We use pump-probe metrology based on the magneto-optic Kerr effect to measure the anisotropic thermal conductivity of (001)-oriented MoS2 crystals. A ≈20 nm thick CoPt multilayer with perpendicular magnetization serves as the heater and thermometer in the experiment. The low thermal conductivity and small thickness of the CoPt transducer improve the sensitivity of the measurement to lateral heat flow in the MoS2 crystal. The thermal conductivity of MoS2 is highly anisotropic with basal-plane thermal conductivity varying between 85–110 Wm-1K-1 as a function of laser spot size. The basal-plane thermal conductivity is a factor of ≈50 larger than the c-axis thermal conductivity, 2.0±0.3Wm-1K-1.

Molybdenum disulfide (MoS2) has been extensively studied in recent years for potential applications in two-dimensional (2D) electronic devices.1–3 In contrast to graphene, MoS2 has a finite bandgap (increasing from the bulk value 1.3 eV to 1.9 eV at one monolayer thickness2) that facilitates device applications.2 Although the electronic properties of MoS2 have been thoroughly studied,1,3 the thermal conductivity of MoS2 has not yet been established. The purpose of our study is to establish the baseline thermal conductivity of bulk MoS2 that will serve as a point of comparison for understanding the thermal conductivity of thin MoS2 and related dichalcogenide 2D electronic materials.

Large anisotropy in the thermal conductivity of MoS2 is expected because the strength of atomic interactions along the c-axis, predominately of van der Waals character, are much weaker than atomic interactions within the a-b or basal-plane, predominately of covalent character. Muratore et al.4 measured the c-axis thermal conductivity of a bulk MoS2 crystal (≈2.5 W m−1 K−1) and sputtered films that were ≈30 nm thick (≈0.3 W m−1 K−1). Yan et al.5 measured the basal-plane thermal conductivity of exfoliated monolayer MoS2 (≈35 W m−1 K−1) using temperature-dependent Raman spectroscopy. Jo et al.6 measured the basal-plane thermal conductivity of exfoliated few-layer MoS2 (44–52 W m−1 K−1) using suspended micro-devices. Sahoo et al.7 measured the basal-plane thermal conductivity of few-layer MoS2 prepared by high-temperature vapor-phase growth (≈52 W m−1 K−1) using temperature-dependent Raman spectroscopy.

Time-domain thermoreflectance (TDTR) is a widely used method for determining the thermal conductivity of materials but the sensitivity of TDTR to the lateral or in-plane thermal conductivity is low when conventional choices are made for laser spot sizes, modulation frequency of the pump beam, and the geometry of overlapping pump and probe beams.8 TDTR measures the thermal properties of materials by heating the sample surface using a train of laser pulses in the pump beam and monitoring the temperature-dependent surface reflectivity change with a time-delayed probe beam.9 The modulation of the pump beam at rf frequencies is used for lock-in detection of the thermoreflectance signal and to generate useful heat accumulation effects.10 The in-phase signal of lock-in amplifier Vin at positive delay time and high modulation frequencies is approximately proportional to the temperature response of the sample to heating by a single pump pulse. The out-of-phase signal Vout is approximately proportional to the imaginary part of the temperature oscillations at the modulation frequency of the pump beam.9 

If the lateral thermal diffusivity is sufficiently large, a useful approach for measuring lateral thermal conductivity in a TDTR experiment is to first measure through-plane thermal conductivity using a beam spot size much larger than the in-plane thermal diffusion length, and then extract the in-plane thermal conductivity using data collected with a beam spot size that is comparable to the in-plane thermal diffusion length.10–12 Recently, we described an improved approach for measuring lateral heat transport using spatially offset pump and probe beams, i.e., beam-offset TDTR.13–16 The variation in Vout as a function of beam offset x broadens due to in-plane heat spreading. The full-width at half-maximum (FWHM) of Vout measured as a function of x and collected at negative delay time reduces the propagation of systematic errors in a measurement of lateral heat transport.15 

In both conventional and beam-offset TDTR measurements, the sample is coated with a relatively thick metal film that absorbs the pump energy and enables measurement of the surface temperature through the changes in the optical reflectivity of the metal with temperature. Rigorous analysis of TDTR data depends on the fact that changes of intensity of the probe beam are proportional to changes in the surface temperature of the sample; i.e., the metal film must be optically opaque to prevent the temperature dependence of the optical properties of materials below the metal film transducer from influencing the transient reflectivity.

