Introduction

Devices integrating two-dimensional (2D) transition metal dichalcogenides (TMDC) have stimulated tremendous interest due to their promising optoelectronic applications1,2,3. The Schottky barrier height (SBH) at the metal-semiconductor junction (MSJ) is a measure of the barrier to charge injection and a strong determinant of device performance4,5,6. A large number of studies have been devoted to understanding the SBH at metal/2D TMDC interfaces7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36. Unfortunately, it has been challenging to directly measure the SBH at these interfaces and the SBH values extracted from electrical measurements can depend on the model and measurement technique5. However, experimental measurements can clearly indicate whether the carriers are n-type or p-type. The majority of studies have shown that MoS2/metal contacts are n-type7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24, while WSe2/metal contacts are ambipolar or p-type26,27,28,29,30,31,32,33,34,35,36, and these observations hold for a range of metal contacts. MoS2 and WSe2 are both prototypical H-phase TMDCs and this contrasting behaviour between the two very similar TMDC materials is not understood.

We illustrate the confusion over the polarity of these TMDC-based MSJs using the commonly studied MoS2 and WSe2 TMDCs on Au. MoS2/Au devices have shown predominantly n-type polarity in both experimental7,8,9,10,11,12,13,14,15 and theoretical37,38,39,40,41 studies. However, a recent experimental study revealed p-type behaviour for defect-free MoS2/Au contacts, suggesting that the n-type behaviour observed in previous experiments arose from the presence of defects at the interface25. Similarly, a previous study on MoS2/Au devices16 found that both p- and n-type contacts could be fabricated on the same MoS2 sample, with n-type contacts being present for regions with a higher concentration of S vacancies. In general, MoS2/metal MSJs have exhibited strong n-type behaviour in regions with low S concentration15,16,17,18,19. These chalcogen vacancies have defect states near the conduction band minimum (CBM) and can explain the pinning of the Fermi level close to the CBM observed in MoS2/metal contacts15,16,17,18,18,19,42,43,44. However, other studies have claimed that Fermi level pinning at MoS2/metal interfaces does not require the presence of defects39,40,41, and instead can be attributed directly to interfacial effects41 and metal-induced gap states (MIGS)12,15,19,24 that act to align the Fermi level of the system to the intrinsic charge neutrality level (CNL) of the semiconductor. First principles density functional theory (DFT) calculations on MoS2/Au interfaces also reveal clear n-type contacts37,38,39,40,41 even in systems without any defects.

If chalcogen vacancies result in n-type behaviour for MoS2/metal contacts, one should expect the same to be true for WSe2/metal contacts since the defect formation energies in MoS2 and WSe2 are very similar45. In particular, chalcogen vacancies give rise to in-gap defect states close to the conduction band minimum for both MoS2 and WSe243. Yet, WSe2/metal contacts are predominantly ambipolar or p-type26,27,28,29,30,31,32,33,34,35,36. In ref. 34, where p-type WSe2/metal contacts were reported, it was further observed that the ratio of W to Se elements was 1:1.96, indicating that Se vacancies were likely to be present. These seemingly contradictory observations underscore major gaps in the understanding of SBH at TMDC/metal junctions, despite the large number of studies on this important topic.

