The giant tunneling electroresistance effect in monolayer In₂SSeTe-based lateral ferroelectric tunnel junctions

Abstract

Two-dimensional (2D) asymmetric Janus materials display in-plane and out-of-plane intrinsic ferroelectricity due to their asymmetrical structures, which makes them suitable for ferroelectric data storage devices. Herein, by performing density functional calculations combined with nonequilibrium Green function simulations, we systematically study the ferroelectric properties of the 2D Janus In₂SSeTe monolayer and the electronic transport properties of the related ferroelectric tunnel junctions (FTJs) by employing graphene/germanene as the electrode. It is highlighted that both ferroelectric states of graphene/In₂SSeTe heterostructures show Ohmic contact, which is beneficial for decreasing the power dissipation of devices. Furthermore, the tunneling electroresistance (TER) ratios of the In₂SSeTe-based FTJs increase with the length of the devices. Interestingly, the FTJs of 9 nm central scattering region length with graphene/In₂SSeTe and germanene/In₂SSeTe electrodes can achieve maximum TER ratios of 2.24 × 10⁷% and 2.98 × 10⁸%, respectively. We believe that our findings will shed light on the design and application of the In₂SSeTe monolayer in FTJ devices.

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Introduction

Ferroelectric tunnel junctions (FTJs), composed of two metallic electrodes separated by a thin ferroelectric material, have attracted global attention due to their potential applications in nonvolatile memory devices.^1–4 The spontaneous polarization of ferroelectric materials can be switched by an external electrical field, which results in the tunneling electroresistance (TER) effect in FTJs.^5–7 In the early years, FTJs with thin films of three-dimensional (3D) ferroelectric materials were employed as tunnel barriers.^8,9 Conventional 3D ferroelectric materials prefer perovskite structures, such as BaTiO₃ and PbTiO₄.^10,11 Up to now, a number of strategies have been put forward to achieve considerable TER ratios in conventional 3D FTJs. For example, a TER ratio of 400% at room temperature can be achieved in the BaTiO₃-based FTJ by reducing the BaTiO₃ layer thickness to two unit cells (∼0.8 nm).¹² By introducing Na (or Li) substitutions for Ti atoms at the right interface of Pt/BaTiO₃/Pt ferroelectric tunnel junctions, a TER ratio up to 10⁵% is achieved based on density-functional-theory calculations.¹³ Recently, by engineering the Schottky barrier at the Nb:SrTiO₃ interface, an optimum TER ratio of 6 × 10⁶ has been realized in Pt/BaTiO₃/Nb:SrTiO₃ FTJs.¹⁴ However, stability and reproducibility at room temperature are intractable obstacles to these conventional 3D FTJs, with the ever-growing commercial requirements of low-power and high-speed in nanoscale nonvolatile memory devices.^15,16 Besides, with the ferroelectric material reduced to the nanoscale size, the inhibiting effect of the depolarization field on the ferroelectric properties is more apparent.¹⁷ More importantly, the electronic coupling between the ferroelectric and electrode materials is greatly destroyed due to the dangling bonds and defects at the interface.¹⁸ Therefore, new ferroelectric materials that can eliminate the above problems are greatly sought after for developing high-performance FTJs.

