Optoelectronic crystal of artificial atoms in strain-textured molybdenum disulphide

1Straining two-dimensional (2D) materials with a spatially varying ‘designer' strain can lead to new artificial materials with exotic properties. Assembling such tuned artificial materials in condensed matter is an emerging field and has employed tools such as atomic manipulation and lithographic techniques. Here we focus on monolayer molybdenum disulphide (MoS2), a direct band gap semiconductor that shows promise for applications in photonics and optoelectronics due to its extraordinary physical properties. Elastic strain offers a novel and exciting opportunity to tune the band gap of monolayer MoS2 (refs,,, ) since it can sustain very high elastic strain before rupturing compared with its bulk counterpart. For instance, uniaxial strain has been shown to modulate the electronic structure and reduce the optical band gap (OBG) of monolayer MoS2 up to 100 meV.

2Besides pushing the magnitude of the strain, the ability to apply a spatially controllable strain is even more crucial because it enables the realization of a graded band gap semiconductor eagerly sought for wider photonic, optoelectronic and photovoltaic applications. It has been calculated that indenting monolayer MoS2 creates a tensile strain field that reduces the local quasiparticle band gap (QBG). The resulting modified electronic potential falls off inversely with distance from the indentation, playing the role of an effective electronic potential centred on a mesoscopic ‘artificial atom'. This electronic potential funnels photogenerated excitons from larger band gap regions into smaller band gap regions, resulting in potential broader spectrum light absorption and more efficient photocarrier concentration. The exciton funnel concept has been successfully employed to interpret the OBG of wrinkled few-layer MoS2. However, the indirect band gap of few-layer MoS2 prevents the distinctive photoluminescence (PL) intensity enhancement expected from the exciton funnelling process from being directly observed. Assembly of the aforementioned artificial atoms would result in a large-area functional ‘artificial crystal.' Currently there exists no fundamental proof-of-principle of this idea, neither at the single ‘artificial atom' level nor at a more practical macroscopic scale.

3In the following, we apply spatially modulated biaxial tensile strain in monolayer MoS2 using a patterned nanocone substrate to realize the optoelectronic crystal consisting of ‘artificial atoms.' MoS2 on top of the nanocones experiences high strain, which gradually decreases from the tip to the perimeter of the nanocones (Fig. 1a). Since the band gap decreases with increasing tensile strain, the nanocone apex marks the ‘nucleus' of the ‘artificial atom'. The strain profile has been optimized for maximum exciton solar funnel collection by controlling the geometry and dimensions of the nanocones.

4The as-grown MoS2 sheet (Supplementary Fig. 1) is transferred onto the SiO2 nanocones (Fig. 1b) assembled using nanosphere lithography (Supplementary Fig. 2). The as-transferred MoS2 is soaked in ethylene glycol to remove the trapped air bubbles and optimize the strain (Supplementary Fig. 3b). The evaporation of ethylene glycol that fills the gap between the MoS2 and nanocones generates capillary force that pulls down the MoS2 sheet, causing it to conform to the topography of the nanocones and accomplishing the nanoindentation. The clearly visible wrinkles between nanocones (Fig. 1c) indicate the presence of deformation and strain in the MoS2 sheet, which is also verified by atomic force microscopy (AFM; Fig. 1d). A scanning tunnelling microscopy (STM) topograph (Fig. 1e) shows the details of a single MoS2 artificial-atom element. We note that a similar attempt for templating strain has been carried out in graphene with limited strain magnitude due to a not-yet optimized process.

5The spatially varying strain distribution is verified by micro-Raman spectroscopy. Figure 2a shows the typical Raman spectra of the most strained-MoS2 (on tip of nanocones), less strained-MoS2 (between nanocones) and unstrained-MoS2 (on flat SiO2 surface) [Supplementary Fig. 4]. The unstrained-MoS2 has the typical Raman spectrum of monolayer MoS2 with two dominant peaks at 385.6 and 404.9 cm−1 (A1g). The strained MoS2 samples show significant redshifts for both and A1g peaks: 0.8 and 0.3 cm−1 for less strained-MoS2, and 2.4 and 0.6 cm−1 for most strained-MoS2. From an overall fit to the redshift magnitudes and the unstrained values, we estimate that (0.230±0.035)% and (0.565±0.025)% biaxial tensile strains are sampled on average by the 450-nm diameter laser beam in less strained-MoS2 and most strained-MoS2 according to our theoretical calculation discussed later. The Raman mappings of the (Fig. 2b) and A1g (Fig. 2c) peak frequencies show that the periodically varying strain is consistent over the entire scanned artificial crystal (25 μm2). The darker (lower frequency) and brighter (higher frequency) colours (Fig. 2b,c) indicate that tensile strain is highest on the tips of nanocones—at ‘artificial atom' nuclei—and gradually decreases to a minimum towards the perimeters of the nanocones.

