Interfacial Coupling Effect on Electron Transport in MoS2/SrTiO3 Heterostructure: An Ab-initio Study

A variety of theoretical and experimental works have reported several potential applications of MoS2 monolayer based heterostructures (HSs) such as light emitting diodes, photodetectors and field effect transistors etc. In the present work, we have theoretically performed as a model case study, MoS2 monolayer deposited over insulating SrTiO3 (001) to study the band alignment at TiO2 termination. The interfacial characteristics are found to be highly dependent on the interface termination. With an insulating oxide material, a significant band gap (0.85eV) is found in MoS2/TiO2 interface heterostructure (HS). A unique electronic band profile with an indirect band gap (0.67eV) is observed in MoS2 monolayer when confined in a cubic environment of SrTiO3 (STO). Adsorption analysis showed the chemisorption of MoS2 on the surface of STO substrate with TiO2 termination which is justified by the charge density calculations that shows the existence of covalent bonding at the interface. The fabrication of HS of such materials paves the path for developing the unprecedented 2D materials with exciting properties such as semiconducting devices, thermoelectric and optoelectronic applications.


Computational Methods
To study the electron transport properties of MoS 2 /STO HS, density functional theory (DFT) 44 calculations were carried out by Quantum Espresso Package 45 . The system is analysed by fully relaxing the HS with TiO 2 terminated STO substrate containing supercell of size 2 × 2 × 1 and 4 × 4 × 1 MoS 2 monolayer supercell as shown in Fig. 1(a). Perdew and Zunger functionals 46 within local density approximations (LDA) 47 is used to treat the electronic exchange-interaction. The input parameters, i.e. kinetic energy cutoff and K-mesh are fully optimized before proceeding to the calculations of electronic properties of the HS. Monkhorst-Pack 48 6 × 6 × 1 K-mesh for Brillouin zone integrations were employed with 544 eV of kinetic energy cutoff. We have taken the value of U = 4eV for effective Coulomb repulsion. All the calculations are based on projector-augmented waves (PAW) 49 method. Generally, the PAW potentials are more accurate than ultrasoft pseudopotentials, because (1) Core radii of PAW potentials are smaller than the radii used for ultrasoft pseudopotentials, (2) PAW potentials reconstruct the exact valence wavefunction with all nodes in the core region. A vaccuum of 28 Å is provided normal to the interface in order to present the isolated slab boundary condition. Here, we have chosen a lateral lattice parameters of cubic STO a 0 = 7.71 Å, which is optimized for freestanding STO. The lattice mismatch for the interface of HS is found to be 5%, which is expected as the crystal structures of both systems are different i.e. STO is cubic and MoS 2 monolayer is hexagonal. The equilibrium interfacial distance (d eq ) between MoS 2 and surface of TiO 2 terminated STO(001) is found to be d eq = 2.62 Å. This distance is obtained after relaxing the HS. We have studied the electronic band structures of the HS and O − 2p orbitals are observed at the Fermi level without crossing it with a significant band gap. In this work, we have carried out the spin-polarized calculation and our results indicates that MoS 2 /STO HS with TiO 2 termination is nonmagnetic.

