BiFeO3

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Effect of Surface Termination on Charge Doping in Graphene/BiFeO3(0001) Hybrid Structure Jian-Qing Dai, Tian-Fu Cao, and Xiao-Wei Wang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b04142 • Publication Date (Web): 12 Jul 2018 Downloaded from http://pubs.acs.org on July 17, 2018

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The Journal of Physical Chemistry

Effect of Surface Termination on Charge Doping in Graphene/BiFeO3(0001) Hybrid Structure Jian-Qing Dai,* Tian-Fu Cao, and Xiao-Wei Wang Faculty of Materials Science and Engineering, Kunming University of Science and Technology, Kunming 650093, P. R. China

*Corresponding author. Fax: +86 871 65107922. E-mail address: [email protected] (J.-Q. Dai). ORCID: 0000-0003-4352-0789 (Jian-Qing Dai)

Abstract: Electrostatic charge doping in graphene by ferroelectric polarization is an intriguing avenue for graphene-based nanoelectronic devices. Here, based on the thermodynamic stable BiFeO3(0001) surfaces, we present first-principles calculations to study the influence of surface termination on interface chemistry and charge doping in graphene/BiFeO3 hybrid system. Our results reveal that the doping type and carrier density in graphene are not directly determined by the polarization direction of the ferroelectric substrate but by the electronegativity difference between graphene and the surface termination of the BiFeO3 substrate. This finding indicates that the intrinsic resistance change in graphene on the ferroelectric substrate can show proper-hysteresis or anti-hysteresis behavior, depending on the surface terminations and hence on the particular chemical conditions. In addition, we find that highly spin-polarized (~ -31%) Dirac fermions in graphene can be induced by depositing on the insulating BiFeO3(0001) negative surface terminated by -Bi-O3-Fe trilayer. Besides shedding light on the underlying mechanism of charge doping effect in the graphene/ferroelectric interfaces, our results also put forward practical strategies for developing/improving advanced functionalities of the graphene-based ferroelectric field-effect devices.

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Introduction Graphene, which shows unique electronic structure and robust chemical and mechanical

properties, is of great current interest in exploring potential applications in nanoelectronics, photonics, and optoelectronics. 1 , 2 , 3 , 4 , 5 Especially, the graphene-based hybrid structures combined with functional materials such as ferroelectric oxides have attracted remarkable attention in recent years.6,7,8,9 On one hand, the high dielectric constants of ferroelectric perovskites facilitate higher carrier density and mobility by electric-field-gating of graphene as compared to other dielectric materials. 10 , 11 , 12 , 13 On the other hand, the attractive characteristics of the graphene/ferroelectric hybrid systems stem from the switchable spontaneous polarization of the ferroelectric substrates, which enables non-volatile resistance hysteresis and therefore the potential memory applications. 14 , 15 More recently, the controllable p-n junctions in graphene, which are of critical importance for the next generation of nanoelectronic and optoelectronic devices, have been fabricated by the underlying periodically polarized or uniformly polarized ferroelectric substrates.16,17 Contrary to the intuition that n-type and p-type charge doping will occur respectively in graphene

on

the

up-

and

down-polarized

ferroelectric

substrates,

experimental

observations18,19,20,21,22,,23,24 revealed that the carrier type and density as well as the transport properties in the graphene/ferroelectric hybrid structures exhibited more complicated behavior than we previously thought. According to previous reports,12,15,18,19 the observed resistance hysteresis in the graphene sheet was opposite to that of the ferroelectric polarization direction and hence named as ″anti-hysteresis″. This unusual anti-hysteresis behavior was explained by extrinsic dynamic response of interfacial screening charges arising from the surrounding H2O molecules and H+/OH- ions.18,19 For these extrinsic surface/interface adsorbates, due to the slow charge trapping process and the subsequent equilibration with the ambient conditions, the observed characteristics in ferroelectric-gated graphene strongly depended on the ramping speed of gate voltage18,19 and showed a slow conductance relaxation after the ferroelectric polarization switching,22 which severely limit the applicability of the graphene/ferroelectric hybrid systems. For clean graphene/ferroelectric interfaces with minimum adsorbates and

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contaminants,

experimental

observations16,23,24

have

demonstrated

the

intrinsic

proper-hysteresis of resistance change in the graphene channel, while the induced carrier concentration is much lower than the value estimated by entirely compensating of the bulk ferroelectric polarization. However, the intrinsic anti-hysteresis behaviors showing much faster time-response than the adsorbate-associated process were still observed in the clean graphene/ferroelectric interfaces.21,24 For the graphene filed-effect transistors with ferroelectric La-doped PZT as the gate,21 after removing the adsorbed polar molecules by vacuum annealing process, the intrinsic resistance change pattern in the graphene channel was unambiguously characterized by the anti-hysteresis behavior. As reported in Ref. [24], for the adsorbate-removed graphene/ferroelectric hybrid structure, the resistance change in the graphene channel could be switched from ferroelectric hysteresis to anti-hysteresis, depending on the surface characteristics of the ferroelectric superlattice PbTiO3/SrTiO3 substrate. Although the different surface characteristics had negligible effect on the capacitance-voltage curves of the ferroelectric substrate, they did play a key role in determining the gating behavior in the graphene channels.24 Atomic-scale understanding of the intrinsic coupling between graphene and the ferroelectric oxide surfaces is essential to the fundamental interest and their practical applications. As we know, for the polar surfaces of ferroelectric oxides, the surface atomic and electronic structures as well as the stoichiometry are very distinct from the bulk phase and show significant dependence on the direction of ferroelectric polarization. 25 , 26 , 27 The atomic-scale characteristics of the stable ferroelectric oxide surfaces are directly associated with the particular thermodynamic conditions. In order to determine the coupling mechanism between graphene and the ferroelectric surfaces, we should adopt the thermodynamic stable surface terminations in theoretical investigations. Unfortunately, to the best of our knowledge, except for Ref. [16], the existing first-principles density functional theory (DFT) calculations 28 , 29 , 30 , 31 have ignored this issue. For instance, previous theoretical and experimental results 32 , 33 , 34 have demonstrated that the thermodynamically preferred terminations of ferroelectric LiNbO3(0001) polar surfaces are nonstoichiometry and display