6The effect of strain on the OBG of MoS2 strain crystal is examined by micro-PL spectroscopy. Figure 3a compares the representative PL spectra of the most strained-MoS2, less strained-MoS2, and unstrained-MoS2, where the strong PL peaks arise from the direct band gap emissions in monolayer MoS2. First, unstrained-MoS2 shows a typical PL spectrum of monolayer MoS2 with a principal peak at 1.83 eV (A exciton) and a minor peak at 1.95 eV (B exciton). Second, the strained MoS2 clearly exhibits redshift of the A exciton energy: 18 and 50 meV for the less strained-MoS2 and most strained-MoS2, respectively, indicating a strain-induced OBG reduction. From the magnitude of the redshift and our theoretical calculation, we estimate approximately 0.2 and 0.5% biaxial tensile strains are optically sampled in less strained-MoS2 and most strained-MoS2, respectively. These values agree well with the strains derived from Raman peak shifts above. Third, the mapping of the PL wavelength (Fig. 3b) shows that spatially varying OBG reduction is consistently observed over scanned areas. Finally and significantly, the A exciton peak intensity is more than doubled in the most strained-MoS2 (Fig. 3a), and the intensity increase is highly reproducible over the scanned region (Fig. 3c). There are a few factors that may affect the PL intensity including strain-modulated oscillator strength, varying local emission geometry, variation in underlying SiO2 thickness and strain-induced exciton funnelling. First, according to our exciton calculations (see Discussion below), the change of the oscillator strength on elastic strain is relatively small (∼6% increase under 1% biaxial strain), which cannot explain the observed >100% PL intensity enhancement. Second, the geometry-dependent PL intensity is expected to be enhanced on a flat substrate as the PL intensity of monolayer MoS2 peaks at normal collection angle, which is opposite to our observation. Third, a recent study of PL emission from MoS2 shows a flat dependence on underlying SiO2 thickness in the range of 180–270 nm, corresponding to oxide thicknesses variations in our samples from etching the nanocones. In fact, the PL emission intensity of homogeneously strained monolayer MoS2 was experimentally found to decrease when strain increases due to the increased probability of non-radiative relaxations, again opposite our observations. Finally, we note that enhanced PL intensity due to exciton drifting and concentrating has been observed in strained semiconductor nanowires. Therefore, we rule out alternate factors discussed above and attribute the anomalous enhanced PL intensity to the novel 2D exciton funnel effect. The Raman mappings (Fig. 2b,c) show that the tensile strain increases from the perimeters to the tips of the nanocones, so the band gap of MoS2 decreases from the perimeters to the tips of the nanocones. Consequently, a built-in electric field pointing from the tip towards the perimeter of the nanocone is created (Fig. 3d) and the photogenerated excitons drift towards the funnel center, as can be modelled analytically and numerically. Since the photogenerated excitons in monolayer MoS2 can drift up to 660 nm before recombination, the majority of photogenerated excitons are able to drift from the valleys to the tips of nanocones (245 nm from pitch radius) without significant recombination. As a result, excitons are concentrated at the tips of nanocones upon illumination and they eventually recombine, giving rise to the enhanced PL emission localized at the nanocone tips (Fig. 3c,d) and supporting the artificial atom and energy funnel concept.

7The local electronic structure modulation of MoS2 caused by strain is directly verified by STM. Figure 4a shows an STM topograph (V=2.4 V, I=18 pA) in the vicinity of three nanocones with height variations of 80 nm. Scanning tunnelling spectroscopy (STS) is performed in different regions of the area shown, and representative dI/dV tunnel spectra for unstrained-MoS2, less strained-MoS2, and most strained-MoS2 are shown in Fig. 4b. It is worth noting that these spectra show the Fermi level near mid-gap position due to the electron depletion caused by the gold substrate. The QBG sizes extracted from the dI/dV spectra (Supplementary Fig. 5) are labelled at each strain level. Unstrained-MoS2 shows a QBG of 2.29 eV, which is consistent with the OBG of 1.83 eV obtained by PL measurement considering the exciton binding energy ∼0.5 eV. The extracted local QBG varies from 2.29 eV down to 1.83 eV from STS measurements acquired from unstrained-MoS2 (topographic valley), through less strained-MoS2 (intermediate regions) and to most strained-MoS2 (topographic peak) locations. This corresponds to a measured local strain approaching ∼3% for most strained-MoS2. These strains are much higher than the maximum of ∼0.6% measured by Raman spectroscopy, which can be explained by the inherently atomic scale measurement of STM/STS compared with the optical measurements, which average over the finite laser beam size (∼450 nm).

