Toward an Understanding of the Electric Field-Induced Electrostatic

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Towards an understanding of the electric field-induced electrostatic doping in Van der Waals heterostructures: a first-principles study Anh Khoa Augustin Lu, Michel J.C. Houssa, Iuliana P. Radu, and Geoffrey Pourtois ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.6b14722 • Publication Date (Web): 13 Feb 2017 Downloaded from http://pubs.acs.org on February 14, 2017

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Towards an Understanding of the Electric Field-Induced Electrostatic Doping in van der Waals Heterostructures: a First-Principles Study Anh Khoa Augustin Lu* 1,2 , Michel Houssa 1 , Iuliana P. Radu 2 , Geoffrey Pourtois* 2,3 1

Semiconductor Physics Laboratory, Department of Physics and Astronomy, University of Leuven, Celestijnenlaan

200 D, B-3001 Leuven, Belgium 2

IMEC, 75 Kapeldreef, B-3001 Leuven, Belgium

3

Department of Chemistry, Plasmant Research Group, University of Antwerp, B-2610 Wilrijk-Antwerp, Belgium

Corresponding authors: [email protected], [email protected]

KEYWORDS First-principles calculations, two-dimensional materials, electrostatic doping, electron tunneling, van der Waals heterostructures.

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ABSTRACT Since the discovery of graphene, a broad range of two-dimensional (2D) materials has crystallized the attention of the scientific communities. Materials such as hexagonal boron nitride (hBN) and the transition metal dichalcogenides (TMDs) family, have shown promising semiconducting and insulating properties that are very appealing for the semiconductor industry. Recently, the possibility of taking advantage of the properties of 2D-based heterostructures has been investigated for low-power nanoelectronic applications. In this work, we aim at evaluating the relation between the nature of the materials used in such heterostructures and the amplitude of the layer-to-layer charge transfer induced by an external electric field, as is typically present in nanoelectronic gated devices. A broad range of combinations of TMDs, graphene and hBN has been investigated using density functional theory. Our results show that the electric field induced charge transfer strongly depends on the nature of the 2D materials used in the van der Waals heterostructures and to a lesser extent on the relative orientation of the materials in the structure. Our findings contribute to the building of the fundamental understanding required to engineer electrostatically the doping of 2D materials and to establish the factors that drive the charge transfer mechanisms in electron tunneling based devices. These are key ingredients for the development of 2D-based nanoelectronic devices.



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1 INTRODUCTION Over the years, two-dimensional (2D) materials have emerged as potential replacement for silicon-based transistors. Since the discovery of graphene in 20041, a plethora of new twodimensional materials have been isolated, going from silicene, hexagonal boron nitride (hBN) to transition metal dichalcogenides (TMDs). These intriguing materials have been shown to display promising properties for future nanoelectronic devices2,3,4,5, such as high carrier mobility6 and electronic properties ranging from a semimetal to semiconductor ones, as reported for graphene and MoS2, respectively. As the physical dimensions of the silicon-based transistors are being scaled down, leading to a tremendous increase in power dissipation and to the degradation of the device performances7,8, the research community has been focusing on the implementation of alternatives to silicon channels and new device concepts that would potentially solve these scaling issues. In recent years, III-V materials and 2D materials appeared to be potential building blocks to pave the way to a possible solution. Among the alternatives, TMDs such as MoS2 and WS2 have been extensively studied and successfully integrated in transistor structures9,10. Recent works on lowpower devices such as the tunnel field effect transistor (TFET) using III/V heterostructures showed that promising sub-60 mV/dec subthreshold swings could be reached at the expense of a low drive current11. While monolayer 2D materials have been intensively investigated12, the understanding of the mechanisms that drive the so-called van der Waals heterostructures13,14 is still in its infancy. Recent modeling works suggested that a proper selection of 2D materials can be used to tune the band alignment, enabling for instance the possibility to build a broken band gap one. The selfpassivated nature of these 2D material makes them very attractive to pave the way to the building 3 ACS Paragon Plus Environment