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remarkable dependence on the polarization direction. However, in Ref. [28], the thermodynamic unstable Nb-terminated surface was adopted to explore the interface coupling between graphene and the LiNbO3(0001) surface. Another example is PbTiO3 (001) surface, in Ref. [31], the stoichiometric TiO2-terminated surface was used to investigate the charge doping mechanism in a zigzag graphene nanoribbon. If limited to the stoichiometric termination, the TiO2-terminated PbTiO3(001) surface is slightly more stable than the PbO-terminated surface.35 However, thermodynamically, the preferred PbTiO3(001) clean surface should be terminated by nonstoichiometric PbO atomic layer containing different Pb/O ratios with variation of the polarization direction and environmental conditions.36 Multiferroics have captured remarkable attention over the last decade because of the coexistence of ferroelectricity and magnetism and the inherent coupling between these two orders37,38 BiFeO3 (BFO) is the prototypical multiferroic with large ferroelectric polarization (~90 µC/cm2) and G-type antiferromagnetic order well above room-temperature.39,40 The bulk BFO belongs to the rhombohedral space group of R3c with ferroelectric polarization along the [0001] direction.41 The G-type antiferromagnetic order indicates that the Fe spins are ferromagnetically aligned in the (0001) planes and coupled antiferromagnetically between neighboring (0001) planes. Integrating graphene with the BFO(0001) polar interfaces is an intriguing issue and deserved to be investigated in detail. In our previous reports, 42,43 first-principles DFT calculations have been performed to study the surface characteristics of the BFO(0001) polar surfaces and the thermodynamic stable surfaces for both the negative (Z−) and positive (Z+) polarization direction have been determined. In present work, for the thermodynamically preferred BFO(0001) surfaces, we carry out a comprehensive theoretical survey on interface chemistry and charge doping effect for the graphene/BFO hybrid system (details of the first-principles calculations are provided in the Supporting Information). We find that the charge doping type in graphene is not directly related to the polarization direction of the ferroelectric substrate. It is the electronegativity difference between graphene and the surface terminations of the BFO substrate which determines the charge doping type and carrier density in the graphene sheet. Our results indicate that both proper-hysteresis and

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anti-hysteresis could be the intrinsic resistance change in the graphene/ferroelectric interface, depending on the particular chemical conditions and surface terminations. In addition, highly spin-polarized (~ -31%) Dirac fermions can be injected into graphene from the BFO(0001) negative surface with -Bi-O3-Fe termination.

2.

Methodology First-principles DFT calculations with plane-wave basis set are performed using the

generalized gradient approximation (GGA), as implemented in the VASP package.44 The projector augmented wave (PAW) potentials45,46 and the exchange-correlation functional with Perdew-Burke-Ernzerhof parameterization for solids (PBEsol)47 are used to perform the collinear spin-polarized calculations, and the effect of van der Waals interactions48 is also taken into account. The C 2s22p2, Bi 5d106s26p3, Fe 3s23p63d64s2, and O 2s22p4, are treated as valence electrons, respectively. All the calculations employ 400 eV as the cut-off energy and the accuracy of 10-5 eV is used for total energy calculations. For structural optimizations and self-consistent calculations, a Γ-centered 3×3×1 k-point mesh is used. The k-points mesh is increased to 5×5×1 for density of states (DOS) calculations and the Bader’s topological charge analysis49. According to previous reports,42,43,50 we use the DFT+U method51 with Ueff of 2.5 eV to treat the on-site Coulomb correlation of Fe 3d electrons. The spin-orbital coupling (SOC) is not taken into account due to the negligible influence on interface coupling and charge doping effect. The lattice parameter of graphene is 2.464 Å and that of the BFO (0001) polar surface is 5.578 Å. To model the graphene/BFO(0001) hybrid structure, we assume 4×4 supercell of graphene on √3×√3 BFO (0001) surface unit cell with a vacuum layer ≥13 Å due to the small lattice mismatch of ~2%. We use slabs containing five -Fe-O3-Bi- trilayers (15 atomic layers) plus the surface termination to simulate the clean BFO (0001) surfaces, which were determined as described in Ref. [42,43]. The positive (negative) BFO (0001) surface with the ferroelectric polarization pointing toward (away) the termination layer is denoted as Z+ (Z−). To determine interface configurations of the graphene/BFO hybrid system, we fix the in-plane lattice parameters and the atomic positions of the backside three trilayers of the BFO slab,

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while allow the outer two -Fe-O3-Bi trilayers plus the surface termination, as well as all the C atoms to relax in all directions until the residual force appearing on each atom is less than 0.02 eV/Å. In addition, the dipole correction 52 is included to eliminate the spurious interaction introduced by the periodic slab images.

3.

