Anharmonicity in Raman-active phonon modes in atomically thin MoS 2
Suman Sarkar, Indrajit Maity, H.L. Pradeepa, Goutham Nayak, Laetitia Marty, Julien Renard, Johann Coraux, Nedjma Bendiab, Vincent Bouchiat, Sarthak Das, Kausik Majumdar, Manish Jain, Aveek Bid
AAnharmonicity in Raman active phonon modes of atomically-thin MoS Suman Sarkar, Indrajit Maity, and H.L. Pradeepa
Department of Physics, Indian Institute of Science, Bangalore-560012, India
Goutham Nayak, Laetitia Marty, Julien Renard, Johann Coraux, Nedjma Bendiab, and Vincent Bouchiat
Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
Sarthak Das and Kausik Majumdar
Department of Electrical Communication Engineering,Indian Institute of Science, Bangalore 560012, India
Manish Jain and Aveek Bid ∗ Department of Physics, Indian Institute of Science, Bangalore 560012, India
Phonon-phonon anharmonic effects have a strong influence on the phonon spectrum; most promi-nent manifestation of these effects are the softening (shift in frequency) and broadening (changein FWHM) of the phonon modes at finite temperature. Using Raman spectroscopy, we studiedthe temperature dependence of the FWHM and Raman shift of E and A modes for single-layerand natural bilayer MoS over a broad range of temperatures ( < T < K). Both the Ramanshift and FWHM of these modes show linear temperature dependence for
T >
K, whereas theybecome independent of temperature for
T <
K. Using first-principles calculations, we show thatthree-phonon anharmonic effects intrinsic to the material can account for the observed temperature-dependence of the line-width of both the modes. It also plays an important role in determining thetemperature-dependence of the frequency of the Raman modes. The observed evolution of the line-width of the A g mode suggests that electron-phonon processes are additionally involved. Fromthe analysis of the temperature-dependent Raman spectra of MoS on two different substrates –SiO and hexagonal boron nitride, we disentangle the contributions of external stress and internalimpurities to these phonon-related processes. We find that the renormalization of the phonon modefrequencies on different substrates is governed by strain and intrinsic doping. Our work establishesthe role of intrinsic phonon anharmonic effects in deciding the Raman shift in MoS irrespective ofsubstrate and layer number. PACS numbers:Keywords:
I. INTRODUCTION
MoS is a well-studied two-dimensional transitionmetal dichalcogenide having a direct bandgap in its singlelayer form [1]. Its discovery [1, 2] has opened up new pos-sibilities for the semiconductor industry in terms of next-generation optoelectronics and valleytronics devices. Thepredicted, and observed exotic properties of atomically-thin flakes of MoS – direct bandgap in the monolayerlimit, strong correlations giving rise to three-body trionstate observable even at room-temperature [3], ambipo-lar transport [4, 5], superconductivity [6, 7], highly ef-ficient light-matter interactions [8] and strong valley-selectivity [9, 10] – make it a very interesting materialfrom an academic perspective. Optical measurementslike Raman and photoluminescence (PL) spectroscopyhave become the techniques of choice to probe theseproperties of MoS and other related transition metaldichalcogenides.These optical properties of these materials are influ-enced by presence of intrinsic defects (primarily chalco-genide vacancies) [11–13], effect of ambient, the substrate or capping layer [12, 14], temperature, [15, 16]. Analyz-ing the optical properties thus provide a wealth of in-formation about defect-dynamics, various energy trans-fer processes, Coulomb interactions, influence of electric,magnetic field and strain on spin- and valley-splittingof the electronic energy bands [17] and temperature-dependent multi-phonon scattering processes [18]. Ad-ditionally, valuable information can be gleaned from thepeak-positions and full width at half-maximum (FWHM)of the Raman-active modes about the dielectric environ-ment [19, 20], strain effects [21–23], anharmonicity in thelattice potential energy [24–26], thermal expansion [26–28], and thermal conductivity [26, 29–31] of these materi-als. Characterizing the effect of the latter (temperature)is essential to understand the limitations to charge car-rier mobility and thermal conductivity, hence the per-formance of devices based on these materials. To thisrespect, interactions involving two or more phonons [18]and electron-phonon interactions are essential. Theircharacteristic temperature-dependence