Ferroionic heterostructures with reconfigurable free-energy surface and band alignment across CuInP₂S₆ van der Waals interface with boron nitride and graphene

Abstract

Two-dimensional ferroelectric semiconductors with nonvolatile polarization hold great promise for next-generation electronics and photovoltaics. Here, we report reconfigurable band alignment in van der Waals heterostructures based on CuInP₂S₆ (CIPS) combined with hexagonal boron nitride (h-BN) and graphene (GR), arising from coupled ionic displacement and ferroelectric polarization. Driven by the Cu⁺ ion-related energy landscape, the ferroelectric polarization order acts as a “pump” that modulates interfacial charge transfer, band alignment configurations, and carrier transport barriers in ferroionic heterostructures. In the h-BN/CIPS stack, polarization switching converts the band alignment from type-H to type-II and reduces the switching barrier to ∼230 meV across the insulating interface. In contrast, in the GR/CIPS heterostructure, it transforms an n-type Schottky barrier into a quasi-Ohmic contact while preserving bistable polarization behavior up to 370 K and producing an asymmetric switching potential with a barrier height of ∼260 meV. These findings highlight the distinct modulation of electronic structure and transport characteristics under different contact environments for ferroionic heterostructures.

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New concepts

We introduce a two-dimensional van der Waals (vdW) ferroionic heterostructure in which ferroelectric polarization, coupled with local ionic displacements, enables reconfigurable band alignments. Unlike conventional approaches that treat ferroelectricity as a static electrostatic boundary, our strategy exploits ion-driven polarization in CuInP₂S₆ (CIPS) as an active and reversible “pump” that modifies interfacial interactions, enabling reversible tuning of band alignment types and carrier transport barriers. A key feature of this mechanism is its strong dependence on the contact environment. Ferroelectric switching in h-BN/CIPS is found to induce a type-H to type-II band alignment transition with a reduced barrier, whereas in GR/CIPS, the same switching process leads to a transition from a Schottky contact to a quasi-Ohmic contact, accompanied by bistable polarization switching observed up to 370 K under simulation conditions. The results highlight the coupled role of ionic dynamics and interfacial contacts in governing ferroionic responses, and provide a mechanistic picture for understanding tunable electronic properties in ferroionic heterostructures. These findings suggest the potential for contact-dependent control of interfacial transport characteristics in vdW systems.

Introduction

Two-dimensional (2D) ferroelectric (FE) materials, possessing tunable polarization field, have attracted significant attention for their ability to modulate carrier densities and enhance anomalous photovoltaic effects.^1–3 Layered materials such as monochalcogenides (SnS, SnSe),^4–6 dichalcogenides (MoTe₂, WTe₂),^7,8 α-In₂Se₃,^9,10 and CuInP₂S₆ (CIPS)^11,12 exhibit remarkable ionic displacive responses under an electric field. Their intrinsic electric-field-driven ionic ordering provides an additional degree of freedom for modulating the redox potential in FE-based catalysts with tailored catalytic environments^13–15 and offering screening ability for nonvolatile memory.^16–18 Amongst all 2D FE systems, CIPS is unique and highly appealing due to its ideal Curie temperature, which is near room temperature.^19,20 It exhibits reversible out-of-plane (OOP) polarization controlled by the OOP displacements of Cu⁺ cations^21–23 for forming FE states,^24,25 and demonstrates a duality of electric polarization and electric-field-driven high ionic conductivity.^26,27 Due to its moderate band gap, FE CIPS has been employed in constructing nonvolatile memories^28–31 and in generating bulk photovoltaic effect that potentially surpass the Shockley–Queisser limit.³²

2D ferroelectronic materials typically function in conjunction with other materials by forming heterostructures. The electronic band alignment between 2D ferroelectrics and electrode/nanoalloys (e.g., Au, Cu), or passivating 2D layers (such as hexagonal boron nitride and graphene, hereafter abbreviated as h-BN and GR), governs the redox and photoelectric performance of these hybrids.³³ A built-in potential, which is reversible under an external poling field, forms within CIPS upon contact with GR.³² In a recent study, a polarization-modulated asymmetric potential was revealed in transport measurements at a ∼10 nm thick GR/CIPS interface.³⁴ Additionally, integration with monolayer MoS₂ induces strong modulation of second-harmonic generation in CIPS.³⁵ However, for ferroionic layers like CIPS, the mechanisms by which thermally activated displacive ions—and consequently, the degree of ferroionic ordering—modulate band alignment at the heterointerface remain unclear. Similarly, the effect of the contacting layer on the polarization switching in the FE layer is still poorly understood. While substantial experimental evidence infers the presence of diverse contact behaviors associated with the 2D FE layer,³⁶ atomic-scale mechanisms correlating ionic disordering with band alignment are lacking.

