Supporting Information: Probing Interlayer Interactions in Transition Metal. Dichalcogenide Heterostructures by Optical Spectroscopy: MoS 2 /WS 2 and

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1 Supporting Information: Probing Interlayer Interactions in Transition Metal Dichalcogenide Heterostructures by Optical Spectroscopy: MoS 2 /WS 2 and MoSe 2 /WSe 2 Albert F. Rigosi, Heather M. Hill, Yilei Li, Alexey Chernikov, and Tony F. Heinz %* Departments of Physics and Electrical Engineering, Columbia University, New York, NY 10027, United States % Present address: Department of Applied Physics, Stanford University, Stanford, CA 94305, United States and SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, United States KEYWORDS 2D materials, heterostructures, transition metal dichalcogenides, lifetime broadening, charge transfer 1. Sample preparation and characterization Sample preparation Bulk crystals of MoS 2, WS 2, MoSe 2, and WSe 2 were mechanically exfoliated onto fused quartz to obtain monolayers. The monolayer thickness was verified using photoluminescence (PL) and atomic-force microscopy (AFM) measurements, as discussed below. Other monolayers were prepared on polypropylene carbonate (PPC) transferable film. These monolayers were transferred to build heterostructures as illustrated below in Figure S1 and Figure S2. 1

2 Figure S1. Schematic representation of the first part of the transfer process for the formation of TMDCHs. 2

3 Figure S2. Schematic representation of the second part of the transfer process for the formation of TMDCHs. The thermocouple is combined with the heating stage, which allows for temperature increases. 3

4 Sample characterization: atomic force microscopy The TMDCH systems are characterized using atomic force microscopy measurements and by comparing the relevant thicknesses of the individual layers to that of the heterostructure. Representative AFM images of the sulfur- and selenium-based heterostructures are shown in Figure S3. 5 μm 5 μm Figure S3. (Left) AFM images for a sulfur-based TMDCH. (Right) AFM profiles for the a seleniumbased TMDCH. Height profiles are shown along the indicated black lines. The dashed lines show the boundaries between different regions of the structure, with the zone inside both the blue and red boundaries corresponding to the heterostructure of the two labeled monolayers. 4

5 2. Photoluminescence and Raman spectra Photoluminescence spectra For further characterization of the individual layers and heterostructures, we carried out photoluminescence measurements of both selenium-based TMDCHs and sulfur-based TMDCHs. The measurements were performed using continuous-wave laser excitation at 532 nm in a commercial (Renishaw InVia) Raman microscope. As shown in Figure S4 for both types of heterostructures, we obtain PL spectra for both the separated monolayers and the overlapping heterostructure. The individual layers exhibit a strong peak corresponding to emission from the corresponding A exciton. For the overlapped region of TMDCHs, one observes PL features of the individual monolayers of which they are composed (Figure S4). Just as for the absorption spectra discussed in the main text, these features are not significantly shifted in energy in the heterostructure. The emission features do, however, exhibit a significant decrease in emission strength, with the tungsten chalcogen layers showing greater quenching than their molybdenum counterparts. In the tungsten chalcogen layers, the emission strength of the A exciton is reduced by a factor of 9x- 14x when the heterostructure is formed, while the molybdenum chalcogen layers experience slightly less quenching (7x-8x), as shown in Figure S4. The strong quenching of the A exciton emission in the heterostructures is expected based on the rapid charge separation predicted for the heterostructures, as discussed and analyzed in the main text. Indeed, the observed quenching by only a factor of ~10 in the PL emission appears to be anomalously small. For a charge separation time tens of fs and a reported emission lifetime of an isolated monolayer at room temperature in the range of a few hundred picoseconds 1, the expected quenching factor should be as large

6 We attribute the much lower measured PL quenching to the role of sample inhomogeneity. While the AFM data indicate that majority of the TMDCH exhibits direct contact between the two layers, there are also regions where bubbles appear to have formed between the monolayers. For a separation above a few nanometers, the coupling between the two layers will be very slight and the PL emission is expected to be largely unperturbed. We can thus understand our PL quenching observation as the result of ~10% of the TMDCH where poor interlayer contact is achieved. Because of the very strong quenching in the ideal part of the heterostructure sample, the measured PL can be dominated by the unquenched emission from the separated layers. Indeed, somewhat larger quenching factors (~60) have been reported for epitaxially-grown systems. 2 These systems might be expected to exhibit better contact between the layers and nearly approach behavior of an ideal, fully-coupled system. We note that the absorption measurements presented in the main text, unlike PL measurements described here, weight all portions of the sample equally. The absorption measurements can thus be taken as representative of the ideal part of the sample, with only a small correction from the separated regions, despite the fact that the PL may be dominated by uncoupled regions of the heterostructure. 6

