Reversible doping polarity and ultrahigh carrier density in two-dimensional van der Waals ferroelectric heterostructures

Abstract

Van der Waals semiconductor heterostructures (VSHs) composed of two or more two-dimensional (2D) materials with different band gaps exhibit huge potential for exploiting high-performance multifunctional devices. The application of 2D VSHs in atomically thin devices highly depends on the control of their carrier type and density. Herein, on the basis of comprehensive first-principles calculations, we report a new strategy to manipulate the doping polarity and carrier density in a class of 2D VSHs consisting of atomically thin transition metal dichalcogenides (TMDs) and α-In₂X₃ (X = S, Se) ferroelectrics via switchable polarization field. Our calculated results indicate that the band bending of In₂X₃ layer driven by the FE polarization can be utilized for engineering the band alignment and doping polarity of TMD/In₂X₃ VSHs, which enables us to control their carrier density and type of the VSHs by the orientation and magnitude of local FE polarization field. Inspired by these findings, we demonstrate that doping-free p−n junctions achieved in MoTe₂/In₂Se₃ VSHs exhibit high carrier density (10¹³−10¹⁴ cm⁻²), and the inversion of the VHSs from n−p junctions to p−i−n junctions has been realized by the polarization switching from upward to downward states. This work provides a nonvolatile and nondestructive doping strategy for obtaining programmable p−n van der Waals (vdW) junctions and opens the possibilities for self-powered and multifunctional device applications.

Graphical abstract

Keywords

van der Waals heterostructures / ferroelectric polarization / carrier type / band alignment / density-functional theory

1 Introduction

Semiconductor heterostructures (SHSs) are a basic building block for electronic and optoelectronic devices since they not only combine the properties and functionalities of constituent materials but also exhibit various exotic effects due to the interfacial interactions [1-3]. Traditional synthetic methods of SHSs, such as chemical and physical epitaxial growth, suffer from the limitation of lattice mismatch that easily leads to the formation of interface defects and lattice disorders, which greatly restricts their device applications [4, 5]. Emerging 2D layered semiconductor materials, such as transition metal dichalcogenides (TMD) [6,7], black phosphorus (BP) [8], and group-VA elements and compounds [9], provide a state-of-the-art approach to design SHSs via van der Waals (vdW) integration. Owing to the dangling-bond-free surface with weak interlayer interactions, the integration of these 2D materials into vdW semiconductor heterostructures (VSHs) without the limitation of lattice mismatch. Hence, VSHs offer a large degree of freedom for the device design with desired interface structures and band alignments and become an ideal platform for exploring novel physical properties [10,11]. A typical example is twisted TMD VSHs that possess unconventional moiré excitons and charge density wave (CDW) state [12,13]. Great achievements have been made in the last years on the synthesis of 2D VSHs, such as MoS₂/WS₂ [14], MoSe₂/WSe₂ [15], SnSe/MoS₂ [16], and SnS/SnS₂ [17], and BP/MoS₂ [18]. 2D VSHs exhibit huge potential for nanoelectronics and optoelectronics, including light emitting diodes, field-effect transistors, photodetectors, memories, lasers, and solar cells, etc. [19,20].

The device applications of 2D VSHs depend on the manipulation of the type, density, and spatial distribution of charge carriers. The impurity doping is the most common way to produce charge carriers by means of intentional introduction of impurity atoms into the host lattice. However, this approach implemented in 2D semiconductors remains a large challenge due to their ultrathin atomic structures and limited physical space [21]. In particular for the heavy doping, excessive incorporation of impurities into 2D host lattices easily causes severe structural damage and lattice disorder [22]. Therefore, various new doping strategies were developed to program the carrier type and concentration of 2D materials, including chemical intercalation [23], surface charge transfer [24], electron-beam irradiation [25], laser light illumination [26], and electrostatic doping [27, 28]. However, most of these doping methods inevitably introduce chemical species or induce the formation of lattice defects [23-26], consequently resulting in the degeneration of device performance. Moreover, the polarity and transfer characteristics of p−n junctions are difficult to be changed once these doping methods have been implemented in 2D semiconductors and VSHs [29]. Although the gate-tuned electrostatic doping method provides a flexible way to tune the charge carriers, it requires an additional voltage to maintain the type and density of carriers therefore is volatile [30]. Hence, the development of nonvolatile and nondestructive doping ways to realize p-n junctions in atomically thin semiconductor materials is highly desired.