In this work, we elucidate the interplay between interfacial charge transfer and reconfigurable polarization across van der Waals (vdW) FE heterolayers. We demonstrate that the CIPS monolayer strongly modifies the band alignment across heterointerfaces formed with h-BN or GR through controlling the amount of transferred charge in two FE states. Conversely, the contact layers exert a pronounced influence on Cu⁺ ion kinetics in CIPS, significantly renormalizing the free-energy landscapes of Cu⁺ switching. Our study reveals that asymmetric double-well potentials emerging in these heterostructures stabilize the FE order of CIPS down to the 2D limit (∼7 Å), which is crucial for potential electronic applications such as efficient electron–hole separation at CIPS-based heterointerfaces.

Results and disscussions

Interfacial rigidity modulated by the polarization reversal in CIPS

In a freestanding CIPS, FE polarization is stabilized at temperatures below the Curie point (T_c = 315 K).³⁷ This polarization arises from the preferential occupation by Cu⁺ cations of one of the two symmetrically equivalent and vertically aligned empty sites, within the octahedral unit formed by sulfur that sit on the upper and lower basal planes. From a dynamical perspective, the configurational behaviors of Cu⁺ ions can be characterized into two distinct types of motion in CIPS. The first is a local, bistable off-centering displacement of Cu⁺ within the P₂S₆²⁻ framework, which gives rise to spontaneous polarization.³⁸ The stability of these polarization states has been confirmed by first and second-harmonic piezo-response force microscopy (PFM) measurements, with contributions from electrochemical-strain and electrostatic effect carefully excluded.³⁹ The second type corresponding to long-range Cu⁺ migration, a nonequilibrium process governed by multiple factors, including the electric field amplitude and cycling history, as well as localized defects and available interlayer migration pathways.^31,40,41 In this work, we focus exclusively on the intrinsic equilibrium polar switching of pristine, stoichiometric CIPS monolayer, and further investigate its modulation through interfacial coupling in heterostructures. Our first-principles density functional theory (DFT) simulations are performed through Vienna ab initio Simulation Package (VASP),⁴² and details are listed in Section I and II in the SI. Switching the polarization direction involves collective displacement of Cu⁺ cations from one site type to the other, passing through the high-symmetry midpoint (Fig. 1a). When stacked with h-BN or GR, for discussion purpose, the two polarization states are denoted as the “NEAR” and “FAR” states: in the NEAR state, the occupying Cu⁺ cations are close to the h-BN or GR layer, whereas in the FAR state, they are situated away from it (Fig. 1b–e).

Fig. 1 (a) Schematic illustration of switchable polarization states in CIPS: the NEAR state corresponds to the upward displacement of Cu⁺ cations close to the passivation layer, and conversely for the FAR state. Arrows indicate the direction of polarization in CIPS (P↑ and P↓ for NEAR and FAR states, respectively). Top views (b and c) and side views (d and e) of the h-BN/CIPS and GR/CIPS heterostructures. The interlayer binding energy of h-BN/CIPS (f) and GR/CIPS (g) heterostructures as a function of interlayer distance (Δd). The discrete solid circles denote energy values from DFT calculations; solid lines represent fitted curves based on the Buckingham potential.

In the stacking configurations considered here, the h-BN and GR layers serve as inert passivation layers, effectively blocking environmental contaminants (e.g., O₂ and H₂O) and suppressing unintended migration of Cu⁺ ions. The binding energy per CIPS formula unit is calculated according to the formula:

E_b = (E_hete − E_CIPS − E_h-BN/GR)/n (1)

where E_hete, E_CIPS, and E_h-BN/GR are the energies of total heterostructure, isolated CIPS monolayer, and isolated passivation layer (h-BN or GR monolayer) respectively, and n represents the number of CIPS formula units in the heterostructure. For both h-BN and GR based heterostructures (Fig. 1f and g), the NEAR state exhibits stronger interlayer binding: E_b at equilibrium configuration are −566.7 meV (NEAR state) and −477.5 meV (FAR state) for h-BN/CIPS, with a discrepancy of 89.2 meV; for GR/CIPS, E_b are −566.4 meV (NEAR state) and −494.8 meV (FAR state), with a difference of 71.6 meV. For both types of heterostructures, the interlayer interactions are dominated by weak vdW forces and are highly sensitive to the polarization states of CIPS.