First principles calculations have traditionally played an important role in elucidating structure-property relationships at a level of detail not attainable in experiments. However, the widely-used DFT approach for computing and analyzing the SBH in TMDC/metal interfaces fails to capture the non-local exchange and correlation effects that determine the energy level alignment (ELA) at the interface46,47,48,49. Many-body perturbation theory within the GW approximation50 explicitly accounts for such effects, and can quantitatively predict the ELA in complex interface systems46,47,48,49. In this work, we perform GW calculations to quantitatively predict the ELA at monolayer TMDC/metal junctions, considering both pristine TMDC systems as well as TMDCs with defects. Our results show that the self-energy corrections arising from non-local exchange and correlation effects change qualitatively the contact polarity at the pristine MoS2/Au interface, from n-type at the DFT level to p-type at the GW level. This is in contrast to the pristine MoS2/Ag interface which is predicted to be n-type. GW calculations on MoS2/Au junctions with S vacancy defects predict clear n-type behavior, thus demonstrating that chalcogen vacancies are responsible for the n-type behavior in the MoS2/Au interface. The pinning of the Fermi level at the chalcogen defect states also explains the n-type polarity for MoS2/metal contacts in general7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24. We reconcile the absence of n-type polarity in WSe2/metal contacts26,27,28,29,30,31,32,33,34,35,36 by noting that, unlike the S vacancies in MoS2, the Se vacancies in WSe2 are readily passivated by oxygen atoms at room temperature51. Our GW calculations show that oxygen passivation of Se vacancies removes the Se vacancy gap states and changes the contact polarity in the Se-deficient WSe2/Au interface from n-type to p-type. Taken together, our many-body calculations enable clear conclusions to be drawn regarding the contact polarity of TMDC junctions with and without defects, and, together with knowledge about the defect formation energies and chemistry, provide a much-needed consistent understanding across a large body of experimental data on contact polarities in TMDC/metal junctions.

Results and discussion

Pristine interfaces

We begin by exploring the ELA for pristine TMDC/metal interfaces. Computational details are presented in the Methods section.

The ELA for monolayer MoS2/Au has been extensively studied at the DFT level37,38,39,40,41. Our DFT calculations with the Perdew-Burke-Ernzerhof (PBE)52 approximation to the exchange-correlation functional predict an n-type MoS2/Au contact, with a valence band offset (VBO) of 1.1 eV and a conduction band offset (CBO) of 0.7 eV, so that the metal Fermi level is closer to the conduction band. These observations are consistent with other DFT calculations37,38,39,40,41. To extract the VBO and CBO, the wavefunctions of the interface are projected onto the valence band maximum (VBM) and conduction band minimum (CBM) of the pristine, isolated MoS2 layer. The interface states having major overlap with the VBM and CBM of the isolated layer are assigned as the VBM and CBM at the MoS2/Au interface. This assignment is corroborated by comparing the designated interface VBM and CBM to a separate projected band structure plot, shown in Fig. 1a, where the red circles indicate the projections onto Mo and S orbitals. Further details are provided in Supplementary Note 1.

Fig. 1: Band structures of pristine TMDC/metal junctions.
figure 1

a MoS2/Au and (b) MoS2/Ag, with projection onto Mo/S orbitals plotted as coloured circles. The size of the circles is proportional to the weight of the orbital projection. The DFT valence band offsets (VBO) and conduction band offsets (CBO) are indicated. The quasiparticle (QP) VBO and CBO, obtained from separate GW calculations, are also indicated. Energies are referenced to the Fermi level, EF. Atomic structures are shown as insets: Au (gold); Ag (silver); Mo (purple); S (yellow).

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GW calculations performed on the MoS2/Au interface result in a p-type ELA, qualitatively different from the n-type ELA predicted by DFT. At the GW level, the VBO is 0.8 eV, smaller than the CBO of 1.2 eV (Table 1 and Fig. 1a). This p-type ELA is also in apparent contrast to the predominant n-type polarity observed in MoS2/Au contacts7,8,9,10,11,12,13,14,15, but is, however, in agreement with a recent experimental study where the Au contact was physically laminated onto few-layer MoS2 (Table 1)25. We have performed additional calculations for a three-layer MoS2/Au interface in order to provide a more quantitative prediction of the ELA for systems with thicker MoS2 flakes. These calculations give a p-type contact with a SBH of 0.6 eV, consistent with the smaller band gap of thicker MoS2 and closer to the experimental SBH extracted in ref. 25.

