Research ArticlePHYSICS

Giant gate-tunable bandgap renormalization and excitonic effects in a 2D semiconductor

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Science Advances  19 Jul 2019:
Vol. 5, no. 7, eaaw2347
DOI: 10.1126/sciadv.aaw2347

Abstract

Understanding the remarkable excitonic effects and controlling the exciton binding energies in two-dimensional (2D) semiconductors are crucial in unlocking their full potential for use in future photonic and optoelectronic devices. Here, we demonstrate large excitonic effects and gate-tunable exciton binding energies in single-layer rhenium diselenide (ReSe2) on a back-gated graphene device. We used scanning tunneling spectroscopy and differential reflectance spectroscopy to measure the quasiparticle electronic and optical bandgap of single-layer ReSe2, respectively, yielding a large exciton binding energy of 520 meV. Further, we achieved continuous tuning of the electronic bandgap and exciton binding energy of monolayer ReSe2 by hundreds of milli–electron volts through electrostatic gating, attributed to tunable Coulomb interactions arising from the gate-controlled free carriers in graphene. Our findings open a new avenue for controlling the bandgap renormalization and exciton binding energies in 2D semiconductors for a wide range of technological applications.

INTRODUCTION

Atomically thin two-dimensional (2D) semiconductors usually exhibit large bandgap renormalization and extraordinary excitonic effects due to quantum confinement and reduced dielectric screening (14). As a result, light-matter interactions in these systems are primarily governed by the enhanced excitonic effects, which have been exploited to develop exciton-based devices operated at room temperature (RT) (5). Future progress in this area hinges on the ability to control the excitonic effects of 2D semiconductors by precisely tuning their exciton binding energies (Eb). This is crucial for realizing the full potential of 2D semiconductors in photonic and optoelectronic applications.

One unique aspect of 2D semiconductors is their unprecedented tunability in both their electronic and optical properties, due to high susceptibility to the doping and environmental screening (1, 612). It has been theoretically predicted and experimentally demonstrated that Coulomb interactions in 2D semiconductors can be engineered to tune their quasiparticle (QP) bandgap (Eg) and Eb using different methods such as chemical doping (6), electrostatically gating (7), and engineering environmental screening (1, 8, 9, 11, 12). Among all the methods reported, electrostatic gating offers additional advantages including continuous tunability and excellent compatibility for integration in modern device technologies. Recent studies involving the use of optical measurements demonstrated that gate-controlled excitonic effects can be achieved in monolayer transition metal dichalcogenides (TMDs) (7). However, an overlap of the band-edge absorption step with strong excitonic resonances generally makes it challenging to accurately determine Eg of 2D semiconductors from their optical absorption spectrum (13).

To probe Eb of 2D semiconductors directly, one can use scanning tunneling spectroscopy (STS) and optical spectroscopy (e.g., differential reflectance or photoluminescence spectroscopy) to measure Eg and optical bandgap (Eopt), respectively (1, 14). Here, we used this approach to demonstrate the gate-tunable Eg and excitonic effects in monolayer ReSe2 on a back-gated graphene field-effect transistor (FET) device, as sketched in Fig. 1A. We observed a large Eb of 520 meV for monolayer ReSe2 at zero gate voltage (Vg = 0 V). Moreover, we show that Eb of monolayer ReSe2 can be continuously tuned from 460 to 680 meV by electrostatic gating, which can be mainly attributed to screening from gate-controlled free carriers in graphene. This is distinct from the previous study of gate-tunable Eb in 2D semiconductors wherein the semiconductors’ own free carriers play a major role (7). These 2D semiconductor/graphene heterostructures have been widely used in the fabrication of transistors (1517), photo detectors (18), and energy-harvesting devices (19). The ability to precisely tune the bandgap and excitonic effects of 2D semiconductors on graphene provides a new route for the optimization of the interfacial charge transport or light-harvesting efficiency. Therefore, we expect that our findings would have a profound impact in the field of novel electronic and optoelectronic devices based on artificially engineered van der Waals heterostructures.

