Efficient energy transfer in a hybrid organic-inorganic van der Waals heterostructure

Abstract

Two-dimensional (2D) materials offer strong light-matter interaction and design flexibility beyond bulk semiconductors, but an intrinsic limit is the low absorption imposed by the atomic thickness. A long-sought-after goal is to achieve complementary absorption enhancement through energy transfer (ET) to break this limit. However, it is found challenging due to the competing charge transfer (CT) process and lack of resonance in exciton states. Here, we report highly efficient ET in a 2D hybrid organic-inorganic heterostructure (HOIST) of Me-PTCDI/WS₂. Resonant ET is observed leading to enhanced WS₂ photoluminescence (PL) by 124 times. We identify Dexter exchange between the Frenkel state in donor and an excited 2s state in acceptor as the main ET mechanism, as supported by density functional theory calculations. We further demonstrate ET-enhanced phototransistor devices with enhanced responsivity by nearly 1000 times without sacrificing the response time. Our results expand the understanding of interlayer relaxation processes in 2D materials and open opportunities in optoelectronic devices.

Efficient Dexter energy transfer was demonstrated by coupling Frenkel state in Me-PTCDI and excited 2s exciton state in WS₂.

INTRODUCTION

Stacking atomically thin two-dimensional (2D) materials into van der Waals (vdW) heterostructures can form artificial quantum materials where interlayer charge or energy relaxation processes lead to new physics and devices (1–5). However, for optoelectronic applications, a fundamental limit of 2D materials is the low absorption due to the atomic thickness. To overcome this fundamental limit, a promising approach is to create a heterointerface with complementary photosensitive materials (donors) and harvest the excitations therein (6–16). The interlayer relaxation process mainly consists of two competing pathways. The first pathway is charge transfer (CT) due to the built-in electrical potential, which has been the dominating process due to the ultrashort time constant ~50 fs (17, 18). However, the separation of electrons and holes leads to quenching of photo- and electroluminescence and substantially elongated device response time due to traps at the heterointerface, which is a common issue in CT-enhanced optoelectronic devices (9–11). The second pathway is energy transfer (ET), which refers to nonradiative transfer of excitations in the form of excitons (12–16). Compared to CT, ET can avoid the effect of interface traps and is desirable for ultrafast devices. However, it has been proved very challenging to achieve efficient ET in 2D heterostructures due to the competing CT process (12), spatial separation of donor and acceptor (14, 15), or difficulties in realizing donor-acceptor resonance (19). In addition, for inorganic vdW heterostructures, the interlayer overlap of excitonic wave functions is small because they are mainly composed of localized d-orbitals confined within the plane (20).

On the other hand, integrating organic molecules into vdW heterostructures can vastly expand the existing functionalities owing to the complementary properties and chemical tunability at molecular level (19, 21–29). In particular, many molecular dyes host localized Frenkel excitons with large oscillator strength and photoluminescence (PL) quantum yield. They can be assembled into layered crystalline films on many 2D materials to form hybrid organic-inorganic heterostructure (HOIST) (27–31). Now, ET in diverse HOISTs has been explored but with low ET enhancement limited to several times (table S1). Here, we exploit the unique properties of organic dye molecules and demonstrate highly efficient ET to 2D semiconductors, enabled by the resonantly coupling of Frenkel exciton in dimethyl-3,4,9,10-perylenete- tracarboxilic diimide (Me-PTCDI) molecular crystal and Wannier-Mott exciton in WS₂. The ET is manifested by shortening of lifetime in the donor and simultaneous enhancement of PL intensity (by as much as 124 times) and optical anisotropy in the acceptor. Density functional theory (DFT) calculations show that the ET rate is more than one order of magnitude higher than pure inorganic heterostructures due to the reduced interlayer spacing and spatial delocalization of the 2s state. By harvesting ET, we break the limit of far-field absorption in 2D semiconductors and demonstrate ET-enhanced phototransistor devices without sacrificing the operation speed.