Because of atomic-scale thickness and ultraflat surface, the band structures of 2D vdW crystals and heterostructures are sensitive to the modulation of external and local electric fields. Considering that an external electric field cannot provide a nonvolatile doping way for the control of charge carriers, the creation of a local electric field is an alternative strategy to achieve this goal. Ferroelectric materials possess a spontaneous polarization that can be reversed by an electric field stimulus. Therefore, the integration of 2D semiconductors on ferroelectric (FE) substrates create a local and nonvolatile electric polarization field at the interface [31], which can be used to modulate the carrier type and density of 2D channel materials without sacrifice of their intrinsic physical properties. For example, the selective p- and n-type doping in atomically thin TMDs such as MoS₂, MoTe₂, and WSe₂ have been demonstrated on a series of FE substrates, including BiFeO₃ [32], PbTiZrO₃ [33], LiNbO₃ [34], Na_0.5Bi_4.5Ti₄O₁₅ [35], and P(VDF-FrFE) [36,37]. However, most of FE materials require a large thin-film thickness to maintain their polarization due to the depolarization field effect [38], which is incompatible with the trend of device minimization. Moreover, the insulator nature of FE oxides with large band gap (> 3.5 eV) [39] makes them difficult to be integrated into SHSs as the channel materials for device applications. Instead, the rapid development of 2D layered FE materials such as CuInP₂S₆ [40], In₂Se₃ [41], SnS [42], and MoTe₂ [43] brings new possibility for the realization of nonvolatile doping by means of a local electric polarization field. Some 2D ferroelectrics exhibit robust spontaneous polarization down to single-layer limit [42-44]. Especially for 2D α-In₂X₃ (X = S, Se) ferroelectrics, they are semiconductors with the band gap range of 1.4−2.8 eV [45]. Therefore, the combination of 2D semiconductors (e.g., TMDs and BP) with α-In₂X₃ ferroelectrics into FE VSHs can induce several aspects of advantages compared with other types of SHSs. (i) The dangling-bond-free surfaces lead to the formation of VSHs with a sharp atomic interface that is conductive to the doping modulation by the local polarization-field. (ii) The switchable FE field can be used to engineer the band alignment of the VSHs, including type-I (straddling gap), type-II (staggered gap), and type-III (broken gap) [46], which is essential for exploiting multifunctional devices. (iii) The ultrathin structure of FE VSHs is adapted to the trend of device minimization. Although the FE polarization field has been confirmed as a feasible way for regulating the carrier density and type in 2D semiconductors, the FE polarization effect on the band alignment, doping polarity, and carrier density in 2D FE VSHs remains unexplored.

In this work, we report a nonvolatile doping strategy in 2D ferroelectric VSHs consisted of TMD monolayers (MoSe₂ and MoTe₂) and experimentally available α-In₂X₃ (X = S, Se) nanosheets. The local FE polarization-field effect on the band alignment and carrier density of TMD/In₂X₃ VSHs is systematically studied by the first-principles calculations. Different from conventional 2D semiconductors, there is a layer-by-layer band shift in α-In₂X₃ semiconductors induced by the FE polarization field, which creates a favorable condition for the modulation of band alignment and carrier density in TMD/In₂X₃ VSHs. We demonstrate that free-doping and nonvolatile p−n or p−i−n junctions with ultrahigh carrier concentration (10¹³−10¹⁴ cm⁻²) can be achieved in MoTe₂/In₂Se₃ VSHs, and their carrier type and spatial distribution can be modulated by the control of FE polarization states. These findings suggest huge potential of 2D MoTe₂/In₂Se₃ VSHs for self-powered multifunctional device applications.

2 Methods

2.1 Computational details

All density functional theory (DFT) calculations were performed in the Vienna ab initio Simulation Package (VASP) code with the projector augmented wave (PAW) method [47]. The electronic exchange-correlation energy was treated by the generalized-gradient approximation (GGA) functional in the form of Perdew−Burke−Ernzerh (PBE) [48]. The vdW interactions were treated with the DFT-D3 correction in Grimme’s scheme [49]. A kinetic energy cutoff was set to 500 eV for the plane-wave expansion set. A vacuum layer of more than 20 Å along the z-axis (or out-of-plane) direction was added to avoid the interactions between adjacent periodic slabs. Since the PBE functional usually underestimates the band gap of semiconductors, electronic structures of all 2D structures were predicted by the hybrid functional of Heyd−Scuseria−Ernzerhof (HSE06) [50]. The dipole correction along the z-axis direction was adopted to meet the convergence criterion. The Monkhorst−Pack scheme was used for the k-point sampling in the Brillouin zone with the grid of 16 × 16 × 1 for 2D materials and 12 × 12 × 1 for 2D VSHs, respectively. All geometry optimization was carried out using the conjugate-gradient method and the convergence criteria of energy and force was set to 10⁻⁴ eV/atom and 10⁻² eV/Å, respectively. The out-of-plane electric polarization was evaluated by using the Berry phase method [51]. Bader charge analysis was performed to examine the interfacial charge transfers [52].

