Spatial variation of geometry, binding, and electronic properties in the moiré superstructure of MoS₂ on Au(111)

We grow MoS₂ on Au(111) by reactive MBE see section 4 for details. The preparation parameters of samples for STM/STS and for XPS/XSW are virtually identical, except that a higher coverage ($\lessapprox$1 ML) was used for the photoemission experiments.

Figure 1(a) shows an STM image (see section 4) containing two MoS₂ islands on Au(111). A multi-color scale is used, so that the gold surface (exhibiting the characteristic herringbone reconstruction [20]) appears blue and the MoS₂ islands brown with an apparent height of 1.9 Å. On the islands a hexagonal moiré superstructure is visible, resulting from the superposition of the MoS₂ and Au(111) lattice.

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Following previous studies, we identify the islands as MoS₂ nanoflakes of one monolayer height [10–15, 18, 19, 21, 22]. The apparent height of the islands is small compared with the thickness of a single MoS₂ layer as defined by the layer spacing in bulk MoS₂ of 6.147 Å [23]. However, the apparent height determined by STM strongly depends on the electronic structure and can be very different from the geometric height, especially for a semiconducting material as MoS₂. This can be illustrated by the strong dependence of the apparent height of MoS₂ on tunneling voltage [18].

The atomically-resolved STM image in figure 1(b), shows the small scale periodicity of the MoS₂ lattice and the superimposed long range periodicity of the moiré pattern where we label the different regions as top, hcp, and fcc, following [19]. The rationale of this nomenclature will be explained below. LEED (figure 1(c)) displays the characteristic moiré pattern consisting of first order spots of Au(111) and MoS₂, surrounded by satellite spots in a hexagonal arrangement.

LEED indicates the precise alignment of the lattice vectors of MoS₂ and Au(111). In consequence, also the lattice vectors of MoS₂ and those of the moiré superstructure are strictly parallel. This is well visible the STM image in figure 1(b) where even a small misalignment would be well visible due to the amplifying effect of the moiré [24]. Our finding of rotationally aligned growth of MoS₂ on Au(111) is in line with a recent study using spot profile analysis (SPA) LEED [13], a globally averaging technique with high resolution (HR) in reciprocal space.

Figure 1(d) shows the apparent height profile taken along the main diagonal of the moiré cell (gray arrow in figure 1(b)). We find a global maximum at the top and a local maximum at the bridge sites in between fcc and hcp. The peak to peak corrugation varies with tunnel conditions and tip, the largest value we found is ≈1 Å. For bias voltages close to zero the difference between the two minima is rather small. For high positive as well as large negative voltages $(\approx \pm 2$ V, not shown) one minimum appears significantly higher, which allows us to identify this region as fcc [19].

We use the moiré pattern to determine the lattice parameters with high precision, and without errors caused by piezo creep, drift, STM calibration or distortion [24]. In the case of precise alignment of both lattices as found here, the moiré unit cell is formed by $(m \times m)$ MoS₂ unit cells on $([m+1] \times [m+1])$ Au(111) unit cells ($a_{\textrm{Au}} = 2.884$ Å [25]). We find $m = 10.6~\pm 0.1$ (error is the standard deviation resulting from several measurements at different positions), leading to $a_{\textrm{MoS}_2} = (3.157~\pm 0.003)$ Å and $a_{\textrm{moir}\acute{\text{e}}} = (33.3~\pm 0.3)$ Å. The closest commensurate approximation of the moiré cell is $(11~\times 11)$ MoS₂ unit cells on $(12~\times 12)$ Au(111) unit cells, or 11-on-12 for short.

Our lattice constant agrees within error bars with the bulk lattice constant of $a_{\textrm{MoS}_2} = 3.1602$ Å [23]. The result for the periodicity of the moiré superstructure differs from recent findings. Bana et al find a 10-on-11 unit cell by SPA LEED [13]. The discrepancy may be due to difficulties in the calibration of electron diffraction patterns. Tumino et al find lattice constants of $a_{\textrm{MoS}_2} = (3.18~\pm 0.05)$ Å and $a_{\textrm{moir}\acute{\text{e}}} = (33~\pm 1)$ Å [18] determined via Fourier transformation of a large MoS₂ area, and decided to use a 10-on-11 unit cell in DFT [22]. However, the 11-on-12 supercell is also within their limits of error. Our results have increased accuracy as we take advantage of the magnifying effect of the moiré.