RESULTS

Our HOIST consists of Me-PTCDI molecular crystal and WS₂ (both are monolayers; see fig. S1) sandwiched by hexagonal boron nitride (h-BN) on both sides (Fig. 1, A and B). The samples were fabricated by vapor phase transport growth of Me-PTCDI on h-BN (30) with high thickness uniformity (fig. S2), followed by sequential dry transfer of exfoliated WS₂ and top h-BN flake. The high-quality interface between Me-PTCDI and WS₂ was further verified by high-resolution cross-sectional transmission electron microscope (TEM) with interlayer distance of ~493 pm (see fig. S3) The optical measurements were carried out in an optical cryostat at 77 K, unless otherwise stated (details of sample fabrication and measurements are described in Materials and Methods). The differential reflectance of the HOIST showed several well-defined resonances from Me-PTCDI and WS₂ (fig. S4), which confirmed that the optical properties of the individual layers and the molecular packing were preserved. Figure 1D plots the derivative of reflectance contrast of WS₂. We observed all the major resonance features, including neutral (X⁰) and charged (X⁻) A excitons, excited states (2s and 3s) and B exciton (32). A unique feature of the HOIST is that the Frenkel exciton in Me-PTCDI is energetically resonant with the first excited (2s) state of A exciton in WS₂ (Fig. 1D and fig. S4). Besides, the ground states are quite close in the HOIST, which facilitates the excitons in Me-PTCDI transferring into WS₂ (Fig. 1C, note S1, and fig. S5). Figure 1E plots the PL spectrum of a typical HOIST, together with the isolated WS₂ and Me-PTCDI regions from the same sample. We observed simultaneous enhancement of WS₂ emission (by ~50 times) and quenching of Me-PTCDI (by ~73%) in the heterostructure, which was strong evidence of ET (6–8). The brightening of WS₂ in the HOIST was also evident from PL image (Fig. 1B), which was distinct from PL quenching in typical vdW heterostructures (17, 18, 33).

Fig. 1. Me-PTCDI-WS₂ HOIST.

(A) Schematic illustration of the sample structure. (B) PL image of Me-PTCDI on h-BN before transferring WS₂ on top (left, 300 K), optical micrograph (middle, 300 K), and PL image (right, 77 K) of HOIST. Scale bar, 5 μm. (C) Band structure of HOIST and the Dexter ET process. (D) Derivative of reflection contrast of WS₂ (blue) and PL spectrum of Me-PTCDI (orange), both measured at 77 K. (E) PL spectra of WS₂ (left) and Me-PTCDI (right) in heterostructure and nonheterostructure regions from the same sample. The left and right panels are excited with 2.24- and 2.33-eV laser, respectively. a.u., arbitrary unit.

We further investigated ET by PL excitation (PLE) spectroscopy. Figure 2A plots the PLE intensity maps of WS₂ and HOIST, respectively, from the same sample. The WS₂ showed weak PL emission from X⁰ (2.075 eV) and X⁻ (2.05 eV), with enhanced response when excited at A and B excitons. The HOIST, in contrast, showed a new dominant excitation peak at ~2.24 eV, corresponding to the Frenkel exciton of Me-PTCDI. This peak was attributed to ET from the Me-PTCDI donor. Under the resonant excitation of Me-PTCDI, the PL of WS₂ was significantly broadened and red-shifted compared to the nonheterostructure region (Figs. 1E and 2A), which was possibly due to interaction effects at high exciton density (34, 35). Another possible explanation of the new peak was the transfer of photo-induced carriers (photodoping) by Me-PTCDI to influence the PL of WS₂. However, this scenario was ruled out because the X⁻/X⁰ ratio remained nearly constant across multiple excitation energies, which was inconsistent with photodoping (fig. S6) (12). The absence of strong ET in HOIST consisting of multilayer Me-PTCDI (although it has stronger optical absorption) also suggested that CT was not the dominant process (fig. S7). The weak CT was further supported by the band structure of the heterostructure characterized experimentally. As shown in Fig. 1C, the conduction band minimum (valance band maximum) of WS₂ is energetically very close to the electron affinity (ionization potential) of Me-PTCDI, which is not expected to generate strong built-in field and CT.

Fig. 2. Optical spectroscopy of HOIST.

(A) PLE of WS₂ (top, intensity multiplied by three times) and HOIST (bottom). (B) Top: PL intensity of X⁻ as a function of excitation energy in WS₂ and HOIST, obtained from the horizontal dashed line cuts from (A); Middle: PL enhancement factor derived from (B) (red open symbols) overlapping with PLE intensity of Me-PTCDI (blue dashed line). Bottom: Degree of polarization in excitation (solid symbols) and emission (open symbols) as a function of excitation energy. (C) Polar plot of PL intensity of WS₂ X⁻ in HOIST as a function of excitation polarization angle (red solid circles) and emission polarization angle (red open symbol) with the excitation polarization angle where ET effect is strongest. The blue solid circles give the PL intensity of pristine WS₂ X⁻ as a function of excitation polarization angle (×50 for clarity).