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of future low-power devices, using tunneling as a switching mechanism15. Further, the twodimensional nature of those materials also allows reaching an improved electrostatic control with respect to classical 3D semiconductors and could enable their usage as plane capacitors and thereby indirectly allows controlling the doping concentration through the application of an external electric field. The absence of a third dimension in these materials hinders the use of classical chemical doping by atomic substitution as is for instance used in Si. Indeed, substituting atoms would strongly alter their structural and electronic properties. As an alternative, various studies have been focusing on the possibility to exploit molecular doping, where charges are transferred to the 2D layers from polar molecules such as F4TCNQ or Oleylamine16. As far as van der Waals heterostructures are concerned, the relation between the nature of the different 2D materials used in these heterostructures, as well as the relative orientation of these layers with respect to each other, is still unclear, especially in terms of the quantification of the interaction between the layers and their surroundings. In multilayer materials, the orbital overlap can potentially induce an electron delocalization so that their properties differ from that of the monolayer ones. In this work, we investigate this electron transfer process for van der Waals heterostructures placed under an external electric field, using density functional theory17,18 (DFT) with corrections for the dispersion forces.



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2 METHODOLOGY Van der Waals heterostructures consisting of graphene, hBN and MX2, for which M = Mo, W, Zr, Hf, Sn and X = S, Se, Te are being investigated. Heterostructures containing SnTe2 were found to be unstable in our calculations, so they were excluded from this study. We considered different stacks made of the combination of bi-layers, as illustrated in Figure 1, whose electronic properties were computed using density functional theory (DFT), as implemented in the Quantum Espresso software package19. The use of periodic boundary conditions implies that the lattice mismatch of the different 2D unit cells has to be minimized. A standard approach to solve this problem consists in stretching one (or both) layer(s) until their lattice parameters match. However, this process has to be done carefully, since the application of a too large strain can lead to a significant modulation of the electronic properties20,21. In order to keep the strain imposed by the mismatch as low as possible (in this case, lower than 4 %), we allowed a rotation of the upper layer with respect to the bottom one. This results in computationally tractable supercells, whose number of atoms varies from 6 to 48 atoms. Note however that despite our efforts to minimize the strain applied to the supercell, we cannot completely exclude that it impacts on the electronic properties of the stacked layers. To reduce this effect, the changes in electronic properties and surface energies of the layered materials are compared to the values obtained for the isolated 2D material within the same strain conditions as the ones used to model their corresponding heterostacks. For the cases in which the lattice mismatch allows building stacks without imposing a rotation of the layers, we considered a AA’ topology for the stacked layers, with the transition metal atoms of the top layer being located over the chalcogenide sites of the bottom one, and vice-versa. The 5 ACS Paragon Plus Environment

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impact of a rotation and of a translation operation on one of the two stacked layers on the stack properties are also evaluated. We used the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional22 combined with projector-augmented waves (PAW) pseudopotentials23 and a plane-wave basis sets to solve the Kohn-Sham equations. The kinetic energy cutoff for the integration of the wave functions is set to be 40 Ry and a 18x18x1 Monkhorst-Pack k-point mesh24 is used for the sampling of the Brillouin zone for all the systems. These parameters ensure that an accuracy of 2 meV/atom is reached on the total energy. Due to the three-dimensional nature of the periodic conditions used to model our systems, a vacuum region of 15 Å is added to minimize the impact of unwanted interactions between the model and its periodic images through long range interactions.

WS2 MoS2 Figure 1: Schematic representation of a MoS2|WS2 van der Waals heterostructure. x and y define the in-plane directions, while z is the out-of-plane one.

A saw-like potential is then added to the bare ionic potential within the vacuum region to simulate the effect of an electric field perpendicular to the 2D material layers25. Finally, the DFT formalism is corrected using the scheme proposed by Grimme26 to obtain a proper description of the weak van der Waals forces that dominate in these structures. The interaction energy, normalized to the area, is computed as follows:

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where Estack, Etop layer and Ebottom layer are the total energies of the stacked materials and of the isolated monolayers, respectively and Sunit cell is the surface area of the unit cell. In order to analyze the interaction between the stacked layers and to quantify their impact on the electronic structure, we projected the wavefunctions onto orthogonalized atomic wavefunctions for each point in the band structure: " !" #

!"