allows to unraveltheir role.Even after intense research for more than a decade, an a r X i v : . [ c ond - m a t . m e s - h a ll ] S e p in-depth, combined experimental and theoretical studyof the temperature evolution of the phonon-modes; insingle- and few-layer MoS is missing. Previous stud-ies employed semi-quantitative models for the calcula-tion of the temperature dependent Raman shift [32, 33].Two contradictory conclusions have been reported by fit-ting the experimental data to such models for 300 K 500 K. Najmei et-al. concluded that the three-phonon process are irrelevant in explaining the observedphonon-frequency shifts of Raman active modes, whereasYang et-al. found the three-phonon processes to bemore dominant [32, 33]. Lanzillo et-al. [34] performedfirst-principles molecular dynamics simulations includingboth the three- and four-phonon processes, predictinga characteristic temperature-dependence of the Ramanshift. However testing this scenario against experimen-tal data was made difficult by the rather limited resolu-tion ( ∼ − ) of the measured Raman spectra. Stud-ies conducted at high temperatures (300 K< T <450 K)show that the positions of the Raman peaks of single-layer MoS are linearly red-shifted with increasing tem-perature [35–38]. This shift was attributed primarily tofour-phonon processes for the E mode while for the A mode, thermal expansion was also found to play a signif-icant role [39].In this letter, we report the results of combined ex-perimental and theoretical studies of the temperaturedependence of the Raman shifts and full-width at halfmaxima (FWHM) of Raman-active modes in single-layer(SL) and natural bilayer (NBL) MoS samples. We findthat at low temperatures, the FWHM and Raman shiftare practically independent of T while above 125 K theyvary almost linearly with temperature. Our theoreticalcalculations, based on density functional perturbationtheory [40] (DFPT), faithfully reproduce the observedtemperature dependencies of FWHM of the Raman ac-tive vibrational modes of SL MoS over the entire tem-perature range. We find that three-phonon anharmoniceffects are the predominant factor determining the ob-served temperature dependence of the FWHM for thetwo prominent Raman modes in MoS . We also find thathigher order phonon processes contribute significantlyto the observed high-temperature softening of phononmodes with the temperature. By comparing the tem-perature dependence of the FWHM and the Raman shiftsamples prepared on two types of substrate – SiO /Si ++ and single crystal hexagonal boron nitride (hBN) – wefind that strain and electronic doping only contributea temperature-independent change of the Raman-shiftsand FWHMs. II. METHODS AND MEASUREMENTS MoS flakes were exfoliated from single crystals of nat-urally occurring MoS (SPI supplies) on polydimethyl- hBN SL SL SiO NBL NBLSL SLATL (b) (a) µ m 9 µ m Figure 1: (a) Optical image of Sample1 prepared onSiO /Si ++ substrate – the SL region is outlined in solid-redline and NBL in solid-green line. (b) Optical image of Sam-ple2 prepared on a hBN sample – the MoS on hBN portionis outlined by a solid-red line and the MoS on SiO by asolid-green line. siloxane (PDMS). These were transferred on 290 nmSiO /Si ++ substrates using the well-established dry-transfer technique [41, 42]. We also prepared hBN/MoS heterostructures on SiO /Si ++ substrates by sequentiallyaligning and transferring the different atomic layers. Thetransfers were carried out in an inert atmosphere inside aglove-box using a custom-built system based on a Thor-labs 3-Axis motorized linear-translation stage (MTS-Z8)under an optical microscope. During transfers, the speedof approach and retraction of the microscope stage waskept less than 1 µ m s − to avoid wrinkling and tearing ofthe flakes. The number of layers in the flakes was initiallyestimated from the colour-contrast of the optical imagesand later confirmed from AFM measurements, Ramanspectroscopy, and photoluminescence measurements. Wehave presented high-frequency and low-frequency Ramanmeasurement along with PL measurement on appendixsection Fig 7 to identify the number of layers in our sam-ple. We also have identified SL and NBL sample withlow-frequency Raman measurement as discussed in theappendix section in the Fig 8.We studied two different classes of samples. Multiplesamples of each type were studied, and the data on dif-ferent samples of the same class were qualitatively con-sistent. In this letter, we focus on the data obtained froma single sample of each