Band engineering in a van der Waals heterostructure using a 2D polar material and a capping layer

Van der Waals (vdW) heterostructures are expected to play a key role in next-generation electronic and optoelectronic devices. In this study, the band alignment of a vdW heterostructure with 2D polar materials was studied using first-principles calculations. As a model case study, single-sided fluorographene (a 2D polar material) on insulating (h-BN) and metallic (graphite) substrates was investigated to understand the band alignment behavior of polar materials. Single-sided fluorographene was found to have a potential difference along the out-of-plane direction. This potential difference provided as built-in potential at the interface, which shift the band alignment between h-BN and graphite. The interface characteristics were highly dependent on the interface terminations because of this built-in potential. Interestingly, this band alignment can be modified with a capping layer of graphene or BN because the capping layer triggered electronic reconstruction near the interface. This is because the bonding nature is not covalent, but van der Waals, which made it possible to avoid Fermi-level pinning at the interface. The results of this study showed that diverse types of band alignment can be achieved using polar materials and an appropriate capping layer.

Scientific RepoRts | 6:27986 | DOI: 10.1038/srep27986 can be more finely tuned when a capping layer (CL) is employed 22 . This approach allows fine tuning beyond the digital control of the thickness of the polar materials. An insulator-metal transition was observed below the critical thickness for LaAlO 3 /SrTiO 3 with a SrTiO 3 CL 23 . Depending upon the choice of the metallic CL, the spin polarisation or an additional carrier injection can be achieved at the interface 24,25 . This is because the CL provides an electrostatic boundary condition for the polar materials, which changes the properties.
Despite numerous studies 26 , there is lack of understanding of how polar heterojunctions influence the band alignment. This is because the complex secondary effects make it difficult to isolate the effects of polar materials, particularly in covalently bound heterostructures. Numerous variables can affect the band alignment due to covalent bonding at the heterojunction. The induced energy level of a covalent bond can result in Fermi-level pinning, which influences band alignment 27 . Also, band bending and charge transfer occurs, in order to meet the charge state at the interface, and these also influence the band alignment 17 . Furthermore, atomistic defects near the interface can hinder the effects of a polar material by pinning the Fermi level 28 .
Fortunately, those problems can be avoided in a vdW heterostructure because it does not rely on covalent bonds. For this reason, a pure response to the polarity might be observable when polar materials are employed in vdW heterostructures. Recently, it has been reported that 2D polar materials like single-sided fluorographene (C 4 F) can modulate the band alignment and other functional characteristics 29,30 . For instance, the C 4 F can be used modulate the band alignment in the BN/C 4 F supercells and can induce an insulator-metal transition by controlling the thickness of each component. Though polarity-triggered band engineering at vdw interface has been reported, the response to polarity at the interface has not been systematically investigated. Considering that the band alignment of polar materials depends on the boundary conditions, it is necessary to investigate the band alignment for various the boundary conditions. For these reasons, investigating vdw heterostructure with polar materials can not only provide fundamental understanding of the interface physics of the polarity, but also guidelines for band engineering.
In this study, we investigated the band alignment of vdW heterostructures using 2D polar materials. We chose C 4 F as a representative 2D polar material. The effect of polarity on the band alignment was studied at the heterostructure, and the effect of CL on the band alignment was also invenstigated. Band alignment was expected to respond differently with polar materials because the presence of a CL changes the electrostatic boundary from vacuum to metallic or dielectric. To investigate this effect, monolayer graphene and BN were adopted as a representative metallic and insulating CLs, respectively. We found that the band modulation caused by polarity depended on the potential step of C 4 F, and this potential step can be tuned with a boundary condition change using a CL.

