MoB2 Driven Metallic Behavior and Interfacial Charge Transport Mechanism in MoS2/MoB2 Heterostructure: A First-Principles Study

We have performed the density functional theory calculations on heterostructure (HS) of MoS2 and MoB2 monolayers. The aim of this study is to assess the influence of MoB2 on electron transport of adjacent MoS2 layer. In present investigation we predict that the electronic properties of MoS2 monolayer is influenced by 4d-states of Mo in MoB2 monolayer. Whereas, the B atoms of MoB2 and S atoms of MoS2 exhibit overlapping of intermediate atomic orbitals thereby collectively construct the interfacial electronic structure observed to be metallic in nature. From charge density calculations, we have also determine that the charge transfer is taking place at the interface via B-2p and S-3p states. The bonds at the interface are found to be metallic which is also confirmed by adsorption analysis. Thermoelectric performance of this HS is found be in good agreement with available literature. Low Seebeck coefficient and high electrical conductivity further confirms the existence of metallic state of the HS.

Scientific REPORTS | (2018) 8:14444 | DOI: 10.1038/s41598-018-32850-z be applied in the analysis of mineral compositions 28 , light emitting diodes 29,30 and surface plasmon mapping 31 . Compared to photoluminescence the cathodoluminescence offers a much higher excitation energy allowing the study of wide band gap materials including diamond 32 and hexagonal boron nitride (hBN) 33 . The thermoelectric (TE) properties in few layer and bulk MoS 2 and MoS 2 monolayer have been theoretically investigated and found to be reasonably good for TE applications [34][35][36][37] . TE power factor of 8.5 mWm −1 K −2 for MoS 2 monolayer at room temperature had been reported by Kedar et al. which is the highest among all TE materials and twice that of commercially used bismuth telluride (Bi 2 Te 3 ) 38 . Whereas, for MoS 2 monolayer deposited on substrates, Hasan et al. had reported a poor response in the TE power factor 39 . For improving the TE performance of MoS 2 based systems, the hybridization and doping have been commonly explored. Moreover SiGe alloys, hybrid BN/graphene and MoS 2 /WS 2 nanoribbons show higher thermoelectric properties than single nanostructures 40,41 . We reviewed that the investigation for HSs of MoS 2 with intermetallic material need to be explored. The transition metal diborides XB 2 (X = V, Nb, Ta, Cr, Mo, and W) having hexagonal AlB 2 structure received much attention because for their interesting physical and chemical properties such as electronic structure, high melting point, corrosion resistance, wear resistance, high hardness factor and possibility of extensive industrial applications 16,[42][43][44][45][46] . Recently, ReB 2 and OsB 2 has been analyzed for exhibiting high bulk elastic moduli in a particular direction(c-axis) owing to the high valence electron density in the lattice which is comparable to that of diamond 47,48 . Recently it is been reported that lattice mismatches in the cell parameters and comparable thermal expansion with GaN, ZrB 2 can be optimized as a substrate for hetero epitaxial growth of GaN 49,50 . For the reinforcements in various composite materials e.g. steel and TiB 2 has often been used 51,52 . With reference to the above discussion we have motivated to theoretically examine the electronic and thermoelectric properties of MoS 2 /MoB 2 HS. We have selected this combination of monolayers due to their interesting electronic properties, specifically the Boron terminated MoB 2 layer with a wide range of thermodynamically allowed chemical potentials 53 . In Section I, we have elaborated the computational details applied to probe several significant features of interfacial electronic structure of MoS 2 /MoB 2 . The results for electronic structure of HS and isolated sub-systems along with chemisorption, chemical bonding and thermoelectric properties occurring at the interface near to the Fermi level (E f ) are reported and discussed in Section II.