$ % & !" #"

where & !" #" are the set of pseudo-atomic orbitals read from the pseudopotentials used. Then the contributions coming from the atomic sites located in the same layer were grouped, such that the weight of each layer is observed and differentiated in the band structure, allowing the determination of the band offsets and orbital delocalization in the stack. This projection is computed for each k-point of the band structure, and a color is assigned with respect to the contribution from each layer, as illustrated in Figure 2. In this scheme, colors vary from red (corresponding to a contribution from the bottom layer only) to deep blue (contribution from the top layer only), with intermediary shades of purple depicting the degree of delocalization of the wavefunctions on the two layers. Note that depending on the system considered, the delocalization of the wavefunction on the layers can vary strongly. As a result, allocating unambiguously the bands to each layer in the stack is not always a straightforward process. To fix this issue, we assumed that a band is characteristic of a layer whenever the weight of its wavefunction is localized at 60 % (or more) on that layer. This allows extracting the modulation of the electronic structure upon stacking. Globally, a modulation of the band gap of the layers up to 0.5 eV can occur due to the layer interaction, with respect to the electronic properties of their isolated counter parts. Finally, the band offset is defined by the difference in energy of the top of 7 ACS Paragon Plus Environment

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the valence band (TVB) and bottom of the conduction band (BCB) of each layer and allows determining the type of band alignment (I – straddling, II – staggered and III – broken band gap) in the heterostructure, as well as the effective band gap of the stack. The latter is evaluated as the difference between the lowest conduction band found in the heterostructure, and the highest valence one. Note that a zero or negative effective band gap corresponds to a broken band gap (type III) alignment. This one is generally desired for heterostructure-based TFET11.

(a)

(b)

(c) Figure 2: Band structure of (a) a MoS2|WS2, (b) a MoS2|ZrS2 and (c) a MoS2|graphene heterostructures. The contribution of MoS2 is colored in red while the contribution of the other layer is displayed in blue.



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As stated below, the application of an electric field perpendicular to the stack leads to a partial transfer of the electron density from one layer to the other. This field-induced charge accumulation/depletion, which results in an electrostatic doping, is quantified using a Bader charge population analysis scheme27. Among the different existing electronic partition schemes, the Bader population analysis has the advantage to conserve the total electronic density, which is crucial to evaluate the charge exchanged between the layers. This is not the case for alternative charge population analysis techniques such as the Löwdin or Mulliken ones28,29. The FastFourier-Transform (FFT) mesh used to generate the charge density has been set to be 216x216x216 to ensure a proper convergence of the atomic charges, within 0.001 electron/cell. The equilibrium geometry used in these calculations corresponds to the configuration obtained in the absence of an electric field. Finally, we determined the amount of charge transferred between the layers by applying an electric field whose intensity was gradually increased by a step of 1 V/nm. The evolution of the doping concentration achievable is then normalized to account for the contacting area. We applied electric fields with amplitudes up to 5 V/nm, which are comparable to the ones typically used in 2D devices30 or for the electrostatic doping of graphene31. Given that the interlayer distance is in the range of 0.3 nm, this is equivalent to the application of a potential difference of ~1.5V, though these values may seem at first sight to be too large, they lie within the electric field values typically used experimentally, as reported for instance by Chu and coworkers32 for bilayer MoS2.


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3 RESULTS AND DISCUSSION

3.1 STRUCTURAL AND ELECTRONIC PROPERTIES It is expected that the out-of-plane orbitals, such as the π ones in graphene or pz ones in MX2 material will play a key role in the interaction between the layers which form the stack. We considered 120 combinations of bilayer heterostructures built from 2H-MoS2, 2H-WS2, 2H-ZrS2, 2H-HfS2, 1T-SnS2, 2H-MoSe2, 2H-WSe2, 2H-ZrSe2, 2H- HfSe2, 1T-SnSe2, 2H-MoTe2, 2HWTe2, 2H-ZrTe2, 2H-HfTe2, hBN and graphene. We found that the inter-layer distances for all the heterostructures considered vary from 3 to 4 Å, which lies within the boundaries of typical van der Waals materials such as the one reported for graphene-MoS2 heterostructures, for which our result (3.34 Å) matches the one observed by scanning

high-resolution

transmission

electron

microscopy

(STEM)