2.2 Heterostructure models

Prior to constructing In₂X₃/TMD (X = S, Se) VSHs, the geometrics of 2D freestanding TMD monolayers (i.e., MoSe₂ and MoTe₂) and α-In₂X₃ (X = S, Se) were firstly optimized. For hexagonal H-phase TMD monolayers, the optimized in-plane lattice constant a is 3.32 Å and 3.55 Å for the monolayer MoSe₂ and MoTe₂, respectively. α-In₂X₃ (X = S, Se) nanosheets also possess hexagonal lattice with the atom sequence of Se−In−Se−In−Se in each layer. The optimized lattice constant a is 3.95 Å and 4.11 Å for α-In₂S₃ and α-In₂Se₃, respectively. The increase of layer number from the monolayer to tetralayer brings few changes of the in-plane lattice constants (< 0.1 Å). Based on the optimized 2D freestanding structures, 2D In₂X₃/TMD VSHs were created by vertically stacking a (2 × 2) TMD monolayer on a ($\sqrt{3}$ × $\sqrt{3}$) α-In₂X₃ nanosheet, which makes that the lattice mismatch of all considered VSHs is less than 2.7%. According to the polarization orientation, TMD/In₂X₃ VSHs were classed into TMD/In₂X₃(↑) and TMD/In₂X₃(↓), respectively. The optimal interfacial configuration of each In₂X₃/TMD VSH was obtained by the energy comparison [see Fig. S1 in the Electronic Supplementary Material (ESM) for details]. The interfacial interactions of the VSHs were determined by calculating interfacial binding energies (γ_int) as follows:

(1)${\gamma }_{\mathrm{i}\mathrm{n}\mathrm{t}}=(E_{\mathrm{t}\mathrm{o}\mathrm{t}}-E{}_{\mathrm{T}\mathrm{M}\mathrm{D}}-E{}_{\mathrm{I}{\mathrm{n}}_2{\mathrm{X}}_3})/S_A,$

where $E_{\mathrm{t}\mathrm{o}\mathrm{t}}$, $E_{\mathrm{T}\mathrm{M}\mathrm{D}}$, $E_{\mathrm{I}{\mathrm{n}}_2{\mathrm{X}}_3}$ are the total energies of a given In₂X₃/TMD VSH, monolayer TMD monolayer, and α-In₂X₃ nanosheet, respectively, S_A is the interfacial area. The optimized lattice parameters and energetic data of MoTe₂/In₂Se₃ and MoSe₂/In₂S₃ VSHs were listed in Tables S1 and S2 of the ESM, respectively.

2.3 Calculation of carrier density

The carrier density of electrons (σ_n) and holes (σ_p) in 2D semiconductors and VSHs was determined as follows [46]:

(2)${\sigma }_{\mathrm{n}}={\displaystyle \frac{4\pi m_e^{\ast }kT}{h^2}}\mathrm{l}\mathrm{n}\left[1+\mathrm{e}\mathrm{x}\mathrm{p}\left({\displaystyle \frac{E_{\mathrm{F}}-E_{\mathrm{C}}}{kT}}\right)\right],$

(3)${\sigma }_{\mathrm{p}}={\displaystyle \frac{4\pi m_h^{\ast }kT}{h^2}}\mathrm{l}\mathrm{n}\left[1+\mathrm{e}\mathrm{x}\mathrm{p}\left({\displaystyle \frac{E_{\mathrm{V}}-E_{\mathrm{F}}}{kT}}\right)\right],$

where m_e^* (m_h^*) is electron (hole) effective mass, T is the temperature, k is Boltzmann constant, h is Plank constant. E_F−E_C and E_V−E_F are the separation from Fermi level to CBM and VBM, respectively, and they can be directly extracted from the calculated band structures. The m_e^* and m_h^* were calculated from the band curvature at the CBM and VBM, respectively, by using the following formula [46]:

(4)${\displaystyle \frac{1}{m^{\ast }}}={\displaystyle \frac{1}{{\hslash }^2}}{\displaystyle \frac{{\mathrm{d}}^{2}E(k)}{\mathrm{d}{k}^2}},$

where E(k) is the energy of band-edge states (VBM and CBM) at wave-vector k, and $\hslash$ is the reduced Plank constant.