RESULTS

Topographic imaging of monolayer ReSe2 on graphene

Unlike hexagonal TMDs, monolayer ReSe2 adopts a distorted 1T structure with triclinic symmetry (Fig. 1B), wherein four Re atoms slip off from their regular octahedral sites due to the charge decoupling from their d3 electrons. This results in the formation of a 1D chain-like structure consisting of interconnected diamond-shaped Re4 units along the a direction as shown in Fig. 1B (20, 21). Because of this, monolayer ReSe2 exhibits unique in-plane anisotropic electronic and optical properties, making it particularly attractive for near-infrared polarization-sensitive optoelectronic applications (22).

Fig. 1 A monolayer ReSe2 on a back-gated G/h-BN device.

(A) Schematic illustration of a back-gated ReSe2/graphene/h-BN device. (B) Top view of the atomic structure of monolayer ReSe2. The two lattice vectors (a and b) are outlined by red lines. The lattice constants are a = 6.6 Å and b = 6.7 Å. The angle between a and b is 118.9°. (C) A representative STM image of a monolayer ReSe2 flake on graphene/h-BN. Inset shows the STM line profile along the step edge. (D) Atomically resolved STM image of monolayer ReSe2. The STM image reveals the unique 1D chains consisting of diamond-shaped Re4 units along a direction (highlighted by orange line). The cross (X) marks the position where the differential conductance (dI/dV) spectra were taken.

To probe the carrier-dependent excitonic effects, we transferred a monolayer ReSe2 flake onto a clean back-gated graphene FET device consisting of a chemical vapor deposition–grown graphene monolayer placed on a hexagonal boron nitride (h-BN) flake that rests on a SiO2 layer above a doped Si wafer (Fig. 1A). In contrast to the SiO2 substrate, the atomic flatness of the underlying h-BN markedly reduces the surface roughness and charge inhomogeneity in graphene (6, 23, 24). The use of graphene not only enables the direct scanning tunneling microscopy (STM) measurement of the gated single-layer ReSe2 but also improves the electrical contact to monolayer ReSe2 (2527).

Figure 1C shows a representative STM image of a monolayer ReSe2 flake placed on the monolayer graphene/h-BN substrate. The STM height profile across the step edge of the ReSe2 flake reveals an apparent height of ~0.8 Å, suggesting monolayer thickness (fig. S1). Further, the atomically resolved STM image (Fig. 1D) reveals a diamond chain-like structure as expected for monolayer ReSe2 with a distorted 1T atomic structure (21). The lattice constants of ReSe2 along the a and b directions (as marked in Fig. 1, B and D) are determined to be 6.6 ± 0.1 Å and 6.7 ± 0.1 Å, respectively, which are in good agreement with the previous study (20). It is also expected that moiré patterns would arise when the graphene was overlaid with the monolayer ReSe2 at different twist angles. Several representative moiré patterns have been successfully captured in our STM images of different spatial regions of different samples (Fig. 2, A to C). Distinct from most twisted 2D heterostructures such as graphene on h-BN (28), the moiré patterns of ReSe2/graphene exhibit two different periods along two crystallographic orientations (as marked by L1 and L2 in Fig. 2, A to F). This is due to the stacking of monolayer ReSe2 with triclinic lattice symmetry on graphene with a honeycomb lattice. The unique moiré patterns observed here can be well reproduced (Fig. 2, D to F) using the geometrical analysis of twist angle–dependent moiré patterns of ReSe2/graphene heterostructures (refer to section S2 for more details).

Fig. 2 STM images of moiré pattern in monolayer ReSe2/graphene.

(A to C) Representative moiré patterns observed in the experiment. (D to F) Calculated moiré patterns obtained from the geometrical analysis. θ is the stacking angle between ReSe2 and graphene.

