Based on the computational 2D materials database (C2DB)^[39,40], 2D transition metal phosphorus chalcogenides ABP₂X₆ (A = Au, Ag, Cu, etc.; B = In, Ga, Bi, etc.; X = S, Se, Te) with a D₃ symmetry were first created and screened by high-throughput DFT calculations using a series of feature parameters, including formation energy, bandgap, carrier effective masses, and FE polarization. The formation energy (E_f) of these 2D FE semiconductors was calculated as follows:

(1) $$ E_{f}=E_{tot}-\sum_{i} n_{i} \mu_{i} $$

where E_tot is the total energy of a given ABP₂X₆ monolayer structure, μ_i is the chemical potential of element i, and n_i is the number of atoms of element i. The corresponding lattice, electronic, and polarization parameters of optimized 2D ABP₂X₆ structures were listed in Supplementary Tables 1-3. Then, the computationally screened 2D ABP₂X₆ candidates were used to construct 2D VFSHs by vertically stacking them along the out-of-plane direction, as shown in Supplementary Figure 1. The allowed lattice mismatch of 2D VFSHs was smaller than 5%; their optimal interfacial structures were determined by an energy comparison of various potential configurations. According to the FE polarization orientation, these VFSHs can exhibit multiple stable polarization states, including ↑↑, ↑↓, ↓↑ and ↓↓ [Supplementary Figure 1]. The interfacial coupling strength of 2D VFSHs was determined by their interlayer binding energy (E_b) as follows:

(2) $$ E_{b}=E_{tot}-E_{F E 1}-E_{F E 2} $$

where E_tot is the total energy of a given 2D VFSH; E_FE1 and E_FE2 are the total energies of two FE layers in the heterojunction, respectively.

DFT calculations were carried out using the Vienna ab initio Simulation Package (VASP)^[41,42] as implemented by the projector augmented wave (PAW) method^[43]. The exchange-correlation functional was treated by the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) version^[44]. The interlayer interactions of 2D VFSHs were expressed by the PBE functional with the vdW correction in Grimme’s scheme (DFT-D3)^[45]. A plane-wave kinetic energy cutoff was set to 500 eV for the plane-wave expansion set, and a vacuum spacing of > 20 Å was inserted between adjacent slabs to eliminate spurious periodic interactions. The dipole corrections along the out-of-plane direction were also included in the calculations to remove artifacts arising from asymmetric periodic boundary conditions. The Monkhorst-Pack scheme was used for the k-point sampling in the Brillouin zone with the grid of 15 × 15 × 1 and 9 × 9 × 1 for 2D ABP₂X₆ monolayers and VFSHs, respectively. All structural models were fully relaxed until the energy and force acting on each atom were less than 10^-6 eV/atom and 10^-2 eV/Å, respectively. The CI-NEB method, incorporating six intermediate images, was used to determine the transition energy barrier between any two polarization states^[46]. The out-of-plane FE spontaneous polarization of 2D ABP₂X₆ was determined using the Berry phase method^[47]. Owing to the well-known fact that the PBE functional often underestimates the bandgap of 2D semiconductors, the electronic structures and optical properties of 2D ABP₂X₆ monolayers and VFSHs were calculated using the hybrid Heyd-Scuseria-Ernzerhof (HSE06) functional^[48]. Ab initio molecular dynamics (AIMD) simulations were performed to examine the thermodynamic stability of 2D ABP₂X₆ candidates. Here, a 3 × 3 supercell was used to expand the structural constraints, and the simulations were carried out in the canonical (NVT) ensemble for 10 ps with a 1.0 fs time step at 300 K. Since the AIMD simulations are highly time-consuming, a k-point mesh of 2 × 2 × 1 was used for the Brillouin-zone integration.

Electronic transport of 2D VFSH devices was simulated using the NEGF formalism as implemented by the Nanodcal package^[49]. The physical quantities were expanded in a linear combination of atomic orbitals (LCAO) basis at the double-zeta basis plus polarization (DZP) level^[50], and the exchange-correlation potential was expressed by the PBE functional. The plane-wave cutoff energy was set to 80 Hartree, and the energy convergence criterion for the Hamiltonian matrix was set to 10^-4 eV. The device models were constructed from the optimized 2D VFSHs, and they were composed of three regions: a central scattering region flanked by left and right electrodes. The device is periodic along the y direction, while the two electrodes are treated as semi-infinite along the x direction (extending to ±∞). The k-point mesh of the central scattering region and the electrode regions was set to 1 × 10 × 1 and 100 × 10 × 1, respectively. The tunneling equilibrium conductance (G) of the system was obtained using:

