Twist-Dependent Tuning of Excitonic Emissions in Bilayer WSe2.

Monolayer (ML) transition metal dichalcogenides (TMDCs) have been rigorously studied to comprehend their rich spin and valley physics, exceptional optical properties, and ability to open new avenues in fundamental research and technology. However, intricate analysis of twisted homobilayer (t-BL) systems is highly required due to the intriguing twist angle (t-angle)-dependent interlayer effects on optical and electrical properties. Here, we report the evolution of the interlayer effect on artificially stacked BL WSe2, grown using chemical vapor deposition (CVD), with t-angle in the range of 0 ≤ θ ≤ 60°. Systematic analyses based on Raman and photoluminescence (PL) spectroscopies suggest intriguing deviations in the interlayer interactions, higher-energy exciton transitions (in the range of ∼1.6-1.7 eV), and stacking. In contrast to previous observations, we demonstrate a red shift in the PL spectra with t-angle. Density functional theory (DFT) is employed to understand the band-gap variations with t-angle. Exciton radiative lifetime has been estimated theoretically using temperature-dependent PL measurements, which shows an increase with t-angle that agrees with our experimental observations. This study presents the groundwork for further investigation of the evolution of various interlayer excitons and their dynamics with t-angle in homobilayer systems, critical for optoelectronic applications.

Introduction

Van der Waals (vdW) coupling is emerging as a powerful method to engineer and tailor the physical properties of atomically thin two-dimensional (2D) materials.[1−4] Transition metal dichalcogenides (TMDCs) with the chemical formula MX2 (M = W, Mo, and so on and X = S, Se, or Te) are a class of 2D materials consisting of predominantly vdW-coupled atomically thin layers and exhibiting interesting optical properties governed by their structural symmetry[5,6] and interlayer coupling,[7−9] which are highly susceptible to stacking. As these ultrathin materials are very sensitive to the dielectric environment and interlayer interactions, understanding these interactions is a key scientific challenge for building functional homo- or heterojunction devices and novel hybrid 2D materials.[10] In the evolving era of twistronics, twisted vdW hetero- and homostructures have demonstrated a plethora of novel phases and functionalities.[11−13] They have many advantages over conventional heterostructures including atomically sharp interfaces, no interdiffusion of atoms, and no lattice parameter constraints.[2]

Synthesis of monolayer (ML)-to-few-layer TMDCs using chemical vapor deposition (CVD) has already been reported by many research groups,[14−17] and their layer-dependent electronic, optical, and vibrational properties have also been investigated in sufficient detail.[18−23] In the last few years, there has been a surge of interest in the heterojunction of these ML TMDCs.[24−28] Owing to a large number of TMDCs being available, a variety of combinations have been implemented in the literature to observe several unique intriguing optical and electrical features.[29−32] This leads to a strong motivation to understand how the twist affects interlayer interactions and the excitonic level properties in these materials. However, limited investigations are available on homobilayer systems, which are essential for emerging applications in twistronics, spintronics, valleytronics, and optoelectronics. A few reports on homobilayers, such as Van Der Zande et al.[10] showing optical and vibrational properties of mechanically stacked t-BL MoS2 bilayers, Ji et al.[33] showing changes in the photoluminescence (PL) pathway in t-BL WS2, and Scuri et al.[34] demonstrating gate-controlled valley dynamics in t-BL WSe2, can be found. The limitations in the study on homo-t-BL TMDCs are, so far, due to the difficulties involved in the transfer process and challenges involved in determining the exciton dynamics, the exact origin of PL peaks, and evolution of interlayer interactions with t-angle.

In this paper, we demonstrate an intriguing effect of t-angle on the exciton–trion transition and the evolution of interlayer coupling in t-BL WSe2. We predict the presence of interlayer excitations for different t-angles in the range of 0 ≤ θ ≤ 60°. Artificially stacked t-BLs on SiO2/Si substrate with different t-angles demonstrate tunable PL emissions including a drastic red shift at room temperature (RT) PL and competition between different excitonic emission peaks with increasing t-angle relative to 0 and 60°. The observed variations provide evidence of a t-angle-dependent change in stacking symmetry, leading to variation in interlayer coupling strength and interlayer excitons (IEs) in our t-BL systems.