3 Results and discussion

3.1 Polarization effect on electronic properties of 2D In₂X₃ ferroelectrics

Before addressing the FE polarization effect on the band alignment and carrier density of 2D TMD/In₂X₃ VSHs, it is necessary to first understand ferroelectric and electronic properties of 2D layered α-In₂X₃ (X = S, Se) nanosheets. Fig.1(a) shows atomic structures of In₂X₃ nanosheets in α and β phases. The α-In₂X₃ nanosheets have a hexagonal lattice with asymmetric distribution of X−In−X−In−X atomic layers in each In₂X₃ sheet that causes spontaneously aligned electric dipoles along the out-of-plane direction, which is responsible for the formation of FE polarization. According to the polar-axis orientation, the FE polarization can be divided into downward and upward states (P_down and P_up), respectively. In contrast, the X−In−X−In−X atomic arrangement in β-In₂X₃ nanosheets is spatially symmetric along the out-of-plane direction [Fig.1(a)], which makes β-In₂X₃ nanosheets as paraelectric (PE) phase without spontaneous polarization. When α-In₂X₃ nanosheets are loaded by an external electric field, their polarization orientation can be switched between the P_down and P_up states via the PE phase. The intrinsic FE polarization leads to a build-in electrostatic field in α-In₂X₃ along the out-of-plane direction, which can be confirmed by electrostatic potential distributions (EPDs). The electrostatic potential (Φ) of a trilayer (3L) α-In₂Se₃ nanosheet shows an asymmetric distribution [Fig.1(b)], resulting in an electrostatic potential difference (ΔΦ) of 3.20 eV between two surface terminations and electric dipole moment (μ) of 1.01 Deby. The similar results have been appeared in other 2D α-In₂X₃ (Fig. S2 in the ESM). For β-In₂Se₃ nanosheets, their Φ shows completely a symmetric distribution along the out-of-plane direction (Fig. S3 in the ESM) and corresponding ΔΦ and μ values are zero. Hence, ΔΦ and μ values reflect the magnitude of spontaneous polarization in In₂X₃ ferroelectrics. We plot the μ of eight 2D α-In₂X₃ as a function of ΔΦ in Fig.1(c). There is a nearly linear relationship between ΔΦ and μ, and it can be fitted by an expression μ = 0.33ΔΦ. So a large ΔΦ means the accumulation of more surface dipole charges, which corresponds to a large polarization field. Hence, the intrinsic polarization of α-In₂S₃ is correspondingly stronger than that of α-In₂Se₃. For example, based on Berry-phase method [51], the intrinsic polarization (P) is 1.41 μC/cm² and 1.09 μC/cm² for monolayer α-In₂S₃ and α-In₂Se₃, respectively. In addition, the increase of layer number leads to the increase of ΔΦ and μ values in 2D α-In₂X₃ ferroelectrics. Nevertheless, the ΔΦ and μ values are gradually saturated when the layer number is beyond 3L (Fig. S4 in the ESM), which agrees well with previous report about the thickness-dependent polarization in 2D α-In₂Se₃ [53].

Fig.1 Atomic structures and intrinsic polarization of 2D α-In2X3 ferroelectrics. (a) Top and side views of the atomic structure of trilayer In2X3 nanosheets in FE and PE phases. The arrows ↓ and ↑ denote the ferroelectric α-In2X3 nanosheet in Pdown and Pup states, respectively. The rhombic frames represent the range of a unit cell. The blue and orange balls denote In and X atoms, respectively. (b) The average EPD (Φ) of a trilayer α-In2Se3 along the out-of-plane direction. Here ΔΦ denotes the electrostatic potential difference between two surface terminations. (c) The μ of 2D α-In2X3 ferroelectrics as a function of ΔΦ.

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The local FE polarization-field effect on electronic properties of 2D α-In₂X₃ is evaluated by their band structures and density of states (DOS) obtained by the HSE06 functional. Fig.2(a) presents the projected band structure and DOS of a trilayer α-In₂Se₃. It seems that it is a metal due to the lack of band gap. Actually, each In₂Se₃ layer in the trilayer structure remains semiconducting characteristic with the band gap values of 1.4−1.5 eV, but there is a layer-by-layer band shift [Fig.2(a)]. More specifically, the top-layer bands indicate a notable upward shift relative to the bottom-layer ones when the polarization direction points from the bottom layer to the top layer. The charge-density isosurface distributions of the trilayer α-In₂Se₃ display that its conduction band minimum (CBM) and valence band maximum (VBM) are dominated by the bottom-layer and top-layer electronic states [Fig.2(b)], respectively. The result confirms the layer-by-layer band shift induced by the polarization field [i.e., so-called quantum-confined Stark (QCS) effect] that drives the separation of electron and hole wave functions. Hence, there is an inclined band structure or band bending in the trilayer α-In₂Se₃ nanosheet [Fig.2(c)]. Similar results can be also found in other 2D α-In₂X₃ structures (Fig. S5 in the ESM).

Fig.2 Polarization effect on electronic properties of 2D α-In2X3 nanosheets. (a) Projected band structure and DOS of a trilayer α-In2Se3 nanosheet obtained by the HSE06 functional. The Fermi level is set to the energy zero point. (b) Charge density isosurfaces of CBM and VBM states in the trilayer α-In2Se3 nanosheet. (c) Schematic of the polarization-induced layer-by-layer band shift in a trilayer α-In2X3 nanosheet. (d) Band-edge energies of eight 2D α-In2X3 structures relative to the vacuum level. EC and EV correspond to the energy of CBM and VBM, respectively. The arrows indicate the polarization direction.