Results and Discussion
Electronic band structure. MoS 2 /STO Heterostructure. We have studied the effect of MoS 2 monolayer on the electronic properties of TiO 2 terminated STO (001). The lattice constant of freestanding STO is 68% larger than that of MoS 2 monolayer which could effect our results of the HS. Hence, we constructed a supercell consisting of a TiO 2 terminated STO containing 2 × 2 × 1 substrate and 4 × 4 × 1 MoS 2 monolayer. The remaining lattice mismatch is only about 5%, which is small enough and it does not effect the electronic structures in the interfaces. The fully relaxed atomic structure of the HS is shown in Fig. 1(a), where clear bonding at the interface can be seen between the two subsystems (STO and MoS 2 monolayer). To make sure that the results we have obtained for the HS are correct, we rotated the MoS 2 monolayer by 45° along x-y plane keeping the STO substrate fixed as shown in Fig. 1(b) and (c) and performed the calculations and found similer results as that of the HS with no rotation of MoS 2 monolayer. To investigate the band alignment of MoS 2 /TiO 2 interfaced HS, we have plotted the band structure of the HS. The band diagrams of the sub-systems of the HS are also studied to get a clear insight of the mechanism taking place in the complex HS. The band structure of MoS 2 /TiO 2 interface HS is shown in Fig. 2. It can be seen that a band is sitting at the E f at the valance band maximum (VBM) and energy gap (0.85eV) is visible in TiO 2 terminated HS making it a semiconducting material. The band gap is found to be a direct gap at Γ. The effect of interfacial coupling in this HS gives exciting electronic nature as, an ideal monolayer of MoS 2 is supposed to be a direct band gap material which is found at K high symmetry point while STO in bulk is an indirect band gap (M-Γ) 50 insulating material. Here, when we couple these systems together, it gives out a semiconducting band gap of 0.85eV at Γ. This property brings the HS in the list of potential materials for optoelectronic devices. The conduction band minimum (CBM) is composed of Mo-4d electron states in Fig. 2.
Now we are interested to study the band structure of STO by removing the MoS 2 monolayer. The electronic band structure of STO without MoS 2 monolayer is shown in Fig. 3. We observed from Fig. 3 that when MoS 2 is removed from TiO 2 terminated HS, the VBM shifts down and CBM move towards E f and reduced band gap (0.72eV). Hence, the effect of MoS 2 monolayer on STO can be analysed as, when MoS 2 monolayer is deposited on STO, a relatively large band gap is obtained and in place of Mo-4d states, now Ti-3d states are seen at CBM. The monolayer is influencing the energies of atoms of STO. Also, we found from Fig. 3 that, the direct band gap is not coming due to the monolayer but STO itself is giving out a direct semiconducting gap at Γ. Therefore, from Fig. 2, we conclude that MoS 2 /TiO 2 interface is a semiconductor with a direct narrow energy gap. This indicates the effect of STO substrate with TiO 2 termination on the electronic properties of MOS 2 . It shows that STO substrate can be used as an ideal substrate for MoS 2 -based device applications. Band gaps obtained for other HSs based on MoS 2 are enlisted in Table 1.

