Research Article www.advmat.de Thickness-Dependent Elastic Softening of Few-Layer Free-Standing MoSe2 Visnja Babacic, David Saleta Reig, Sebin Varghese, Thomas Vasileiadis, Emerson Coy, Klaas-Jan Tielrooij, and Bartlomiej Graczykowski* 1. Introduction Few-layer van der Waals (vdW) materials have been extensively investigated in terms of their exceptional electronic, optoelectronic, optical, and thermal Since the discovery of graphene, there properties. Simultaneously, a complete evaluation of their mechanical has been a growing interest in semi- properties remains an undeniable challenge due to the small lateral sizes conducting materials with 2D crystal structures, such as van der Waals (vdW) of samples and the limitations of experimental tools. In particular, there layered, transition metal dichalcogenides is no systematic experimental study providing unambiguous evidence on (TMDCs). The mechanical, electrical, whether the reduction of vdW thickness down to few layers results in elastic thermal, and optical properties of few- softening or stiffening with respect to the bulk. In this work, micro-Brillouin layer TMDCs, which due to confinement, light scattering is employed to investigate the anisotropic elastic properties differ from those observed in bulk, have made them useful for electronics, energy of single-crystal free-standing 2H-MoSe2 as a function of thickness, down to storage, catalysis, photonics, and phono­ three molecular layers. The so-called elastic size effect, that is, significant and nics.[1–6] For instance, strong spatial systematic elastic softening of the material with decreasing numbers of layers confinement can change TMDCs from is reported. In addition, this approach allows for a complete mechanical indirect to direct bandgap semiconductors examination of few-layer membranes, that is, their elasticity, residual stress, enabling their use as transistors, photo- and thickness, which can be easily extended to other vdW materials. The pre- detectors, and light emitters.[1] Moreover, ultrathin TMDCs are used as a research sented results shed new light on the ongoing debate on the elastic size-effect platform for studying light-matter inter- and are relevant for performance and durability of implementation of vdW actions, exciton-polariton transport, and materials as resonators, optoelectronic, and thermoelectric devices. developing next-generation photonic devices.[7–11] Uniform, thin vdW materials, down to one layer, are easy to fabricate by V. Babacic, Dr. T. Vasileiadis, Dr. B. Graczykowski liquid[12] or mechanical[13] exfoliation from bulk. Owing to their Faculty of Physics relatively simple preparation, high-quality factor at low tem- Adam Mickiewicz University peratures, and high elastic moduli, ultrathin membranes of Uniwersytetu Poznanskiego 2, Poznan 61-614, Poland TMDCs can be used as mechanical resonators for sensors.[3,14] E-mail: bartlomiej.graczykowski@amu.edu.pl All the unique features of few-layer TMDCs must go hand- D. Saleta Reig, S. Varghese, Dr. K. J. Tielrooij in-hand with their mechanical and thermal durability to be Catalan Institute of Nanoscience and Nanotechnology (ICN2) CSIC and BIST applied in everyday devices. These aspects are inherently con- Campus UAB, Bellaterra, Barcelona 08193, Spain nected with the elastic/phononic properties, which in the case of Dr. E. Coy vdW materials are expected to be highly anisotropic and, poten- NanoBioMedical Centre tially, size-dependent.[15–19] The elastic properties of single-crystal Adam Mickiewicz University TMDCs are anisotropic, and in the case of the hexagonal sym- Wszechnicy Piastowskiej 3, Poznan 61-614, Poland metry, they are described by five non-zero independent compo- Dr. B. Graczykowski Max Planck Institute for Polymer Research nents of the elastic tensor Cij. Notably, a complete evaluation of Ackermannweg 10, 55128 Mainz, Germany Cij for vdW materials is already challenging for bulk. Indeed, The ORCID identification number(s) for the author(s) of this article there is an inherent obstacle in preparing volumetric samples can be found under https://doi.org/10.1002/adma.202008614. with flat surfaces, except for the cleavage (vdW) plane. To date, the anisotropic elastic properties of bulk TMDCs were partially © 2021 The Authors. Advanced Materials published by Wiley-VCH GmbH. measured employing ultrasound,[20,21] transient grating spectros- This is an open access article under the terms of the Creative Commons copy,[22] inelastic X-ray,[23] Raman,[24] and neutron[25] scattering. Attribution-NonCommercial License, which permits use, distribution and In the case of few-layer vdW materials, the elastic evaluation reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes. becomes even more difficult due to their lateral size, typically in The copyright line for this article was changed on 15 June 2021 after original the range from a few to hundreds of micrometers. On the one online publication. hand, atomic force microscopy (AFM) nanoindentation,[15] buck- ling-based metrology,[26] bulge test,[27] and nonlinear dynamic DOI: 10.1002/adma.202008614 response,[28] measure the spatial average of elastic properties. Adv. Mater. 