The successful synthesis of graphene opened an emerging horizon to develop artificial two-dimensional (2D) materials.¹⁹ 2D materials show a lot of advantages in practical applications, such as ultrathin atomic thickness, smooth surfaces and the absence of dangling bonds on the surface.^20–22 Therefore, it is of interest to answer the question if 2D ferroelectric materials are good choices for overcoming the inherent disadvantages of 3D FTJs. A significant number of 2D ferroelectric materials, such as CuInP₂S₆,^23–25 α-In₂Se₃^26,27 and MX (M = Sn, Ge; X = S, Se),^28,29 have been prompted to possess in-plane or out-of-plane spontaneous polarization theoretically and experimentally. For instance, 2D CuInP₂S₆ is confirmed in the experiment to exhibit room temperature ferroelectricity with a transition temperature of ∼320 K, and the CuInP₂S₆/Si ferroelectric heterostructure has been demonstrated to exhibit good memory performance with an on/off ratio of ∼100.²⁴ Layered α-In₂Se₃ is predicted to maintain room-temperature out-of-plane polarized ferroelectric behavior with the thickness down to a single layer limit.²⁶ Recently, the out-of-plane ferroelectricity in van der Waals layered α-In₂Se₃ nanoflakes has been demonstrated experimentally.²⁷ Furthermore, some high-performance FTJs with 2D ferroelectric materials have been predicted in recent years.³⁰ A lateral FTJ based on the In- and Sb-doped SnSe monolayer with a large TER of 1460% has been proposed.³¹ Moreover, a giant TER ratio as high as 10⁴% is realized in ferroelectric tunnel junctions with top contact between Au(010) and In₂Se₃.³² The recent theoretical studies on a lateral 2D FTJ constructed by graphene and ferroelectric α-In₂Se₃ achieved an excellent TER ratio of ∼1 × 10⁸%, suggesting its potential for ferroelectric memory devices.³³ Nevertheless, the study of integrating ferroelectrics into devices is still in its infancy, and it is urgent to search for new 2D ferroelectric materials with distinguished device performance.

Among various 2D materials, asymmetric Janus 2D materials has caught a lot of attention because they display different fascinating characteristics on two opposite surfaces.^34,35 Janus MXY (M =Mo or W, X/Y = S, Se, or Te) monolayers show distinguished out-of-plane piezoelectric polarization, which reveals their potential applications in actuators, sensors and surface acoustic waves.³⁶ Besides, Janus In₂X₂Y (X/Y = S, Se, and Te) monolayers are predicted to be desirable in the overall water splitting and piezoelectric devices.³⁷ It is worth noting that Janus 2D materials display in-plane and out-of-plane intrinsic piezoelectricity and ferroelectricity, due to their asymmetric structures.³⁸ On the other hand, due to the outstanding transport properties of the Dirac fermions in graphene layers, graphene-based heterostructures show a conceptually new degree of flexibility in the design of materials and devices.^39–41 2D Dirac semimetals, like graphene and germanene, are promising atomically thin electrodes in designing novel devices.^42,43 Therefore, a systematical understanding of the corresponding Janus monolayer as well as the corresponding 2D Dirac semimetal heterostructures for application in FTJs is of great interest and importance.

Herein, inspired by the unique features of α-In₂Se₃ and the related Janus In₂X₂Y (X/Y = S, Se, and Te) monolayers,⁴⁴ which have excellent prospects for applications in multifunctional energy conversion, we construct a 2D Janus In₂SSeTe monolayer by replacing two different elements on the surfaces of the α-In₂S₃ monolayer to investigate the potential application in ferroelectric data storage devices. The phonon dispersion curves and AIMD simulations demonstrated the stability of two ferroelectric states of the In₂SSeTe monolayer. Furthermore, the tunneling electroresistance performances of the two types of FTJs are investigated using graphene/In₂SSeTe or germanene/In₂SSeTe electrodes. Meanwhile, the FTJs with different central scattering region lengths are considered to investigate the tunneling electroresistance performance versus the central scattering region lengths. Large TER ratios have been achieved in graphene and germanene-based FTJs, which verifies their great potential application in ferroelectric data storage devices.

Computational details

The different stacking configurations for In₂SSeTe/graphene and In₂SSeTe/germanene heterostructures were built using the ALKEMIE platform.^45,46 Based on the density functional theory (DFT) calculations, the structural relaxations were implemented in the Vienna ab initio Simulation Package (VASP).⁴⁷ The generalized gradient approximation (GGA) with the Perdew–Burk–Ernzerhof (PBE)⁴⁸ functional was adopted for the exchange and correlation potentials. The plane-wave cutoff energy was set to 500 eV, and 14 × 14 × 1 and 9 × 9 × 1 k-points were utilized for the optimization and self-consistent calculations of monolayers and heterostructures. The van der Waals interaction was described by the DFT-D3 method.^49,50 The vacuum thickness was set to 20 Å to avoid interlayer interaction. The convergence energies for electrons and forces for atoms were 1 × 10⁻⁶ eV and 0.01 eV Å⁻¹, respectively. The PHONOPY code⁵¹ was employed to study the lattice dynamic stabilities of monolayers. Besides, ab initio molecular dynamics (AIMD) simulations^52,53 were performed to understand the thermodynamic stability of monolayers and heterostructures. The dipole correction⁵⁴ was taken into consideration. The Heyd–Scuseria–Ernzerhof (HSE06)⁵⁵ hybrid density functional was employed for the calculation of electronic structures to get precise band gaps. The nudged elastic band (NEB)^56,57 method was employed to determine the energy barriers of the kinetic processes from P_↑ to P_↓ of monolayers and heterostructures.