Results and discussion

3.1 BFO(0001) surface and graphene/BFO interface The thermodynamic stability and surface phase diagram of BFO(0001) surfaces have been determined in our previous report.43 We have used -Fe-Ox-Biy as the Z+ surface termination and -Fe-Biv-Ou as the Z− surface termination (x, u = 0, 1, 2, 3 and y, v = 0, 1, 2).43 In present work, we use Pyx and Nvu to denote the positive (Z+) and negative (Z−) terminations with different surface stoichiometries. According to this naming rule, the positive surfaces terminated with -Fe-O3-Bi and -Fe-O3 atomic layer are labeled as P13 and P03, respectively. On the other hand, the negative surfaces terminated with -Fe-Bi-O3, -Fe-Bi-O2, and -Fe layer are labeled as N13, N12, and N00, respectively. For N00 surface, in order to emphasize its stoichiometric character, the underlying Bi and O3 layers are included and therefore the surface termination is labeled as -Bi-O3-Fe. For the N12 and N13 surfaces, we used -Bi-Ox (x = 2 or 3) instead of -Fe-Bi-Ox. The direction of ferroelectric polarization has important effect on surface stabilization and the oppositely polarized BFO(0001) surfaces exhibit different stoichiometries under the same chemical conditions. Within the thermodynamically allowed region where the BFO bulk phase is stable, there are three types of stable terminations for the Z− surface. In contrast to the -Bi-O2 termination (denoted as N12) which is preferred under most chemical conditions, the -Bi-O3-Fe termination (denoted as N00) is limited in a small region of O-poor and simultaneously Bi-rich chemical environments, while the Z− surface terminated by -Bi-O3 (denoted as N13) atomic layer is favored under the O-rich and Bi-poor conditions. As regard to the BFO Z+ surface, the thermodynamically preferred surface under most chemical conditions is terminated by the -Fe-O3-Bi trilayer (denoted as P13), while the -Fe-O3 surface termination (denoted as P03) begins to appear in both the O-rich and Bi-poor environments. Due to the fact that the preferred Z− and Z+ surfaces under most conditions are

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respectively terminated with the -Bi-O2 and -Fe-O3-Bi atomic layers, therefore the BFO Z− surface should contain less oxygen than the Z+ surface, which had been confirmed by the experimental observations at the BFO/LaxSr1-xMnO3 53 and BFO/CoFeB 54 interfaces. According to Ref. [43], besides the stoichiometry and atomic configurations, the surface electronic and magnetic properties between the BFO Z− and Z+ surfaces also display remarkable differences. In the absence of foreign adsorbates, all of the above mentioned surface terminations are thermodynamic permissible and can be obtained at different growth conditions. In comparison with the band-gap of bulk BFO (~1.7 eV for Ueff = 2.5 eV), the clean BFO(0001) surfaces show different electronic properties.42,43 All the stable BFO(0001) Z− surfaces display insulating behavior with a band-gap of ~0.7 eV. For the BFO(0001) Z+ surfaces, the band-gap of the P13 (-Fe-O3-Bi) surface is ~1.3 eV, while the P03 (-Fe-O3) surface is characterized by half metal-like character. For the clean BFO Z+ and Z− surfaces with different surface terminations, the planar-averaged electrostatic potentials are plotted in Fig. 1 (the planar-averaged electrostatic potentials of the graphene/BFO(0001) hybrid systems are shown in the Supporting Information). The backside of the BFO(0001) slab is assumed to be grounded and has zero electrostatic potential. From the electrostatic potential profile within the BFO slab, it is clear that there exists a depolarizing field pointing opposite to the ferroelectric polarization direction. 55 , 56 However, the electrostatic potential at the BFO(0001) surface exhibits significant dependence on the surface termination. For the bared BFO Z+ surfaces (Fig. 1a), we find that the electrostatic potential of the BFO Z+ surface terminated with -Fe-O3 layer (P03) is much higher by 4.27 V than that of the P13 surface terminated by -Fe-O3-Bi trilayer. As regard to the clean BFO Z− surfaces (Fig. 1b), the electrostatic potential of BFO N00 surface (terminated by -Bi-O3-Fe layer) shows a lower value by 2.14 V and 2.37 V than the N12 and N13 surface, respectively. It is well known that electrostatic modulation of electronic structure and transport properties plays a crucial role in modern electronic and optoelectronic devices.57 Due to the remarkable dependence of surface electrostatic potential on the surface termination, we expect that the intrinsic charge doping effect and hence the transport

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properties in the graphene/BFO(0001) hybrid system will display distinct behavior depending on the particular chemical environments. Based on the above mentioned surface terminations, several typical interfacial configurations of the graphene/BFO(0001) systems 58 are explored to determine the energetically favored interfaces (details in the Supporting Information Fig. S1 and S2). We then employ the energetically preferred interface configurations to carry out further calculations. For graphene on the -Fe-O3-Bi Z+ (G@BFO P13) and -Bi-O3-Fe Z− (G@BFO N00) hybrid structures, the side- and top-view of the interfacial configurations are shown in Fig. 2. From Fig. 2a and 2c, it can be seen that the favorable G@BFO P13 interface is characterized by the configuration that two third of the outmost Bi cations stay just below the carbon atoms and the remaining Bi cations are located under the hollow-sites of the graphene sheet. As regard to the G@BFO N00 interface (Fig. 2b and 2d), the preferred adsorption configuration of graphene is very distinct from that on the BFO Z+ surface since all the outmost Fe cations stay near the bridge site positioned at the center of C-C bond. For other BFO(0001) surfaces with -M-Ox (M = Bi or Fe, x = 2 or 3) as the outmost atomic layer, however, we cannot find such high-symmetric adsorption sites due to the complex interfacial configurations. The calculated distances, dG-BFO, between graphene and various BFO(0001) surfaces are collected in Table 1. In spite of a large distance of about 3.4 Å between graphene and the BFO P13 surface, the distances between graphene and other BFO(0001) surfaces are in the range of 2.6 Å ~ 2.8 Å. From the calculated binding energy, Wb, we can see that the interaction strength between graphene and the BFO P13 surface (Wb = 0.31 J·m-2) is very weak. However, the binding energies show much higher values of 1.30 J·m-2 and 1.11 J·m-2 for graphene adsorbed on N12 and N13 of the BFO Z− surfaces, while the interaction strengths of the G@P03 and G@N00 systems (0.65 J·m-2 and 0.57 J·m-2, respectively) are moderate. Due to adsorption, the arrangement of the carbon atoms in the graphene sheet is deviated from an ideal two-dimensional honeycomb lattice and shows some rumpling along the z-direction. From Table 1, it can be seen that the rumpling, δG, is about 0.1 Å for G@P13, G@P03, and