Results
To investigate the band alignment between single-sided fluorographene and the substrates, we plotted the band structure and corresponding band diagram in Fig. 1. In the band structure, the vacuum level of the substrate side was set to zero on the energy scale. This side of the vacuum level provided a reference value for different systems because the substrate was thick enough to avoid interfering with the interface. Using this reference value, we compared all possible interface terminations of the C 4 F, C-side and F-side contact with BN and graphite substrates. As shown in the band structures, the band alignment at the interface is highly dependent on the termination. The F-side contact of C 4 F and BN (C 4 F/h-BN) had a narrow gap of 0.18 eV. On the other hand, when the C-side of C 4 F was in contacted with BN (FC 4 /h-BN), a staggered gap of 2.51 eV formed with a conduction band minimum (CBM) of C 4 F and a valence band maximum (VBM) of h-BN. Considering the bandgap is underestimated when using DFT with PBE functional, we also calculated the staggered gap using a hybrid functional calculation. The 1.45 eV and 3.81 eV were obtained for the staggered gap of C 4 F/h-BN and FC 4 F/h-BN interfaces, respectively. The obtained values showed that the PBE functional still captured the essential trends of band alignment including the band shift between the two terminations. This termination dependency was also observed at the interface between C 4 F and graphite. The Ohmic contact was formed on the F-side contact (C 4 F/Grpt), while the C-side contact (FC 4 /Grpt) showed a Schottky nature.
As shown in the plot, the band alignments at the interface were mainly determined by the C 4 F band. While the position of the band of the substrates was kept constant, the band of C 4 F shifted depending on the termination. This shift is because of the dipole moment of C 4 F. A strong dipole moment is generated in C 4 F due to the asymmetric electronegativity between carbon and fluorine 31 . This dipole moment along the z direction was calculated using the following equation.
Here, Z i is the charge of core of ions i, and z i is the position of the ion along the z side. The planar-averaged electron density of the slab along the z-direction is ρ. The calculated dipole moment for single layer C 4 F along the z-side is 0.270 eÅ. This dipole moment was quite large value and corresponds to the 7 layers of LaAlO 3 21 . This dipole moment induced an electrostatic potential difference between the C-side and F-side of C 4 F. The electrostatic potential difference was evaluated using the Helmholtz' equation.
Here, φ is the electrostatic potential, ε 0 is the dielectric constant, and A is the area of the supercell. The potential difference was 2.33 eV, which corresponds to the amount of the band shift between the C-side contact and the F-side contact in C 4 F on the BN substrate. Furthermore, this large potential difference is sufficient to convert the Schottky contact on the C-side in FC 4 /Grpt to an Ohmic contact on the F-side in C 4 F/Grpt because the Schottky barrier is only 1.19 eV.
Considering the side-dependency of the band alignment of C 4 F, we expected that the band alignment with the next overlayer, CL, will be affected by the polarity of C 4 F. Thus, the effect of CL on the band alignment was also investigated. The BN and graphene layers were selected as representative CLs and were deposited onto the C 4 F on the BN substrate and graphite substrate. A schematic band diagram of the interfaces is provided in Fig. 2. Interestingly, the behavior of the band alignment between the substrate/C 4 F/CL highly depends on the combination of the CL and substrates. This is because the substrate and CL provide different electrostatic boundary conditions for C 4 F. For this reason, we classified these interfaces into three categories according to their electrostatic boundary conditions: type-A has two insulators, type-B has one insulator and one metal, and type-C has two metals.
