International Centre for Materials Science and CSIR Centre of Excellence in Chemistry, New Chemistry Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur PO, Bangalore 560064 (India)
International Centre for Materials Science and CSIR Centre of Excellence in Chemistry, New Chemistry Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur PO, Bangalore 560064 (India)===
We report the temperature-dependent Raman spectra of single- and few-layer MoSe2 and WSe2 in the range 77–700 K. We observed linear variation in the peak positions and widths of the bands arising from contributions of anharmonicity and thermal expansion. After characterization using atomic force microscopy and high-resolution transmission electron microscopy, the temperature coefficients of the Raman modes were determined. Interestingly, the temperature coefficient of the A22u mode is larger than that of the A1g mode, the latter being much smaller than the corresponding temperature coefficients of the same mode in single-layer MoS2 and of the G band of graphene. The temperature coefficients of the two modes in single-layer MoSe2 are larger than those of the same modes in single-layer WSe2. We have estimated thermal expansion coefficients and temperature dependence of the vibrational frequencies of MoS2 and MoSe2 within a quasi-harmonic approximation, with inputs from first-principles calculations based on density functional theory. We show that the contrasting temperature dependence of the Raman-active mode A1g in MoS2 and MoSe2 arises essentially from the difference in their strain–phonon coupling.
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Two-dimensional materials such as graphene1–7 and transition-metal dichalcogenides, such as MoS2,8–24 WS2,25–28 MoSe2,29–32 WSe2,33–39 GaS,15, 40 GaSe,15, 40 h-BN,41–44 and MoO345, 46 have attracted much attention due to their extraordinary electrical, optical and magnetic properties. MoS2 has been widely investigated for its possible use in transistors,8–13 photodetectors,16 field emitters,18 gas sensors19–21 and for photocatalytic hydrogen production47 in solar cells,48–50 supercapacitors,51 and heterostructures.11 In their bulk forms, MoSe2 and WSe2 are composed of two-dimensional layers stacked vertically. A single-layer of these materials consists of a one-atom layer of Mo/W sandwiched between two one-atom layers of Se, connected through covalent bonds where Mo/W is located at the body center of a trigonal prism of six Se atoms. The two-dimensional layered structures of MoSe2 and WSe2 give rise to unusual electronic and optical properties. Bulk MoSe2 and WSe2 are layered semiconductors with indirect bandgaps of ∼1.1 and ∼1.21 eV, respectively. In the monolayer form they exhibit direct bandgaps of 1.55 and 1.25 eV, respectively, allowing the fabrication of switchable transistors and photodetector devices. Recent investigations on ultra-thin nanosheets of MoSe2 show a room-temperature mobility of ∼50 cm2 Vs−1,31 which increases almost four-fold when the temperature decreases to 78 K. Bulk WSe2 field-effect transistors show an intrinsic hole mobility of ∼500 cm2 Vs−1.52 Because single- and few-layer MoSe2 and WSe2 are potential candidates for use in next-generation nanoelectronic devices,33–39 it is important to investigate electron–phonon interactions and vibrational properties of single- and few-layer materials. Given the above considerations, we thought it important to study the changes in Raman spectra with temperature in order to delineate them from the changes that are due to the number of layers, for example. The temperature coefficients of the Raman-active bands in single- and few-layer MoSe2 and WS2 are expected to be different from those of the multilayer samples. Such differences might help to distinguish single-layer samples. We present the temperature dependence of the Raman spectra of single- and few-layer MoSe2 and single-layer WSe2 in the 77–623 K range. We have carried out first-principles calculations to understand the contrasting temperature dependence of the phonon modes of a single layer of MoSe2 in comparison with that of single-layer MoS2.
2. Results and Discussion
Figure 1 a and c shows side views of the crystal structure of MoSe2/WSe2, and Figure 1 b and d shows views from the top. Figure 2 a shows the optical image of single-layer and few-layer MoSe2 deposited on 300 nm SiO2–Si substrates using a micromechanical exfoliation method. Figure 2 b shows typical low-resolution and high-resolution (inset) transmission electron microscopy (TEM) images of a few-layer MoSe2 nanosheet. Figure 2 c shows the atomic force microscopy (AFM) image of single-layer and multilayer MoSe2 deposited on 300 nm SiO2–Si substrates. Figure 2 d shows the corresponding AFM height profiles for single-layer (vertical height ∼1 nm) and three-layer (vertical height ∼1.8 nm) MoSe2.
