## Introduction

Layered two-dimensional (2D) transition metal dichalcogenide (TMDC) semiconductors are promising beyond silicon materials owing to their attractive optoelectronic properties1,2,3,4 and weak inter-layer coupling that overcomes vital engineering challenges of bulk materials regarding heteromaterial integration and miniaturization. Among potential applications for 2D-TMDCs are stacked nanosheet field effect transistors,5,6 lateral heterojuction diodes7,8,9,10, or photodetectors11,12, which all require high-quality 2D-TMDCs with tunable electronic properties. Hence, huge effort is devoted to establish high-quality scalable production13, controlled doping14,15,16,17,18,19,20,21,22, and optimized electronic contacts23,24,25,26,27,28,29.

In recent years, epitaxial growth of wafer-scale substitutionally doped semiconducting 2D-TMDCs such as MoS2, WS2, and WSe2 has been successfully established using metalorganic chemical vapor deposition (MOCVD). Doping with nonisovalent transition metals such as V21 and Nb30 or Re18,31 and Mn32 yielded the expected p-type or n-type behavior, respectively, but it was noted that dopant ionization energies are significantly higher in the monolayer limit due to strong defect state localization33. Moreover, for metal-TMDC contacts, Fermi level pinning because of metal–induced gap states (MIGS) at the interface or due to disorder-order induced gap states, which originate from vacancies or substitutional defects, reduce the tunability of the Schottky barrier height and results in high contact resistance, thus limiting device performance24,27,28,34,35,36,37. Van der Waals semimetals like graphene or graphite greatly suppress the formation of MIGS owing to their low density of states at the Fermi level while at the same time reducing interface disorder through the absence of dangling bonds.

Here we investigate the layer-dependent valence and conduction band onsets of a prototypical semimetal–TMDC contact formed between multilayer WSe2 grown on quasi-freestanding epitaxial graphene on 6H-SiC(0001) (QFEG/SiC) (Fig. 1a, b). By means of scanning tunneling microscopy and spectroscopy (STM/S) we compare the band onset evolution from 1 to 7 monolayers (ML) between p-type V-doped (0.44%, 4.7  1012 cm−2) and nominally undoped WSe2. For the V-doped WSe2 we find that the Fermi level is pinned to the defect state energy from 3 ML on, whereas the Fermi level resides in the band gap in the mono- and bilayer case, suggesting a charge depletion region of around 1.6 nm.

## Results and discussion

### Layer-dependent STS of undoped WSe2

Figure 1c, d show large-scale STM topography images of undoped and V-doped WSe2 samples grown on QFEG/SiC. For both samples multilayer WSe2 regions can be found. After identifying the QFEG and single-layered WSe2 by their distinct STS fingerprints, we determine the number of WSe2 ML by counting the number of discrete steps of 0.65 nm height, as depicted in the height-profiles shown in Fig. 1e, f.

Figure 2 summarizes the layer-dependent STM/STS results obtained for undoped WSe2. As exemplarily shown in the STM image of 1 ML of undoped WSe2 in Fig. 2a, the dominant type of defect that we observe occurs with a density below 0.02% and is identified as molybdenum atoms that substituted W38. As depicted in Fig. 1b, the local density of states of 1 ML undoped WSe2 revealed by STS exhibits distinct valence and conduction band edges with the Fermi level (at zero sample bias VB) close to the center of the 2.34 eV band gap. The layer dependence of the valence and conduction band edges and of the band gap for undoped WSe2 is shown in Fig. 2b, c. Independent of the number of layers, the Fermi level is close to the center of the band gap for undoped WSe2. With increasing number of layers, both, the conduction and the valence band edge of undoped WSe2 move symmetrically toward the Fermi energy, hence lowering the band gap for thicker films due to inter-layer hybridization. The evolution of the band gap with the number of layers is qualitatively in good agreement with previous reports39,40,41.