Here, we describe an alternate approach for probing the temperature at the surface of the sample that depends on the temperature dependence of the polarization of reflected light rather than the temperature dependence of the intensity of reflected light. In this approach, a ferromagnetic metal film serves as the transducer; the rotation of the polarization of the reflected probe produced by the magneto-optical Kerr effect (MOKE) follows the temperature dependence of the magnetization. Using MOKE thermometry enables the use of thin metal films that are not optically opaque. A thinner transducer minimizes lateral heat flow in the transducer and improves the sensitivity of the measurements to lateral heat flow in the sample.

To quantify the advantages of decreasing the thickness of the metal film transducer, we calculate the sensitivity of the FWHM of Vout at negative delay time to changes in selected geometrical factors (laser spot size, layer thickness) or thermal properties (thermal conductivity, heat capacity) of the experiment and sample. The sensitivity parameters Σα for the FWHM of Vout with respect to beam offset x at negative delay time is defined by

Σα=[ln(FWHM)][ln(α)],
(1)

where the symbol α represents one of the geometrical factors or thermal properties. Systematic errors in the experiment, i.e., the propagation of errors from uncertainties in the properties used in the modeling, are controlled by ratios of the sensitivity parameters.17 (In the analysis of conventional TDTR data, we typically use a notation where the symbol S is the sensitivity defined by the logarithmic derivative of the ratio signal −Vin/Vout with respect to changes in parameters of the thermal model.9 In Ref. 15, we unfortunately used S to denote the analogous sensitivity parameters for the FWHM of Vout. To avoid confusion here and in future publications, we are using a notation where the symbol Σ is the sensitivity parameters for the FWHM of Vout as defined by Eq. (1).)

In Figure 1, we plot the relative sensitivity |Σα/ΣΛ| as a function of film thickness d and the in-plane thermal conductivity of metal transducer Λm. We use this analysis of the relative sensitivities to help us choose experimental parameters that reduce error propagation in the measurement of Λ. Λ with no subscript is the in-plane thermal conductivity of the sample. The sensitivity ratios plotted in Figure 1 are for a single value of the modulation frequency (f=1MHz), time delay (t=100ps), laser spot size (w0=1.2μm), heat capacities (Cm=2.93Jcm3K1 and C=1.89Jcm3K1), and through-plane thermal conductivity of the samples (Λz=2Wm1K1); two values of the thermal conductance of metal-film/sample interface (G = 25 and 200 MW m−2 K−1); and three values of the in-plane thermal conductivity of the sample (Λ = 10, 30, and 100 W m−1 K−1). Figure 1(a) shows that |Σα/ΣΛ| (both α=w0 and α=Λm) decreases with decreasing d, which indicates that a thinner metal transducer reduces the propagation of errors from uncertainties in the laser spot size and thermal conductivity of the metal transducer. Figure 1(b) shows that |Σα/ΣΛ| (α=Λm) decreases strongly with decreasing Λm and |Σα/ΣΛ| (α=w0) increases slightly with decreasing Λm, with similar trends for different values of Λ. To reduce the error propagation in measuring Λ, a thinner metal transducer with lower thermal conductivity should be used. This selection is more critical with smaller G, as shown in the comparison of (a) and (b) to (c) and (d).

FIG. 1.

The relative sensitivity |Σα/ΣΛ| as a function of d and Λm calculated for a sample configuration of a metal transducer on an anisotropic bulk substrate at measurement conditions t=100ps, w0=1.2μm, and f=1MHz. For the metal transducer: Cm=2.93Jcm-3K-1; Λm = 20Wm-1K-1 for (a) & (c), and d = 20 nm for (b) & (d). For the substrate: Λz=2Wm-1K-1 and C=1.89Jcm-3K-1. The interfacial thermal conductance between metal transducer and substrate is G = 25 MW m−2 K−1 for (a) & (b), and G = 200 MW m−2 K−1 for (c) & (d). The blue lines and red lines represent α=w0 and α=Λm, respectively. Solid lines, dash lines, and dot lines are for Λ=100Wm-1K-1, Λ=30Wm-1K-1, and Λ=10Wm-1K-1, respectively. The lower the relative sensitivity |Σα/ΣΛ|, the smaller the errors due to parameter α propagated into systematic errors in measuring Λ.

