Universal Fermi-Level Pinning in Transition-Metal Dichalcogenides.

Understanding the electron transport through transition-metal dichalcogenide (TMDC)-based semiconductor/metal junctions is vital for the realization of future TMDC-based (opto-)electronic devices. Despite the bonding in TMDCs being largely constrained within the layers, strong Fermi-level pinning (FLP) was observed in TMDC-based devices, reducing the tunability of the Schottky barrier height. We present evidence that metal-induced gap states (MIGS) are the origin for the large FLP similar to conventional semiconductors. A variety of TMDCs (MoSe2, WSe2, WS2, and MoTe2) were investigated using high-spatial-resolution surface characterization techniques, permitting us to distinguish between defected and pristine regions. The Schottky barrier heights on the pristine regions can be explained by MIGS, inducing partial FLP. The FLP strength is further enhanced by disorder-induced gap states induced by transition-metal vacancies or substitutionals at the defected regions. Our findings emphasize the importance of defects on the electron transport properties in TMDC-based devices and confirm the origin of FLP in TMDC-based metal/semiconductor junctions.

Introduction

Transition-metal dichalcogenides (TMDCs) (MX2, where M = Mo or W and X = S, Se, or Te) are two-dimensional materials with a wide range of electronic properties, for instance, insulating, semiconducting, and semi-metallic.[1,2] These layered materials are constituted of hexagonal-packed transition-metal atoms sandwiched between two layers of chalcogens, with a strong intralayer covalent bond between the different atoms. These individual trilayers are held together by van der Waals bonds. The optical and electronic properties of TMDC materials depend on their composition, stacking order, and thickness.[2−6] Especially, the semiconducting TMDCs are interesting for (opto-)electronics because of their relatively high carrier mobility and their tunable band gap[7−9]

The metal–semiconductor junction (MSJ) is a critical component in electronic and optoelectronic devices. One of the most important parameters in the MSJs is the Schottky barrier height (SBH, ϕB), the height of the potential barrier formed at the metal–semiconductor interface, which has a significant impact on the device performance. Tuning the SBH is necessary in order to reduce the contact resistance, modulating the charge carrier type in transistors, and to enhance the selectivity of carrier extraction for photovoltaic cells.[10−14]

Because of the van der Waals interlayer bonding, it was expected that the contact metal is also weakly bonded to the TMDC layer, so that the SBH would approach the Schottky–Mott limit of weak pinning and could easily be tuned.[15,16] However, experiments and simulations showed the opposite behavior, the SBH depends only weakly on the contact metal.[10,17−20] This was attributed to Fermi-level pinning (FLP).[17,19−21] The origin of the FLP has been debated for a long time. There are two well-known models describing FLP; metal-induced gap states (MIGS)[22] and extrinsic disorder-induced gap states (DIGS).[23] For DIGS, the FLP originates from the electronic structure of the host semiconductor within the MSJ. On the other hand, the MIGS model predicts that the metal will dominate over the substrate in pinning the Fermi level. To reveal the MIGS effect experimentally within TMDCs, a reduction of the extrinsic factors, such as defects and stacking faults, is a prerequisite.

Several works have been conducted to find the origin of FLP and subsequently control its strength.[10,17,19−21,24−26] Theoretical studies predicted that the FLP effect in the MSJ is mainly induced by two interface effects: first, due to modification of the metal’s work function by dipole formation at the interface and second, by the introduction of gap states due to the reduction of the chalcogen/transition-metal bonding strength.[21] Later, Guo et al. performed simulations for several TMDCs, showing that the TMDC/metal junctions largely follow the MIGS model, similar to three-dimensional semiconductors despite their different structure and bonding.[17] However, it is difficult to experimentally access the pinning mechanism because of the high density of surface defects, which alter the properties of these materials.[20,24,27−29] To experimentally confirm the pinning mechanism of the TMDC-based MSJ, a defect-free MSJ has to be constructed.