class. Fig 1(a) is an optical imageof a sample prepared on a SiO /Si ++ substrate havingSL, NBL and artificial trilayer (ATL) regions (henceforthreferred to as ‘Sample1’). On this class of samples, westudied the temperature evolution of Raman spectra forthe SL and NBL. In the second class of samples, SL MoS was transferred to lie partially on SiO and partly on a ∼ 20 nm thick hBN flake on the surface of SiO . An opti-cal image of one such sample (referred to as ‘Sample2’) isshown in Fig. 1(b). These samples were used for the com-parative study of the temperature dependence of Ramanspectra of SL MoS on SiO and hBN.We have performed the low-temperature Raman ex-periments in reflectance mode on HORIBA Scientific In-strument LABRAM HR Evolution attached with a ARScryo-free cryostat which can reach till 4K base temper-ature. 532 nm laser source in our measurement systemhaving a spatial resolution of 1 µ m is been used. TheRaman spectra were recorded using 1800 lines/mm grat-ing at very low laser power levels ( ∼ µ W) to avoidheating of the sample. The resolution of our set up isabout 1 cm − . In this report we have concentrated ourresult over the spectral-range 350-450 cm − though wehave measured the spectra over the range of spectral-range 200-800 cm − . In the appendix section we haveshown in Fig. 6 a typical Raman spectra over completerange taken at 300 K.The phonon frequencies, Raman shifts and FWHMwere computed using DFPT [40] and the D3Q code [43]based on density functional theory as implemented in theQUANTUM ESPRESSO package [44–46]. We used op-timized norm-conserving Vanderbilt (ONCV) pseudopo-tentials [47, 48] for Mo and S atoms and the generalizedgradient approximation [49] for the exchange-correlation.For SL MoS and NBL MoS , we used plane-waves ki-netic energy cut-off of 80 Ry ensuring convergence ofphonon frequencies at Γ point within 0.1 cm − . To avoidinteraction between periodic images along z -direction, an18 Å vacuum spacing was used. For total energy calcu-lations, we used a × × (cid:126)k point sampling of theBrillouin zone, whereas the phonon frequencies, third or-der force constants were calculated using a × × (cid:126)k point sampling of the Brillouin zone. Raman shift andFWHM calculations using the third order force constantswere performed by summing over discrete uniform (cid:126)q gridpoints ( × × ) which were randomly shifted fromthe origin. A Gaussian function with a smearing of − was used [43] to replace the delta function. III. RESULTS AND DISCUSSIONSA. Temperature dependence of the life-times ofRaman modes in MoS High frequency Raman spectrum (we define high-frequency in this letter to be the spectral-range 350-450 cm − ) of SL and NBL MoS consists of two Ramanactive modes – denoted by E (cid:48) and A (cid:48) for SL and by E and A for multi-layers [50–53]. The E modes arisesfrom in-plane, anti-phase oscillations of the two S atomswith respect to the Mo atom while the A modes are dueto the anti-phase, out-of-plane oscillations of only the S atoms [54]. For notational simplicity, we will refer tothe in-plane modes as E and the out-of-plane modes as A for both SL and multi-layers. The measured Ramanspectra in the range 370 - 420 cm − over the temperaturerange 8 K to 300 K are shown in Fig. 2(a) for SL region for 371 378 385 406 413 4200400080001200016000 370 380 390 400 410 4202004006008001000Raman shift ( cm - ) I n t e n s it y ( a r b . un it ) (a) A E Raman shift ( cm - ) (b) I n t e n s it y ( a r b . un it ) S SS SMo Mo Figure 2: (a). Raman spectra of Sample1 measured at differ-ent temperatures between 8 K and 300 K. The dotted linesare the guide for the eye for marking the evolution of Ramanshift with temperature. (b) An individual Raman spectra at300 K. The blue and olive solid lines are Lorentzian fits tothe experimental data. The inset schematics show the E and A vibrational modes. Sample1. The dotted lines are guides to the eye showingthe evolution of the peak positions with temperature T .We found that even in the SL limit, our MoS sampleshave FWHM of about ∼ . − and ∼ . − for E and A respectively which confirms the high crys-talline quality of the MoS flakes [37].To extract the peak positions and peak FWHM, wefitted the Raman spectra at every temperature with twoLorentzian peaks. An example is shown in Fig. 2(b) forthe data obtained at 300 K. We have also used Voigtfitting to determine the peak position and FWHM shownin appendix section Fig. 9 and Fig. 10 . We found that incase of Voigt fitting both Lorentzian width and Gaussianwidth contribute to the Voigt width and as a result weend up with a minimum FWHM for E and A peakis about ∼ . − and ∼ . − respectively whilefrom Lorentzian fit to our Raman spectra provides theminimum FWHM is about ∼ . 