In-plane ferroelectric tunnel junctions based on 2D α-In2Se3/semiconductor heterostructures

Ferroelectric tunnel junctions (FTJs) have great potential for application in high-density non-volatile memories. Recently, α-In2Se3 was found to exhibit robust in-plane and out-of-plane ferroelectric polarizations at a monolayer thickness, which is ideal to serve as a ferroelectric component in miniaturized electronic devices. In this work, we design two-dimensional van der Waals heterostructures composed of an α-In2Se3 ferroelectric and a hexagonal IV–VI semiconductor and propose an in-plane FTJ based on these heterostructures. Our first-principles calculations show that the electronic band structure of the designed heterostructures can be switched between insulating and metallic states by ferroelectric polarization. We demonstrate that the in-plane FTJ exhibits two distinct transport regimes, tunneling and metallic, for OFF and ON states, respectively, leading to a giant tunneling electroresistance effect with the OFF/ON resistance ratio exceeding 1 × 104. Our results provide a promising approach for the high-density ferroelectric memory based on the 2D ferroelectric/semiconductor heterostructures.


INTRODUCTION
Ferroelectric materials are useful for information storage applications due to their spontaneous polarization which can be switched by an applied electric field. Driven by the demands of device miniaturization and non-volatility, a ferroelectric tunnel junction (FTJ) has been proposed and considered as one of the most promising memory types, as compared to the current commercial dynamic random-access memories [1][2][3][4][5] . A typical FTJ is composed of two different electrodes separated by an ultrathin ferroelectric barrier layer [6][7][8][9] . Due to the two electrodes and/or interfaces in a FTJs being asymmetric, the reversal of ferroelectric polarization leads to the variation of the height and/or width of the electron tunneling potential barrier, resulting in two distinct resistance states 7,[9][10][11][12] . This phenomenon is known as the tunneling electroresistance (TER) effect [12][13][14] . So far, most FTJs utilized oxide perovskite ferroelectrics as barrier layers. Unfortunately, ferroelectricity of perovskite ferroelectric films often deteriorate at the nanoscale due to the well-known size effect 15 , making the miniaturization of the memory devices challenging.
In recent years, ferroelectricity was found in a few twodimensional (2D) van der Waals (vdW) materials, such as CuInP 2 S 6 16,17 , WTe 2 18,19 , and In 2 Se 3 20-22 . 2D vdW ferroelectrics are appealing due to their uniform atomic thickness, absence of dangling bonds, and the ability to be integrated with other vdW materials which allows useful functionalities. For example, in combination with conducting 2D materials, these 2D vdW ferroelectric materials can be used as ultrathin barriers in FTJs.
Here we focus on α-In 2 Se 3 which exhibits robust ferroelectricity even at a monolayer thickness and possesses intrinsically coupled out-of-plane (OOP) and in-plane (IP) ferroelectric polarizations 20,23 . Its sizable polarization and a moderate ferroelectric switching energy barrier make α-In 2 Se 3 attractive for memory devices, especially FTJs 24 .
Since the discovery of ferroelectricity in 2D α-In 2 Se 3 , plenty of experimental and theoretical works have been devoted to exploring its application in non-volatile memories [25][26][27][28][29][30][31][32][33][34] . Wan et al. demonstrated a ferroelectric field-effect transistor (FeFET) using ultrathin α-In 2 Se 3 as a non-volatile ferroelectric gate and graphene as a conducting channel, which were separated by an insulating hexagonal boron nitride layer 35 . Si et al. reported an asymmetric metal/α-In 2 Se 3 /Si crossbar ferroelectric semiconductor junction with an ON/OFF ratio >10 4 at room temperature 36 . Also, several theoretic works have been published focusing on the band alignment of 2D α-In 2 Se 3 heterostructures controlled by the OOP polarization of α-In 2 Se 3 , which leads to about 1.1 eV potential difference between its two surfaces [37][38][39] . Ferroelectric control of the band alignment is important for the design of FTJs and other types of memory devices. Wang et al. summarized different categories of the band alignment between ferroelectric α-In 2 Se 3 and 2D semiconductors or metals 38 .