Table 1 Band gaps and band offsets of TMDC/metal junctions. Quasiparticle (QP) band gap (Eg) of the TMDC, the valence band offset (VBO) and the conduction band offset (CBO) for the systems reported in the main text.
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For comparison, we also compute the ELA for the monolayer MoS2/Ag interface. Here, we find that both the DFT and GW calculations predict n-type contacts (Fig. 1b and Table 1). The GW CBO is 0.3 eV, much smaller than the VBO of 1.3 eV. The MoS2/Ag interface was chosen for a comparative study because Au and Ag share the same valence shell structure. At the same time, Ag binds to MoS2 more strongly than Au; the average binding distances of MoS2 on Au and Ag are 2.9 Å and 2.7 Å, respectively, in agreement with previous DFT results41. Another key difference between Au and Ag is that their most stable (111) surfaces (used in our models) have quite different work functions. The work function Φ for Au(111) is ~5.2 eV while that for Ag(111) is ~4.6 eV. If Fermi level pinning were absent, we would expect that the smaller work function for Ag would lead to a smaller CBO compared to Au. If Fermi level pinning were present, we would expect both metals to result in the same CBO with respect to MoS2, despite the difference in work function. The degree of pinning can be assessed via the interface pinning parameter, S, which can be defined individually for the VBO and CBO as \({S}^{VBO}=| \frac{d(VBO)}{d{{\Phi }}}|\) and \({S}^{CBO}=| \frac{d(CBO)}{d{{\Phi }}}|\). From the GW results in Table 1, we find that SVBO is ~0.8, substantially larger than 0 (i.e. full pinning), indicating only partial, weak pinning of the Fermi level. We find SCBO ~1.5, which exceeds the Schottky–Mott limit of S = 1.0. Furthermore, we note that the value of SVBO is ~0.7 smaller than SCBO. These results therefore indicate that there can be ambiguities in using S as an indicator for Fermi level pinning, because of complexities arising from the metal-TMDC interaction, e.g. differences in the TMDC band gap on different metal surfaces, as discussed below.

We illustrate the physical origins of the ELA using the level diagrams in Fig. 2. When MoS2 approaches Au or Ag, electronic charge is transfered from MoS2 to the metal, because the charge neutrality level of MoS2 is higher in energy than the Fermi level of the metal. This charge transfer is more significant for the MoS2/Au interface due to the larger work function of Au compared to Ag. This interface-induced charge redistribution can be quantified using the dipole potential53 (see Supplementary Note 2). The induced dipole potentials, Δdipole, for the MoS2/Au and MoS2/Ag interfaces are 0.23 eV and 0.07 eV, respectively. In both cases the dipole acts to reduce the metal workfunction (i.e. bring the Fermi level closer to the vacuum). Figure 2a illustrates the ELA taking into account the DFT energy levels of isolated MoS2 and Au as well as the interface-induced dipole. Figure 2b illustrates the ELA at the MoS2/Au interface computed from first principles using DFT. A comparison of Fig. 2b and a provides information on hybridization-induced changes in the ELA. It can be observed that interface hybridization stabilizes both the MoS2 VBM and CBM by ~0.2 eV for MoS2/Au. On the other hand, for MoS2/Ag (see Fig. 2d, e), interface hybridization stabilizes the MoS2 VBM and CBM by ~0.1 eV and ~0.3 eV, respectively, leading to a reduction in the band gap by ~0.2 eV. From Fig. 1b, it is seen that monolayer MoS2 on Ag has an indirect band gap, unlike isolated monolayer MoS2 or MoS2 on Au. The CBM is shifted to the M point and results from hybridization between the Mo d orbitals and Ag. The larger hybridization-induced changes to the ELA for MoS2/Ag is consistent with the smaller average binding distance on Ag.

Fig. 2: Schematic of the energy level alignment (ELA) for pristine TMDC/metal junctions.
figure 2

Schematics are shown for (a, b, c) MoS2/Au and (d, e, f) MoS2/Ag. a, d show the ELA obtained by the alignment of the isolated materials, taking into account the calculated dipole correction (Δdipole). b, e show the DFT ELA at the interfaces. c, f show the GW quasiparticle (QP) ELA at the interfaces. The valence band maximum and conduction band minimum levels are indicated by blue and yellow lines, respectively. Energies are given in eV, referenced to the Fermi level in each case (dashed grey lines). Atomic structures are shown as insets: Au (gold); Ag (silver); Mo (purple); S (yellow).