45 cm − and ∼ . − respectively shown Fig. 10 (a) and (b) respectively. InFig. 3(a) and (b) we show the temperature dependenceof the FWHM of the E and A mode respectively forthe SL region of Sample1. We observe that the FWHMdecreases with decreasing T and tends to saturate below100 K. The same trend is seen for the FWHM of the E and A modes measured on the NBL portion of Sample1– the data are plotted in Figs. 3(c) and (d) respectively.Raman modes have a finite FWHM due to both in-trinsic phonon scattering processes and extrinsic factors(linked to defects, the finite size of crystals, etc). Ata finite temperature, the intrinsic FWHM of the Ra-man modes γ in are determined by both electron-phonon SL E F W H M ( c m - ) (a) SL A (b) F W H M ( c m - ) T (K) NBL E (c) NBL A T (K) (d) Figure 3: Temperature dependence of the FWHM of the Ra-man modes. The experimentally obtained data are plotted onthe left-axis in open red circles for (a) the E peak of the SLregion, (b) the A peak of the SL region. The correspondingtheoretical results are plotted on the right-axis in solid bluelines. The green dashed lines are linear fits to the experimen-tal data for T > K. (c), (d) are the corresponding plotfor NBL region. The data are for Sample1. interactions and phonon-phonon anharmonic effects i.e. γ in = γ e − ph + γ ph − ph [26, 55]. Extrinsic factors linked todefect-dynamics can cause broadening of the Raman linesin several possible ways – by changing the anharmonic-ity, causing local fluctuations of the frequency of optical-phonons, causing phonon confinement-induced relaxationof the Raman wave vector selection rules or leading to achange of phonon wave-function as the solution of thedynamic problem [56].We compute the FWHM using third-order phonon-phonon anharmonic effects for both SL and NBL sam-ples (the details of the calculations are given in the fol-lowing section). The calculated change in FWHM overthe temperature range < T < K of SL MoS ( ∼ . 48 cm − and 1 . − and for E and A re-spectively) matches quite well with our measured val-ues ( ∼ . − and 1 . 55 cm − for E and A respec-tively). The data are plotted in Figs. 3(a) and 3(b) re-spectively for the two modes.Just like the experimental data the calculated temper-ature dependence of FWHM of both A and E modesfor SL MoS , saturates below 100 K and increases lin-early for T > K with a coefficient we call β . Thecalculated and measured values of β of the E and A peaks for SL and NBL are presented in Table. I while thecalculated value of β is in good agreement with experi-ment for in-plane vibrational mode, it is underestimatedfor the out-of-plane mode. This discrepancy can notbe assigned to four-phonon or higher order phonon pro- (b) SL A P ea k po s i t i on ( c m - ) (a) SL E NBL E P ea k po s i t i on ( c m - ) T (K) (c) NBL A T (K) 394.6394.8395.0395.2 (d) Figure 4: Temperature dependence of the Raman shift. Theexperimentally obtained data are plotted on the left-axis inopen red circles for (a) the E peak of the SL region, (b) the A peak of the SL region, (c) the E peak of the NBL region,and (d) the A region of the NBL sample. The correspondingtheoretical results are plotted on the right-axis in solid bluelines. The measurements were performed on Sample1. Thegreen dashed lines are the linear fits to experimental data for T > K. cesses. If four-phonon or higher order phonon processesplayed an important role then both the modes shouldhave shown the discrepancy. In contrast, the electron-phonon process mostly affects the A modes by reduc-ing its life-time, hence by increasing the FWHM. Nat-urally, our calculations addressing the case of undopedMoS cannot properly account for the observed electron-phonon interaction-related increase of the FWHM. B. Temperature dependence of frequency ofRaman modes in MoS The experimentally measured temperature dependenceof the Raman shifts of the E and A modes from 300 Kdown to 10 K in the SL region of Sample1 are shown inFigs. 4(a) and (b) respectively. The corresponding datafor the NBL region of Sample1 are shown in Figs. 4(c)and (d), respectively. We find that above 100 K, theRaman shift of both the E and A modes, in both SLand NBL, decrease with temperature. Below 100 K, theRaman shift in all cases saturates. Over the temperaturerange from 100 K to 300 K the Raman shifts can be fittedto a relation: ω ( T ) = ω − αT (1)Here ω is the peak-position extrapolated to zero temper-ature and α = dω/dT is the temperature coefficient of theRaman shift. From linear fits to the data for T > K,we obtain, for both SL and NBL, α − ∼ . 