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. 2021 Sep 28;6(40):26345–26353. doi: 10.1021/acsomega.1c03556

Electrostatic Modulation and Mechanism of the Electronic Properties of Monolayer MoS2 via Ferroelectric BiAlO3(0001) Polar Surfaces

Jin Yuan 1, Jian-Qing Dai 1,*, Cheng Ke 1
PMCID: PMC8515565  PMID: 34660994

Abstract

graphic file with name ao1c03556_0007.jpg

In the present work, first-principles density functional theory calculations were carried out to explore the intrinsic interface coupling and electrostatic modulation as well as the effect of ferroelectric polarization reversal in the MoS2/BiAlO3(0001) [MoS2/BAO(0001)] hybrid system. In addition to the interaction mechanism of the large ionic–van der Waals (vdW) coupling, our results indicate that the electronic properties of monolayer MoS2 on the BAO(0001) polar surface can be effectively modulated by reversing the ferroelectric polarization and/or engineering the domain structures of the substrate. Due to the unusual charge transfer between the MoS2 overlayer and the down-polarized ferroelectric BAO(0001) substrate, in the final analysis, the physical mechanism determining the interfacial charge transfer in the MoS2/BAO(0001) hybrid system is attributed to the specific band alignment between the clean BAO(0001) surface and the freestanding monolayer MoS2. Furthermore, our study predicts that MoS2-based ferroelectric field-effect transistors and various types of seamless p–i, n–i, p–n, p+–p, and n+–n homojunctions possessing an extremely steep built-in electric field can be fabricated by reversing the ferroelectric polarization and/or patterning the domain structure of the BAO(0001) substrate.

1. Introduction

For low-power logic applications and nonvolatile memory, ferroelectric field-effect transistors (FeFETs) based on a two-dimensional (2D) channel and ferroelectric gating are very attractive candidates owing to the switchable electric polarization and high dielectric constant of ferroelectric materials.1−5 Back in 2010, an experimental study reported that such graphene-based FeFETs fabricated on a ferroelectric Pb(Zr0.2Ti0.8)O3 substrate show an unusual resistance hysteresis.6 Subsequently, FeFETs with a 2D van der Waals (vdW) transition-metal dichalcogenide MX2 (M = Mo and W; X = S, Te, and Se) channel have also been experimentally demonstrated.2,3,7−12 Furthermore, a recent experimental investigation revealed that p–n homojunctions in a MoTe2 monolayer can be obtained using a periodically polarized ferroelectric P(VDF–TrFE) substrate.13 The integration of 2D monolayers with ferroelectric materials is becoming a hot research subject, as it offers the possibility to develop novel devices for nanoelectronic and optoelectronic applications. To realize practical applications, gaining an atomic-scale understanding of the intrinsic interface coupling as well as electrostatic modulation in 2D/ferroelectric hybrid systems is the first step.

As a representative member of the family of 2D vdW MX2 materials, monolayer MoS2 has attracted intensive attention from researchers.2,3,7,11,12 In addition to possessing optoelectronic and electronic properties similar or even superior to those of graphene, monolayer MoS2 is a semiconductor with a direct band gap of 1.90 eV, which renders it widely applicable to investigate photocatalyst processes and optoelectronic nanodevices.2,3,7,11,12,14 In experiments, monolayer MoS2 can be prepared via chemical vapor deposition (CVD), hydrothermal synthesis, liquid-phase stripping, and mechanical stripping methods.15−17 Furthermore, owing to its unique electronic structure and high flexibility, monolayer MoS2 is also considered as a promising candidate to explore flexible electronic devices.18

Ferroelectric BiAlO3 (BAO) with the R3c space group exhibits outstanding piezoelectric and ferroelectric properties along the [0001] direction and is a promising alternative material to the lead-based Pb(Zr, Ti)O3 (PZT) piezoelectric material.19−21 The theoretical spontaneous polarization of BAO is about 80 μC/cm2.22 Epitaxial BAO thin films can be fabricated using the pulsed laser deposition (PLD) method.23 In addition, a recent theoretical study24 indicated that due to the coexistence and coupling of bulk Rashba spin-splitting and ferroelectricity, bulk BAO can be an attractive ferroelectric Rashba semiconductor. Note that in our previous reports22,25 regarding BAO(0001) polar surfaces, the thermodynamic surface phase diagram and the corresponding electronic properties and spin textures were determined. It was found that the thermodynamically preferred positive (Z+) and negative (Z−) polar surfaces are terminated by the −Al–O3–Bi atomic layer and the −O3–Bi2 layer, respectively. Note that the BAO Z+ and Z– surfaces represent the spontaneous polarization pointing toward and away from the surface termination, respectively.