We perform a DFT calculation (see section 4) for one $(11~\times 11)$ MoS₂ layer on top of three ($12~\times 12$) Au layers. The relaxed structure is shown in figure 2. Three regions of high symmetry (white circles) are evident that we label by the position of S in the lower layer with respect to Au(111), because this determines the local interaction. In the top region S is on top of a gold atom, whereas in the fcc-region (hcp-region) it resides in a threefold-hollow site of fcc (hcp) type. The latter two regions behave very similarly and are often summarized as hollow region. Figure 2(b) shows the side view cut along the main diagonal exposing the (1$\bar{1}$0) plane. The height of S in the upper layer along this cut is plotted in figure 1(c). It is obvious that the apparent corrugation in STM is inverted and has a larger amplitude. We will show in the following that the apparent height in STM is dominated by electronic effects, meaning that the maxima in the top region are caused by a high local density of states that overcompensates the small distance between MoS₂ and Au(111) in these areas.

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The vertical distribution of the atoms is described in table 1. The minimum height of $h_{\textrm{min}} = 2.50$ Å of the S atoms in the lower layer (S1) is found for the top region. The Mo layer and the upper S layer (S2) follow the lower layer with very similar corrugation. The average thickness of the MoS₂ monolayer (defined as the S-S distance) is 3.11 Å, which is slightly reduced with respect to bulk 2 H-MoS₂ (3.19 Å [23]).

Table 1. Mean height $\bar{h}$, minimum height h_min, maximum height h_max and corrugation $\Delta h = h_{\textrm{max}} - h_{\textrm{min}}$ of the atoms in the lower (S1) and upper (S2) sulfur layer as well as the Mo layer, referenced to the topmost Au layer. All values in Å.

	S1	Mo	S2
$\bar{h}$	2.72	4.28	5.83
hmin	2.50	4.43	5.64
hmax	2.87	4.08	5.97
$\Delta h$	0.37	0.35	0.33

The charge density difference in the central (1$\bar{1}$0) plane is shown in figure 2(c). The regions are markedly different: In the top region charge accumulates between S and Au, indicating a chemical bond (chemisorption). The charge stems from the p_z atomic-like orbitals of the S atoms and the d-orbitals of the Au atoms underneath. There is much less charge transfer in the hollow regions. Moreover, the charge accumulation at the hybrid MoS₂-Au(111) interface goes along with a site-dependent charge rearrangement between the interfacial S atoms and the Mo atoms. This rearrangement modulates the strength of S-Mo chemical bond in the MoS₂ layer.

In order to scrutinize the DFT calculation we applied the method of XSW (see section 4 for experimental details). We prepared samples using virtually identical parameters except an increased number of growth cycles leading to a higher coverage (see section 4). The LEED pattern (inset of figure 3(a)) is qualitatively equivalent to the one shown in figure 1(c). The higher coverage of MoS₂ is reflected in the increase of the intensity ratio between MoS₂- and Au-related spots and the increased sharpness of the moiré satellites.

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The number of cycles is still low enough to avoid the growth of bilayers [12]. The absence of bilayers is also indicated by the LEED pattern: a significant coverage with bilayers should lead to a decrease of the moiré satellite spots, as in STM it is found that the moiré superstructure is not present on bilayers [12]. In our experiments, we find the opposite behavior.

Figure 3 shows HR-XPS of the core levels Mo 3d and S 2s (figure 3(a)), as well as S 2p (figure 3(b)). The fitting parameters of the main components are given in table 2. For S 2p we also find a minority component S^C 2 p$_{3/2}$ ($E_{\textrm{B}} = 161.60$ eV, $\Gamma = 0.75$ eV). As demanded for XSW experiments, a higher incident photon energy of 2.63 keV (off-Bragg condition) has been used for the spectra depicted in figures 3(c) and (d), which changes the photoelectron cross sections and reduces resolution and surface sensitivity (partly compensated by detecting photoelectrons under a more grazing emission angle.) We observe an additional doublet Mo^B 3d at a lower binding energy of 228 eV (light blue in figure 3(c)).