The quantum transport calculations based on the nonequilibrium Green's function (NEGF)⁵⁸ of the FTJs were performed using the QuantumWise Atomistix Toolkit (QuantumATK) Q-2021.06 package.⁵⁹ The GGA-PBE functional with a linear combination of atomic orbitals (LCAO) norm-conserving PseudoDojo pseudopotential⁶⁰ was employed. The double-zeta basis set was employed to expand wave functions.⁶¹ The plane-wave cutoff of 105 Hartree was employed. The convergence criterion of the force was 0.01 eV Å⁻¹. The 7 × 1 × 128 and 7 × 1 × 1 Monkhorst k-point meshes were utilized for the self-consistent calculation of the electrodes and central scattering regions for the transport calculations, and the denser 121 × 1 Monkhorst-point meshes were used for the transport calculations. The tunneling conductance as a function of electron energy E is defined as⁶²

where is the k-point averaged transmission function at energy E, and T(k_‖,E) is the k-resolved transmission function with k_‖ = k_x. The tunnel electroresistance (TER) ratio is calculated by the formula⁶³where G_↑ and G_↓ are the tunneling conductances of the FTJs when the In₂SSeTe ferroelectric layer is in the up-polarized (P_↑) state and the down-polarized (P_↓) state, respectively.

Results and discussion

The In₂SSeTe monolayers were obtained by replacing S atoms on the surface terminations with Se and Te atoms in the ferroelectric α-In₂S₃ monolayer. Fig. 1(a) and (b) show the structures of two different ferroelectric states of the proposed In₂SSeTe monolayers, for which S atoms sitting right across the lower and upper In atoms are named as In₂SSeTe-P_↓ and In₂SSeTe-P_↑, respectively. The optimized lattice constants for In₂SSeTe-P_↓ and In₂SSeTe-P_↑ are 4.183 and 4.179 Å, respectively. To check the stability of the proposed In₂SSeTe monolayers, the phonon calculations and AIMD simulations were performed, as shown in Fig. S1 (ESI†). Minor imaginary frequencies at Γ points are observed from the phonon dispersion curves. Such minor imaginary frequency could be eliminated by using larger supercells or applying small strain,^64,65 revealing that In₂SSeTe-P_↓ and In₂SSeTe-P_↑ are stable from the lattice dynamic point of view. Besides, after annealing the In₂SSeTe monolayer for 9 ps at 300 K in AIMD simulations, the total energies of In₂SSeTe-P_↑ and In₂SSeTe-P_↓ are limited in a narrow window. Also, no significant distortion can be found in the final structures, demonstrating their thermal stabilities.⁶⁶ Therefore, both the phonon calculations and AIMD simulations confirm the stabilities of In₂SSeTe-P_↓ and In₂SSeTe-P_↑, which might verify their feasibility in the experiment. Furthermore, we unravel the electronic structures of the proposed In₂SSeTe monolayers. The band structures of In₂SSeTe-P_↓ and In₂SSeTe-P_↑ using the HSE06 method are exhibited in Fig. 1(c) and (d), respectively. Both ferroelectric states of In₂SSeTe show semiconducting electronic structure features. Herein, In₂SSeTe-P_↓ holds an indirect band gap, in which its conduction band minimum (CBM) is located at the Γ point, and its valence band maximum (VBM) is located between Γ and M points. On the other hand, In₂SSeTe-P_↑ has a direct band gap, where both the CBM and VBM are located at the Γ point. Interestingly, the predicted band gaps for In₂SSeTe-P_↓ and In₂SSeTe-P_↑ are 2.20 and 0.25 eV, respectively. The significant difference of band gaps will lead to different electron transmission capacities in the application of FTJ devices. It is worth noting that an appropriate electric field could induce the transition between In₂SSeTe-P_↓ and In₂SSeTe-P_↑, similar to In₂X₃ (X = S, Se, Te).⁶⁷ Therefore, In₂SSeTe is a promising candidate for ferroelectric switching devices.