Computational Details
High-throughput density functional theory (DFT) 54 calculations were performed with the Quantum Espresso simulation package 55 within the generalized gradient approximation proposed by Perdew, Burke, and Ernzerhof (PBE) 56 . We sampled the Brillouin zone (BZ) in the Monkhorst-Pack scheme 57 , and tested the convergence in energy as a function of number of k-points for the calculations. The k-point sampling of (7 × 7 × 1) was found to be suitable for the BZ corresponding to the primitive unit cell. Atomic positions were optimized using conjugate gradient method, where total energy and atomic forces were minimized. The energy convergence value between two consecutive steps was chosen as 10 4 eV. The energy interval chosen for density of states (DOS) calculations is 0.1 eV and the broadening used in Gaussian type. The standard value of broadening is considered as 0.001 Ry. An equivalent plane wave cutoff of 750 eV is chosen in all the simulations. Relaxed geometries are obtained with the conjugate gradient method, where all the atoms in the super cell are allowed to relax until the force on each atom is less than 0.02 eV/Å. We modeled the MoS 2 /MoB 2 HS by putting a 3 × 3 × 1 super cell of MoS 2 monolayer (lattice constant a MoS 2 = 3.12 Å) 58 on top of a 3 × 3 × 1 super cell of MoB 2 monolayer (a MoB 2 = 2.98 Å) 53 , which reduced the lattice mismatch between the two layers to 4.4% and resulted in a simulation cell containing 32 atoms. This lattice mismatch is small enough that will not effect the electronic properties of the HS, however such contraction in lattice spacings may results in increased DOS 16 . To minimize interactions between periodic images due to 3D boundary conditions, we introduced a vacuum layer such that the distance between periodic images was at least 25 Å. We have modeled the interaction of the valence electrons with the pseudo atomic cores of all the atomic species present in our studied structures by normconserving pseudopotentials explicitly including the semi-core Mo 4d electrons in the calculations. The equilibrium interfacial distance (d eq ) between MoS 2 and surface of MoB 2 monolayers is found to be 1.96 Å which is obtained from a fully relaxed HS. To analyze the thermoelectric properties of HS, semi-classical theory of the Boltzmann package 59 has been used.

Results and Discussion
Electronic Structure. MoS 2 /MoB 2 Heterostructure. The lattice arrangement of the MoS 2 /MoB 2 HS shown in Fig. 1 represents the clear existence of bonds at the interface between bottom S atoms and surface B atoms. These bonds indicates that the interaction among the atoms at the interface is not the Van der Waals interaction. In bulk, MoB 2 is a non-layered structure with metallic bonding 16,53 unlike MoS 2 which possess a layered structure with interlayer Van der Waals interaction. The metallic bonding of MoB 2 is possibly the reason for the absence of Van der Waals interaction at the interface of the HS. The electronic band structure of HS is shown in Fig. 2 where crossing of bands can be seen across the E F showing the existence of metallic nature. The maximum dispersion of electronic bands is observed at high symmetry point M. In order to further elucidate the band structure we have studied the partial density of states (PDoS) of the HS. attributed to Mo-4d and B-2p states of MoB 2 monolayer. MoB 2 is not only making the HS a metallic system but it has also modulated the MoS 2 monolayer to behave as a metallic system. The valance band (VB) in the range from −0.8 to −2 eV, is mainly composed of B-2p and Mo-4d (of MoB 2 ) states. Whereas, in the conduction band (CB), the energy range from 0.7 to 2 eV is mainly composed of Mo-4d states (of MoS 2 and MoB 2 ) and S-3p states. From energy range −0.7 to 0.5 eV, dominance of Mo-4d and B-2p states can be clearly seen in Fig. 3. The metallic nature in such type of HSs can be optimized for device applications like gas sensors based on resistivity alterations of the system. Band gaps obtained for other HSs based on MoS 2 are enlisted in Table 1. The PDoS diagrams of the sub-systems of the HS i.e. MoS 2 and MoB 2 are also studied to get a clear insight of the mechanism taking place within the HS and at its interface.    