Recently, nanoscopic MSJs have been obtained using conductive atomic force microscopy (C-AFM). In C-AFM, the tip can act as a nanoscopic metal electrode.[6,20,30−33]I(V) characteristics recorded with a C-AFM of the Pt-coated tip/MoS2 junction revealed variations in the SBH.[31,32] This method was also used to investigate the effect of local defects,[20] stacking faults,[6] plasma functionalization,[34] and charge variations due to doping[33,35] on the charge transport across the MSJ. Because of the nanoscopic size of the contact metal, small variations at the surface can be measured. Substitution or removal of the transition metal or the chalcogen atoms lead to defect sites with different electronic properties compared to the pristine regions[28,36−38] including small SBH and strong FLP.[6,20] On MoS2, defects located at the Mo layer enhance further the FLP strength compared to pristine surface or regions with S-vacancies.[20]

In this work, we use the C-AFM to construct nanoscopic MSJs on several TMDCs, in order to investigate the exact mechanism behind FLP on TMDCs. We performed high-spatial-resolution C-AFM and scanning tunneling microscopy (STM) imaging in order to characterize defects present on several TMDC surfaces (MoSe2, WSe2, WS2, and MoTe2). For the studied TMDCs, we find defects with similar appearance and influence; STM reveals that chalcogen defects have almost no influence on their surroundings, whereas transition-metal defects lead to a strong localized contrast that depends on the used set point. The barrier heights of the pristine surface can be explained by the MIGS mechanism, which normally applies to three-dimensional semiconductors. Spatially resolved Schottky barrier maps reveal a decrease of the SBH and a stronger FLP at defect sites because of DIGS. The DIGS decrease the pinning factor by approximately 30–40%. Our results provide new insights into the physics governing the contact properties and charge transport through the TMDC-based MSJ.

Results and Discussion

Defects in TMDCs

Figure a shows topographic AFM and lateral force images (see the inset of Figure a) of a freshly cleaved MoSe2 surface. The surface appears smooth and defect-free in both images. However, within the simultaneously recorded C-AFM image, the surface is inhomogeneous when a negative voltage is applied to the sample. Multiple dark circular features (with radii ranging between 3 and 4 nm) appear (see Figure b). The current recorded at these features is higher than that for the pristine surface. The density of the features varies between 1010 and 1011 cm–2 dependent on the sample and location. Imaging a region without round depressions requires a high magnification of a small area. Figure c shows an example of a high-resolution STM image where the atomic structure of WSe2 is observed, revealing the expected hexagonal pattern with a unit cell of (0.33 ± 0.02) nm. The structure is consistent with the semiconducting 2H phase. In addition to the observed hexagonal pattern, several missing atoms are observed. At these positions, Se atoms are missing, inducing Se vacancies. The electronic influence on the surrounding of the Se vacancies is small (<1 nm in radius), excluding them from being the origin of the dark round features in the C-AFM image (see Figure b). Besides, the density of the Se vacancies (1012 to 1013 cm–2) is 2 orders of magnitude higher compared to that of the dark circular features (1010 to 1011 cm–2) observed in the C-AFM.

Figure 1

(a) Topographic AFM image (inset: corresponding lateral force image) of a freshly cleaved MoSe2 crystal (600 × 600 nm2, the scale bar is 200 nm). (b) Simultaneously recorded C-AFM image recorded at −1.2 V sample bias. (c) STM topography image of the WSe2 surface, revealing missing selenium atoms (10 × 10 nm2, the scale bar is 3 nm). The tunneling parameters are 1.1 nA and −0.6 V. (d) STM topography image of dark circular features (30 × 30 nm2, the scale bar is 8 nm, tunneling parameters: 100 pA and 1.5 V). (e) Current cross section recorded with C-AFM at the dark round features induced by defects in the first and second trilayers, respectively [inset: the C-AFM image indicating the defects where the cross section was taken (20 × 20 nm2, SB is 1.2 V)].