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In order to offer a comprehensive understanding of the polarization effect on the band alignment of 2D α-In₂X₃ ferroelectrics, their band-edge energies (E_C and E_V) relative to the vacuum level are plotted in Fig.2(d). Different from the conventional 2D semiconductors (e.g., TMDs), all 2D α-In₂X₃ (X = S, Se) structures possess inclined band alignment along the direction of polar axis. Their band gaps (E_g) show a rapid reduction with increasing layer number due to the cooperation of quantum size effect and QCS effect. For example, the E_g is 1.43, 0.11, and 0 eV for the monolayer (1L), bilayer (2L), and trilayer (3L) α-In₂Se₃, respectively. Moreover, the VBM energy of top-layer In₂X₃ is higher than the CBM energy of bottom-layer In₂X₃ when the thickness is beyond 2L due to the layer-by-layer band shift, consequently leading to the formation of self-doped p−n junctions in 2D α-In₂X₃ [54]. Moreover, the self-doping characteristics can be stabilized even if the layer thickness is further increased due to the Fermi-level pinning caused by the crossover of band-edge states between the top and bottom layers.

3.2 Band alignments and tunable carrier types in TMD/In₂X₃ VSHs

Thanks to the polarization-induced band bending (or layer-by-layer band shift) in 2D α-In₂X₃ (X = S, Se) ferroelectrics, the integration of them with the conventional 2D semiconductors (e.g., MoSe₂ and MoTe₂) creates the possibility to control their band alignments and carrier distribution via switchable FE polarization. We selected 2D MoTe₂/In₂Se₃ VSHs as an example to demonstrate the polarization-field effect on their electronic structures and doping polarity, and the thickness of α-In₂Se₃ layer in the VHSs is considered from 1L to 4L. The VSHs were constructed by vertically stacking a 2 × 2 MoTe₂ monolayer on $\sqrt{3}$ × $\sqrt{3}$ α-In₂Se₃ nanosheets for the minimization of lattice mismatch. Based on the polar-axis orientation (P_down and P_up), the VSHs were classified into MoTe₂/In₂Se₃(↓) and MoTe₂/In₂Se₃(↑) (Fig.3). The interfacial structure of each VSH was determined by the energy comparison among six potential interfacial configurations (see Fig. S1 in the ESM for details), and the most stable one was selected for the study of electronic properties. The optimized lattice and energetic parameters of the lowest-energy VSHs in P_down and P_up states are listed in Tables S1 and S2. All MoTe₂/In₂Se₃ VSHs have negative interfacial binding energies (γ_int), indicating that the formation of vdW heterojunctions is energetically favorable. Moreover, the γ_int values of these VSHs (−0.32− −0.45 J/m²) are comparable with other 2D vdW crystals (−0.2− −0.5 J/m²) [55], indicating the heterointerfaces are interacted by the vdW force. By comparison, the γ_int of MoTe₂/In₂Se₃(↓) VSHs is correspondingly larger than that of MoTe₂/In₂Se₃(↑) ones, resulting in relatively small interlayer distances (d = 3.39−3.44 Å) in MoTe₂/In₂Se₃(↓) VSHs due to stronger interfacial interactions. The difference of interfacial interactions between the two types of VSHs plays an important role in the determinization of their band alignments, which will be discussed later.

Fig.3 Top and side views of the atomic structure of 2D MoTe2/In2Se3 VSHs in Pdown and Pup states. The solid frames denote the supercells of α-In2Se3 and MoTe2 used for the construction of VSHs, and the dash frames denote the primitive cell of α-In2Se3 and MoTe2. T-In2Se3 and B-In2Se3 denote the top-layer and bottom-layer In2Se3, respectively.