8To quantify this argument and verify the complete strain profile of the crystal, we simulate the strain induced in a monolayer MoS2 sheet by applying a constant pressure on the sheet, and Lennard–Jones interatomic interactions between the sheet and substrate (Fig. 4c, Supplementary Fig. 6). To calibrate the mapping between the local tunnelling measurements and the optically averaged Raman/PL measurements, we plot in Fig. 4d the cone-to-cone calculated strain profiles (Fig. 4c) before and after a convolution step. The raw atomic strain is convolved with a 2D Gaussian of 450-nm 1/e2 width, corresponding to the 450-nm diameter Gaussian beam used in our optical experiments. With no fitting parameters, this yields a predicted optically averaged strain sampled by scanning Raman/PL; this average strain ranges from 0.233 to 0.562% and is in excellent agreement with the Raman/PL results from less strained-MoS2 and most strained-MoS2 regions presented above. This result provides confirmation that the local atomic strain is approaching the unprecedentedly high value of 3%.

9We use this calibration to unify all experimental (closed symbols) and theoretical (open symbols) results (Fig. 4e). We calculated Raman spectra under from 0 to 1% (red and blue triangles in Fig. 4e; Supplementary Fig. 7a). As increases from 0 to 1%, the and A1g peaks shift towards lower frequencies. Such Raman peak shifts vary linearly with biaxial strain, and the slopes are −4.48 and −1.02 cm−1 per 1% of biaxial strain for and A1g modes, respectively (dashed red and blue lines in Fig. 4e). The fit to all Raman data in unstrained, less strained and most strained regions with respect to these two lines yields values quoted earlier, (0.230±0.035)% (less strained) and (0.565±0.025)% (most strained) that are shaded in Fig. 4e. The calculated A exciton energy at various ranging from 0 to 1% is shown in Fig. 4e (lower panel, open purple triangles; Supplementary Fig. 7b). The A exciton peak exhibits a linear redshift rate of −0.11 eV per 1% of biaxial tensile strain (dashed purple line in Fig. 4e, also in good agreement with other calculations). Our recorded PL energies when assigned to the Raman-extracted strain values above fall along this redshift line within experimental error.

10The above discussion correlates OBG measurements to. To make the final quantitative link to the intrinsic QBG and the local atomic strain within the artificial crystal, we use the results of the convolution analysis elaborated above. Accordingly, we show in Fig. 4e a local atomic strain axis, which is linked to the optically averaged strain axis by the ratio of:=2.85:0.562 ∼ 5:1. On this axis we first plot the calculated theoretical QBG from 0 to 5% local strain for direct (open cyan triangles) and indirect (open cyan circles) transitions. The fit to the direct gap calculations (Fig. 4e, dashed cyan line) also diminishes at −0.11 eV per % biaxial strain and the gap axis there is scaled by the same 5:1 ratio to show this match. The calculations furthermore reveal a direct-to-indirect gap transition at ∼2% biaxial tensile strain, resulting in an increased drop of ∼−0.24 eV per % of the (now indirect) gap with strain (Fig. 4e, dotted cyan line). We add other acquired STS data to this plot. The closed cyan star symbols correspond to the curves shown in Fig. 4b and provide the anchor for the strain measurement: the highest QBG of 2.29 eV corresponds to zero local strain, and the lowest QBG of 1.83 eV corresponds to the highest strain at the artificial-atom nanocone tips, and must correspond to the largest optically averaged strains deduced. The remaining STS measurements have known gap values, and strain values that can be inferred by assigning to each value along the dotted line: gaps falling at −0.11 eV per % from the unstrained-MoS2 value and rising at 0.24 eV per % from the most strained-MoS2 value, meeting at the 2% direct-to-indirect transition. We note that the strain magnitude of 3% is calculated based on biaxial strain. This is the lower bound as larger strain magnitude is necessary to achieve the observed band gap modulation if the strain is uniaxial, which could exist in local areas due to the imperfect geometry of the nanocones.