cross-section

measurements33 (3.4 ± 0.1 Å). In Figure 3, the interlayer distance is shown with respect to the computed interaction energy normalized to a surface of 1 m2. The correlation between the interaction energy and the interlayer distance is illustrated in Figure 3b for configurations made of a layer of MoS2 and a layer of another 2D material. Note that the evolution depends very much on the nature of the couples considered (see Figures S1 and S2 of the supplementary material) and that the relation between the composition of the heterostack, their interaction energies and inter-layer distances is complex. Some qualitative trends can however be established. First, for a given chalcogen, the inter layer distance depends on the nature of the cation present in the layers. Also, the p orbitals of Te being very diffuse, they lead to stronger interaction energies than the ones obtained for selenides and sulfides for the same interlayer distance (Figure S2a). Finally, the combination of layers with different chalcogen species results



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to an interaction regime intermediate to the one obtained for configurations sharing a common chalcogen, as shown in Figure S2(b-d).

(a)

(b)

Figure 3: Distribution of the interlayer distance distribution in van der Waals heterostructures with respect to the computed interaction energy per surface unit for (a) all the considered stacks and (b) for stacks built using MoS2 in their composition. In the latter, the red labels depict the 2D material contacted with MoS2.

Recent works have already evaluated the absolute band alignment, using a hydrogen atom to align the bands of isolated monolayers34. Our approach is somewhat different, since the electronic signatures extracted accounts for the interaction between the layers. Consequently, our results are sensibly different from the ones previously reported, since the band gap of one layer can change due to the interaction with the other one. For instance, contacting MoS2 with another two-dimensional material results in a band gap varying between 1.2 eV and 1.8 eV. The analysis of the band alignments of the set of 2D materials with respect to MoS2 shows different types of electrostatic alignments: some couples display a staggered (type II) band gaps 11 ACS Paragon Plus Environment

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alignment (for couples such as MoS2|WS2 and MoS2|MoSe2) while other ones (such as MoS2|HfS2 and WS2|SnS2) have nearly a broken band gap (type III) profile35. It turns out that the 120 different heterostacks that we considered, fall into these three categories (Figure 2). The rationale of this modulation is illustrated for the case of the MoS2|WS2 stack with an AA’ alignment (Figure 2a). In this type II band alignment, the coloring of the contribution of each layer to the band structure (red for MoS2 and blue for WS2) shows that the stacking leads to a hybridization of the sulfur pz orbitals between the different layers, as illustrated by the purple color adopted along the Γ-M symmetry line. To evaluate the impact of stacking on the band structure, we computed the band structures of the separated layers with the same lattice parameter as the one used in the stack and compared the results to that of the heterostack configuration (see Figure 4 and S3). Note that for the sake of conciseness, we focus this section on the results obtained for the stacks containing MoS2; the evolution of the electronic properties of the other combinations is available in the supplementary materials. We evaluated that the band gap of MoS2 in the heterostructure was 1.64 eV and that of WS2 was 1.37 eV, to be compared to 1.64 eV and 1.82 eV in the non-interacting case. The impact of the interaction is reflected in the WS2 layer, that undergoes a reduction of 0.45 eV of its band gap. The modulation of the band gap in stacks containing a layer of MoS2 is illustrated in Figure 4. This hybridization process is driven by the coincidence of the sulfur atomic sites between the layers. A similar interaction has already been observed in homo-stacks such as MoS2, where the band gap decreases with the number of layers9.



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Figure 4: Change in band gap in heterostacks containing MoS2 due to the interlayer interaction. The change in band gap for the MoS2 layer is shown in dashed red and the one for the other layer is colored in dotted green.

For the MoS2-ZrS2 heterostructure (Figure 2b), the large lattice mismatch (11 %) prevents the occurrence of AA’, AB and similar stacking configurations to occur, which would otherwise induce an extremely large stress in the layers. The rotation of one layer with respect to other help accommodating the geometric constraints and minimize artificial strains in the simulation cell. However, this results in a lowering of the orbital overlap as a perfect alignment in an AA’ stacking (or similar) is not achievable. This results in a much reduced band gap change as illustrated in Figure 4. The resulting band alignment is a staggered one (type II), but close to a broken band gap (type III) one, with the top of the valence band of MoS2 being located at 0.26 eV from the bottom of the conduction band of ZrS2. Interestingly, such an alignment could favor the implementation of an efficient band-to-band tunneling process as is required for the development of vertical TFETs36. It is also expected to have a strong impact on the charge 13 ACS Paragon Plus Environment