In this work, by integrating monolayer MoS2 with the ferroelectric BAO(0001) polar surface, the intrinsic interface coupling as well as electrostatic modulation in the MoS2/BAO(0001) heterostructure was studied via first-principles density functional theory (DFT) calculations. The results exhibit that in addition to the unusual charge transfer opposite the polarization compensation mechanism, the electronic properties of monolayer MoS2 adsorbed onto the BAO(0001) substrate can be effectively modulated by reversing the ferroelectric polarization and/or patterning the domain structure. Regarding the band alignment between the clean BAO(0001) polar surface and the freestanding monolayer MoS2, the physical mechanism behind the interfacial charge transfer is well explained. Our research provides theoretical evidence for the fabrication of FeFETs based on MoS2/BAO(0001) heterostructures as well as various types of p–i, n–i, p–n, p+–p, and n+–n homojunctions in monolayer MoS2 on the ferroelectric BAO(0001) polar surface by reversing the ferroelectric polarization and/or patterning the domain structure.

2. Methodology

All first-principles DFT calculations with the projector augmented wave (PAW) potentials were simulated using the Vienna ab initio simulation package (VASP).26 The exchange–correlation functionals were described via the Perdew–Burke–Ernzerhof form revised for solids (PBEsol) of the generalized gradient approximation (GGA), which has been confirmed to be very precise in predicting the spontaneous polarization of ferroelectric materials.27−29 To consider the weak interactions existing between the BAO(0001) polar surface and monolayer MoS2, the dispersion-corrected DFT-D3 method was employed.30 The Bi 5d106s26p3, Al 3s23p1, O 2s22p4, Mo 4p64d55s1, and S 3s23p4 electrons were treated as valence electrons. In the structural optimization and self-consistent calculations, the Brillouin zone was sampled with a Đ-centered 5 × 5 × 1 k-point mesh. However, for the calculations of the density of states (DOS) and electronic band structures, a Đ-centered 11 × 11 × 1 k-point mesh and a dense k-point string of ∼250 points per Å–1 were employed, respectively. Furthermore, to quantitatively evaluate the charge transfer between the BAO(0001) surface and monolayer MoS2, the Bader topological charge analysis with a Đ-centered 11 × 11 × 1 k-point mesh was also carried out.31 The cutoff energy of the plane wave expansion and the convergence criterion of the energy were set to 500 and 10–6 eV, respectively. Importantly, the dipole correction was turned on to counteract the interaction between periodic slab images.32 Due to the existence of a prominent Rashba–Dresselhaus spin-splitting in the BAO(0001) polar surface and bulk,24,25 the influence of the spin–orbit coupling (SOC) on the obtained results and conclusions was also investigated.

For monolayer MoS2 and the BAO(0001) substrate, the calculated lattice constants were 3.140 and 5.363 Å, respectively, which are consistent with those obtained in previous reports.24,33 The MoS2/BAO(0001) hybrid system with a vacuum layer with thickness > 20 Å was constructed by placing the √3 × √3 MoS2 supercell on the 1 × 1 BAO(0001) slab. Due to the ∼1% lattice mismatch between the √3 × √3 MoS2 supercell and the 1 × 1 BAO(0001) slab, the lattice constant of the BAO(0001) slab was increased to match that of the MoS2 supercell so that no strain is introduced into the MoS2 overlayer. The BAO Z+ and Z– slabs as well as the polarization-reversed BAO Z+ (denoted as BAO Z+↓) and Z– (denoted as BAO Z–↑) slabs were constructed via surface termination and the six −Al–O3–Bi– trilayers. For the MoS2/BAO(0001) hybrid system, in addition to the full structural optimization of the surface termination and the two outer −Al–O3–Bi– trilayers, fully atomic relaxations were performed on the MoS2 overlayer until the residual force appearing on each atom was less than 0.01 eV/Å. The in-plane lattice constants and atomic positions of the backside of the BAO(0001) slabs were fixed. In addition, as shown in Figure S1, the five typical interfacial configurations between the BAO Z± surface and monolayer MoS2 were explored. In terms of the calculated total energy for the relaxed MoS2/BAO Z+ and Z– heterostructures, the preferred adsorption configuration respectively exhibits lower total energies by about 306 and 328 meV/supercell (0.19 and 0.21 J/m2) than the configuration with the highest energy. The top views of this energetically preferred adsorption configuration are plotted in Figure S1b,g, respectively. Further calculations were carried out, choosing the interfacial configurations with the lowest total energy.

3. Results and Discussion

3.1. Freestanding Monolayer MoS2

As mentioned in the introduction, monolayer MoS2 exhibits distinctive optical, electronic, and catalytic properties and is a direct band-gap semiconductor.14 Previous theoretical and experimental results14,34 showed that the band gap of monolayer MoS2 is 1.90 eV. To check our calculated results using the DFT–PBEsol approach, the obtained lattice constants of monolayer MoS2 (a = b = 3.140 Å) were compared with the value of 3.160 Å reported in ref (33). Such a small error is perfectly acceptable for first-principles calculations. The calculated lattice constants of the BAO(0001) substrate (a = b = 5.363 Å) are also in good agreement with the value of 5.375 Å obtained in a previous experimental result.19 Therefore, the DFT–PBEsol approach seems to be a reasonable choice for these calculations.