2021, 33, 2008614 2008614 (1 of 8) © 2021 The Authors. Advanced Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.advmat.de On the other hand, scattering techniques, such as Raman spec- single layer. The crystallographic structure of this material troscopy,[24] Brillouin light scattering (BLS),[29] pump–probe is illustrated in Figure 1a. Five non-zero, independent elastic experiments,[30] and picosecond acoustics,[31] allow accessing constants describe the elastic properties of MoSe2, that is, C11, certain components of the elastic tensor. Overall, the literature C13, C33, C44, and C66 (Voigt notation). In addition, C12 can regarding experimentally determined elastic properties of both be expressed as C12 = C11 − 2C66.[36]By mechanical exfoliation bulk and few-layer vdW materials is limited. Additionally, there from the bulk, we prepared MoSe2 membranes (>15 μm in dia­ is no consensus on whether the elastic constants change when meter) of different thicknesses d = Nt, where N is the number reducing the material thickness and to which extent.[15–18] of layers. The fabrication of freely suspended MoSe2 flakes was 2H phase molybdenum diselenide (2H-MoSe2) is one of the done utilizing dry-transfer from a viscoelastic polydimethylsi- prominent TMDCs for which a search of the literature shows that loxane (PDMS) stamp, which does not involve wet chemistry or the elastic constants are not fully known. Surprisingly, out of five capillary forces, thus leading to relatively clean surfaces.[37] The independent Cij of MoSe2, only two have been determined experi- sample side view scheme with respect to the crystallographic mentally utilizing Raman spectroscopy[24,32] (C44) and laser pump– orientation and Cartesian coordinates is shown in Figure 1b. probe experiment[30] (C33) both for bulk and few-layer films/mem- As a result of the used transfer method, MoSe2 membranes branes. Furthermore, the averaged Young modulus of a few-layer are possibly pre-stressed. Here, we describe this residual stress MoSe2 was measured using buckling-based metrology[26] and in in the form of the Cauchy stress tensor of two non-zero and situ tensile testing,[33] whose results were incompatible, showing equal components σ 11 = σ 22 = σ 0, as illustrated in Figure 1a,b. about a 23% difference between the techniques. Figure 1c,d displays the optical and scanning electron micros- In this work, we systematically investigate the anisotropic copy (SEM) images, respectively, for the exemplary samples elastic properties of bulk and few-nanometer-thick free-standing of different thicknesses. The membranes were also examined MoSe2 using micro-Brillouin light scattering (μ-BLS).[34] Using by high-resolution transmission electron microscopy (TEM) this contactless and non-destructive technique, we deter- (Figure 1e) showing the single crystalline structure with an mine C11, C66, and C44 for bulk as well as C11 and C66 for few- interplanar distance ≈0.28 nm in agreement with the litera- nanometer-thick membranes. For the latter materials, we report ture.[38] More details about the fabrication and characterization substantial thickness-dependent elastic softening under nano- utilizing the optical contrast method, AFM, and Raman spec- confinement. Also, we show that μ-BLS can be an accurate troscopy are provided in Section 1 and Supporting Information technique for measuring membrane thicknesses. (Sections S1 and S5, Supporting Information). To determine the elastic constants of bulk MoSe2, we per- formed μ-BLS experiments in the backscattering geometry, 2. Results and Discussion illustrated in Figure 2a. We used p–p and s–p (p–s) polarization regarding incident-scattered light, where p and s correspond 2H-MoSe2 forms a layered hexagonal structure (belonging to the polarization of the light being parallel (TM polarization) to space group D64h ) with lattice constants a ≈ 0.33 nm and and normal (TE polarization) to the sagittal plane, respectively. c = 2t ≈ 1.29 nm,[35] where t = 0.645 nm is the thickness of a As a light source, we used a single-mode laser of wavelength λ = 523 nm, for which the real and the imaginary parts of the refractive index are n1 = 4.7995 and n2 = 2.0796, respectively.[41] In Figures 2a and 3a ki, and ks denote the wave vectors for the incident and scattered light, respectively, while θ is the inci- dent angle. The surface and bulk acoustic wave vectors are represented with q and Q, respectively. A BLS experiment per- formed on homogeneous semiconductors allows probing Ray- leigh surface waves (RSWs), pseudo-RSWs, bulk acoustic waves (BAWs) and so-called high-frequency pseudo-surface acoustic waves (HFPSAWs).