Large-scale STM images reveal the presence of dark depressions similar to the ones observed in the C-AFM (Figure d). High-resolution STM images show a depression without disrupting the atomic lattice, confirming that the effect is purely electronic (see the Supporting Information). The average defect density of 1010 to 1011 per cm–2 is comparable to the density found in the C-AFM images. The appearance and density of the defects are very similar to the defects observed on MoS2.[20,24] In these studies, the origin of the dark round features was attributed to metal-like defects or impurities located underneath the outermost S layer. Mo-vacancies and antisite (Mo-substitutional) defects occur on the subsurface without a structural modification of the top S layer. These defects ionize the sulfur atoms. Coulomb repulsion around these sulfur atoms leads to electron depletion and causes the appearance of the dark disk observed in both C-AFM and STM.[20,39] We note here that the observed defects are intrinsic in nature, as the samples have not gone through any treatment (except exfoliation) prior to scanning. In addition, similar features with similar densities were found in other types of TMDCs, such as WS2[6,40] and WSe2,[29,41,42] attributed to impurity atoms (such as Re, Na, and Li) present in the crystal.[29,43] Therefore, we suggest that the dark circular features originate from metal-like defects (Mo/W vacancies or substitutionals), which change the electronic landscape of their surroundings. Next to the dark circular defects, bright defects are observed in the STM image (Figure d). These defects are attributed to trapped electron states around a donor on the surface chalcogen atom layer.[28,44] However, these defects are not observed in the C-AFM images.

A closer look at the metal-like defects reveals that they fall into two categories: defects with current amplitudes of approximately −150 and −50 pA (at a bias voltage of 1.2 V), as shown in Figure e. These differences are caused by the position of the metal-like defect. When located in the top MoSe2 trilayer, the electronic influence is larger compared to defects located in the second MoSe2 trilayer, as observed previously for MoS2 and conventional semiconductors.[20,45,46] These results suggest that the conductance of MoSe2 can be influenced by metal-like defects in the first and second trilayers.

Similar defects are found in the C-AFM images on WS2, WSe2, and MoTe2 (see the Supporting Information). These defects have similar appearances as the metal-like defects on MoS2[20] and MoSe2 (see Figure b). Earlier studies emphasized the similarities between the defect types in the different TMDCs.[47−49] The energies needed to create defects within the different types of semiconducting TMDCs are comparable[38,50,51] as well as the structural conformations.[52] Therefore, we conclude that the defects observed with C-AFM on the studied TMDCs are all metal-like defects.

SBHs on Pristine and Defected Regions

Because it is now possible to distinguish between defected and pristine regions (note here that the pristine regions still contains chalcogen defects), the local electron transport through nanoscopic MSJ between a Pt tip (ϕM = 5.64 eV) and the semiconducting TMDC can be investigated. For zero charge transfer in the MSJ (Schottky limit), the electron SBH is given by the difference between the work function of the metal (ϕM) and the electron affinity of the semiconductor (χS)

A characteristic I(V) curve for the MoSe2-based MSJ is shown in Figure a. The measured I(V) curve on the pristine region shows a diode-like behavior, as expected for a MSJ.[53] The negative sample bias is defined as the forward bias regime. For larger negative voltages, the SBH lowers and the current increases exponentially with the voltage. The current in the MSJ under forward bias is described by the thermionic emission model and is given by[54]where V is the applied bias, kB is the Boltzmann constant, T is the temperature, η is the ideality factor, this is the deviation of the current transport from ideal thermal emission, and q is the electron charge. For values of V larger than 3kT/q, the second term in eq becomes negligible. The reverse saturation current (I0) is a constant and depends on the Schottky barrier ϕBwith A being the MSJ area, that is, the tip contact area and A* is the Richardson constant (, with m* the effective mass and h the Planck constant). The contact area of the Pt tip is estimated using the Hertz model[55,56] and is approximately 2.7 nm2 at a load of 5–10 nN. The ideality factor is obtained fromand the ϕB for electron injection is acquired using