The interlayer interaction energies of these heterostructures are fitted using the Buckingham and Lennard-Jones (LJ) potentials:^43,44

E_b,Buckingham = ae^−bΔd − c/Δd⁶ (2)

E_b,LJ = 4ε[(σ/Δd)¹² − (σ/Δd)⁶] (3)

where a, b, c, ε, and σ are fitting parameters, and Δd is the interlayer distance between the CIPS and the passivation layer. In the NEAR state, the equilibrium Δd values corresponding to the lowest-energy configuration are 3.52 Å and 3.54 Å for h-BN/CIPS and GR/CIPS, respectively; in the FAR state, these values increase to 3.54 Å and 3.58 Å. Similar results are reproduced in the fitted Lennard-Jones potential (Fig. S1 and Table S1). Therefore, h-BN/CIPS and GR/CIPS heterostructures are comparable in terms of E_b magnitude, both displaying polarization-sensitive interlayer interactions. The reversal of polarization in CIPS effects on the structures of both the CIPS and passivation layers are also given in Tables S2–S4 and Section III in the SI.

Additionally, the interfacial elastic constant (C₃₃) associated with the deformation vdW gap is derived via , where Δd₀ is the equilibrium distance determined in the Δd–E_b curve and S is the area of the supercell. The fitted C₃₃ value for h-BN/CIPS is slightly larger than that for GR/CIPS (Table S5). Interestingly, reversing the polarization states in CIPS tunes C₃₃, dropping from 14.3 GPa (NEAR state) to 10.7 GPa (FAR state) for h-BN/CIPS, and from 11.3 GPa (NEAR state) to 10.4 GPa (FAR state) for GR/CIPS; all values are much weaker than that of graphite (38 GPa). The observed softening of interlayer interactions in the FAR state arises from diminished electron density within the vdW gaps, indicating the possibility of achieving tunable structural flexibility by poling the surface of the heterostructure. The tunable C₃₃ of CIPS-based heterostructures highlights an efficient electromechanical response.

Proximity effect and interlayer charge transfer across CIPS and h-BN or GR

Upon contacting CIPS with h-BN or GR, a redistribution of charges occurs across both layers. The charge transfer is quantified through the planar-averaged differential charge density Δρ = ρ_hete − ρ_CIPS − ρ_h-BN/GR and the transferred charge (ΔQ):^45,46where ρ_hete is the charge density of the heterostructure, ρ_CIPS and ρ_h-BN/GR denote the charge density of the isolated CIPS monolayer and h-BN or GR layer, respectively, and z is the vertical distance measured from the bottom of the simulation box. The net transferred charge from h-BN or GR to CIPS corresponds to the value of ΔQ at the nodal (zero-crossing) plane of the Δρ(z) profile within the interfacial region.

As shown in Fig. 2a and c, electrons transfer from the h-BN or GR side to the CIPS side upon integration, with GR exhibiting a stronger charge donation ability than h-BN, regardless of polarization states of CIPS. This may account for the stronger interlayer interactions between GR and CIPS (Fig. 1g). In the case of h-BN/CIPS, CIPS in the FAR state tends to attract more electrons (1.45 × 10⁻² e per CIPS formula unit) than in the NEAR state (1.30 × 10⁻² e per CIPS formula unit). This indicates that the Cu⁺ ions at a greater separation from h-BN attract more electrons to the CIPS side (red lines in Fig. 2a and b). A similar trend is observed for GR/CIPS (Fig. 2c and d), where electron transfer in the FAR state is 2.20 × 10⁻² e per CIPS formula unit, higher than in the NEAR state (1.58 × 10⁻² e per CIPS formula unit)—approximately 50% and 20% greater than those in the h-BN/CIPS case, respectively. Therefore, integrating CIPS with h-BN or GR effectively induces n-type doping in CIPS and p-type doping on the h-BN or GR side. In short, the Cu⁺ ions, with their positions and ordering controlled by temperature and external electric field, act as an effective “pump” to regulate the amount of transferred charge to CIPS.