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transfer induced upon the application of an external perpendicular electric field, as discussed in the following section. Finally, the last category arises from the specific band structure of graphene and the properties of its Dirac cone. The presence of graphene in contact with MoS2 has little impact on the electronic properties of the stack, thanks to the weak overlap between the pz orbitals of C and S and to the mismatch in lattice coincidence sites between the two layers. Indeed, the signature of the graphene band structure (colored in blue at the point K of the Brillouin zone in Figure 2c) clearly appears to maintain its pristine character in contact with the other 2D material, as illustrated in the case of the MoS2-graphene stack. The distribution of the band alignments for all the stacks considered is available in the supplementary information (Table S1), together with literature values whenever available. As stated above, the modulation of the band structure of MoS2 for a given stack depends very much on the relative alignment of the layers with respect to each other and on the value of their lattice parameters. For combinations of 2D materials that lead to a small lattice mismatch, such as for example MoS2|WS2, it is possible to achieve an almost perfect alignment of the monolayers in an AA’ or AA stacking, the first one having a lower total energy. In the latter case (AA), the orbital overlap is maximized and results therefore to a band alignment different from that of an AA’ stack, as shown in Figure 5.



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(a)

(b) Figure 5: Band structures of MoS2|WS2 in a a) AA stacking and b) AA’ stacking. The colors depict the relative contribution of each layer, red reflecting MoS2 and blue the WS2 one

Interestingly, this interaction remains weak from an energetic point of view and the difference in energy between these two configurations is only 0.07 eV per unit cell, which shows that the layers have a lot of degrees of freedom with respect to each other. The impact on the electronic structure is however more drastic and there is a 150 meV modulation of the top of the valence band (with modulation of the band offset, going from AA (Figure 5a) to the AA’ (Figure 5b) stacking). On the other hand, in configurations with a large lattice mismatch and unless a rotation is being performed, such high symmetric stacking patterns cannot be achieved. As a


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consequence, the band offsets vary by less than 10 meV. The impact on the electric-field induced charge transfer will be discussed in the following section.

3.2 CHARGE TRANSFER Designing heterostacks to induce an intra-layer electron transfer upon the application of a perpendicular electric field is conceptually similar to the approach developed for molecular doping. The main difference being that a charge is not given by a molecule such as F4TCNQ, but exchanged between the layers. It consists in taking advantage of the delocalization of the wave function between stacked layers, as well as of their band alignments, to modulate the electronic density by the application of an external perpendicular electric field. We found that in most cases, packed 2D materials act as parallel plate capacitors and an electric field of 1 V/nm induces a charge transfer up to 5 x 1012 |e|/cm2, a value comparable to the ones obtained using molecules such as polyvinyl alcohol37. Increasing the electric field to 5 V/nm induces a charge transfer that spans from 5 x 1012 |e|/cm2 to 2.8 x 1013 |e|/cm2. Thus, there is about a five-to-one ratio between the highest and lowest charge transfer values. The order of magnitude is in line with values experimentally reported38,39 and corresponds to an equivalent surface capacitance ranging from 0.2 µF/cm2 to 1.2 µF/cm2 for an applied electric field of 5 V/nm, which is somewhat similar to the capacitance reported in graphene40.



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Figure 6: Evolution of the charge transfer from WS2 to MoS2 (in electron) with respect to the interlayer distance in a MoS2|WS2 stack. A positive (negative) value indicates an n-type(p-type) doping of the MoS2 layer. The interlayer distance values are 3.0 Å (blue squares), 3.4 Å (green triangles), 4.0 Å (red circles), 5.0 Å (teal crosses) and 6.0 Å (purple diamonds).

Because the charge transfer process reflects the modulation of the electronic properties and hence the degree of delocalization of the wave function, it also depends on the interlayer distance. We illustrated this point for the case of the MoS2|WS2 system, where we observed a 2to-1 modulation when considering interlayer distances spanning from 3 to 4 Å between the layers, see Figure 6. This dependency stresses the need to use a proper van der Waals force corrections scheme in the DFT calculations, to evaluate interlayer distances that are as close as possible to the actual ones. The application of an external electric field modulates the localization/delocalization of the wave function and leads to a linear dependence of the electron transfer on the applied field. Its impact on the orbitals can be visualized in Figure 7, which displays an isovalue of the local density of states integrated from the top of the valence band to 0.5 eV, as a function of the applied electric field.