Table 2. Key parameters of the components observed in photoemission (HR-XPS, XPS, and XSW). Binding energy E_B, full width at half maximum Γ, mixing parameter for Voigt-like function β, spin-orbit-splitting $\Delta_{\textrm{so}}$, intensity relative to the most intense component for soft (I_soft) and hard (I_hard) x-rays. Coherent position P^H ($\Delta P^H = \pm 0.02$) and coherent fraction f^H ($\Delta f^H = \pm 0.04$).

	HR-XPS					XPS	XSW
Component	EB (eV)	Γ (eV)	β	$\Delta_{\textrm{so}}$ (eV)	Isoft	Ihard	PH	fH
Mo 3d$_{5/2}$	229.19	0.26	1.00	3.14	1	1	0.81	0.90
S 2s	226.41	2.00	0.55	—	1	1	0.35	0.39
SA 2p$_{3/2}$	162.16	0.25	0.85	1.18	1	1	0.42	0.50
SB 2p$_{3/2}$	162.46	0.51	0.75	1.18	0.20	0.25	0.07	0.89

Our highly-resolved spectra are very similar to those presented by Bana et al [13], and the fitting parameters are almost identical. This also implies that in both studies the same phase, namely 2 H, is present. We observe two additional minor components (Mo^B 3d and S^C 2p) which could be due to differences in the growth procedure. We tentatively attribute S^C 2p to S atoms at the edges of MoS₂ islands with reduced coordination [15]. Mo^B is assigned to metallic Mo on or embedded in Au(111) which was found at the very same binding energy in previous studies [15].

We performed an XSW analysis to determine the distribution of Mo and S perpendicular to the surface. In short, such an analysis yields two structural parameters: the coherent position $\left(P^{H}\right)$ and the coherent fraction $\left(f^{\,H}\right)$ [27]. P^H is the average height of all atoms of the analyzed species and f^H indicates the distribution of atoms around this mean height ($f^{\,H} = 1$ for a δ-like distribution). The average height of a species is given by ${\bar{h} = \left(P^{H} + n\right)} \times d_\textrm{Au(111)}$, where $d_\textrm{Au(111)} = 2.3545$ Å [25] is the Bragg plane spacing of Au(111). The dependence of the photoelectron yield on the x-ray energy for the main Mo 3d$_{5/2}$ peak, the S 2s peak, and the two most intense S 2p$_{3/2}$ peaks is presented in figure 4. The resulting structural parameters coherent position P^H and coherent fraction f^H are given in table 2. However, only for Mo a direct interpretation of these parameters is possible: $P^H = 0.81~\pm 0.02$ yields a mean Mo height of ($4.26~\pm 0.05$) Å above the virtual unrelaxed surface, $f^H = 0.90~\pm 0.04$ indicates a very flat layer. The S components are a convolution of different species, and thus an interpretation is only possible by comparison to the DFT calculation.

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Table 3 compares P^H and f^H derived from the DFT-calculated atomic positions (see section 4) with the experiment. For Mo the assignment of the atoms to an atomic species is simple and we obtain a good agreement between theory and experiment, especially for the more robust parameter coherent position: whereas f^H is diminished by thermal disorder as well as by any contamination (adatom, incorporated in bulk, island edges, grain boundaries), such presumably broadly distributed atoms have a negligible effect on P^H .

Table 3. Comparison between the structural parameters determined by XSW for each component and by a model for the assigned species based on DFT. The model is based on an attenuation factor of α = 0.76 and a strongly bound fraction of the lower S layer of f = 0.45, see text. Experimental values are indicated in bold.

	Component	Mo 3d$_{5/2}$	S 2s	SA 2p$_{3/2}$	SB 2p$_{3/2}$
	Species	Mo	S1$^{\textrm{h}}+$S1$^{\textrm{t}}+$S2	S1$^{\textrm{h}}+$S2	S1t
PH	Experiment	0.81	0.35	0.42	0.07
	Model	0.82	0.35	0.41	0.12
fH	Experiment	0.90	0.39	0.50	0.89
	Model	0.97	0.53	0.66	0.98

For sulfur, the comparison is not as simple. First, there are different species of S in MoS₂/Au(111), and second, not all photoelectrons from the lower S layer reach the detector due to attenuation by the Mo layer and the upper S layer. We propose a model (guided by DFT) where we distinguish three different species of S: all sulfur atoms in the upper layer belong to one species (S2), but for the lower layer we distinguish two species: a fraction of $(1-f)$ belongs to S1^h that are sulfur atoms weakly bound to the gold substrate (S-hollow), and a fraction of f belong to a strongly bound species S1^t (S-top). We describe the attenuation with a parameter α defined as the fraction of photoelectrons from the lower S layer reaching the detector as compared with the upper one.

