆E C1s (at least for similar coverages and tilt angles), as the non-interacting biphenyl monolayer is used as the reference for both quantities.
connecting the two benzene rings are shifted by 0.5 eV relative to the other carbon atoms of the rings. Additionally, 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 ∆Φ 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 ∆Φ vs. ∆EC1s (at least for similar coverages and tilt angles), as the non-interacting biphenyl monolayer is used as the reference for both quantities. . Correlation between the change in work function, ∆Φ, and the shift in binding energy, ∆EC1s, for all systems relative to system VIa (as non-interacting reference system in which no interface dipole occurs). The black line indicates a linear curve with a slope of 1 through the origin. The shaded area represents the range over which the values for ∆EC1s vary between systems I, VII, and VIII.

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 . Correlation between the change in work function, ∆Φ, and the shift in binding energy, ∆E C1s , for all systems relative to system VIa (as non-interacting reference system in which no interface dipole occurs). The black line indicates a linear curve with a slope of 1 through the origin. The shaded area represents the range over which the values for ∆E C1s vary between systems I, VII, and VIII.

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 -NH 2 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. Additionally, in VIII the shift of the peak remains comparably small (amounting to only 0.19 eV), as there are only the topmost carbon atoms in the two molecules per unit cell that are affected by the presence of the amine. This means 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.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 21 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. Additionally, in VIII the shift of the peak remains comparably small (amounting to only 0.19 eV), as there are only the topmost carbon atoms in the two molecules per unit cell that are affected by the presence of the amine. This means 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 3.1. Figure 5. (a) Simulated shifts of carbon 1s orbital energies, ∆EC1s, as a function of the escape depth of the electrons for the equally docked systems I, VII, and VIII and (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 x-axis 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 the Methods Section and the Supplementary Materials). Based on the Helmholtz solution to the Poisson equation, one would expect a linear dependence of the dipole density and, thus, of ∆Φ and ∆EC1s on coverage. The actual coverage-dependence of ∆Φ and ∆EC1s is shown in Figure 6 for the same systems that had already been considered in Figure 3. Interestingly, one observes that ∆Φ 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 [140][141][142][143][144][145][146][147][148]. 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 [149]. (a) Simulated shifts of carbon 1s orbital energies, ∆E C1s , as a function of the escape depth of the electrons for the equally docked systems I, VII, and VIII and (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 x-axis 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.
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 3.1.

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 the Methods Section and the Supplementary Materials). Based on the Helmholtz solution to the Poisson equation, one would expect a linear dependence of the dipole density and, thus, of ∆Φ and ∆E C1s on coverage. The actual coverage-dependence of ∆Φ and ∆E C1s is shown in Figure 6 for the same systems that had already been considered in Figure 3. Interestingly, one observes that ∆Φ 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 [140][141][142][143][144][145][146][147][148]. 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 [149].
Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 21 Figure 6. Core level shift, ∆EC1s, (circles) and work function change ∆Φ (square symbols) for systems I, III, IV, and VI as a function of coverage (varied between full, a quarter, and 1/16 coverage, where the latter approaches the single molecule limit, see Supplementary Materials). All energies are reported relative to the values of the non-interacting reference system VIa.
Another observation in Figure 6 is that the coverage-dependence of the core level binding energies (circles and solid line) is much weaker than that of ∆Φ (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 ∆Φ values is significantly larger than that for ∆EC1s. As a result, the slope of the linear fit to the dependence of ∆Φ on ∆EC1s (black lines in Figure 7) significantly decreases with decreasing coverage. Figure 6. Core level shift, ∆E C1s , (circles) and work function change ∆Φ (square symbols) for systems I, III, IV, and VI as a function of coverage (varied between full, a quarter, and 1/16 coverage, where the latter approaches the single molecule limit, see Supplementary Materials). All energies are reported relative to the values of the non-interacting reference system VIa.
Another observation in Figure 6 is that the coverage-dependence of the core level binding energies (circles and solid line) is much weaker than that of ∆Φ (squares and dotted line). This is particularly obvious for system VI, for which there is almost no change of ∆E C1s 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 ∆Φ values is significantly larger than that for ∆E C1s . As a result, the slope of the linear fit to the dependence of ∆Φ on ∆E C1s (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 full-coverage case, see above) ∆E C1s is no longer a direct measure for the interface dipole. This can be explained by the different degrees of locality with which ∆Φ and ∆E C1s probe the electronic structure of the interface [48,148,150]. The value of ∆Φ 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 [48]. 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 subsystems 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).
Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 21 Figure 7. Core level shift, ∆EC1s, as a function of the work function change, ∆Φ, for system I (blue), system II (red), system III (orange), system IV (green), and system VI (violet). Results for full, ¼, and 1/16 coverage are compared. The black lines are fits to all systems for specific coverages, while the colored lines were fitted to the coverage-dependence for a specific system.
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 ∆Φ and ∆EC1s probe the electronic structure of the interface [48,148,150]. The value of ∆Φ 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 [48]. 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, Figure 7. Core level shift, ∆E C1s , as a function of the work function change, ∆Φ, for system I (blue), system II (red), system III (orange), system IV (green), and system VI (violet). Results for full, 1 /4, and 1/16 coverage are compared. The black lines are fits to all systems for specific coverages, while the colored lines were fitted to the coverage-dependence for a specific system.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 21 For all systems we assumed perfectly ordered structures, which is triggered by the fact that especially for thiol-bonded SAMs highly ordered monolayers can be routinely obtained in carefully performed experiments. Still, in the following the possible consequences of deviations from perfect interfaces shall be briefly summarized: reduced dipole densities diminish the observed shifts, as can be inferred from the description in Section 3.1 and as discussed explicitly in Section 3.3.3. This also applies, when disorder reduces the net dipole per docking group perpendicular to the surface, i.e., although the shifts discussed in Section 3.3.1 are comparably large, for imperfect samples high- For all systems we assumed perfectly ordered structures, which is triggered by the fact that especially for thiol-bonded SAMs highly ordered monolayers can be routinely obtained in carefully performed experiments. Still, in the following the possible consequences of deviations from perfect interfaces shall be briefly summarized: reduced dipole densities diminish the observed shifts, as can be inferred from the description in Section 3.1 and as discussed explicitly in Section 3.3.3. This also applies, when disorder reduces the net dipole per docking group perpendicular to the surface, i.e., although the shifts discussed in Section 3.3.1 are comparably large, for imperfect samples high-resolution measurements will be necessary. In passing we note that lateral inhomogeneities of the dipole density can result in a significant broadening of the spectra and in extreme cases even in the occurrence of multiple peaks, as we showed for mixed monolayers of embedded-dipole SAMs [48]. This is a consequence of XPS probing the local electrostatic potential at the atom from which the electron is excited. Similar considerations would apply to substrates with laterally inhomogeneous local work functions. Finally, it should be noted that the actually measured electrostatic shifts are determined by the "true" interface dipoles, where contaminants at the interface, e.g., for ex-situ prepared samples (or also the presence of ad atoms) can change the situation compared to the model case assumed in simulations. When dealing with strongly bonded adsorbates, like thiolates, one, however, is in the fortunate situation that their bonding to noble metal substrates typically displaces contaminants, which also explains, why for the XPS simulations on model systems mentioned in the introduction section, we typically obtained a favorable agreement with experiments on ex-situ prepared samples [22,48,49,63,64,90].

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 an 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 1 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).