Figure 2B shows quantitative comparison of the PLE of HOIST and WS₂ (derived from horizontal line cuts in Fig. 2A). The PL enhancement had two contributions. The first was the overall enhancement due to the change in PL quantum yield with the h-BN encapsulation (the red dashed baseline in Fig. 2B, middle) (36) independent of excitation. The second (and main) contribution was from ET, with distinct optical signatures of Me-PTCDI. Consequently, the overall enhancement followed the spectral response of Me-PTCDI and reached ~48 times under resonant excitation (Fig. 2B, middle). After subtracting the effect of h-BN encapsulation, we calculated that the monochromatic (at 2.24 eV) and broadband (from 2.07 to 2.6 eV, covering both A and B excitons) absorption of WS₂ was increased by ~20 and ~2.5 times, respectively, via ET. The large PL enhancement was reproducible among multiple samples with the highest enhancement factor reaching ~124 times, which is the highest compared with the type I CT and fluorescence resonance energy transfer (FRET) (fig. S8 and table S1). Because of the giant oscillation strength of the Frenkel excitons in the monolayer Me-PTCDI, the ET performance of the HOIST can exceed the HOISTs using bulk organic layers for almost two orders of magnitude (37, 38).

Besides enhanced PL intensity, ET also caused optical anisotropy in WS₂. Isolated WS₂ did not exhibit linear anisotropy in PL (Fig. 2C, blue solid circles) (39). In the HOIST, however, both PL and excitation of WS₂ were highly anisotropic (Fig. 2C, red solid and open circles; see Materials and Methods for measurement details). The polarization angle was consistent with the PL of Me-PTCDI donor and independent of excitation polarization angle (fig. S9), and the degree of polarization, $P=\frac{I_{\text{max}}-I_{\text{min}}}{I_{\text{max}}+I_{\text{min}}}$ , reached 77% at resonant excitation. The anisotropic behavior was most distinct at the absorption peaks of Me-PTCDI (Fig. 2B, bottom). Because the absorption of WS₂ keeps isotropic in the HOIST (fig. S10), the strong exciton excitation polarization of WS₂ indicates that the absorption of HOIST is mainly from Me-PTCDI through ET when resonant with Me-PTCDI. The relationship between the enhancement factor and the excitation polarization angle can be well fitted with $c\ast {\text{cos}}^2(\frac{x-a}{180}\ast \mathrm{\pi })+b$ , where a is the molecular crystal orientation angle, b represents the change in the quantum yield of PL in WS₂ due to the doping effect, c is the maximum enhancement factor due to ET (fig. S11). The observed PL polarization behavior indicated that electrons and holes are transferred into WS₂ coherently, i.e., it preserved the exciton dipole moment of the donor. The excitons transferred into WS₂ are finally relaxed to trions that simultaneously excite both −K and + K valleys and transfer the optical coherence to valley quantum coherence (fig. S12). Our observation was fundamentally distinct from the separation of electron-hole pairs and subsequent CT in type-I heterostructures, which was incoherent and would give isotropic PL emission (13, 16). The ability to control the polarization behavior in monolayer transition metal dichalcogenides (TMDCs) could also open new possibilities toward coherent manipulation of valley degree of freedom (40).