Figure 3 a shows Raman spectra of single-layer and bulk MoSe2 samples while Figure 3 b shows the expanded Raman spectrum in the 230–250 cm−1 range to indicate the difference between the single-layer and bulk samples. Changes in the peak position, width and intensity can be clearly seen. The intensity of the Raman bands increases with decrease in the number of layers. The Raman spectrum of single-layer MoSe2 exhibits bands due to E1g (167 cm−1), A1g (240 cm−1), E12g (282 cm−1), and A22u (351.4 cm−1) modes. Figure 4 a shows the Raman spectra of single-layer MoSe2 sample recorded at different temperatures. Figure 4 b shows the expanded 235–245 cm−1 region of the spectrum. Figure 4 c and d show the temperature dependence of the frequencies of Raman-active A1g and A22u modes in single-layer MoSe2 respectively. As the temperature increases, the A1g and A22u modes soften. The observed softening of the Raman bands is consistent with the fact that there is a reduction in interlayer coupling29 with increasing temperature.
The temperature dependence of Raman spectra was examined with several single-layer MoSe2 samples to ensure reproducibility of the results. The observed data of the peak positions obtained from Lorentzian fittings for A1g and A22u modes versus temperature were fitted using the Grüneisen model [Eq. (1)]:53(1)
Here, ωo is the peak position at 0 K and χ is the first-order temperature coefficient. The plot of the peak position versus temperature gives the slope χ. The temperature coefficient of the frequencies of the A1g and A22u bands of single-layer MoSe2 are −0.0054 and −0.0086 cm−1 K−1 respectively. These temperature coefficient values of the A1g mode are one order smaller than those reported for single- and few-layer MoS2.54–56 Furthermore, the values of the full width at half maximum of all the modes of single-layer MoSe2 increase with rising temperature. The observed behavior is due to phonon–phonon and electron–phonon interactions. Notably, the change in the Raman-peak positions with temperature in single-layer MoSe2 arises from the anharmonicity as well as from the thermal contribution.
Figure 5 a shows the Raman spectra of three-layer MoSe2 sample recorded at different temperatures and Figure 5 b shows the expanded 235–245 cm−1 region of the spectrum. Figure 5 c and d show the temperature dependence of the frequencies of Raman-active A1g and A22u modes in three-layer MoSe2 respectively. The coefficient of thermal expansion in few-layer nanosheets is expected to be different from that of the single-layer nanosheet. Our experimental estimates of the temperature coefficients of the A1g and A22u band frequencies of three-layer MoSe2 were found to be −0.0045 cm−1 K−1 and −0.0085 cm−1 K−1 respectively, the former value being significantly lower than that of single-layer MoSe2.
Figure 6 a shows an optical image of single- and few-layer WSe2, layered to different degrees on 300 nm SiO2–Si substrate using micromechanical exfoliation. Figure 6 b shows typical AFM images of single- and multilayer WSe2. Figure 6 c shows the Raman spectra at room temperature. The Raman spectra of single-layer WSe2 excited using a 514.5 nm laser source shows bands at A1g-LA (135 cm−1), E12g (247 cm−1), A1g (255 cm−1), inactive B2g (306 cm−1), 2E1g (356 cm−1), A1g+LA (371 cm−1) and 2A1g-LA (393 cm−1) modes, where LA stands for longitudinal acoustic singly degenerate vibrations in the lattice. The A1g and E1g bands of single-layer WSe2 are separated by ∼11 cm−1.35
In Figure 7 a, we show the Raman spectra of single-layer WSe2 at different temperatures. Figure 7 b shows the expanded 240–255 cm−1 region of the spectrum. The temperature dependence of the frequencies of Raman-active E1g, A1g, A1g+LA, and 2A1g-LA bands of single-layer WSe2 is shown in Figure 8a–d, respectively. The temperature coefficients of frequencies of the E1g, A1g, A1g+LA and 2A1g-LA modes of single-layer WSe2 were found to be −0.0048, −0.0032, −0.0067 and −0.0067 cm−1 K−1 respectively. The intensity of the Raman bands of single-layer WSe2 decreases with increasing temperature.