Next, we focus on the electronic properties of the freestanding monolayer MoS2. Figure 1a,c describes the electronic band structures of the primitive cell of the freestanding monolayer MoS2 without SOC and with SOC, respectively. Obviously, monolayer MoS2 exhibits the characteristics of a direct band-gap material as the valence band maximum (VBM) and conduction band minimum (CBM) are both located at the K point in the Brillouin zone. The band gaps without SOC and with SOC are respectively 1.79 and 1.71 eV, which are only about 0.11–0.19 eV less than a previously reported experimental value.14 Due to the usual underestimation of the band gap obtained with the PBE functional,29 such a difference in the band gap is still within an acceptable range. Figure 1b,d shows the electronic band structures of the √3 × √3 supercell of the freestanding monolayer MoS2 without SOC and with SOC, respectively. It can be seen that in addition to the negligible change in the band gap with respect to that in the primitive cell in the Brillouin zone, the K point in the primitive cell in the Brillouin zone is folded into the Γ point in the √3 × √3 supercell in the Brillouin zone. Furthermore, by comparing the band structures without SOC and with SOC, another interesting phenomenon can be found, i.e., the band gap for the case with SOC is slightly decreased by about 0.06–0.08 eV relative to that without SOC due to band-splitting.35

Figure 1.

Figure 1

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(a, c) Band structures of the freestanding monolayer MoS2 primitive cell without SOC and with SOC, respectively. (b, d) Band structures of the freestanding monolayer MoS2 √3 × √3 supercell without SOC and with SOC, respectively. The Fermi level is indicated by a black short dashed line. The inset exhibits the first Brillouin zone of the hexagonal supercell.

3.2. The MoS2/BAO Z+ and Z+↓ Heterostructures

This section focuses on the interface coupling and electrostatic modulation in the MoS2/BAO Z+ heterostructure as well as the effect of polarization reversal. The side views of the atomic structures for the relaxed √3 × √3/1 × 1 MoS2/BAO Z+ and Z+↓ heterostructures are illustrated in Figure 2. It can be observed that after full structure relaxation, the BAO Z+ substrate is still terminated with the −Al–O3–Bi atomic layer (as shown in Figure 2a), which is the same as the initial thermodynamically preferred BAO Z+ surface termination without MoS2 adsorption.22,25 Such information indicates that the adsorption of MoS2 has no significant influence on the atomic structures of the BAO Z+ surface. Similar conclusions can also be obtained for the relaxed MoS2/BAO Z+↓ heterostructure (as shown in Figure 2b). Note that the MoS2/BAO Z+↓ heterostructure was constructed without changing the surface chemical composition of the BAO Z+ substrate; only the ferroelectric polarization was reversed. In addition, Figure 2 displays the energy difference (ΔE) of the potential well for the √3 × √3/1 × 1 MoS2/BAO Z+ and Z+↓ heterostructures. The ΔE value of 0.82 J/m2 indicates that the MoS2/BAO Z+ hybrid system is more stable than the MoS2/BAO Z+↓ system due to the lowest surface free energy of the thermodynamically preferred surface termination.

Figure 2.

Figure 2

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(a, b) Side views of atomic structures and energy difference (ΔE) of the potential well for √3 × √3/1 × 1 MoS2/BAO Z+ (a) and Z+↓ (b) heterostructures.

For the relaxed MoS2/BAO Z+ and Z+↓ heterostructures, the calculated layer spacings (dS-BAO) between the BAO substrate and monolayer MoS2 are respectively 2.59 and 2.35 Å (as listed in Table 1), which are much bigger than the interface spacing (0.11–0.76 Å) of the metal–oxide contact.36 According to ref (37), the vdW gap (gvdW) could be approximated as gvdW ≈ dvdW – ra – rb, where dvdW and ra (or rb) represent the vdW distance and covalent radii of individual atoms, respectively. In the case of the investigated MoS2/BAO Z+ and Z+↓ heterostructures, the gvdW is defined as gvdW ≈ dS-BAO – rBi – rS and gvdW ≈ dS-BAO – rO – rS, respectively. Therefore, the calculated gvdW values for the MoS2/BAO Z+ and Z+↓ heterostructures are 0.11 and 0.60 Å, respectively, which are much smaller than the gvdW value of 1.80 Å obtained for bulk MoS2.37 Furthermore, being an important parameter to investigate the interface coupling mechanism, the binding energy (Wb) between the BAO substrate and monolayer MoS2 was calculated according to Wb = −(EMoS2/BAO – EMoS2 – EBAO)/S, where EMoS2/BAO, EMoS2 (EBAO), and S respectively indicate the total energy of the MoS2/BAO heterostructure, the total energy of the MoS2 isolated monolayer (BAO substrate) with fixed atomic positions in the MoS2/BAO system, and the area of the 1 × 1 BAO(0001) surface unit cell. As listed in Table 1, the binding energies of the MoS2/BAO Z+ and Z+↓ heterostructures are 5.63 and 5.98 J/m2, respectively. In contrast with pure vdW interactions of about 0.19 J/m2 (0.34 J/m2) in bulk MoS2 (graphite),38,39 the values obtained in the present study are an order of magnitude higher. Due to the much smaller gvdW value and much bigger Wb value, it is reasonable to assume that the interface interaction mechanism of the MoS2/BAO Z+ and Z+↓ heterostructures is not only the pure vdW coupling.

