Electrical Control of Exciton Diffusion via Tuning Exciton States

Stacking of monolayer 2D transition metal dichalcogenides (TMDs) into van der Waals heterostructures can enable the formation of interlayer excitons (IXs) with long lifetimes and permanent out‐of‐plane electric dipoles, allowing them to propagate over long distances. While early studies on TMD heterobilayrs show efficient electrical control of excitonic transport of IXs by creating different energy potentials, the electrically controllable exciton states and associated spatial migration remain elusive. Here, an electrical control of exciton diffusion through the change of exciton states between charged IXs (CIXs) and charged intralayer excitons is reported. The repulsive dipolar interaction of IXs accounts for the growing exciton cloud size and increasing diffusion length in the power‐dependent PL study. More importantly, the electrically tunable spatial exciton distribution is demonstrated by switching the exciton states, which shows a 1.5‐fold change in diffusion length and an order of magnitude increase in lifetime from charged intralayer excitons to CIXs. The electrical control of exciton states and the relevant diffusion dynamics provide another knob to study the interplay between propagation and many‐body interactions for the development of excitonic devices.


Introduction
[3] Particularly, in the case of type-II band alignment TMD heterobilayers, electrons and holes tend to reside in separated layers, forming interlayer excitons (IXs) with the lowest DOI: 10.1002/apxr.202200083[6] Due to the reduced overlap of the wavefunction of spatially separated electron-hole pairs, [7] IXs have been reported to exhibit longer lifetimes than intralayer excitons, [8][9] which can reach hundreds of nanoseconds. [10][12] Furthermore, lattice mismatch and twist angle between the two layers can lead to the existence of moiré patterns, where the periodic potentials modify the electronic behaviors of IXs. [13,14]hese properties ensure that IXs are promising candidates for studying exciton migration in electrical controllable excitonic devices. [15]By employing the long-lived IXs, pioneers have demonstrated that IXs can transport across the entire sample driven by exciton concentration gradient from local excitation. [10,16] However, such excitonic devices always require multiple pre-patterned electrodes with specific shapes/angles to alter the energy landscape [17] or an additional insulating separator to reduce the moiré interaction, [16] which increases the difficulty and cost of device preparation.Therefore, it is urgent to explore alternative approaches to achieve effective exciton diffusion manipulation without complex procedures.
Our previous study has already demonstrated prominent interlayer emission in 2D perovskite/monolayer TMDs heterostructures irrespective of stacking angles and momentum mismatch. [23]In particular, the exciton behaviors can be further electrically controlled in the 2D perovskite/monolayer WS 2 devices, where the exciton states can be electrically tuned from charged IXs (CIXs) to charged intralayer excitons by switching from type-II to type-I band alignment. [24]In this way, we can control the exciton flux by changing its exciton states to trace the dynamics of the exciton distribution.In addition, 2D perovskites are also promising as charge-delivery materials with long-range exciton transport ability. [25,26]Here, we report on the electrical control of exciton diffusion by switching between the CIXs and charged intralayer excitons, where the diffusion length varies from 1.99 to 2.89 μm with lifetime changes from 0.09 to 1.94 ns.Our findings provide an alternative method to control the exciton motion by electrically switching the exciton states, paving the way toward the exciton dynamics and excitonic devices.