The band alignment between the substrate and the CL was determined by the potential difference between the sides of C 4 F. To observe this potential difference, we compared the band diagrams of the two systems, the CL/C 4 F/substrate and the CL/substrate. In the CL/substrate, the interlayer spacing was fixed to at least 5 Å, in order to observe the alignment reference to vacuum and exclude the interface interaction between the substrate and the CL. Here, we calculated the band structure by optimising the system when the C 4 F layer was removed. This distance of 5 Å was sufficient to avoid the interactions between the layers, allowing us to observe the band alignment with respect to the vacuum level 18,32 . Figure 3 shows a comparison of the representative case for each alignment type. The BN on C 4 F/h-BN (BN/C 4 F/h-BN), the graphene on C 4 F/h-BN (G/C 4 F/h-BN), and graphene on C 4 F/Grpt (G/C 4 F/Grpt) were chosen as the representative cases for type-A, type-B, and type-C, respectively. In type-A, the band of the CL shifted by 2.33 eV in the CL/C 4 F/substrate as compared to CL/substrate. This amount of shift exactly matched the intrinsic potential difference of C 4 F. This means that the band alignment of type-A was determined by the intrinsic potential difference of C 4 F. On the other hand, the shifts in type-B and type-C did not correspond to the intrinsic potential difference of C 4 F. In type-B, the amount of the shift was 1.49 eV, which was a remarkably lower than the intrinsic potential difference of C 4 F, 2.33 eV. The same tendency was observed in type-B. The shifts were 1.41 and 1.30 eV in BN/FC 4 /h-BN and BN/FC 4 /Grpt, respectively (see supporting information). All of these values were less than the intrinsic potential difference, 2.33 eV. Interestingly, CL was aligned with the same energy leveln type-C, which means that there was no potential shift arises in type-C. These results for type-B and type-C indicate that the band alignment was not determined merely by the intrinsic potential difference of C 4 F.
To understand this kind of different behavior, we also calculated the electron redistribution function as follows. 4 4 The results for the representative cases of type-A, B, and C are plotted in Fig. 4. Though the magnitude of the redistribution is different for each type, the patterns in the accumulation and depletion regions of the redistribution were quite similar. Electron depletion was observed on the substrate side of the space between the C 4 F and the substrate, while the electrons are accumulated on the C 4 F side. On the other hand, the electrons between the C 4 F and CL interface accumulated on the C 4 F side, but depleted on the CL side. This kind of redistribution can be interpreted as spatial polarisation or charge transfer. This phenomenon is apparent in the band structure in Fig. 3.
If an electron was transferred to C 4 F, it should occupy the conduction band minimum (CBM) of C 4 F. However, as shown in Fig. 3, the conduction band of C 4 F was empty. Therefore, the redistribution can be interpreted as spatial polarisation rather than charge transfer. This spatial polarisation also induced a dipole moment, and the direction of this polarisation was opposite to the intrinsic dipole moment of C 4 F. This means that the intrinsic dipole moment of C 4 F was screened by spatial polarisation. Considering the band shifts of CL, the intrinsic dipole of C 4 F was partially screened in type-B and completely screened in type-C. The magnitude of the screening depended on whether the boundary conditions contained a metal or not. Here, graphene or graphite screened the dipole moment of C 4 F. One interesting feature was that the spatial polarisation was not localized at the region near the metal. As shown in Fig. 4b, redistribution in the region of C 4 F/h-BN was also observed. Originally, when the CL was absent, the magnitude of the redistribution was very similar to that of type-A in Fig. 4a (see supporting information). However, when metallic CL is added, the electron redistribution increased substantially, as shown in Fig. 4b. The redistribution between the substrate and C 4 F changed the barrier height between C 4 F and h-BN. Before the graphene CL was deposited, the staggered gaps between C 4 F and h-BN is 0.18 eV and 2.51 eV for C 4 F/BN and FC 4 /BN, respectively, as shown in Fig. 1. When the graphene was used as the CL for C 4 F on h-BN substrate, the staggered gap of C 4 F/h-BN increased from 0.18 eV to 0.65 eV, and the gap of FC 4 /h-BN is decreased from 2.51 eV to 2.21 eV, as shown in Fig. 2. Furthermore, by depositing CL, the junction properties between the graphite substrate and C 4 F were controlled by depositing CL. The C 4 F/Grpt interface junction was the Ohmic in nature, as shown in Fig. 1c. This Ohmic nature was converted to a Schottky contact after the graphene cap was applied, as shown in Fig. 2c. The p-type Schottky barrier of 1.19 eV in FC 4 /Grpt showed a remarkable reduction to 0.24 eV after the capping with graphene. This change in the interface property was due to electron redistribution where the intrinsic dipole of C 4 F was screened. On the other hand, the   type-C. The accumulation region is red, and the depletion region is blue. The redistribution generates an electric field with a direction that canceled out the intrinsic electric field of C 4 F. type-A interface, which had a negligible screening effect by capping, preserved its own barrier height. This means that the barrier height was modulated due to the screening effect by the metallic CL.
