Introduction

Molybdenum disulfide (MoS2)1,2 and graphene3,4 are rapidly emerging and already successfully emerged nanoelectronic materials. In many ways, MoS2 is compared with its predecessor graphene for their beneficial properties such as outstanding carrier mobility5,6,7,8,9,10, high structural flexibility3,11, and bandgap modulation under external perturbations12,13,14,15,16,17,18,19. However, in contrast to gapless graphene, pristine MoS2 shows a sizable bandgap of ~1.3 eV in its bulk state, which further increases up to ~1.9 eV upon exfoliating. For this reason, extensive efforts have been carried out to take advantages from each material and combine them into a single device. Prominent accomplishments in such efforts are the synthesis of stacked graphene-MoS2 junctions20,21,22,23 and their application to field effect transistors (FETs)24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39 in which MoS2 and graphene are used as a channel and source(S)-drain(D) electrodes, respectively.

In FETs, an ohmic contact is usually desired for easy current flows between semiconductor and S/D electrodes. To fulfill this requirement, relevant contact searching is primarily focused on avoiding materials with the rectifying responses to forward and backward biases. Reported S/D electrodes on MoS2 channel are pure metals such as Ti5,6,8,40,41,42,43,44, Au40,45,46,47,48,49,50, and Sc42,43, and the most popular material amongst them tends to become Au/Ti deposition followed by a post-annealing process44. This choice follows from a prior estimation based on the Schottky-Mott rule51,52,53, which states that the potential barrier height at the interface is given by the energy difference between the semiconductor electron affinity and the metal work function. Because the electron affinity of MoS2 is reported as 4.0 eV and the work functions of graphene and Ti are known as 4.5 and 4.3 eV, respectively, MoS2-Ti contact is expected to form a smaller Schottky barrier, leading to a more ohmic behavior. Contrary to this expectation, however, graphene-contacted MoS2 shows higher on-current and lower off-state behaviors, displaying an on/off ratio over ~7.5 × 106 29. To understand this seemingly anomalous feature, we first constructed graphene/MoS2 and Ti/MoS2 stacking structures, and investigated their electronic band structures by using the first-principles density functional method54. In this work, we explicitly show the absence of graphene-induced gap-states, which otherwise would cause a Fermi level (EF) pinning55 within the bandgap. We then attribute the sensitive variations of EF and work function under gate-voltages to the strong decoupling between graphene and MoS2 bands in their heterojunction.

Computational Methods

To investigate the gate-voltage tuning effects on the graphene(S/D)-MoS2 and Ti(S/D)-MoS2 FETs, we have performed self-consistent density functional calculations using the SIESTA code54. Exchange and correlation were treated with the local density approximation (LDA)56. Core electrons were replaced by standard norm-conserving pseudo-potentials57 as transformed into fully nonlocal Kleinman-Bylander form58. Valence states were described by numerical atomic orbitals of double-ζ plus polarization basis-set to account for the deformation density induced by bond formations. Electronic wavefunctions and charge densities were projected onto a real space grid with an equivalent energy cutoff of 500 Ry. We used 24 × 24 k-grid sampling in the full Brillouin zone (BZ) for the slab systems. To describe naturally n-doped MoS2, we performed the virtual crystal approximation (VCA) by replacing 1.3 × 10−4 atomic % of sulfur atoms with chlorine atoms. This corresponds to 5.0 × 1016cm−3 electron doping in bulk MoS2 as consistent with experimental observations40,59,60,61,62. After the VCA, additional electron charging effects under gate-voltages were simulated by direct electron addition or subtraction methods. For the graphene stacking on MoS2, we considered two different heterostructures with commensurability conditions: (i) graphene sheet (6.51 Å) was stacked on 2 × 2 MoS2 monolayer (6.32 Å) which includes 2.9% lattice contraction of graphene. (ii) 4 × 4 graphene sheet (9.84 Å) was adjusted to 3 × 3 MoS2 monolayer (9.48 Å), resulting in 3.7% lattice contraction of graphene. For the Ti stacking on MoS2, 4-layered Ti lattice (a = 2.95 Å) was placed on 1 × 1 MoS2 monolayer (3.16 Å) which includes 6.7% lattice expansion of Ti.