[42] Figure 2a displays schematics of displace- ment profiles for RSWs and BAWs, that is, longitudinal (L) and transverse (T1, T2) waves, relevant for the further discussion. Figure 2b,c displays exemplary BLS spectra recorded for bulk MoSe2 at θ = 45° and light polarized in p–p and p–s configura- tions, respectively. As shown in Figure 2b, the BLS spectrum . recorded in the p–p polarization reveals two peaks which we assigned to RSW and HFPSAW.[42] RSWs propagate in close Figure 1. a) Scheme of MoSe2 crystal lattice, where d = Nc/2 denotes vicinity of the free surface and contribute to BLS spectra mostly the thickness of the membrane (N stands for number of layers and due to the surface ripple (SR) mechanism. In this case, the c = 1.29 nm,[35] is the lattice constant along [001]). Two non-zero in-plane acoustic wave vector q lies in the free surface, and its magni- components of the stress tensor are denoted by σ11 = σ22. b) Schematic tude is q = 4πsinθ/λ due to momentum conservation that holds side view of the MoSe2 membrane suspended over circular (15 μm in only for the in-plane components.[34,43,44] By changing the θ, we diameter) hole in gold-coated Si3N4 substrate. c) Optical microscopy and measured the dispersion relation of RSWs, that is, their fre- d) SEM images of exemplary samples. Scale bars in (c) and (d) are 20 and 5 μm, respectively. e) Atomic-resolution TEM image of exemplary MoSe2 quency f as a function of q that is plotted in Figure 2d. Here, membrane. Scale bar in (e) is 1 nm. from the BLS data linear fit, we determined the phase velocity Adv. Mater. 2021, 33, 2008614 2008614 (2 of 8) © 2021 The Authors. Advanced Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.advmat.de Figure 2. a) Schematic illustration of BLS backscattering geometry and the deformations corresponding to Rayleigh surface wave (RSW), longitudinal (L), and transverse waves (T1 and T2) bulk acoustic waves (BAWs). Symbols ki, ks, q, and ​Q denote incident light, scattered light, surface acoustic, and bulk acoustic wave vectors, respectively, while θ is the incident angle. b,c) Experimental and calculated BLS spectra for bulk MoSe2 obtained at θ = 45° for p–p polarization (b) and s–p polarization (c). Symbols I1, I2, and I3 stand for the calculated BLS intensity corresponding to acoustic waves of polarization in x1, x2, and x3 axes, respectively (Section S4.2, Supporting Information for details). HFPSAW denotes high-frequency pseudo-surface acoustic wave while the red arrow stands for the L BAW threshold. d) The measured dispersion relation for observed modes (circles) and their fitting (solid lines) for the bulk MoSe2. The shaded regions indicate dispersions calculated according to theoretical data available in the literature.[39,40] of RSW as vRSW = 1620 ± 13 ms−1. For the (001) plane of the and other vdW materials.[29] Notably, their acoustic wave vectors hexagonal symmetry materials, vRSW can be calculated from:[45] are identical to that of RSW, and thereby, their phase velocities can be directly determined from the dispersion relations f(q)  2 C  2 C C2  2  2 C11  plotted in Figure 2d. In this way, we calculated the velocities C33  v RSW − 44   v RSW − 11 + 13  = C 44 v RSW 4  v RSW −  (1) of HFPSAW and T1 modes as vHFPSAW = 5256 ± 38 ms−1 and  ρ  ρ ρC 33   ρ   vT1 = 3209 ± 19 ms−1, respectively. These values are reasonable with respect to vRSW and in good agreement with the theoretical where ρ = 6900 kgm−3 denotes the mass density of MoSe2.[14] literature data (shaded areas in Figure 2d).[39,40] Employing this formula, we calculated vRSW using theoretically For a hexagonal crystal belonging to the D64h space group, predicted elastic constants available in the literature.[39,40] In the phase velocities of L, T1, and T2 waves propagating Figure 2d, the light blue shading stands for the range of disper- in (001) are given as vL = (C11/ρ)1/2, vT1 = (C66/ρ)1/2, and sion relations that correspond to the calculated vRSW. As we can vT2 = (C44/ρ)1/2,[47] respectively. Here, we assume that the notice, the BLS results are in this range but close to its lower velocity of HFPSAW coincidences with the longitudinal velocity limit. This can be explained by an overestimation of the theo- (vHFPSAW = vL).[29,42] Hence, from the measured velocities, we retical values discussed later in this work. obtained the elastic constants C11 = ρ v HFPSAW 2 = 191 ± 3 GPa The HFPSAW is a leaky surface wave of pronounced longi- and C66 = ρ v T1 = 71 ± 1 GPa. Further, from C11 and C66, we 2 tudinal polarization and displacement field localized close to determined C12 = C11 − 2C66 = 49 ± 4 GPa. Although T2 cannot the free surface. HFPSAWs, also known as longitudinal reso- be resolved in our experiment due to selection rules[42,47] nances[42] or skimming longitudinal waves,[46] can propagate (Section S4.2, Supporting Information), we deduced C44 from with velocities almost identical to that of L BAWs. Their detec- the measured phase velocity of RSW. Since the vRSW is mostly tion by BLS is possible only for highly opaque materials due sensitive to C44 and only weakly dependent on C13 and C33,[48] to sub-surface photo-elastic (PE) coupling.