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G@N13 systems, while δG reach large values in the G@N00 and G@N12 systems. For instance, the rumpling of carbon atoms is as large as 0.3 Å in graphene on the BFO N00 surface. On the other hand, the graphene sheet also has influence on the surface geometries of the BFO(0001) substrates. The atomic displacements of various BFO(0001) surfaces are summarized in Table S1 and S2 of the Supporting Information. It is clear that the surface relaxation is closely related to the binding energy between graphene and the BFO(0001) substrate. Generally speaking, the stronger interaction strength between graphene and the BFO substrate, the more pronounced atomic displacements occur at the BFO(0001) surface. As an example, the largest binding energy (1.30 J·m-2) occurs in the G@N12 system, the displacements of the outmost O atoms at the BFO N12 surface (denoted as OI′) are 0.49 Å and -0.22 Å in the xy-plane and along the z-direction, respectively. 3.2 Charge doping in graphene/BFO Z+ system To explore the charge doping effect in graphene on the BFO Z+ surfaces, we plot the top-view of differential charge density in Fig. 3a and 3b (the side-view of differential charge density is shown in Fig. S3). For the G@P13 interface (Fig. 3a and Fig. S3a), we find that electrons are transferred to the adjacent graphene sheet from the outmost Bi cations of the BFO substrate, which is consistent with our expectation that graphene is n-type doped by adsorbing on the up-polarized ferroelectric substrate. As regard to graphene on the BFO P03 surface (Fig. 3b and Fig. S3b), it is clear that a more significant charge transfer effect occurs between graphene and the BFO Z+ substrate. More importantly, the charge transfer effect is characterized by holes accumulation in the graphene sheet accompanied by electrons transferring to the BFO P03 surface. This charge transfer behavior is just opposite to our intuition that the up-polarized ferroelectric substrates will provide n-type charge doping in graphene. From Fig. S3b, we can identify that the depleted electrons in graphene come from the π-bonds of C-2pz orbitals and that the gained electrons of the BFO substrate are mainly accumulated in the outmost O3 atomic layer. The distinct charge transfer effects occurred at these two G@BFO Z+ interfaces cannot be understood from compensation of the bulk ferroelectric polarization. In fact, the seemingly

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quite complicated charge transfer behavior can be explained by the relative magnitude of electronegativity between graphene and the outmost atomic layer of the BFO substrate. In Ref. [59], the Pauling’s electronegativity was successfully used to identify the degree of iconicity for various metal overlayers on Al2O3 substrate. As we know, the values of the Pauling’s electronegativity for Bi, O, and C are 2.02, 3.44, and 2.55, respectively. For the BFO P13 surface with the -Fe-O3-Bi surface termination, as illustrated in Fig. 2a, the outmost atomic layer is composed of Bi cations, the lower electronegativity of Bi compared with C is the driving force for electron transferring to the graphene sheet. For the BFO P03 surface which has the -Fe-O3 termination, O3 is the outmost atomic layer. In this case, due to the much higher electronegativity of O than that of C, the charge transfer between graphene and the BFO P03 surface was manifested in electrons transferring from graphene sheet to the underlying O3 atomic layer of the BFO substrate, which will lead to p-type charge doping in the graphene overlayer. Furthermore, from the much larger electronegativity difference between O and C than that between Bi and C, we can also predict the more prominent charge transfer effect at the BFO/P03 interface. In addition, this electronegativity-dominated charge transfer effect at the graphene/BFO interface is also demonstrated in graphene adsorbed on the down-polarized BFO Z− substrates, which will be presented in the next section. From the viewpoint of electrostatic potential, the underlying mechanism of charge doping in graphene is determined by the difference of electrostatic potential between graphene and the BFO substrates. As shown in Fig. 1, the electrostatic potential of bared BFO(0001) surfaces displays strong dependence on the surface termination. According to the interaction strength between graphene and the BFO substrates (Table I), we can identify that the dominant adsorption mechanism of graphene on the BFO(0001) substrates is the weak van der Waals (vdW) bonding. Since the electrostatic potential of pristine graphene is fixed, the BFO(0001) substrates showing different surface terminations should have different electrostatic charge doping effects on the graphene overlayer. Taking the bared BFO(0001) Z+ surfaces as examples. The -Fe-O3 terminated P03 surface shows a much higher electrostatic potential by 4.27 V than the -Fe-O3-Bi terminated P13 surface. The higher electrostatic

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potential of the P03 surface indicates the larger electron affinity than the P13 surface. For the graphene/BFO(0001) hybrid systems, we show the planar averaged electrostatic potential in Fig. S8. We find that the difference of electrostatic potential between G@P03 and G@P13 is reduced to 0.24 V. This indicates that the adsorption of graphene took on the extra 4.03 V to compensate the electrostatic potential difference between the bared P03 and P13 surfaces. Due to the vdW bonding nature, such compensation is dominated by accumulating and depleting electronic charges at the P03 and P13 surface, respectively. In other words, the charge doping in the graphene overlayer on the P03 and P13 substrates will respectively show p-type and n-type character. This mechanism is also suitable for the bared BFO Z− surfaces and the G@BFO Z− systems. Obviously, this electrostatic modulating mechanism is consistent with the analysis from the Pauling electronegativities. The electron localization functions (ELFs) are plotted in Fig. S3 to inspect the effect of graphene adsorption on chemical bonding behavior because of the included Pauli repulsion interaction.60,61 From Fig. S3c and S3bd, the large π-bonds composed of C-2pz electrons can be easily identified. The absence of bond attractor at the graphene/BFO interface implies the unshared-electron feature of the coupling between graphene and the BFO(0001) surface. We find that the π-bonds of graphene on the BFO P13 surface are mainly interacted with the 6s lone pair electrons of the outmost Bi cations, while it is the outmost O-2p orbitals which contribute to the coupling with the π-bonds in graphene for the G@P03 system. The qualitative information about charge doping in graphene can also be provided by the projected DOS as shown in Fig. 3c and 3d. For graphene on the BFO P13 surface (Fig. 3c), profile of the projected DOS is almost the same as pristine graphene but an overall downward shift in energy is obvious. On the other hand, the surface DOS of the BFO P13 surface (Fig. 3e) remains unchanged. In case of the G@P03 system, the DOS of graphene (Fig. 3d and Fig. S4) suffered from significant upward shift in energy as well as tiny deformation of the overall shape. The surface DOS of the BFO P03 substrate (Fig. 3f) is characterized by some weight transfer from above the Fermi energy to below it. Detailed information about the site- and orbital-resolved DOS of the BFO Z+ surfaces can be found in Fig. S5 of the Supporting

