Open Access Article
Zichao
Ma
and
Changjian
Zhou
*
School of Microelectronics, South China University of Technology, Guangzhou, 511442, China. E-mail: zhoucj@scut.edu.cn
First published on 4th September 2025
Two-dimensional (2D) semiconductors exhibit strong light absorption, yet their large bandgaps limit broadband photodetection. While van der Waals (vdW) heterostructures of 2D materials enable infrared excitation through narrowed interlayer bandgaps, achieving efficient control over these interlayer transitions remains a fundamental challenge. Through first-principles simulations and electrostatic engineering approaches, this study establishes a direct correlation between interfacial charge redistribution and enhanced interlayer excitations in 2D vdW structures. The results demonstrate that versatile strategies such as external electric field application, substitutional doping, and graphene interlayer integration effectively reduce interlayer bandgaps by several hundred millielectronvolts while significantly increasing interfacial charge exchange. These engineered heterostructures achieve exceptional absorption coefficients greater than 105 cm−1 spanning visible to mid-infrared wavelengths. These findings provide essential design principles and offer engineering strategies for developing broadband photodetectors using 2D vdW structures.
Typically, vdW structures assembled from 2D materials with differing bandgaps exhibit a staggered (type-II) band alignment. This configuration facilitates charge transfer across the atomically sharp junctions and induces built-in electric fields influencing carrier dynamics.8,9 In such heterostructures, the interlayer bandgap can be several hundred millielectronvolts (meV) smaller than the intrinsic bandgaps of the constituent monolayer. This reduced optical bandgap has enabled interlayer exciton recombination and subsequent infrared photon emission through ultrafast excitonic processes at cryogenic temperatures, for example, in heterostructures consisting of large bandgap MoSe2 and WSe2 when pumped with green lasers.10–13 In contrast, interlayer absorption as a reverse process, where an incoming photon excites electron–hole pairs spatially separated in two 2D layers, encounters significant inefficiency challenges. Such excitonic absorptions require extremely high incident light intensities, often exceeding 1010 W cm−2, which are orders of magnitude greater than typical photodetector operating conditions (nW cm−2 to mW cm−2).14 This stark contrast in light intensity illustrates the severe inefficiency of exciton-mediated interlayer-bandgap absorption for high-performance infrared photodetection applications.
Furthermore, excitonic effects in 2D materials, which are typically weakly bound and require cryogenic operating temperatures, contribute to sub-bandgap absorption only about 0.1 eV below the band edge. Given that most 2D semiconductors have bandgaps between 1 and 2 eV, this limited spectral extension, combined with the stringent excitation conditions, makes excitonic mechanisms impractical as an engineering route for high-performance photodetection device applications. As a result, the absorption spectra of 2D vdW heterostructures remain largely confined to the visible and near-infrared range, and practical strategies to extend absorption threshold into the mid-infrared via interlayer excitons have seen limited progress.15–17
These fundamental limitations highlight the need for alternative approaches, such as band engineering through a combined heterostructure design and electrostatic modulation. This makes the strategic design and control of the electronic structure of 2D vdW heterostructures essential for achieving tunable and efficient absorption beyond the limitations of intrinsic excitonic processes. Furthermore, efficient interlayer tunneling and momentum conservation are essential for strong interlayer excitations,18,19 which in turn are vital for high-response photodetection. However, many existing studies rely on multilayer 2D materials with indirect bandgaps, which suffer from momentum mismatch and reduced quantum yield.20,21 Moreover, their small bandgaps can lead to significant dark current, thereby degrading the sensitivity and signal-to-noise ratio of the photodetector. Moreover, exploring different 2D material combinations alone remains challenging because few materials simultaneously offer transparent tunneling barriers and narrow bandgaps, both of which are critical for efficient infrared photon absorption via interlayer excitons. To address these gaps, researchers have turned to interface dielectric engineering and gate biasing to tailor optical responses.22–25 In particular, interfacial electric fields have emerged as a key lever for boosting photocarrier separation, underscoring the intimate link between interface electrostatics and optical absorption in 2D vdW heterostructures.
