Dipole-induced Ohmic contacts between monolayer Janus MoSSe and bulk metals

Utilizing a two-dimensional material in an electronic device as channel layer inevitably involves the formation of contacts with metallic electrodes. As these contacts can dramatically affect the behavior of the device, we study the electronic properties of monolayer Janus MoSSe in contact with different metallic electrodes by first-principles calculations, focusing on the differences in the characteristics of contacts with the two sides of MoSSe. In particular, we demonstrate that the Fermi level pinning is different for the two sides of MoSSe, with the magnitude resembling that of MoS2 or MoSe2, while both sides can form Ohmic contacts with common electrode materials without any further adaptation, which is an outstanding advantage over MoS2 and MoSe2.


INTRODUCTION
A Schottky contact between a semiconductor and a metal can be characterized by the Schottky barrier height (SBH), that is, the energy barrier that must be overcome by charge carriers to cross the contact. A sizable SBH would reduce the injection efficiency and therefore compromise the device performance 1 . Consequently, the choice of an adequate electrode material to realize a small SBH is essential 2 . Regulation of the SBH by varying the work function of the electrode often is hindered by Fermi level pinning due to metal-induced gap states (particularly originating from dangling bonds) 3 and defect-induced gap states 4 . In the case of Fermi level pinning the Schottky-Mott rule is violated and the transport across the contact is greatly suppressed. The effect of Fermi level pinning turns out to be reduced at weakly interacting van der Waals contacts 5,6 .
Two-dimensional MoS 2 suffers from high resistance at contacts with usual metallic electrodes (sizable SBH and Fermi level pinning) 7 . Countermeasures include the introduction of point defects in MoS 2 8,9 , the reduction of the electrode thickness 10 , and the utilization of two-dimensional metals as electrodes 11,12 . Interestingly, introduction of an insulating buffer layer can induce an interface dipole that reduces the SBH, but regrettably this gives rise to an additional tunnel barrier [13][14][15] . We propose to overcome this issue by applying a material with an intrinsic dipole to achieve the same effect while avoiding the additional tunnel barrier.
The two-dimensional Janus transition metal dichalcogenide MoSSe was first prepared in 2017 by substituting the S atoms on one side of MoS 2 with Se atoms 16 . Similar to MoS 2 , its band gap and carrier mobility feature a distinct thickness dependence 17,18 , while the intrinsic dipole of MoSSe (the structural symmetry of MoS 2 is broken) strongly modifies the electronic properties [19][20][21] . A number of theoretical studies have concluded that MoSSe performs well in gas sensing 22,23 , photocatalytic water splitting [24][25][26] , field-effect transistors 27 , and solar cells 28 . On the other hand, application of MoSSe as channel layer in electronic or photoelectric devices requires insights into the contacts with metallic electrodes [29][30][31][32] , as the achieved device efficiency will strongly depend on the characteristics of these contacts 33 . In the present work, we therefore study the contacts of Janus MoSSe with the potential electrode materials Al, Ti, Cu, Mo, Ag, and Au, considering both the S and Se sides of MoSSe. Al, Ti, Cu, Ag, and Au are chosen as they are common experimental electrode materials for MoS 2 34-38 and Mo as it is predicted to provide suitable contact properties 39 . We find that the weak interaction at the contacts paves the way to Ohmic behavior without any further adaptation, indicating that MoSSe is a highly promising candidate for the channel layer of electronic devices.