Table 1. Layer Spacing (dS-BAO) and Binding Energy (Wb) between the BAO Substrate and Monolayer MoS2 and the Change in Charge in the Interfacial S Atomic Layer (ΔQS), Mo Layer (ΔQMo), and Monolayer MoS2 (ΔQtot) with Respect to the Freestanding Monolayer MoS2 as well as the Carrier Density n in the MoS2 Overlayer on BAO(0001) Substratesa.

  dS-BAO (Å) Wb (J/m2) ΔQS (e) ΔQMo (e) ΔQtot (e) n (1013 cm–2)
MoS2/BAO Z+ 2.59 5.63 0.049 0.022 0.067 –2.62
MoS2/BAO Z+↓ 2.35 5.98 –0.197 –0.003 –0.199 +7.77
MoS2/BAO Z– 2.67 6.22 0.223 0.035 0.251 –9.80
MoS2/BAO Z–↑ 2.48 6.21 0.282 0.060 0.332 –12.96
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a

Note that the negative (positive) sign of n denotes an electron (hole) carrier.

Figure 3 shows the side views of the electron localization functions (ELFs) and differential charge densities for the MoS2/BAO Z+ and Z+↓ heterostructures to further investigate the interface coupling mechanism.40,41 Due to the included Pauli repulsion effect, the ELFs could be directly employed to observe the nature of the three-dimensional bonding. For the MoS2 overlayer adsorbed at the BAO Z+ and Z+↓ surfaces, as shown in Figure 3a,b, the electron cloud of the interfacial S atomic layer shows a clear deformation with respect to the freestanding monolayer MoS2 (not shown). Moreover, compared with the ELFs of the clean BAO Z+ and Z+↓ surfaces (as shown in Figure S6a,b), it can be seen that the 6s lone-pair electron of the interfacial Bi atom in the MoS2/BAO Z+ heterostructure disappears. The above information indicates that the electronic properties of monolayer MoS2 are effectively modulated by the ferroelectric BAO Z+ and Z+↓ surfaces. Additionally, there is no shared electron cloud (bond attractors) in both the MoS2/BAO Z+ and Z+↓ interfaces, which rules out the possibility of covalent coupling in the MoS2/BAO Z+ and Z+↓ interfaces. Indeed, according to ref (42), the interface interaction mechanism in the MoS2/BAO Z+ and Z+↓ hybrid systems should be defined as an ionic–vdW coupling combining electrostatic interactions with vdW interactions. From the differential charge densities of the MoS2/BAO Z+ and Z+↓ interfaces (as shown in Figure 3a,b), the remarkable charge transfer does indicate the nature of the electrostatic interactions, i.e., the characteristics of the ionic type. In addition to the significant charge transfer observed, the differential charge density images indicate that the MoS2 overlayer adsorbed onto the BAO Z+ and Z+↓ surfaces shows a gain in electrons and holes, respectively, which suggests possible corresponding n- and p-type doping in this MoS2 overlayer.

Figure 3.

Figure 3

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(a, b) Side views of ELFs and differential charge densities for MoS2/BAO Z+ (a) and Z+↓ (b) heterostructures. The blue and green colors in differential charge density images respectively represent the gain of holes and electrons. Note that the ELFs and differential charge density maps are plotted for the isosurfaces of 0.7 and 9 × 10–4 e/Å3, respectively. The symbols of Bi, Al, O, Mo, and S atoms are shown in Figure 2.

To confirm the respective n- and p-type doping in the MoS2 overlayer adsorbed onto the BAO Z+ and Z+↓ substrates, the Bader topological charge analysis31 with an accuracy exceeding 10–3e was employed to quantitatively estimate the interfacial charge transfer. As presented in Table 1 for the MoS2 overlayer on the BAO Z+ surface, the interfacial S atomic layer, Mo layer, and monolayer MoS2 were calculated to gain charges of 0.049, 0.022, and 0.067 e, respectively, per supercell surface area relative to the freestanding monolayer MoS2. This is equivalent to electrostatic n-type doping with a carrier density of ne = 2.62 × 1013 cm–2. However, for the MoS2 overlayer on the BAO Z+↓ surface, the situation is different. The results of the Bader topological charge analysis indicate that the interfacial S atomic layer, Mo layer, and monolayer MoS2 lost 0.197, 0.003, and 0.199 e, respectively, per supercell surface area relative to the freestanding monolayer MoS2. This corresponds to a p-type carrier density of nh = 7.77 × 1013 cm–2. We note that the transferred charges in the MoS2/BAO Z+ and Z+↓ heterostructures show the same order of magnitude as that of the graphene/BiFeO3(0001) hybrid systems.43,44 Simultaneously, the calculated carrier density difference between the n- and p-type monolayer MoS2 on the BAO(0001) surface is 1.04 × 1014 cm–2, which is two order magnitudes higher than the theoretical value and experimental observation in graphene/LiNbO3 hybrid structures.45 Due to the significant change in resistance in the MoS2 channel before and after the polarization reversal, i.e., the large Ion/Ioff ratio, for nanoelectronic and optoelectronic applications, this is a great advantage. More importantly, these results are well consistent with the conclusion obtained from the differential charge density images discussed above, and the more remarkable charge transfer in the MoS2/BAO Z+↓ interface could also be observed in the differential charge density images. In addition, both the differential charge density images and Bader topological charge analysis indicate that the charge transfer mainly involves the interfacial atoms in the MoS2/BAO Z+ and Z+↓ heterostructures. Note that due to the transition from n- to p-type doping in the MoS2 overlayer caused by polarization reversal, the MoS2/BAO(0001) heterostructure could be a promising platform to explore FeFETs based on the MoS2 channel.