This paper adopts a band-structure-based derivation of the absorption process to examine how band structures and interface electrostatics deterministically influence infrared optical absorption in vdW structures composed of well-established 2D monolayer materials for photodetector applications. Through first-principles simulations, this study demonstrates that deliberate tuning of the band alignment effectively modulates interlayer excitations, thereby enabling efficient infrared absorption. In particularly, the work examines the impact of electric biasing and doping on regulating the band alignment and interlayer excitation in 2D vdW structures, providing device engineering strategies to optimize infrared absorption for high-performance photodetection applications.
Without loss of generality, the electronic structures of a MoS2/WSe2 vdW structure are investigated as a representative example. Fig. 1(a) displays the relaxed atomic structure. The vdW gap or interlayer distance, measured between the centers of interfacial Se1 in WSe2 and S2 in MoS2 atoms, is 3.72 Å, while the separation between the Mo and W atom centers is 7.05 Å. Fig. 1(b) presents the band structure, projected DoS spectrum, and localized DoS mapping for the MoS2/WSe2 heterostructure. The results reveal a distinct direct bandgap at the high-symmetry K-point of the vdW structure, with EC originating from the MoS2 layer and EV from the WSe2 layer. The spatial separation of conduction and valence bands arises from a staggered-gap alignment and results in a reduced energy gap of the vdW heterostructure for interlayer excitons.26
Notably, the energy levels at which the DoS of transition metal atoms (Mo and W) diminish correspond to EC and EV, indicating bandgap values of 1.78 eV for monolayer WSe2 and 1.66 eV for monolayer MoS2, in good agreement with experimental results.17 The tunnelling layer between MoS2 and WSe2, identified as the interfacial dark gap in the localized DoS map, has a thickness of 1.56 Å. This region contains no allowed states and forms a tunnelling barrier that impedes interlayer charge transfer and exciton transitions, which is a universal feature in vdW structures, typically 1.5 Å to 2 Å wide.27 These values are consistent with experimental measurements reported in high-resolution TEM studies of the MoS2/WSe2 heterostructure,28 validating the computational model.
Several 2D materials used for photodetection applications, including MoS2, WS2, WSe2, InSe, NbS2, and graphene, in the form of free-standing monolayers as well as combined double-layer and triple-layer vdW structures, were simulated in this work. The lattice parameters for the unit cells are listed in Table 1. As shown in Fig. 1(c), the band diagrams of various 2D vdW heterostructure combinations alongside those of their free-standing monolayers, with calculated energy levels and band alignments consistent with the literature.9,17 All atomic structures were initially acquired from well-established databases (https://www.materialsproject.org) and subsequently rescaled to specific unit cell configurations, with each undergoing lattice constant adjustments of less than 2.5%. For structure modeling, periodic boundary conditions were applied to simulate an extended 2D film, and a vacuum layer exceeding 20 Å was implemented along the z-axis (out-of-plane direction) for every simulation unit cell to inhibit inter-cell charge exchange.