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(a)

(b)

(c)

Figure 7: Evolution of the local density of states in a MoS2|WS2 stack under (a) no applied external electric field, (b) 1 V/nm and (c) 5 V/nm. The surfaces are isovalues of the local density of states integrated from the valence band to 0.5 eV below it. Note that the position of the atoms is displayed in the first unit cell only to ease the visualization of the stack.

Interestingly, this factor, although being important, is not dominant for the charge transfer process in all the stacks. Indeed, some heterostructures such as HfS2|MoSe2, HfS2|WSe2 and SnS2|graphene display the three highest charge transfers, despite the fact that their interlayer distances are lying within the averaged values computed for the different stacks (see Table S1, supplementary information).



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(a)

(b)

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(c)

Figure 8: Charge transfer computed with a Bader analysis scheme from one layer to the other one, as a function of the applied electric field (a) in a MoS2|WS2 heterostructure, (b) in a MoS2|ZrS2 heterostructure and (c) in a MoS2|graphene heterostructure. The charge transferred to the MoS2 layer is represented in solid red while the one transferred to the other layer is shown in dashed blue.

Out of the 120 configurations, we observed that some couples show a linear charge transfer, symmetric with respect to the direction of the electric field, while other ones display an asymmetric one. An example for the first case consists of a MoS2|WS2 heterostructure, which has a staggered band alignment (Type II, Figure 2a) and displays a symmetric charge transfer (Figure 8a). In contrast, for heterostructures with close-to-broken band gap alignments (Type III), for example MoS2|ZrS2 and MoS2|graphene, (Figure 2b and Figure 2c), the electrostatically driven charge transfer depends on the direction of the applied electric field, and is enhanced when the top of the valence band of one layer lies close in energy to the bottom of the conduction band of the other layer. Depending on this offset, the amplitude of the asymmetric charge transfer can either be strengthened or weakened, hence favoring a p- or a n-type doping in the top or bottom layer of the heterostructure (Figure 8b and Figure 8c), thanks to the electron tunneling process. In MoS2|ZrS2 and stacks displaying the (close to) broken band gap alignment, i.e. for the conditions that promotes a band to band tunneling process, the application of the electric field leads to an enhanced charge transfer. The MX2|graphene couples behave similarly: electrons can 19 ACS Paragon Plus Environment

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be injected in the conduction band of the MX2 material depending on the position of the Fermi level, as illustrated in Figure 8c, and which was also observed experimentally by Yang et al.41.

(a)

(b)

Figure 9: Charge transfer versus band offset at an applied electric field of (a) 1 V/nm and (b) 5 V/nm. Each point represents one of the stack configuration.

We illustrate in Figure 9 the impact of the applied out-of-plane electric field on the effective band offset of various heterostructures, and the corresponding charge transfer between the layers. Depending on the material present in the stack, the band offset can be significantly modulated, coming close to a broken band gap configuration. This promotes the tunneling of electrons from one layer to the other, and therefore the electrostatic doping. When the systems enter the regime of a broken band gap (negative or zero band offset), the amount of charges transferred rises sharply, as shown in Figure 9b.



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Figure 10: Evolution of the total surface energy of 2D stacks with respect to the relative positioning of the layers, the angle (xaxis) is the rotation angle applied to the layer that is contacted with MoS2. The reference (zero) energy is the total energy for the initial configuration, which is considered as the one with a zero angle. The considered combinations are MoS2|WS2 (blue diamonds), MoS2|ZrS2 (green circles) and MoS2| graphene (red squares).