Figure 2

(a) I(V) curves recorded with a Pt tip on a pristine (red) and defected (black) region of MoSe2. Inset: the corresponding semi-logarithmic I(V) curves from which the SB is extracted. (b) Spatially resolved current map (200 × 200 nm2, scale bar 50 nm) obtained via 128 × 128 individual current–voltage curves, recorded from −0.6 to 1.5 V. The map corresponds to a voltage of −0.15 V. (c) Extracted SBH map of the surface obtained from the individual I(V) curves in (a). Significant differences in the SBH are observed at the positions of the defects in (b). For the ideality factor (η) map, see the Supporting Information. (d) Histogram of the SBH for the white dashed box marked in (c). Three peaks are observed: (0.37 ± 0.03), (0.30 ± 0.02), and (0.24 ± 0.03) eV for the pristine region, defects located in the second trilayer and defects located in the first trilayer, respectively.

The ideality factor is extracted from the slope of the linear part of the ln I(V) curve (like in the inset of Figure a). The intercept of this fit gives the saturation current which is used to extract the SBH according to eq . By applying the above-mentioned equations to the recorded I(V) curves in Figure a, the SBH of the pristine region is approximately (0.37 ± 0.02) eV and the ideality factor is 1.1. The defected region shows a slightly higher current at the reverse bias (see Figure a). This is a result of a change in the SBH and ideality factor. The SBH for the defected region is (0.24 ± 0.04) eV with an ideality factor of 1.5. As the SBH is lower, more current can pass through the junction.

The advantage of using a sharp AFM tip as the metal electrode in the MSJ is the ability to record individual I(V) curves at every point of the surface. Figure b shows a spatially resolved current map extracted from a 128 × 128 grid of individual I(V) curves at a bias voltage of −0.15 V. A clear difference is found between the defects and pristine region, as already observed in the C-AFM image (see Figure ba). We can now extract the SBH for each of the individual curves and construct a SBH map (Figure c). Significant inhomogeneities in the barrier height are observed. Interestingly, the SBH remains constant on the pristine regions of the MoSe2 surface, whereas directly above the defects, a decrease of the barrier height is measured.

The histogram in Figure d is constructed of the current values within a specific part of the SBH map (marked with the dashed box in Figure c). It reveals three peaks: corresponding to the pristine region [at (0.37 ± 0.03) eV], the defected region [(0.24 ± 0.04) eV], and a third peak at (0.30 ± 0.02) eV. A closer look at the current and SBH maps confirms the presence of defects located in the second trilayer, in line with the C-AFM images of Figure b. Recent calculations showed that the influence of defects on the SBH decreases as the dopant-interface distance increases.[57] Therefore, defects in the second trilayer have a weaker influence on the SBH compared to defects in the first trilayer.

We have also observed defect-induced reduction of the SBH for WS2, WSe2, MoTe2 (see the Supporting Information), and MoS2.[20] However, the absolute values of the SBH on the pristine and defected regions differ between the different TMDCs (using the same tip). This is a result of the different electron affinities and electronegativities of the various TMDC semiconductors. According to the Schottky–Mott rule (see eq ), the SBH decreases linearly with increasing electron affinity. Although a decreasing trend is found, it is not linear and the experimentally found SBH values do not match with the prediction of the Schottky–Mott rule.

Metal-Induced Gap States

The discrepancy between the predicted and measured SBHs has also been found in other studies for conventional as well as layered semiconductors.[6,19,24,58−60] The Schottky–Mott rule assumes that there is no charge transfer between the metal and the interface states of the semiconductor. However, other studies suggested that charge transfer should also be included for the metal/two-dimensional (2D) material MSJ.[21,60] Generally, FLP is characterized using two different methods: (1) the Schottky–Mott approach and (2) the electronegativity concept. In the case of the Schottky–Mott approach, the SBH is given bywhere S is the Schottky pinning parameter (S = dϕB/dϕM), χ is the electron affinity of the semiconductor, and ϕCNL is the charge neutrality level with respect to the vacuum level which is given bywhere b is the y-intercept of the ϕB versus ϕM graph. S is dependent on the density of interface states per unit area N and their extend into the semiconductor δ aswith ε0εr being the absolute permittivity of the interface. When S = 1, the Schottky–Mott limit is recovered (no pinning, N ≈ 0, no gap states) and the SBH is given by eq , whereas for S = 0, the SBH is described by the Bardeen limit of strong pinning. In the Bardeen limit, the metal Fermi level is pinned by the interface states at ϕCNL.