(3) $$ G=\frac{2 e^{2}}{h} \sum_{k_{x}} T\left(k_{x}, E\right) $$

The current was calculated using the Landauer-Bütttiker equation as follows^[51]:

(4) $$ I\left(V_{b}\right)=\frac{2 e}{h} \int_{\mu_{L}}^{\mu_{R}} T\left(E, V_{b}\right)\left[f_{L}(E)-f_{R}(E)\right] d E $$

where f_L(R) is the electron distribution function on the left (right) lead, V_b is the loading bias voltage, μ_L(R) is the potential of the left (right) lead, and T(E, V_b) is the transmission coefficient. To evaluate the FE polarization effect on the electronic transport of 2D VFSHs, the TER ratio of the device system was calculated as follows:

(5) $$ T E R=\frac{\left|I_{F E}-I_{A F E}\right|}{\left|\min \left(I_{F E}, I_{A F E}\right)\right|} \times 100 \% $$

where I_FE and I_AFE are the output current of 2D VFSH device in FE states (↑↑ or ↓↓) and AFE states (↑↓ or ↓↑), respectively. For the bias voltage V_ds = 0, the TER ratio was determined as follows:

(6) $$ T E R=\frac{\left|G_{F E}-G_{A F E}\right|}{\min \left(G_{F E}, G_{A F E}\right)} \times 100 \% $$

where G_FE and G_AFE are the tunneling electric conductance for the device in FE and AFE states, respectively.

The photocurrent of 2D VFSH devices was also calculated using a DFT framework combined with the NEGF formalism as implemented by the Nanodcal package mentioned above. The photocurrent flowing from the central scattering region to the electrodes can be written as^[52]:

(7) $$ \begin{aligned} J_{L}^{(p h)}=\frac{i e}{h} \int\left\{c o s^{2} \theta T_{r}\left\{\Gamma_{L}\left[G_{1}^{<(p h)}+f_{L}\left(G_{1}^{>(p h)}-G_{1}^{<(p h)}\right)\right]\right\}\right. \\ +\sin { }^{2} \theta T_{r}\left\{\Gamma_{L}\left[G_{2}^{<(p h)}+f_{L}\left(G_{2}^{>(p h)}-G_{2}^{<(p h)}\right)\right]\right\} \\ \left.\left.+\sin (2 \theta\right) 2 T_{r}\left\{\Gamma_{L}\left[G_{3}^{<(p h)}+f_{L}\left(G_{3}^{>(p h)}-G_{3}^{<(p h)}\right)\right]\right\}\right\} d E \end{aligned} $$

where G_1,2,3^>/<(ph) represents the retarded/advanced Green’s functions that include the photon-electron interactions, which are dependent on the photon frequency ω, photon flux I_ω. The photocurrent can be normalized as

(8) $$ \tilde{I}_{p h}=J_{L}^{(p h)} / e I_{\omega} $$

which still has a dimension of area, i.e., a₀²/ phonon, where a₀ is the Bohr radius and e is the electron charge. Here, the k-point mesh of 1 × 10 × 1 was used for the photocurrent transport calculation. Furthermore, the normalized photocurrent (I_ph) can be transformed into the photocurrent (I_ph) by considering optical power and illumination area as follows:

(9) $$ I_{p h}=e * I * A_{0} * \frac{P_{i n}}{E_{p h}} * \sqrt{\frac{\mu_{r}}{\xi_{r}}} $$

where P_in is the input optical power density, E_ph is the photon energy, A₀ is the area of laser spot, e is the electron charge, μ_r is the relative magnetic susceptibility, and ξ_r is the relative dielectric constant. It should be noted that the lattice of VFSHs was kept at the static optimization geometry, and the temperature effects related to the electron-phonon scattering, phonon-assisted transport, and thermally induced structural fluctuation were not included in the photocurrent calculations.