When examining the layer dependent STS data of undoped WSe2 in more detail, we find that for more than 1 ML WSe2 additional steps in the local density of states of the valence band can be seen (Fig. 2b). Such steps are indicative of a staggered DOS as expected for a 2D system42. Hence, our data suggest that every additional layer of WSe2 introduces another electron subband in the valence band spectrum. This behavior has recently also been observed in transport experiments by Takeyama et al.43 and can be described by a tight binding model of weakly coupled 2D quantum wells. Thereby, the weak van der Waals inter-layer coupling is introduced by an inter-layer electron (hole) hopping term te(h). The resulting energies of the nth subband edge is given by: $${E}_{{{{\rm{e(h)}}}}}^{n}={E}_{{{{\rm{e(h)}}}}}-2{t}_{{{{\rm{e(h)}}}}}cos(\frac{n\pi }{N+1})$$ where Ee(h) are the conduction (valence) band edges of 1 ML WSe2 and N is the number of layers44. In Fig. 2d, we plot the width of the identified energy plateaus E$${}_{{{{\rm{h}}}}}^{n}$$ for 1–7 ML of undoped WSe2. Fitting the quantum well model to the layer dependence of the valence band edge, conduction band edge, and band gap in Fig. 2c, we estimate Eh = −1.05 ± 0.02 eV, Ee = 1.30 ± 0.03 eV, th = 0.29 ± 0.02 eV and te = 0.21 ± 0.02 eV. The derived values for the hopping parameters coincide very well with those reported by Ruiz-Tijerina et al.45 for WSe2 in their kp tight binding model theoretically investigating the intersubband transitions.

### Layer-dependent STS of vanadium-doped WSe2

After having established that undoped WSe2 exhibits the expected layer-dependence, we focus on V-doped WSe2. In Fig. 3, STM images for different numbers of layers of V-doped WSe2 are shown. When comparing the high-resolution STM images of 1 ML of undoped (Fig. 2a) and 1 ML of V-doped (Fig. 3a) WSe2 taken at positive bias voltage, we observe a high density of localized circular depressions in the STM topography for V-doped WSe2. We identify these depressions as V dopants, because their density of about 0.44% is more than an order of magnitude higher than the density of all impurities observed for undoped WSe2 and both, the STM and STS signatures, coincide with the one we previously reported for V atoms substituting W21. In Fig. 3b–i, the layer-dependent appearance of the V dopants is presented. At negative VB, V dopants in the topmost layer appear as circular protrusions, independent of the number of WSe2 layers. At positive VB on the other hand, the contrast changes from a circular (dark) depression for 1 ML and 2 ML, to a hexagonal (bright) orbital shape from 3 ML and beyond.

In Fig. 4, we analyze the layer-dependent progression of the local electronic states of the V dopants. We perform STS centered on the V dopants that are in the topmost layer of n-layered WSe2 for n = {1, 2, ..., 7} and compare the results to STS of n-layered undoped and V-doped WSe2 that are recorded as far from vanadium substituents as possible given the high dopant density. The STS results for V-doped WSe2 are shown in Fig. 4a. While the band gap is also narrowing for increasing number of layers, the shift of the band edges is highly asymmetric. Whereas the conduction band onset stays roughly at the same energy, the valence band onset shifts from −1.18 V (1 ML) to −0.12 V (3ML) and converges to ~0 V for larger number of layers. On individual V dopants (Fig. 4b) we observe additional electronic states above the valence band edge as reported in Ref. 21 confirming their p-type character. Like the valence band maximum (VBM) of V-doped WSe2, the localized dopant states progressively shift toward the Fermi level, where they get pinned for 3ML and thicker samples. At the same time, the difference between the highest occupied defect state and the VBM gets smaller, indicating a weakening of the defect state binding energy. The comparison of the layer-dependent band edge evolution and band gap for V-doped WSe2 and undoped WSe2 is summarized in Fig. 4c, d.

### Layer-dependent Schottky contact

The pinning of the valence band edge of V-doped WSe2 can be understood as a Schottky contact where the p-type dopants in the depletion region of two ML are ionized, i.e., negatively charged. For three or more ML, the charge transition level is just below zero bias voltage, hence when scanning the charge–neutral V dopants with negative bias voltage, thus probing the electronic states below the Fermi level, they exhibit the same STM signature as the negatively charged V dopants in the first and second layer V-WSe2 (Fig. 3a, b, d, f, h). However, when probing the V dopants in the third or higher V-WSe2 layer they appear charge–neutral.