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We now turn to reveal the local polarization-field effect on the band alignment of 2D MoTe₂/In₂Se₃ VSHs. Fig.4 shows the projected band structures and DOS of MoTe₂/In₂Se₃(↑) VSHs calculated by the HSE06 functional. For MoTe₂/1L-In₂Se₃(↑) VSH [Fig.4(a)], it exhibits a typical type-II band alignment in which the CBM and VBM states are contributed by the α-In₂Se₃ and MoTe₂ layers, respectively. The thickness increase in In₂Se₃ layer brings two notable changes in band structures [Fig.4(a)−(c)]: (i) the band gap of In₂Se₃ layer rapidly decrease and disappear due to the size and QCS effects, (ii) the MoTe₂-layer bands show a downward shift towards the low-energy direction. It seems that the increase of In₂Se₃ layer induces the band-alignment transition from the type-II to type-I, to metallic, but the results of projected DOS indicate that the interfacial band alignment of all the VSHs possesses the type-II characteristic. For example, for MoTe₂/2L-In₂Se₃(↑) VSH, the band-edge states of the top-layer In₂Se₃ (T-In₂Se₃) and MoTe₂ layer exhibit a staggered distribution, indicating the type-II band alignment [Fig.4(b)]. Similar result has also been appeared in other VSHs in P_up state. The band bending of In₂Se₃ layer induced by the polarization field makes the electron accumulation at T-In₂Se₃ near the interface of VSHs, especially for the light irradiation condition [Fig.4(d)]. Owing to the existence of build-in electric field, the thickness increase of In₂Se₃ layer will drive the separation of electrons and holes onto T-In₂Se₃ and B-In₂Se₃, respectively. Moreover, the carrier density of the VSHs can be enhanced by the thickness increase of In₂Se₃ layer, resulting in the formation of self-doped p−n junctions in the In₂Se₃ layer. Nevertheless, the distribution of band-edge states in MoTe₂/In₂Se₃(↑) VSHs has few changes when the thickness of In₂Se₃ layer is beyond 3L (Fig. S6 in the ESM), which arises from the crossover of band-edge states. Therefore, the band alignment and doping polarity of the VSHs will be similar to that of MoTe₂/3L-In₂Se₃(↑) VSH [Fig.4(c)] even if the thickness of In₂Se₃ layer is further increased.

Fig.4 Band alignments of 2D MoTe2/In2Se3(↑) VSHs with the thickness range of In2Se3 layer from 1L to 3L. (a−c) Projected band structure and DOS of VSH with (a) 1L-In2Se3, (b) 2L-In2Se3, and (c) 3L-In2Se3. The red and blue bands denote the contribution from In2Se3 and MoTe2 layers, respectively. The horizontal dash lines denote the position of Fermi level. T-In2Se3, M-In2Se3, and B-In2Se3 represent the top-layer, middle-layer, and bottom-layer In2Se3 in the VSHs, respectively. (d) Schematic of band alignments of MoTe2/In2Se3(↑) VSHs. The black and gray arrows denote the carrier transport direction and polarization direction, respectively.

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Fig.5 displays the project band structures and DOS of MoTe₂/In₂Se₃(↓) VSHs. Contrary to the case of MoTe₂/In₂Se₃(↑) VSHs, the CB- and VB-edge states of MoTe₂/In₂Se₃(↓) VSHs are contributed by the B-In₂Se₃ and MoTe₂ layers, respectively. The CBM positions of all these VSHs are lower than the Fermi level and their VBM positions are higher than the Fermi level, leading to the formation of p-MoTe₂/n-In₂Se₃ vdW junctions. Interestingly, all these VSHs have type-II interface band alignment based on the result of projected DOS. Different from the conventional type-II SHSs, the electrons and holes can be rapidly separated into two surface terminations of the VSHs due to the effect of FE polarization field. Hence, the VSHs behave as self-doped p−i−n junction along the polarization direction [Fig.5 (d)]. The tunable band alignments and self-doping characteristic have been also found in 2D MoSe₂/In₂S₃ VSHs (see Figs. S7 and S8 in the ESM), suggesting that the FE polarization field can be regarded as an efficient way to tune the carrier type and density in 2D ferroelectric VSHs.

Fig.5 Band alignments of 2D MoTe2/In2Se3(↓) VSHs with the thickness range of In2Se3 layer from 1L to 3L. (a−c) Projected band structure and DOS of VSH with (a) 1L-In2Se3, (b) 2L-In2Se3, and (c) 3L-In2Se3. The red and blue bands represent the contribution of In2Se3 and MoTe2 layers, respectively. The horizontal dash lines denote the position of Fermi level. T-In2Se3, M-In2Se3, and B-In2Se3 represent the top-layer, middle-layer, and bottom-layer In2Se3 in the VSHs, respectively. (d) Schematic of band alignments of MoTe2/In2Se3(↓) VSHs. The arrows indicate the polarization direction.