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Figure 2c and f show the quasiparticle (QP) ELA, obtained using GW calculations, for MoS2/Au and MoS2/Ag, respectively. Compared to Fig. 2b and e, the QP ELA includes self-energy effects (exchange and correlation effects absent from the DFT calculations). It is known that DFT typically underestimates band gaps. Our calculations show that self-energy effects increase the band gap of isolated monolayer MoS2 by ΔEg,isolated = 1.2 eV, resulting in a QP band gap of 2.9 eV that is consistent with the literature54. The GW QP band gaps of MoS2 on Au and MoS2 on Ag are 2.0 eV and 1.6 eV, respectively, significantly smaller than that in isolated MoS2. These smaller band gaps in the presence of the metal contacts result primarily from electronic screening in the metal55,56,57. The GW band gap for MoS2 on Au is about 0.3 eV larger than the DFT band gap, while the GW band gap for MoS2 on Ag is almost the same as its DFT band gap. These differences reflect the increased screening expected for MoS2 on Ag due to the smaller average binding distance in MoS2/Ag55,56,57. Thus, from Fig. 2, the smaller band gap for MoS2 on Ag compared to MoS2 on Au arises from a combination of increased hybridization in MoS2/Ag, which reduces the DFT band gap, and smaller self-energy corrections for MoS2 on Ag.

We now turn our attention to the reversal of contact polarity when comparing the DFT and GW ELA for MoS2 on Au. This reversal can be understood by the relatively larger self-energy corrections for the CBM compared to the VBM. These differences in self-energy corrections are also reflected in GW calculations for isolated MoS2 and can be attributed to the fact that the CBM wavefunction has a larger spatial localization. We note that this is not observed in MoS2 on Ag, because the CBM for MoS2 on Ag is strongly hybridized. Specifically, the projection weight of the CBM of isolated MoS2 on the CBM of MoS2 on Au is 99%, while that for MoS2 on Ag is distributed over two different states, giving projection weights of 50% and 35%, respectively. The analysis presented here illustrates the subtleties of the interplay between hybridization, screening, self-energy corrections, and the contact polarity and ELA at these TMDC/metal interfaces.

Role of defects

Having established that pristine MoS2/Au interfaces are p-type, it is natural to then conclude that Fermi level pinning and metal-induced gap states are not responsible for the n-type polarity observed in MoS2/Au contacts. Instead, it is very likely that the experimentally observed n-type behaviour for MoS2/Au contacts7,8,9,10,11,12,13,14,15 should be attributed to defects. Proponents of this argument have generally focused on sulfur vacancy (vacS) defects15,16,17,18,19, and indeed, chalcogen vacancies are found to have the lowest formation energy in TMDCs for typical growth conditions45,51. S vacancies have also been observed in scanning tunneling microscopy (STM) and scanning transmission electron microscopy (STEM) images of bare58,59 and Au(111)-supported60 monolayer MoS2.

We therefore perform GW calculations for the ELA in MoS2/Au systems with S vacancies, using models with a defect concentration of ~3.8% (see Methods and inset of Fig. 3a). Figure 3a shows the DFT band structure for such an MoS2-vacS/Au system. Gap states are observed close to the conduction band, and the Fermi level is aligned with these gap states. Self-energy effects increase the MoS2 band gap as well as the VBO and CBO. The resulting ELA at the GW level is n-type (qualitatively similar to the DFT ELA), with a CBO of 0.5 eV and a VBO of 1.3 eV. These results are consistent with the observations of n-type behaviour in regions with high concentrations of vacS15,16,17,18,19 in MoS2/metal systems. It is worth noting that, although sulfur vacancies can switch the polarity of MoS2/Au contacts from p-type to n-type, sulfur vacancies are not donor defects because the gap states of sulfur vacancies, close to the CBM, are unoccupied in isolated MoS245. It is the interaction of MoS2-vacS with metal contacts that induces n-type behaviour, due to the Fermi level being pinned by the gap states.