Results
Figure 1a depicts the schematic of an h-BN-encapsulated WS 2 /(iso-BA) 2 PbI 4 device on a Si 3 N 4 (100 nm)/Si substrate.The detailed preparation process can be found in the Experimental Section.The few-layer graphene (FLG) sheet placed on the top serves as a transparent electrode allowing us to apply uniform vertical electrical fields in the heterostructure between the top gate and the highly doped bottom substrate.Figure 1b shows an optical image of the device, where the WS 2 layer is partly overlaid on the (iso-BA) 2 PbI 4 flake for direct comparison with the heterostructure region.According to previous studies, the energy band between monolayer WS 2 and (iso-BA) 2 PbI 4 is type-II alignment [27,28] (Figure 1c).Therefore, under photoexcitation, electrons and holes tend to move to monolayer WS 2 and (iso-BA) 2 PbI 4 , respectively, resulting in IXs (blue oral in Figure 1c).We first acquire photoluminescence (PL) spectra under a 556 nm laser excitation, as shown in Figure 1d.All measurements were carried out at 78 K, if not otherwise specified.The monolayer WS 2 shows the prominent negative trion (X − ) emission due to the ndoped nature, [29] and the heterostructure region exhibits an appreciable broad emission below the X − emission which can be ascribed to negative CIX (IX − ) based on our previous work. [24]o obtain the spatial diffusion of different exciton states, we have captured the charge-coupled device (CCD) images of the emission from monolayer WS 2 and the heterostructure, respectively.As shown in Figure 1e, the image of the heterostructure region exhibits a larger size of the exciton cloud than that of the monolayer WS 2 , which are both significantly larger than the focused 556 nm continuous wave laser (Figure S1, Supporting Information).To quantitatively analyze the exciton diffusion, we extract the central vertical cross-section profiles of the emission intensity, where the evolution of exciton density can be described by the following equation [30,31] where n is the exciton density, D is the exciton diffusion coefficient, μ is the exciton mobility, and  is the exciton lifetime, respectively.The first term on the right-hand side of Equation ( 1) represents the exciton diffusion while the second term denotes the repulsive exciton-exciton interaction. [32]At a low excitation power regime, we ignore the exciton-exciton annihilation effect due to the low exciton density (Figure S2, Supporting Information) and the long organic cation of 2D perovskite that increases the interlayer distance thus reducing the annihilation rate. [16]Also, the repulsive dipolar interaction is assumed to be disregarded at a low excitation power of 13.5 μW since the repulsive dipole-dipole interaction has a small impact on IX diffusion below this excitation power range (Figure S2, Supporting Information). [20]Thus, we can obtain the analytical solution of the steady-state exciton diffusion equation, given by the convolution of the laser Gaussian function and the modified Bessel function of the second kind K 0 [33]   n where r, L D , and w are distance, diffusion length, and width of the laser spot, respectively.Here, by using a Gaussian profile of the excitation spot, the w of the 556 nm laser is fitted to be 1.03 μm (Figure S1b, Supporting Information).Therefore, the L D of monolayer WS 2 and the heterostructure are fitted to be 1.56 and 1.92 μm by solving Equation (2), respectively (Figure 1f).The larger diffusion length of IX − than that of X − is in accordance with the description of IXs above.We also note that the diffusion length of X − is somewhat larger than that previously reported in monolayer WS 2 , which may arise from the h-BN protection that reduces the dielectric disorder thus facilitating exciton diffusion. [34,35]e have further performed power-dependent diffusion of IXs in this device.Figure 2a shows the PL spectra as a function of laser power at the same excitation spot.With increasing incident power, the peak energy gradually blueshifts (Figure S2a, Supporting Information), which is the hallmark of IXs. [8]Figure 2b,c shows the CCD images of the normalized intensity of IXs obtained at low and high excitation powers, in which the exciton cloud exhibits a growing size along the sample shape at higher incident power.We then calculate the L D from the cross-section spatial profiles, as shown in Figure 2d.The IXs exhibit a L D of 1.92 μm at the excitation power of 13.5 μW and 2.40 μm at the excitation power of 815 μW. Figure 2e further shows the L D as a function of incident power, which shows no appreciable shift at low excitation power and gradually increases as the incident power exceeds 34 μW (Figure