Results and Discussion

In FETs, gate-voltage (VG) always puts into effects of electron charging and electric field variation in a simultaneous way. Once the system reaches a given state of on-current at a specific positive gate-voltage, both direction and strength of current flows are controlled by the drain-voltage (VD). Figure 1(f) and (g) show the approaching steps from an ungated case to an on-current stage in -graphene/2 × 2-MoS2 heterojuncion. To describe a weak positive (negative) gate-voltage, we have set the external electric field as E = ± 0.01 V/Å and the electron charging concentration as nc = ± 8.7 × 1012 cm−2. Here the positive and the negative sign represent the positive and the negative VG, respectively. To describe stronger gate-voltages, we have increased the electric field and the electron charging concentration by 10 times.

Figure 1: Atomic views and electronic band structures.
figure 1

Top-views of (a) 2 × 2 MoS2 monolayer, (b) graphene monolayer, and (c) -graphene/2 × 2-MoS2 heterostructure. Green, yellow, and blue spheres represent Mo, S, and C atoms, respectively. Band structures of (d) 2 × 2 MoS2 monolayer, (e) graphene monolayer, and (f) -graphene/2 × 2-MoS2. Inside the box (orange line), EC, ED, and EF represent the CBM energy of MoS2, the Dirac point energy of graphene, and the Fermi level of the whole system, respectively. Band structures of -graphene/2 × 2-MoS2 under (g) a positive gate-voltage (E = + 0.01 V/Å and nc = 8.7 × 1012 cm−2), (h) a negative gate-voltage (E = −0.01 V/Å and nc = −8.7 × 1012 cm−2), (i) a stronger positive gate-voltage (E = + 0.1 V/Å and nc = 8.7 × 1013 cm−2), and (j) a stronger negative gate-voltage (E = −0.1 V/Å and nc = −8.7 × 1013 cm−2). The direction of a positive electric field is from MoS2 to graphene.

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In graphene/MoS2 systems, the Schottky barrier height is defined as the energy difference between the conduction band minimum (CBM) energy (EC) of MoS2 in the graphene/MoS2 system and the Fermi level (EF) of the whole system. As seen in Table 1, the Schottky barrier (ΔE = EC − EF) in graphene/MoS2 sensitively responds to gate-voltages by decreasing from 0.37 eV (ungated) to 0.03 eV (on-current) in the positive VG, and by increasing from 0.37 eV (ungated) to 0.74 eV (off-state) in the negative VG. Easily reducible Schottky barrier in positive VG means easily diminishable contact resistance33,34,35,36,37 between graphene and MoS2, which induces large current flows in drain-voltages. In contrast, a large Schottky barrier in negative VG reduces the unprofitable current leakage in off-states and contributes to the high on/off ratio in itself. The working principles of VD and VG are similar to each other, except that VD additionally controls the chemical potential of graphene with respect to that of MoS2. Thus, the high sensitivity to gate-voltages involves a similar sensitivity to drain-voltages, resulting in a fast slope increase in the ID-VD curve and a corresponding high on/off ratio. Meanwhile, as evaluated in Table 1, the system response to gate-voltages is not completely symmetric due to the shape-change of the Dirac cone caused by the electric field. In the positive VG, the Fermi velocity near the Dirac point decreases from 8.38 × 105m/s to 8.18 × 105m/s, and the Dirac point position becomes closer to the CBM energy of MoS2. In contrast, in the negative VG, the Fermi velocity increases from 8.38 × 105m/s to 8.45 × 105m/s, and the Dirac point position becomes far away from the CBM energy of MoS2.

Table 1 Work function variations in positive and negative gate-voltages (VG) in graphene/MoS2.
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The energy difference between the CBM and the Dirac point (EC − ED) is decreased by 0.08 eV from the ungated case (0.37 eV) to the positive VG (0.29 eV), and increased by 0.10 eV from the ungated case (0.37 eV) to the negative VG (0.47 eV). This slightly asymmetric response can be assured by the energy difference between the Fermi level and the Dirac point (EF − ED); increment by 0.25 eV from the ungated case to the positive VG, and decrement by 0.27 eV from the ungated case to the negative VG. As the gate-voltages increase more, the asymmetry increases further. Shown in Fig. 1(i) and (j) are the band offsets under the strong positive and negative gate-voltages (E = ± 0.1 V/Å and nc = ±8.7 × 1013 cm−2). Intriguingly, Fig. 1(j) shows a theoretical possibility that the conduction type of real systems may transform from electrons to holes under a strong enough negative VG.