11We note that this summary shows that our local crystal strain is sufficiently high to access the indirect band gap of monolayer MoS2. However, because the Raman/PL measurements are optically averaged, they are dominated by the majority of the points within the laser beam that have direct transition as evidenced by the high PL efficiency. The measurements also confirm a remarkably large exciton binding energy of ∼0.5 eV, only recently verified to be a general feature of dichalcogenides. From the STS measurements, a modulation of over 20% in the QBG is directly observed. From the mapping to the optically averaged strain (Fig. 4) and the deduced exciton binding energy, this represents a huge modulation of the OBG, exceeding 25%.

12This engineered OBG enables a broadband light absorption by increasing the absorption bandwidth from 677 nm (unstrained-MoS2) to 905 nm (most strained-MoS2), which covers the entire visible wavelength and most intensive wavelengths of the solar spectrum. While already without precedent, since these strains are not yet even rupture limited, we anticipate even larger band gap variations and electronic fields can be embedded in such artificial crystals in the future.

13MoS2 monolayers grown by chemical vapour deposition were transferred onto the SiO2 nanocone substrate using the PMMA-assisted wet transfer process. The transferred sample was then baked at 100 °C for 30 min and the PMMA was removed by sequential soaking in acetone at 60 °C for 10 min followed by chloroform at 60 °C for 1 h. Afterwards, the SiO2 nanocone with transferred MoS2 was immersed in ethylene glycol in vacuum for 1 h to ensure that both sides of the MoS2 sheet were wetted by ethylene glycol. Lastly, the sample was dried in ambient air to completely evaporate ethylene glycol.

14The Raman and PL measurements were performed with the excitation laser line of 532 nm using a WITEC alpha500 Confocal Raman system in ambient air environment. The power of the excitation laser line was kept below 1 mW to avoid damage of MoS2. The Raman scattering was collected by an Olympus 100 × objective (N.A.=0.9) and dispersed by 1,800 (for Raman measurements) and 600 (for PL measurements) lines per mm gratings.

15STM/STS measurements were performed at 77 K in ultrahigh vacuum. A bilayer of titanium (10 nm) and gold (80 nm) films were deposited onto the silicon oxide nanocone surface, then monolayer MoS2 flakes were transferred and strained on the metalized nanocone surface. A control sample was prepared alongside the STM sample and characterized using SEM and AFM to ensure conformal coating of MoS2 on the metalized nanocones. The STM sample was annealed in the STM ultrahigh vacuum chamber at 200 oC for 1 h to clean the MoS2 surface for a reliable STM measurement.

16The MoS2 sheet was modelled using honeycomb lattice with Tersoff potential and the substrate was modelled as a fcc lattice. A Lennard–Jones potential was employed to include the Van der Waals interaction between substrate and the MoS2 sheet. A constant force was placed on each atom downward to emulate the pressure difference across the MoS2 sheet (see Supplementary Fig. 6 for more details).

17The theoretical biaxial strain-dependent Raman spectra were calculated using first-principles density-functional perturbation theory implemented in the Quantum-ESPRESSO package with a plane-wave cutoff of 120 Rydberg, a Monkhorst–Pack k-point sampling of 12 × 12 × 1, and an exchange correlation functional of the Perdew–Zunger form within the local density approximation. The spin-orbit coupling was not included. In addition, norm-conserving Hartwigsen–Goedecker–Hutter pseudopotentials were used to take into account the core electrons and reduce the computational efforts. All biaxially strained configuration were fully relaxed with a convergence criteria of 0.0001, a.u. for the maximal residual force. The calculation was carried out in a periodic supercell with a vacuum spacing of 20 Å along the z (plane normal) direction to reduce the spurious interaction between the neighbouring unit cells.

18The theoretical biaxial strain-dependent optical absorption spectra were calculated by solving the Bethe–Salpeter equation within the Tamm–Dancoff approximation. The key parameters used in the Bethe–Salpeter equation including quasiparticle energies and screened-Coulomb interactions calculated were obtained from many-body perturbation theory with the Hedin's GW approximation. All the calculations were performed using the Vienna Ab initio Simulation Package with plane-wave basis and the projector-augmented wave method. A plane-wave cutoff of 350 eV, a Monkhorst–Pack k-point sampling of 18 × 18 × 1, and an exchange correlation functional of the Perdew–Berke–Ernzerhof form within the generalized gradient approximation were used. All biaxially strained configurations were fully relaxed with the maximal residual force of ≤0.0001, eV Å−1 using density-functional theory calculations.

19How to cite this article: Hong, L. et al. Optoelectronic crystal of artificial atoms in strain-textured molybdenum disulphide. Nat. Commun. 6:7381 doi: 10.1038/ncomms8381 (2015).