The ET was further corroborated by transient absorption spectroscopy (note S2 and fig. S13). The Me-PTCDI in the nonheterostructure region showed lifetime τ_Me-PTCDI ~ 1.6 ps (fig. S14), which was approximately the radiative lifetime τ_r as the nonradiative lifetime in monolayer Me-PTCDI was much longer (30). This ultrashort radiative lifetime is related to the super-radiance in J aggregates owing to the large unscreened dipole interactions and suppression of CT process in the monolayer Me-PTCDI (30). Because of the extra ET process, τ_Me-PTCDI was expected to shorten in the HOIST, which was confirmed by our pump-probe measurements (fig. S14). Meanwhile, the dynamics of WS₂ keeps unchanged, which excludes the CT effect (fig. S15). Assuming that ET is the primary nonradiative process in the Me-PTCDI donor, the total decay rate can be written as $k_{\text{Me}-\text{PTCDI}}=\frac{1}{{\mathrm{\tau }}_{\text{Me}-\text{PTCDI}}}=k_{\mathrm{r}}+k_{\text{ET}}$ , where $k_{\mathrm{r}}=\frac{1}{{\mathrm{\tau }}_{\mathrm{r}}}$ and $k_{\text{ET}}=\frac{1}{{\mathrm{\tau }}_{\text{ET}}}$ are radiative recombination and ET rate, respectively. By subtracting $k_{\mathrm{r}}$ , we obtained τ_ET = 3.1 ps, corresponding to ET efficiency ( $\frac{k_{\text{ET}}}{k_{\text{Me}-\text{PTCDI}}}$) ~ 34%, which is close to the maximum ET efficiency through PL quenching of 73%. The discrepancy between the two estimated ET efficiencies is attributed to the additional many-body effects such as the exciton-exciton annihilation under pulsed laser, which will compete with the ET process (41).

Next, we discuss the ET mechanism in our HOIST. ET is nonradiative transfer of excitations in the form of excitons, mediated by either short-range electron exchange (Dexter) (42) or long-range dipole interactions (FRET) (43). The nature of FRET requires large oscillation strength for both the donor and acceptor states, and physical separation in the range of 1 to 10 nm (44). Dexter, on the other hand, depends on the wave function overlap and is not limited by the oscillator strength of the states. FRET is unlikely in our HOIST because the interlayer spacing is much less than 1 nm (Fig. 3A), and the oscillator strength of WS₂ 2s state is very small (fig. S16) (45). The spin conservation law also plays a key role in the ET process. Despite the nonemissive nature of the 2s state in WS₂, it can be resolved from the absorption spectrum, which indicates that a singlet-singlet ET can be supported between Me-PTCDI and WS₂ (42). To elucidate the mechanism, three control experiments were performed. First, we fabricated HOIST using monolayer MoSe₂ as the acceptor, which would give more efficient ET under FRET mechanism due to higher absorption at the Me-PTCDI emission energy (fig. S17) (46). Second, we separated Me-PTCDI and WS₂ by a layer of h-BN, whose thickness was well within the range of Förster dipole interactions (figs. S18 and S19). Only radiative ET with low efficiency is observed, which rules out FRET and suggests Dexter exchange as the ET mechanism. Third, the efficiency of FRET drops with the decrease of temperature. However, the ET enhancement in HOIST reaches the maximum at 77 K when the temperature decreases from room temperature to 4 K (figs. S20 and S21), which is due to the match of energy levels of 2s state of WS₂ and Frenkel states of Me-PTCDI. In addition, we numerically simulate the FRET rate in the HOIST, which generates τ_FRET of 105.4 ns (see note S3). This value is five orders of magnitude longer than the measured ET time ruling out the FRET mechanism.

Fig. 3. Theoretical calculations of exciton wavefunction and ET rates.

(A) Illustration of interlayer distance and exciton wave functions in HOIST (left) and MoS₂/WS₂ heterostructure (right). (B and C) Out-of-plane distribution of exciton wave functions in HOIST (B) and MoS₂/WS₂ heterostructure (C). (D) Normalized ET rates in different 2D heterostructures. For Me-PTCDI/WS₂ HOIST, we use 1s states in Me-PTCDI and consider both 1s and 2s states in WS₂. For MoS₂/WS₂, MoSe₂/WS₂, WSe₂/WS₂, and MoS₂/WSe₂ heterostructures, 1s states are used.

For Dexter exchange, the ET rate can be written as (47)

$$k_{\text{ET}}=K{J}_{\text{norm}}{e}^{(-\frac{2d}{L})}$$ (1)