2D atomically thin ABP₂X₆ (A = Au, Ag, Cu, etc.; B = In, Ga, Bi, etc.; X = S, Se, Te) FE semiconductors are used to construct VFSHs since they exhibit an atomically thin structure, robust spontaneous polarization, and moderate bandgaps (1-3 eV)^[37,38]. The unit cell of 2D ABP₂X₆ is composed of (P₂X₆)^4- anion skeleton packed with A-site and B-site metal cations^[53]. The ferroelectricity of 2D ABP₂X₆ stems from the off-centering of A-site and B-site cations with antiparallel displacements with the layers [Figure 1A], which breaks the inversion symmetry that leads to upward and downward polarization (i.e., P_up and P_dn) states. The switchable spontaneous polarization induces a local built-in electric field that potentially changes the resistance state of FE channel from “0” to “1”. Therefore, the vdW integration of two different 2D ABP₂X₆ FE semiconductors into VFSHs includes at least four stable polarization states [Figure 1B], which offers a flexible platform to tailor the band alignment, electric conductance, and photoresponse by the polarization switching of dual FE semiconductor layers.

Based on the FE-driven tunable electronic and optoelectronic characteristics of 2D ABP₂X₆ VFSHs, they can be used to construct all-in-one optoelectronic architecture for multifunctional applications, as schematically illustrated in Figure 1C. On the one hand, the band alignment of 2D VFSHs can be potentially adjusted by the control of multiple polarization states, leading to a significant modulation of the channel resistance of the VFSH device. Such a behavior enables the VFSH device to achieve in-memory logic operation. On the other hand, reversible band-alignment transition in 2D VFSHs also allows the device to switch between positive and negative photocurrents under light illumination, which facilitates the realization of optoelectronic reconfigurable logic functions in a single device. The tunable polarity and magnitude of photocurrent in the VFSH device associated with the optical intensity, wavelength, and FE polarization states can be utilized to implement in-sensor BCP for sensing images^[54]. Nevertheless, the current work mainly focuses on the utilization of multiple stable polarization states to tailor the band alignment and optoelectronic properties of 2D ABP₂X₆ VFSHs, only offering a theoretical perspective of VFSH devices for multifunctional applications.

To find potential 2D VFSHs for the development of all-in-one device architecture, we first conducted high-throughput computational screening of highly stable ABP₂X₆ semiconductors with strong spontaneous polarization and superior electronic properties. The screening workflow and framework of 2D ABP₂X₆ VFSHs are illustrated in Figure 1D. To obtain highly stable atomically thin ABP₂X₆ FE semiconductors, a fundamental database including 249 initial structures is first established from C2DB^[39,40]. The ABP₂X₆ structures are constructed by varying A-site and B-site cations and X-site anions into CuInP₂S₆ (or Sn₂P₂S₆) template structure. All initial structures have been fully relaxed and then screened by the formation energy (E_f). Only the structures with negative E_f are further screened by a series of feature parameters, including the bandgaps (E_g), electron and hole carrier effective masses (m_e and m_h), and spontaneous polarization (P_S). In order to ensure that selected ABP₂X₆ structures are FE semiconductors with high carrier mobilities, their feature parameters need to satisfy the following conditions [Supplementary Figure 2]: (i) E_g < 3.0 eV, (ii) m_e < 0.5 m₀ and m_h < m₀, (iii) P_S > 2 μC/cm². The conditions (i) and (ii) ensure that the screened structures can be considered as semiconductor channel materials with high carrier mobilities, and condition (iii) enables the selected structures to have strong FE polarization. According to the above criteria, 11 stable ABP₂X₆ candidates with moderate bandgaps (1.58-2.98 eV), small carrier effective masses, and strong FE polarization (> 2.56 μC/cm²) are screened. Moreover, we find that these 2D ABP₂X₆ candidates, typically for CuInP₂S₆, AgInP₂S₆, and AuInP₂S₆, do not show obvious structural distortions after the AIMD simulations for 10 ps, verifying their high thermodynamic stability (see Supplementary Figure 3 for the details). The band structures of the 11 highly stable 2D ABP₂X₆ candidates and their lattice, electronic, and polarization parameters are presented in Supplementary Figure 4 and Supplementary Table 4, respectively. We find that the selected ABP₂X₆ candidates do not include Te-based structures due to their relatively weak structural stability and small spontaneous polarization.

Based on the screened 2D ABP₂X₆ FE semiconductors, 55 VFSHs are created by vertically stacking two different ABP₂X₆ structures along the out-of-plane direction. Since the device performance and functionality of VFSHs essentially depend on their electronic structures, we first reveal the effect of FE polarization on the band alignment of 2D ABP₂X₆ VFSHs. For a given VFSH, it can exhibit six possible band alignments classified into three types (i.e., type I, type II, and type III), as schematically illustrated in Figure 2A. Owing to switchable polarization in the dual FE layers, ABP₂X₆ VFSHs exhibit at least four stable polarization states, including ↑↑, ↑↓, ↓↑, and ↓↓. Among these polarization states, the ↑↑ and ↓↓ states indicate interlayer FE coupling, while the ↑↓ and ↓↑ states exhibit interlayer AFE coupling [Supplementary Figure 1]. The polarization switching of dual FE layers in 2D VFSHs potentially induces a series of band-alignment evolutions, which offers flexibility to tailor their electronic and optoelectronic properties for multifunctional device applications.