The electronic band structures were calculated along high-symmetry directions of the √3 × √3 MoS2 supercell in the Brillouin zone for the MoS2/BAO Z+ and Z+↓ heterostructures (without SOC). As shown in Figure 4, the projected band of the MoS2 overlayer on the BAO Z+ surface undergoes a downward shift of 0.38 eV relative to the freestanding monolayer MoS2. By contrast, an upward shift of 0.64 eV with respect to the freestanding monolayer MoS2 can be observed in the projected band of the MoS2 overlayer on the BAO Z+↓ surface. Such a large band offset of 1.02 eV in monolayer MoS2 on the BAO Z+ and Z+↓ substrates implies that significant changes in resistance will occur in the MoS2 overlayer as a consequence of the ferroelectric polarization reversal of the BAO substrate. This is still in good agreement with the above results of Bader’s topological charge analysis and the differential charge densities. The charge transfer at the MoS2/BAO Z+ and Z+↓ interfaces can be explained by inspecting the band alignment between the BAO(0001) substrate and monolayer MoS2. As shown in Figure 4 for the MoS2/BAO Z+ heterostructure, the calculated Fermi level of the clean BAO Z+ surface is 4.20 eV below the vacuum level (0 eV) and is 0.85 eV higher than the calculated Fermi level of the freestanding monolayer MoS2. Due to the higher Fermi level with respect to the freestanding monolayer MoS2, the electrons will transfer from the BAO Z+ substrate to the MoS2 overlayer, resulting in electrostatic n-type doping. However, the opposite is true for the MoS2/BAO Z+↓ heterostructure. As the Fermi level is 2.15 eV lower than that of the freestanding monolayer MoS2, the hole carriers in the MoS2 overlayer on the BAO Z+↓ surface are bound to appear. Furthermore, after charge transfer, the Fermi level of the MoS2/BAO Z+ and Z+↓ heterostructures is exactly in between the clean BAO surface and the freestanding monolayer MoS2, which confirms the above explanation for the charge transfer at the MoS2/BAO Z+ and Z+↓ interfaces.46 Finally, due to the orbital hybridization with the BAO substrate,47 the band gap of the MoS2 overlayer on the BAO Z+ and Z+↓ surfaces is also effectively modulated by the BAO(0001) ferroelectric substrate, as shown in Figure 4.

Figure 4.

Figure 4

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(a, b) Band structures along high-symmetry directions of the √3 × √3 MoS2 supercell Brillouin zone and band alignment (vacuum level is set to 0 eV) for MoS2/BAO Z+ (a) and Z+↓ (b) heterostructures (without SOC). The red and blue circle dots correspond to the projected band of the MoS2 overlayer on BAO Z+ and Z+↓ surfaces and the band structure of the freestanding monolayer MoS2, respectively. Both the black and red short dashed lines indicate the Fermi level.

In addition, as mentioned in the introduction, bulk BAO is believed to be an attractive ferroelectric Rashba semiconductor owing to the coexistence and coupling of bulk Rashba spin-splitting and ferroelectricity.24 In our former report,25 due to the existence of the heavy element Bi, the BAO(0001) surfaces were also found to exhibit distinctive Rashba–Dresselhaus spin-splittings. It is therefore necessary to explore the influence of SOC on the obtained results and conclusions. Figure S2a,c shows the calculated electronic band structures along high-symmetry directions of the √3 × √3 MoS2 supercell in the Brillouin zone for the MoS2/BAO Z+ and Z+↓ heterostructures (with SOC). Compared with the electronic band structures without SOC, no significant change can be observed in addition to the clear band-splitting of the VBM. Furthermore, Figure S3a–c illustrates the band alignment between the freestanding monolayer MoS2 and the clean BAO Z+ (Z+↓) substrate (with SOC). As expected, the mechanism of band alignment remains valid.