Fig. 1 The structural schematic diagrams and HSE06 band structures of In₂SSeTe monolayers (a) and (c) for In₂SSeTe-P_↓, (b) and (d) for In₂SSeTe-P_↑.

Graphene and germanene possess hexagonal honeycomb structures (see Fig. S2(a) and (b), ESI†) with lattice constants of 2.46 Å and 4.06 Å, respectively. The graphene and 1 × 1 germanene unit cells show small lattice mismatches of 1.86% and 2.94% with the P_↓ state of the In₂SSeTe monolayer. The calculated band structures shown in Fig. S2(c) and (d) (ESI†) reveal their linearly dispersing electronic bands at the Fermi level, indicating the intrinsic high carrier mobility of the Dirac fermions in graphene and germanene.⁶⁸ Herein, we construct the lateral FTJs by employing graphene/In₂SSeTe and germanene/In₂SSeTe heterostructures as the electrodes. Before building the ferroelectric tunnel junctions (FTJs), In₂SSeTe with the P_↓ state regarded as the initial state was employed to construct the heterostructures with graphene or germanene to get the most favorable stacking configurations. For graphene/In₂SSeTe-P_↓ heterostructures, there are three types of stacking configurations, i.e., the atoms of In₂SSeTe-P_↓ located above either the centers of the hexagons, bonds, or C atoms. As depicted in Fig. 2, six different stacking configurations of graphene/In₂SSeTe-P_↓ heterostructures are considered due to two different termination surfaces (i.e., Se and Te terminated surfaces) of In₂SSeTe-P_↓. On the other hand, since each surface of In₂SSeTe-P_↓ has six different stacking configurations with germanene by shifting and rotating the upper germanene layers, there are twelve different stacking configurations for germanene/In₂SSeTe-P_↓ heterostructures, as shown in Fig. 3. To determine the most stable stacking configurations, the binding energies (E_b) and formation energies (E_f) of the heterostructures are calculated, which are defined as

E_b = (E^total_H − E^fix_upper − E^fix_bottom)/S (3)

E_f = (E^total_H − E_upper − E_bottom) (4)

where E^total_H represents the total energy of the heterostructure. E^fix_upper and E^fix_upper are the total energies of the upper and bottom monolayers constrained in the heterostructure lattice constants, respectively. S is the heterostructure interfacial area. And E_upper and E_bottom stand for the total energies of the freestanding upper and bottom monolayers, respectively. Tables 1 and 2 list the calculated results for graphene/In₂SSeTe-P_↓ and germanene/In₂SSeTe-P_↓ heterostructures with different stacking configurations, respectively. All the binding energies around −20 meV Å⁻² reveal that the different monolayers are connected by the long range van der Waals (vdW) force. Comparing the calculated E_b and E_f for graphene/In₂SSeTe-P_↓ and germanene/In₂SSeTe-P_↓ heterostructures, it is deduced that the interlayer binding force of the germanene/In₂SSeTe-P_↓ heterostructure is stronger than that of the graphene/In₂SSeTe-P_↓ heterostructure. In addition, the Se surface of In₂SSeTe-P_↓ is more energetically favorable to absorb on graphene and germanene than the Te surface. The most stable stacking configurations are Cen-Se type for the graphene/In₂SSeTe-P_↓ heterostructure and I-Se type for the germanene/In₂SSeTe-P_↓ heterostructure. As a result, we will focus on these stable configurations in the following analysis.

Fig. 2 The schematic diagrams of different stacking configurations for graphene/In₂SSeTe-P_↓ heterostructures.

Fig. 3 The schematic diagrams of different stacking configurations for germanene/In₂SSeTe-P_↓ heterostructures.