Fig. 3: DFT band structures of TMDC/metal junctions with common point defects.
figure 3

a MoS2-vacS/Au and (b) WSe2-OSe/Au. Projections onto Mo/S and W/Se orbitals are shown as red and blue circles, respectively. The size of the circles is proportional to the weight of the orbital projection. The band structure in (b) includes the effect of spin orbit coupling (SOC). The DFT valence band offsets (VBO) and conduction band offsets (CBO) are indicated. The quasiparticle (QP) VBO and CBO, obtained from separate GW calculations, are also indicated. Energies are referenced to the Fermi level, EF. Atomic structures are shown as insets: Au (gold); Mo (purple); S (yellow); W (grey); Se (green); O (red).

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The above results demonstrate that the widely observed n-type contact polarities at MoS2/Au interfaces7,8,9,10,11,12,13,14,15 arise from defects, which are very likely to be sulfur vacancies. At the same time, the sulfur vacancy gap states will pin the Fermi level in MoS2/metal interfaces, resulting in n-type contact polarities for most metals. It is important to question why the contact polarity of WSe2/metal interfaces (including WSe2/Au) has generally been reported to be p-type or ambipolar, instead of n-type26,27,28,29,30,31,32,33,34,35,36. The defect formation energies of chalcogen vacancies in MoS2 and WSe2 are very similar45, and a deficiency in Se has been observed in WSe2 samples that have p-type contacts34. Point defects attributed to Se vacancies have been observed to be the dominant defect type in scanning transmission electron microscopy (STEM) images of WSe2 monolayers51,61. Thus, one would also expect that the presence of Se vacancies in WSe2 should also pin the Fermi level close to the CBM, resulting in n-type contact polarities for most metals and in contrast to the experimental data.

We perform GW calculations for pristine WSe2/Au interfaces and WSe2/Au interfaces with Se vacancy defects. Similar to the case of MoS2, it is found that pristine WSe2/Au interfaces are p-type (VBO: 0.7 eV, CBO: 1.4 eV) while WSe2-vacSe/Au interfaces are n-type (VBO: 1.9 eV, CBO: 0.3 eV) (Table 1). To understand the absence of n-type polarities in WSe2/Au and WSe2/metal interfaces, even with Se deficiencies34, we note that the Se-deficient WSe2/Au interface is not simply WSe2-vacSe/Au. In fact, recent first principles calculations have shown that the Se vacancies in WSe2 act as active sites for the dissociation of O2 at room temperature, and are also very likely to be passivated by oxygen atoms during growth conditions that involve the use of oxide precursors51. This oxygen passivation forms an oxygen-passivated Se defect (OSe) and removes the Se vacancy gap states (Fig. 3b). The presence of OSe in WSe2 samples was confirmed by STM studies of monolayer WSe2 on graphite, and notably, no Se vacancies were observed in the STM images, even though point defects attributed to missing Se atoms were observed in STEM images in the same work51.

The GW VBO and CBO of WSe2-OSe/Au are 0.8 eV and 1.3 eV, respectively, very close to the values for pristine WSe2/Au (Table 1). Thus, our calculations explain why the Fermi level is not pinned close to the CBM in WSe2/metal contacts, and indicate that the p-type WSe2/Au contacts observed in experiment can be either attributed to pristine WSe2 or the passivation of Se vacancies with oxygen. Ambipolar transport may result from the presence of thicker WSe2 flakes27 or the use of a metal with a smaller work function. We do not rule out the possibility of the predominance of other types of defects which have defect states close to the VBM. However, studies have shown that Se vacancies are often the most common defect in WSe2 layers51,61,62, consistent with theoretical predictions45.

Figure 4 provides a schematic summary of the comparison between theory and experiment for the SBHs and contact polarities of MoS2/Au and WSe2/Au junctions. The yellow and blue shading denote the SBHs for n-type and p-type junctions observed experimentally. The light and dark colored hexagons mark the computed DFT and GW SBHs, defined to be the smaller of the VBO and CBO. The reversal of contact polarity is clear for pristine MoS2 on Au, highlighting the importance of self-energy corrections in determining the SBH and contact polarity of TMDC/metal interfaces. It is noted that our DFT calculations give a p-type ELA for pristine WSe2 on Au, similar to the GW ELA. However, the self-energy corrections increase the p-type SBH by ~0.2 eV for both WSe2/Au and WSe2-OSe/Au. Overall, Fig. 4 summarizes the distinction between MoS2/Au and WSe2/Au contacts, and puts forth a consistent picture for the atomic origin of the experimentally observed contact polarities.