7 Figure S4. (A) and (B) are PL measurements of a sulfur-based TMDCH plotted on a linear and logarithmic scales, respectively. Both the spectra of the individual layers and of the heterostructure are shown. (C) and (D) are analogous figures to (A) and (B) for a selenium-based TMDCH. No background correction has been made to the data. 7

8 Figure S5. Plot of the PL (solids lines) from a WSe 2 /MoSe 2 heterostructure and its two individual components, with the indicated scaling for better comparison. The dashed lines are fits to Lorentzian contributions for main neutral exciton emission, as well as a weaker trion feature. This analysis allows extraction of the PL linewidths, as discussed in the SI. The total PL response of the individual MoSe 2 and WSe 2 layers is presented in Figure S5 together with the corresponding fit curves, using two peaks for each layer: one peak representing the dominating neutral exciton response and weaker feature for the trion (charged exciton) response about 30 mev lower in photon energy. Keeping the transition energies unchanged for the responses of the individual MoSe 2 and WSe 2 components, good fits could be generated for heterostructure spectra (Figure S5). In the fit, the linewidth of the neutral exciton was not significantly increased (i.e., not more than 10 mev). We attribute this lack of significant broadening (as contrasted to the results for the absorption presented in the main text) as 8

9 reflecting the fact that much of the PL response comes from unquenched regions of separated layers, as discussed above. Because the PL data strongly weights imperfect regions with reduced quenching, it does not seem to provide a reliable means for the analysis of spectral linewidths of the heterostructure in our system. We thus consider the absorption measurements, which weight all regions of the sample equally, are more suitable for analysis of the spectral lineshapes of the heterostructures. Raman spectra We have performed Raman spectroscopy measurements for the two types of TMDCHs, recording spectra of the isolated layers and of the heterostructure region for both types of TMDCH (Figure S6). The spectra were recorded using laser excitation at 532 nm in a commercial Raman microscope (Renishaw InVia). The spectra of the heterostructure region roughly match the combined spectra of the individual layers, without significant spectral shifts. 9

10 Figure S6. Raman spectra for the two types of TMDCHs, with results shown for the separated layers, as well as for the overlapping region. The main peaks are labeled for the individual layers and the corresponding heterostructures. 3,4 3. Analysis of the reflectance spectra for the individual TMDC layers and heterostructures Experimental reproducibility In Figure S7, we indicate the reproducibility of the reflection contrast measurements, both from day to day and from sample to sample. Although slight changes are noticed in the amplitude, the position and width of the features are both highly reproducible. Note that measurements from three different samples presented in Figure 7 (right) all correspond to different relative crystallographic orientations for the two layers (which was not controlled in the assembly process). No significant variation is observed. We take the results as representative of a typical sample in which there is no special crystallographic alignment between the layers. 10

11 Figure S7. Reproducibility of reflection contrast measurements. (Left) Variation in reflection contrast spectra obtained by measuring the same MoS 2 /WS 2 heterostructure on different days. (Right) Reflection contrast spectra for three different MoS 2 /WS 2 heterostructure. The three different samples have arbitrary relative crystallographic orientations. Similar results were obtained for the MoSe 2 /WSe 2 heterostructures (not shown). Lorentzian peak fitting In our analysis of the spectra of the heterostructures, we made use of a simple model for the response of the individual layers based on a parameterization with a small number of Lorentzian peaks. In Figure S8, we compare the imaginary part of the dielectric function (determined from a Kramers-Kronig constrained variational analysis of the reflection contrast spectra) to the model with only a few Lorenztian peaks. Although the higher-lying peaks do not necessarily correspond to a single excitonic transition (unlike the two lowest peaks), we are able to describe the spectrum with this phenomenological treatment quite adequately. This parameterization allows us to simulate the heterostructure spectrum by introducing broadening of the peaks (as well as slight spectral shifts), as we discuss in the main text. 11