FIG. 1.

The relative sensitivity |Σα/ΣΛ| as a function of d and Λm calculated for a sample configuration of a metal transducer on an anisotropic bulk substrate at measurement conditions t=100ps, w0=1.2μm, and f=1MHz. For the metal transducer: Cm=2.93Jcm-3K-1; Λm = 20Wm-1K-1 for (a) & (c), and d = 20 nm for (b) & (d). For the substrate: Λz=2Wm-1K-1 and C=1.89Jcm-3K-1. The interfacial thermal conductance between metal transducer and substrate is G = 25 MW m−2 K−1 for (a) & (b), and G = 200 MW m−2 K−1 for (c) & (d). The blue lines and red lines represent α=w0 and α=Λm, respectively. Solid lines, dash lines, and dot lines are for Λ=100Wm-1K-1, Λ=30Wm-1K-1, and Λ=10Wm-1K-1, respectively. The lower the relative sensitivity |Σα/ΣΛ|, the smaller the errors due to parameter α propagated into systematic errors in measuring Λ.

Close modal

When using a semi-transparent thin metal film as the transducer, an advantage of TR-MOKE over TDTR is that the detected signal is dominated by the temperature of the magnetic transducer layer and relatively immune to contamination of the signal by the temperature fields in other parts of the sample. For an optically-thin magnetic layer with thickness d, the complex Kerr rotation angle θ is calculated by dividing Eq. (21) by Eq. (20) in Ref. 18,

θ=Qn2λ4πd(ns21)+i(ns2n2),
(2)

where n and ns are the complex index of refraction of magnetic layer and substrate, respectively. Q is the complex magneto-optical constant (a typical value of Q for CoPt multilayers19 is 0.02+0.02i); λ is the laser wavelength. Whether dQ/dT dominates in dθ/dT or not depends on the relative magnitudes of |nsdQ/dT| and |Qdns/dT|. For example, |dQ/dT|104 for CoPt multilayers and, for many dielectric or semiconducting materials, |dns/dT|105to104 at ∼800 nm.20 Therefore, typically |nsdQ/dT||Qdns/dT|, and the TR-MOKE signal is generated only by the change in temperature of the magnetic layer.

The experimental setup for TR-MOKE is the same as our two-tint TDTR set-up21 with the exception of a different detection scheme; see Fig. 2. A non-polarizing beam-splitter (NBS) is inserted between the polarizing beam splitter (PBS) that steers the pump beam and the microscope objective lens. In the conventional TDTR set-up, the PBS rejects most (≈99%) of the reflected pump. In the TR-MOKE experiment, we cannot use polarization to reject the pump and must instead rely on spectral separation of the pump and probe. (For beam-offset measurements with tightly focused laser beams, we have found it impractical to spatially separate the pump and probe beams at the back focal plane of the objective.) Fortunately, recent advances in optical filter technology have made it possible to improve the spectral separation of the pump and probe in the two-tint approach. We use optical filters with extremely sharp transitions (a Semrock 785 nm Razor Edge® 63 cm−1 transition long pass filter at the pump path, a Semrock 785 nm Razor Edge® 129 cm−1 transition short pass filter at the probe path, and the same short pass filter before the detector) to spectrally separate the pump and probe and to prevent the reflected pump beam from entering the detector.

FIG. 2.

Schematic drawing of the detection scheme in TR-MOKE. The remainder of the experimental setup is the same as the two-tint TDTR system described in Ref. 21. Optical filters with extremely sharp transitions spectrally separate the pump and probe and prevent the reflected pump beam from entering the detector. The polarization states of the probe are split by a Wollaston prism and detected by a balanced detector. A half-wave plate placed before the Wollaston prism is used to balance the average intensities.

FIG. 2.