Fig. 2 Planar-averaged differential charge density (Δρ) and transferred charge (ΔQ) per CIPS formula unit for the h-BN/CIPS (a) and GR/CIPS (c) heterostructures in both FAR and NEAR states. Insets show enlarged views of ΔQ profiles near the interface. Real-space distribution of Δρ for the h-BN/CIPS (b) and GR/CIPS (d) heterostructures in the two polarization states. Iso-surfaces are set at 1.5 × 10⁻⁴ e Å⁻³ with pink and cyan representing electron accumulation and depletion, respectively. (e) Schematic illustration of the net effective electric field (E_eff) resulting from the summation of the built-in interfacial electric field (E_int) arising from charge transfer and the polarization field (E_polar) induced by the Cu⁺ ferroic ordering.

Charge transfer across the interface induces an interfacial electric field (E_int), pointing from h-BN or GR toward CIPS, thereby generating a built-in potential in both h-BN/CIPS and GR/CIPS heterostructures. This induced field is highly localized, as the charge transfer region is largely restricted to the vicinity of the vdW gap (Fig. 2b and d). In principle, this localized and well oriented E_int is superimposed on the intrinsic polarization field (E_polar) associated with the displaced Cu⁺ ions within the CIPS backbone. We introduce a net effective electric field (E_eff), arising from the combined contribution of E_int and E_polar, which is highly sensitive to the ordering of Cu⁺ ions. Fig. 2e schematically illustrates the variation of E_eff during the transition from the NEAR state to the FAR state. In the NEAR state, E_int aligns with E_polar, resulting in a stronger E_eff; conversely, in the FAR state, E_polar oppose E_int, leading to a reduced E_eff. For comparison, the paraelectric (PARA) state of CIPS in heterostructures is also considered (note: the PARA state has been referred to as the antiferroelectric state in other studies^47,48). Fig. S2 shows the structures of h-BN/CIPS-PARA and GR/CIPS-PARA states, where Cu⁺ ions are randomly and uniformly distributed on both the top and bottom docking sites of CIPS. In this case, E_polar vanish, and only E_int contributes to E_eff (Fig. 2e). Since charge transfer is decisive for both direction and intensity of E_eff across the interface, its impact on band alignment, carrier transport, and stability of polarization states are discussed in subsequent sections.

Reversal of polarization for tunable band alignment

Fig. 3a–d shows the local density of states (LDOS) across the interfaces of h-BN/CIPS and GR/CIPS heterostructures. As shown in Fig. 3a, for h-BN/CIPS in the NEAR state, E_polar aligns with E_int This generates a relatively strong E_eff that bends the bands of CIPS, lifting the conduction band minimum and valence band maximum of CIPS (denoted as CBM_CIPS and VBM_CIPS, respectively). Conversely, in the FAR state, the reversed E_polar opposes E_int, suppressing and even reversing E_eff, which lowers the CBM_CIPS and VBM_CIPS. In the GR/CIPS heterostructure, a similar trend of band shifting induced by polarization switching is observed (Fig. 3c and d), where the positions of Cu⁺ ions determine the polarization direction and raise (or lower) the band edge states of CIPS near the GR for the NEAR (or FAR) state. In contrast, the PARA state exhibits a more homogeneous distribution of states in CIPS (Fig. S3), indicating negligible band bending and suppression of E_polar within the CIPS layer. Consequently, the band alignment can be effectively tuned depending on which side of the FE CIPS contacts the passivation layer.

Fig. 3 (a and b) LDOS of h-BN/CIPS in the NEAR and FAR states, respectively. (c and d) LDOS of GR/CIPS in the NEAR and FAR states, respectively. (e and f) Band diagrams of h-BN/CIPS and GR/CIPS heterostructures. The dashed orange lines in (a–d) guide the eye to band bending and tilting within the CIPS layer induced by the interfacial electric field and polarization field. The Fermi level is indicated by horizontal dashed lines in (e) and (f).

Fig. S4 gives a schematic representation of band alignment types and corresponding classification of semiconductor heterostructures. For h-BN/CIPS in the NEAR state, the interface exhibits type-H band alignment, characterized by substantial band mismatch between the CBM of h-BN and CIPS, while the VBM mismatch is negligible (Fig. 3e). This configuration blocks electron transport from CIPS to h-BN while permitting direct hole transport across the interface. Interestingly, polarization switching to the FAR state results in a type-II band alignment at h-BN/CIPS, driven by an upward state shifting of h-BN, positioning VBM_h-BN approximately 0.32 eV above VBM_CIPS.