Table 1 The binding energies (E_b, meV Å⁻²) and formation energies (E_f, eV) of different stacking configurations for graphene/In₂SSeTe-P_↓ heterostructures

Stacking configuration	E b-Se	E b-Te	E f-Se	E f-Te
Bridge	−14.995	−14.398	−0.180	−0.171
Center	−15.308	−14.750	−0.186	−0.177
Top	−14.970	−14.359	−0.181	−0.171

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Table 2 The binding energies (E_b, meV Å⁻²) and formation energies (E_f, eV) of different stacking configurations for germanene/In₂SSeTe-P_↓ heterostructures

Stacking configuration	E b-Se	E b-Te	E f-Se	E f-Te
I	−23.482	−22.413	−0.316	−0.300
II	−18.922	−14.920	−0.243	−0.190
III	−15.454	−15.379	−0.200	−0.197
IV	−22.268	−22.285	−0.299	−0.298
V	−16.062	−15.516	−0.209	−0.199
VI	−17.507	−14.778	−0.223	−0.188

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The phase transition energy barriers of the polarization reversal processes are essential for the switching performance of ferroelectric devices.^69,70 The most effective polarization reversal pathway without an electric field connects the two degenerate states with different polarities.²⁶ Therefore, we calculated the phase transition process of the activation barrier against direct shifting of the central S layer using the climbing-image nudged elastic band (CINEB) method. As shown in Fig. 4, the energy barriers against direct shifting of the central S layer are 0.781, 0.778 and 0.722 eV per unit cell from In₂SSeTe-P_↓ to In₂SSeTe-P_↑, graphene/In₂SSeTe-P_↓ to graphene/In₂SSeTe-P_↑ and germanene/In₂SSeTe-P_↓ to germanene/In₂SSeTe-P_↑, respectively. On the other hand, the energy barriers of reverse processes are 0.782, 0.749 and 0.721 eV per unit cell from In₂SSeTe-P_↑ to In₂SSeTe-P_↓, graphene/In₂SSeTe-P_↑ to graphene/In₂SSeTe-P_↓ and germanene/In₂SSeTe-P_↑ to germanene/In₂SSeTe-P_↓, respectively. The calculated energy barriers of In₂SSeTe are about 0.7–0.8 eV per uc, which are lower than the results of In₂Se₃ (∼0.85 eV).²⁶ Interestingly, it can be deduced that the heterostructures are easier to realize polarization reversal than the In₂SSeTe monolayer.

Fig. 4 Kinetics pathways of polarization reversal processes of (a) In₂SSeTe, (b) germanene/In₂SSeTe heterostructures and (c) graphene/In₂SSeTe heterostructures.