The band structures shown in Fig. 1(d–j) provide two key features on the flexibility of graphene bands: (i) We clearly see the absence of graphene-induced gap-states inside the MoS2 bandgap, which would have a flat-band form in k-space and absorb electrons from metals on stacking. This failure in forming the gap-states unlocks the Fermi level pinning and preferably makes the graphene bands flexible. As shown in Fig. 2, the absence of graphene-induced gap-states is confirmed by the clean density of states (DOS) without extra peaks near the Fermi level. (ii) The linear shape of graphene bands around the Dirac point remains intact and the linearity extends over one electron-volt from the Dirac point with a negligible band mixing between graphene and MoS2. This weak interaction is evidenced from the relatively small binding energy of −0.59 eV and the large equilibrium distance of ~3.23 Å between MoS2 and graphene24,25. In another way, positive electric fields play a role of shifting up the Dirac point toward a higher energy, so if we increase the electric field over ~0.5 V/Å without the electron charging, the Dirac point moves up above the CBM, making the conical vicinity of the Dirac point empty, which then forces EF to be located above the CBM to compensate this charge depletion. Even in this extreme electric field, the linearity is retained around the Dirac point, indicating the strong decoupling between graphene and MoS2 bands.

Figure 2: Total and partial density of states (DOS) of -graphene/2 × 2-MoS2 system.
figure 2

Black line is the total DOS of the graphene/MoS2 system. Pink line is the partial DOS of MoS2 in the graphene/MoS2 system. Blue line is the partial DOS of graphene in the graphene/MoS2 system.

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Thus far, all analyses were performed for the case with the CBM of MoS2 and the Dirac point of graphene coincided at the special k-point K. To extend the validity to more general cases where the CBM point and the Dirac point are mismatched, we consider the supercells of 4 × 4 graphene stacked on 3 × 3 MoS2. In this new stacking, the CBM point is moved to Γ whereas the Dirac point is still located at K as shown in Fig. 3. We see that all features previously analyzed in Fig. 1 are similarly exhibited in Fig. 3. The band lineups in 4 × 4-graphene/3 × 3-MoS2 reproduce sensitive and asymmetric responses to gate-voltages. Also, we see that graphene-induced gap-states do not appear, and the linear dispersion around the Dirac point remains intact on stacking and in onward applications of gate-voltages, leading to the strong decoupling between graphene and MoS2 bands. Thus, Fig. 3 confirms that the flexibility of graphene bands is not confined to the special cases where the CBM and Dirac points are matched up in reciprocal space, but is generalized to their dislocated cases.

Figure 3: Atomic views and electronic band structures.
figure 3

Top-views of (a) 3 × 3 MoS2 monolayer, (b) 4 × 4 graphene monolayer, and (c) 4 × 4-graphene/3 × 3-MoS2 heterostructure. Green, yellow, and blue spheres represent Mo, S, and C atoms, respectively. Band structures of (d) 3 × 3 MoS2 monolayer, (e) 4 × 4 graphene monolayer, and (f) 4 × 4-graphene/3 × 3-MoS2 heterostructure. Band structures of 4 × 4-graphene/3 × 3-MoS2 heterostructure under (g) a positive gate-voltage (E = + 0.01 V/Å and nc = 8.7 × 1012 cm−2), (h) a negative gate-voltage (E = −0.01 V/Å and nc = −8.7 × 1012 cm−2), (i) a stronger positive gate-voltage (E = +0.1 V/Å and nc = 8.7 × 1013 cm−2), and (j) a stronger negative gate-voltage (E = −0.1 V/Å and nc = −8.7 × 1013 cm−2). The direction of a positive electric field is from MoS2 to graphene.

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Before going to Ti stacking on MoS2, we here analyze the position movement of special k-points from the 1 × 1 hexagonal unit cell to a general hexagonal supercell. Figure 4(a) shows the general hexagonal lattice in real space. The supercell lattice vectors (blue lines) are expressed as am,n = m a − n b and bm,n = n a + (m + n) b , where and are the lattice vectors of 1 × 1 hexagonal unit cell (black lines). In Fig. 4(b), we can see how the special k-points of general supercells (blues lines) are mapped onto those of 1 × 1 unit cell (black lines) in reciprocal space. In k-space, the length of supercell lattice vector is contracted by the factor,

Figure 4: Mapping of special k-points.
figure 4

(a) Lattice vectors of a general hexagonal supercell in real space. am,n = m a − n b and bm,n = n a + (m + n) b , where a and b are the lattice vectors of 1 × 1 hexagonal unit cell: and . (b) Location of special k-points in reciprocal space. The geometric condition gives rise to the integer value of , where . If Ns is a multiple of three, the K point of the unit cell Brillouin zone (BZ) coincides with the Γ point of the supercell BZ. Otherwise, it coincides with the K point of the supercell BZ.