where $K$  is a prefactor related to the excitonic orbital interactions, $J_{\text{norm}}$ is the normalized spectral overlap, $d$ is the center-to-center distance between the donor and the acceptor, and L is the characteristic wave function decay length (e.g., vdW radius). Our HOIST has two unique advantages compared to inorganic vdW heterostructures (e.g., MoS₂/WS₂). First, DFT calculations showed that the interlayer center-to-center distance d of HOIST (5.06 Å) was significantly smaller than that of the MoS₂/WS₂ (6.15 Å; Fig. 3A), leading to enhanced wave function overlaps. This was indeed observed in similar HOIST composed of PTCDA and WSe₂ (26). Second, the 2s state of WS₂ was more spatially extended in the out-of-plane direction than its ground state due to the reduced effective dielectric screening (Fig. 3, B and C) (32). Both factors contributed to the increased $k_{\text{ET}}$ according to Eq. 1. DFT calculations show that the wave function overlap mainly through the p_z orbitals of S and C atom (figs. S22 and S23). For quantitative comparison, we calculated $k_{\text{ET}}$ of six combinations using Fermi golden rule (see Materials and Methods) (48, 49). The results are summarized in Fig. 3D (normalized by $k_{\text{ET}}$ of MoS₂/WS₂ 1s states). We can see that the $k_{\text{ET}}$ of all the inorganic TMDC heterostructures is close to 1, but substituting MoS₂ with Me-PTCDI markedly increases the $k_{\text{ET}}$ to 18 due to reduced interlayer distance. The $k_{\text{ET}}$ is further increased to 65 with 2s state of WS₂. The variation of $k_{\text{ET}}$ is consistent with the orbital wave function overlap, which is sensitive to the interlayer distance (fig. S23 and table S2). Our theoretical calculations suggest that the ET is most likely between the resonant 1s Frenkel exciton of Me-PTCDI and 2s Wannier-Mott exciton of WS₂ (fig. 1C).

The observed ET allows the simultaneous transfer of electron-hole pairs to TMDCs within picosecond timescale, which could enable ultrafast broadband optoelectronic devices. To this end, we fabricated Me-PTCDI/WS₂ HOIST phototransistors as shown in Fig. 4 (see Materials and Methods for fabrication details). We first carried out photocurrent (I_ph) mapping using laser excitations in resonance with WS₂ A exciton (2.052 eV), where no ET was expected. We observed photoresponse only near the drain electrode where the contact band bending facilitates electron-hole separation and little difference between the HOIST and WS₂ regions (Fig. 4D, top). We then switched the laser energy in resonance with the Me-PTCDI Frenkel exciton (2.254 eV; Fig. 4D, bottom). We observed huge I_ph enhancement in the HOIST region due to ET. The I_ph of HOIST was higher than WS₂ across a wide range of V_g (Fig. 4F). At V_g = −22 V (close to charge neutrality), the I_ph in the HOIST was enhanced by ~966 times. Meanwhile, the response speed was not affected as shown in fig. S24.

Fig. 4. HOIST phototransistors.

(A) Schematic illustration of the phototransistor. (B) Band diagram of HOIST phototransistors under a bias voltage. (C) Optical micrograph of a typical device with both WS₂ and HOIST channel regions. Scale bar, 10 μm. (D) I_ph mapping of the device in (C) using 2.052 eV (top, multiplied by 10 times) and 2.254 eV (bottom) laser excitation. (E) I_ph spatial profile across the channel region in HOIST from the vertical line cuts in (D). The blue curve is multiplied by 10 for clarity. The positions of source and drain electrodes are marked. (F) I_ph as a function of V_g in the WS₂ (blue) and HOIST (red) channels under 2.254-eV laser excitation.

Another remarkable feature of the HOIST is that the photoresponse extended deep into the channel (~25 μm away from the drain electrode in contrast to ~1 μm in WS₂, Fig. 4E). One possibility is the increase of exciton diffusion constant at high exciton density (50). However, in this scenario, the diffusion length is ~1 μm, which is still one order of magnitude lower than our observation. Another possible mechanism is the reduction of binding energy by dipolar screening (51), making excitons separable under modest electric field away from the electrodes. Quantitative modeling will require further theoretical efforts. Nevertheless, we demonstrated that ET could enhance both the photoresponsivity and effective device area, both of which contributed to photocurrent extraction.

DISCUSSION

The observation of efficient ET in 2D HOIST opens enormous opportunities beyond conventional vdW heterostructures. For example, ET with complementary absorption spectrum through the Dexter mechanism may enable broadband optoelectronics. The ET enhancement in our work can outperform the other mechanism for enhancing the absorption in TMDC such as CT, plasmonic, and electronic structure modification (see table S3). In addition, the ET process provides an additional means to manipulate valley degree of freedom and exciton diffusion in TMDCs. Now, hundreds of organic materials (including small molecules, polymers, and covalently bonded frameworks) are known to adopt layered structure (29–31). With properly designed molecules and tandem structures, broadband absorption enhancement is within reach. Furthermore, combining the solution processability of organic materials and chemical vapor deposition of 2D materials, we can envision large-area HOIST array for image sensor and display applications.