Electronic structure of monolayer ReSe2

We then probed the local electronic properties of ReSe2 using STS. We note that differential conductance (dI/dV) spectra acquired in several moiré regions exhibit similar features (refer to section S3 for more details). Figure 3A shows a representative dI/dV spectrum acquired over monolayer ReSe2 (marked by a cross in Fig. 1D) at Vg = 0 V together with the local density of states (LDOS) calculated by density functional theory (refer to section S5 for more details). A wide bandgap and several prominent resonant peaks located close to both the conduction band (CB) and valence band (VB) edges have been captured in the dI/dV spectrum taken on the clean surface region (solid blue line in Fig. 3A). These features can be well reproduced in the calculated LDOS of a free-standing monolayer ReSe2 (dashed red line in Fig. 3A and refer to section S5 for more details). A close examination of the calculated band structure of monolayer ReSe2 allows us to identify that the origin of the prominent resonant peaks at the CB side (C1) is attributed to the dispersionless electronic bands as indicated in fig. S5.

Fig. 3 Gate-dependent dI/dV and differential reflectance spectra of a monolayer ReSe2 on graphene.

(A) dI/dV spectrum of monolayer ReSe2 (blue line) at Vg = 0 V together with the calculated LDOS (dashed red line). (B) Energy position of VB maximum (VBM; red points) and CB minimum (CBM; dark blue points) as a function of the gate voltage. (C) Gate-dependent dI/dV spectra of the monolayer ReSe2 on graphene/h-BN measured at 4.5 K. As-applied gate voltage is indicated above each STS curve. The VBM and CBM were indicated by light red and light blue points, respectively. (D) Gate-dependent differential reflectance spectra of the monolayer ReSe2 on graphene/h-BN measured at 5 K. The corresponding gate voltage is indicated on the side of each differential reflectance spectrum. Note: The original differential reflectance spectra after background subtraction (circles); fitted curves using the Lorentzian function (solid lines). a.u., arbitrary units.

We identify the band edges of each dI/dV spectrum using the method previously reported (1). The VB maximum (VBM) and the CB minimum (CBM) are found to be located at −1.27 ± 0.01 eV and 0.72 ± 0.01 eV, respectively, which yields Eg of 1.99 ± 0.02 eV for monolayer ReSe2. In addition, we observe the Fermi level (EF) to be closer to the CBM than the VBM, indicating a low n-doping of ReSe2, which is presumably due to the presence of donor-like defects with shallow mid-gap states (fig. S4A).

Gate-tunable QP bandgap renormalization

One unique aspect of this study is that we can probe the QP band structures as a function of gate voltage. Figure 3C shows the gate-dependent dI/dV spectra taken at the same position over monolayer ReSe2. We observed that a gate-dependent rigid shift of the CBM and C1 toward EF when Vg is changed from −63 to +45 V (Fig. 3, B and C). Unexpectedly, the VBM remains nearly constant at different gate voltages as shown in Fig. 3 (B and C). The distinct shift of the CBM and VBM with the increase in the applied gate voltage therefore indicates a monotonic reduction of Eg. The QP bandgap of monolayer ReSe2 is determined to be 2.15 ± 0.01 eV at Vg = − 63 V and 1.93 ± 0.02 eV at Vg = 45 V, respectively.

Probing the optical bandgap of monolayer ReSe2

We performed the differential reflectance spectroscopic measurement of monolayer ReSe2/graphene/h-BN at 5 K to probe its optical bandgap. Differential reflectance spectra of the sample after the background subtraction are shown in Fig. 3D (refer to fig. S6A for more details). At Vg = 0 V, Eopt of monolayer ReSe2 is determined to be 1.47 ± 0.01 eV at 5 K based on the peak position of differential reflectance spectrum (Fig. 3D), consistent with previous results (22). To probe the electrostatic gating effect on Eopt, we monitored the evolution of the peak position of the hybrid ReSe2/graphene device as a function of gate voltage. We found that Eopt remains nearly constant at all the gate voltages as opposed to the monotonic reduction of Eg (Fig. 3, C and D). It reflects that the renormalization of Eg is nearly fully offset by the change of Eb, in agreement with Koopmans theorem adapted for semiconductors and previous experimental studies (9, 29, 30). To further verify this, we performed photoluminescence measurement of monolayer ReSe2/graphene/h-BN at different gate voltages at RT. The gate-dependent photoluminescence spectra acquired at RT also reveal a nearly constant Eopt of monolayer ReSe2 (fig. S6B).