013 cm − / K for the E mode and ∼ . 012 cm − / K for the A mode.In the appendix section, we have shown that the Voigtfitting to the Raman spectra does not gave any appre-ciable difference to the peak-position shown in Fig. 9 (a)and (b).To understand the temperature dependence of the Ra-man shifts, note that at T (cid:54) = 0 K, phonons frequencies getrenormalized due to anharmonic effects. At constant (ex-ternal) pressure, the corresponding temperature depen-dence of the phonon frequencies ω for a semiconductorcan be expressed as ω ( T ) − ω (0) = ∆ ω T ( T ) + ∆ ω V ( T ) ,where ∆ ω T and ∆ ω V are the frequency shifts due to lat-tice thermal expansion and ‘pure’ thermal anharmoniceffects, which typically include third- and fourth-orderphonon-phonon anharmonic effects [57–59]. We computethe frequency shifts by including both the lattice thermalexpansion effects [32] and phonon-phonon anharmonic ef-fects, using three-phonon processes. Two kinds of scat-tering processes are taken into account: (a) a phononof momentum (cid:126)q can decay into two phonons ( − (cid:126)q (cid:48) , − (cid:126)q (cid:48)(cid:48) ),(b) a phonon with (cid:126)q can coalesce with a phonon with − (cid:126)q (cid:48) to eject one with − (cid:126)q (cid:48)(cid:48) . In our first principles based cal-culations we incorporated all such possible three-phononprocesses without any restriction [43, 58].In Figs. 4 (a) and (b), we plot, on the right-axis, thecalculated temperature dependence of the E and A Raman shifts for SL MoS . For T (cid:38) K, the Ramanmodes soften linearly with T while for T (cid:46) K, theRaman shifts saturate and becomes independent of T .This theoretically computed trend captures correctly theexperimental temperature dependence.The temperature dependencies of Raman shifts andFWHM arise from the occupation-probabilities of thephonons (Bose factor) [43, 58]. In order to get an in-tuitive understanding of the temperature dependenceof the Raman shift, let us consider one possible three-phonon decay channel: an optical phonon with energy (cid:126) ω at Γ point decays into two acoustic phonons fromthe same branch while conserving both energy and mo-mentum [59]. Therefore, the acoustic phonon modeshave (cid:126) ω / energy with equal and opposite momen-tum. This process gives rise to a temperature depen-dent Raman shift of the following form: ∆ ω ( T ) ∼ [1 + e (cid:126) ω / kBT − ] [57, 58]. For both the E and A modes,with (cid:126) ω ≈ meV. Thus, at low T with ∆ ω saturatesto a constant value, and becomes linear in T at highertemperature.Note however, that the absolute values of the cal-culated mode frequencies differ from the experimen-tally measured ones by about 4%. The frequency val-ues are in fact sensitive to the choice of the exchange-correlation functional. Generalized gradient application(GGA) overestimates the lattice constant. For example,with GGA at 0 K the in-plane lattice constant is 3.18 Å, which is ∼ . larger than the experimentally mea-sured value [60], and the frequencies of the E (cid:48) and A bands of SL are 373.7 cm − and 396.2 cm − while the ex-perimental values at 8 K are 385.5 cm − and 406.5 cm − .Linear fits to the calculated T dependence of Ramanshifts yield a temperature coefficient α ∼ . 004 cm − / K for both the E and A modes (Table. I). This valueis significantly lower than the experimental values. Thisunderestimation can arise from several parameters (bothintrinsic and extrinsic), which are discussed below.Among the intrinsic phonon-phonon anharmonic ef-fects ignored in our calculations, the principal one is afour-phonon processes. It has been proposed that, therelative contribution to Raman shifts at finite T fromthe three-phonon and four-phonon processes is relatedto the phonon band-gap of the material. The larger theband-gap, the greater the contribution from four-phononprocesses [61]. The band-gap between acoustic and op-tical modes in SL MoS is ∼ meV, which is ratherlow. Thus, we expect that the phase-space availablefor three-phonon decay channels is non-negligible com-pared to higher order four-phonon processes. A signif-icant contribution to the Raman shift temperature de-pendence from four-phonon and higher-phonon processescould thus be expected. Although extrinsic effects linkedto defects [62] or the substrate [63], adsorbates and fab-rication induced disorder [64] in a sample can give a con-stant shift to the Raman shift and FWHM of the Ramanmodes, we show in the next section that contribution totheir temperature dependence is marginal.Compared to single layer, natural bilayer shows a red-shift in the E Raman shift and a blue-shift in the A Raman shift [53]. The blue-shift in the A mode can beaccounted for an additional spring-like interaction, re-lated to short-ranged interaction involving the nearestneighbour S atom. On the other hand, the red-shift inthe E can be attributed to a greater dielectric screen-ing of the Coulomb forces in NBL MoS [65] comparedto the case of single layer. The trends of the calculatedtemperature dependence of Raman shifts for NBL MoS look very similar to those of SL MoS (Figs. 4(c) and(d)), in agreement with our experiment. C. Effect of substrate on doping and strain levelsin MoS The data discussed till now were obtained on MoS ona SiO substrate. We now turn to probe the effect ofsubstrate on the Raman-modes. We have identified thesingle layer MoS by comparing Raman spectra of SLMoS on a SiO with MoS on hBN in Sample2 showed inthe appendix section Fig. 12. We performed temperaturedependent Raman spectroscopy measurements in MoS on hBN substrate – the data are shown in Fig. 5(a) (Wehave shown the Raman spectra for Sample2 measured at Experimental values( cm − K − ) Theoretical values( cm − K − ) α E α A β E β A α E α A β E β A SL on SiO ∼ α ) and FWHM ( β ) for SL and NBL on SiO for the two Raman modes ofMoS . A1g on SiO2A1g on hBNE2g on SiO2E2g on hBN F W H M ( c m - ) T (K) (b) A on SiO A on hBNE on SiO E on hBN P ea k po s iti on ( c m - ) T (K) (a) Figure 5: Plots of (a) the peak positions and (b) the FWHMof the A and E Raman modes of MoS on hBN and SiO substrates – the data were taken on Sample2. The green solidlines are the linear fits to experimental data for T > K. different temperature between 8 K to 300 K in appendixsection Fig. 13). The data show that the E peak getsred-shifted for MoS on the hBN substrate as comparedto the SiO substrate. On the contrary the A peak getsblue-shifted for MoS on the hBN substrate comparedto the case with the SiO substrate. We find a linearvariation of E and A peak-frequencies with temper-ature above 100 K on the hBN substrate while at low-temperatures, the peak-frequencies and FWHM of boththe E and A saturate. The fact that both the sam- ples on SiO and on hBN show a saturation of Ramanshift and FWHM at similar T -scale, points to an intrin-sic origin. Finally we observe from Fig. 5(b) that whilethe FWHM of the E mode is comparable for Sample1and Sample2, the FWHM of the A mode is significantlylower on the hBN substrate than on the SiO substrate.In the following section we present our understanding ofthe origin of these observations.The induced carrier density and strain in MoS is sub-strate dependent. From our electrical transport mea-surements, we found that the mobility of SL MoS ona SiO substrate (on samples prepared in a way similarto Sample1) is ∼ V − s − at 100 K while that ofSL MoS on hBN (obtained on samples similar to Sam-ple2) is ∼ 20 cm V − s − [66]. The impurity numberdensities extracted from conductance fluctuation spec-troscopy measurements for these two classes of samplesare . × cm − eV − and . × cm − eV − re-spectively [66].The higher impurity concentration of SL MoS on aSiO substrate effectively corresponds to a large elec-tron doping. Consistently, the FWHM of the A g peakis larger on the SiO substrate than on the hBN sub-strate (Fig. 5(b)). In order to compute the effects of theelectron doping on the Raman modes, we explicitly adda fraction of electron in the unit-cell of SL MoS in ourcalculations. We find that the A mode softens signif-icantly ( by ∼ − . − for 0.003e/cell) with electrondoping in agreement with large electron-phonon couplingstrength corresponding to this mode [67]. In sharp con-trast, the E mode is practically independent of doping(hardens by ∼ . 