In a metal-semiconductor heterostructure, as in the case of GR/CIPS, the relative alignment of Fermi level with the semiconductor band edges determines the contact type formed—either Schottky or Ohmic. For the GR/CIPS-NEAR state, the Fermi level lies within the CIPS band gap, forming a Schottky contact (Fig. 3f), whereas at the FAR state, a quasi-Ohmic contact emerges. Specifically, there is a substantial band mismatch of ∼0.27 eV between the Dirac cone and the CBM_CIPS in the NEAR state, which disappears in the FAR state (see Fig. S5c and d). Therefore, the contacted semi-metallic GR layer is expected to be more sensitive to polarization reversal in CIPS than the insulating h-BN. Our findings explain previous experimental observations of tunable n-type and p-type doping and a substantial Fermi level shift (up to 1 eV) in multilayer CIPS (∼4 nm thick) upon polarization switching, as confirmed by Kelvin probe force microscopy (KPFM) measurements.²⁸ More generally, polarization-induced modulation of band alignment is a common phenomenon in FE heterostructures.^49,50 Here, the term “reconfigurable” specifically refers to the tunability of band alignment induced by FE polarization switching at atomically clean and structurally uniform interfaces, as described within the DFT framework. As summarized in Table S6, switching the polarization from the NEAR state to the FAR state transforms the GR/CIPS contact from an n-type Schottky to a quasi-Ohmic one, accompanied by a decrease in electron tunneling barrier (Φ_n) and an increase in hole tunneling barrier (Φ_p). The band alignments for the FE and PARA states are also shown in Fig. S6 for comparison.

Apart from the band alignment, the tunneling barrier is another important indicator for interfacial carrier transport. The carrier transport efficiency across the vdW gap is estimated using the tunneling probability (P_TB) according to the Simmons formula:⁵¹

where w_TB and Φ_TB are the width and height of the tunneling barrier, and ħ and m represent the reduced Planck's constant and free-electron mass. The tunneling barriers for h-BN/CIPS and GR/CIPS are extracted from the planar-averaged electrostatic potential profiles (Fig. S7). All heterostructures exhibit relatively low tunneling probabilities due to weak orbital overlap across the vdW gap (Table S7). The P_TB of the h-BN/CIPS interface shows pronounced sensitivity to polarization reversal, indicating that h-BN/CIPS is promising for nanoelectronics and sensing applications based on tunneling junctions with controllable carrier injection. A recent experiment demonstrated this by fabricating a ferroelectric field-effect transistor (FeFET), where an additional InSe channel integrated atop h-BN/CIPS controls the on/off current.⁵² The present model corresponds to the ideal vdW contact limit. Although extrinsic inhomogeneities that are likely to occur in real devices—such as those induced by trapped hydrocarbons or fabrication-related disorder—may reduce spatial uniformity, they do not affect the underlying FE-governed interfacial configuration mechanism.

Renormalized dynamics and free-energy landscape of Cu⁺ ions in vdW heterostructures

We next show that the addition of passivation layers such as h-BN or GR exerts strong effects on ferroic ordering and Cu⁺ ion dynamics in CIPS. Fig. S8 compares the total energy of the CIPS monolayer and the heterostructures in different polarization states. For the CIPS monolayer, the PARA state is slightly more energetically favorable (∼0.04 eV per CIPS formula unit) than the FE state. However, within the heterostructures, the FE NEAR state becomes the ground state, suggesting that interfacial interactions induce a reordering of polarization states in CIPS. The underlying reason is that the interlayer charge transfer compensates and screens the surface polarization bound charges,^53,54 leading to a reduction in depolarization energy, especially for the NEAR state, which exhibiting the largest amount of transferred charge to CIPS side.