MATERIALS AND METHODS

Sample and device preparations

WS₂ flakes and BN for encapsulation were fabricated by mechanically exfoliation using polydimethylsiloxane (PDMS), while the BN for Me-PTCDI growth was exfoliated on 300-nm SiO₂/Si substrate directly. Me-PTCDI crystals were obtained with vdW epitaxy growth on BN on 300-nm SiO₂/Si substrate in a home-built tube furnace. Then, the heterostructure was prepared with WS₂ and BN on PDMS transferred onto Me-PTCDI in the glove box sequentially. The photodetector was made by transferring two gold on the top of WS₂ as source and drain electrodes. For the TEM sample, instead of monolayers that are fragile during the milling process, thick Me-PTCDI and few-layer WS₂ are used to build the heterostructure, which would share the same interface quality and interlayer distances with the heterostructure of monolayer Me-PTCDI and monolayer WS₂. The sample is protected with 150-nm Au electrode and then covered with Pt using electron-beam evaporation before milling.

Optical and spectroscopic measurements

The PL images were collected using an optical microscope (Olympus BX51M). For the room temperature PL images, samples were illuminated by a 450-nm light-emitting diode (LED), and the PL images were collected by a colored charge-coupled device (CCD) camera. The excitation light was filtered by a long-pass filter in front of the CCD. For the low-temperature PL images, the sample was illuminated by a 500-nm LED.

For the low temperature PL test, samples were placed in cryostat chamber (OXFORD INSTRUMENTS_MicrostatHires) cooled by liquid nitrogen. A halogen lamp was connected with a monochromator to generate monochromatic light, which was used to excite samples. The PL signal was collected by 50× objective (numerical aperture = 0.7) and analyzed by a liquid nitrogen–cooled silicon CCD detector with a monochromator. For the PLE test, the wavelength is swept by controlling the monochromator by computer.

For the excitation polarization test, a polarizer was used to turn the monochromatic light to linear polarization light, and a half-waveplate was used to control the polarization of the incident light. For the PL polarization test, another polarizer was placed before the spectrometer to identify the polarization of PL for a given polarization of the incident light. To test the relationship between polarization degree and excitation energy in HOIST, PLE tests were performed at the polarization angle with the maximum intensity and minimum intensity, respectively. A 300 line/mm grating was used for the PL test with negligible polarization effect. The polarization effect of other optical elements in the light path is also ruled out by testing monolayer WS₂ showing no linear anisotropy, which is consistent with (39).

For the differential reflection contrast test, samples were illuminated with white light covering the spectral range from 450 to 900 nm. The refection from substrate (R_substrate) and sample (R_sample) were recorded, respectively. The differential reflection contrast was achieved by (R_sample − R_substrate)/R_substrate.

Photodetector measurements

The measurements were carried out in the same cryostat chamber used for the low-temperature PL test. Keithley 2612 was used to apply the source-drain bias, while Keithley 2450 was used to apply the source-gate bias. A supercontinuum white-light laser source (Fianium WhiteLase SC400) and acousto-optic tunable filter were used to generate monochromatic light. For the photocurrent test, the laser was focused to a light spot around 1 μm. By changing the light spot position, pristine WS₂ and HOIST area in the same device were tested. For the photocurrent mapping, a motorized stage was used to change the sample position with photocurrent recorded.

First-principles calculations

Density functional calculations were performed using the local density approximation implemented in the Quantum Espresso package. The vacuum distance was set to be 30 Å between adjacent layers to avoid spurious interactions. The vdW interaction was included by the DFT-D2 method. We adopted an in-plane herringbone lattice structure for the monolayer Me-PTCDI. The geometric structure was relaxed until the force converges within 0.01 eV/Å. The layer distances were also checked using the Perdew-Burke-Ernzerhof (PBE) functional as implemented in the Vienna Ab initio Simulation Package. The GW and GW + BSE calculations were performed with the BerkeleyGW package. The dielectric matrix was constructed with a cutoff energy of 50 rydberg. The dielectric matrix and the self-energy were calculated on a 16 × 16 × 1 k-grid. The quasiparticle bandgap was converged to within 0.05 eV. In the calculation of optical absorption spectra, the quasiparticle band structure and electron-hole interaction kernel were interpolated onto a 96 × 96 × 1 fine k-grid, with the 1s exciton binding energy converged to within 0.05 eV.