First-principles calculations
We consider contacts of both the S and Se sides of MoSSe with a variety of metals (Al, Ti, Cu, Mo, Ag, and Au) and refer to them as the SeMoS/metal and SMoSe/metal contacts, respectively, see Fig. 1. We obtain for MoSSe a lattice constant of 3.25 Å and a dipole moment of 0.21 Debye, which agrees well with previous reports 40,41 . We define the contact binding energy as where E MoSSe , E metal , and E contact are the total energies of the isolated MoSSe, isolated metal, and combined system, respectively, and N is the number of S or Se atoms forming the contact. We find that the S side always leads to stronger binding than the Se side, especially for the contacts with Ti and Mo (Fig. 2a). Not surprisingly, the contact distance d (distance between the average atomic positions in the atomic layers forming the contact) correlates well with the binding energy (Fig. 2b). Bader charge analysis reveals for each metal a charge transfer Δq to MoSSe, slightly more for the S than the Se side due to the stronger binding (Fig.  2c). Only for Au the charge transfer is almost zero (and in the opposite direction for the Se side). The enhanced charge transfers obtained for Ti and Mo agree with the enhanced contact binding energies in these cases. To evaluate the effect of the charge transfer on the induced dipole moment, we study the quantity D = (D contact -D MoSSe )/N, where D contact and D MoSSe are the dipole moments of the combined system and isolated MoSSe, respectively, and N is the number of S or Se atoms forming the contact. A positive value means that the induced 1 Physical Science and Engineering Division (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia. ✉ email: udo.schwingenschlogl@kaust.edu.sa dipole moment points from the metal to MoSSe. For Al, Ti, Mo, and Ag we obtain positive values, which are larger for the S than the Se side except for Mo (Fig. 2d). For Au the values are negative, i.e., the induced dipole moments point from MoSSe to the metal. Notably, for the SMoSe/Cu and SeMoS/Ag contacts the induced dipole moments are almost zero.
Being a key parameter of a semiconductor-metal contact, the SBH is derived from weighted electronic band structures separating the contributions of MoSSe and the metal electrode (Fig. 3). We obtain Ohmic contacts (negative SBH) for Al, Ti, Mo, and Ag in contact with both sides of MoSSe, in contrast to MoS 2 and MoSe 2 39,42 . A SeMoS-dominated (parabolic) band crosses the Fermi level close to the Γ point in the cases of the SeMoS/Al and SeMoS/Ag contacts, while the band crossing the Fermi level on the path F-K shows distinct hybridization between states of SeMoS and the metal. A similar hybridized band is present in the cases of the SMoSe/Al and SMoSe/Ag contacts. We find generally enhanced hybridization at the contacts involving Ti and Mo, which reflects the previously discussed strong binding. Theoretically, MoS 2 (MoSe 2 ) is predicted to form with Mo (Ti) an n-type Schottky contact with Φ n = 0.13 eV (0.1 eV) 39,42 . Experimentally, the SBH can be reduced to 0.05 eV in the case of monolayer MoS 2 in contact with Ti 11 and to 0.06 eV in the case of tri-layer MoS 2 in contact with Al 36 . We obtain for the SeMoS/Au (SMoSe/Au) contact n-type Schottky characteristics with Φ n = 0.06 (0.40) eV and Φ p = 0.91 (0.78) eV. Finally, for Cu the situation is more complex, as we obtain an Ohmic SeMoS/Cu contact and an n-type Schottky SMoSe/Cu contact with Φ n = 0.11 eV and Φ p = 0.33 eV. In general, contacts with the S side turn out to be advantageous over contacts with the Se side of MoSSe: They are more likely to be Ohmic and achieve lower Φ n (Φ p ) in the case of n-type (p-type) Schottky characteristics.
While an Ohmic contact without Schottky barrier results in favorable transport performance, the tunnel barrier induced by the van der Waals gap due to absence of chemical interaction between the two-dimensional semiconductor and bulk metal also requires attention (Fig. 4a). The tunnel barrier is characterized by the width w TB and height Φ TB (potential barrier that an electron must overcome on its way from the metal to MoSSe). Let Φ gap and Φ min denote the maximum of the tunnel barrier and the maximum effective potential on the MoSSe side of the contact. By definition, the barrier height is Φ TB = Φ gap -Φ MoSSe and the barrier width refers to an effective potential of Φ MoSSe . Lower barrier width and height enhance the electron injection (bottom left corner of Fig. 4b). We find three groups of contacts: group 1 promises the best performance (Ti and Mo), group 2 is intermediate (Cu and SMoSe/Ag), and group 3 suffers from unfavorable tunnel barriers.
We obtain lower work functions for contacts with the S than the Se side of MoSSe, and for each contact the Fermi level is close to the conduction band edge (E C ) of pristine MoSSe (Fig.  5a). The interface dipole due to the Janus structure enables this suitable band alignment as compared to MoS 2 and MoSe 2 . In the case of Au (higher work function than the other metals) the interface dipole is not sufficient to remove the Schottky barrier, which is consistent with our previous discussion that the charge transfer between Au and MoSSe is almost zero. The question remains whether the creation of an Ohmic contact is due to the interface dipole or whether the Fermi level pinning is weaker in the case of MoSSe (i.e., the SBH can be regulated by the work function of the metal, W metal ). Since the Schottky-Mott rule Φ n = W metal -χ, with χ being the electron affinity of the semiconductor, does no longer apply, we study the Fermi level pinning by calculating S = dΦ n /dW metal , where S = 0 represents strong pinning and S = 1 represents a contact without pinning. Due to defects, the theoretical value generally overestimates the   (Fig. 5b, c). Therefore, the Fermi level pinning is weaker for the Se than the S side, which is consistent with our previous discussion that the contact binding energy is smaller for the Se than the S side, highlighting the prevalent effect of the terminating atomic layer. Importantly, our values of S for contacts with the S and Se sides of MoSSe resemble those reported for MoS 2 (S = 0.26) 7 and MoSe 2 (S = 0.67) 42 , respectively, implying that the breaking of the structural symmetry and consequent introduction of a dipole moment are essential for the formation of Ohmic contacts.