Gate-tunable exciton binding energy

The exciton binding energy is directly determined from the equation(Eb = EgEopt). As shown in Fig. 4A, a large gate-tunable bandgap renormalization of ReSe2 can be achieved in our hybrid device, whereby Eb can be precisely tuned over a wide energy range from 680 ± 20 meV to 460 ± 20 meV when Vg increases from −63 to +45 V. The pertinent question to be addressed in this work is the physical origins of the gate-tunable QP bandgap renormalization and exciton binding energy in monolayer ReSe2. We are able to exclude the contribution from the out-of-plane field-induced polarization of CBM and VBM wave functions (namely, Stark effects). The vertical field induced polarization of electrons and holes in monolayer TMDs is negligible due to their extreme confinement in the in-plane direction (7). In addition, the screening by graphene substrate substantially reduces the vertical electric field effect for monolayer ReSe2.

Fig. 4 Gate-tunable bandgap renormalization and exciton binding energy of monolayer ReSe2 on graphene.

(A) A plot of QP bandgap Eg (black points), optical bandgap Eopt (red points), and exciton binding energy Eb (blue points) as a function of gate voltage. Note: The Eopt = 1.47 ± 0.01 eV remains constant when the gate voltage increases from −40 to 40 V. Note: The same Eopt is used for the calculation of Eb at the gate voltage of −63, −60, −50, and +45 V. The solid blue line refers to the theoretically predicted Eb as a function of the gate voltage (refer to section S8 for more details). (B) Illustration of the screening of electron-hole interactions in monolayer ReSe2 by the gate-controlled free carriers in graphene. (C) Schematic illustration of gate-tunable Eg and Eb of monolayer ReSe2 at the gate voltage of −63 and +45 V, respectively.

On the other hand, free carriers in both ReSe2 and adjacent graphene can, in principle, contribute to the renormalization of Eg and tunable Eb in single-layer ReSe2. It has been predicted that Eg of a free-standing 2D semiconductor can be substantially reduced because of the presence of free carriers (31, 32). Further, the dominant contribution to the QP bandgap renormalization in these systems is predicted to arise from the Coulomb-hole self-energy and screened-exchange self-energy (31). However, a detailed analysis of the experimental data reveals that the renormalization of Eg and tunable Eb is not likely to arise from the presence of free carriers in ReSe2. First, the set of gate-dependent dI/dV spectra shows that EF never crosses the band edge of ReSe2 (Fig. 3C), suggesting the absence of free carriers residing in the band edge states. We also considered the potential free carriers contributed from point defects with shallow mid-gap states in ReSe2 (refer to section S4 for more details), although our gate-dependent dI/dV spectra of monolayer ReSe2 are taken in the region free of defects. However, our STM imaging and spectroscopy measurements reveal that these defects with a low density of ~3.9 (± 1.5) × 1011 cm−2 are electronically isolated from each other (fig. S4). Therefore, the carriers localized around these defects are not likely to play a significant role in the renormalization of Eg.

These observations suggest that bandgap renormalization and tunable Eb of monolayer ReSe2 are the result of the gate-induced free carriers in graphene. To further examine our hypothesis, we performed the gate-dependent STS measurement of a new device consisting of monolayer graphene stacked on top of a monolayer ReSe2 on SiO2/Si substrate. By reversing the stacking order (graphene/ReSe2), we are able to measure gate-dependent Dirac point (ED) of graphene and Eg of monolayer ReSe2 simultaneously (refer to section S7 for more details). The results also show a gate-tunable bandgap renormalization of monolayer ReSe2 (fig. S7F). Moreover, it is observed that Eg of ReSe2 reaches the maximum close to the charge neutrality point of graphene and reduces monotonically upon increase in either n-doping or p-doping of graphene (fig. S7F). Thus, a simultaneous measurement of both Eg of ReSe2 and doping in graphene demonstrates that the observed gate-tunable bandgap renormalization and excitonic effects in monolayer ReSe2 are attributed to the screening from the gate-controlled free carriers in the adjacent graphene.