We start with the core level S 2s (top-right in figure 4). As the corresponding photoemission peak shows just one component, all sulfur atoms must contribute (S1$^{\textrm{h}}+$S1$^{\textrm{t}}+$S2). The calculated structural parameters, corresponding to all S atoms present in the DFT model, are $P^H_{\textrm{S2s}} = 0.32$ and $f^H_{\textrm{S2s}} = 0.51$, clearly deviating from experiment (see table 2). This discrepancy can be solved by taking into account that the weight of the lower S layer is reduced by α due to attenuation. The best description of our experimental data is found using α = 0.76.

With α = 0.76 it is clear that the XPS component S^B 2p$_{3/2}$ cannot be due to the full lower layer, because in this case its relative intensity should just be $I_{{\textrm{S}}^{\textrm{B}} 2{\textrm{p}}_{3/2}} = \alpha = 0.76$, in clear contrast to the experimental value $I_{{\textrm{S}}^{\textrm{B}} 2{\textrm{p}}_{3/2}} = 0.25$. Under the assumption that only strongly bound atoms of the lower layer (S$1^{\textrm{t}}$, fraction f) contribute to the component S^B, while all other S atoms contribute to S^A, we find $I = \frac{\alpha f}{1+\alpha(1-f)}$, yielding f = 0.45. In other words, roughly half of the lower S qualify as strongly bond, the other half as weakly bound. Thus one can calculate the structural parameters P^H and f^H corresponding to 45% of S atoms closest to the Au surface as the best model for the component S^B 2p$_{3/2}$, leading to satisfactory agreement (see table 3).

The remaining S atoms contribute to the component S^A 2p$_{3/2}$. Here, both parameters α and f enter in the respective weight of the atoms used to determine P^H and f^H . The good agreement, especially for the coherent position, verifies our approach. Another piece of evidence for our model is the very low coherent fraction of $f^H_{{\textrm{S}}^{\textrm{A}} 2{\textrm{p}}_{3/2}} = 0.50$, which cannot be explained in a model that attributes this component to the top layer alone (DFT prediction $f^H_{\textrm{S2}} = 0.97$).

The comparison between the experimental results and the model based on DFT calculations is summarized in an Argand diagram (figure 5). The good agreement validates the DFT calculation and our advanced model. In a complex system as found here, where the same chemical species is present in different layers, an interpretation of the XSW data is only possible by a comparison to a dedicated model as performed here. The failure of a straightforward interpretation of S^A 2p$_{3/2}$ as the upper S1 layer and S^B 2p$_{3/2}$ as the lower S2 layer is directly visible in the Argand diagram: in this case, the symmetry of MoS₂ demands that Mo^A 3d$_{5/2}$ forms the bisector of the two S components, which is clearly not found in experiments.

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To reiterate: we observe two main sulfur species in MoS₂ on Au(111). However, the straightforward interpretation that one belongs to the sulfur atoms in close contact with the substrate in the Au-S-Mo-S sequence, and the other one belongs to sulfur atoms at the vacuum side, does not agree with our experimental findings. Instead, we have to distinguish between sulfur atoms in the lower layer that can form a comparatively strong bond to Au atoms due to a favorable on-top-registry (significant chemical shift), and all other sulfur atoms, both in the lower and the upper layer (no chemical shift).

Our assignment of the components forming the S 2p$_{3/2}$ peak differs from the one presented in [13]. Whereas in this paper the two peaks are ascribed to the sulfur in the different layers, our data indicates that the distinction is between S strongly bound to Au(111) and nearly undisturbed sulfur atoms from both layers. As the component S^B 2p$_{3/2}$ stems exclusively from the lower layer, and the XPS signal from the component S^A 2p$_{3/2}$ is dominated by the upper layer, the conclusions drawn from the x-ray photoelectron diffraction (XPD) in [13] may still remain valid.