Methods

The ML WSe2 flakes on a sapphire substrate were synthesized using a low-pressure chemical vapor deposition (LPCVD) method similar to that in our earlier report.[35] The as-grown ML WSe2 flakes were transferred onto a 300 nm SiO2/Si substrate using a PMMA-assisted transfer process.[35] The transfer process was repeated another time on WSe2/(SiO2/Si) prepared earlier to synthesize BL WSe2 flakes. To enhance the coupling between the two layers, the samples were annealed in vacuum (<0.1 Pa) with a flow of Ar gas (100 sccm) at 300 °C for 12 h. BL flakes with selected twist angles ranging from 0 ≤ θ ≤ 60° were chosen for Raman and PL analyses.

Optical microscopy (OM) images were taken on an Olympus (model no. BX51RF) microscope, with a 100X objective lens with NA ∼ 0.95. Both low-frequency (LF) and high-frequency (HF) Raman measurements were performed at RT using a confocal Raman system (Wi-Tech, model no. Alpha 300 M+) with backscattering geometry under 488 nm laser excitation. The laser was focused to a spot size of ∼1 μm on the sample, obtained with 1800 gr/mm grating. PL spectra of WSe2 flakes prepared on 300 nm SiO2/Si substrates were obtained using a high-resolution μRaman spectrometer (LabRam 800, Horiba Jobin Yvon) in backscattering geometry. Green laser (514 nm) and red laser (632 nm) were used as excitation sources for RT measurement, which were focused to a spot size of ∼1 μm on the sample, obtained with 600 gr/mm grating. Low-temperature (LT) PL measurement was carried out with 488 nm laser excitation with the same configuration as mentioned before. The laser power was kept low (∼50 μW) to avoid local heating.

Results and Discussion

In this work, we consider various BL WSe2 samples with different t-angles in the range of 0 ≤ θ ≤ 60° as shown in Figure , and their corresponding schematics are given in Figure S1 (Supporting Information). The thickness of vertically stacked ML flakes is confirmed by AFM measurements, illustrated in Figure S2 (Supporting Information), and found to be consistent with earlier reports.[36−38] LF RT Raman spectra of t-BL WSe2 samples shown in Figure reveal shear (S) and layer breathing (LB) modes in symmetric 0° (60°) stacking at ∼19 (∼16.5) cm–1 and ∼33 (∼28) cm–1, respectively, analogous to the MoX2 system.[39,40] LB modes in symmetric stacking are addressed as LB1. Here, 0 and 60° are shifted with respect to each other. This is in accordance with their difference in the stacking orders (R and H, respectively). Decrease (Increase) in the intensity of S (LB1) mode from 60 to 0° and greater separation of the two peaks for 0° confirm the different polytypes,[41,42] while an extra LB (called LB2) mode emerges for asymmetric stacking with no evidence of S mode, confirming the absence of restoring forces in intermediate t-angles. The emergence of the LB2 mode may be attributed to the misaligned structure in the asymmetric stackings. On examining the variation of LB1 with t-angle, softening of the mode for asymmetric stackings is noted, indicating weaker interlayer coupling. In contrast, HF RT Raman spectra do not show considerable shifts with t-angle, eliminating the presence of significant strain in the samples.

Figure 1

[a–f] OM images of t-BL WSe2 samples on SiO2/Si substrate with different t-angles indicated by θ.

Figure 2

LF Raman spectra of t-BL WSe2 with different t-angles in the range of 0 ≤ θ ≤ 60°. Shear (S) and layer breathing (LB1 and LB2) modes are marked.