In₂SeTe-P_↓ and In₂SeTe-P_↑ own different electrical conductivities due to their distinguishable electronic structures, which could be one of the physical origins to realize high TER ratios in the corresponding FTJs. At the same time, the different conducting states of the electrodes of graphene/In₂SSeTe and germanene/In₂SSeTe heterostructures can be another crucial reason for the huge TER ratios of these FTJs. Therefore, we turn our attention to the electronic structures of graphene/In₂SSeTe and germanene/In₂SSeTe heterostructures, and the results using HSE06 and PBE methods are plotted in Fig. 5 and Fig. S3 (ESI†), respectively. For graphene/In₂SSeTe-P_↓ and graphene/In₂SSeTe-P_↑ heterostructures, the projected band structures (PBSs) of graphene, In₂SSeTe-P_↓ and In₂SSeTe-P_↑ show the same shape as the band structures of their isolated monolayers using both methods. It is due to graphene and In₂SSeTe layers connecting with vdW force, which results in little hybridization between these two layers. The PBSs of heterostructures show an upward or downward shift compared with the band structures of the corresponding monolayers. For the PBSs of graphene/In₂SSeTe-P_↓ and graphene/In₂SSeTe-P_↑ heterostructures shown in Fig. 5(a) and (c), the PBS of graphene moves up with respect to the Fermi level, and that of In₂SSeTe possesses a conversely downward shift. As shown in Fig. 5(b), for germanene/In₂SSeTe-P_↓ heterostructures, the PBSs of graphene and In₂SSeTe move upward and downward, respectively. However, the PBSs of germanene and In₂SSeTe for germanene/In₂SSeTe-P_↑ heterostructures shown in Fig. 5(d) move downward and upward, respectively, which is converse to that of germanene/In₂SSeTe-P_↓ heterostructures. The different band structures for the different heterostructures are mainly determined by the interlayer charge transfers, as shown in Fig. S4 (ESI†). It can be seen that In₂SSeTe layers obtain electrons and graphene/germanene layers lose electrons for graphene/In₂SSeTe-P_↓, graphene/In₂SSeTe-P_↑ and germanene/In₂SSeTe-P_↓ heterostructures, hence the PBSs of In₂SSeTe and graphene or germanene show a downward and upward shift, respectively. Nevertheless, the germanene layer of germanene/In₂SSeTe-P_↑ heterostructures obtains electrons and the In₂SSeTe layer loses electrons, resulting in a converse shift of the projected band structures. Besides, it is noted that the PBSs of In₂SSeTe-P_↓ for graphene/In₂SSeTe-P_↓ and the PBSs of In₂SSeTe-P_↑ for graphene/In₂SSeTe-P_↑ heterostructures cross the Fermi level, resulting in Ohmic contacts, which can significantly improve the carrier transfer and injection efficiency.^71,72 For germanene/In₂SSeTe heterostructures, the PBSs of In₂SSeTe-P_↓ for germanene/In₂SSeTe-P_↓ heterostructures are separated by the Fermi level showing Schottky contact, which is not beneficial for the carrier transfer. Moreover, the PBSs of germanene/In₂SSeTe-P_↑ heterostructures show Ohmic contact, which is similar to the graphene/In₂SSeTe heterostructures. These results will lead to a more significant difference in conductivity between the P_↓ and P_↑ states of germanene-based FTJs, indicating that germanene-based FTJs might have a better performance than graphene-based FTJs.

Fig. 5 The projected band structures of (a) graphene/In₂SSeTe-P_↓, (b) germanene/In₂SSeTe-P_↓, (c) graphene/In₂SSeTe-P_↑ and (d) germanene/In₂SSeTe-P_↑ heterostructures using the HSE06 method.

To understand why graphene/In₂SSeTe and germanene/In₂SSeTe heterostructures show different charge transfer natures, we calculated the electrostatic potential of different isolated monolayers, as depicted in Fig. 6. The work function determines the direction of electron transfer when isolated monolayers form heterostructures,⁷³ as shown in the corresponding figures. For In₂SSeTe-P_↓ and In₂SSeTe-P_↑, the work functions of the Te surface of W_Te-P_↓/W_Te-P_↑ are different from those of the Se surface due to the broken spatial inversion symmetry. The different work functions on two surfaces will result in a built-in electric field (Δφ). The Δφ of In₂SSeTe with the P_↓ state is 1.49 eV, hence the direction of the electric field is from the Te surface to the Se surface. The Δφ of In₂SSeTe with the P_↑ state is 0.90 eV, hence the direction of the electric field is from the Se surface to the Te surface. Besides, the calculated work functions of graphene and germanene are 4.26 eV and 4.60 eV, respectively. When two different two-dimensional materials form a heterostructure, the electrons will flow from the lower work function side to the higher work function side until their Fermi levels are equal.⁷⁴ Therefore, the work functions of the Se surface of In₂SSeTe with P_↓ and P_↑ states are lower than those of graphene and germanene, and the Se surfaces of In₂SSeTe in graphene/In₂SSeTe-P_↓, graphene/In₂SSeTe-P_↑ and germanene/In₂SSeTe-P_↓ heterostructures lose electrons, while graphene/germanene layers gain electrons. Besides, the Se surface of In₂SSeTe in germanene/In₂SSeTe-P_↑ heterostructures gains electrons while graphene/germanene layers lose electrons, due to the work function of the Se surface of In₂SSeTe with P_↑ states being lower than that of germanene.

Fig. 6 The electrostatic potential of (a) and (b) monolayered In₂SSeTe with P_↓ and P_↑, (c) graphene (W_gr) and (d) germanene (W_ge).