Comparison of the XP spectra of MoS₂/Au(111) with those of the closely related material TaS₂/Au(111) measures under very similar conditions [28] reveals qualitative differences: in both systems, two main components for the S 2p level are present, but the intensity ratio is much closer to one for TaS₂, where each component could be assigned to a specific S layer. This further supports our model that for MoS₂ the less intense component stems only from a fraction of the S atoms in the lower layer. We speculate that the reason for the different behavior of TaS₂ is its metallic nature that smooths out strong variations in electron density.

In comparison to other epitaxial 2D materials, the MoS₂ layer on Au(111) is rather flat, even though the chemical difference (as evidenced by XPS) between the strongly and weakly bound region is quite pronounced. The strong corrugation observed in STM (up to 1 Å) is completely due to electronic effects, evidencing the difficulty of a precise determination of the vertical structure using scanning probe methods.

We use STS to investigate the electronic properties of MoS₂/Au(111) (see section 4). Figure 6(b) shows the spectra in the normalized form $[({\textrm{d}} I/ {\textrm{d}} V)/(I/V)]$, where artifacts of voltage and tip-sample separation are reduced [29]. We observe three prominent peaks, one for the occupied states (O1) and two for the empty states (E1, E2). The positions of the peaks depend on the moiré region, see table 4. The peak positions for the fcc and hcp region are very similar, whereas the peaks in the top region are shifted towards lower energies, especially O1.

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Our normalized d$I/$dV spectra are virtually identical to the ones measured in [19], where also O1 (named Q in [19]), E1 (Γ₁), and E2 (Γ₂) are observed. The spectra found in [21] are different. In these studies, the sample was exposed to air between preparation and measurement, which is not the case for our experiments as well as for [19]. By comparing our peak energies with ARPES [14] and the band structure resulting from DFT calculations in a simplified model [21], we assign O1 to the VB minimum at Γ, which ARPES finds at $E = -1.7$ eV. Similarly, we ascribe E2 to the CB minimum at Γ. The assignment for E1 is somewhat more difficult. We find local CB minima at matching energies near M as well as between Γ and Q. Presumably, all these states contribute to E1. However, since the states between Γ and Q have smaller parallel momentum $k_{\parallel}$, they will dominate the tunneling signal and thus we primarily associate E1 with these states (which are found at significantly higher energy than for freestanding MoS₂).

There is agreement as well as disagreement with the assignment of the peaks by Krane et al [19]. The authors based their interpretation on measurements of the decay constant of the tunnel current κ, which contains information on $k_{\parallel}$ [30]. They find a low value of κ for E2 and higher and mutually similar values for E1 and O1. Consequently, they assign E2 to the minimum of the CB at Γ and O1 to the VB minimum at Q. They do not attribute E1 to a specific state. We follow the assignment for E2, but disagree for O1. The energy of the valence band minimum at Q is determined by ARPES as $E \approx -2.3$ eV [14], which is considerably higher than the energy observed by STS. A much better match is found for the band maximum around Γ at $E = -1.7$ eV, which appears very broad and diffuse in ARPES. DFT calculations show that the maximum of a singular band observed for free-standing MoS₂ is destroyed by hybridization with Au(111). Instead new band extrema in the vicinity of Γ appear (approximately halfway between Γ and Q, see figure 5 of [21]), which can explain the value of κ . Therefore, we assign O1 to these new hybridization states near Γ.

We map the electronic structure across one moiré unit cell by taking d$I/$dV spectra at several points along the main diagonal of the moiré cell (see gray line in figure 1(b)) and display them as a color plot (figure 6(a)). The positions of the peaks shift within the moiré structure, especially for O1. In agreement with the point spectra, we observe maxima at the fcc and hcp positions and minima at the top position. Furthermore, we find additional minima at the bridge position, which is at a similar energy as for the top position.