In the electronegativity concept, the SBH is determined usingwith S′ the experimentally obtained pinning factor (S′ = dϕB/dX[61,62]), XM the electronegativity of the metal, XTMDC the electronegativity of the TMDC, and ϕCNL′ the charge neutrality level with respect to the vacuum level. The difference between the concepts is the use of a surface property (work function and electron affinity) for the Schottky–Mott concept and a bulk property (electronegativity) for the electronegativity concept.

In order to determine the pinning factors and charge neutrality levels of the different TMDCs, the dependence of the ϕB on the tip work function and electronegativity should be systematically studied. Therefore, we have performed the same measurements with two additional AFM tips: a PtSi tip (ϕM ≈ 4.9 eV, XM ≈ 2.08, contact area 5.7 nm2) and a highly n-doped Si tip (ϕM ≈ 4.15 eV, XM ≈ 1.9, contact area 1.5 nm2). For both tips, similar maps are obtained as for the Pt tip. Figure a shows the extracted SBH map for a PtSi tip on MoSe2. A decrease of approximately 33% in the SBH is observed compared to the results obtained with the Pt tip on MoSe2 for both the defects [(0.14 ± 0.03) eV] and the pristine region [(0.24 ± 0.02) eV]. This is attributed to the lower work function and electronegativity of the PtSi tip. In addition, defects in the second trilayer are no longer observed. The absolute value of the SBH decreases (as well as the absolute difference) making it no longer possible to resolve the presence of defects in the second trilayer.

Figure 3

(a) Extracted SBH map (200 × 200 nm2, the scale bar is 50 nm) of the MoSe2 surface obtained with a PtSi tip (ϕM ≈ 4.9 eV). The Schottky barrier is lower on both the pristine and defected regions as compared with the measurements obtained with the Pt tip (Figure c). (b) Extracted SBH map (200 × 200 nm2, the scale bar is 50 nm) for MoTe2 with a Pt tip (ϕM = 5.64). The SBH is lower as compared to MoSe2 (Figure c) because of the different electron affinities (χMoSe > χMoTe) and electronegativities (XMoSe > XMoTe). (c,d) SBH for the pristine regions as a function of (c) metal (tip) work function (ϕM) and (d) electronegativity difference (XM – XTMDC) for the various TMDCs. The pinning factors are extracted using eqs and 9.

Measurements performed with a Pt tip on MoTe2 (Figure b) reveal a lower SBH as compared to the same measurements on MoSe2 (Figure c). The distinct difference between the SBHs is in line with the different electron affinities and electronegativities of MoSe2 and MoTe2, where χMoSe > χMoTe[63,64] and XMoSe > XMoTe. According to the Schottky–Mott rule (eq ), the MoTe2 should have a lower SBH. However, the absolute change in the SBHs cannot be explained using the Schottky–Mott rule, as charge transfer is not included in the model.

To explain the discrepancy between the obtained SBH values and the Schottky–Mott rule, the pinning factors and charge neutrality levels of the studied TMDCs have to be obtained. Figure c plots the experimentally obtained SBHs for the pristine region of the studied TMDCs versus the metal work function of the used tips. The SBHs for all of the TMDCs depend linearly on the work function of the metal, despite the different interactions between the TMDCs and the various tips.[59] In all four cases (see Table ), a strong FLP is observed, implying a strong interaction between the metal contact and the TMDC.[17,21,60] The observed pinning factor of the pristine surface of WSe2 (S = 0.28) and MoTe2 (S = 0.11) is in good agreement with the theoretically predicted pinning factors.[17]