A stronger polarization control of the band alignment in ferroelectric α-In 2 Se 3 heterostructures and a simpler cell structure are still in focus for the memory application of 2D ferroelectrics. The recently proposed IP FTJs are especially interesting for the high-density information storage 40 . Using this concept, Kang et al. [41][42][43] explored IP 2D FTJs based on graphene/α-In 2 Se 3 vdW heterostructures, while Ding et al. 44 proposed an antiferroelectriclike behavior of bilayer In 2 X 3 (X = S, Se, Te) to enhance the FTJ performance. Relevant to the above studies, Shen et al. 45 designed a 2D FTJ by p-and n-type doping at the two terminals of IP ferroelectric SnSe.
In this paper, we design a symmetric FTJs where both the ferroelectric barrier and the electrodes consist of layered vdW heterostructures. In these FTJs, the barrier layer represents an α-In 2 Se 3 ferroelectric monolayer deposited on semiconductor monolayers, SnTe or PbSe, of hexagonal group IV-VI 46,47 , while the electrodes are composed of a heavily electron-doped In 2 Se 3 / SnTe bilayer, (In 0.5 Sn 0.5 ) 2 Se 3 /(Sn 0.5 Sb 0.5 )Te. Using first-principles density functional theory (DFT) calculations, we demonstrate a robust ferroelectric polarization-controlled switching behavior between metallic and insulating states in the α-In 2 Se 3 /SnTe (and α-In 2 Se 3 /PbSe) ferroelectric heterostructures. By utilizing the coupled IP and OOP ferroelectricity of α-In 2 Se 3 and the ferroelectric-controlled band alignment of the designed vdW heterostructures, we propose a two-terminal IP 2D FTJ with a giant TER effect (OFF/ON resistance ratio >1.2 × 10 4 ) and low ON state resistance. We infer the physical mechanism for the control of electron tunneling barriers and resulting transport properties for the ON and OFF states to be different and more effective as compared to those in the previous studies of IP FTJs. These results enrich the understanding of the ferroelectric band control in α-In 2 Se 3 heterostructures and indicate a great potential for the 2D or ultrathin ferroelectrics for application in electronic devices.

RESULTS AND DISCUSSION
2D α-In 2 Se 3 /semiconductor vdW heterostructures We consider heterostructures of 2D ferroelectric α-In 2 Se 3 interfaced with 2D semiconductors SnTe and PbSe. The three-fold rotational symmetry of all these 2D materials results in the same IP triangular cell shapes, as shown in Fig. 1a The total energies of the four heterostructures ( Fig. 1d-g) are calculated to be −1.971, −2.127, −1.947, and −1.978 eV per unit cell, respectively (the total energy of separate In 2 Se 3 and SnTe monolayers is set to be 0). It is seen that, the P ↑ state (where polarization of In 2 Se 3 pointing away from SnTe) has 156 meV lower energy than the P ↓ state (where polarization of In 2 Se 3 pointing into SnTe) for the Sn-Se interface heterostructure. This energy difference is much larger than the energy difference of 31 meV between the two polarization states for the Te-Se interface heterostructure. The larger energy difference between the two polarization states in the Sn-Se interface heterostructure relative to that in the Te-Se interface heterostructure originates from the interfacial Coulomb interaction. Due to the ionic bonding between the Sn cation and Se anion at the Sn-Se interface which reduces the electrostatic energy, this type of heterostructure is sensitive to the polarization direction of In 2 Se 3 . When the polarization points away from the interface (P ↑ state), a negative polarization charge of the P ↑ state further reduces the electrostatic energy and leads to a smaller interlayer distance and an interfacial charge transfer (discussed below). On the contrary, due to the Coulomb repulsion between the Te and Se anions, the interfacial interaction at the Te-Se interface is much weaker. As a result, ferroelectric polarization reversal induced changes in the energy, interlayer distance, and interfacial charge transfer are insignificant. The obtained polarization states are stable and switchable as follows from the polarization switching study discussed in Supplementary  Next, we investigate the band alignment in the In 2 Se 3 /SnTe heterostructures. Figure 2 displays the calculated band structures of the four heterostructures shown in Fig. 1d-g. For the P ↓ state of the Sn-Se interface heterostructure, the valence band maximum (VBM) and the conduction band minimum (CBM) are mainly contributed by SnTe and In 2 Se 3 , respectively, resulting in an indirect band gap of 0.84 eV (Fig. 2a). If the polarization is reversed upward (P ↑ ), the heterostructure becomes metallic (Fig. 2b) with the VBM (mainly contributed by SnTe) being 0.39 eV higher in energy than the CBM (mainly contributed by In 2 Se 3 ). This transition to the metallic state is caused by the negative ferroelectric polarization charge at the In 2 Se 3 /SnTe interface lifting the electrostatic potential energy of SnTe up and resulting in an electron charge transferred from the SnTe valence band to the In 2 Se 3 conduction band. This fact is evident from the atomic layerresolved density of states (LDOS) and the charge transfer at the interface as illustrated in Supplementary Figs. 4 and 5. The predicted transition between insulating and metallic states for the Sn-Se interface heterostructure driven by polarization reversal from P ↓ to P ↑ is consistent with the type II to type III band alignment transition as defined in ref. 38 . The ferroelectric band control effect predicted in our study appears to be much more pronounced than those found in the similar 2D α-In 2 Se 3 / semiconductor heterostructures 37,38,50 .