Figure 6(c) shows the DOS calculated by DFT for top and fcc/hcp hollow moiré regions. Two prominent peaks for the empty states, which correlate to E1 and E2, are visible. The peak with the highest intensity in the occupied states can be associated with O1. There are additional peaks, particularly for the conduction and valence band onsets at K, that are not or only faintly visible in ${\textrm{d}}I/{\textrm{d}}V$ spectra. Furthermore, the DOS of the top area is shifted compared to the DOS of the hollow sites, in the same direction as in experiment.

In agreement with experiment, the shift is largest for O1 and smallest for E1. The shift is significantly larger than the experimentally observed shift, especially for E1 and E2, but not rigid. This discrepancy may be caused by including the vdW interaction in our DFT calculations as a correction term, which improves the structural results, but does not act on the electronic properties.

The energy of O1 is strongly modulated by the moiré structure as already indicated in [19]. We attribute this modulation to the varying degree of hybridization between this state and states of the substrate. The overlap of the corresponding orbitals is not a simple function of the S-Au distance as the energy of O1 at the bridge position is similar to the one at the top position, even though the local MoS₂ height is very different (see figure 1(c)). The interaction is rather determined by the relative position of the lowest S atoms towards the surface Au atoms and the involved orbitals (S p_z and Au d$_{z^2}$): if the dense packed S atomic rows are in phase with the dense packed rows of the Au surface (top and bridge regions), the interaction is strongest. In the fcc and hcp moiré areas the S p_z -orbitals point into the fcc and hcp gaps of the Au surface. Correspondingly, the impact is strongest for O1, since the VB edge at Γ is foremost of out-of-plane (S p_z , Mo 4d$_{z^2}$) orbital character [21, 31]. In contrast, the CB at Γ (E2) mostly originates from in-plane (S p_x , p_y ) orbitals, thus interacting less strongly with the substrate (or their interaction depends less strongly on the local registry) and stays at nearly constant energy.

In addition to ${\textrm{d}}I/{\textrm{d}}V$ point spectra we map the electronic effects of the moiré potential at different energies (figure 6(d)). While there are certainly subtle changes in the STM images (as discussed in [19]), more significant differences are found in the STS maps. The relative intensity of the top, hcp and fcc regions strongly depends on the bias voltage. Most obvious are four contrast inversions between top and hollow moiré sites: between −2 eV and −1.5 eV the contrast changes from bright top and dark hollow to dark top and bright hollow areas. The next contrast inversion happens between −0.5 eV and 0.5 eV in reversed order. At 1.5 eV the top areas again appear dark surrounded by a network of bright hollow regions. The contrast changes back to bright top and dark hollow regions at 2.5 eV. The contrast inversions are accompanied by slight changes in the intensity distribution of fcc and hcp sites. At 1 and 2 eV all intensity is focused on fcc (downward pointing triangles) and hcp sites (upward pointing triangles), respectively.

The contrast inversion between −2 and −1.5 eV reflects the shift of O1. The nuanced changes at positive bias voltages reveal a more complex influence of the moiré pattern to the conduction band states, in agreement with subtle changes found in constant current $\left(\partial I/ \partial V \right)_I$ spectra by Krane et al [19].

The apparent height profile of the moiré corrugation measured with STM and the height profile calculated with DFT are exactly inverted. Whereas STM finds a strong corrugation with high top and low hollow regions, DFT predict a very low corrugation with low top and high hollow regions, in agreement with XSW results. Spatially depended STS measurements reveal that the moiré corrugation observed in STM is a pure electronic effect and we attribute the moiré modulation to the varying degree of hybridization between states of the bottom S atoms and substrate states.

The spatial variation of O1 also explains the diffuse appearance of the VB maximum at Γ in ARPES [14]. Our ${\textrm{d}}I/{\textrm{d}} V$ spectra exhibit a well defined peak for O1, showing that locally the state is well-defined. The key effect behind the broadening is the moiré dependent modulation of the substrate interaction. Since the ARPES signal is averaged over several moiré unit cells, these local variation of the VB maximum can not be resolved.

An alternative explanation of the peak shifts could be based on screening of MoS₂ states by the highly polarizable metal substrate [16, 17], which becomes stronger with decreasing height of the MoS₂. Screening is expected to move states towards the Fermi level. However, for O1 we observe the opposite behavior as it moves away from E_F when we go from the weakly to the strongly bonded regions. This implies that screening effects are not significant in our system.