12 Figure S8. Imaginary parts of the complex dielectric functions for individual TDMC layers as obtained from the reflectance contrast data by the Kramers-Kronig constrained variational analysis and using the model with a small number of Lorentzians. In the latter, each spectrum is simulated by three (Mocompounds) or four (W-compounds) Lorentzian peaks. 4. Calculation of energy transfer rate In the main text, we consider the potential role of resonant energy transfer between the two monolayers of the heterostructure as a process contributing to the observed line broadening. We were able to exclude this as the dominant process, since the lowest energy transition in the system (for which their would be no acceptor state in the other monolayer) consistently exhibited line broadening. 12

13 It is, however, still interesting to estimate the possible rate of resonant energy transfer between the two layers under circumstances where the transition of interest in one layer (donor) does have an acceptor state in the other material. To this end, we model the energy transfer process using a treatment introduced by Prins et al. 6 to describe resonant energy transfer from a localized chromophore above a thin 2D layer. The rationale for applying this analysis to the present case of excitation into a 2D layer from another 2D layer is the fact that the initial excitation takes the form of a tightly bound exciton, for which energy transfer is expected to be similar to that from a localized chromophore. Within this framework, there is a simple analytic expression for the ratio of the rate of resonant energy transfer to the radiative rate of the donor : = Im Here is the donor emission wavelength, is the thickness of the acceptor layer, is the separation of the donor from the acceptor layer, = / is effective permittivity of the acceptor, and = / / is its anisotropy, where parallel and perpendicular denote directions in the plane of the acceptor layer. We have applied this formalism to the case of energy transfer from the WS 2 A exciton to the absorbing MoS 2 layer. The emission wavelength is taken to be = 626. The sample thickness = 0.65 is chosen as that of the layer separation in the MoS 2 van der Waals solid, in keeping with the choice made in deducing the dielectric function of the layer. The separation of the chromophore to the layer = 0.65 is the distance between the central atomic layer of the donor to the central atomic layer of the acceptor, based on van der Waals thicknesses. The in- 13

14 plane dielectric function of the MoS 2 is extracted from previously taken data 5 and a value of 7.1 is used for the perpendicular dielectric response based Prins et al 6. We then obtain for the dielectric parameters: = / = [ (7.1)] / and = / / = [ /(7.1)] /. For an estimated radiative rate of ~0.1 based on work by Sun et al 1, we then calculate by numerical evaluation of the integral above an energy transfer time of ~200 fs. Although fast for an energy transfer process, this time scale would still only account for a minor contribution to the observed line broadening in the heterostructure. References 1 Sun, D.; Rao, Y.; Reider, G. A.; Chen, G.; You, Y.; Brezin, L.; Harutyunyan, A. R.; Heinz, T. F. Observation of Rapid Exciton-Exciton Annihilation in Monolayer Molybdenum Disulfide. Nano Lett. 2014, 14, Yu, Y.; Hu, S.; Su, L.; Huang, L.; Liu, Y.; Jin, Z.; Purezky, A. A.; Geohegan, D. B.; Kim, K. W.; Zhang, Y.; Cao, L. Equally Efficient Interlayer Exciton Relaxation and Improved Absorption in Epitaxial and Nonepitaxial MoS 2 /WS 2 Heterostructures. Nano Lett. 2015, 15, Lee, C.; Yan, H.; Brus, L. E.; Heinz, T. F.; Hone, J.; Ryu, S. Anomalous Lattice Vibrations of Single- and Few-Layer MoS2. ACS Nano 2010, 4, Berkdemir, A.; Gutierrez, H. R.; Botello-Mendez, A. R.; Perea-Lopez, N.; Elias, A. L.; Chia, C.-I.; Wang, B.; Crespi, V. H.; Lopez-Urias, F.; Charlier, J.-C.et al. Identification of Individual and Few Layers of WS2 Using Raman Spectroscopy. Sci. Rep. 2013, 3. 5 Li, Y.; Chernikov, A.; Zhang, X.; Rigosi, A.; Hill, H.; Van Der Zande, A. M.; Chenet, D. A.; Shih, E.; Hone, J.; Heinz, T. F. Measurement of the optical dielectric function of monolayer 14

15 transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2. Phys. Rev. B 2014, 90, Prins, F.; Goodman, A. J.; Tisdale, W. A. Reduced Dielectric Screening and Enhanced Energy Transfer in Single- and Few-Layer MoS2. ACS Nano 2014, 14,