HF Raman spectra are separated into two parts, as shown in Figure S3a,b. Intralayer E2g1 [Γ] (∼248.7 cm–1) and A1g [Γ] (∼251.5 cm–1) modes, seldom resolved together due to excitation polarization dependency,[43] are indicated along with a higher-order resonance 2LA[M] mode in Figure S3a. Moreover, improved interlayer coupling due to annealing of artificially stacked samples is confirmed from the emergence of B2g1 [Γ] mode at ∼308 cm–1 in t-BL samples and its absence in ML samples, as shown in Figures S3b and S4. Also, the intensity variation of this mode with t-angle agrees with the conclusion drawn from the softening of the LB1 mode regarding the interlayer interactions. In addition, its higher intensity for 60° than 0° t-BL confirms the stronger interlayer coupling in the former owing to its H-type stacking as discussed earlier.

Furthermore, RT PL spectra are depicted in Figure a for ML and t-BL WSe2 samples to analyze t-angle dependency on excitonic transition. ML WSe2 shows a sharp peak at ∼1.68 eV, attributed to direct-band-gap (BG) K–K transition. The asymmetric nature of the PL envelope of ML WSe2 indicates contributions from neutral exciton (AX0) and charged exciton (AX–) separated by ∼28–32 meV, which is in good agreement with earlier reports.[44] The narrow full width at half-maximum (FWHM) of ∼41 meV for AX0 gives an inference of highly crystalline WSe2 flakes with minimal defect states. The wider spectrum in BL samples is the result of several momentum dark exciton states and trion states in close proximity to the highest-energy bright exciton peak. The additional peak (indirect in nature) at ∼1.58 eV (0° t-BL) is regarded as a momentum dark exciton or a localized exciton and labeled IX. IX is apparent for stable stackings at 0 and 60° but not for asymmetric stackings, indicating a direct BG nature for the latter. Interestingly, an unintuitive red shift in PL is observed for intermediate t-angles compared to stable stackings, as illustrated in Figure b. Contradictorily, in the literature, several earlier works have reported a blue shift in PL with increasing t-angles in BL WSe2.[45,46][45,46] But these studies carried out at cryogenic temperatures (<10 K) are for momentum indirect Q–K or Q–Γ emissions at lower energies (∼1.5–1.6 eV). As opposed to Mo-based TMDs,[47−49] the direct emission peak near ∼1.7 eV in WSe2 is strongly quenched at lower temperatures due to the presence of lower-lying dark exciton states (see Supporting Information, Figure S5). This makes it difficult to resolve the peaks near AX0 even at low temperatures. However, the red shift in the direct exciton peak of W-based TMDs is evident in recent reports by Zheng et al.[50] and Ji et al.[33] Also, in the report by Merkl et al.,[46]the K–K peak is seen to shift closer to the Q–K peak with increasing t-angles at 4 K in WSe2. Although the results in these reports indicate such an interesting feature, a discussion on the origin of such a shift is clearly missing.

Figure 3

[a] RT PL spectra at 633 nm excitation for ML and t-BL-WSe2 with different t-angles, respectively. [b] Peak position of AX0 and AX– with different t-angles. [c] Peak intensity ratio of trion and exciton with different t-angles.

For confirmation, RT PL measurements were repeated using a different laser excitation (514 nm) on all t-angles, and the same trend was found, as shown in Figure S6 (Supporting Information). Initially, one may come up with two possible explanations of either strain-induced (due to twist) red shift or K–K band-gap reduction. However, on the one hand, Raman measurements indicate the absence of any significant strain, and on the other hand, our density functional theory (DFT) calculations (details in Supporting Information Note 1) show the negligible effect of t-angle on K–K BG as shown in Figure . At 60 and 21.78° (chosen to reduce computational complexity) t-angles, a similar BG of ∼1.3 eV is obtained at K valley with merely a ∼9 meV difference. For 0 and 27.79°, refer to the Supporting Information Figure S7. This is widely expected in group VI-based TMDs due to the major contributions from d orbitals of transition metal at K point, leading to comparatively weaker interlayer coupling at the band edge state. Further, the AX0 peak blue-shifts from ML to symmetrically stacked BL WSe2 as shown in Figures a and S6, which is significant in LT PL (Figure a). This will be an unexpected result if we consider the AX0 peak to be solely from intralayer A exciton emission. Here, we consider AX0 in t-BL samples not to be from K–K intralayer exciton owing to the red shift with t-angle and blue shift from ML to BL. This strongly indicates the presence of interlayer excitons (IEs). As explained earlier, the difficulty in resolving these peaks even at cryogenic temperatures makes it more challenging to determine the exact origin. However, we try to present an intuitive and logical explanation here.