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Information. As we know, for pristine graphene, the Dirac point is located just at the Fermi energy. According to Fig. 3c and 3d, from the downward and upward energy shift of projected DOS with respect to the pristine graphene, we can identify that the n-type and p-type charge doping have been occurred for graphene adsorbed on the BFO P13 and P03 surface, respectively. However, more quantitative information about the charge doping effect cannot be obtained from the above DOS analysis due to the insufficient k-points mesh (5×5×1), although such a k-points mesh is enough to determine the DOS of the BFO substrate.42,43 According to Ref. [16], an extremely dense k-point mesh (30×60×1 for graphene on 2×1 LiNbO3(0001) surface unitcell) is necessary to obtain reliable quantitative information of charge doping in graphene because the Dirac cone must be sampled in the Brillouin zone. For large systems such as our graphene/BFO hybrid structures, such dense k-point mesh requires huge computation cost. The quantitative charge doping effect in graphene can be obtained by evaluating the band structure29,30 since dense k-points along specific direction can be selected to include the Dirac cone. However, another complicating issue comes from the supercell approach which is necessary for our graphene/BFO hybrid system. In spite of the equivalence between the primitive cell and the supercell representations for the graphene sheet, the supercell approach results in an inconvenience due to the folding of the calculated bands into a smaller supercell Brillouin zone, for which the complicated band structure is difficult to relate to that of the primitive cell representation. By using the band unfolding technique,62,63 the primitive cell representation can be recovered by an effective band structure (EBS), which is exact for perfect supercell and can still give meaningful physical picture even for non-perfect cases. Another advantage of the effective primitive-cell representation of the band structure comes from the capability which enables direct comparisons with the experimental measurements. As we know, angle-resolved photoemission spectroscopy (ARPES), a direct experimental technique to observe the distribution of the electrons, is often performed along high-symmetry directions in the primitive-cell Brillouin zone. For the G@BFO Z+ systems, the calculated EBS of the up-spin channel is shown in Fig. 4

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(the down-spin EBS can be found in the Supporting Information Fig. S7). We can unambiguously identify the band structure of graphene including the Dirac cone. For the G@P13 system (Fig. 4a), the difference in EBS between the adsorbed graphene and the pristine one is difficult to distinguish in such a large energy range. As regard to the G@P03 system (Fig. 4c), it is clear that the EBS of graphene on the BFO P03 surface shows considerable upward shift with respect to the pristine graphene. In order to quantitatively evaluate the charge doping effect, the EBS near the K-point is recalculated by using dense k-points string (170 points per Å-1) and small energy grid with intervals of 0.01 eV. We show in Fig. 4b and 4d the zoom-in of the Dirac cone for the up-spin channel (for the down-spin channel, the zoom-in near the K-point is plotted in Fig. S7). According to Fig. 4b, the n-type charge doping in graphene on the BFO P13 surface can be identified from the downward shift of the Dirac point by 0.12 eV. As shown in Fig. 4d, the p-type charge doping in graphene on the BFO P03 surface is characterized by the large upward shift (1.10 eV) of the Dirac point. In addition, we should point out that, for these two thermodynamic stable BFO Z+ surfaces, there is no sign of spin-dependent charge doping in the graphene sheet. As demonstrated in our previous work,58 the carrier density can be estimated by performing the Bader’s charge analysis since it is a useful technique to decompose the charge density into individual atoms. The accuracy of our calculated Bader’s charge is higher than 10-3 e. The Bader’s charge analysis shows that the graphene sheet on the BFO P13 surface obtained 0.090 electrons per supercell surface area, while the graphene overlayer lost 0.868 electrons per supercell surface area when adsorbed on the BFO P03 surface. The above results correspond to the n-type carrier density of ne = 1.13×1013/cm2 and p-type carrier density of nh = 1.08×1014/cm2 in graphene on the BFO P13 and P03 surface, respectively (collected in Table 1). The calculated carrier density in the G@P13 system is one order of magnitude lower than the G@P03 system. It should be noted that the ratio of nh/ne (about 0.10) is in well consistent with that of the corresponding shift of the Dirac point (0.12/1.10 = 0.11). This consistency indicates that the Bader’s charge analysis provides the itinerant charges near the Fermi level as carriers.