3.3. The MoS2/BAO Z– and Z–↑ Heterostructures

Similarly, the MoS2/BAO Z–↑ heterostructure was constructed without changing the surface chemical composition of the BAO Z– substrate; only the ferroelectric polarization was reversed. As plotted in Figure S4, after full structural optimization, the thermodynamically preferred polarized BAO Z– surface with MoS2 adsorption is still terminated by the −O3–Bi2 atomic layer, and the atomic structure of the polarization-reversed Z– (Z–↑) surface also shows only a slight change. This reveals that the adsorption of MoS2 has no significant influence on the atomic structure of the BAO Z– and Z–↑ surfaces. Such information is consistent with the MoS2/BAO Z+ and Z+↓ heterostructures. The fact that the potential well energy was reduced by 1.68 J/m2 (as shown in Figure S4) also indicates that the MoS2/BAO Z– system is still more stable than the MoS2/BAO Z–↑ system. According to our previous calculations regarding the thermodynamic surface phase diagram of the BAO(0001) surface,22 the polarization-reversed BAO Z+ (Z+↓) and Z– (Z–↑) surface terminations should be energetically metastable and will therefore possess higher surface free energy with respect to the thermodynamically preferred surface terminations. Such information also implies that to construct a thermodynamically favorable 2D/ferroelectric hybrid system, using thermodynamically preferred ferroelectric surface termination should be an important prerequisite.

Next, we pay attention to the interface coupling mechanism in the MoS2/BAO Z– and Z–↑ heterostructures. As presented in Table 1 for the MoS2/BAO Z– (MoS2/BAO Z–↑) heterostructure, the layer spacing (dS-BAO) and binding energy (Wb) between the BAO substrate and the MoS2 overlayer are 2.67 Å (2.48 Å) and 6.22 J/m2 (6.21 J/m2), respectively. The calculated gvdW values for the MoS2/BAO Z– and Z–↑ heterostructures are 0.19 and 0.00 Å, respectively. These values are very similar to those of the MoS2/BAO Z+ and Z+↓ heterostructures. Combining the ELFs with the differential charge density (as shown in Figures S5 and S6c,d), the interface coupling mechanism in the MoS2/BAO Z– and Z–↑ heterostructures should still be the same ionic–vdW interaction as in the MoS2/BAO Z+ and Z+↓ systems.

Next, we focus on the electrostatic modulation and mechanism of the electronic properties of monolayer MoS2 on the BAO Z– and Z–↑ polar surfaces. As plotted in Figure 5, the projected bands of the MoS2 overlayer on the BAO Z– and Z–↑ surfaces exhibit downward shifts of 0.90 and 0.74 eV, respectively, which indicates that both MoS2 overlayers on the BAO Z– and Z–↑ polar surfaces are electrostatically n-doped. To quantitatively explore the charge doping effect in the MoS2 overlayer adsorbed at the BAO Z– and Z–↑ substrates, the Bader topological charge analysis31 was employed to estimate precisely the interfacial charge transfer. As listed in Table 1 for the MoS2 overlayer on the BAO Z– (Z–↑) surface, the interfacial S atomic layer, Mo layer, and monolayer MoS2 were found to gain 0.223 (0.282), 0.035 (0.060), and 0.251 e (0.332 e), respectively, per supercell surface area relative to the freestanding monolayer MoS2. This is equivalent to electrostatic n-type doping with a carrier density of ne = 9.80 × 1013 cm–2 (ne = 12.96 × 1013 cm–2). Note that as displayed in Table 1, the carrier density introduced in the MoS2 overlayers on both polarization-unreversed BAO Z+ and Z– surfaces is much lower than that in the polarization-reversed BAO Z+ (Z+↓) and Z– (Z–↑) surfaces. This is due to the characteristics of metastability of the polarization-reversed BAO(0001) surface terminations relative to the thermodynamically preferred polarization-unreversed BAO Z+ and Z– surface terminations.22 More interestingly, different from the so-called polarization compensation mechanism of ferroelectric BAO(0001) substrates,4,13,43,48 an unusual charge transfer opposite the polarization compensation can be seen in the MoS2 overlayer of the MoS2/BAO Z– heterostructure, as shown in Figure 5. In other words, the MoS2 overlayer on the down-polarized (Z−) ferroelectric BAO(0001) surface is electrostatically n-doped.

Figure 5.

Figure 5

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(a, b) Band structures along high-symmetry directions of the √3 × √3 MoS2 supercell Brillouin zone and band alignment (vacuum level is set to 0 eV) for MoS2/BAO Z– (a) and Z–↑ (b) heterostructures (without SOC). The red and blue circle dots correspond to the projected band of the MoS2 overlayer on BAO Z– and Z–↑ surfaces and the band structure of the freestanding monolayer MoS2, respectively. Both the black and red short dashed lines indicate the Fermi level.