Fig. 4: Schematic illustrating the polarity of experimentally-measured TMDC/metal junctions.
figure 4

Data are shown for (a, c) MoS2/Au and (b, d) WSe2/Au interfaces. Yellow-shaded bands (a, b) indicate the approximate n-type Schottky barrier heights (SBH) extracted from experiments, while blue-shaded bands (c, d) indicate the approximate extracted p-type SBH. Note that the entire box in (d) is shaded blue since explicit SBH values were not listed in the experiments. Experimental values have been extracted from refs. 10,12,13,14,15,25,26,27,28. Calculated QP (DFT) SBH values from this work are shown as filled (shaded) red (MoS2) and blue (WSe2) hexagons. “prist.” stands for “pristine”.

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The GW calculations show that, whether the TMDC is MoS2 or WSe2, the VBO and CBO for pristine monolayers on Au are similar, and both p-type. Likewise, in the presence of chalcogen vacancies, the VBO and CBO are also similar. The structure-ELA relationship elucidated by these state-of-the-art calculations indicate that the differing polarities observed experimentally for MoS2/Au and WSe2/Au contacts arise largely from defect chemistry or growth conditions. In particular, DFT calculations showed that the probability of O2 dissociation at sulfur vacancies in MoS2 at room temperature is exponentially smaller than the same process at selenium vacancies in WSe251,63. Our results can be generalized to other types of metal contacts, because the gap states of chalcogen vacancies are expected to pin the Fermi level close to the CBM for most metals. The large body of experimental data on contact polarity for MoS2 and WSe2, together with our GW ELAs, provides compelling evidence that in the majority of samples, chalcogen vacancies are unpassivated in MoS2 but passivated by oxygen in WSe2, confirming the differing reactivity of chalcogen vacancies in the two TMDCs toward O2 dissociation under ambient conditions. These findings are particularly relevant for the bottom-up design of quantum technology devices, where chalcogen vacancies are intentionally created in TMDCs for quantum emission64. It is worth noting that sample preparation can change the nature of defects in the TMDCs. For example, in a recent work where MoS2 was heated at 333 K65, oxygen-passivated sulfur vacancies were observed. Exposure of MoS2 to ambient conditions over the course of more than one year also results in the passivation of sulfur vacancies by atomic oxygen66. Thus, by controlling the sample preparation conditions, it is in principle possible to manipulate the SBH and contact polarity in the TMDC/metal interfaces. Our calculations suggest that if sulfur vacancies can be passivated in MoS2, one can tune the SBH according to the work function of the metal.

Methods

Computational details

The pristine MoS2/Au and MoS2/Ag supercells are constructed using a 2 × 2 expansion of the (111) surface of the metal and a \(\sqrt{3}\times \sqrt{3}\) expansion of the monolayer TMDC. In all cases the lattice parameter of the metal is adjusted to match that of the TMDC, resulting in a compressive strain of 5.1% for Au and 5.3% for Ag paired with MoS2. Our metal slabs consist of four layers.

In Supplementary Table 1 we list the calculated workfunctions for strained and unstrained Au(111) and Ag(111), along with their experimental values. From these results it is clear that the calculated strained and and unstrained workfunctions are close for both Au and Ag. Moreover, the calculated workfunctions are in very good agreement with experimental ones. Based on these data, we can justify the use of strained metals for the purposes of determining the energy level alignments at the TMDC–metal interfaces.

To accommodate defects we increase the expansion of the Au slabs to 4 × 4. These defective interfaces with MoS2 use a \(\sqrt{13}\,\times\, \sqrt{13}\) expansion of the TMDC, while all interfaces with WSe2 (i.e. both defective and pristine) use a \(\sqrt{12}\,\times\, \sqrt{12}\) expansion of the TMDC. Correspondingly, compressive strain on Au at these large MoS2 and WSe2 interfaces is 1.2%.