We then used a quasi-classical model based on the Thomas-Fermi screening theory (refer to section S8 for more details) to calculate Eb of monolayer ReSe2 on graphene/h-BN as a function of the carrier density in graphene (n). The screening model comprises two components: the Thomas-Fermi screening radius due to the free electrons in graphene and an effective dielectric constant (εeff = 6.09) that accounts for the combined dielectric permittivity of h-BN and ReSe2 (see section S8 for derivation). Our theoretical results show that a moderate doping (n about 8 × 1012 cm2) in graphene substantially reduces the exciton binding energy by hundreds of milli–electron volts, resulting in a monotonic decrease in Eb as the free-carrier concentration in graphene increases (fig. S8A).

To directly compare with experimental results, we need to convert the carrier density in graphene to the corresponding gate voltage (Vg). The carrier density in the ReSe2/graphene hybrid system depends linearly on the gate voltage: n = α(VgV0). Here, α is estimated to be around 7.1 × 1010 cm−2 V−1 using a standard capacitor model (consisting of ~285-nm SiO2 and ~15-nm h-BN as dielectric materials) (33, 34). Note that αV0 is the initial doping of the system at Vg = 0 V. Since the density of defects with mid-gap states is extremely low (3.9 (± 1.5) × 1011 cm−2) compared with the total gate-induced free-carrier density (Δn = 7.7 × 1012 cm−2) and EF is away from band edges of ReSe2, this rationalizes that most of the gate-induced free carriers are injected into the underlying graphene. When V0 is set as −64 V, we find the calculated Eb as a function of gate voltage agrees with the observed gate-dependent Eb (Fig. 4A). This suggests that the graphene underneath monolayer ReSe2 is strongly n-doped at Vg = 0 V, in line with the charge transfer analysis discussed in section S9.

DISCUSSION

In summary, we have successfully tailored the QP bandgap and the exciton binding energy in a 2D semiconductor by controlling the doping in the underlying graphene using electrostatic gating. Our results show that screening from a graphene substrate has a profound impact on Coulomb interactions in adjacent 2D semiconductors and leads to broad tunability of the electronic bandgap and exciton binding energy. Our findings not only result in the unprecedented understanding of many-electron physics in hybrid 2D semiconductor/graphene systems but also pave the way toward controlling the excitonic effects and precisely tuning the exciton binding energies in 2D semiconductors for a wide range of technological applications.

MATERIALS AND METHODS

Sample preparation

We fabricated the graphene/h-BN sample based on the recipe reported previously (35). We then used the well-established dry transfer technique to place a monolayer ReSe2 on top of graphene/h-BN sitting on SiO2/Si substrate (36). The key steps for the sample treatment include the following: (i) The h-BN/SiO2/Si substrate was annealed in the furnace at 500°C for 2 hours before the transfer of graphene. (ii) After the transfer of graphene, graphene/h-BN/SiO2/Si sample was annealed in furnace with a flow of 100 sccm (standard cubic centimeters per minute) H2 and 200 sccm Ar at 350°C for 5 hours. (iii) ReSe2/graphene/h-BN was annealed at 300°C in the ultrahigh vacuum chamber for 12 hours.

STM and STS measurements

Our STM and STS measurements were conducted at 4.5 K in the Omicron LT-STM system with a base pressure lower than 10−10 mbar. The STM tip was calibrated spectroscopically against the surface state of Au(111) substrate. All the dI/dV spectra were measured through a standard lock-in technique with a modulated voltage of 5 to 10 mV and the frequency of 700 to 800 Hz.

Differential reflectance and photoluminescence measurements

The differential reflectance measurements and photoluminescence measurements were conducted at 5 K and at RT, respectively, using a custom-built confocal spectrometer. For differential reflectance measurements, samples were illuminated by the white light from broadband source (hydrogen-halogen lamp) focused into the spot of ~2 μm. Reflectance spectra from monolayer ReSe2 (RReSe2) and substrate (Rsub) were collected in confocal geometry. Differential reflectance spectra (DR) are obtained by DR = (RsubRReSe2)/Rsub. For photoluminescence measurements, samples were excited with a 532-nm laser through the 100× objective lens (numerical aperture of 0.9) with a power below 0.5 mW.

SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/7/eaaw2347/DC1

Section S1. Atomic force microscopy measurement of monolayer ReSe2

Section S2. Moiré pattern of single-layer ReSe2 on graphene

Section S2.1. Moiré patterns for various twist angles

Section S2.2. A comparison between experimental and theoretical moiré patterns

Section S3. Gate-dependent dI/dV spectra of a different ReSe2/graphene device

Section S4. Probe the defects in monolayer ReSe2

Section S5. Band structure of monolayer ReSe2

Section S6. Differential reflectance spectrum and gate-dependent photoluminescence spectra of monolayer ReSe2

Section S7. Gate-dependent dI/dV spectra of graphene/monolayer ReSe2

Section S8. Calculation of Eb in monolayer ReSe2 as a function of the carrier density in graphene substrate

Section S9. Charge transfer at the interface of ReSe2/graphene

Fig. S1. Identify the thickness of monolayer ReSe2.

Fig. S2. Moiré lengths of ReSe2/graphene as a function of twist angle.

Fig. S3. Gate-dependent dI/dV spectra of a different device.

Fig. S4. STM images and STS measurements of defects in ReSe2.

Fig. S5. Band structure of monolayer ReSe2 calculated using the first-principle density functional theory calculations with the Perdew-Burke-Ernzerhof exchange-correlation functional using the QUANTUM ESPRESSO code.

Fig. S6. Differential reflectance spectrum and gate-dependent photoluminescence spectra of monolayer ReSe2 on graphene/h-BN.

Fig. S7. Gate-dependent dI/dV spectra of graphene/monolayer ReSe2.

Fig. S8. Exciton binding energy (Eb) and Thomas-Fermi screening radius (rs) as a function of electron concentration (n) in graphene.

Fig. S9. Charge transfer at ReSe2/graphene interface.

Table S1. Geometrical properties of the moiré patterns of ReSe2/graphene.

References (3746)

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REFERENCES AND NOTES

Acknowledgments: We acknowledge the valuable discussion with J. Martin and K. Novoselov. Funding: J. Lu acknowledges the support from Ministry of Education (MOE) Tier 2 grants (R-143-000-682-112 and R-143-000-A06-112). M.Tr. is supported by the Director’s Senior Research Fellowship from CA2DM at NUS (NRF Medium Sized Centre Programme R-723-000-001-281). S.A. acknowledges support from the Singapore MOE AcRF Tier 2 (MOE2017-T2-2-140) and the National University of Singapore Young Investigator Award (R-607-000-094-133). S.G. and L.Y. are supported by the NSF CAREER grant no. DMR-1455346 and the Air Force Office of Scientific Research grant no. FA9550-17-1-0304. The computational resources were provided by the Stampede of Teragrid at the Texas Advanced Computing Center through XSEDE. A.H.C.N. acknowledges the support from National Research Foundation of Singapore under its Medium-Sized Centre Programme. G.E. acknowledges the support from the MOE, Singapore, under AcRF Tier 2 (MOE2015-T2-2-123 and MOE2017-T2-1-134) and AcRF Tier 1 (R-144-000-387-114.). Author contributions: J. Lu supervised projects. Z.Q. performed STM measurements and data analysis with the help of H.F. H.F. performed atomic force microscopy measurements. M.Tr. devised the model with contributions from A.H.C.N. and S.A. E.L. performed the geometrical analysis of the moiré pattern under the supervision of S.A. I.V. performed photoluminescence measurements and data analysis with the help of H.F. under the supervision of G.E. S.G. performed the density functional theory calculation under the supervision of L.Y. M.Y. performed the calculation for estimating charge transfer at ReSe2/G interface. K.W. and T.T. grew the h-BN for device. P.L., J. Li, and Z.Q. fabricated the device. J.S. and M.Te. helped with the STM measurements. J. Lu and Z.Q. prepared the manuscript with the contribution from M.Tr., I.V., G.E., S.G., L.Y., E.L., and J.W. All authors contributed to the scientific discussion and helped in writing the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.
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