To verify whether the reversible band-alignment evolution of 2D ABP₂X₆ VFSHs can be achieved by manipulating their polarization states, we perform DFT calculations to determine the valence band maximum (VBM) and conduction band minimum (CBM) energies (i.e., E_V and E_C) of 11 screened 2D FE semiconductors relative to the vacuum level [Supplementary Figure 5]. Unlike the conventional 2D semiconductors, the E_V and E_C of 2D FE semiconductors are completely different at two surface terminations because of the band bending induced by the polarization field^[33]. This means that the polarization switching of each FE layer will potentially change the band-alignment type and band-offset values of 2D VFSHs. Based on the calculated E_V and E_C values, the band-alignment type of 55 2D VFSHs in four polarization states is predicted in Figure 2B. Here, the purple and cyan squares represent two type-I band alignments, and the orange and red squares denote two type-II band alignments [Figure 2A], respectively. It needs to be noted that the interlayer stacking of 2D VFSHs can potentially change the E_V and E_C of each FE layer in the heterojunctions due to the interface effect. However, the energy shift of E_V and E_C induced by the interface effect is usually not very large, so it can affect the prediction of band-offset values but scarcely change the band-offset type of 2D VFSHs. As shown in Figure 2B, the band alignment of 2D ABP₂X₆ VFSHs shows several important characteristics: (i) the band alignment transition in most of 2D ABP₂X₆ VFSHs can be driven by reversing the FE polarization states. For example, AuInP₂S₆/CuInP₂Se₆ VFSH exhibits a type-I band alignment in ↑↑ and ↑↓ states and has type-II band alignment in ↓↑, and ↓↓ states, respectively. However, the band alignment of not all of VFSHs can be changed by FE polarization switching. We find that nine VFSHs remain the type-I band alignment irrespective of FE polarization. (ii) The switching of FE polarization states can induce changes in both the bandgaps and band offsets (ΔE_V and ΔE_C) of all these VFSHs, regardless of band-alignment transition. For instance, AgInP₂S₆/CuInP₂S₆ VFSHs remain a type-II band alignment in both ↓↓ and ↑↓ states [Supplementary Figure 6], but the polarization switching from ↓↓ to ↑↓ state leads to the bandgap variation from 1.27 to 1.42 eV, and ΔE_V (ΔE_C) correspondingly changes from 0.19 eV (0.60 eV) to 0.06 eV (0.26 eV). This arises from the band bending or band inclination of dual FE layers as well as the band shift driven by the polarization-induced built-in electric field. (iii) Among the considered VFSHs, they do not exhibit type-III band alignments owing to their relatively large bandgaps (1.58-2.98 eV) and comparable work functions (4.94-5.85 eV). Specifically, the band bending induced by the electric polarization field is insufficient to induce a large band shift to achieve the crossover of band-edge states (i.e., type-III broken band alignment). The development of all-in-one optoelectronic devices requires screened 2D VFSHs with largely tunable bandgaps among different polarization states and a reversible band-alignment transition. The former allows for tailoring the photocurrent magnitude and the latter facilitates the control of photocurrent polarity for achieving reconfigurable optoelectronic properties. Therefore, the selected 2D VFSHs should exhibit a series of band-alignment evolutions, such as from type II, type I, to type II by manipulating the polarization states. Based on the above requirements, 19 VFSHs can be considered as potential candidates [Figure 2B]. Considering that selected 2D VFSHs should be experimentally synthesizable, CuInP₂S₆/AuInP₂S₆, AgInP₂S₆/CuInP₂S₆, and AuInP₂S₆/AgInP₂S₆ are optimal candidates for the exploration of multifunctional device applications since the constitutive 2D FE semiconductors have been experimentally demonstrated^[53,55].