Figure 4

DFT calculated band structure of t-BL WSe2 for 60° [a] and 21.78° [b]. Red arrows indicate the direct BG transitions. Blue and yellow arrows correspond to the indirect BG transitions.

Figure 5

[a] PL spectra at 100 K and 488 nm excitation for ML and t-BL-WSe2 with angles 0, 35, and 60°, respectively. [b] Lorentzian FWHM for AX0 is extracted from Voigt profile fitting done on the PL spectra obtained at various temperatures for ML and t-BL flakes.

First, due to the contributions from W d orbitals at K/K′ point in BL WSe2, the interlayer hopping amplitude of both the electrons and holes is less than the spin-splitting at the conduction and valence bands (specifically for H stacking), respectively. This restricts the carriers to a single layer at the K point of the Brillouin zone.[48,51] However, this restriction is valid only at the band edge K point of the Brillouin zone and not at a point close to K.[30] Owing to the finite momentum of the incident photon, the excitons can be excited at a position slightly away from the band edge state. Das et al.[52] provide details on the finite probability of formation and emission of this direct interlayer exciton. Hence, for the case of symmetric stackings (0 and 60° t-BL), the presence of momentum direct interlayer exciton at K can be considered. As the binding energy of interlayer exciton is less than that of intralayer exciton and the K–K electronic BG does not have a considerable variation, the blue shift of the AX0 peak observed from ML to BL is justified. Also, a difference in the peak position of AX0 between 0 and 60° t-BL, shown in the PL spectra, can be explained using the deviation in spin-splitting and spin-valley locking of interlayer excitons in the two symmetrically different systems.[30] The formation of direct interlayer exciton at K occurs from the upper (lower) conduction band minimum in 0° (60°) t-BL WSe2. However, justification for the red shift in the AX0 peak with t-angle is still needed. Higher interlayer separation and momentum mismatch in the asymmetric stackings indicate lower binding energy of the interlayer exciton, as compared to symmetric stackings. This should, in general, lead to a blue shift in the peak position with t-angle, the inverse of the observed variation.

Earlier theoretical investigations on interlayer excitons in BL WSe2 indicate the presence of several momentum dark exciton states (K–Γ and K–K′) in close proximity to the K–K transition (<∼60 meV) peak that remain unresolved to date in experiments. Moreover, spin-splitting in K valley leads to two different indirect K–Γ excitons that are shown to be red-shifted with respect to K–K exciton by ∼40 and ∼100 meV.[53] Interestingly, the peak position of AX0 does not vary for the intermediate t-angles and is approximately ∼45 meV red-shifted from that of symmetric stackings. We assume the AX0 peak in asymmetric stackings to be from the phonon-assisted emission of K–Γ excitons with the electrons in the upper conduction band minimum at K valley. But again, intervalley scattering of holes in WSe2 is considered to be forbidden due to large momentum mismatch and spin orbit splitting at K or K′ valleys. However, as explained earlier, we have carriers near to but not exactly at K point, which makes this scattering to be allowed in nature. Importantly, this scattering is more prominent for thermally excited carriers, i.e., at RT. This is precisely our observation. RT PL spectra show a significant red shift from symmetric to asymmetric stacking when compared to those of LT PL. Furthermore, with the increase in interlayer separation and momentum mismatch, the K–K transition is expected and observed to drastically quench. However, due to delocalization of the holes at the zone center, we have significant contributions from the momentum dark K–Γ excitons for intermediate t-angles.