The origin of this type of band modulation by the CL was also observed in an oxide interface. A more significant band modulation is observed at the LaAlO 3 /SrTiO 3 interface when CL was metallic rather than insulating. However, the mechanism for the band modulation in the oxide heterostructure was different from that of a vdw heterostructure. In the oxide heterostructure, the Fermi-level pinning induced by the metallic CL is the key factor that determines the band alignment 25,33 . Due to the pinning, the band alignment between metal and SrTiO 3 in metal/LaAlO 3 /SrTiO 3 was very similar to that of metal/SrTiO 3 24 . Fermi-level pinning can trigger a charge transfer resulting in occupation of the conduction band of SrTiO 3 . This electron in the conduction band of SrTiO 3 screens the intrinsic electric field of LaAlO 3 . On the other hand, such remarkable Fermi-level pinning or charge transfer has not been observed in vdW heterostructures. Instead, the response to the polarity in vdW heterostructure was mainly derived from the electron redistribution in the interface region. This redistribution screens the dipole moment of the C 4 F, and thus modulates the band alignment. This change implies that types of bonding in a heterostructure is an important factor in determining the response to the polarity at the interface.

Conclusion
In summary, we investigated band alignment in vdW heterostructures with polar materials and a CL. The band alignment was found to be highly dependent on the intrinsic electric field of the polar materials, and this can be additionally modified with a CL. The staggered gap of C 4 F/BN can be controlled by depositing a CL on the polar materials. Furthermore, even Ohmic-Schottky transition in C 4 F/Grpt can be triggered by a CL. This wide range of tunability results from the polarity screening of the CL due to the different responses to the polarity in vdW heterostructures. Because of the absence of covalent bonding in the heterostructure, the response mainly spatial involves polarisation at the interface region. This demonstrates that band engineering with polar materials and a CL is highly effective for achieving a desired device deisgn.

Methods
First-principle calculation were performed using the Vienna ab-initio simulation package (VASP) 34 . The interactions between the ions and electrons were described using the projector-augmented-wave method with a 500 eV cutoff energy for the plane wave basis set 35 . The kinetic energy cutoff in the construction of the plane wave basis was set to 500 eV. To include vdw interaction in the exchange-correlation energy, the optB88-vdW functional was chosen for the exchange part and the Perdew-Burke-Ernzerhof (PBE) functional was chosen for the correlations part. All of the self-consistent loops were iterated until the total energy difference of the systems between the adjacent iterating steps was less than 10 −5 eV. The h-BN and graphite substrate was described using 6 layers of graphene and BN. The thickness of the six layers was at least 1.5 nm for both cases, and this prevented the surface effects of the substrate from influencing the interface interactions. In order to avoid dipole-dipole interaction between the periodic images, a vacuum level of at least 15 Å was inserted and a dipole correction was applied. All the atoms were fully relaxed until the maximum total Hellmann-Feynmann force was less than 0.01 eV/Å. The calculated lattice parameter of C 4 F was 4.92 Å, which agrees well with previous theoretical studies 29,31 . The periodicity of the interface is based on 1 unit cell of C 4 F and (2 × 2) cells of graphene and BN. The modeled interface was calculated using 9 × 9 × 1 sampling with the Monkhorst-Pack method in the Brillouin-zone 36 . The lattice mismatch was below 1% in this periodicity because the lattice constant of both materials was 2.46 Å.
For calculated band structure, each of bands are projected onto the spherical harmonics of each atom. Based on this projection, we decided which bands belonged to which component using the following equation.
Here, the P is the value of projection of component j, Ψ is the wave function, and Y is the spherical harmonics of each atom in component. We determined the components of the bands based on the largest value of P j .