The Te-Se interface heterostructure behaves differently. In this case, the negative ionic charge of the Te atom at the interface bends the SnTe bands down thus pushing the In 2 Se 3 up into the band gap of SnTe. As a result, when polarization of In 2 Se 3 is reversed, the change in the polarization charge at the interface is not sufficient to make the heterostructure metallic. We find that the P ↓ state exhibits an indirect band gap of 1.08 eV (Fig. 2c) with both VBM and CBM derived mainly from the In 2 Se 3 layer, whereas the P ↑ state behaves an indirect band gap of 0.28 eV (Fig. 2d), where the VBM and CBM are contributed mainly by the SnTe and In 2 Se 3 , respectively. This transition is consistent with the type I to type II band alignment transition as defined in ref. 38 .
The qualitative picture of the band alignment at the In 2 Se 3 /SnTe interface, being dependent on ferroelectric polarization of In 2 Se 3 and the interface termination, is described in Supplementary Note 6. The In 2 Se 3 /PbSe heterostructures show similar electronic properties (Supplementary Note 7) to those of the In 2 Se 3 /SnTe heterostructures.
In-plane ferroelectric tunnel junctions The significant polarization-induced band tuning effect and the resulting transition between insulating and metallic states, makes the α-In 2 Se 3 ferroelectric heterostructures promising for application in memory and logic devices, such as FeFET and FTJs. In this work, we design an IP FTJ based on the Sn-Se terminated interface In 2 Se 3 /SnTe heterostructure. The transport direction of the FTJ is set along the IP polarization direction of α-In 2 Se 3 (see Fig. 1a, b), which allows the simultaneous switching of OOP and IP polarizations through the application of an IP external electric field between the two electrodes. Figure 3 shows the atomic structures of the IP FTJs for the P ↓ and P ↑ states, respectively. The tunneling barrier in the FTJs consists of integer multiples (N) of the orthorhombic cells (denoted by the green rectangles in Figs. 1a and 3a) stacked along the transport direction. N is set to be ranging from 3 to 6. The lattice constant along the transport direction of each orthorhombic cell is 0.71 nm. Heavily electrondoped In 2 Se 3 /SnTe heterostructures, namely (In 0.5 Sn 0.5 ) 2 Se 3 / (Sn 0.5 Sb 0.5 )Te, are used as electrodes in the FTJs. Their electronic properties are obtained using the VCA 51 by mixing 50% Sn on the In site and 50% Sb on the Sn site (see Supplementary Note 8 for the band structures of the electrodes).