ET rates estimation

The Dexter ET rates can be analytically expressed via the Fermi golden rule (48, 49)

$$\begin{array}{c}K=\frac{2\mathrm{\pi }}{\mathrm{\hslash }}\sum _A\sum _D\left|V({\mathrm{\varphi }}_A^e,{\mathrm{\varphi }}_A^h,{\mathrm{\psi }}_D^e,{\mathrm{\psi }}_D^h)\right|{}^2\mathrm{\delta }(E_D-E_A)\hfill \end{array}$$ (2)

with the exciton orbits ${\mathrm{\varphi }}_A^e{\mathrm{\varphi }}_A^h$ of the TMDC monolayer as the acceptor and the excitonic states ${\mathrm{\psi }}_D^e{\mathrm{\psi }}_D^h$ of the molecule Me-PTCDI as the donor. The delta function makes sure that only energy-conserving processes contribute. The exciton energy of 1s state of Me-PTCDI and the 2s state of WS₂ is nearly perfect aligned, suggesting large ET in this type heterostructure.

In the exchange Coulomb interaction V, which is determined by

$$V=⟨{{\mathrm{\varphi }}^{\ast }}_A^e{\mathrm{\psi }}_D^e\mid H_I\mid {\mathrm{\varphi }}_A^h{{\mathrm{\psi }}^{\ast }}_D^h⟩$$ (3)

where H_I is the system Hamiltonian. The Coulomb interaction strength is determined by

$$H_I=\frac{e^2}{4\mathrm{\pi ϵ}(r-r^{\prime })}$$ (4)

The screening dielectric constant ϵ is determined experimentally, with values of ~5.6 for Me-PTCDI/WS₂ and 6.0 for WS₂/MoS₂. Overall, the screening effect has only a minor influence on the transition rate between Me-PTCDI/WS₂ and WS₂/MoS₂, as the dielectric constants of the two heterostructures are relatively similar. Instead, the interlayer separation plays a more dominant role, as the Dexter transfer rate follows the relation $K_{\text{Dexter}}~e^{-\mathrm{\beta }r}$ , where $\mathrm{\beta }$ is a decay factor dependent on the wave function overlap and $r$ is the interlayer distance—both of which are strongly correlated with the separation between layers.

For the case of exciton in our manuscript, V can be further derived as

$$\begin{array}{c}V=⟨{\mathrm{\Psi }}_{2s}^{{\text{WS}}_2}{\mathrm{\Psi }}_0^{\text{Me}-\text{PTCDI}}\mid H_I\mid {\mathrm{\Psi }}_0^{{\text{WS}}_2}{\mathrm{\Psi }}_{\text{Frenkel}}^{\text{Me}-\text{PTCDI}}⟩\hfill \end{array}$$ (5)

${\mathrm{\Psi }}_0^{\text{Me}-\text{PTCDI}}$ and ${\mathrm{\Psi }}_0^{{\text{WS}}_2}$ represent the ground states of the exciton in each layer of the bilayer system, respectively. ${\mathrm{\Psi }}_{2s}^{{\text{WS}}_2}$ and ${\mathrm{\Psi }}_{\text{Frenkel}}^{\text{Me}-\text{PTCDI}}$ is the exciton sate that is determined by

$${\mathrm{\Psi }}_{2s}^{{\text{WS}}_2}={\sum }_{cv}{A}_{\mathit{cv}}^{2s}\mid c⟩\mid v⟩$$ (6)

$${\mathrm{\Psi }}_{\text{Frenkel}}^{\text{Me}-\text{PTCDI}}={\sum }_{hl}{A}_{\mathit{hl}}^{\text{Frenkel}}\mid h⟩\mid l⟩$$ (7)