The probability distribution (p) of Cu⁺ species as a function of their relative position along the OOP direction (r_z) in the CIPS layer, from which free-energy profiles for Cu⁺ switching (F, see right panels in Fig. 4a and b) are extracted as:⁵⁵

F(r_z) = − k_BT ln p(r_z) (6)

where k_B is the Boltzmann constant and T is the temperature. For each temperature point, a 10 ps molecular dynamics (MD) is performed in the canonical (NVT) ensemble to maintain the system under isothermal–isochoric condition, and the final 5 ps of the equilibrated trajectories are used to deriving the r_z distribution. The free-energy barrier heights of Cu⁺ switching (ΔF = F_NEAR − F_saddle in heterostructures, or ΔF = F_upper − F_saddle in CIPS monolayer) for transiting between NEAR and FAR states at various temperatures are compiled in Fig. 4c and d (also see Table S8 for detailed values). For the freestanding CIPS monolayer, Cu⁺ cations exhibit a symmetric free-energy profile and favor equivalent population at both upper and lower sites (Fig. 4c). Above 330 K, rapid thermally activated Cu⁺ switching is triggered, promoting a uniform ion distribution across both facets and indicating that FE states are dynamically unstable in the freestanding CIPS monolayer (Fig. S9). This observation aligns well with the experimentally determined critical temperature of 315 K for CIPS.³⁷ It should be emphasized that the activation barriers reported here correspond to Cu⁺ off-centering switching between FE states, rather than long-range Cu⁺ migration. The former is associated with the reversibility and thermal response of the reconfigurable band alignment, whereas the latter primarily influences device endurance and leakage behavior in thicker FE systems.³¹

Fig. 4 (a and b) Temporal evolution of the relative OOP position of Cu⁺ ions in h-BN/CIPS and GR/CIPS heterostructures at various temperatures obtained from MD simulations. The right panels show the corresponding free-energy profiles of Cu⁺ ions. (c and d) Temperature-dependent potential energy profiles of Cu⁺ ions in freestanding CIPS and vdW heterostructures. Asymmetric potential profiles emerge at elevated temperatures in the heterostructures, with NEAR state becoming energetically favorable at larger r_z values. (e) Temperature-dependent χ_Cu-NEAR exhibits two distinct behaviors: negligible variation below T_c and a rapid decrease above T_c. (f) Temperature-dependent |ΔF|. Exponential fitting, with fitted decay rate τ, is applied to the data above T_c (≈370 K for heterostructures and ≈330 K for the CIPS monolayer). The solid and dashed lines in (e) and (f) represent the DFT calculated and fitted values, respectively.

In the h-BN/CIPS and GR/CIPS heterostructures, the NEAR state is thermodynamically favored at low temperatures (Fig. S10 and S13), consistent with its lower energy compared to the FAR state (Fig. S8b and c). Furthermore, the potential energy surfaces in these heterostructures are asymmetric (Fig. 4d), likely due to the built-in electric field E_int (Fig. 2) formed across the interface, which affects F according to the Landau–Ginzburg formula:^56,57

F = αP_polar² + βP_polar⁴ + γP_polar⁶ + λE_int − ζ(P_polar·E_int) (7)

where α, β, γ, λ, and ζ are coefficients, and P_polar denotes the dipole moment induced by ionic polar displacement within the CIPS layer. In the NEAR state, P_polar is parallel to E_int, hence lowering F (ζ being positive); whereas in the FAR state, they are antiparallel, thereby elevating F. Additionally, the varying magnitude of E_int also contributes to the asymmetric potential surface in these heterostructures (Fig. 2).

At elevated temperatures, akin to the freestanding case, Cu⁺ ions become strongly activated and gradually distribute more uniformly across the top and bottom docking sites (Fig. S10 and S13). With the NEAR state as the starting configuration, the proportion of Cu⁺ ions remaining in the NEAR state (denoted as χ_Cu-NEAR) evolves linearly with temperature, exhibiting two distinct linear regimes: being constant at low temperatures and decreasing linearly at high temperatures, with an inflection point being at T_c ≈ 370 K for both heterostructures (Fig. 4e). The fitted slopes at high temperatures are k_h-BN/CIPS = −3.1 × 10⁻⁴ K⁻¹ and k_GR/CIPS = −6.1 × 10⁻⁴ K⁻¹ for h-BN/CIPS and GR/CIPS, respectively. The enhancement of T_c in both heterostructures compared to freestanding CIPS is attributed to the adhesive binding between h-BN or GR and Cu⁺ ions, which promotes and stabilizes the FE ordering in heterostructures. Notably, at all temperatures, χ_Cu-NEAR of GR/CIPS exceeds that of h-BN/CIPS, likely due to stronger interfacial binding in the former case (Fig. 1). Temperature-dependent polarization kinetics are also verified by initializing MD simulations from the FAR and PARA states, yielding the same T_c ≈ 370 K for both heterostructures (Fig. S11, S12, S14, and S15).