DISCUSSION
By studying the interaction between monolayer Janus MoSSe and common electrode materials, using first-principles calculations, we discover that the asymmetric structure of MoSSe enables the creation of Ohmic contacts, for both terminations (S and Se sides). The Ohmic contacts, which are desirable from the perspective of electronic device applications, are attributed to the interface dipole formed when MoSSe is in contact with a metal with sufficiently low work function. At the same time, the symmetry breaking results in weaker Fermi level pinning for the Se (0.28) than the S (0.50) side. We find that Ti performs best among the studied metals to contact MoSSe, for both terminations, as not only an Ohmic contact is formed, but also the tunnel barrier is lower than 7 eV. Our results suggest that MoSSe is a promising replacement for MoS 2 as channel material in electronic devices, and we identify suitable electrode materials to contact MoSSe.

First-principles calculations
All calculations are performed with the Vienna ab initio simulation package (plane-wave cutoff of 500 eV) 44 . The optB88-vdW functional is used 45 , as it provides a reliable description of the van der Waals interaction in layered materials 46 . The convergence criteria are set to 10 −5 eV for the total energy and 0.01 eV/Å for the maximal residual force. A very fine Monkhorst-Pack ksampling with a separation of 0.015-0.020 Å −1 between grid points is employed. A simulation model is built for the energetically favorable surface of each metal 47 , using for the in-plane lattice constant the bulk value of the metal. The lattice mismatch to MoSSe is minimized by choosing individual matching patterns. More specifically, we attach a 2 × 2 × 1 supercell of (111) Al, Ag, or Au to a √3 × √3 × 1 supercell of MoSSe, a 2 × 2 × 1 supercell of (001) Ti to a √3 × √3 × 1 supercell of MoSSe, a √7 × √7 × 1 supercell of (111) Cu to a 2 × 2 × 1 supercell of MoSSe, and a 2 × 2 × 1 supercell of (111) Mo to a √7 × √7 × 1 supercell of MoSSe. This results in lattice mismatches of 1.7%, 4.7%, 4.0%, 3.4%, 2.4%, and 2.4% to Al, Ti, Cu, Mo, Ag, and Au, respectively. For the metals a thickness of six (12 in the case of MoSSe/Mo) atomic layers is adopted, with the outward four (eight in the case of MoSSe/Mo) fixed in the structure relaxation. A vacuum