The supercells were relaxed using first-principles molecular dynamics with the conjugated gradient method, achieving an energy convergence of 10−6 eV and a force convergence of 0.02 eV Å−1. Self-consistent field (SCF) calculations were conducted using the projector-augmented wave (PAW) method with the Perdew–Burke–Ernzerhof (PBE) exchange and correlation functional within the generalized gradient approximation. A gamma-centered k-point grid was adopted for SCF calculations. To further confirm the band alignment of the 2D vdW heterostructures, we additionally verified our simulation results by calculating the band structures using the hybrid functional HSE06, with the results shown in supplementary Fig. S1. These simulations were performed using DS-PAW and Nanodcal software developed by Hongzhiwei Technology.29
The simulation results reveal that most vdW structures exhibit staggered band alignments, with energy level shifts relative to their free-standing forms. For example, the conduction band offset in WSe2/MoS2, WSe2/InSe, and WSe2/NbS2 bilayer heterostructures is reduced by tens to hundreds of meV compared to that of the free-standing monolayers, which is evidence of a built-in potential at the junction interface. When two atomically thin layers come into contact, their Fermi levels equilibrate through charge transfer or charge screening, creating an interfacial dipole. This redistributed charge alters the Coulomb interaction between layers, directly tuning the interlayer coupling strength. The magnitude of charge transfer is set by the Fermi-level shift (ΔEF) between the constituent layers in their free-standing forms and their coupled forms in the vdW heterostructure. These energy potential variations are quantitatively comparable to the first-principles simulation results. These findings demonstrate that charge exchange governs interlayer interaction strength in 2D vdW systems, with the degree of coupling determined by the initial Fermi level alignment of the constituent monolayers.
To clarify this mechanism, this work explicitly compares the InSe/WSe2 and NbS2/WSe2 structures, which exhibit staggered-gap (type-II) and broken-gap (type-III) band alignments, respectively. Fig. 2(a) and (d) display the changes in effective potential (ΔVeff) and redistribution of charge density (Δρ) in the constituent 2D layers of the vdW junction. The InSe/WSe2 heterostructure, composed of two 2D monolayers with closely matched charge neutrality levels, exhibits a weak interfacial dipole, suggesting suppressed interlayer charge exchange. In contrast, the NbS2/WSe2 heterostructure exhibits a pronounced interfacial dipole that generates a large built-in potential, shifting the conduction band of NbS2 upward by approximately 0.9 eV, resulting in p-type doping of the WSe2 layer.
The linear potential drop across the vacuum region of the unit cell arises as a secondary effect of charge redistribution within the 2D heterostructure, and it follows Poisson's equation. For instance, in the WSe2/NbS2 heterostructure, charge transfer leads to accumulated positive charge in WSe2 and negative charge in NbS2, and such charge density can penetrate through the monolayers and cause residue charge density on the top and bottom surface of the vdW structure. Due to the use of periodic boundary conditions in all spatial directions in simulation, the residue negative charges in NbS2 generate an electric field that extends across the vacuum region, terminating at the residue positive charges in WSe2 in neighboring unit cells. To aid understanding, we have included in the supplementary document an illustration of the periodic boundary conditions used in the atomistic simulations, along with a schematic showing the redistributed charges, the induced electric field, and the resulting changes in the potential profile, presented as supplementary Fig. S2. Since the vacuum region contains no free charges, the electric field remains constant within it. Notably, because of the thick (>20 Å) vacuum spacer, this electric field does not cause significant dielectric screening or perturb the intrinsic electronic structure of the vdW heterostructures.
These interlayer interactions are further illustrated in the band structures presented in Fig. 2(b) and (e). The band structures, projected onto WSe2, InSe, and NbS2 (colored in blue, yellow, and orange), reveal significant joint dispersion relations near the high-symmetry Gamma-point in both heterostructures. These correlated E-k dispersion relations provide additional paths for momentum-conserved carrier exchange and interlayer excitations. For example, the NbS2/WSe2 heterostructure not only supports the interband transition of WSe2 from EV to EC, but also creates an interlayer excitation pathway at the high-symmetry K-point, from the EV of WSe2 to the conduction band levels of NbS2. A similar effect is observed for the InSe/WSe2 heterostructure. The interband transitions occur inherently within monolayer WSe2 and InSe, as indicated by the excitation paths from EV to EC of each layer, while an additional allowed excitation pathway arises at the Gamma-point due to the joint dispersion relations.