As is well known, due to the polarization compensation mechanism, the MoS2 overlayer on the down- and up-polarized ferroelectric surfaces should be electrostatically p- and n-doped, respectively.4,13,43,48 However, the real situation may be more complex. For example, in refs (49) and (50) as well as in our previous reports44,51 regarding the graphene/ferroelectric hybrid system, such an unusual charge transfer depending on the surface characteristics of the ferroelectric substrate has also been found. In the final analysis, for the MoS2/BAO Z– heterostructure, the unusual interfacial charge transfer can still be explained in terms of the specific band alignment between the clean BAO Z– polar surface and the freestanding monolayer MoS2. As plotted in Figure 5, the Fermi level of the clean BAO Z– polar surface is 3.37 eV higher than that of the freestanding monolayer MoS2, which inevitably leads to the introduction of n-type carriers in the MoS2 overlayer on the BAO Z– surface. Furthermore, the interfacial charge transfer in the MoS2/BAO Z–↑ heterostructure satisfies the mechanism of band alignment, as plotted in Figure 5. After the charge transfer, the Fermi level of the MoS2/BAO Z–↑ heterostructure is exactly in between the clean BAO Z–↑ polar surface and the freestanding monolayer MoS2. As a result, as mentioned in our previous work,51 the band alignment between the clean ferroelectric BAO(0001) polar surface and the freestanding monolayer MoS2 should be regarded as a universal mechanism, thereby confirming the interfacial charge transfer in MoS2/BAO(0001) hybrid systems. Indeed, the band alignment between ferroelectric polar surfaces and 2D materials should be a universal criterion determining the interfacial charge transfer in the 2D/ferroelectric hybrid systems.

Finally, the influence of the SOC on the results and conclusions obtained for the MoS2/BAO Z– and Z–↑ heterostructures is explored. As displayed in Figure S2b,d, when the SOC is taken into consideration, the projected bands of the MoS2 overlayer onto the BAO Z– and Z–↑ surfaces undergo downward shifts of 0.90 and 0.74 eV, respectively, which is the same as that of the MoS2 overlayer on the BAO Z– and Z–↑ surfaces without SOC, as shown in Figure 5. In addition to the band-splitting of the VBM, no change can be found in the electronic band structures of the MoS2/BAO Z– and Z–↑ heterostructures with SOC (as shown in Figure S2b,d), which is consistent with the above discussions on the MoS2/BAO Z+ and Z+↓ heterostructures. When the SOC is taken into consideration, the mechanism of band alignment similarly remains valid, as shown in Figure S3c–e.

4. Discussion

First, an important issue is how to construct a thermodynamically favorable 2D/ferroelectric hybrid system using reasonable ferroelectric surface termination. In the material surface and interface science scientific communities, surface reconstruction is a crucial issue. Particularly for a ferroelectric polar surface, the surface stoichiometry, geometry, and electronic structure exhibit a clear dependence on the ferroelectric polarization direction.52−54 Therefore, it is necessary to use reasonable surface termination in the calculations of 2D/ferroelectric hybrid systems. However, to the best of our knowledge, most existing theoretical calculations regarding 2D/ferroelectric heterostructures have failed to use a system with thermodynamically preferred ferroelectric surface termination.45,55−59 From the energy difference of the potential well for the √3 × √3/1 × 1 MoS2/BAO(0001) heterostructure before and after polarization reversal, it can be inferred that it is clearly not a reasonable choice to employ a 2D/ferroelectric hybrid system with thermodynamically impossible or nonpreferred ferroelectric surface termination as the preferred system due to the much higher potential energy.

Second, according to the change in carrier type (MoS2 overlayer on the polarization-reversed BAO Z+ surface) or remarkable increase in the carrier density (MoS2 overlayer on the polarization-reversed BAO Z– surface) in the MoS2 overlayer on the BAO(0001) substrate after ferroelectric polarization reversal, the MoS2/BAO(0001) heterostructure is also believed to be promising in MoS2-based FeFET applications. As mentioned in the introduction, for low-power logic applications and nonvolatile memory, FeFETs based on a 2D channel and ferroelectric gating are very attractive candidates owing to the switchable electric polarization and high dielectric constant of ferroelectric materials.1−5 Additionally, due to the n-type doping in MoS2 overlayers on both BAO Z+ and Z– polar surfaces as well as the respective electrostatically doped p- and n-type MoS2 in the MoS2/BAO Z+↓ and Z–↑ heterostructures, various types of seamless p–i, n–i, p–n, p+–p, and n+–n homojunctions in monolayer MoS2 on the ferroelectric BAO(0001) polar surface are predicted to occur by reversing the ferroelectric polarization and/or patterning the domain structure. At the same time, the remarkable band offset in the MoS2 monolayer on BAO(0001) substrates with different domain patterns implies that various types of seamless p–i, n–i, p–n, p+–p, and n+–n homojunctions possessing an extremely steep built-in electric field can be fabricated.60 As is well known, in modern nanoelectronics and optoelectronics, various p–i, n–i, p–n, p+–p, and n+–n homo/heterojunctions are fundamental components for realizing the desired functionalities.61 Such seamless p–i, n–i, p–n, p+–p, and n+–n homojunctions in monolayer MoS2 on the ferroelectric BAO(0001) substrate are very attractive candidates for novel nanoelectronic and optoelectronic devices. Indeed, a p–n homojunction in monolayer MoTe2 on a periodically polarized ferroelectric P(VDF-TrFE) substrate has been already experimentally prepared.13 In addition, by patterning the domain structures of a ferroelectric LiNbO3(0001) substrate, periodic arrays of a p–i homojunction in a graphene channel have been confirmed.45