S2b, Supporting Information).This trend suggests that the repulsive dipolar interaction can be ignored at low excitation regimes (<34 μW), while the dipole-dipole repulsion becomes dominant at elevated exciton densities, which acts as a source of drift force that drives the exciton motion across the sample in Figure 2c. [16,32]In contrast, the individual monolayer WS 2 shows little variation in L D at different excitation power, due to the random dipole directions of intralayer excitons and suppressed exciton-exciton annihilation by h-BN encapsulation [35,36] (Figure S3, Supporting Information).We also recorded the variation of L D with temperature in Figure S4 (Supporting Information).As the temperature increases, the IX emission gradually redshifts and becomes negligible above 240 K, consistent with our previous work. [23]Meanwhile, the L D decreases at elevated temperatures, probably due to enhanced phonon scattering that facilitates nonradiative recombination. [21,37]o reveal the electrical control of exciton diffusion, we have captured CCD images of the heterostructure as a function of applied voltage.Because of the relatively small valance band offset between WS 2 and (iso-BA) 2 PbI 4 , the type-II band alignment can be switched to type-I band alignment by electric field control (Figure S5a, Supporting Information), [24,38] which manifests itself as a transition from the IX − emission to X − emission (Figure 3a).Further considering the different diffusion behaviors of IX − for heterostructure and the X − of monolayer WS 2 in Figure 1, we can also study the electrically controllable spatial extent of the PL emission.As shown in Figure 3b-d, the CCD images of the  device exhibit a growing exciton cloud size from −30 to 30 V, corresponding to the X − emission at the negative voltage and IX − emission at the positive voltage, respectively.By fitting the crosssection profiles at different voltages with Equation (2), we can obtain the L D of 1.99, 2.53, and 2.89 μm at −30, 0, and 30 V, respectively (Figure 3e).The noticeable changes in the CCD images of the device under different voltages indicate that it is feasible to modulate the spatial motion of excitons by electrically switching the exciton states, providing a new approach to achieve excitonic devices.
Figure 4a further summarizes the L D evolution as a function of gate voltage, where the L D gradually increases from −30 to 30 V, accompanied by the transition of exciton states from the X − of monolayer WS 2 to the IX − of the heterostructure.This variation in diffusion length follows the same trend as the change in the lifetime for different exciton states.As shown in Figure 4b, the lifetime of the device is enhanced by a factor of 20 as the voltage changes from negative to positive, which is estimated to be 0.09 ns at −30 V, gradually increasing to 1.94 ns at 30 V with a single exponential fit (Figure S5b, Supporting Information).For this reason, the oriented dipole direction and the reduction in wavefunction overlap of electrons and holes enable IX − a longer radiation lifetime compared to the X − , thus allowing the electrically tunable exciton diffusion by changing their states.For comparison, we also record the dynamics of X − distribution in the individual monolayer WS 2 in Figure S6 (Supporting Information), where the L D almost unchanged under electric field modulation due to the barely changed exciton state.This contrast further illustrates the high diffusion tunability between IX − and X − , which is promising for electrically controllable excitonic devices.
We have further studied the stacking sequence on the exciton diffusion manipulation.Figure S7a,b (Supporting Information) describes the heterostructure device with (iso-BA) 2 PbI 4 on the top of monolayer WS 2 .The PL evolution in Figure S7c (Supporting Information) shows an opposite tendency to Figure 3a, in which the PL emission is switched from IX − at negative voltages to X − at positive voltages.Moreover, the diffusion length also decreases from 2.15 to 1.59 μm (Figure S7d, Supporting Information), along with the lifetime reduction from 3.88 to 0.1 ns (Figure S7e, Supporting Information).Besides, this ability to regulate the exciton diffusion under electric field control can be maintained up to 230 K until the IX − emission disappears.To this end, the use of an electric field to alter the exciton states and thus change the diffusion length is highly effective, and this manipulation is independent of the stacking angles and sequences, overcoming the rigorous atomic registry of the original TMD heterobilayers and further promoting the development of electrically driven excitonic devices.