[42] However, this (Figure S7, Supporting Information), we calculate the elastic requires strong suppression of usual bulk BLS backscattering constant from Equation (1). Thus, using C11 determined from (Figure 2a) from bulk acoustic waves with the wave number BLS and taking for consistency C13 = 9.8 GPa and C33 = 54.9 GPa Q = 4πn1/λ. This condition is met for MoSe2 as the penetra- from the literature,[30,39] we obtained C44 = 18.8 ± 0.7 GPa. The tion depth of light (532 nm) is δp = λ/4πn2 = 20 nm and hence latter deviates from predictions of DFT theory in the literature, the relevant peak is not detected by BLS (Figure S6, Sup- namely C44 = 32.9 GPa[39] and C44 = 15.9 GPa.[40] This difference porting Information). The sub-surface PE coupling also ena- explains the discrepancy between measured and predicted dis- bles detection of the fast transverse wave (T1) wave in the s–p persions of RSW evident in Figure 2d. However, C44 obtained BLS configuration as evident in Figure 2c. Both HFPSAW and in this work agrees well with previous Raman studies finding T1 waves have been previously detected using BLS in GaAs [42] C44 = 17.75 ± 1.9 GPa.[24,32] Previously reported theoretical and Adv. Mater. 2021, 33, 2008614 2008614 (3 of 8) © 2021 The Authors. Advanced Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.advmat.de Figure 3. a) Schematics of the backscattering BLS geometry and displacements of the fundamental antisymmetric (A0), symmetric (S0 Lamb), and shear horizontal (SH0) waves. b–d) Normalized experimental and calculated BLS spectra of 6.9 nm-thick MoSe2 membrane obtained at θ = 45°. e) Experimental (circles) and theoretical (solid lines) dispersion relation obtained for 6.9 nm-thick MoSe2 membrane. f) Experimental (circles) and calculated (solid line) v(q) dispersion relation of the A0 mode. The red arrow indicates the cut-off phase velocity v0. The dashed line denotes the cal- culated v(q) dispersion relation of A0 mode for σ0 = 0. experimental elastic constants of bulk MoSe2 are listed in q = 4πsinθ/λ.[50–52] Under spatial confinement of the medium Table S5, Supporting Information. The elastic constants deter- in one direction, the BAWs turn into families of symmetric (S), mined from BLS are positive and satisfy the thermodynamic antisymmetric (A) Lamb, and shear-horizontal (SH) waves. The stability criteria.[49] From the perspective of other vdW mate- zero-order (fundamental) modes relevant for this work are illus- rials (Table S6, Supporting Information), the elasticity of bulk trated in Figure 3a.[53,54] MoSe2 is typical for the TMDCs family. In principle, C11 that Figure 3b,c displays measured and calculated BLS spectra corresponds to the in-plane elasticity is significantly larger than of A0 and S0 waves (p–p polarization) for 6.9 nm-thick MoSe2 the out-of-plane component given by C33 due to the weak inter- membrane. Changing polarization to p–s or s–p allows us to actions between the layers. In Figure 2b,c we compared experi- resolve SH0, as illustrated in Figure 3d. The peaks are fitted mental data with the BLS spectra calculated employing the with Lorentzian functions to determine their spectral posi- elastodynamic Green’s functions at the free surface (x3 = 0) and tions. As for the bulk, we performed angle-resolved BLS experi- using the measured Cij.[42–44] The calculated and experimental ments to evaluate the elastic properties of the membranes. spectra consistent in terms of the peak positions and spectral Figure 3e displays the dispersion relations f(q) of A0, SH0, and lineshapes. In particular, the peak associated with HFPSAW is S0 modes propagating in the MoSe2 membrane. For the meas- centered at the frequency that coincides with L BAW threshold ured range of wave numbers, the dispersion relations of S0 and (red arrow in Figure 2b), which justifies the assumption SH0 modes are linear and do not depend directly on the mem- regarding the equality of velocities for these waves. The details brane thickness (Figure S11, Supporting Information). There- of the calculations and further discussion of the spectral line- fore, S0 and SH0 waves are identical to L and T1 waves of bulk shapes are provided in Section S4.2, Supporting Information. MoSe2, and their phase velocities are given by vS0 = (C11/ρ)1/2 To evaluate the elastic properties of a few-layer MoSe2 and vSH0 = (C66/ρ)1/2, respectively. In practice, this allows for the membranes with varying thicknesses, we applied the back- straightforward evaluation of C11 and C66 of the membranes. scattering BLS geometry as shown in Figure 3a. In this case, In general, for small, reduced wavenumbers (qd → 0), the the magnitude of the acoustic wave vector is defined again as dispersion relation f(q) of the A0 mode is parabolic (f ∝ q2). Adv. Mater. 