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and the geometric condition results in the integer value of Ns,

The location of special k-point K for a general hexagonal supercell is determined by the conditions,

In striking contrast to graphene/MoS2, the band offsets in Ti/MoS2 show very insensitive behaviors to gate-voltages. To see the differences between graphene/MoS2 and Ti/MoS2, we constructed three different Ti/MoS2 stacking configurations (T1, T2, and T3) as shown in Fig. 5(a–c). Among them, T1 configuration has the lowest total energy, but all the band structures of T1, T2, and T3 configurations are very similar to one another. Figure 5(f–h) show the band structures of T1 configuration. Distinct from graphene/MoS2, Fig. 5(f) shows that Ti/MoS2 has a strong band mixing along the Γ-M-K-Γ line in the energy range from −1.0 to 1.0 eV. This strong interaction is expected from a short equilibrium distance ~1.60 Å between Ti and MoS2, which is less than half the distance ~3.23 Å between graphene and MoS2. The binding energy between 2 × 2-Ti and 2 × 2-MoS2 is found to be −8.32 eV, which indicates that Ti and MoS2 stick together 14 times stronger than graphene and MoS2. Comparing Fig. 5(f) with Fig. 5(g) and (h), we see that the position and the shape of Ti bands exhibit negligible changes under VG (E = ±0.01 V/Å and nc = ±8.7 × 1012 cm−2). Even when we increase the gate-voltages by 10 times (E = ±0.1 V/Å and nch = ±8.7 × 1013 cm−2), the relative positions of Ti bands are not significantly altered from those in Fig. 5(g) and (h), implying that the intrinsic small Schottky barrier at the interface remains nearly constant without diminishing or rising under the strong gate-voltage. This insensitivity to the gate-voltage is also found in other ohmic metals such as Au (See Supplementary Information).

Figure 5: Atomic views and electronic band structures.
figure 5

(a) Top-view of monolayer MoS2. (b) Top-views of 4-layer Ti slabs with three different origin choices, denoted as T1, T2, and T3. (c) Ti/MoS2 heterostructures. (d) Band structure of 1 × 1 MoS2 monolayer. (e) Band structure of 4-layer Ti. Band structures of Ti/MoS2 in the T1 configuration (f) without the gate-voltage, (g) under a positive gate-voltage (E = + 0.01 V/Å and nc = 8.7 × 1012 cm−2), and (h) under a negative gate-voltage (E = −0.01 V/Å and nc = –8.7 × 1012 cm−2). The direction of a positive electric field is from MoS2 to Ti.

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In conclusion, by simultaneous control of external electric fields and electron charging concentrations, we have compared the band offsets in graphene (S/D)-MoS2 with those in Ti(S/D)-MoS2. Under gate-voltages, the Dirac point positioning inside the MoS2 bandgap is easily modulated with respect to the co-varying Fermi level, while the linearity of graphene bands remains intact around the Dirac point. Band lineups in graphene/MoS2 explicitly confirms the absence of graphene-induced gap-states, which is thought to prevent the Fermi level pinning and preferably make graphene bands flexible. In contrast to Ti-MoS2, graphene-MoS2 interactions are very weak as evidenced from the small binding energy of −0.59 eV and the large equilibrium distance between graphene and MoS2 ~3.23 Å, which is more than twice the equilibrium distance ~1.60 Å between Ti and MoS2. In effect, the strong decoupling between graphene and MoS2 bands causes a high sensitivity to gate-voltages. We respectively analyzed the fast increasing on-current and the steadily maintained (or lowered) off-current states, which originate from such a sensitive work function tuning of graphene under positive and negative VG; such work function tuning, in sum, leads to the high on/off ratio in graphene/MoS2.

Additional Information

How to cite this article: Baik, S. S. et al. Work Function Tuning in Two-Dimensional MoS2 Field-Effect-Transistors with Graphene and Titanium Source-Drain Contacts. Sci. Rep. 7, 45546; doi: 10.1038/srep45546 (2017).

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