Conclusion
In summary, we have demonstrated the electrically tunable exciton diffusion based on the switch of exciton states in the WS 2 /(iso-BA) 2 PbI 4 heterostructure.Power-dependent PL images of IXs show an obvious exciton diffusion extension due to the repulsive dipolar interaction.More importantly, we can visualize the exciton propagation of different exciton states under electric field control, where the oriented dipole direction enables CIXs a larger diffusion length and a longer lifetime than charged intralayer excitons.Our finding provides a new paradigm of electrical control of excitonic diffusion/drift.Further studies to achieve excitonic devices could include tunable exciton states, enabling the efficient control of exciton diffusion utilizing different exciton species and associated physical properties.

Experimental Section
Sample Preparations: The 2D perovskite single crystals were synthesized by solution methods according to previous work.WS 2 , h-BN, and FLG bulks were purchased from 2D semiconductors and HQ graphite.The corresponding monolayer or thin flakes were mechanically exfoliated on the polydimethylsiloxane (PDMS) stamps first and then transferred to the substrate by the dry-transfer method.The Au (50 nm)/Cr (10 nm) electrodes were prefabricated onto wafers by photolithography or electron beam lithography and thermal evaporation.All samples were not thermally annealed to avoid the degradation of 2D perovskites.
Optical Measurements: Optical images were captured with the microscope (Olympus BX53M).Samples were sealed in a liquid nitrogen bath cryostat (Cryo Industries of America Inc.) with a 10 −7 Torr vacuum.PL spectra were obtained on a home-built Raman spectrometer (Horiba iHR-320) with a 50× objective lens (NA = 0.65) under the excitation of a continuous wave 556 nm laser.For time-resolved PL measurement, the sample was excited by a supercontinuum white light laser (NKT) with a repetition frequency of 80 MHz (NKT) together with the acousto-optic tunable filter (OYSL photonics), then synchronized to a single photon counting module (PicoQuant TimeHarp 260) and a single photon detector (Micro Photon Devices).For electrically controllable PL measurement, the voltage was supplied by a sourcemeter (Keithley 2400).For the fitting procedure, the process of exciton diffusion was simulated by solving Equation (2) in MATLAB.

Figure 1 .
Figure 1.Exciton diffusion in a WS 2 /(iso-BA) 2 PbI 4 heterostructure.a) Schematic of an h-BN encapsulated WS 2 /(iso-BA) 2 PbI 4 heterostructure with the top gate on the Si 3 N 4 /Si substrate.b) Optical image of the device.The yellow, pink, gray, orange, and cyan dashed lines highlight the FLG, top h-BN, WS 2 , (iso-BA) 2 PbI 4 , and bottom h-BN layers.Scale bar, 20 μm.c) Type-II band alignment between WS 2 and (iso-BA) 2 PbI 4 and the formation of IXs.d) PL spectra of the individual WS 2 and the heterostructure under the excitation of the 556 nm laser.e) CCD images of the normalized X − and IX − PL intensity of WS 2 and the heterostructure with the power of 13.5 μW, respectively.The white dashed lines indicate the shape of the sample.Scale bar, 1 μm.f) Cross section of the normalized intensity profiles along the yellow vertical dashed line in the center of (e).

Figure 2 .
Figure 2. Power dependence of IXs diffusion in the WS 2 /(iso-BA) 2 PbI 4 device.a) Power-dependent PL spectra of IX − emission.The gray dashed line indicates the peak energy shift.b,c) CCD images of the normalized IX − PL intensity under the power of 13.5 and 815 μW, respectively.The white dashed lines indicate the shape of the heterostructure.Scale bar, 1 μm.d) Cross section of the normalized intensity profiles along the vertical line in the center of (b) and (c).e) Diffusion length as a function of incident power.

Figure 3 .
Figure 3. Electric field control of exciton diffusion in the WS 2 /(iso-BA) 2 PbI 4 device.a) Color map of PL spectra as a function of voltage, which shows the PL emission from X − to IX − .b-d) CCD images of the normalized PL intensity at −30, 0, and 30 V under the power of 13.5 μW, respectively.The gray dashed grid spacing is 1 μm.e) Cross section of the normalized intensity profiles along the vertical line in the center of (b)-(d).

Figure 4 .
Figure 4. Electrical control of exciton diffusion dynamics.a) Diffusion length and b) lifetime of the exciton emission as a function of voltage.The gradient gray area indicates the instrumental response function.