Schematic drawing of the detection scheme in TR-MOKE. The remainder of the experimental setup is the same as the two-tint TDTR system described in Ref. 21. Optical filters with extremely sharp transitions spectrally separate the pump and probe and prevent the reflected pump beam from entering the detector. The polarization states of the probe are split by a Wollaston prism and detected by a balanced detector. A half-wave plate placed before the Wollaston prism is used to balance the average intensities.

Close modal

Transient changes in polarization are monitored by splitting the probe with a Wollaston prism and detecting the changes in the relative intensities of the orthogonal polarization states with a balanced detector. A half-wave plate placed before the Wollaston prism is used to balance the intensities of the orthogonal polarization states. The output of the balanced detector is sent to the rf lock-in amplifier after passing through a low-pass filter to remove high harmonics. For example, a 1.9 MHz low-pass filter is inserted in the signal path when the modulation frequency is 1 MHz.

The CoPt multilayer with perpendicular magnetization has the structure Pt(1)/[Co(0.5)Pt(1)] × 6/Pt(10) from top to bottom, where the numerical values in parenthesis are the layer thickness in nanometers. The total thickness of the multilayer, 20±1 nm, was confirmed by X-ray reflectivity measurement. We use volumetrically-averaged heat capacity for the CoPt multilayer of Cm = 2.93Jcm3K1. This metallic multilayer is deposited by magnetron sputtering in a system with a base pressure < 5 × 10−8 Torr and a working pressure of 3 mTorr. We flip the direction of the magnetization using a magnetic field of 0.3 T generated by a NdFeB permanent magnet. The coercivity of the CoPt multilayer is ≈0.1 T and the remanent magnetization is equal to the saturation magnetization. All TR-MOKE measurements were conducted at remanence, i.e., without an applied magnetic field.

The MoS2 crystal was purchased from SPI supplies®, and is a natural mineral mined from Otter Lake, Canada with a purity > 99%. We used an oxidized Si wafer with ≈315 nm SiO2 as a validation sample and as a substrate for measuring the lateral thermal conductivity of the CoPt multilayer. The oxide thickness was measured by ellipsometry and confirmed by picosecond acoustics using a longitudinal speed of sound of 5.97 nm/ps.22 The thermal oxide was coated with ≈20 nm CoPt or ≈80 nm Al; the MoS2 crystal was coated with ≈20 nm CoPt, ≈80 nm Al, or ≈65 nm NbV (Nb0.43V0.57 as measured by Rutherford backscattering spectrometry) after exposing a clean surface of MoS2 by cleaving. The thickness of Al and NbV films was measured by picosecond acoustics using a longitudinal speed of sound of 6.42 and 5.40 nm/ps, respectively.15Λm of the Al film is calculated by the Wiedemann-Franz law from the electrical resistivity measured on the Al/SiO2/Si sample. Λm of ≈65 nm NbV film is 18Wm1K1 and Cm of NbV is 2.65Jcm3K1 at room temperature.15 

Figure 3(a) shows the Vin and Vout signals as a function of time delay between pump and probe measured for the CoPt/SiO2/Si sample by TR-MOKE. We do not observe picosecond acoustics echoes in the TR-MOKE signals at short delay times, indicatng that the Kerr rotation of CoPt is much less sensitive to strain than the reflectivity of Al or NbV. Both Vin and Vout change sign when the magnetization of the CoPt layer is flipped from M+ to M. The ratio Vin/Vout=(VinM+VinM)/(VoutM+VoutM) is used as the experimental signal for fitting. This approach of taking the difference in the signals for positive and negative magnetization removes any contribution to the signal from the thermoreflectance that remains because of imperfect nulling of the balanced detector.

FIG. 3.

Example TR-MOKE signals used for measuring the through-plane thermal conductivity using 10.7 MHz modulation frequency and 5× objective lens. (a) The in-phase Vin (blue) or out-of-phase Vout (red) signal measured for a CoPt/SiO2/Si sample. Filled circles (M+) and open circles (M) represent opposite directions of magnetization. (b) The measurement signal Vin/Vout (open circles) and thermal model fitting (solid lines) for CoPt/SiO2/Si and CoPt/MoS2 samples.

FIG. 3.