By employing graphene/In₂SSeTe and germanene/In₂SSeTe heterostructures as the electrodes and In₂SSeTe monolayer as the central scattering region, the FTJ models with different polarizations of In₂SSeTe (P_↓ and P_↑) namely Gr-P_↓, Gr-P_↑, Ge-P_↓ and Ge-P_↑ FTJs are constructed as shown in Fig. 7. To comprehensively investigate the transport properties versus the lengths of the central scattering region in FTJs, we calculated the electronic transport-related behavior of such FTJs with the central scattering region lengths of 5 nm, 7 nm and 9 nm. The zero-bias transmission coefficient curves are shown in Fig. 8. For the transmission coefficient curves of Gr-P_↓ FTJs, there is a sharp dip at −1 eV below the Fermi level and a sharp rise near the Fermi level. As a result, the energy region from −1 eV to −0.2 eV has much lower transmission coefficients. For the transmission coefficient curves of Gr-P_↑ FTJs, there is a sharp dip at −0.1 eV below the Fermi level, and the transmission coefficient curves dip to a much deeper level with the central scattering region length increasing from 5 nm to 9 nm. On the other hand, there are two small trenches for the transmission coefficient curves of the Ge-P_↑ FTJs with different central scattering region lengths located at the Fermi level and around 0.2 eV, respectively. The lowest transmission region of Ge-P_↓ FTJs occurred at −0.4 to −0.1 eV, which shows a distinct magnitude difference from the Ge-P_↑ FTJs and implies that huge TER ratios will be achieved below the Fermi level. There is a sharp rise around the Fermi level, and the transmission coefficients are almost coincident when the energy is higher than 0.2 eV, indicating a sharp drop of TER ratios.

Fig. 7 The schematic diagrams of the FTJs with downward (P_↓) and upward (P_↑) polarization. (a) Gr-P_↓ and (b) Gr-P_↑ FTJs, for the graphene/In₂SSeTe heterostructure as electrodes. (c) Ge-P_↓ and (d) Ge-P_↑ FTJs for the germanene/In₂SSeTe heterostructure as electrodes. The lengths of the central scattering regions are set to 5 nm, 7 nm and 9 nm, respectively.

Fig. 8 The zero-bias transmission coefficient curves for (a), (c) and (e) graphene(Gr)-based FTJs, (b), (d) and (f) germanene (Ge)-based FTJs with the central scattering region lengths of 5 nm, 7 nm and 9 nm.

The zero-bias tunnel electroresistance (TER) ratio curves with the energy region from −1.5 eV to 1.5 eV are shown in Fig. 9. The results of graphene-based and germanene-based FTJs are given in the left and right panels, respectively. It should be noted that the highest TER ratios occurred at around −0.7 eV and −0.4 eV for graphene-based and germanene-based FTJs, respectively. The values of the highest TER ratios increase exponentially with the length of the central scattering region. Table 3 summarizes the calculated transmission coefficients and TER ratios at the Fermi level of the Gr-P_↓ (T_Gr-P↓), Gr-P_↑ (T_Gr-P↑), Ge-P_↓ (T_Ge-P↓) and Ge-P_↑ (T_Ge-P↑) FTJs. Herein, the transmission coefficients for the FTJs with P_↑ states are much higher than those of the P_↓ states, resulting in an apparent TER effect. The best performances are found at the FTJs with 9 nm central scattering region length for both graphene-based and germanene-based FTJs due to their huge TER ratios of 2.24 × 10⁷% and 2.98 × 10⁸%, respectively. Besides, the calculated TER ratios reveal that germanene-based FTJs have better application potential than graphene-based FTJs, regardless of the thickness of the devices, which agrees well with our previous electronic structure analysis.

Fig. 9 The zero-bias tunnel electroresistance (TER) ratio curves for (a), (c) and (e) graphene(Gr)-based FTJs; (b), (d) and (f) germanene (Ge)-based FTJs with the central scattering region lengths of 5 nm, 7 nm and 9 nm.