Table 1

Pinning Factors for Both the Pristine and Defected Regions for Different TMDCsa

TMDC	Spristine	Spristine′	Spristine′ → Spristine	Sdefect	Sdefect′	Sdefect′ → Sdefect
MoS2[20]	0.30 ± 0.03	0.65 ± 0.07	0.28 ± 0.03	0.11 ± 0.02	0.22 ± 0.04	0.10 ± 0.02
MoSe2	0.19 ± 0.03	0.38 ± 0.04	0.17 ± 0.02	0.11 ± 0.02	0.23 ± 0.04	0.10 ± 0.02
MoTe2	0.11 ± 0.02	0.21 ± 0.03	0.10 ± 0.02	0.04 ± 0.01	0.08 ± 0.01	0.04 ± 0.01
WS2	0.21 ± 0.03	0.42 ± 0.06	0.19 ± 0.03	0.08 ± 0.01	0.16 ± 0.03	0.07 ± 0.01
WSe2	0.28 ± 0.03	0.61 ± 0.07	0.27 ± 0.03	0.09 ± 0.02	0.17 ± 0.04	0.08 ± 0.02

The pinning factors are obtained via two different concepts: (1) Schottky–Mott relation (S) and (2) electronegativity concept (S′). S′ is converted to S (S′ → S) using the relation S′ = 2.27S.[62] The pinning factors are extracted from Figures c,d and 5a,b.

Figure 5

(a,b) SBH for the defected regions as a function of (a) metal (tip) work function (ϕM) and (b) electronegativity difference (XM – XTMDC) for the various TMDCs. The pinning factors are extracted using eqs and 9.

The SBHs for MoSe2 (S = 0.19) and WS2 (S = 0.21) are slightly lower as compared to theory but still agree reasonably well.[17] The small deviation may be a result of the doping level. In our study, all of the TMDCs are n-type doped (see the Supporting Information), whereas for many calculations, p-type-doped TMDCs are used.[17] The different pinning factor values emphasize that a different degree of pinning occurs for different TMDCs, which from eq implies that a different density of gap states is causing the FLP in each case (the penetration depth δ is approximately constant for all of the TMDCs).[17,59,60]

The linear dependence of the SBH as a function of the metal work function (Figure c) shows that an electric-dipole layer exists at the TMDC-Schottky contacts.[21,60] Together with the strong FLP between the metal and the TMDC, it is suggested that the band-structure line up at the Schottky contact is determined by the same mechanism as for conventional semiconductors, which is described by the MIGS model. Within the MIGS model, the main origin of the gap states, which causes the pinning, is the evanescent states of the metal plane waves as they decay in the semiconductor band gap. Later, Gong et al.[21] refined the exact pinning mechanism for TMDCs. They claimed that two interface effects induce FLP: first, the dipole formation is altering the work function and second, interface interactions weaken the transition-metal/chalcogen bonding, which introduces the formation of gap states.

To explore the effect of dipole formation in more detail, the SBH is plotted as a function of the respective electronegativity (X) difference between the metal and the semiconductor (see Figure d). A linear trend is observed in agreement with Figure c. The extracted pinning factors S′ are consistent with the pinning factors in Table . The obtained charge neutrality levels for all four TMDCs are located in proximity of the conduction band (see Table ), which is expected for n-type Schottky barriers. The charge neutrality levels for the electronegativity concept do not match with the charge neutrality levels obtained using eq , but are comparable to previously found charge neutrality levels for other layered semiconductor compounds.[65] The difference between the two concepts is attributed to the use of surface (work function and electron affinity) and bulk properties (electronegativities). The preference for using the electronegativity rather than the work function for calculating the charge neutrality level was led by the difference between the internal work function related to the electronegativity and the measured work function due to the additional electronic contribution from the surface dipole of the metal.[60,66,67]

Table 2

Charge Neutrality Levels (with Respect to Conduction Band Minimum) for Both the Pristine and Defected Regions for Different TMDCsa