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3.3 Charge doping in graphene/BFO Z− − system Next, we focus on the interfacial electronic properties in the graphene/BFO Z− hybrid structures. From the differential charge density shown in Fig. 5a-5c and Fig. S5a-S5c, the charge transfer effect between graphene and the BFO Z− substrate exhibits regular evolution as the surface termination changes from N00 (-Bi-O3-Fe) through N12 (-Bi-O2) to N13 (-Bi-O3). For the BFO N00 surface (Fig. 5a), the outmost atomic layer is Fe, and it is the lower electronegativity of Fe (1.83) with respect to C (2.55) that drives the electronic charges transferring from the BFO substrate to the graphene sheet. On the other hand, the underlying O3 layer is responsible for holes accumulation in the graphene overlayer. As demonstrated latter, the overall charge transfer in the G@N00 system results in n-type doping in the graphene, which is inconsistent with the intuition of p-type doping for graphene adsorbed on the down-polarized ferroelectric substrates. For both the BFO N12 and N13 surfaces, the outmost layer is oxygen atoms and the charge transfer between graphene and the BFO substrates is dominated by holes accumulation in the graphene due to the much higher electronegativity of O (3.44). For the BFO N12 surface with -Bi-O2 termination, we have determined that one half O relaxed down into the underlying Bi plane, while the other half O was located above the Bi plane to form the outmost layer.43 As demonstrated in Fig. 5b, besides the holes accumulation in the graphene caused by the outmost oxygen layer, there also exist some electrons transferring from interfacial Bi cations to the graphene layer. In case of the BFO N13 surface (Fig. 5c), for which -Bi-O3 is the termination and the outmost layer is composed of O3 atoms, the charge transfer effect is entirely characterized by significant holes accumulation in the graphene sheet. From the charge density differences, we can conclude that the graphene adsorbed on the BFO N12 and N13 surfaces should display p-type doping behavior, which is in agreement with the expectation for graphene on the down-polarized ferroelectric substrate. In addition, the ELFs of the G@BFO Z− hybrid systems and the clean BFO Z− surfaces are shown in Fig. S4. We also show the projected DOS of the graphene (Fig. 5d-5f) and the BFO Z− surfaces

14


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(Fig. 5g-5i). For graphene on the BFO N00 substrate (Fig. 5d), accompanied with an overall energy downward, the projected DOS shows a remarkable distortion with respect to the pristine graphene, especially for the states near and above the Fermi level. More importantly, the up- and down-spin channels of graphene have been splitted by interacting with the -Bi-O3-Fe surface termination. As demonstrated latter, this spin-splitting indicates the spin-polarized charge doping in the graphene sheet. According Ref. [64,65], spin-polarized carries can be injected into graphene by contacting with ferromagnetic metals such as Co and Ni. In our case, the spin-polarized carries can be induced by depositing graphene on the insulating BFO N00 substrate, which is of crucial importance for spin-dependent transport of the massless Dirac fermions. The insulating behavior of the BFO N00 surface is demonstrated in Fig. 5g. In comparison to the clean BFO N00 surface, the graphene overlayer causes remarkable modification in the down-spin conduction states. Further information concerning the interaction between graphene and the BFO N00 surface can be found in Fig. S6 of the Supporting Information. As shown in Fig. 5e and 5f, the spin-polarized behavior has disappeared for graphene on the BFO N12 and N13 surfaces and the upward energy shift of the overall DOS can be identified in both cases. For the G@N12 system, we find that the weight of C-2pz states (Fig. 5e) shows some variation with respect to the pristine graphene in the energy range from -1.5 eV to -0.8 eV, and that the change of projected DOS for the BFO N12 surface (Fig. 5h) occurs in the same energy range. As regard to the G@N13 system (Fig. 5f and 5i), the upward energy shift of the overall DOS of graphene is enhanced and the weight change becomes more considerable with respect to the pristine graphene. From the DOS of the G@N12 and G@N13 systems, we suggest that there are some orbital hybridization between the graphene C-2pz orbitals and the surface electronic states of the BFO Z− substrates. Therefore, in addition to the electrostatic and van der Waals interactions, the orbital hybridization also contributes to the large binding energy (1.30 J/m2 and 1.11 J/m2 for the G@N12 and G@N13 system, respectively) between graphene and the BFO Z− substrates. Detailed information about hybridization between C-2pz orbitals and the BFO Z − surface states is offered in Fig. S9.

15



In Fig. 6, we show the shift of Dirac cone in the graphene sheet for the G@BFO Z− systems. The information of the overall EBS is provided in the Supporting Information Fig. S10. For graphene on the BFO N00 surface (Fig. 6a and Fig 6d), the n-type charge doping in graphene is identified by the downward shift of the Dirac point with respect to the Fermi level. The spin-polarized Dirac fermions are demonstrated by the different downward shift for the two spin channels. As collected in Table 1, the downward shifts for the up- and down-spin channels are 0.11 eV and 0.21 eV, respectively. As we know, the Fe spins in the BFO(0001) planes show ferromagnetic order. In our case, the up-spin states are the major-spin channel. Assuming that only the carriers near the Fermi level are taken into account, the estimated spin polarization p = (n↑−n↓)/(n↑+n↓) is -31%, which is higher than the predicted value of 24% for graphene grown on the low-ferromagnetic insulator EuO.66 According to the total carrier density calculated from the Bader’s charge analysis (ne = 8.7×1012/cm2 shown in Table 1), we estimate the carrier densities of the up- and down-spin Dirac fermions are 5.7×1012/cm2 and 3.0×1012/cm2, respectively. Furthermore, we note that the lower half of the spin-split Dirac cones suffers from considerable influences of the BFO N00 substrate, while the upper half of the Dirac cones remains intact, which is important for the spin-dependent transport properties.64,65 According to Fig. 6 and Table 1, for the G@N12 and G@N13 systems, the p-type charge doping behavior in the graphene sheet is quantitatively characterized by the upward shift of 0.25 eV and 0.34 eV of the Dirac point, respectively. There is no sign of spin-dependent doping behavior in both systems. For G@N12 system, the estimated carrier density is 2.59×1013/cm2, and it is 4.71×1013/cm2 for the G@N13 system. For these two hybrid systems, the upper half of the Dirac cones is exposed to some influence of the BFO Z− substrates, while the effects of the BFO substrates on the lower half of the Dirac cones are negligible.

4.