2021, 33, 2008614 2008614 (4 of 8) © 2021 The Authors. Advanced Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.advmat.de This implies a linear dependence (v ∝ q) of the phase velocity membrane thickness. This apparent softening of the material v = 2πf/q on the wave number q.[50,51,54] However, the experi- is indicative of the so-called elastic size effect in vdW mate- mental v(q) of the A0 mode plotted in Figure 3f deviates from rials.[15–18,57–59] To date, this phenomenon remains controversial the expected linear trend (dashed line) what can be explained as the experimental studies have not concluded whether the by the residual stress in the membrane. The latter can be well- nanoconfinement results in softening or stiffening. The prior estimated from the cut-off phase velocity v0(qd → 0) = (σ 0/ρ)1/2 works employing diverse techniques have reported somewhat fitted from the dispersion v(q) plotted in Figure 3f.[51] For the scattered values of averaged Young modulus (see Table S8, Sup- considered acoustic wavelengths, being much larger than the porting Information).[15,18,23,25,27,28,58,60–66] The anisotropic elas- membrane thickness, the dispersion relation of A0 mode mostly ticity probed by Raman spectroscopy has revealed that C44 and depends on three parameters: C11, σ 0 and d, while the effect of C33 constants remain the same for 2D MoS2 with respect to the the remaining constants is negligible (Figure S12, Supporting bulk.[67] This approach is, however, indirect and simplifies inter- Information). Thus, the dispersion of the A0 mode can be used layer interactions to a linear chain model. On the other hand, to determine the membrane thickness. In principle, for aniso- our finding goes hand in hand with the recent femtosecond tropic materials, this requires a numerical approach described pump–probe measurements of MoSe2 revealing the softening in Section S4.3, Supporting Information, with thickness and of C33 with a reducing number of layers.[30] residual stress as the fitting parameters. The d and σ 0 obtained For specific techniques and engineering problems, the Young in this way are listed in Table S4, Supporting Information, and modulus and Poisson ratio are much more common than the compared with the results of Raman spectroscopy, AFM, and elastic tensor. We used the experimental results to calculate the optical contrast method. In particular, the thickness-dependent in-plane component E11 of the Young modulus (Section S8, Sup- frequency of the A1g Raman mode is consistent with the thick- porting Information). This parameter is more convenient for com- ness measured using BLS (Section S5 and Figure S10, Sup- parison with the values obtained by other techniques. According porting Information). In terms of the absolute values, we found to BLS data plotted in Figure 4c, E11 systematically decreases good agreement between the results from AFM and optical with a reducing number of layers from 177 ± 4 GPa for bulk to contrast measurements and the values extracted from BLS data. 122 ± 3 GPa for 2L MoSe2. Our results significantly differ from the Therefore, μ-BLS provides a new contactless means for evalu- size-independent Young modulus E = 224 ± 41 GPa obtained by ating the thickness and residual stress of ultrathin membranes the buckling metrology for 5–10L MoSe2.[26] Also, a very recent, in and can be an alternative or a supporting method for more situ tensile testing has evaluated the in-plane Young modulus of established techniques. Further details and discussion can be one- and two-layer free-standing MoSe2 as E = 177.2 ± 9.3 GPa.[33] found in Sections S1, S4.3, and S5, Supporting Information. Notably, the latter value is consistent with E11 of bulk MoSe2 Figure 4 displays measured C11, C66, and E11 (in-plane com- obtained in our study, albeit the limited number of samples does ponent, details in Section S8, Supporting Information) as a not allow for any statement regarding the elastic size effect.[33] We function of the membrane thickness (number of layers) and note that the residual stress cannot explain the behavior observed compared with the literature values.[33,39,40,55,56] To the best in Figure 4 as it does not correlate with the membrane thickness, of our knowledge, elastic constants of a few-layer and bulk and in principle, it is too low (from 0 to 188 MPa) to affect the MoSe2 presented in this work are the first obtained from a elastic constants due to the elastic nonlinearity.