Given that the main interlayer interaction force is a weak van der Waals one, layers are relatively free to move with respect to each other, as illustrated in Figure 10. Indeed, the evolution of the total energy of the system with respect to the relative positioning of the layers reveals variations smaller than 130 mJ/m2 for MoS2|WS2. However, this interaction is minimized to reach values below 10 mJ/m2 in the case of MoS2|ZrS2 and MoS2|graphene stacks. As a consequence, their relative alignment is likely to vary from stack to stack, or to depend on the process used for the transfer/synthesis of the 2D materials in a device. This could, in turn, induces a source of variability in the charge transfer and on the device characteristics. To quantify to which extent this would impact on the device performances, we evaluated the impact of a change in the relative position of two layers on the amount of charge transferred in the heterostructure: we translated one layer with respect to the other, for the three representative categories identified 21 ACS Paragon Plus Environment

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here-above. Starting from the original configuration as a reference, we computed the interlayer charge transfer for configurations in which the top layer (WS2, ZrS2 or graphene) are gradually translated by 1, 2 or 3 Å along the in-plane x or y axis (as defined in Figure 1). Interestingly, the symmetry or asymmetry of the charge transfer and the order of magnitude of the electrostatic doping are maintained by the translation process (Figure 11). However, a subtlety appears for the case of the MoS2|WS2 heterostructure (Figure 11a), where a difference up to 15% in the amplitude of the charge transfer is observed when translating the WS2 layer with respect to its original (AA’ stack) configuration. In this case, the band offset varies by up to 0.2 eV, from 1.1 eV in a AA’ stacking configuration to 1.3 eV in a AA one. This enhanced variation is induced by the fact that MoS2 and WS2 have very similar lattice parameters42 (within 0.01 Å), which favors the alignment of the sulfur atoms between the layers, and hence increases the interaction between their pz orbitals (and the associated charge transfer). For the second case (MoS2|ZrS2, Figure 11b), the lattice mismatch between the two layers prevents such an alignment of the sulfur atoms to occur. As a result, all the configurations become mostly equivalent, and no significant differences are found for the charge transfer process and the band offset. Finally, for the last case (MoS2|graphene, Figure 11c), the overlap between the pz orbitals of the sulfur atoms of MoS2 and the carbon ones of graphene impacts on the charge transfer (by about 10 %), though in a lesser extent than for the first case, with no significant change in the band offset.



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(a)

(b)

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(c)

Figure 11: Impact of the relative position of the two dimensional layers on the electric field induced charge transfer to the MoS2 layer in (a) in a MoS2|WS2 heterostructure, (b) in a MoS2|ZrS2 heterostructure and (c) in a MoS2|graphene heterostructure. The configurations are the original one (black squares) and configurations where the layer on top of MoS2 is moved along either the x axis by 1 Å (blue circles), 2 Å (green squares) and 3 Å (purple hexagons); or along the y axis by 1 Å (red ‘x’), 2 Å (yellow stars) and 3 Å (magenta ‘+’).

Aside from translational effects, the layers can also be rotated with respect to each other. To account for this effect, we studied the evolution of the electric field induced charge transfer upon rotation steps of 60 degrees. These allow building low strain models of the structures, due to the hexagonal symmetry present in the 2D materials. Unsurprisingly, the amplitude of the charge modulation induced by the rotation follows, as for the translational case, the changes in orbital overlap. While for dissimilar MX2 lattices, the rotation does not impact on the charge transfer, systems showing similar lattice parameters (such as MoS2|WS2) display a more pronounced dependence on the relative orientation, with variations up to ~ 30 % (as illustrated in Figure 12). Although these variations are important, they remain relatively minor with respect to the ones obtained when changing the composition of the heterostack. For instance, a 5-to-1 ratio in the charge transfer can be obtained, for instance between MoTe2|ZrSe2 and WSe2|graphene. Overall, the highest charge transfers are found for cases in which, the chalcogenide atoms of both layers are located just on top of each other.


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(a)

(b)

(c)

Figure 12: Impact of a rotation of the two dimensional layers on the electric field induced charge transfer to MoS2 in (a) a MoS2|WS2 heterostructure, (b) a MoS2|ZrS2 heterostructure and (c) a MoS2|graphene heterostructure. The original configuration is shown in black (squares). The layer in contact with MoS2 is rotated about the out-of-plane direction by 60° (blue circles), 120° (green squares), 180° (purple hexagons), 240° (red stars) and 300° (yellow triangles) with respect to MoS2.