TMDC	ϕCNL,pristine [eV]	ϕ′CNL,pristine [eV]	ϕCNL,defect [eV]	ϕ′CNL,defect [eV]
MoS2[20]	0.07 ± 0.02	0.6 ± 0.05	0.13 ± 0.03	0.22 ± 0.03
MoSe2	0.06 ± 0.02	0.39 ± 0.05	0.13 ± 0.2	0.25 ± 0.04
MoTe2	0.06 ± 0.02	0.20 ± 0.03	0.04 ± 0.1	0.13 ± 0.03
WS2	0.11 ± 0.02	0.55 ± 0.05	0.07 ± 0.1	0.24 ± 0.03
WSe2	0.03 ± 0.01	0.71 ± 0.09	0.08 ± 0.2	0.28 ± 0.04

The charge neutrality levels are obtained via two different concepts: (1) Schottky–Mott relation (ϕCNL) and (2) electronegativity concept (ϕCNL′). ϕCNL and ϕCNL′ are determined using the relations 7 and 9.

When the electronegativities of both the metal and the semiconductor are equal, no charge transfer is expected to occur at the interface. The linear dependence observed between the SBH and the electronegativity difference demonstrates that dipoles indeed exist within metal/TMDC interfaces and follow the same trend as conventional semiconductors.[60] In most cases, the semiconductor is more electronegative than the metal resulting in an electron accumulation on the TMDC side and depletion on the metal side of the interface. In other words, charge transfer from the metal toward the more electronegative TMDC occurs, increasing the work function of the metal in agreement with refs (21) and (68). Only for the case of a metal tip on MoTe2, the dipole moment switches, reducing the work function of the metal.

Further evidence that TMDC-based MSJs follow the MIGS model is presented in Figure , where the experimentally obtained inverse pinning factor is plotted versus the optical part of the dielectric constant, ε∞. In 1978, Schlüter proposed that there is a relation between the SBH of conventional semiconductors and their dielectric constant.[66] Later, Tersoff[69] suggested a correlation with the optical dielectric constant, ε∞, which was later extended by Mönch,[70] who found that S obeys the empirical relation

Figure 4

Experimental values of the pinning factor (S) for conventional semiconductors[71] (△), for the 2D conventional semiconductor[72] (◇), for TMDCs in this study for the pristine region (○) and defected region (□) and calculated TMDCs[17] (*) as a function of the optical dielectric constant (ε∞). The solid lines are a guide to the eye based on eq . For all the data point labels, see the Supporting Information.

The solid lines in Figure clearly show that all types of semiconductors (including TMDCs) follow the relation given in eq and that FLP in TMDCs can be described by the MIGS model.[17] The vertical shift of the TMDC data (□ in Figure ) with respect to the conventional semiconductors (△ in Figure ) to lower pinning factors is caused by a lower net density of gap states (N) in eq . Using eq , the density of gap states can be estimated. Assuming that the penetration depth is δ ≈ 3 Å[59] and ε ≈ 7[73] (note here: this is not ε∞) for the various TMDCs (except MoTe2), the density of gap states N is estimated at 1 × 1014 states/eV cm2. The obtained density is lower than the theoretically calculated value 2.3 × 1014 states/eV cm2 for a jellium/diamond interface[67,74] (in good agreement with Figure , where Sdiamond < STMDC). From Figure , the low pinning factor for MoTe2 with respect to the other TMDCs is also explained. The number of MIGS is inversely dependent on the width of the optical band gap.[61] As MoTe2 has a smaller optical band gap than the other TMDCs, more MIGS are present in the Schottky junction and a stronger FLP is observed.