Next, we explore the electron transport and the TER effect in In 2 Se 3 /SnTe IP FTJs. Supplementary Fig. 9 shows the calculated transmission (T) as a function of electron energy (E) for the FTJs  with N = 5. It should be pointed out that the electronic structures of the electrodes for the P ↓ and P ↑ states are not the same due to the electrodes being constructed using the VCA from different atomic structure corresponding to P ↓ and P ↑ (Supplementary Fig.  8). To eliminate the effect of electrodes and obtain the genuine TER effect of the FTJ, the transmission of the pure electrodes is calculated and shown in Supplementary Fig. 10. Then, the resistance of the FTJ is calculated according the formula: 52 , where T FTJ and T el are the calculated transmissions of the FTJ (Supplementary Fig. 9) and electrodes ( Supplementary Fig. 10), respectively, and d is the lattice constant perpendicular to the transport direction (0.41 nm). The calculated resistance (R) as a function of electron energy (E) of the FTJ with N = 5 for the P ↓ and P ↑ states is plotted in Fig. 4a. It is seen that, for the P ↓ state, the resistance increases significantly when the electron energy increases from E F −0.6 eV to E F −0.3 eV, and stays high until the energy increases up to E F (E F stands for the Fermi energy). Then the transmission gradually drops from E F to E F +0.2 eV again as the energy keeps increasing. On the contrary, for the P ↑ state, the FTJ maintains a low resistance state under the considered electron energy range. The TER ratio (OFF/ON resistance ratio R(P ↓ )/R(P ↑ )) of the FTJ at E = E F is estimated to be 2.85 × 10 3 . For E = E F − 0.3 eV, the OFF/ON ratio is found to be as large as 1.28 × 10 4 .
Then, the barrier width dependence of the TER effect is studied by calculating the resistance of FTJs at E = E F with the barrier layer width varying from 3 to 6 orthorhombic unit cells. It is seen from Fig. 4b that the resistance of the ON state (P ↑ state) stays low and is enhanced slowly when the barrier width increases. This is because, in the P ↑ state, the heterostructure is metallic, allowing the FTJ to behave like a conductor. On the contrary, for the OFF state (P ↓ state), the calculated resistance increases exponentially with increasing the barrier width, exhibiting a typical tunneling behavior. As a result, the OFF/ON resistance ratios are calculated to be 1.51 × 10 3 , 2.76 × 10 3 , 2.85 × 10 3 , and 1.21 × 10 4 for the barrier layer width varying from 3 to 6 orthorhombic cells (Fig. 4b).
We conclude, therefore, that the ferroelectric polarization induced TER effect in the designed In 2 Se 3 /SnTe IP FTJ can be enhanced significantly by increasing the barrier width.
In order to understand the origin of this transport behavior, the electronic structure of the FTJ is analyzed. Figure 5 shows the calculated layer-resolved density of states (LDOS) along the width direction. Each panel in Fig. 5 displays the DOS projected on half an orthorhombic cell in the electrode and barrier regions for P ↓ (Fig. 5a) and P ↑ (Fig. 5b) states, respectively. As seen from Fig. 5a, the barrier layer exhibits a band gap from about −0.6 eV to 0.2 eV relative to E F . This feature of the band structure well illustrates why the resistance of the P ↓ state increases and decreases at the energy of E F −0.6 eV and E F +0.2 eV, respectively, as shown in Fig. 4a (blue line). On the contrary, for the P ↑ state, as shown in Fig. 5b, there is no band gap across the barrier layer, leading to good conductivity under the entire considered energy range (see Fig. 4a, red line). The band structure-controlled insulating and conducting properties of the barrier layer for the P ↓ and P ↑ states also explain the barrier width dependence of the transport behavior shown in Fig. 4b.
To further clarify the transport mechanism of the designed IP FTJ, the partial charge densities in the real space are analyzed. Figure 6 visualizes the partial charge densities in the range of energies from E F −0.1 eV to E F for P ↓ and P ↑ states, respectively. It is seen from Fig. 6a that, for the P ↓ state, the partial charge density at E F only exists in the electrodes and a few atomic layers of the barrier near the interfaces, agreeing well with the LDOS of the FTJ at the Fermi energy in Fig. 5a. On the contrary, for the P ↑ state, as seen from Fig. 6b, there is abundant charge distributed within the barrier region, corresponding to the LDOS in Fig. 5b. From the spatial distribution, the partial charge density is mainly concentrated on the SnTe layer and the In 2 Se 3 /SnTe interface in the Fig. 4 The TER effect of FTJ. a The resistance (R) of the In 2 Se 3 /SnTe IP FTJs with N = 5 for the P ↓ and P ↑ states as a function of electron energy E. b The resistance (R) and OFF/ON ratio of the FTJs at E F while the orthorhombic cell number (N) of the barrier layer is varying from 3 to 6. barrier region, which indicates that the electrons will transport along this channel as in a conductor under the external bias.