08 cm − for 0.003e/cell). The temper-ature coefficient of the FWHM of the Raman modes ofhBN-MoS sample actually compares well with the the-oretically calculated slopes from three-phonon process.On the contrary, on a SiO substrate, the experimen-tal values are not well reproduced by our calculations,which yield significantly smaller estimates. In the case ofhBN substrate charge impurity concentration is two or-ders of magnitude lower so electron-phonon processes areless pronounced. So the three-phonon process becomesthe primary life-time determining mechanism in case ofhBN-substrate device.On the other hand, the strain induced due to hBN onMoS is large as compared to that by SiO . The lat-tice constant difference is more than 20 percent betweenhBN and MoS . As the heterostructures are made byvan der Waals interaction, we do not expect the strainis generated by lattice mismatch. Rather we believe thestrain arises from deformed heterostructure due to fabri-cation. In our case we have prepared the heterostructureby stacking MoS on pre-transferred hBN flake by dryPDMS transfer technique. In this process the air beentrapped in the interface of the heterostructure. As weanneal our sample through heating in vacuum at about300 ◦ C, the MoS got stretched by cleaning up most ofthe interface area and deformed the hBN. After anneal-ing the MoS tries to relax but it got held by the de-formed hBN. This does not allow the MoS to relax com-pletely. As a result some residual strain sustain on the MoS . Xu Han et.al. show that in SL MoS the straincan be up to . in presence of hBN environment [68].To investigate the effects of uniaxial compressive strainon the high-frequency Raman modes, we apply . to . strain to the unit-cell of SL MoS and computethe phonon mode frequencies using DFPT. We find thatfor MoS on hBN substrate, the E mode softens signifi-cantly ( ∼ − . − ) more than the A ( ∼ − . − ). SiO as a substrate induces less strain, which results ina stiffer E mode compared to that of hBN. The com-bined effect of these two phenomenon – namely higherelectron doping levels on SiO substrate and higher strainon hBN substrate – provide a natural explanation of theexperimentally observed red-shift for the E peak andblue-shift in A peak for MoS on the hBN substrate ascompared to that on the SiO substrate (see Fig. 5(a)).Interestingly, irrespective of the substrate, the tempera-ture dependent Raman shift shows similar slopes overtthe temperature range 100 K to 300 K signifying thatthe doping and strain does not play an important role indetermining the temperature dependence of Raman shift(Table. I). This strongly supports our explanation of thistrend using only intrinsic anharmonic processes. IV. CONCLUSION We have performed a detailed study of temperatureon Raman active modes in MoS and analyzed the ef-fects of strain and electronic doping imposed by the sub-strate. Both the Raman shift and FWHM shows lineartemperature dependence T > K, below T < Kthey became independent of the temperature. Usingfirst principle based calculations, we show that the ob-served temperature dependence of the Raman shift onSL and on NBL MoS arises from both three-phonon andfour-phonon processes while the life-time of these phononmodes primarily arises from three-phonon process for thein-plane mode while for the out-of plane mode electron-phonon process plays an important role too. The higherorder phonon processes are present in the system but life-time of those higher-order process is much longer than thethree-phonon process due to much lower scattering prob- abilities and momentum and energy conservation rules.The higher value of FWHM in the out-of-plane vibra-tional mode as compared to that of the in-plane vibra-tion is consistent with a scenario with a three-phononprocess. To understand the contribution of other extrin-sic effects like the presence of impurities and strain dueto substrate on Raman shifts and Raman modes, lifetimea comparison of the data on samples fabricated on a hBNand on a SiO substrates has been performed. The theo-retical calculations suggest that the observed differencesarise from a larger strain and lower density of impuritieson a hBN substrate. Lastly irrespective of sample qual-ity, strain the temperature coefficient of Raman shift forin-plane and out-of-plane component is constant and it islinear throughout the temperature range 300 K to about125 K. Below 100 K the Raman shift became independentof temperature and saturates. This extrinsic effect playsa static role in Raman-shift throughout the temperaturerange. V. ACKNOWLEDGMENT A.B. acknowledges financial support from SERB, DST,Govt. of India and Indo-French Centre for the Promo-tion of Advanced Research (CEFIPRA) and supports un-der FIST program, DST. The authors thank Supercom-puter Education and Research Centre at IISc for provid-ing computational resources. AppendixFull range Raman spectra and identification of layernumber on SiO substrate 200 300 400 500 600 7000500100015002000 I n t e n s it y ( a r b . un it ) Raman shift (cm -1 ) Figure 6: Raman