We found that the temperature coefficients of both the modes (A1g and A22u) of single-layer MoSe2 are larger than in single-layer WSe2. In the case of MoSe2, χ values of the single-layer are larger than of the triple-layer material, the χ value of the A1g mode being larger than that of the A22u mode. By comparison with the χ values found for the Raman modes of single-layer MoS2 and of the G band of graphene, the χ values of MoSe2 or WSe2 are much smaller.
To understand the mechanism and origin of the contrast between temperature coefficients of Raman modes in MoS2 and MoSe2, we use first-principles theoretical calculations. We determined the variation in phonon frequencies (ω) with temperature (T) within a quasi-harmonic approximation (QHA) in which the effects of thermal expansion are included through changes in phonon frequencies with change in the lattice constant a [Eq. (2)]:
where ao is the equilibrium lattice constant and α is the linear thermal expansion coefficient. ∂ω/∂a, the variation of phonon frequency with lattice constant a, is the third-order coupling between phonons and long-wavelength acoustic phonons, analogous to the Grüneisen parameter. In this treatment, the contribution of other anharmonic terms to the temperature dependence of frequencies (entering in the partial derivative of ω with respect to temperature T) is ignored. The factor of 2 takes into account the variation in the other lattice parameter b, which is equal to lattice parameter a.
The linear thermal expansion coefficient (α) under the QHA for monolayers of MoS2 and MoSe2 was estimated using Equation (3):57(3)
where ωk,s is the frequency of mode s at wave-vector k, and Nk are the number of k points in the equispaced 10×10×1 mesh (here Nk=100). ΔV is the difference between volume at strained and equilibrium lattice constants. Δωk,s is the corresponding change in frequency with change in volume, B is the bulk modulus and kB is the Boltzmann constant. We calculated the volume with lattice parameter c=6.5 Å in the estimation of B. We determined the change in A1g and A22u phonon frequencies with respect to a for monolayers of MoS2 and MoSe2 (see Figure 9). Our estimates of the frequencies for the A1g and A22u modes at the equilibrium lattice constant are 396 and 459 cm−1, and 235 and 343 cm−1 for MoS2 and MoSe2 respectively, and these are in good agreement with their experimental values. From the calculated values of dω/dT for A1g and A22u modes with α at T=300 K for monolayers of MoS2 and MoSe2 (see Table 1 along with other results), it is striking that the temperature coefficients of both A1g and A22u modes in MoS2 are noticeably larger than those of MoSe2 (see Table 1). Our first-principles estimate of the temperature coefficients of the A1g mode agrees well with experimental results for monolayers of MoS2 (−1.3×10−2 cm−1 K−1)55 and MoSe2 (−0.51×10−2 cm−1 K−1). The temperature coefficient of A1g in MoS2 is approximately 2.5 times that of MoSe2, which is consistent with our experimental results. The temperature coefficient of A1g is smaller than that of A22u of both MoS2 and MoSe2 (see Table 1), which also is in agreement with experimental data. However, our calculated temperature coefficient for the A22u mode is overestimated for both MoS2 (−3.7×10−2 cm−1 K−1) and MoSe2 (−2.3×10−2 cm−1 K−1) with respect to observed values. This discrepancy is likely due to the anharmonic coupling between the A1g and A22u modes, which is expected to renormalize the frequency of A22u. Similarly, WSe2 monolayers are expected to exhibit the same trend in the temperature coefficients of A1g and A22u modes.
Table 1. Bulk modulus (B), linear thermal expansion coefficient (α) at 300 K, and dω/dT for a monolayer of MoS2 and MoSe2.The experimental values are denoted in brackets.
2∂ω/∂a [cm−1 Å−1][c]
dω/dT [cm−1 K−1]
[a] Value taken from work by Satyaprakash et al.55 [b] Our experimental observations.
For a three-layer system, the temperature coefficients of the A1g and A22u modes of MoSe2 follow the same trend as for the monolayer. The interaction between the layers of MoSe2 is of a weak van der Waals type, and its effects can also be seen in the temperature coefficients of the Raman-active modes. In the case of the A22u mode, the out-of-plane vibrations of the atoms in the adjacent layers are in phase with each other. This does not change the interlayer Se–Se separation, and hence the interaction between the layers. Thus, the temperature coefficient for the A22u mode is not affected significantly by the number of layers. On the other hand, since the out-of-plane vibrations of atoms in adjacent planes are out of phase for the A1g mode, the interlayer Se–Se separation changes and the van der Waals interaction between the layers also changes. This leads to a significantly lower temperature coefficient (−0.45×10−2 cm−1 K−1) of the A1g mode as compared to that in single-layer MoSe2.
