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Momentum resolved ground/excited states and the ultra-fast excited state dynamics of monolayer MoS2

The emergence of transition metal dichalcogenides (TMD) as crystalline atomically thin semiconductors has created a tremendous amount of scientific and technological interest. Many novel device concepts have been proposed and realized (1-3). Nonetheless, progress in k-space investigations of ground/excited state electronic structures has been slow due to the challenge to create large scale, laterally homogeneous samples. Taking advantage of recent advancements in chemical vapor deposition, here we create a wafer-size MoS2 monolayer with well-aligned lateral orientation for advanced electron spectroscopy studies (4-6). Low energy electron diffraction and scanning tunneling microscopy (STM) demonstrate atomically clean surfaces with in-plane crystalline orientation. The ground state and excited state electronic structures are probed using scanning tunneling spectroscopy (STS), angle-resolved photoemission (ARPES) and time-resolved (tr-)ARPES. In addition to mapping out the momentum-space quasiparticle band structure in the valence and conduction bands, we unveil ultrafast excited state dynamics, including inter- and intra-valley carrier scattering and a rapid downward energy shift by ~ 0.2eV lower than the initial free carrier state at Sigma point.


Introduction
Monolayers of semiconducting transition-metal dichalcogenides (TMDs) and their heterostructures have emerged as a powerful system to design novel devices for scientific and technological applications.
Although many novel device concepts have been realized in recent years (1)(2)(3), realizing a scalable and high-quality materials platform remains an outstanding challenge. Scientifically, the difficulty in preparing large area, well-oriented monolayer TMDs has slowed the progress in utilizing momentum space probe of electronic structures except in some limited cases, for example, molecular beam epitaxial growth of MoSe2 and MoS2 on bilayer graphene (7,8). Recently, progress has been made in creating large area monolayer TMDs by exfoliation thus enabling applications of advanced electronic structure probing tools (9,10).
Nevertheless, the tedious exfoliation step remains a bottleneck and limits its wide applicability.
Recently, there has been significant progress made in creating wafer scale, highly oriented TMD monolayers on a sapphire substrate using chemical vapor deposition (CVD) (4)(5)(6), albeit utilization of such platform for advanced electron spectroscopy has yet to be demonstrated. Taking advantage of these recent developments of CVD growth, we demonstrate the ability to create a large scale, atomically clean monolayer TMD (e.g. MoS2) on graphite substrate for electron spectroscopy investigations. More importantly, using a collection of electron microscopy and spectroscopy tools, we provide a consistent picture of the ground state electronic structures and access the otherwise unoccupied excited state dynamics.
Scanning tunneling microscopy (STM) and low energy electron diffraction (LEED) reveal a wafer-scale, well-aligned crystallographic orientation. The high-quality sample enables us to apply angle-resolved photoemission (ARPES) and time-resolved (tr-)ARPES to map out ground/excited state electronic structures with high energy and momentum resolution. The capability of observing both the momentum resolved valence band and conduction band states in tr-ARPES permits the direct determination of the quasi-particle band gap. Remarkably, all the critical points energy locations are corroborated with the scanning tunneling spectroscopy. Moreover, we access the dynamical behavior of excited states, including inter-and intra-valley carrier scattering and a rapid energy shift (~0.2 eV) of quasiparticles at the S point. Figure 1 depicts the process in preparing the large scale well-aligned monolayer MoS2 for advanced electronic structure probe. First, we grow monolayer TMDs on a 2" sapphire wafer using CVD. The growth is based on a "substrate guided growth" procedure reported previously (4-6) but with significant refinement to reduce defect density and obtain monolayer TMDs with well-aligned orientation, i.e., all domains have either the same orientation or its mirror twin (Fig. S1). Figure 1a shows a slice (5 cm x 1 cm) of the wafer after monolayer MoS2 growth. Depending on the location at the gas flow stream, the growth leads to either a continuous film (region A), a densely covered region (region B showing 80 ~ 90% coverage), or a low coverage (region C).

Results
For STM, ARPES and tr-ARPES studies, the sample needs to have an electrical contact to complete the circuit loop when the electron is injected or ejected. While previous experiments mostly used side electrical contacts on a continuous film, the presence of a Schottky barrier at the contacts often induces a lateral field (11,12) along with the carrier motion. Moreover, upon excitation of photoelectrons, transient field can build up (i.e. a photovoltage effect), introducing complications in the interpretation of experimental observations (9,13,14). Finally, in the STM investigation, there will be significant tipinduced band bending along the lateral direction (15), hindering a comparison between different electron spectroscopic studies. To circumvent these limitations, we have chosen to transfer the sample to a highly oriented pyrolytic graphite (HOPG) or a graphene substrate which prevents the formation of a surface photovoltage during photoemission and eliminates the tip-induced band bending during STM operation (16,17). Figure 1a is chosen (instead of the continuous film region A) so that the contrast in optical images can be used to gauge the success in sample transfer. Detailed description of sample transfer can be found in the Supplementary (Fig. S2). We obtain a large sample size (0.4" x 0.4") limited by the sample holder, which is essential for subsequent measurements. The LEED image shows a well-defined pattern of six dots, confirming the high crystalline quality of the MoS2 monolayers including their twin pairs. The ring pattern is produced by the HOPG. The presence of the twin pairs prevents the spin or degenerate valleys to be resolved in spectroscopy measurements. The same LEED pattern is obtained when the electron beam scans across the sample, indicating a large size, atomically clean surface. The STM measurement was carried out at 77 K, revealing a lattice constant of 3.17 ± 0.03Å, close to the well-accepted value of 3.16 Å . Additionally, ambient stability of MoS2 monolayers on HOPG substrate was also investigated to ensure the consistency of the sample quality when taken out from different chambers to air for different measurements (Fig. S3). The excited state electronic structure and dynamics are investigated using high-repetition rate, extreme-ultraviolet(XUV) tr-ARPES (19). Here we focus on two aspects: (a) direct determination of quasi- The photoexcitation instantaneously shifts the K-point valence band by ~0.1 eV downward versus the equilibrium state (Fig. S4), then remains relatively steady during the measurement. This effect is observed at both temperatures and its origin will be discussed elsewhere. Since both valence/conduction band states are detected simultaneously, the determination of quasi-particle band gap is not influenced by this effect.