The nature of van der Waals heterostructures allows building various types of stacks, including the possibility of having more than two layers. As the band alignment plays a central role in the charge transfer, the order in which the layers are stacked is expected to have an impact on the electron transfer. As an attempt to quantify this effect, we considered tri-layered stacks made of different combinations of MoS2 and ZrS2. For a tri-layered stack, there are six possible configurations from all-MoS2 to all-ZrS2 ones. Their charge transfer characteristics are summarized in Figure 13. In the homo-stack cases (MoS2|MoS2|MoS2 and ZrS2|ZrS2|ZrS2), the electron transfer takes place between the top and bottom layers, with no contribution from the middle layer (Figure 13a and Figure 13f). MoS2|MoS2|ZrS2 and MoS2|ZrS2|ZrS2 configurations show negligible differences compared to the MoS2|ZrS2 case (Figure 13b and Figure 13d). In contrast, whenever a 2D monolayer is sandwiched between two layers of a different nature, as it is the case in MoS2|ZrS2|MoS2 (Figure 13c) and ZrS2|MoS2|ZrS2 (Figure 13e), the middle one only take one doping “polarity”, leading to a higher doping compared to the bilayer case.



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(a)

(b)

(c)

(d)

(e)

(f)

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Figure 13: Charge transferred to the bottom (red squares), middle (green circles) and top (blue diamonds) layers in MoS2|ZrS2 based tri-layered stacks. The stacking configurations are (a) MoS2| MoS2| MoS2, (b) MoS2| MoS2| ZrS2, (c) MoS2| ZrS2| MoS2, (d) MoS2| ZrS2| ZrS2, (e) ZrS2| MoS2| ZrS2 and (f) ZrS2| ZrS2| ZrS2, respectively.


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4 CONCLUSIONS By combining density functional theory with a dispersion force correction scheme, we studied the electronic properties of 120 bi-layer two-dimensional heterostructures, with a focus on the impact of the application of an external perpendicular electric field on their electronic structures. Different band alignments have been obtained, depending on the pair of materials used, which ranges from a broken band gap configuration to a staggered one. Interestingly, the application of an electric field modulates enough the electronic properties to induce a charge transfer between the layers. This phenomenon can be exploited to generate a controlled electrostatic doping in a 2D based transistor channel, whose amplitude depends on the voltage used. We found that a doping as high as 5 x 1012 e/cm2 can be achieved for an electric field of 1V/nm and up to 2.5 x 1013 e/cm2 can be achieved for an electric field of 5 V/nm. The charge transfer is found to be material dependent, with a 5-to-1 variation between the highest and lowest values and to depend mainly on the alignment of the band structures in the stack under an applied electric field. We also observed that the relative position of each layers in the heterostructure has an impact on the charge transfer, though to a lesser extent. The highest doping values are achieved for material stacks with either a natural broken band gap or an induced one by an external electric field. In this case, a tunneling process of electrons from the top of the valence band to the bottom of the conduction band is taking place. Our findings suggest that the electrostatic doping of two-dimensional heterostructures is very promising for future nanoelectronic devices. Though such an electrostatic control requires four terminals to operate the devices, it potentially offers the possibility to tune the nature of the transistor at will. The doping could hence be switched from a n- to a p-type one and thus provides an ambipolar



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signature. Also, depending on the association of 2D materials chosen for the stacking, it is also possible to build an electron tunneling device (TFET), a diode or a capacitor.

5 ACKNOWLEDGEMENTS A. K. A. Lu, I. P. Radu and G. Pourtois acknowledge the financial support from the imec beyond CMOS research program. M. Houssa acknowledges the financial support from the KU Leuven Research Funds, project GOA/13/011. Part of this work has been financially supported by the ERA-NET 2Dfun project (2D functional MX2/graphene heterostructures), in the framework of the Graphene Flagship. Within this framework, the authors acknowledge the support from Flanders Innovation and Entrepreneurship (VLAIO).

SUPPORTING INFORMATION Detailed results for each heterostructure, accounting for the charge transfer, the interlayer distance, the band offset and the interaction surface energy in bilayer van der Waals heterostructures are listed. The surface interaction energy versus the interlayer distance are mapped for all the stacks considered as well as the change in band gap induced by the stacking. Values reported in literature are also presented, whenever available43,44,45,46,47,48,49.


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ZrS2-based van der Waals Heterostructures, Energy Environ. Sci., 2016, 9, 841-849.


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