Example TR-MOKE signals used for measuring the through-plane thermal conductivity using 10.7 MHz modulation frequency and 5× objective lens. (a) The in-phase Vin (blue) or out-of-phase Vout (red) signal measured for a CoPt/SiO2/Si sample. Filled circles (M+) and open circles (M) represent opposite directions of magnetization. (b) The measurement signal Vin/Vout (open circles) and thermal model fitting (solid lines) for CoPt/SiO2/Si and CoPt/MoS2 samples.

Close modal

Figure 3(b) shows the data and fits of the data to the thermal model9 using CoPt as the transducer and TR-MOKE for detection. To minimize the in-plane heat spreading and facilitate an accurate measurement of the through-plane thermal conductivity Λz, a modulation frequency of 10.7 MHz and a relatively large beam spot size (5× microscope objective lens, w0=11.7μm) was used. The best fit for Λz of SiO2 is Λz=1.3±0.1Wm1K1 and the interfacial thermal conductance between CoPt and SiO2 is G=180±20MWm2K1. These measurement results by TR-MOKE agree with Λz=1.3±0.1Wm1K1 and G=150±20MWm2K1 measured by TDTR at f=9.8MHz and 5× objective lens, using Al as the metal transducer. The error bars in the measurements are calculated using the method described previously,17 with the assumption of a 5% uncertainty in w0, a 2% uncertainty in C and Cm, a 5% uncertainty in Λm and Λz, a 5% uncertainty in d of the CoPt film, and a 4% uncertainty in d of the Al and NbV films.

For the MoS2 sample, the volumetric heat capacity is taken from the literature, C=1.89Jcm3K1.23 The best fit for through-plane thermal conductivity of MoS2 and interface conductance using TR-MOKE is Λz=2.0±0.2Wm1K1 and G=26±2MWm2K1. These data agree with measurements by conventional TDTR at f=9.8MHz and 5× objective lens using an ≈80 nm Al transducer, Λz=2.0±0.2Wm1K1 and G=20±4MWm2K1, and with a ≈65 nm NbV transducer, Λz=2.0±0.2Wm1K1 and G=25±4MWm2K1. It is interesting to note that the interfacial thermal conductance is essentially independent of the choice of the metal films and is unusually small. A low thermal interfacial thermal conductance, 73±5MWm2K1, has also been measured between sputtered Al film and highly ordered pyrolytic graphite in our previous work.13 Such small interfacial thermal conductances between metal films and bulk layered materials are possibly due to phonon focusing effects24 created by strong anisotropy of the phonon group velocities.

We measured the in-plane thermal conductivity of the CoPt transducer by beam-offset TR-MOKE using the CoPt/SiO2/Si sample, a relatively small beam spot size (50× objective lens, w01.2μm), and a low modulation frequency of 2 MHz. Figure 4 shows the beam-offset TR-MOKE measurement following the procedure described in Ref. 15. First, we measured the laser spot size using the in-phase beam-offset signal Vin at high modulation frequency (f = 9.8 MHz) at small positive delay time (t = 50 ps). The laser spot size was extracted by fitting Vin to a Gaussian function, Vinexp(x2/w02). Then, we measured the FWHM of the out-of-phase beam-offset signal Vout at low modulation frequency (f = 2 MHz) at small negative delay time (t=−100 ps). By simulating the FWHM as a function of Λm and comparing to the measured FWHM, the Λm of the CoPt multilayer can be determined: Λm=27±4Wm1K1.

FIG. 4.

Beam-offset TR-MOKE data for CoPt/SiO2/Si (open circles) and CoPt/MoS2 (open squares) and the model fitting (solid lines). Blue color: Vin at positive time delay (t = 50 ps) and high modulation frequency (f = 9.8 MHz) used to measure the beam spot size. Red color: −Vout at negative time delay (t = −100 ps) and low modulation frequency (f = 2 MHz for CoPt/SiO2/Si and f = 1 MHz for CoPt/MoS2), used to extract the FWHM.

FIG. 4.

Beam-offset TR-MOKE data for CoPt/SiO2/Si (open circles) and CoPt/MoS2 (open squares) and the model fitting (solid lines). Blue color: Vin at positive time delay (t = 50 ps) and high modulation frequency (f = 9.8 MHz) used to measure the beam spot size. Red color: −Vout at negative time delay (t = −100 ps) and low modulation frequency (f = 2 MHz for CoPt/SiO2/Si and f = 1 MHz for CoPt/MoS2), used to extract the FWHM.