Based on the above screening procedures, here we choose CuInP₂S₆/AuInP₂S₆ (CIPS/AIPS) VFSHs as a prototype to evaluate the feasibility of achieving reconfigurable electronic and optoelectronic devices by the manipulation of FE polarization states. The selection of CIPS/AIPS VFSHs is derived from their small lattice mismatch (3.1%), large interfacial binding energies (-3.12~-3.78 eV), multiple reversible band-alignment transitions, and superior electronic properties. The lattice, energetic, and electronic parameters of 2D CIPS/AIPS VFSHs in four polarization states (i.e., ↑↑, ↑↓, ↓↑, and ↓↓) are listed in Supplementary Table 5. The multistate polarization switching in 2D ABP₂X₆ VFSHs can be experimentally achieved using a vertical dual-gate device structure. The applied top and bottom gate voltages are used to control the polarization state of the dual FE layers in either P_up or P_dn, and the polarization switching of each FE layer between P_up and P_dn states can be triggered by reversing the polarity of the top and bottom gate voltages via an intermediate paraelectric (PE) state [Supplementary Figure 7]. The transition of polarization states is inherently associated with a cooperative displacement of A- and B-site cations in the dual FE layers. The switching characteristics of multiple polarization states in CIPS/AIPS VFSHs are investigated by calculating transition energy barriers of ionic movements between any two given polarization states by using the climbing image nudged elastic band (CI-NEB) method, as shown in Figure 3A. The energy barrier for activating the transition from ↑↑ to ↑↓ state is 0.82 eV through the polarization switching of the CIPS layer from P_up to P_dn state. Then, further FE switching of the AIPS layer from P_up to P_dn state induces the transition of polarization states from ↑↓ to ↓↓, which needs to overcome an energy barrier of 0.34 eV. In contrast, the polarization switching from ↓↓ to ↑↑ needs to proceed via the AFE ↓↑ state. As shown in Figure 3A, the energy barrier is 0.21 eV for driving the transition from ↓↓ to ↓↑ and 0.34 eV for activating the transition from ↓↑ to ↑↑ state, respectively. The moderate energy barriers (0.21-0.82 eV) not only ensure the stability of these polarization states in CIPS/AIPS VFSH but also allow for the manipulation of these polarization states by the external gate-voltage modulation.

We now turn to reveal the effect of polarization switching on electronic properties of CIPS/AIPS VFSHs. Figure 3B-E shows the projected band structures of CIPS/AIPS VFSH in four stable polarization states. The heterojunction has a type-II band alignment with a direct bandgap of 2.52 eV in the ↑↑ state. The spatial distribution of charge-density isosurfaces indicates that the CBM and VBM states are mainly contributed by AIPS and CIPS layers [Figure 3B], respectively, verifying that it is a type-II heterojunction. The transition of polarization state from ↑↑ to ↑↓ induces the band upshift of the AIPS layer and band downshift of the CIPS layer, resulting in the formation of a new type-II band alignment in the ↑↓ state [Figure 3C]. Specifically, the CBM state is mainly contributed by the CIPS layer while the VBM state is dominated by the AIPS layer, indicating a reverse carrier spatial distribution relative to the ↑↑ state. For the ↓↓ state, its band alignment is similar to that of the ↑↓ state (i.e., type II), but the conduction and valence band offsets (i.e., ΔE_C and ΔE_V) have been further increased compared with the band alignment of the ↑↓ state [Figure 3D], resulting in the smallest bandgap (2.40 eV). When the polarization state is switched to ↓↑, it indicates a type-I-like band alignment where the VBM state is contributed by the CIPS layer but the CBM state includes the contribution of both the CIPS and AIPS layers [Figure 3E]. In addition, we find that it remains a momentum-matched (or direct bandgap) heterojunction in all four polarization states, which contributes to high optical absorption efficiency and photoresponse.