Furthermore, it was suggested that the presence of defects gives rise to extra pinning because of DIGS.[10,17,24,75]Figure a,b shows the SBH for the defected regions of the TMDCs as a function of the metal work function and the electronegativity difference, respectively. Tables and 2 give an overview of the extracted pinning factor and charge neutrality levels. In the investigated cases, the FLP is stronger at the positions of the defects. In the majority of the cases, a drop of approximately 30–40% in the pinning factor is observed for defected regions with respect to the pristine surface. This is the result of DIGS. Defects lead to the formation of dangling bonds, which result in variations of the transition-metal orbital symmetry.[26] Consequently, some empty states become occupied and move into the band gap to form DIGS.[76,77] The effect of the defects on the SBH, pinning factor, and charge neutrality level is independent of the TMDC type (complimentary with the observation in the current image of the C-AFM and in the STM), implying that the defects are of the same origin. As already mentioned earlier, these defects are most probably transition-metal vacancies or substitutionals.[29,36,37]

Several experimental[10,24] and theoretical studies[17,26,38] also observed an increase in FLP because of defects. In these studies, chalcogen vacancies were assigned as the origin of the DIGS. Similar to MoS2,[20] the strong FLP in this study is not caused by chalcogen vacancies as these are (1) still present on the pristine surface, (2) do not influence the conductivity, and (3) do not significantly alter their surroundings within the C-AFM and STM images (see Figure c). In addition, the pinning factors of the pristine regions (including chalcogen defects) are in good agreement with theory. In contrast, the pinning factor of the defected regions (induced by transition-metal vacancies or substitutionals) corresponds well to the pinning factors found in previously reported experimental studies.[19,20]

When the pinning factors of the defected regions for the various TMDCs are plotted as a function of the optical dielectric constant (□ in Figure ), the same trend is observed for the pristine regions. The points are shifted to lower pinning factors as the DIGS increase the net density of gap states (N). The defected TMDC curve coincides with the curve for conventional semiconductors, implying that the net density of gap states (N) is similar.

Unfortunately, FLP still occurs when MSJs are constructed using a conventional metal and TMDCs as a semiconductor, on contrary to the expectations based on their weak bonding with other materials. Several studies proposed promising paths to reduce FLP in TMDCs, such as the use of buffer layers[25] or the use of other van der Waals materials as the contact material.[78,79] Even in these junctions, subsurface defects will lower the SBH and will have a tremendous impact on the device performance. Furthermore, the effect of defects will be more pronounced when electronics are scaled down, wherein the contact area is just a few nanometers. Therefore, the conductance variations induced by transition-metal vacancies (or substitutionals) should be considered in device characterization and predictability.

Conclusions

In summary, using C-AFM and STM, we have studied the underlying mechanisms behind FLP in various TMDCs. Using a nanoscopic MSJ, we were able to distinguish between intrinsic and extrinsic factors responsible for the FLP. Spatially resolved SBH maps reveal a substantial difference between pristine and defected regions of the TMDC surface depending on the work function of the metal AFM tip. A strong FLP was observed on the pristine regions which can be explained by the MIGS model in line with conventional semiconductors. The extracted pinning factors are in good agreement with the theoretically predicted values.[17] The defects induce an even stronger FLP (30–40% increase) because of DIGS. The pinning factor found in defected regions agrees well with the experimental values obtained in previous studies where large metal contacts were used.[19] Our findings show that on van der Waals semiconductor surfaces without dangling bonds, the Fermi level is still heavily pinned because of MIGS. Moreover, the FLP is enhanced in the surroundings of subsurface defects because of DIGS. These defects can provide an alternative route for surface functionalization for device applications.

Methods

The TMDCs were mechanically cleaved and subsequently inserted in the AFM environmental chamber. The measurements were performed in N2 environment by continuously purging with N2 gas in order to reduce the influence from contaminants. The samples were imaged in the contact mode with an Agilent 5100 AFM using conductive probes. For the C-AFM measurements, the tip was grounded, whereas a bias voltage was applied to the various TMDC crystals. The conductive tips used are: Pt tips (12Pt400B, Rocky Mountain Nanotechnology), PtSi tips (PtSi-CONT, NANOSENSORS), and highly n-doped Si tips (Hi-res-C14/Cr–Au. MikroMasch, resistivity: 0.01–0.025 Ω cm) (for detailed information see the Supporting Information). STM and scanning tunneling spectroscopy measurements were performed in an Omicron low-temperature STM operating at a base pressure below 1 × 10–10 mbar and a base temperature of 77 K.