Close modal

The in-plane electrical resistivity of the CoPt layer, measured using a four-point probe, was 340±17nΩm. The Wiedemann-Franz law and the Sommerfeld value of the Lorenz number predicts an electrical component to the thermal conductivity of the CoPt film of 21±2Wm1K1.

The same beam-offset TR-MOKE measurement procedure was applied to the MoS2 sample. We calculated ΣαFWHM for all of the geometrical factors and thermal properties α for 20 nm CoPt film on bulk MoS2 at td=100ps using a modulation frequency of 1 MHz and 20× objective (w0=2.7μm). ΣΛFWHMΣCFWHM, indicating that the FWHM is sensitive to the in-plane thermal diffusivity, Λ/C. Moreover, FWHM is more sensitive to the laser spot size w0 than any other parameter: precise measurement of w0 is critical for accurately determining the in-plane thermal conductivity.

Figure 5 shows beam-offset TR-MOKE measurements of the in-plane thermal conductivity of the MoS2 crystal using three beam spot sizes. For comparison, we repeated the measurements using beam-offset TDTR with a MoS2 sputter-coated by a ≈65 nm NbV transducer. The measurement results using beam-offset TR-MOKE are consistent with those by beam-offset TDTR, but with smaller error bars. Especially when using the 50× microscope objective, the error bars are reduced by almost a factor of 3 when using ≈20 nm CoPt compared to ≈65 nm NbV.

FIG. 5.

The beam-offset TR-MOKE (red filled circle) and beam-offset TDTR (blue filled triangle) measurement results of the in-plane thermal conductivity Λ of the MoS2 crystal using three different beam spot sizes w0. The ab initio calculations of Λ for monolayer MoS2 by Li et al.25 and by Gu et al.26 as a function of length L are included for comparison. The results of the TR-MOKE and TDTR experiments are plotted at L=2w0.

FIG. 5.

The beam-offset TR-MOKE (red filled circle) and beam-offset TDTR (blue filled triangle) measurement results of the in-plane thermal conductivity Λ of the MoS2 crystal using three different beam spot sizes w0. The ab initio calculations of Λ for monolayer MoS2 by Li et al.25 and by Gu et al.26 as a function of length L are included for comparison. The results of the TR-MOKE and TDTR experiments are plotted at L=2w0.

Close modal

The in-plane thermal conductivity Λ decreases from 110±20Wm1K1 (measured using the 10× objective) to 85±6Wm1K1 (measured using the 50× objective) with decreasing w0. A similar phenomenon is also found in TDTR measurements of Si and Si:B with w0<5μm, whose high-wavevector phonons have a high thermal diffusivity.16 Due to phonons with mean free path larger than 2w0 carrying heat ballistically in the MoS2 crystal, the measured apparent Λ decreases ≈ 25% from 2w012μm (using 10× objective lens) to 2w02μm (using 50× objective lens). The connection between the spot-size dependence of the thermal conductivity and the distribution of phonon mean-free-paths is not direct16 but we can conclude that a comparable fraction of approximately 25% of heat is carried by phonons with mean free path larger than ≈2 μm in the a-b plane of MoS2.

Our measurement values agree with the ab initio calculations by Li et al.,25 which calculated the basal-plane thermal conductivity of monolayer MoS2 using the single-mode relaxation time approximation. The 2D MoS2 sheet with an infinite lateral length is sandwiched between two reservoirs with a distance L apart and with diffusive boundary conditions at the contacts between the sample and the thermal reservoirs; sample length L varies from 50 nm to 10 μm. Our measurements also agree with the trend of the recent calculations by Gu et al.26 who used an iterative approach to solve the Boltzmann transport equation without making the assumption that all three-phonon scattering processes are resistive. In Ref. 25, in-plane thermal conductivity at room temperature of isotopically pure and natural isotope abundance MoS2 were compared. For an L = 1 μm sample, the isotope effect is approximately 10%. We are not aware of calculations for the thermal conductivity of bulk MoS2 crystals. We believe, however, that calculations for monolayer MoS2 are a useful upper-bound for the thermal conductivity of bulk MoS2 and that bulk and monolayer MoS2 will have similar thermal conductivities for the reasons discussed briefly below.