spectrum for SL MoS on SiO substrateat 300 K. In our main article, we have concentrated on the in-plane E g and out-of-plane A g vibrational modes. Wehave analyzed the Raman spectra only in the range of370 cm − to 420 cm − . But our measurement consistof the spectra ranges 200 cm − to 800 cm − for all thetemperatures. In the Fig. 6 we have presented a full rangespectra for SL MoS on SiO substrate at 300 K. SLNBL P L i n t e n s it y ( a r b . un it ) Energy (eV) (c) 370 380 390 400 410 420 430050100150200250300350 1920212223 R a m a n I n t e n s it y ( a r b . un it ) Raman shift (cm -1 ) SLNBL (a) NBL δ ω ( c m - ) (b) SL Figure 7: (a) Raman spectrum for SL and NBL MoS on SiO substrate at room temperature. (b) Raman shift δω measuredat SL and NBL MoS on SiO substrate. (c) Photolumines-cence spectra for SL and NBL MoS on SiO substrate atroom temperature. We have identified a single layer (SL) and natural bi-layer (NBL) MoS sample through Raman and PL spec-tra. In Fig. 7(a) Raman spectra have been shown forSL and NBL samples. Raman spectra is fitted with twoLorentzian to identify the peak position and to calculatethe difference in Raman shift between two peaks. Wefound that the difference in Raman shifts are 19.5 and22 cm − respectively shown in Fig. 7(b) which are com-parable to the previous report from the literature [14].On the other hand, the comparative PL spectra identi-fied the SL and NBL samples. SL has a much higher PLintensity than the NBL one shown in Fig. 7(c).We also have identified SL and NBL with low-frequency Raman measurement. In the case of SL sam-ple, interlayer shear mode (ISM) and layer breathingmode (LBM) are absent while on bilayer sample ISMand LBM are present at about 20 cm − and 40 cm − re- - 6 0 - 4 0 - 2 0 2 0 4 0 6 09 4 09 6 09 8 01 0 0 01 0 2 01 0 4 0 L B MI S M Raman intensity (arb. unit) R a m a n s h i f t ( c m - 1 ) S L N B LI S ML B M Figure 8: Raman spectra at room temperature in low fre-quency region for SL and NBL MoS on SiO . We havemarked the peak position of interlayer shear mode and layerbreathing mode. spectively.The presence of interlayer modes confirms thelayer number of the sample shown in Fig. 8. Results obtained from Voigt fitting to the spectrum We have fitted our experimental result with Lorentzianin our manuscript. We have also used Voigt fitting todetermine the peak position and FWHM. Peak positionwith temperature obtained from Voigt and Lorentzianfits are very similar for both E g and A g peak shown inFig. 9(a) and (b) respectively. We found that in case ofVoigt fitting both Lorentzian width and Gaussian widthcontribute to the Voigt width and as a result, we endup with a minimum FWHM for E g and A g peak isabout 1.8 cm − and 2.5 cm − respectively while fromLorentzian fit to our Raman spectra provides the mini-mum FWHM is about 1.45 cm − and 2.3 cm − respec-tively shown in Fig. 10(a) and (b) respectively. In bothLorentzian and Voigt fitting FWHM follows the sametrends with the temperature.We have plotted the intensity of the Raman peaks forE g and A g mode for SL MoS on SiO substrate withtemperature in Fig. 11. The peak intensity for E g peakremains almost unchanged with temperature while A g peak intensity decreases as we increase the temperature. Detection of SL MoS on hBN substrate andtemperature-dependent Raman spectra We have identified SL MoS on the hBN substrate andcompared the Raman spectra with the SiO substratesample shown in Fig. 12(a) and calculated the peak po-sition difference. We found that the peak position dif- Figure 9: Plot of peak position with temperature for SLMoS on SiO by using Voigt and Lorentzian fitting to theRaman spectra for (a) E g (b) A g mode. ference is 18.8 cm − and 19.5 cm − for SiO and hBNsubstrate sample respectively shown in Fig. 12(b).We have presented the temperature dependent Ramanspectra for hBN substrate SL MoS on sample2 from300 K to 8 K temperature range shown in Fig. 13. Thespectra shows the blue shift with temperature till 100 Kand then saturates below that temperature. The FWHMdecreases with decreasing temperature can also be no-ticed from the data. ∗ Electronic address: [email protected][1] K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz,Physical review letters , 136805 (2010).[2] B. Radisavljevic, A. Radenovic, J. Brivio, i. V. Gi-acometti, and A. Kis, Nature nanotechnology , 147(2011).[3] K. F. Mak, K. He, C. Lee, G. H. Lee, J. Hone, T. F.Heinz, and J. Shan, Nature materials , 207 (2013).[4] W. Bao, X. Cai, D. 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