Table 3 The transmission coefficients and TER ratios at the Fermi level for the Gr-P_↓ (T_Gr-P↓), Gr_-P_↑ (T_Gr-P↑), Ge-P_↓ (T_Ge-P↓) and Ge_-P_↑ (T_Ge-P↑) FTJs

Central scattering region length	T Gr-P↓	T Gr-P↑	TER ratio	T Ge-P↓	T Ge-P↑	TER ratio
5 nm	1.25 × 10^−6	4.06 × 10^−4	3.24 × 10^4%	3.55 × 10^−9	8.63 × 10^−6	2.43 × 10^5%
7 nm	1.88 × 10^−8	4.94 × 10^−5	2.63 × 10^5%	2.54 × 10^−11	6.45 × 10^−7	2.54 × 10^6%
9 nm	1.33 × 10^−10	2.99 × 10^−5	2.24 × 10^7%	1.49 × 10^−13	4.42 × 10^−7	2.98 × 10^8%

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In order to better understand the behaviors of transmission states and transmission channels, the eigenfunctions of 5 nm, 7 nm and 9 nm FTJs for the Fermi level and (k_x, k_y) = (0, 0) wave vector space were calculated and are plotted in Fig. 10, Fig. S5 and S6 (ESI†), respectively. The transmission channels of the electrons in P_↑ and P_↓ states are shown as 3D contour plots, the isosurface value is chosen to be 0.02 e.u., which is sufficient to show the contribution of each atom. As shown in Fig. 10(a) and (c), the transmission eigenstates of Gr-P_↓ and Ge-P_↓ FTJs decay from the left electrode to the right electrode, resulting in electronic states that are only localized at the left part of FTJs. In this case, the electrons cannot pass from the left to the right electrode, and the FTJs are in a high resistance state. As depicted in Fig. 10(b) and (d), the transmission eigenstates of Gr-P_↑ and Ge-P_↑ FTJs can be found in the whole FTJs, revealing that the electrons can flow effortlessly from the left electrode and right electrode, and this is a typical conductive mode.

Fig. 10 The contour plot of the transmission eigenstates at the Fermi level and (k_x, k_y) = (0, 0) of (a) Gr-P_↓, (b) Gr-P_↑, (c) Ge-P_↓ and (d) Ge-P_↑ FTJs with the central scattering region length of 5 nm. The isosurface value is 0.02 a.u.

Conclusion

In summary, based on density functional theory and the nonequilibrium Green's function method, we systematically studied two types of lateral ferroelectric tunnel junctions (FTJs) by employing Janus monolayer In₂SSeTe as the central scattering region and In₂SSeTe/graphene or In₂SSeTe/germanene as electrodes. The constructed FTJs have different electrical conductivities when In₂SSeTe of the FTJs has P_↓ and P_↑ states, resulting in an apparent tunneling resistance effect. Except for In₂SSeTe with P_↓ and P_↑ states of the central scattering regions showing different electrical conductivities due to the difference in monolayer band structures, the different conducting behaviors of In₂SSeTe in the electrode regions can be another crucial reason for the huge TER ratios. Further analysis indicates that the different conducting behaviors of In₂SSeTe in the electrodes arise from the difference in work functions of the two surfaces of In₂SSeTe. To determine the length dependence on the performance of FTJs, we investigated the electronic transport-related behavior of graphene and germanene-based FTJs with 5 nm, 7 nm and 9 nm central scattering region lengths. The results show that the TER ratios of both types of FTJs increased with the increase of the device length, and the maximum TER ratios were 2.24 × 10⁷% and 2.98 × 10⁸% for graphene and germanene-based FTJs with 9 nm central scattering region length. These results reveal that such FTJs show great potential application in nonvolatile memory devices.

Author contributions

Zhou Cui: Investigation, formal analysis, and writing – original draft. Ting Li: data curation, and validation. Rui Xiong: data curation and validation. Cuilian Wen: visualization, formal analysis, and writing – review & editing. Yinggan Zhang: formal analysis and writing – review & editing. Jingying Zheng: formal analysis and writing – review & editing. Bo Wu: writing – review & editing. Baisheng Sa: project administration, supervision, and writing –review & editing.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

This work was supported by the National Key Research and Development Program of China (No. 2022YFB3807200), the National Natural Science Foundation of China (No. 21973012, 21905050 and 52201022), the Natural Science Foundation of Fujian Province (No. 2021J06011, 2020J01351, 2020J01474, 2021H6011 and 2021J01590), and the ‘‘Qishan Scholar’’ Scientific Research Project of Fuzhou University.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2ma01079h

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