Region B in
At 80 K, the valence band spin-orbit splitting (~ 140 meV) at the K point is well-resolved, but slightly smeared out at 300 K. The CBM at the K point appears at 0.25 eV at 80 K and becomes 0.18 eV at 300 K.
The excited-state VBM at K does not change its energy location as a function of temperature beyond the energy resolution (-1.85 eV), yielding a quasi-particle band gap of 2.10 ± 0.08eV at 80 K and 2.03 ± 0.07eV at 300 K as shown in Fig. 3b. Shown as the inset is the measured quasi-particle gap value at 80 K as a function of the excitation fluence which shows a very weak trend (if any) of smaller gap at higher fluence.
The determination of the quasi-particle bandgap has been a central issue in TMD for several years (20). Many groups have tackled this issue using different techniques but rather inconsistent results (16,(21)(22)(23)(24)(25). The ability to view simultaneously the valence and conduction band states in the momentum-space using tr-ARPES enables the unambiguous determination. As well, in this study, the acquired quasi-particle band structure using tr-ARPES at 80 K shows excellent agreement with the STS acquired at 77 K on MoS2 on graphite (shown in Fig. 3c) where the VBM is identified at -1.84 eV and CBM at 0.31 eV: with a band gap of 2.15 ± 0.06eV. STS also identifies another threshold at 0.2 ± 0.05 eV above at CBM which is assigned as a local minimum at S point (also referred to as Q point (23)). The S threshold is confirmed by using a !" !# spectrum acquired at constant current (green curve in Fig. 3c); this method for identifying different critical points in TMD monolayers was discussed previously (23). This S state is also observed in tr-ARPES and visualized with an enhanced contrast in Fig. 4a albeit with a much lower count rate than the K point. Fig. 4a are color rendering images of intensity versus energy and momentum for states at K and S respectively acquired at 300 K with a pump energy of 2.2 eV (above the quasi-particle gap) at two different delay times (0.13 ps and 1.27 ps). We integrate the photoemission signal over a range in the momentum space (pink and blue dashed boxes) to enhance the signal to noise. The signal strength at S is more than an order of magnitude smaller than that at K. We first analyze the dynamics as a function of energy. From the EDCs shown in Fig. 4b, one can observe that at the K point, the spectral peak shows a  (27,28), its contribution should be minimal given that the intensity at Sc is smaller by an order of magnitude. This analysis shows that the K-valley dynamics is dominated by hot electron cooling with the above gap excitation.

Shown in
On the other hand, the rapid evolution of Sc to S * suggests a different origin. We note that in a recent study of tr-ARPES of WSe2, a similar rapid shift has been observed for both K-and S-valleys which was interpreted as the formation of exciton (K) and dark exciton (S) respectively (13). In our case, however, the large energy shift is observed only for S-valley and not for K-valley. One possibility is that bound states are formed at both valleys but the K-valley exciton signal is overshadowed by the free carrier signal at K-valley whose population is orders of magnitude higher. It is known that photoluminescence of monolayer MoS2 on graphite is quenched by more than two orders of magnitude in comparison to MoS2 monolayers on insulating substrates (24).
In conclusion, by successfully creating large scale monolayer MoS2 with well-aligned in-plane orientation and atomically clean surface, we investigate its ground and excited state electronic structure.
The equilibrium band structure is measured via ARPES and is confirmed to be consistent with DFT calculations. Using extreme-ultraviolet tr-ARPES as a tool to access the unoccupied conduction band across momentum space, we found a remarkable agreement on the electronic gap using STM and photoemission measurements. Moreover, tr-ARPES provides access to valley-specific excited-state dynamics. While a nearly instantaneous energy shift (~0.2 eV) to a lower energy state is observed at the S point the dynamics at the K valley is dominated by hot carrier decay over a few picoseconds for the abovegap excitation. Future experiments that fully explore the complex electron dynamics in time, energy, and momentum will guide the search for new valley and exciton physics and devices based on TMD monolayers and heterostructures.

ARPES and trARPES
The regular ARPES measurements of the occupied band structure (Fig. 2) were performed at room temperature. A Helium lamp (21.2 and 40.8 eV) was used as the photon source. The spectra were collected using a Scienta R3000 analyzer. During the Helium lamp operation, the pressure was maintained under  (19). During the XUV-trARPES measurements, the pressure was maintained at 3 × 10 $%& Torr.

Density functional theory(DFT) calculation
The DFT calculation was carried out using the Quantum Espresso package (29,30)

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.     (c) Time delayed electron density distribution integrated over Δ6 = 0.25 Å !" at Σ and K conduction bands. The black Gaussian function (9 = 140 fs) represents the cross-correlation between the pump and probe pulses. Time delayed signal from K point conduction band was fitted with a biexponential function (solid red curve) and Σ point conduction band was fitted with a single exponential decay function convoluted with a Gaussian function (solid blue curve).