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In order to reveal the effect of FE polarization on the band alignment and doping polarity of MoTe₂/In₂Se₃ VSHs, their EPDs and interface charge transfers have been investigated. Fig.6(a) indicates the EPDs of MoTe₂/3L-In₂Se₃ VSH in two polarization states. The electrostatic potentials (Φ) at two surface terminations of the VSHs are different due to the existence of a polarization field. The calculated ΔΦ of MoTe₂/3L-In₂Se₃(↑) VSH (3.26 eV) largely approaches that of freestanding 3L-In₂Se₃ (3.20 eV) but is far large than that of MoTe₂/3L-In₂Se₃(↑) VSH (1.61 eV). Similar results can be also found in other VSHs [Fig.6(b)]. The reduction of ΔΦ implies that the polarized charges of In₂Se₃ layer have been partially counteracted by interfacial charge transfers, weakening the FE polarization field [56]. To examine the interfacial charge transfers, the differential charge densities of MoTe₂/3L-In₂Se₃ VSHs in two polarization states have been calculated [Fig.6(c)]. The red and green charge-density isosurfaces denote the charge accumulation and depletion, respectively. It can be clearly identified the charge localization at T-In₂Se₃ and the charge depletion at the MoTe₂ layer for the VSH in P_down state, corresponding to the electron transfer (~0.27 e) from the MoTe₂ layer to T-In₂Se₃ based on the analysis of Bader charges. In contrast, the charge accumulation and depletion at the interface of MoTe₂/3L-In₂Se₃ in P_up state are relatively small. Bader analysis shows few charge transfers (~0.1 e) from the T-In₂Se₃ layer to the MoTe₂ layer. In addition to the charge transfers, the interfacial electron tunneling is another important factor for the change of ΔΦ in the VSHs. For the VSHs in P_up state, they present the type-II band alignment [Fig.4(d)]. Hence, the valence electrons of the MoTe₂ layer cannot spontaneously transfer into the In₂Se₃ layer due to the interfacial energy barriers. This is the reason why the layer-dependent ΔΦ of MoTe₂/In₂Se₃(↑) VSHs is very similar to that of the isolated α-In₂Se₃. In contrast, for the VSHs in P_down state, the CBM position of the bottom-layer In₂Se₃ is lower than the VBM position of the MoTe₂ layer when the layer number of In₂Se₃ is beyond 1L [Fig.5(d)], resulting in a type-III band alignment between the bottom-layer In₂Se₃ and the MoTe₂ layer. Hence, the electrons can be tunneled from the MoTe₂ layer into the In₂Se₃ layer, which weakens the FE polarization field. Therefore, the ΔΦ values of MoTe₂/In₂Se₃(↓) VSHs are far smaller than those of the isolated α-In₂Se₃. The similar results have been also found in MoSe₂/In₂S₃ VSHs.

Fig.6 Average electrostatic potential (Φ) and interfacial charge transfer of MoTe2/In2Se3 VSHs. (a) Electrostatic potential distribution of MoTe2/3L-In2Se3 VSH in Pup (red line) and Pdown (blue line) states. (b) Electrostatic potential differences (ΔΦ) of MoTe2/In2Se3 VSHs and isolated In2Se3 nanosheets as a function of In2Se3 layer thickness. (c) The charge-density difference and interfacial charge transfer (Q) of MoTe2/3L-In2Se3 VSH in Pdown (left) and Pup (right) state.

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3.3 Polarization-tuned carrier density and spatial distribution in TMD/In₂X₃ VSHs

To qualitatively describe the polarization-induced self-doping effect in TMD/In₂X₃ VSHs, the carrier density of MoTe₂/In₂Se₃ VSHs in two polarization states have been calculated. The density of electrons (σ_n) and holes (σ_p) of the VSHs in P_up and P_down states as a function of temperature are plotted in Fig.7(a) and (b), respectively. The intrinsic carrier density of MoTe₂ monolayer has been also provided for the comparison. For MoTe₂/In₂Se₃(↑) VSHs [Fig.7(a)], the σ_n and σ_p are sensitive to the variation of In₂Se₃ layer. For instance, σ_n increases from ~10⁻² to 4.3 × 10¹³ cm⁻² and σ_p increases from ~10⁶ to 1.2 × 10¹³ cm⁻² with the thickness increase of In₂Se₃ layer from 1L to 3L at the room temperature (298 K). Here it needs to be mentioned that the further increase of In₂Se₃ layer (e.g., >3L) does not significantly change the σ_n and σ_p values due to the Fermi-level pinning induced by the crossover of band-edge states mentioned above. In contrast, the carrier density of MoTe₂/In₂Se₃(↓) VSHs displays a relatively smaller change with the variation of In₂Se₃ layer. Moreover, the carrier density of the VSHs is not very sensitive to the temperature change [Fig.7(b)]. For example, σ_n largely keeps at 2.1 × 10¹², 4.2 × 10¹³, and 6.7 × 10¹³ cm⁻² and σ_n basically maintains at 1.6 × 10¹¹, 4.8 × 10¹³, and 8.3 × 10¹³ cm⁻² for the VSH with 1L-, 2L-, and 3L-In₂Se₃, respectively. The results originate from the formation of tunneling p−n junctions [Fig.5(d)] where the carrier transport is dominated by the tunneling mechanism [57]. The similar result has been demonstrated in the tunneling BP/ReS₂ p−n heterojunctions [58]. Moreover, the carrier density of MoTe₂/In₂Se₃ VSHs is far larger than that of the pristine MoTe₂ (< 10⁶ cm⁻²). Importantly, the doping level in TMD/In₂X₃ VSHs induced by the local FE polarization exceeds most of electrically and chemically modified TMD junctions, including lateral MoTe₂ homojunction [(3−5) × 10¹² cm⁻²] [59], MoTe₂/MoS₂ VSHs (10¹¹−10¹² cm⁻²) [60], lateral WSe₂/MoSe₂ heterojunctions (10¹¹ cm⁻²) [61], and WSe₂/MoS₂ VSHs (~10¹² cm⁻²) [62].