At the graphene/TMDC interface, the position of the Fermi level with respect to the TMDC bands is determined by the work function and is essentially the same for doped and undoped WSe2 samples. In the bulk limit, the Fermi level assumes the intrinsic value in the center of the band gap for the undoped TMDC, whereas it gets pinned at the dopant state for the V-doped TMDC, respectively. Here we quantify over how many TMDC layers this transition is happening corresponding to the depletion depth of the Schottky contact. We find that the depletion depth for the technologically relevant 2D–3D interface of layered 0.44% V-doped WSe2 on QFEG/SiC to be between 2 ML and 3 ML, which is between 1.3 nm and 1.95 nm.

In summary, we identified a distinct layer dependence of the electronic structure of pristine and p-type V-doped WSe2 on a QFEG/SiC substrate using STM/S. For pristine WSe2, the band gap narrows symmetrically, with the Fermi level fixed to the center of the band gap. Moreover, we find that each additional WSe2 layer introduces an extra subband in the valence band spectrum. The progression of the conduction and valence band edge for 0.44% V-doped multilayer WSe2 on the other hand exhibits a prototypical Schottky contact behavior. While for monolayer V-doped WSe2 the Fermi level resides close to the center of the band gap, it gets pinned to the highest dopant state upon exceeding 2 ML, corresponding to a depletion depth of about 1.6 nm.

## Methods

### MOCVD growth of undoped and V-doped WSe2 films

The undoped and V-doped WSe2 samples were synthesized in a custom-designed vertical cold wall gas-source CVD reactor as reported previously in Refs. 17,46. Tungsten hexacarbonyl (W(CO)6) (99.99%, Sigma-Aldrich), hydrogen selenide (H2Se) (99.99%, Matheson), and vanadium (V(C5H5)2) (sublimed, 95% Strem Chemicals) were used as metal, chalcogen, and dopant precursors, respectively, in a 100% H2 ambient.

The metal and dopant precursors are kept inside stainless-steel bubblers where temperature and pressure are constantly maintained at 25 °C and 970 mbar, and 40 °C and 970 mbar, respectively. H2Se is supplied from a separate gas manifold. All three precursors are introduced from separate lines to prevent intermixing before reaching the reactor inlet. The growth of undoped and V-doped WSe2 followed the three-step growth reported in Ref. 47, which consists of a nucleation, a ripening, and a lateral growth stage on c-plane sapphire (Cryscore Optoelectronic LTd, 99.95%. ). At all three stages, the growth temperature, pressure, and H2Se flow rate were kept constantly at 800 °C, 930 mbar, and 7 sccm.

For the growth of undoped WSe2, the metal precursor is inserted with a flow rate of 20 sccm for 2 min during the nucleation phase. At the ripening stage, the W(CO)6 flow is switched off and the formed nuclei are annealed in H2Se for 10 min. During the lateral growth phase, W(CO)6 is re-introduced with a constant flow of 4.5 sccm.

For the growth of V-doped WSe2, V(C5H5)2 was additionally inserted simultaneously with W(CO)6 during the nucleation phase with a flow of 60 sccm and with a flow of 5 sccm during the lateral growth phase. The vanadium density was deduced from STM measurements.

### Scanning probe microscopy

Undoped and V-doped WSe2 were prepared ex situ on QFEG on SiC substrates followed by a final 450 °C anneal in ultrahigh vacuum. The measurements were performed with a commercial LT STM from Scienta Omicron operated at 5 K and at pressures below 2  10−10 mbar. The tungsten tip was prepared on a clean Au(111) surface (sputtering: 10 min, Ar+, 1 kV; annealing: 10 min, 450 °C) and confirmed to be metallic. STM topographic measurements were taken in constant current mode with the bias voltage given with respect to the sample. STS measurements were recorded using a lock-in amplifier at 860 Hz and a modulation amplitude of 10 mV. The band gap was determined as described in Ref. 48 by fitting the valence and conduction band edge and the band gap intensities of the logarithmic STS data with a line.