Third, different from the polarization compensation mechanism, in the MoS2/BAO Z– heterostructure, an unusual interfacial charge transfer is found, i.e., an electrostatically doped n-type MoS2 overlayer on the down-polarized (Z−) ferroelectric BAO(0001) surface. As mentioned above, due to the polarization compensation mechanism, the MoS2 overlayer on down- and up-polarized ferroelectric surfaces is usually electrostatically p- or n-doped, respectively. Although the doping carrier type in the MoS2 overlayer on the BAO Z+, Z+↓, and Z–↑ polar surfaces satisfies the mechanism of polarization compensation, in the final analysis, the universal mechanism determining the interfacial charge transfer should be attributed to the specific band alignment between the clean BAO(0001) substrate and the freestanding monolayer MoS2 due to the unusual interfacial charge transfer in the MoS2/BAO Z– hybrid system. Indeed, the band alignment method has been used to explain charge doping in graphene on a ferroelectric SrTiO3(111) substrate.62 In our former studies regarding graphene/BAO(0001) hybrid systems and 1T-VSe2/BiFeO3(0001) heterostructures,51,63 such a mechanism has also been confirmed. As a result, the band alignment between ferroelectric polar surfaces and 2D materials should be a universal criterion determining the interfacial charge transfer in 2D/ferroelectric heterostructures.

Finally, it is worth mentioning that in the present work, only the intrinsic interface coupling and electrostatic modulation were explored in the MoS2/BAO(0001) heterostructure excluding adsorbates (contaminants) and defects. However, in experiments, 2D monolayer materials are usually transferred onto a clean single-crystal ferroelectric substrate using a one-touch wet transfer method,45 which inevitably introduces OH–, H+, or even a defective MoS2/BAO(0001) interface, i.e., interfacial adsorbates (contaminants) and defects. For actual MoS2/BAO(0001) hybrid systems, these interfacial adsorbates (contaminants) and defects can play a key role in the interfacial charge transfer process.45,49,50,57 In other words, for the real systems, due to the existence of adsorbates (contaminants) as well as defects, various surface reconstructions may take place, which will inevitably lead to more complicated situations. For example, experimental observations show that surface characteristics and adsorbates (contaminants) play an important role in the electrostatic doping of graphene on ferroelectric polar surfaces. As reported in ref (50), for graphene-based FeFETs with La-doped PZT gating, the intrinsic resistance change shows an antihysteresis behavior when the adsorbed molecules are removed via a vacuum annealing process. In addition, in ref (49), a transformation from a ferroelectric hysteresis to an antihysteresis was observed in the graphene channel for the adsorbate-removed graphene/ferroelectric hybrid system using superlattice PbTiO3/SrTiO3 substrates with different surface characteristics. Therefore, the extrinsic effect of adsorbates (contaminants) and defects at the MoS2/BAO(0001) interface deserves further exploration.

5. Conclusions

In conclusion, based on the thermodynamically preferred ferroelectric BAO(0001) polar surfaces, we investigated the intrinsic interface coupling and electrostatic modulation as well as the effect of ferroelectric polarization reversal in a MoS2/BAO(0001) heterostructure via first-principles DFT calculations. First, our study points out that to construct a thermodynamically favorable 2D/ferroelectric hybrid system, thermodynamically preferred ferroelectric surface termination should be an important prerequisite. Second, the effect of the ferroelectric polarization reversal of the BAO(0001) substrate, the n-type doping in the MoS2 overlayers on both the BAO Z+ and Z– polar surfaces, and the respective electrostatically doped p- and n-type MoS2 in the MoS2/BAO Z+↓ and Z–↑ heterostructures show that the MoS2/BAO(0001) heterostructure holds much promise for MoS2-based FeFETs. Furthermore, this heterostructure could be a potential candidate for the application of various types of seamless p–i, n–i, p–n, p+–p, and n+–n homojunctions possessing an extremely steep built-in electric field. Third, different from the polarization compensation, in the final analysis, the potential physical mechanism determining the interfacial charge transfer in the MoS2/BAO(0001) heterostructure should be attributed to the specific band alignment between the clean BAO(0001) substrate and the freestanding monolayer MoS2. This should be regarded as a universal criterion dictating the interfacial charge transfer in 2D/ferroelectric heterostructures. Finally, the interaction mechanism of the large ionic–vdW coupling in MoS2/BAO(0001) heterostructures should also be an important point worth considering.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (grant nos. 52073129 and 51762030).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.1c03556.

  • Further details on the top views of respective five typical interfacial configurations for MoS2/BAO Z+ and MoS2/BAO Z– heterostructures, band structures along high-symmetry directions of the √3 × √3 MoS2 supercell Brillouin zone for MoS2/BAO Z+, Z+↓, Z–, and Z–↑ heterostructures (with SOC), band alignment between the freestanding monolayer MoS2 and clean BAO(0001) substrate (with SOC), side views of atomic structures, ELFs, and differential charge densities as well as the energy difference (ΔE) of the potential well for √3 × √3/1 × 1 MoS2/BAO Z– and Z–↑ heterostructures, and side views of ELFs for the clean BAO Z+, Z + ↓, Z–, and Z–↑ surfaces (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao1c03556_si_002.pdf (666.9KB, pdf)

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ao1c03556_si_002.pdf (666.9KB, pdf)

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