27 . In order to analyze the nature of adsorption at MoS 2 /MoB 2 interface with equilibrium interfacial distance (d eq = 1.96 Å), we have randomly shifted MoS 2 monolayer upward upto 4.76 Å and then downward upto 0.56 Å normal to the plane of MoS 2 /MoB 2 HS. The result obtained from adsorption curve in terms of change in potential energy with respect to interfacial distance is shown in Fig. 6(a), whereas the inset of Fig. 6(a) represents conventional potential energy versus interfacial distance curve. The diagrammatic representation of shifting of MoS 2 monolayer over MoB 2 is provided in Fig. 6(b). With reference to Fig. 6(b) the distance d eq is set to 0 Å which indicates the minima of potential energy curve in Fig. 6(a). Again from Fig. 6(b) the maximum separation between MoS 2 and MoB 2 is ~4.76 Å which is then reduced to a minimum value ~0.56 Å. In Fig. 6(a) the two regions I and II can be allocated as chemisorption

Heterostructure
Band Gap E g (eV) and physisorption respectively. With reference to d eq , the chemisorption occurs in the region from A (maxima at 2.1 Å) to C (minima at d eq = 1.96 Å), where chemical bonds possibly exist at the interface of MoS 2 /MoB 2 HS. The potential energy curve attains the minimum potential energy value (at C) by change in slope via point B. The rate of change of potential energy with respect to the interfacial distance between A and B i.e. Δ AB is greater than that between B and C (Δ BC ). This variation in slope is attributed to initial electronic repulsion. In other words the anomaly at B in the potential energy curve appears due to electronic repulsion between MoS 2 and MoB 2 layers. Tending from B towards C the actual orbital overlapping between the atomic species of corresponding layers can be realized. Conclusively, at C in the potential energy curve the valley-like feature at d eq indicates a clear existence of chemical bonding at the interface. If we further continue to decrease this distance, the energy will tend to infinity under the effect of nuclear repulsion. We can see from Thermoelectric Properties. The performance of a thermoelectric material reflects in the dimensionless figure of merit ZT = S 2 σT/κ, where S is the Seebeck coefficient, σ is the electrical conductivity and κ (κ = κ e + κ l ) is the thermal conductivity which consist electronic κ e as well as lattice κ l thermal conductivity and T is absolute temperature respectively. Previous studies signified that the mono-layered MoS 2 is semiconductor in nature with band gap 1.8 eV 60 . Due to high S and low κ, MoS 2 system presents a good candidature for the thermoelectric applications. However, small ZT is reported for this system due to low electrical conductivity induced by the large band gap energy. The mono-layered MoB 2 have metallic nature as represented in PDoS (Fig. 5) discussed in above section. We propose that wide band gap of MoS 2 semiconductor can be tuned by HS with MoB 2 that possibly results in enhanced power factor and thereby improve thermoelectric properties. Aiming this, we are the first to attempt the calculation and analysis of thermoelectric properties of MoS 2 /MoB 2 HS using BoltzTrap code 59 .
The Seebeck coefficient (S) as a function of chemical potential (μ) from −1.5 eV to 1.5 eV at temperatures 300 K and 800 K for MoS 2 /MoB 2 HS show two peaks in the profile (Fig. 9a) which are located at a chemical potential near around −0.85 eV and −0.91 eV. It can be noticed that the resultant magnitude is larger for a p-type character. The maximum value of S is 134 μV/K, at 300 K which decreases with increasing temperature. The perpendicular component is higher in magnitude which is good for thermoelectric properties. The temperature dependence of Seebeck coefficient at a certain value of chemical potential is shown in Fig. 9(b). For MoS 2 /MoB 2 HS the values of S in the entire temperature range are found to be positive which reveals that p-type charge carriers are dominant and increases with increasing temperature. Dimple et al. 41 observed the thermoelectric properties of MoS 2 monolayer which signify p-type character. However, the magnitude of S is very low (=10 −6 ) due to metallic nature of MoS 2 /MoB 2 HS. The MoS 2 monolayer is a semiconductor that possess large band gap therefore its Seebeck coefficient must be larger than that of purely metallic MoB 2 which is shown in inset of Fig. 9(b). Moreover with reference to the electronic structure as discussed above for this HS, the band gap of MoS 2 monolayer is modulated by MoB 2 . It can also be observed from PDoS of HS (Fig. 3) that the band gap of HS acquires metallic behavior and hence the Seebeck coefficient of mixed-layer MoS 2 /MoB 2 is smaller than MoS 2 monolayer 61 .