In graphene, calculations27,28 and some experiments8 suggest that the in-plane thermal conductivity of a monolayer is larger than the thermal conductivity of graphite. We expect that the in-plane thermal conductivity of MoS2 is less affected by increasing the thickness or number of layers from monolayer to bulk than graphene. In a one-atom-thick 2D material (e.g., graphene), symmetry selection rules require that an even number of out-of-plane phonons be involved in each phonon-scattering process.29 In other words, an out-of-plane phonon in graphene can only interact with another out-of-plane phonon and an in-plane phonon; these selection rules restrict the phase space for phonon-phonon scattering of the out-of-plane phonons. This type of selection rule does not hold for few-layer graphene and graphite due to interlayer coupling. This selection rule does not apply to monolayer MoS2 since MoS2 is a three-atom-thick 2D crystal. Therefore, the phase space of phonon-phonon scattering process for the out-of-plane modes in MoS2 is much larger than graphene and the contributions from the out-of-plane modes to in-plane thermal conductivity of MoS2 should be much lower compare to that in graphene. This conclusion is supported by the ab initio calculations of Gu et al.26 

Our data for the in-plane thermal conductivity of the MoS2 crystal (85–112 Wm1K1) are much higher than recently reported data for exfoliated monolayer5 (35Wm1K1), exfoliated few-layer MoS2 (4452Wm1K1), or high-temperature vapor-phase grown MoS2 (≈52 W m−1 K−1).5–7 One possible reason is that exfoliated monolayer or few-layer MoS2 are often prepared using a polymer-film-assisted transfer process,5,6 where organic residues might contaminate the samples and reduce the basal-plane thermal conductivity. Pettes et al. showed that organic residue can significantly suppress the measured thermal conductivity of suspended bilayer graphene.30 Another reasonable speculation is that water vapor and oxygen in the atmosphere can lead to oxidation of MoS2, e.g., preferentially at grain boundaries or other surface defects.31–33 The resulting surface disorder could scatter phonons and decrease the basal-plane thermal conductivity of monolayer and few-layer MoS2. This mechanisms for the reduction in thermal conductivity of thin MoS2 is also discussed in Ref. 6. The temperature-dependence of the thermal conductivity of few-layer MoS2 data can be fit well with the ab initio calculation for monolayer MoS2 reported in Ref. 25 in combination with a constant phonon-boundary scattering length in the range between 100 and 200 nm.6 Such a relatively small boundary scattering length compared to the grain size is likely due to phonon scattering by surface disorder. In our studies of MoS2 crystals, surface disorder does not affect the measurement of in-plane thermal conductivity since the thermal penetration depth is ≈600 nm.

The effect of surface oxidation has been observed in measurements of the in-plane thermal conductivity of Bi2Te3 nanoplates.34 In Ref. 34, the in-plane thermal conductivity of some samples is much lower than that of samples with similar thicknesses and the literature values of bulk Bi2Te3. Transmission electron micrograph of these samples shows an amorphous layer at the edge of the samples after being exposed in air for 2–24 h, which is believed to be a native oxide layer.

In summary, we developed an ultrafast-laser pump-probe technique based on TR-MOKE to improve measurements of anisotropic thermal conductivity of bulk and thin film materials. By using a thin (≈20 nm) perpendicularly magnetized CoPt multilayer as the transducer, beam-offset TR-MOKE can measure in-plane thermal conductivity more accurately than beam-offset TDTR. The measurement of the anisotropic thermal conductivity of MoS2 crystals provides a baseline value for further studies of thermal conductivity of dichalcogenide 2D materials and thermal management of 2D electronic devices.

The development of beam-offset TR-MOKE was supported by Seagate Technology and the applications of TR-MOKE to phonon transport in MoS2 were supported by AFOSR contract number AF FA9550-12-1-0073. TDTR and TR-MOKE measurements used equipment in the Laser Facility of the Frederick Seitz Materials Research Laboratory (MRL) at the University of Illinois at Urbana-Champaign. We thank R. B. Wilson for his help with the experiments and many useful discussions; and Judith Kimling for providing SQUID data for the magnetization of the CoPt multilayer.

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