The temperature dependence of ferroionic kinetics is summarized in Fig. 4f. For all systems, |ΔF| generally decreases with increasing temperature, and beyond T_c it follows an exponential trend: |ΔF| ∝ exp(−τ × T), where τ is the decay rate. Interestingly, h-BN and GR exhibit distinct T − |ΔF| characteristics compared with the freestanding CIPS monolayer. For the GR/CIPS heterostructure, the highest |ΔF| of 257.1 meV occurs at 350 K, and the fitted barrier height (dashed red line) shows a slower decay (τ_GR/CIPS = 236.0 K⁻¹) than that of the CIPS monolayer (τ_CIPS = 47.2 K⁻¹). In the h-BN/CIPS case, the maximum |ΔF| (229.5 meV) is less pronounced and occurs at a higher temperature of 370 K (blue point), together with a faster decay (τ_h-BN/CIPS = 23.8 K⁻¹, dashed blue line). In the low-temperature regime (T < T_c), |ΔF| values in vdW heterostructures are comparable to that of freestanding CIPS monolayer, whereas for high temperatures (T > T_c), |ΔF| for GR/CIPS becomes higher than that of h-BN/CIPS and monolayer CIPS, again due to its relatively stronger interfacial binding.

Previous studies report an energy barrier of ∼1.1 eV for OOP Cu⁺ interlayer migration in CIPS, which enables long-range ion migration in bulk under a strong electric field.⁵⁸ For comparison, the corresponding barriers for OOP Cu⁺ migration in CIPS-based heterostructures obtained from DFT calculations are shown in Fig. S16a. In these heterostructures, Cu⁺ migration across the vdW gap toward the GR (h-BN) side requires overcoming a barrier of 2.96 eV (4.31 eV), followed by a substantially larger energy increase of 18.45 eV (15.47 eV) associated with penetration into the GR (h-BN) passivation layer. Such extremely high barriers arise from the forced penetration of Cu⁺ through pristine, defect-free passivation layers rather than a realistic diffusion pathway. Therefore, cross-interface migration is energetically prohibitive under ideal conditions. Consistently, no long-range Cu⁺ migration is observed in MD simulations, indicating that the dynamics are dominated by reversible bistable off-centering rather than ionic diffusion.

We next reveal the correlation and dynamic coupling of Cu⁺ species. In Fig. 5a, the four peaks at 65, 185, 210, and 310 cm⁻¹ correspond to in-plane (IP) modes involving Cu⁺ atoms, while the 105 cm⁻¹ peak corresponds to the OOP polar mode with significant Cu⁺ vibration (detailed vibration patterns are given in Fig. S17b). Adhesion of h-BN or GR does not noticeably affect vibrational peak positions. However, substantial vibrational density of states (VDOS) intensity appears at zero frequency for the h-BN/CIPS and GR/CIPS heterostructures (Fig. 5b and c), especially at elevated temperatures (>400 K), indicating diffusive Cu⁺ motion likely driven by the interfacial electric field upon stacking h-BN or GR. In contrast, this behavior is absent in freestanding CIPS. For both freestanding CIPS and heterostructures, strong peak broadening and reduced intensity occur at elevated temperatures, indicative of phonon anharmonicity. Interestingly, the OOP mode near 105 cm⁻¹ strongly broadens and softens with increasing temperatures in freestanding CIPS, while remaining rigid in both heterostructures. Therefore, passivation of 2D vdW heterolayers promotes the flexural stability of Cu⁺ species in CIPS.

Fig. 5 (a–c) VDOS of Cu⁺ ions at different temperatures, computed from the velocity autocorrelation function. (d–f) Synchronous 2D correlation spectra of simulated Cu⁺ VDOS. The off-diagonal regions in red (blue) color indicate positive (negative) correlation between vibrational modes. The white line marks the characteristic peak at 65 cm⁻¹.