The variation of electrical conductivity (σ/τ) as a function of chemical potential (μ) from −2 eV to 2 eV at the temperatures 300 K and 800 K for MoS 2 /MoB 2 HS is shown in Fig. 10(a). We have observed that the electrical conductivity for negative chemical potential is 3.73 × 10 19 (S/ms) and 3.423 × 10 19 (S/ms), whereas for positive chemical potential it is 5.21 × 10 19 (S/ms) and 4.588 × 10 19 (S/ms) for 300 K and 800 K respectively. This indicates that the p-type composition possess higher electrical conductivity than n-type. Comparable phenomena had also   41 . Further, the electrical conductivity (σ/τ) as a function of temperature for a certain value of chemical potential (μ) is shown in Fig. 10(b). This figure shows that the electrical conductivity increases almost linearly with increasing temperature which indicates metallic nature, also confirmed by DoS study (Fig. 3). The electrical conductivity of MoS 2 monolayer have been provided in the inset of Fig. 10(b) which shows a similar trend like MoS 2 /MoB 2 HS. However, the electrical conductivity of MoS 2 monolayer found lesser as compared to the investigated HS.
Further, we have also focused on the thermal conductivity of MoS 2 /MoB 2 HS. In general, the thermal conductivity κ (κ = κ e + κ l ) is a combination of electronic thermal conductivity κ e and phononic thermal conductivity κ l . In the present study, we have used the BoltzTrap code 59 which calculates electronic contribution only. The consideration of lattice thermal conductivity κ l , remains as future task. The calculated electronic thermal conductivity (κ e /τ) of MoS 2 /MoB 2 HS as a function of chemical potential (μ) at 300 K and 800 K is shown in Fig. 11(a). It is indicated that a significant increase in κ e /τ occurs with increasing temperature. The highest value of κ e /τ induced by 800 K while the lowest κ e /τ induced by 300 K. Therefore, 300 K is the optimal temperature that gives the lowest thermal conductivity. Moreover, the variation in thermal conductivity with respect to temperature is represented in Fig. 11(b). It shows a linear dependence with respect to temperature because the increasing  temperature enhances the number of charge carriers attributed to the metallic nature of MoS 2 /MoB 2 HS which is in good agreement with the previous study 62 . However, the thermal conductivity of MoS 2 is found less as compared to that of MoS 2 /MoB 2 HS as shown in the inset of Fig. 11(b). It is due to the large band gap semiconducting nature of MoS 2 monolayer 63 .
The average power factor is plotted against the chemical potential (μ) at 300 K and 800 K illustrated in Fig. 12(a). The positive (and negative) chemical potential scale indicates the electron (and hole) concentration, respectively. The power factor is maximum near μ = −0.99 eV attributed to significant increment in the electrical conductivity at high electron concentration level. Further, Fig. 12(b) represents the power factor with respect to increasing temperature which initially increases rapidly and then becomes almost linear till 1000 K. The comparative power factor of MoS 2 monolayer is shown in the inset of Fig. 12(b). It is clear that the investigated MoS 2 /MoB 2 HS exhibits comparatively better power factor value than MoS 2 monolayer. The large magnitude of power factor is obtained in the case of large electrical conductivity. Consequently, it is clear that the heterostructure of MoS 2 /MoB 2 HS exhibit good thermoelectric response at the higher temperatures.

Conclusions
In conclusion, our study suggests that deposition of MoS 2 monolayer over single layer of MoB 2 in a bilayer MoS 2 /MoB 2 heterostructure can have noticeable effects on the electronic properties of the MoS 2 layer. In presence of MoB 2 layer in the HS, monolayer of MoS 2 becomes a metallic system. Under the influence of 4d and 2p states of Mo and B atoms respectively of MoB 2 layer, 4d and 3p states of Mo and S atoms of MoS 2 monolayer appeared to cross the E f . While in absence of MoB 2 layer, MoS 2 monolayer shows its ideal electronic structure. Hence the metallic nature of the HS is driven by MoB 2 layer. We also observed some bonds at the interface which were analyzed via charge density calculation and adsorption curve and found to be metallic in nature. Based on the calculated Seebeck effect and power factor of MoS 2 /MoB 2 HS as a function of chemical potential and temperature, the maximum power factor is estimated successfully which can offer useful guidelines for tuning and improving the thermoelectric performance of such type of HS.