Discussion According to the surface phase diagram,43

under most chemical conditions, the

thermodynamically preferred terminations of the BFO(0001) Z+ and Z− surfaces are -Fe-O3-Bi (P13) and -Bi-O2 (N12), respectively. Our previous report58 focused on the charge

16


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doping effect in graphene on these two oppositely polarized BFO(0001) surfaces. The carrier type in graphene on these two surfaces is consistent with the intuitive sense, i.e., n-type doping on the BFO Z+ surface and p-type doping on thee BFO Z− surface. One implication of this result is that engineering domain structure of the BFO substrate can be used to fabricate the graphene-based p-n junctions. The state-of-the-art film growth technique40,67 provides us a feasible approach to integrate multiple p-n junctions into one graphene sheet. For instance, periodic arrays of graphene p-i (intrinsic) junctions (gate-tunable to p-n junctions) have been experimentally demonstrated in air by depositing graphene on the periodically polarized LiNbO3 substrate.16 Another implication is that the carrier density in graphene on the ferroelectric substrate cannot be estimated by entirely compensating of the bulk ferroelectric polarization. From the spontaneous polarization (90 µC/cm2) of the R3c BFO bulk phase,42 we estimated that the carrier density in graphene should be 5.62×1014/cm2 by fully compensating of the bulk polarization. However, as shown in Table 1, except for the G@P03 system (BFO Z+ surface with -Fe-O3 termination), the calculated carrier densities are reduced by one or two orders of magnitude. In fact, the carrier densities of 1012~1013 cm-2 are typical values in experimental observations for graphene on ferroelectric substrates.12,14,16,23 Besides the carrier density, even the carrier type cannot be definitely predicted by the direction of ferroelectric polarization. Based on the results obtained from the thermodynamic permissible BFO(0001) surfaces, we find that the doping type in graphene is directly determined by the relative magnitudes of electronegativity between graphene and the surface atomic layer of the ferroelectric substrate. In contrary to our intuitive sense, the charge doping type is not directly related to the direction of ferroelectric polarization. For example, graphene on the BFO Z+ substrate with -Fe-O3 surface termination (P03), which is thermodynamic stable under the O-rich and Bi-poor conditions, shows p-type charge doping. On the other hand, the BFO Z− surface with -Bi-O3-Fe termination (N00), which is favorable only in the O-poor and Bi-rich chemical environments, induces n-type doping in the graphene sheet. Generally speaking, the outmost metal atomic layer (-Fe-O3-Bi and -Bi-O3-Fe) facilitates n-type doping due to its lower electronegativity with respect to graphene, while the

17



oxygen-rich surfaces (-Fe-O3, -Bi-O2, and -Bi-O3) are beneficial to p-type doping in graphene because of the much higher electronegativity of oxygen. Our results are consistent with previous experimental observations that graphene usually shows p-type characteristics in air at ambient temperature and n-type graphene can be obtained under vacuum conditions.6 In addition, the recent theoretical investigation of graphene on a polar SrTiO3(111) surface with SrO3 termination also predicted p-type doping in the graphene channel.68 Since the charge doping type in graphene/ferroelectric hybrid system is not directly determined by the polarization direction, both the proper-hysteresis and anti-hysteresis can be occurred for intrinsic resistance change in graphene channel with the ferroelectric polarization reversal. Assuming the doping type in graphene is consistent with the direction of ferroelectric polarization, we then regard the proper-hysteresis behavior of the resistance change as a matter of course. Taking the BFO Z+ surface with -Fe-O3-Bi termination (P13) as an example: The polarization direction of R3c bulk BFO is determined by the displacement of Bi relative to the O octahedral along the [0001] direction, the ferroelectric polarization reversal will change the -Fe-O3-Bi sequence into -Fe-Bi-O3, which is just the BFO Z− surface with -Bi-O3 termination (N13), therefore the proper-hysteresis from n-type to p-type doping is expected in the graphene channel. We also expect the same hysteresis behavior will occur in graphene on the BFO Z− surface with -Bi-O2 termination (N12) despite of its nonstoichiometry. On the other hand, for the charge anti-doping behavior occurred in the graphene sheet on the BFO(0001) substrates such as the Z+ P03 (-Fe-O3) and the Z− N00 (-Bi-O3-Fe) surfaces, the surface relaxations accompanied with the ferroelectric polarization reversal may lead to the anti-hysteresis behavior in the graphene sheet. As mentioned above, both the proper-hysteresis and the anti-hysteresis behavior have been experimentally observed in graphene on the clean surfaces of the ferroelectric oxides such as La-doped Pb(Zr,Ti)O3 and PbTiO3/SrTiO3.21,24 In addition, the asymmetric charge doping in graphene on the oppositely polarized ferroelectric substrates will lead to the asymmetric resistance change in the graphene-based FeFETs, which is important for practical memory applications. Although our calculations are based on spontaneous polarization of the R3c BFO bulk at 0

18


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K, an important issue deserves to be mentioned is the temperature-dependent hysteresis behavior in the graphene/ferroelectric hybrid systems. In experiments, as we know, graphene was deposited on the clean ferroelectric oxide surfaces at or well above the room temperature. For the graphene/ferroelectric system with proper charge doping, the polarization of the ferroelectric substrate increases as the temperature drops to lower value and the carrier density in graphene will become larger in order to compensate the additional ferroelectric polarization. Therefore, the resultant proper-hysteresis behavior in the graphene channel becomes more and more

remarkable

as

the

temperature

is

progressively

reduced.

This

kind

of

temperature-dependent proper-hysteresis behavior in the graphene channel has been experimentally demonstrated in Ref. [24]. However, as regard to the graphene/ferroelectric system with anti-doping effect, the carrier density should be gradually counteracted by the enhanced bulk polarization as decreasing the temperature, even the doping type should be inversed when charge screening of the additional polarization exceeds the anti-doping effect. In this case, the resistance change in the graphene channel will display an intriguing crossover from anti-hysteresis to proper-hysteresis as the temperature decreased to the critical value. Experimentally, such crossover process has recently been observed in graphene field-effect devices based on (Ba,Sr)TiO3 thin films20 and PbTiO3/SrTiO3 superlattice substrates.24

5.