In order to quantify the band-alignment evolution in CIPS/AIPS VFSHs, the CBM and VBM energies of the CIPS and AIPS layers in the four polarization states are presented in Figure 4A, where the polarization states evolve sequentially as ↑↑ → ↑↓ → ↓↓ (downward switching) and then ↓↓ → ↓↑ → ↑↑ (upward switching). The CBM (VBM) energy (i.e., E_C and E_V) of the AIPS layer firstly increases from -4.62 (-7.29) to -4.21 (-7.09) eV and the E_C (E_V) of the CIPS layer gradually decreases from -4.14 (-7.14) to -4.69 (-7.51) eV with a sequential switching of dual FE layers from P_up to P_dn states (i.e., from ↑↑ to ↓↓), resulting in an inversion of type-II band alignment in the VFSH. In contrast, the E_C and E_V of the AIPS layer decrease and those of the CIPS layer increase with a sequential switching of dual FE layers from P_dn to P_up states (i.e., from ↓↓ to ↑↑), also leading to the inversion of type-II band alignment in the VFSH. It should be noted that the intermediate ↓↑ and ↑↓ states serve as transition states connecting the two type-II alignments. In particular, the ↓↑ state exhibits the type-I-like band alignment shown in Figure 3E, in which the VBM is mainly contributed by the AIPS layer and the CBM involves contributions from both the CIPS and AIPS layers. This reversible band-alignment evolution between the two type-II states allows for the manipulation of the band edges and the spatial distributions of photogenerated carriers, which is essential for electronic and optoelectronic applications of 2D VFSHs. To understand the band alignment evolution induced by FE polarization switching, the electrostatic potential distribution (Φ) of the VFSH in different polarization states is calculated. For the VFSH in the ↑↑ state, the electrostatic potential shows an asymmetric distribution along the out-of-plane direction. Specifically, the vacuum level of CIPS termination is 0.48 eV higher than that of AIPS termination and the FE polarization points from CIPS to AIPS [Figure 4B], resulting in the band bending towards the polarization direction. Thus, the photogenerated electrons and holes can be spontaneously separated into the AIPS and CIPS layers respectively due to the existence of the built-in electric field. In contrast, for the VFSH in the ↓↓ state, the vacuum level of CIPS termination is 0.45 eV lower than that of AIPS termination [Figure 4C], enabling the FE polarization to point from AIPS to CIPS. Thanks to the band bending along the polarization direction, it shows a reverse spatial distribution of photogenerated carriers as compared to the ↑↑ state. For the ↑↓ and ↓↑ states, the VFSH exhibits the interlayer AFE configuration. Their electrostatic potentials display a nearly symmetric distribution along the out-of-plane direction due to the cancellation of the electric polarization field between the dual FE layers [Figure 4D and Supplementary Figure 8], resulting in smaller band bending in both the ↑↓ and ↓↑ states. Hence, a sequential switching of polarization states from ↑↑, ↑↓, to ↓↓ induces the band upshift of the AIPS layer and the band downshift of the CIPS layer [Figure 4E], while the FE polarization switching from ↓↓, ↓↑, to ↑↑ leads to a reverse band shift of the dual FE layers [Supplementary Figure 9]. Such a result confirms that the sequential polarization switching leads to a reversible type-II band alignment transition in the VFSH.

In addition to the manipulation of band alignment, the optical absorption ability of 2D VFSHs is also important for evaluating their potential in optoelectronic applications. The absorption spectra and optical absorptivity of CIPS/AIPS VFSH are presented in Supplementary Figure 10. The optical properties of independent CIPS and AIPS monolayers are also calculated for comparison. The absorption coefficients of VFSH in all polarization states are 10⁵-10⁶ cm^-1 from the visible (VIS) to the ultraviolet (UV) region and the maximum absorptivity arrives at ~30%, which are nearly two times larger than those of the freestanding CIPS and AIPS monolayers. This means that the formation of 2D VFSHs contributes to the promotion of optical absorption efficiency. Meanwhile, we find that the absorption coefficients and photoresponse range of CIPS/AIPS VFSH in four polarization states are very close. However, the four polarization states yield different band alignments that alter the spatial distribution of photogenerated carriers upon polarization switching, which enables the polarity-tunable photocurrent in VFSH devices. Such a result will be discussed later.

The FE polarization effect on the electrical transport of CIPS/AIPS VFSH is studied by using a transistor model in which the heterojunction is used as the channel and the four polarization states can be manipulated by loading bottom/top gate voltages through the piezoelectric force microscopy (PFM) tip in experiment, as schematically illustrated in Figure 5A. Here, quantum transport simulations are performed using the NEGF method within the DFT framework (see the Methods section for details). Figure 5B shows the output characteristic (I-V) curves of CIPS/AIPS VFSH devices in four polarization states. The output current (I_ds) of the device in all polarization states rises with increasing bias voltage (V_ds). It can be found that there exists a threshold voltage (V_th) in all polarization states due to their type-II (or type-I) band-alignment nature. Interestingly, the I_ds of two FE states (i.e., ↑↑ and ↓↓) is far larger than that of two AFE states (↑↓ and ↓↑) when V_ds is beyond 1.2 V. For instance, the I_ds of the ↑↑ and ↓↓ states arrives at 620-750 nA, while the I_ds of the ↑↓ and ↓↑ states is only 100-200 nA at V_ds = 2 V. The large discrepancy of I_ds can be understood by the transmission spectra of the VFSH device, as shown in Figure 5C. The transmission coefficients of two FE states are notably larger than those of two AFE states, which benefits from the polarization-induced band bending that facilitates electron tunneling via available conduction channels^[33]. Hence, the large I_ds of two FE states makes the device operate in a low resistance state (LRS), while the smaller I_ds of two AFE states corresponds to the device at a high resistance state (HRS). Considering the polarization states manipulated by the top and bottom gate voltages (V_TG and V_BG), the switching between HRS and LRS in the device can be achieved by alternating positive and negative V_TG and V_BG.