Fig.7 Polarization-dependent carrier density in 2D MoTe2/In2Se3 VSHs. The σn (solid lines) and σp (dash lines) of MoTe2/In2Se3 VSHs in (a) Pup state and (b) Pdown state. The VSH-nL (n = 1−3) denote the MoTe2/In2Se3 VSH with nL-In2Se3 layer. The spatial distribution of (c) σn and (d) σp in MoTe2/3L-In2Se3 VSH along the FE switching pathway from the Pup state, PE phase, to Pdown state.

Full size|PPT slide

In addition to the promotion of carrier density, the polarization switching can be also used to manipulate the carrier spatial distribution of TMD/In₂X₃ VSHs. For example, the electrons and holes of MoTe₂/In₂Se₃(↑) tend to be localized at T-In₂Se₃ and B-In₂Se₃ layers, respectively. While the polarization switching into P_down state leads to the carrier separation into the MoTe₂ and B-In₂Se₃ layers. In order to better insight into the evolution of carrier spatial distribution in TMD/In₂X₃ VSHs during the polarization switching, we used MoTe₂/3L-In₂Se₃ VSH as an example and plotted its spatial distribution of carrier density isosurfaces along the phase transition pathway from the P_up state to the PE state to the P_down state, as shown in Fig.7(c) and (d). The corresponding band structure evolution of MoTe₂ and In₂Se₃ layers in the VSH associated to the sequential phase switching has been presented in Fig. S9. When the polarization state transforms from the P_up state to the PE state, the FE polarization of In₂Se₃ layer will be gradually reduced to zero. The layer-by-layer band shift in the In₂Se₃ layer is weakened and the band-edge-states of MoTe₂ layer indicate an upward shift in this process (Fig. S9 in the ESM). Hence, we observe the electron delocalization from the T-In₂Se₃ layer to the whole In₂Se₃ layer [Fig.7(c)] and the hole localization from the B-In₂Se₃ layer to the MoTe₂ layer [Fig.7(d)], respectively. The decreased FE polarization leads to the reduction of σ_n and σ_n in this process due to the carrier delocalization and band shift. When the polarization state transforms from the PE state to the P_down state, the FE polarization of In₂Se₃ layer will be gradually enhanced. The band-edge states of In₂Se₃ layer are changed from degenerate into dispersed with a layer-by-layer shift (Fig. S9 in the ESM), promoting the electron localization in the B-In₂Se₃ layer. The enhanced polarization and band bending are responsible for the increase of σ_n and σ_n in the process [Fig.7(c) and (d)]. The results suggest that the carrier density and spatial distribution of TMD/In₂X₃ VSHs can be simultaneously modulated by the FE polarization switching.

4 Conclusions

In summary, we have theoretically demonstrated the feasibility to modulate the band alignment and spatial carrier density of 2D TMD/In₂X₃ VSHs via switchable FE polarization. Our calculated results indicate that the layer-by-layer band shift of In₂X₃ layer driven by the FE polarization field induces TMD/In₂X₃ VSHs with tunable band alignments and doping polarities, which enables us to manipulate the carrier type and density in the VSHs by the control of polarization orientation and magnitude. Based on this strategy, nonvolatile vdW p−n junctions have been achieved in MoTe₂/In₂Se₃ VSHs with ultrahigh carrier density (10¹³−10¹⁴ cm⁻²). Moreover, the switching of FE polarization from P_up to P_down state can lead to the transition of the VSHs from n−p junctions to p−i−n junctions. This work provides a new doping strategy for modulating the carrier type and density of 2D VSHs without any structural damages, paving the way for exploiting versatile 2D electronics and optoelectronics.

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Electronic supplementary materials

Supplementary materials (interfacial configurations and stabilities of 2D TMD/In₂X₃ VSHs, electrostatic potentials and band structures of 2D α-In₂X₃ nanosheets, thickness effect on projected band structures of MoTe₂/In₂Se₃ VSHs, band alignments of MoSe₂/In₂S₃ VSHs, and the band evoltion of In₂Se₃ and MoTe₂ layer in MoTe₂/In₂Se₃ VSHs associated to the ferroelectric phase transition) are available in the online version of this article at http://doi.org/10.1007/s11467-022-1244-4 and https://journal.hep.com.cn/fop/EN/10.1007/s11467-022-1244-4.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 62174151 and 61775201) and the Fund of Zhejiang Provincial Natural Science Foundation of China (Grant No. LZ22F040003 and LY22A040002). Computational resources from the Shanghai Supercomputer Center are acknowledged.

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