Next, the energy of the peak labeled IX (∼100 meV red-shifted from K–K), observed in the symmetric stackings, lies close to the expected K–Γ excitons with the electrons in lower conduction band minimum at K valley. The intensity of the IX peaks is observed to drastically quench in the asymmetric stackings, resembling a competition between the two K–Γ excitons. Similarly, in Figure c, competition in the intensity of AX– and AX0 peaks is evident with t-angle. Also, AX– energy shows a similar red shift as discussed earlier. This suggests the interlayer nature of the peak with contributions from K valley. The exact nature of the AX– and IX peaks requires further investigation, which is out of the scope of this work.

Now, we attempt to address exciton dynamics to some extent using the temperature-dependent steady-state PL spectra (Figure S8, Supporting Information). Comprehending radiative recombination processes in TMDCs is challenging and requires precise time-resolved measurements and pump–probe measurements. Also, a complex technique such as four-wave mixing spectroscopy[54] needs to be employed for the determination of homogeneous and inhomogeneous components. Therefore, it is always beneficial to have a theoretical approach for estimating the value of a desired observable that requires an intricate experimental setup for its determination. For radiative lifetime variation with t-angle, a specific approach (Supporting Information Note 2) involving temperature-dependent homogeneous line width (γ) is used. It should be noted that this method is suitable only for the most significant peak (AX0 in our case), as other peaks are mostly dominated by inhomogeneous broadening. Figure a demonstrates the deconvoluted peaks at 100 K for ML and t-BL WSe2 samples. The significant blue shift observed in moving from ML to symmetric t-BL is unusual and only indicates the existence of interlayer excitons as discussed earlier. Here, γ of the AX0 peak (in red) is extracted at temperatures ranging from 100 to 300 K (shown in Figure b) and fitted with Rudin’s function[55] to obtain γ at 0 K, needed for lifetime estimation (refer Supporting Information Note 2). The radiative lifetime calculated for AX0 at RT for ML (∼1.2 ns) and t-BL (0, 35, and 60°) samples (∼4.4, ∼5.2, and ∼4.1 ns, respectively) show a longer lifetime in BL, confirming the indirect nature of excitons in momentum and/or real space. The lifetime evaluated for the ML indicates a slower relaxation channel that dominates at RT[47] and a fast relaxation process that is predominant at low temperatures (∼400 fs for ML and ∼600–800 fs for t-BL at 0 K). However, our focus is based on trends rather than the actual values obtained from the theoretical approximations. Previous reports show improved overall lifetime in BL systems compared to ML due to either trion contribution[30] or indirect excitons. However, in our analysis, we observe an increase in the lifetime of AX0 alone, discarding the role of AX–. Also, the longest lifetime of AX0 obtained for the misaligned stacking (35°) agrees with the transition from K–K to K–Γ excitons, as detailed above. K–K is momentum direct for the case of symmetric stackings yet has a longer lifetime compared to intralayer excitons due to dielectric screening and spatial misalignment. But for other t-angles, the IEs at play are momentum indirect in nature (K–Γ) and are further spatially separated, resulting in the suppression of nonradiative relaxation channels and improvement in radiative lifetimes. Hence, a longer radiative lifetime of AX0 is observed with a red shift in its peak position due to twists relative to stable stackings. These intriguing observations demand further intense investigations into theoretical and experimental aspects to fully comprehend twisted bilayer systems.

Conclusions

In this work, we present various experimental observations in Raman and PL spectra highlighting t-angle dependency in the interlayer coupling, nature of BGs, and interlayer excitons. One major observation was the red shift in PL spectra from symmetric to asymmetric stacking in t-BL WSe2, prominent at RT. Possible explanations for this observation were made corroborating with the existing literature and DFT calculations. Evolution of the interlayer nature in the highest-energy peak from 1L to BL was predicted. Deviations in the interlayer excitons and radiative lifetimes were observed with the variation of stacking symmetry arising from the twist. The higher-energy PL peaks in W-based TMDCs tend to quench with lowering of temperature, increasing the complexity of resolving the peaks close to this energy. Hence, this work demands more rigorous theoretical investigations on twist-dependent evolution of trions and high energy interlayer excitons in these homobilayer systems.