Single- and few-layer MoSe2 and WSe2 sheets obtained by micromechanical exfoliation were deposited onto 300 nm SiO2–Si substrates and their thickness and layering characterized using optical microscopy, AFM and Raman spectroscopy. Temperature-dependent Raman spectra of single- and few-layer MoSe2 and single-layer WSe2 show changes in peak position and width with changing temperature, due to contributions from anharmonicity and thermal expansion. The trends in the temperature coefficients of the Raman bands of nanosheets of MoSe2, WSe2, MoS2 and graphene are interesting and reflect the sensitivity of χ to changes in the materials’ properties. Our first-principles estimates of the temperature coefficients of the A1g mode of monolayer form of MoS2 (−1.3×10−2 cm−1 K−1) and MoSe2 (−0.51×10−2 cm−1 K−1) agree well with experimental values. Our analysis shows that the disparity in these coefficients of MoS2 and MoSe2 arises essentially from the difference in their strain–phonon coupling.
Bulk MoSe2 and WSe2 crystals (crystal size ∼10 mm) were purchased from Nanoscience Instruments, Inc. (Phoenix, AZ; Part #: NS00182). Single-layer and few-layer MoSe2 and WSe2 nanosheets were then deposited at room temperature by mechanically exfoliating bulk crystals onto pre-cleaned 300 nm SiO2–Si. Finally, contaminants from the Scotch tape were removed by dipping the SiO2 substrates along with flakes of MoSe2 and WSe2 in acetone for 5 min. A Nikon LV150NL trinocular upright optical microscope with an M1m imager was used to locate the single-to-few layers of MoSe2 and Wse2. The single-layer or few-layer nature of these flakes deposited on 300 nm SiO2/Si was then identified using specific color contrast. The color images were acquired with LED illumination and using bright-field imaging modes with Plan EPI 100× objectives (MPI, Japan) and 10× eyepiece. AFM tapping-mode images were recorded using an ICON system (Bruker, Santa Barbara, CA). High-resolution TEM images were acquired using an FEI Tecnai TF-30 (field-emission gun) instrument. Temperature-dependent Raman spectroscopy was performed with a LabRAM HR microscope using an Ar laser (514.5 nm) in the back-scattering geometry with laser power of ∼0.5 mW as described earlier.20 The spectra were collected under the same experimental conditions and the band positions and widths obtained by fitting them with a Lorentzian function. The spectra showed no damage to the materials after heating to 625 K.
Our first-principles calculations are based on density functional theory (DFT) as implemented in the Quantum ESPRESSO code,58 employing a generalized gradient approximation with Perdew–Burke–Ernzerhof functional for exchange correlation energy.59 Ultrasoft pseudopotentials60 were used to capture the interaction between ionic cores and valence electrons, and the interaction between the periodic images of the sheets was kept low through introduction of vacuum of 10 Å along the z direction. An energy cutoff of 35 Ry was used to truncate the plane-wave basis in representation of wave functions, and of 280 Ry in representing charge density and potentials. The structures were relaxed until the magnitude of Hellman–Feynman force on each ion was smaller than 0.02 eV Å−1. Brillouin-zone integrations in the Kohn–Sham self-consistent calculations were sampled over a Monkhorst pack61 mesh of 21×21×1 k points. We used DFT linear response to determine the dynamic matrices and phonons at wave vectors on a 3×3×1 mesh, and Fourier-interpolated to obtain phonons on an equispaced mesh of 10×10×1 k vectors (100 k points). The latter are used in the determination of the linear thermal expansion coefficient within a QHA.
D.J.L. thanks the DST (Government of India) for the Ramanujan fellowship. The research was primarily supported by the National Chemical Laboratory-Major Laboratory Project (NCL-MLP) project grant MLP 028626. S.N.S. is thankful to the Council of Scientific and Industrial Research, India, for a Research Fellowship. U.V.W. acknowledges support from an Outstanding Researcher Grant of the Department of Atomic Energy, India (DAE).