By solving the $A_{\mathit{cv}}^{2s}$ and $A_{\mathit{hl}}^{\text{Frenkel}}$ with the Bathe-Salpeter equation, from the Bathe-Salpeter-Equation using the BerkeleyGW package,

$$\begin{array}{c}(E_c-E_v)A_{\mathit{cv}}^S+\sum _{v^{\prime }{c}^{\prime }}(K_{\mathit{vc},v^{\prime }{c}^{\prime }}^{\mathit{eh},d}+K_{\mathit{vc},v^{\prime }{c}^{\prime }}^{\mathit{eh},x})A_{c^{\prime }{v}^{\prime }}^S=E_S{A}_{\mathit{cv}}^S\hfill \end{array}$$ (8)

where the direct and exchange electron-hole interaction kernels are

$$\begin{array}{c}{K}_{\mathit{vc},v^{\prime }{c}^{\prime }}^{\mathit{eh},d}=-\int {\mathit{\text{drdr}}}^{\prime }{\mathrm{\psi }}_c^{\ast }\left(r\right){\mathrm{\psi }}_{c^{\prime }}\left(r\right)\frac{e^2}{4\mathrm{\pi ϵ}\mid r-r^{\prime }\mid }{\mathrm{\psi }}_v\left(r^{\prime }\right){\mathrm{\psi }}_{v^{\prime }}^{\ast }\left(r^{\prime }\right)\hfill \end{array}$$ (9)

$$\begin{array}{c}{K}_{\mathit{vc},v^{\prime }{c}^{\prime }}^{\mathit{eh},x}=\int {\mathit{\text{drdr}}}^{\prime }{\mathrm{\psi }}_c^{\ast }\left(r\right){\mathrm{\psi }}_v\left(r\right)\frac{e^2}{4\mathrm{\pi }{\mathrm{ϵ}}_0\mid r-r^{\prime }\mid }{\mathrm{\psi }}_{c^{\prime }}\left(r^{\prime }\right){\mathrm{\psi }}_{v^{\prime }}^{\ast }\left(r^{\prime }\right)\hfill \end{array}$$ (10)

the ET rate can be calculated by

$$\begin{array}{c}\begin{array}{c}\begin{array}{c}K=\frac{2\mathrm{\pi }}{\mathrm{\hslash }}{\left|\sum _{\mathit{cv}}\sum _{\mathit{hl}}\int \mathit{dr}\int d{r}^{\prime }{A}_{\mathit{cv}}^{2s}{A}_{\mathit{hl}}^{\text{Frenkel}}{\mathrm{\psi }}_v^{\ast }\left(r\right){\mathrm{\psi }}_h\left(r\right)\frac{e^2}{4\mathrm{\pi ϵ}(r-r^{\prime })}{\mathrm{\psi }}_l^{\ast }\left(r^{\prime }\right){\mathrm{\psi }}_c\left(r^{\prime }\right)\right|}^2\hfill \\ \mathrm{\delta }(E_{2s}-E_{\text{Frenkel}})\hfill \end{array}\hfill \end{array}\hfill \end{array}$$ (11)

Orbital wave function simulation

DFT calculations were performed using the generalized gradient approximation for the exchange-correlation potential, the projector-augmented wave method, and a plane wave basis set as implemented in the Vienna ab initio simulation package. A plane-wave basis set was used, with a kinetic energy cutoff of up to 400 eV applied consistently across all computations. For geometry optimization, the Heyd-Scuseria-Ernzerhof hybrid functional (HSE06) was used. Brillouin zone integration was carried out using a k-mesh of 15 × 15 × 1 for the 1 × 1 H-WS₂ monolayer and a coarser mesh of 2 × 1 × 1 for Me-PTCDI. During these optimizations, the shape and volume of each supercell were maintained at their respective monolayer values while allowing all atoms within the cell to relax until the residual forces on each atom were below 0.03 eV/Å. The heterostructure modeling the Me-PTCDI/WS₂ interface comprised a 5 × 5√3 WS₂ lattice and a 1 × 1 Me-PTCDI molecule, incorporating a 1% tensile strain on the WS₂ layer. In the electronic structure calculations, dispersion corrections were included at the DFT-D3 level using the PBE functional. For sampling the first Brillouin zone of the PTCDI/WS₂ heterostructure, a k-mesh of 2 × 1 × 1 was adopted.

Supplementary Materials

This PDF file includes:

Notes S1 to S3

Tables S1 to S4

Figs. S1 to S24

References