Fig. 2(c) and (f) compare the absorption spectra of the NbS2/WSe2 and InSe/WSe2 heterostructures with those of their free-standing layers. Both vdW heterostructures exhibit high absorption coefficients (>105 cm−1) in the ultraviolet and visible spectral ranges, arising from inherent intralayer excitations from EV to EC within the same material, and show notably enhanced absorption in the infrared spectral range due to allowed interlayer excitations across the layers. The computed absorption coefficients are consistent with those obtained from experimental measurements.30,31 Notably, the InSe/WSe2 heterostructure shows a threefold increase in the absorption coefficient for a photon energy of 1 eV due to the joint dispersion relations created in the vdW heterostructure. In contrast, stacking a monolayer of WSe2 with NbS2 enhances the absorption spectrum across the range of 0.5∼1 eV.
The absorption coefficient α(ℏω) is calculated using a classical approach based on electronic transitions between occupied and unoccupied Kohn–Sham states.32,33 In this framework, α(ℏω) at photon energy ℏω is correlated to the joint density of states (JDoS) ρJD(ℏω), as given by (1),
| α(ℏω) ∝ |〈kV|HVC(k)|kC〉|2ρJD(ℏω)[f(EV) − f(EC)], | (1) |
The divergent absorption properties stem from the distinct band alignments in the vdW heterostructures. In the NbS2/WSe2 heterostructure, a large built-in potential creates a broken-gap band alignment associated with significant charge redistribution that promotes substantial electron exchange and heavy doping of WSe2. According to field emission theory, the resulting strong interfacial electric field enhances tunneling efficiency.20 Moreover, the correlated dispersion relations increase the DoS available for interlayer excitons, promoting electron transitions from the WSe2 valence band to the NbS2 conduction band, and enhancing infrared photon absorption. In contrast, the staggered gap band alignment in the InSe/WSe2 heterostructure leads to modest charge redistribution at the junction interface. This results in limited interlayer electron exchange and primarily enhances the DoS for interband excitations within the constituent monolayers. These results highlight that deliberate modulation of interfacial electrostatics, with transforming a staggered band alignment into a broken-gap configuration being an effective strategy, synergistically activates interlayer excitation and enhances infrared absorption in 2D vdW structures.
Fig. 3(c) shows the absorption spectra of the MGW heterostructure. Graphene begins absorbing photons at 1 eV, while MoS2 and WSe2 start absorbing photons at about 1.7 eV, corresponding to the inherent absorption of the individual monolayers due to intralayer excitations from EV to EC, which contribute primarily to the ultraviolet and visible spectral ranges. Notably, with a positive electric field of 0.08 to 0.1 V Å−1 (8 to 10 MV cm−1), which is achievable in practical devices,34,35 the infrared absorption coefficient has been significantly enhanced to 5 × 105 cm−1 for wavelengths beyond 2 μm. In contrast, a negative electric field as strong as −0.1 V Å−1 shows a negligible impact on the optical absorption properties in the spectrum of the MGW heterostructure. The absorption threshold energies of MoS2, WSe2, and graphene are consistent with previously reported experimental measurements.36–38 Notably, charge transfer from MoS2 and WSe2 has doped graphene and shifted its Fermi level by ΔEF, resulting in a modified absorption threshold for interband transitions within the graphene layer. According to momentum-conserved optical transition rules, interband absorption in graphene becomes allowed only when the photon energy exceeds 2|ΔEF|.39 This doping-dependent shift in the absorption threshold in the simulated spectra shows agreement with experimental trends.