[54,68] direct experiment. As we can notice from Figure 4, all three Overall, BLS of acoustic phonons in MoSe2 shows a con- elastic parameters monotonically decrease with reducing the siderable reduction of elastic constants with decreasing the Figure 4. a,b) Elastic constants C11 (a), andC66 (b), and c) in-plane Young modulus E11 as a function of the membrane thickness (number of layers). The open circles in (a–c) are from the experimental data in this work, while the other symbols (stars) stand for the single-layer theoretical data found in the literature.[33,55,56] Bulk elastic properties obtained in this work and from the theoretical data found in the literature[39,40] are denoted in (a–c) by shaded areas and symbols (triangles, squares), respectively. The solid lines are guides to the eye. Adv. Mater. 2021, 33, 2008614 2008614 (5 of 8) © 2021 The Authors. Advanced Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.advmat.de number of layers (Figure 4). Notably, this behavior goes hand Information) on the suspended regions of the MoSe2 flake showed sub- in hand with the red-shift of the A1g Raman mode in ultrathin nanometer flatness over several microns, confirming the absence of small (sub-micrometer) wrinkles. TMDCs (Section S5, Supporting Information). The latter was Brillouin Light Scattering: For the backscattering experiment, CW explained in prior works as resulting from softening of the laser (Spectra-Physics, Excelsior 300) of wavelength λ = 532 nm and low effective restring forces acting on the atoms due to decreased power (about 100 μW for thin up to 750 μW for the thickest free-standing vdW interlayer interactions with reducing the number of sample) was used as the light source. Laser light was partially reflected layers.[69,70] Nevertheless, a comprehensive understanding of from the pellicle beamsplitter (R:T,8:92) and then focused on the sample, the size-effect reported in this work requires further experi- with the incident angle θ, by 20× long WD microscope objective. In the ments and theoretical modeling. used geometry, the same objective collected the scattered light, which was focused on the pinhole (aperture was set to be 3 mm, depending on the particular sample) of a Fabry–Perot interferometer (JRS Scientific Instruments). The beam spot size on the samples was less than 1 μm, 3. Conclusions which was much less than the diameter of the membrane. Thus, it allowed the evaluation of mechanical properties from flat parts of the We applied micro-Brillouin light scattering to investigate dis- membranes. (Figure S1, Supporting Information). persion relations of GHz acoustic waves in single-crystal bulk and few-layer thick MoSe2 down to three molecular layers. In this way, we determined the elastic constants C11, C66 being Supporting Information consistent with prior theoretical predictions, and C44 in good Supporting Information is available from the Wiley Online Library or agreement with the values obtained from Raman spectroscopy. from the author. To the best of our knowledge, these elastic constants have been directly measured for the first time, even though MoSe2 is a prototypical and heavily studied member of the TMDCs family. Acknowledgements Next, we employed μ-BLS to study the dispersion of acoustic The work was supported by the Foundation for Polish Science Lamb waves propagating in MoSe2 membranes and deter- (POIR.04.04.00-00-5D1B/18). ICN2 was supported by the Severo mined C11, C66, E11, and membrane thickness. We observed Ochoa program from Spanish MINECO (Grant No. SEV-2017-0706). a significant elastic softening of MoSe2 with decreasing the K.J.T. acknowledges funding from the European Union’s Horizon 2020 numbers of layers, which is already clearly discernible for 10L. research and innovation program under Grant Agreement No. 804349 This elastic size effect can have profound implications for the (ERC StG CUHL), RyC fellowship No. RYC-2017-22330 and IAE project accurate design, construction, and control of nanodevices, for PID2019-111673GB-I00. E.C. acknowledges the partial financial support from the National Science Centre (NCN) of Poland by the OPUS grant example, nanomechanical resonators for sensors. Also, modi- 2019/35/B/ST5/00248. fied elasticity at the nanoscale should affect phononic thermal Open access funding enabled and organized by Projekt DEAL. transport, and hence it has significant consequences for the thermal conductivity of TMDCs. Finally, by all the above and thorough comparison of the existing experimental studies, we Conflict of Interest note that elastic size effects might be present in other TMDCs but remain unnoticed due to inconsistent results from the var- The authors declare no conflict of interest. ious experimental approaches. Data Availability Statement 4. Experimental Section The data that support the findings of this study are available from the corresponding author upon reasonable request. Materials: Bulk 2H-MoSe2 was purchased