We would like to emphasize that the mechanism of TER considered in this work is different from those discussed previously, where asymmetry of an FTJ, i.e., different electrodes and/or different interfaces, was the necessary factor to obtain a large TER value. Here, a metal-insulator transition in the whole barrier layer is driven by the OOP polarization of In 2 Se 3 and the FTJ asymmetry is not required. Contrary to the previous studies, the ferroelectric polarization that controls TER is pointing perpendicular to the transport direction, and the type of electrodes is not essential. Such design of the FTJ may be beneficial for applications because ON/OFF switching can be achieved in two ways: (1) by applying a bias voltage between the two electrodes to reverse the OOP polarization via reversal of the IP polarization as they are intrinsically coupled in ferroelectric In 2 Se 3 , or (2) by applying a bias voltage to the top gate electrode to directly switch the OOP polarization as in a three-terminal FeFET.
In conclusion, we have designed vdW heterostructures with α-In 2 Se 3 ferroelectric and hexagonal group IV-VI 2D semiconductor layers (SnTe and PbSe). Based on systematic first-principles studies, we demonstrated that these heterostructures exhibit a pronounced ferroelectric polarization control of the band alignment, which is promising for electronic device applications. We predicted that the In 2 Se 3 /SnTe heterostructure with Sn-Se interface termination can be switched from the insulating state with a large band gap to the metallic state, when the OOP ferroelectric polarization of α-In 2 Se 3 is reversed from pointing into to pointing away from 2D semiconductor layer. Driven by the polarizationcontrolled band alignment and the coupled IP and OOP ferroelectric polarizations in the designed In 2 Se 3 /SnTe heterostructures, we proposed a functional two-terminal IP 2D FTJ. We predicted that the designed FTJ has two distinct electron transport mechanisms−tunneling and metallic for the OFF and ON states, respectively, resulting in a giant TER effect with the OFF/ON resistance ratio exceeding 1 × 10 4 . The predicted TER effect is significantly amplified by further increasing the barrier width of the FTJ. Our results are promising for the design of 2D ferroelectric heterostructures and FTJ-based non-volatile memories. We hope therefore that they will stimulate experimental efforts to explore such kind of FTJs in practice and demonstrate the predicted properties.

METHODS
Geometry optimization and electric structure calculations DFT calculations using the projector augmented-wave as implemented in VASP code 53 are preformed to optimize the monolayer 2D materials and heterostructures and study their electronic structures. The exchange-correlation effects are described by the Perdew-Burke-Ernzerhof generalized gradient approximation 54 .
The plane-wave cutoff energy is set to be 500 eV. The 12 × 12 × 1 and 21 × 21 × 1 Monkhorst-Pack k-point meshes for the irreducible Brillouin zone sampling are used in the geometric optimization and subsequent self-consistent calculation of the heterostructures. Vacuum layers thicker than 15 Å are set along the normal direction to avoid the interaction between the top and bottom surfaces. The vdW interactions are treated using the DFT-D3 corrections 55 . The IP lattice parameters and atomic positions are fully relaxed until the Hellmann-Feynman force on each atom is less than 0.005 eV/Å.

Electron transport calculations
The IP FTJs are constructed along the IP polarization direction based on the relaxed In 2 Se 3 /SnTe heterostructures. The barrier region consists of several unit cells of In 2 Se 3 /SnTe, and the electrodes are treated using the virtual crystal approximation 51 where the In site of In 2 Se 3 is occupied by In 0.5 Sn 0.5 and the Sn site of SnTe is occupied by Sn 0.5 Sb 0.5 thus simulating the n-type doping. The electron transmissions across the FTJ are calculated within the general scattering formalism 56 as implemented in Quantum ESPRESSO 57 . The designed IP FTJs and the (In 0.5 Sn 0.5 ) 2 Se 3 /(Sn 0.5 Sb 0.5 )Te heterostructures are used as the scattering regions and semi-infinite leads, respectively. A uniform 50 × 10 k || -mesh is used to sample the twodimension Brillouin zone in transmission calculation.

DATA AVAILABILITY
The data that support the findings of the work is in the manuscript's main text and Supplementary Information. Additional data are available from the corresponding author upon reasonable request. Fig. 6 The partial charge densities. The Partial charge densities for the designed FTJs in the energy range from E F − 0.1 eV to E F for a P ↓ and b P ↑ state.
Z. Liu et al.