Owing to the large discrepancy in the output current between the FE and AFE states, the device exhibits a large TER ratio, as shown in Figure 5D. It should be emphasized that the TER values are ideal estimates from DFT-based quantum transport calculations. The ultrahigh TER values (10⁸%-10¹²%) obtained at small bias voltages (-1 V < V_ds < 1 V) mainly arise from the large difference in the near-zero off-state current between the FE and AFE states, which is associated with a relatively large bandgap of the VFSH (≥ 2.4 eV). Therefore, these ultrahigh TER values have little practical significance because of ultralow output current (I_ds < 1 nA). In order to ensure the device functionality, the VFSH device needs to work at a relatively larger V_ds. Typically, for 1 V < V_ds < 1.5 V, the device operates with a moderate output current in the ↑↑ and ↓↓ states (I_ds > 1 nA) and simultaneously exhibits relatively large TER values (~10⁶%) between the ↓↓ and ↑↓ states at the bias voltage of 1.5 V, enabling the realization of device logic functions. Figure 5E shows the I_ds of CIPS/AIPS devices in four polarization states at V_ds = 1.5 V. The I_ds of the device is 41, 0.01, 106, and 3 nA for ↑↑, ↑↓, ↓↓, and ↓↑ states, respectively. Using 10 nA as a benchmark, the I_ds is beyond the threshold value (i.e., I_th = 10 nA) as the logic output “1” and smaller than I_th as the logic output “0”. Thus, the VFSH device can be used to perform XNOR logic gate using V_TG and V_BG as the input ports with the sequence of 0-0, 1-0, 0-1, and 1-1, and the corresponding truth table for the XNOR gate operation is shown in Figure 5F. Here, the positive gate voltages (i.e., +V_TG and +V_BG) are defined as the logic input “1”, and the negative gate voltages (i.e., -V_TG and -V_BG) are defined as the logic input “0”. In addition, considering the plasticity of FE polarization, the I_ds of CIPS/AIPS device can be nonlinearly changed by short gate-voltage pulses; the device is also potential for simulating the post-synaptic neurons in a human neural network utilizing the FE-tuned conductance state as a synaptic weight.

The FE polarization effect on optoelectronic characteristics of 2D CIPS/AIPS devices is explored using a photodetector model in which light illumination on the VFSH induces the photocurrent through the photogalvanic effect (PGE), as schematically displayed in Figure 6A. Here, the device photocurrent is calculated by using the DFT framework combined with NEGF formalism (see the Methods section for details). The generation of photocurrent in semiconductor materials induced by the PGE is usually associated with their non-centrosymmetric structures. For CIPS/AIPS VFSHs, the polarization-induced built-in electric field can further amplify the PGE because of spontaneous separation of photogenerated electron–hole pairs driven by the built-in electric field, resulting in the generation of a finite photocurrent in the VFSH device without external bias voltage. As mentioned above, reversible type-II band-alignment transition in CIPS/AIPS devices has been demonstrated by the switching of polarization state from ↑↑ to ↓↓, resulting in a reverse distribution of photogenerated carriers in two polarization states [Figure 6B and C]. Such a characteristic allows for achieving reconfigurable photoresponse and optoelectronic logic functions via the utilization of polarity-tunable photocurrent in 2D CIPS/AIPS devices.