from HQ Graphene. A custom-built dry-transfer stage, inspired by the design of Castellanos- Gomez et al.,[71] was used to transfer MoSe2 flakes of different thicknesses (in the range from 1 to 20 nm) over large-area (175 μm2) Keywords holes. First, bulk flakes of MoSe2 were mechanically exfoliated by Scotch elastic constants, elastic size effect, few-layer MoSe2, micro-Brillouin tape onto an about 1 mm-thick PDMS stamp, made by mixing silicone light scattering, van der Waals materials curing agent and elastomer (SYLGARD, in 1:10 proportions). The clean, transparent PDMS allowed optical thickness identification, alignment, Received: December 21, 2020 and transfer of suitable flakes over single-hole (15 μm), silicon nitride Revised: March 16, 2021 windows (Norcada, NTPR005D-C15). The transfer yield was increased by Published online: May 3, 2021 gold-coating the target substrates with 5/50 nm of Ti/Au in an E-beam evaporator (AJA Orion), thanks to the enhanced adhesion of TMDCs on gold surfaces.[72] It was crucial to use high-quality, crystalline flakes (with sharp edges, no cracks or wrinkles) and to release them very gently through the suspended region to avoid their collapse at the point of [1] Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, M. S. Strano, transfer. Scanning electron Micrographs (SEM) were obtained under low Nat. Nanotechnol. 2012, 7, 699. current conditions (1 kV) in a 7001TTLS (JEOL) instrument. Finally, high- [2] Y. Zhang, T.-R. Chang, B. Zhou, Y.-T. Cui, H. Yan, Z. Liu, F. Schmitt, resolution transmission electron microscopy (HR-TEM) images were J. Lee, R. Moore, Y. Chen, H. Lin, H.-T. Jeng, S.-K. Mo, Z. Hussain, collected at 80 kV in an ARM-200f (JEOL) equipment. The thicknesses A. Bansil, Z.-X. Shen, Nat. Nanotechnol. 2014, 9, 111. were determined by the optical contrast method and AFM (Section S1, [3] N. Morell, A. Reserbat-Plantey, I. Tsioutsios, K. G. Schädler, Supporting Information). AFM measurements (Figure S5, Supporting F. Dubin, F. H. L. Koppens, A. Bachtold, Nano Lett. 2016, 16, 5102. Adv. Mater. 2021, 33, 2008614 2008614 (6 of 8) © 2021 The Authors. Advanced Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.advmat.de [4] J.-S. Rhyee, J. Kwon, P. Dak, J. H. Kim, S. M. Kim, J. Park, Y. K. Hong, [36] B. A. Auld, Acoustic Fields and Waves in Solids, vol. 1, Wiley, New W. G. Song, I. Omkaram, M. A. Alam, S. Kim, Adv. Mater. 2016, 28, York, 1973. 2316. [37] R. Frisenda, E. Navarro-Moratalla, P. Gant, D. Pérez De Lara, [5] A. Roy, H. C. P. Movva, B. Satpati, K. Kim, R. Dey, A. Rai, P. Jarillo-Herrero, R. V. Gorbachev, A. Castellanos-Gomez, Chem. T. Pramanik, S. Guchhait, E. Tutuc, S. K. Banerjee, ACS Appl. Mater. Soc. Rev. 2018, 47, 53. Interfaces 2016, 8, 7396. [38] Z. Chen, H. Liu, X. Chen, G. Chu, S. Chu, H. Zhang, ACS Appl. [6] A. Eftekhari, Appl. Mater. Today 2017, 8, 1. Mater. Interfaces 2016, 8, 20267. [7] J. Yang, Z. Wang, F. Wang, R. Xu, J. Tao, S. Zhang, Q. Qin, [39] C. K. Ghosh, D. Sarkar, M. K. Mitra, K. K. Chattopadhyay, J. Phys. D: B. Luther-Davies, C. Jagadish, Z. Yu, Y. Lu, Light Sci. Appl. 2016, 5, Appl. Phys. 2013, 46, 395304. e16046. [40] Y. Asadi, Z. Nourbakhsh, J. Elec. Materi. 2019, 48, 7977. [8] F. Hu, Y. Luan, M. E. Scott, J. Yan, D. G. Mandrus, X. Xu, Z. Fei, [41] A. R. Beal, H. P. Hughes, J. Phys. C: Solid State Phys. 1979, 12, Nat. Photon. 2017, 11, 356. 881. [9] H. Zhang, B. Abhiraman, Q. Zhang, J. Miao, K. Jo, S. Roccasecca, [42] P. Mutti, C. E. Bottani, G. Ghislotti, M. Beghi, G. A. D. Briggs, M. W. Knight, A. R. Davoyan, D. Jariwala, Nat. Commun. 2020, 11, J. R. Sandercock, Surface Brillouin Scattering—Extending Surface 3552. Wave Measurements to 20 GHz, Springer US, Boston, MA, USA [10] B. Munkhbat, D. G. Baranov, M. Stührenberg, M. Wersäll, A. Bisht, 1995, pp. 249–300. T. Shegai, ACS Photonics 2019, 6, 139. [43] A. G. Every, J. D. Comins, In Handbook of Advanced Nondestructive [11] H. Lin, Z.-Q. Xu, G. Cao, Y. Zhang, J. Zhou, Z. Wang, Z. Wan, Z. Liu, Evaluation (Eds: N. Ida, N. Meyendorf), Springer International Pub- K. P. Loh, C.-W. Qiu, Q. Bao, B. Jia, Light Sci. Appl. 2020, 9, 137. lishing, Cham, Switzerland 2019, pp. 327–359. [12] V. Nicolosi, M. Chhowalla, M. G. Kanatzidis, M. S. Strano, [44] A. Every, B. Mathe, J. Comins, Ultrasonics 2006, 44, e929. J. N. Coleman, Science 2013, 340, 1226419. [45] S. A. Lee, S. M. Lindsay, Phys. Status Solidi B 1990, 157, K83. [13] H. Li, J. Wu, Z. Yin, H. Zhang, Acc. Chem. Res. 2014, 47, 1067. [46] A. M. Lomonosov, X. Yan, C. Sheng, V. E. Gusev, C. Ni, Z. Shen, [14] N. Morell, S. Tepsic, A. Reserbat-Plantey, A. Cepellotti, M. Manca, Phys. Status Solidi RRL 2016, 10, 606. I. Epstein, A. Isacsson, X. Marie, F. Mauri, A. Bachtold, Nano Lett. [47] Laser Handbook (Eds: F. T. Arecchi, E. O. Schulz-Dubois) Vol. 1, 2019, 19, 3143. North-Holland Publ. Co, Amsterdam, The Netherlands, reprinted [15] S. Bertolazzi, J. Brivio, A. Kis, ACS Nano 2011, 5, 9703. edition 1988. [16] K. Choudhary, G. Cheon, E. Reed, F. Tavazza, Phys. Rev. B 2018, 98, [48] G. Carlotti, D. Fioretto, G. Socino, E. Verona, J. Phys.: Condens. 