The projected band structures in Fig. 3(d) and (f) further clarify the mechanism. The dispersion relations, color-coded for MoS2 (blue), WSe2 (orange), and graphene (green), reveal that a positive electric field converts the staggered-gap alignment between MoS2 and graphene into a broken-gap alignment. Such a change in band alignment induces heavy n-type doping in MoS2 and strengthens the dipole at the graphene/WSe2 interface, promoting low-energy interlayer excitations. As a result, electrons in the WSe2 valence band can transition to the MoS2 conduction band through graphene, resulting in enhanced infrared absorption. Conversely, a negative bias widens the energy gap between the WSe2 valence band and the MoS2 conduction band, inhibiting interlayer excitations. As such, applying an electric field that simultaneously narrows the interlayer bandgap and promotes interlayer charge transfer in 2D vdW heterostructures facilitates stronger interlayer excitations, resulting in enhanced absorption coefficients and broadened infrared spectral bandwidths. In addition, selecting 2D materials that naturally form heterostructures with smaller interlayer bandgaps may allow such effects to be achieved using lower electric fields, enabling more efficient infrared absorption through engineered band alignment. Furthermore, leveraging a positive bias to enhance infrared absorption and a negative bias to suppress unwanted carrier transitions provides a strategic pathway to enhance the spectral range and sensitivity of 2D vdW heterostructure-based photodetectors.
Beyond gate biasing, substitutional doping provides a robust alternative for generating substantial interfacial charge and inducing strong interfacial electric fields in 2D materials. This approach offers advantages such as simplifying device architecture and reducing parasitic effects.40–43 Therefore, substitutional doping in 2D materials is regarded as a favorable technique and a key building block in the roadmap for advanced device applications.44 Substitutional doping with Re and Fe (for n-type), and Nb, V and Ta (for p-type), which are compatible with the host lattice, has proven to be an exceptionally efficient approach for modulating charge concentrations in many 2D materials, such as MoS2, MoSe2, MoTe2, and WSe2 in their monolayer and multilayer forms.45–48 These extensive experimental and theoretical studies have shown that substitutional doping produces stable materials and enables precise control over carrier concentrations with negligible lattice distortion, offering excellent material stability, structural compatibility, minimal defect states, and preserved band structures—features essential for engineering device-level functionality.
Fig. 4(a) illustrates the atomic structure of a vdW-stacked p–n junction comprising n-type Re-doped and p-type Nb-doped MoS2 monolayers, each with a doping concentration of 1014 cm−2. This doping concentration corresponds to a dopant atomic ratio of less than 2.7%, which is readily attainable through established synthesis techniques.49,50 The doping concentrations in each layer are kept identical, and lower doping levels can be realized by increasing the size of the simulation supercell while keeping the dopant atom count fixed. Fig. 4(b) shows that an increased doping level simultaneously broadens the absorption spectral bandwidth and enhances infrared absorption, directly correlated with intensified electron exchange, as illustrated in Fig. 4(c).
To clarify the mechanism, Fig. 4(d) and (e) present a comparative analysis of the band diagrams for the doped bilayer MoS2 p–n junction and the intrinsic bilayer MoS2, respectively. While the undoped bilayer MoS2 exhibits a large indirect bandgap that confines absorption to the visible and ultraviolet ranges, increased doping narrows the interlayer energy gap and intensifies electron exchange. At a doping concentration of 1014 cm−2, a broken-gap band alignment is established, enabling absorption to extend into the far-infrared region and achieving absorption coefficients comparable to those observed in the visible and ultraviolet ranges. Notably, the enhanced infrared absorption in the bilayer MoS2 p–n junction arises from strong interlayer charge transfer, driven by the alignment of band edges relative to the Fermi level. This mechanism offers an electrically tunable threshold for interlayer optical transitions. It is important to emphasize that achieving such tunability is inherently challenging in metal–semiconductor Schottky contacts, particularly when 2D materials are involved. In these systems, strong Fermi-level pinning at the metal–semiconductor interface constrains the alignment between the metal Fermi level and the semiconductor band edges, thereby severely limiting the effectiveness of electrostatic modulation of the band structure.
Supplementary information is available: the band structures of 2D monolayers and heterojunctions computed using HSE06 hybrid functional, the periodic boundary condition setups, and the basic theory of JDoS and absorption. See DOI: https://doi.org/10.1039/d5na00648a.
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