Figure 6D shows the normalized photocurrent ($$ \tilde{I} $$_ph) of the VFSH device in ↑↑ and ↓↓ states as a function of photon energy (E_ph) at zero bias voltage (i.e., V_ds = 0). The device exhibits a broadband photoresponse from VIS to UV in both ↑↑ and ↓↓ states, but it presents different magnitudes and reverse polarity of $$ \tilde{I} $$_ph in the two polarization states. Under illumination, the device in the ↑↑ state yields positive $$ \tilde{I} $$_ph in the range of 0-18.1 a₀²/photon as the photon energy increases from 1.5 to 4.0 eV, while the device in ↓↓ state produces negative $$ \tilde{I} $$_ph in the range of 0~-16.6 a₀²/photon. The positive and negative photoresponse arises from the FE-polarization-driven type-II band-alignment transition. To better understand the positive and negative photoresponse characteristics, the I_ph of the device in two polarization states under different optical intensities at E_ph = 2.6 eV (i.e., 477 nm) is plotted in Figure 6E. As the optical power density (P_in) rises from 1.0 to 2.5 W/m², the absolute value of I_ph increases from 0.98 to 2.45 nA at the ↑↑ state and from 0.67 to 1.70 nA at the ↓↓ state. The polarization-state-dependent positive and negative I_ph allows for manipulating the photogenerated carrier dynamics at the device level. On the other hand, there exists a large difference for the magnitude of I_ph between ↑↑ and ↓↓ states under most of illumination conditions [Figure 6D], suggesting that the transition of polarization states induces a change in not only the photocurrent polarity but also the magnitude of I_ph. In order to quantify the difference of I_ph between the two polarization states, the magnitude ratio of the normalized photocurrent (|I_↓↓/I_↑↑|) as a function of E_ph is plotted in Figure 6F. It can be seen that the |I_↓↓/I_↑↑| is 0.3-14.8 for E_ph in the range of 2.4-4.0 eV and reaches a maximum value of 14.8 at E_ph = 2.9 eV. Utilizing the light-dependent and FE-dependent I_ph, the CIPS/AIPS VFSH device can be theoretically used to implement reconfigurable in-sensor BCP for sensing images, as illustrated in Supplementary Figure 11. The input image can be described by the incident light with different intensities (P_in) and wavelengths. The output photocurrent I_ph can be expressed as I_ph = ΣR_jP_j, where R_i is the photoresponsivity of a pixel and it can be regarded as the convolution weight value^[54]. The in-sensor BCP is implemented by tunable R_i values for each pixel that is set to certain positive and negative values that correspond to different directions of photocurrent; they can be tuned by the polarization states through the top/bottom gate-voltage pulses. Thus, the convolutional kernels can be reconfigured into different kernels for describing input images. The weights used for the conversion process are encoded by the gate-voltage matrices, and the output I_ph corresponds to the weighted pixels in the input broadband images and represents the processed images. It should be emphasized that this work only provides a basic theoretical architecture; the practical feasibility for performing in-sensor BCP remains to be validated by further experimental investigations.

In addition to implementing in-sensor BCP applications, the reconfigurable positive and negative photoresponse can also be utilized to achieve complex optoelectronic logic operations. The optoelectronic logic gates are realized on the basis of a complementary CIPS/AIPS phototransistor consisting of a center drain and bilateral sources [Figure 6G], which actually includes two VFSH devices and two optical input terminations (i.e., A and B). The input light and polarization state of the VFSH are used to control the magnitude and polarity of photocurrent. Here, the logic input “0” represents the light-off state and the logic input “1” denotes the light-on state under the specified photon energy and optical intensity. The logic output is defined by the magnitude of the output photocurrent. More specifically, the logic output “0” corresponds to |I_ph| < 1 nA and the logic output “1” corresponds to |I_ph| ≥ 1 nA. Typically, for the polarization state of two VFSH devices in the ↑↑ state with E_ph = 2.6 eV and P_in = 2.0 W/m², the two optical terminations A-B with the input sequence of 0-0, 1-0, 0-1, and 1-1 induce an output sequence of 0, 1, 1, 1 [Figure 6H], which acts as an OR logic gate. Similarly, tuning the polarization state of the two VFSH devices in the ↓↓ state with E_ph = 2.6 eV and P_in = 1.0 W/m², the above input sequence will yield an output sequence of 0, 0, 0, 1 [Supplementary Figure 12], corresponding to an AND logic gate. When the polarization state of two VFSH devices is tuned into ↑↑ and ↓↓ states with E_ph = 2.6 eV and P_in = 2.0 W/m² [Figure 6I], the optical input sequence of 0-0, 1-0, 0-1, and 1-1 will yield an output sequence of 0, 1, 1, 0 [Figure 6J], indicating an XOR logic gate. It needs to be emphasized that these optoelectronic logic operations have been achieved at zero bias voltage. In principle, other optoelectronic logic gates can also be realized by combining with bias voltage modulation.