014107. Matter. 1995, 7, 9147. [17] K. Liu, J. Wu, J. Mater. Res. 2016, 31, 832. [49] F. Mouhat, F.-X. Coudert, Phys. Rev. B 2014, 90, 224104. [18] A. Falin, Q. Cai, E. J. Santos, D. Scullion, D. Qian, R. Zhang, [50] J. Cuffe, E. Chávez, A. Shchepetov, P.-O. Chapuis, E. H. El Boud- Z. Yang, S. Huang, K. Watanabe, T. Taniguchi, M. R. Barnett, outi, F. Alzina, T. Kehoe, J. Gomis-Bresco, D. Dudek, Y. Pennec, Y. Chen, R. S. Ruoff, L. H. Li, Nat. Commun. 2017, 8, 15815. B. Djafari-Rouhani, M. Prunnila, J. Ahopelto, C. M. Sotomayor [19] Y. Cai, Q. Ke, G. Zhang, Y. P. Feng, V. B. Shenoy, Y.-W. Zhang, Adv. Torres, Nano Lett. 2012, 12, 3569. Funct. Mater. 2015, 25, 2230. [51] B. Graczykowski, M. Sledzinska, M. Placidi, D. Saleta Reig, [20] M. S. Skolnick, S. Roth, H. Alms, J. Phys. C: Solid State Phys. 1977, M. Kasprzak, F. Alzina, C. M. Sotomayor Torres, Nano Lett. 2017, 17, 10, 2523. 7647. [21] M. Gatulle, M. Fischer, A. Chevy, Phys. Status Solidi B 1983, 119, [52] B. Graczykowski, A. Gueddida, B. Djafari-Rouhani, H.-J. Butt, 327. G. Fytas, Phys. Rev. B 2019, 99, 165431. [22] T. Kim, D. Ding, J.-H. Yim, Y.-D. Jho, A. J. Minnich, APL Mater. 2017, [53] H. Lamb, Proc. R. Soc. London, Ser. A 1917, 93, 114. 5, 086105. [54] B. Graczykowski, J. Gomis-Bresco, F. Alzina, J. S Reparaz, [23] A. Bosak, M. Krisch, M. Mohr, J. Maultzsch, C. Thomsen, Phys. Rev. A. Shchepetov, M. Prunnila, J. Ahopelto, C. M Sotomayor Torres, B 2007, 75, 153408. New J. Phys. 2014, 16, 073024. [24] X. Zhang, Q.-H. Tan, J.-B. Wu, W. Shi, P.-H. Tan, Nanoscale 2016, 8, [55] F. Zeng, W.-B. Zhang, B.-Y. Tang, Chinese Phys. B 2015, 24, 097103. 6435. [56] A. Kandemir, H. Yapicioglu, A. Kinaci, T. Çağin, C. Sevik, Nanotech- [25] J. Feldman, J. Phys. Chem. Solids 1976, 37, 1141. nology 2016, 27, 055703. [26] N. Iguiñiz, R. Frisenda, R. Bratschitsch, A. Castellanos-Gomez, Adv. [57] B. Chitara, A. Ya’akobovitz, Nanoscale 2018, 10, 13022. Mater. 2019, 31, 1807150. [58] A. Castellanos-Gomez, M. Poot, G. A. Steele, H. S. J. van der Zant, [27] J. W. Suk, Y. Hao, K. M. Liechti, R. S. Ruoff, Chem. Mater. 2020, 32, N. Agraït, G. Rubio-Bollinger, Adv. Mater. 2012, 24, 772. 6078. [59] H. Zhan, D. Guo, G. Xie, Nanoscale 2019, 11, 13181. [28] D. Davidovikj, F. Alijani, S. J. Cartamil-Bueno, H. S. J. van der Zant, [60] O. L. Blakslee, D. G. Proctor, E. J. Seldin, G. B. Spence, T. Weng, M. Amabili, P. G. Steeneken, Nat. Commun. 2017, 8, 1253. J. Appl. Phys. 1970, 41, 3373. [29] R. T. Harley, P. A. Fleury, J. Phys. C: Solid State Phys. 1979, 12, [61] J.-U. Lee, D. Yoon, H. Cheong, Nano Lett. 2012, 12, 4444. L863. [62] D. Metten, F. Federspiel, M. Romeo, S. Berciaud, Phys. Rev. Appl. [30] P. Soubelet, A. A. Reynoso, A. Fainstein, K. Nogajewski, 2014, 2, 054008. M. Potemski, C. Faugeras, A. E. Bruchhausen, Nanoscale 2019, 11, [63] C. Lee, X. Wei, J. W. Kysar, J. Hone, Science 2008, 321, 385. 10446. [64] R. J. Nicholl, H. J. Conley, N. V. Lavrik, I. Vlassiouk, Y. S. Puzyrev, [31] E. C. Hadland, H. Jang, N. Wolff, R. Fischer, A. C. Lygo, V. P. Sreenivas, S. T. Pantelides, K. I. Bolotin, Nat. Commun. 2015, G. Mitchson, D. Li, L. Kienle, D. G. Cahill, D. C. Johnson, Nanotech- 6, 8789. nology 2019, 30, 285401. [65] I. W. Frank, D. M. Tanenbaum, A. M. van der Zande, P. L. McEuen, [32] T. Kuzuba, M. Ishii, Phys. Status Solidi B 1989, 155, K13. J. Vac. Sci. Technol. B 2007, 25, 2558. [33] Y. Yang, X. Li, M. Wen, E. Hacopian, W. Chen, Y. Gong, J. Zhang, [66] R. C. Cooper, C. Lee, C. A. Marianetti, X. Wei, J. Hone, J. W. Kysar, B. Li, W. Zhou, P. M. Ajayan, Q. Chen, T. Zhu, J. Lou, Adv. Mater. Phys. Rev. B 2013, 87, 035423. 2017, 29, 1604201. [67] Y. Zhao, X. Luo, H. Li, J. Zhang, P. T. Araujo, C. K. Gan, J. Wu, [34] G. Carlotti, Appl. Sci. 2018, 8, 124. H. Zhang, S. Y. Quek, M. S. Dresselhaus, Q. Xiong, Nano Lett. [35] P. B. James, M. T. Lavik, Acta. Cryst. 1963, 16, 1183. 2013, 13, 1007. Adv. Mater. 2021, 33, 2008614 2008614 (7 of 8) © 2021 The Authors. Advanced Materials published by Wiley-VCH GmbH www.advancedsciencenews.com www.advmat.de [68] D. J. Dunstan, S. H. B. Bosher, J. R. Downes, Appl. Phys. Lett. 2002, [71] A. Castellanos-Gomez, M. Buscema, R. Molenaar, V. Singh, L. Janssen, 80, 2672. H. S. J. van der Zant, G. A. Steele, 2D Mater. 2014, 1, 011002. [69] C. Lee, H. Yan, L. E. Brus, T. F. Heinz, J. Hone, S. Ryu, ACS Nano [72] S. B. Desai, S. R. Madhvapathy, M. Amani, D. Kiriya, M. Hettick, 2010, 4, 2695. M. Tosun, Y. Zhou, M. Dubey, J. W. Ager, D. Chrzan, A. Javey, Adv. [70] L. Liang, V. Meunier, Nanoscale 2014, 6, 5394. Mater. 2016, 28, 4053. Adv. Mater. 2021, 33, 2008614 2008614 (8 of 8) © 2021 The Authors. Advanced Materials published by Wiley-VCH GmbH