Structural optimizations were performed using the DFT-D3 van der Waals correction67. All DFT calculations were carried out within Quantum ESPRESSO68,69 using the SG15 optimized norm-conserving Vanderbilt (ONCV) pseudopotentials70,71. The Perdew-Burke-Ernzerhof (PBE)52 exchange-correlation functional was used with a 60 Ry kinetic energy cutoff for wavefunctions. To compute the projected band structures, shown in the main text, and the projected DOS calculations, shown in Supplementary Figure 2, the PAW method72,73 was used to allow for the projection onto atomic states, which is not possible using the standard SG15 ONCV set. We stress that these projected bands/DOS plots are used only as visual aids, and emphasize that all relevant energy levels and offsets were determined via the ONCV calculations. Additionally, we compared the band structure of Au/MoS2 generated using both the ONCV pseudopotentials and PAW potentials, and noted negligible difference in a wide energy window around the Fermi energy, extending beyond the valence band maximum (VBM) and conduction band minimum (CBM) energies. In these cases the kinetic and charge density cutoffs were set to at least the minimum recommended values. Periodic images normal to the surfaces were separated by a vacuum of 15 Å. Charge density calculations employed a dipole correction74 in order to allow for a more precise calculation of the induced dipole potential. For the pristine MoS2/Au and MoS2/Ag interfaces, the Brillouin zone was sampled using a uniform 12 × 12 × 1 grid for structural optimizations and charge density calculations. For the large interfaces with WSe2 and defects, both structural optimization and charge density calculations used a uniform 6 × 6 × 1 grid.

GW calculations were performed using BerkeleyGW75. The calculations of the dielectric matrix for MoS2/Au and MoS2/Ag used a 9 × 9 × 1 sampling of the Brillouin zone with band energy cutoff set to 6 Ry, while similar calculations for the larger interfaces used a 4 × 4 × 1 Brillouin zone sampling and a 4 Ry band cutoff. All dielectric matrix and self-energy calculations were performed with a 16 Ry energy cutoff for the sum over reciprocal lattice vectors. A slab Coulomb truncation scheme76 was employed, for which the 15 Å vacuum height was verified to be appropriate. The QP Fermi level energies were obtained via BerkeleyGW’s inteqp.x utility. We verified that off-diagonal elements were negligible for the assigned VBM/CBM states at the MoS2/Au and MoS2/Ag interfaces, providing justification for the use of the standard one-shot \({{{{\rm{{G}}}_{0}W}}}_{{{{\rm{0}}}}}\) approach to GW.

Spin-orbit coupling (SOC) corrections were found to reduce the WSe2 band gap by approximately 0.3 eV, in agreement with previous theoretical calculations77, consisting of an adjustment toward the Fermi level of the VBM and CBM by 0.2 eV and 0.1 eV, respectively. These corrections were consistent for the WSe2-based MSJ considered, and were applied perturbatively to the WSe2 levels presented in the main text.

Standard GW calculations on the large pristine WSe2 and all defective interfaces are computationally prohibitive. We therefore used the XAF-GW approach48 to substantially reduce the required computational effort. XAF-GW utilizes sub-unit cells that are expanded to match the full-interface supercell lattice parameters. Example sub-unit cells for Au and MoS2 are shown in Supplementary Fig. 1.

Accordingly, the dielectric matrix of the expanded cell represents a structure that is subtly different from the fully-relaxed supercell used to compute the wavefunctions. In order to ensure a good match, we set the in-plane positions of atoms to their ideal positions (i.e. their positions before relaxation), while the coordinate along the surface-normal axis for each layer was fixed to the average value of the corresponding layer in the relaxed supercell. This approach yields excellent results despite the deviations of the atomic coordinates from their ideal positions due to structural relaxation. To verify this, we compared ~20 eigenvalues above and below the Fermi level for Au/MoS2, obtained via both standard GW and XAF-GW calculations. The mean absolute error in the eigenvalues across all k-points was 0.03 eV, while the maximum absolute error was 0.07 eV.

The XAF-GW code is available at https://github.com/quek-group/XAF-GW. The atomic structure images shown in the figures were produced using VESTA78.