Conclusions To summarize, based on the surface phase diagram of the BFO(0001) substrate, we have

investigated the effect of surface termination on interface chemistry and charge doping effect in the graphene/BFO(0001) hybrid system by performing first-principles DFT calculations. We demonstrate that the charge doping type in graphene is directly determined by the relative magnitudes of electronegativity between graphene and the outmost atomic layers of the BFO(0001) surface rather than the polarization direction of the ferroelectric substrate. We find that, in most cases, the carrier density in graphene is lower by one or two orders of magnitude than the value estimated from entirely compensating of the bulk ferroelectric polarization. Furthermore, we predict that, on the insulating BFO Z− surface with -Bi-O3-Fe termination, the highly spin-polarized (~ -31%) Dirac fermions are injected into the graphene sheet due to

19



Page 20 of 28

the G-type antiferromagnetic order of the BFO substrate. For the graphene/BFO system, our results indicate that both proper-hysteresis and anti-hysteresis are possible for the intrinsic resistance change in graphene channel with the ferroelectric polarization reversal, depending on the surface terminations which are thermodynamically preferred under particular chemical conditions.

Besides

confirming

graphene/ferroelectric

systems,

the our

importance results

of

provide

interface practical

chemistry

in

the

implications

for

designing/enhancing the electronic and transport properties of the graphene-based ferroelectric field-effect devices.

Supporting Information. Further details on first-principles calculations, various interfacial configurations of the graphene/BFO systems, influence of graphene on atomic displacements at the BFO(0001) surface, electron localization functions and the planar averaged electrostatic potential of the graphene/BFO structures, the projected DOS of graphene and BFO(0001) surface, and effective band structures of down-spin electrons of G@BFO Z+ and overall EBS for G@BFO Z− systems.

Conflicts of interest There are no conflicts of interest to declare.

Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 51762030 and 51462019).

20


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Table 1. The distance dG-BFO, binding energy Wb between graphene and the BFO (0001) surfaces, the rumpling of carbon atoms δG within the graphene layer, and the carrier density n of graphene due to interaction with the BFO (0001) surfaces. The negative and positive sign of n indicates electrons and holes doping, respectively. The shift of Dirac point ∆EDP is also listed. The positive (negative) value of ∆EDP represents the upward (downward) shift of the Dirac point with respect to the Fermi level. Note that values of ∆EDP for up-spin and down-spin electrons are given out and in parentheses, respectively.

G@P13

dG-BFO (Å)

Wb (J·m-2)

3.38

0.31

δG (Å) n (1013/cm2)

∆EDP (eV)

0.09

−1.13

−0.12 (−0.12)

+10.84

+1.10 (+1.10)

G@P03

2.83

0.65

0.10

G@N00

2.57

0.57

0.31

−0.87

−0.11 (−0.21)

G@N12

2.75

1.30

0.18

+2.59

+0.25 (+0.25)

G@N13

2.77

1.11

0.11

+4.71

+0.34 (+0.34)

Fig. 1. The planar averaged electrostatic potential for the clean BFO(0001) surface. (a) BFO Z+ and (b) BFO Z− surface. Note that the backside of the BFO(0001) slab is grounded and shows zero potential.

21



Fig. 2. Side-view of atomic structure for graphene adsorbed on the √3×√3 BFO (0001) stoichiometric surface with (a) -Fe-O3-Bi Z+ termination and (b) -Bi-O3-Fe Z− termination. The black arrow indicates the direction of ferroelectric polarization. (c) and (d) show the top-view of graphene on the Z+ and Z− surface, respectively. For the top-views, only graphene and the outmost Fe-O3-Bi trilayer are shown for clarity.

Fig. 3. Differential charge density (a-b) and projected DOS (c-f) for the G@BFO Z+ systems. Top-view of the charge density difference for G@P13 and G@P03 system is shown in (a) and (b), respectively. The red (blue) color indicates the accumulation (depletion) of electronic charges. Maps for G@P13 and G@P03 systems are respectively plotted for isosurface of 0.5×10-3 and 1×10-3 e Å-3. (c) and (d) display the projected DOS on C-2pz orbitals for the G@P13 and G@P03 system, respectively. The DOS of the outmost Fe-O3-Bi trilayer for BFO P13 and P03 surfaces are shown respectively in (b) and (d). The cyan shadows denote the corresponding DOS of the pristine graphene or the clean BFO (0001) Z+ surfaces.

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Fig. 4. Effective band structure (EBS) of the up-spin electrons unfolded along high-symmetry directions of the graphene’s primitive-cell Brillouin zone for (a-b) G@P13 and (c-d) G@P03 system. The overall EBS is shown in (a) and (c), while zoom-in of the EBS near Dirac point is plotted in (b) and (d), in which K-point is at k = 0. The positive (negative) k value denotes the direction along K−M (K−Γ) direction and the unit of k is Å-1. The color scale represents the number of unfolded primitive-cell bands, while the purple curve denotes the band structure of pristine graphene.

Fig. 5. Differential charge density (a-c) and projected DOS (d-i) for the G@BFO Z− systems. Top-view of the charge density difference for G@N00, G@N12, and G@N13 system is shown in (a), (b), and (c), respectively. The red (blue) color indicates the accumulation (depletion) of electronic charges. Maps are

23



plotted for isosurface of 1×10-3 e Å-3. The projected DOS on C-2pz orbital for G@N00, G@N12, and G@N13 system are plotted in (d), (e), and (f), respectively. While (g), (h), and (i) show respectively the projected DOS of the outmost Fe-O3-Bi trilayer for BFO N00, N12, and N13 surfaces. The cyan shadows denote the corresponding DOS of the pristine graphene or the clean BFO (0001) Z− surfaces.

Fig. 6. Shift of Dirac cone for graphene on the BFO Z− substrate. The upper row (a-c) shows the up-spin band while the down-spin channel is plotted in the lower part (d-e). (a) and (d) for G@N00 system, (b) and (e) for G@N12 system, while (c) and (f) for G@N13 system. The K-point is at k = 0. The positive (negative) k value denotes the direction along K−M (K−Γ) direction and the unit of k is Å-1. The color scale represents the number of unfolded primitive-cell bands.

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