Subsystems-STO and MoS 2 Monolayer.
We have also studied the band structure of STO and MoS 2 monolayer confined within the structural parameters of the STO (001) (2 × 2 × 1) seperately in order to have a comparative study. We can see in Fig. 4, the ideal cubic STO substrate appears to have a direct band gap (at Γ) of 1.77 eV which  is reduced from the bulk STO band gap (3.2eV) arising from p x , p y orbitals 51 on the surface layer O ion whose on-site energy is raised by the absence of interations along c-axis. In Fig. 5, the band structure of MoS 2 monolayer is shown. Here, we find an unexpected and unique character of monolayer confined in a cubic unit cell of STO, i.e. it gives out an indirect band gap of 0.67eV. Hence, we can say that the direct band gap of the HS is obtained only due to the contribution of STO with TiO 2 termination. We know that, Silicon is an indirect band gap (1.1 eV) semiconductor (X-L). This reduces its efficiency in electron transport. Hence, we propose a hypothetical view based on our results of monolayer in Fig. 5 Partial Density of states. The partial density of states (PDoS) further elucidate the electronic band structure. We have displayed the PDoS of TiO 2 -terminated HS in Fig. 6. We have observed that the band we saw in   Chemical Bonding. In further calculations, we have investigated the nature of adsorption of MoS 2 on substrate STO, i.e., whether it is chemisorbed or physisorbed. In chemisorption, chemical reaction occurs between the surface of subtrate and the adsorbate (MoS 2 ) and hence, the new chemical bonds are generated at the interface. Whereas, in case of physisorption, also called as physical adsorption, the electronic properties of the adsorbate are barely perturbed upon adsorption. The bonds can be seen at the interface between the substrate and the adsorbate in Fig. 1(a). This motivates us to investigate the nature of adsorption of the MoS 2 monolayer. In general, vdW interactions exists at the interface of honeycomb like HSs, but in this case, the lattice arrangement is having the cubic STO dimensions hence it is considered that the interactions at the interface will no longer be weak vdW interactions. In order to analyse the nature of adsorption, we randomly shifted the MoS 2 monolayer from the equilibrium distance at the interface d eq where the MoS 2 /TiO 2 interface distance is 2.62 Å, upwards upto 5.62 Å and downwards upto 0.3 Å normal to the surface of TiO 2 terminated STO substrate. We have shown the results in Fig. 8. Here we can see two regions I and II. Region I shows the adsorption charateristics of MoS 2 monolayer when the distance from surface of substrate ranges from 2.62 Å to 3.80 Å. We observed an increament in the potential energy of the HS in this region. A deep valley is obtained at d eq which provides the traces of the chemisorption of adsorbate (MoS 2 ) over surface of TiO 2 terminated STO substrate. As the distance at the interface is further increased, the potential energy starts to fall down. This decreament is recorded in the range from 3.8 Å to 5.62 Å, as we have studied this response in range of distance 0.3 Å, upwards upto 5.62 Å only. As we further  decreased the distance lesser than d eq , we can clearly see an abrupt increase in potential energy which indicates the presence of electronic repulsion. If we further decrease this distance, the energy will tend to infinity under the effect of nuclear repulsion. From Fig. 6, we found that the MoS 2 /TiO 2 interface is a semiconductor with covalent bonding occuring between Mo-4d and O-2p states. This hybridization of electronic states makes our statement on chemical adsorption more stronger.
The presence of chemisorption of MoS 2 monolayer over STO surface can be justified by inspecting the nature of chemical bonding between the atoms at the interface. To investigate the bonding characteristics between atoms at the interface, we performed the charge density calculations. Charge density provides the information about bonding/repulsion between MoS 2 and STO. Fig. 9 shows the charge density in (010) plane. Maximum values implies the regions where charge increases when MoS 2 and STO coupling takes place. In the substrate STO, we can see the isolated closed spherical isolines around the bottom atoms. These closed isolines indicates the existence of ionic bonding between the atoms of STO at the bottom layer. As we move upwards, ionic bonding is still present till the surface layer of STO. A clear covalent bonding between the surface atoms of STO and MoS 2 monolayer can be seen at the interface. It is considerd that if ionic bonding exists at the interface, the material should be a metal and if there exists an energy gap, it suggest a covalent bond between the atoms. Thus the presence of semiconducting band gap in HS (0.85eV) justifies our results of existance of covalent bonding obtained from adsorption analysis and charge density calculations. This bonding is arising due to the hybridization of O-2p and Mo-4d states in VB region which can be seen from Fig. 7 where the 2p energy states of O and 4d and 3p states of Mo and S atoms respectively are present in the energy range −0.3eV to far VB region. This mixing of states results in the strong covalent bonds between O-2p and Mo-4d states with small contribution of S-3p states.

Conclusion
In summary, we have investigated the electronic band structure and chemical bonding of the MoS 2 monolayer deposited over the STO substrate with TiO 2 termination within the framework of density functional theory. In order to authenticate our results, we have performed all the calculations for the HS with 45° rotated MOS 2 monolayer along x-y plane keeping the substrate fixed. We obtained similar results for such arrangement and hence validates our findings. The interfacial distance (d eq ) between MoS 2 and surface of TiO 2 terminated STO(001) is found to be 2.62 Å. The conduction band is mainly composed of Mo-4d and S-3p states along with small contribution of Ti-3d states as well, while valance band is containing O-2p states near E f which is playing the major roll in the semiconducting nature of the HS. Surface O atoms of STO substrate are found at E f . A semiconducting band gap is found (0.85eV) and MoS 2 is strongly bonded with the substrate which is seen in the chemical bonding analysis. A unique nature of isolated MOS 2 monolayer confined in STO lattice parameters is observed i.e. it gives an indirect band gap of 0.67eV. This finding can be examined experimentally for application purpose in the case of Si which could be a breakthrough in semiconducting devices. Our adsorption analysis suggests the chemisorption of MoS 2 on surface of STO substrate with TiO 2 termination. MoS 2 /TiO 2 terminated HS with a semiconducting band gap offers a potential candidature in thermoelectric and optoelectronic applications.