Meanwhile, synchronous 2D correlation spectrum analysis is conducted using the temperature-dependent VDOS of Cu atoms, with the averaged synchronous spectrum correlation function (Θ) defined as:^59,60

where the VDOS data are collected within a time interval Δt = t_total/m, t_total is the total simulation time, and m is the number of segments. In the 2D correlation spectrum, the main diagonal contains vibrational modes coupled to themselves (auto peaks), whereas off-diagonal regions represent synchronously or asynchronously linked cross peaks, marked by red (positive value) or blue (negative value) in Fig. 5d–f. For the CIPS monolayer, the primary peak at 65 cm⁻¹ is synchronously coupled with peaks at 185, 210, and 310 cm⁻¹ (Fig. 5d). This is reasonable since all these modes correspond to IP-type Cu motion. Interestingly, these IP modes are asynchronously coupled to the OOP mode at 105 cm⁻¹, but the addition of passivation layers disrupts this synergistic trend. As shown in Fig. 5e, covering with h-BN layer quenches the coupling between the IP vibration at 65 cm⁻¹ with the 185, 210, and 310 cm⁻¹ modes, as indicated by the disappearance of the red block spanning 150–225 cm⁻¹ that observed in freestanding CIPS (Fig. 5d). A similar effect occurs in the GR/CIPS heterostructure, where all off-diagonal regions appear blue, indicating renormalized coupling between FE modes upon the addition of passivation layers. Within the simulation time and temperature window, Cu⁺ ions remain confined to the CIPS layer and do not access the vdW gaps or the h-BN passivation layer. The results indicate that the reversible modulation of band alignment associated with FE states can occur without long-range ionic migration, while the structural integrity of the heterostructure is preserved under the simulation conditions.

Conclusions

In summary, we reveal strong charge redistribution and the reshaping of free-energy landscape in ferroionic systems, based on two prototype CIPS-based heterostructures formed with typical passivation layers: the insulating h-BN and semi-metallic GR electrodes. The activation of Cu⁺ ions and polarization ordering are critical in controlling interlayer interactions, band alignment, carrier transport, and switching barriers. The underlying mechanism involves the coupling between the OOP polarization field of CIPS and the interfacial built-in electric field stemming from interlayer charge transfer. In the h-BN/CIPS heterostructure, the type-H band alignment in the NEAR state converts to a type-II configuration in the FAR state, accompanied by a reduced barrier height for Cu⁺ switching. In contrast, the GR/CIPS heterostructure undergoes a transition from an n-type Schottky contact in the NEAR state to a quasi-Ohmic contact in the FAR state, while enhanced charge transfer elevates the switching barrier. Critically, bistable polarization switching behavior is retained up to ∼370 K under simulation conditions. These findings demonstrate the tunability of electronic properties in ferroionic heterostructures and provide insights into contact-dependent control of carrier transport in vdW systems.

Author contributions

Hejin Yan planned the project with Yongqing Cai. Hejin Yan designed and performed calculations. This paper was written by Hejin Yan and revised by Bowen Wang and Gian-Marco Rignanese.

Conflicts of interest

There are no conflicts of interest to declare.

Data availability

Relevant data that support the findings of this study are available in https://github.com/yanhejin/CuInP2S6_Heterostructures. Supplementary information: LJ potential fitted distance-energy profiles; atomic configurations of h-BN/CIPS and GR/CIPS at PARA state; density of states and band structures; band alignments; planar-averaged electrostatic potential along out-of-plane direction; comparison of energy of CIPS monolayer, h-BN/CIPS and GR/CIPS heterostructures in different polarization states; temperature-dependent state switching dynamics and barriers in the CIPS monolayer, h-BN/CIPS, and GR/CIPS; energy barriers for interlayer Cu⁺ migration; phonon dispersion and vibrational density of states in the CIPS monolayer; stacking energies of the GR/CIPS heterostructure; Section I. Methods of first-principles simulations; Section II. Simulation models; Section III. Polarization switching acting on structures and electronic properties. See DOI: https://doi.org/10.1039/d6mh00443a.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (22022309), the Natural Science Foundation of Guangdong Province, China (2024A1515011161, EF2023-00106-IAPME), the Science and Technology Development Fund from Macau SAR (0122/2024/AFJ, 0120/2023/RIA2) and the University of Macau (MYRG-GRG2024-00028-IAPME, MYRG-GRG2025-00045-IAPME). This work was performed in part at the High-Performance Computing Cluster (HPCC), supported by the Information and Communication Technology Office (ICTO) of the University of Macau.

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Footnote

† Hejin Yan and Bowen Wang contribute equally.

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