Measurement of the anisotropic thermal conductivity of molybdenum disulfide by thetime-resolved magneto-optic Kerr effectJun Liu, Gyung-Min Choi, and David G. Cahill Citation: Journal of Applied Physics 116, 233107 (2014); doi: 10.1063/1.4904513 View online: http://dx.doi.org/10.1063/1.4904513 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/116/23?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Coercivity dynamics and origin of time-delayed magneto-optical hysteresis loops in pump-probe Kerrspectroscopy J. Appl. Phys. 113, 053913 (2013); 10.1063/1.4790390 Time- and vector-resolved magneto-optical Kerr effect measurements of large angle precessional reorientation ina 2 × 2 μ m 2 ferromagnet J. Appl. Phys. 105, 07D308 (2009); 10.1063/1.3056405 Benchtop time-resolved magneto-optical Kerr magnetometer Rev. Sci. Instrum. 79, 123905 (2008); 10.1063/1.3053353 Experimental determination of the inhomogeneous contribution to linewidth in Permalloy films using a time-resolved magneto-optic Kerr effect microprobe J. Appl. Phys. 102, 053910 (2007); 10.1063/1.2772563 Time-resolved Kerr measurements of magnetization switching in a crossed-wire ferromagnetic memory element J. Appl. Phys. 91, 7331 (2002); 10.1063/1.1452681

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Measurement of the anisotropic thermal conductivity of molybdenumdisulfide by the time-resolved magneto-optic Kerr effect

Jun Liu,a) Gyung-Min Choi, and David G. CahillDepartment of Materials Science and Engineering and Materials Research Laboratory, University of Illinois,Urbana, Illinois 61801, USA

(Received 9 October 2014; accepted 8 December 2014; published online 19 December 2014)

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 per-

pendicular 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 W m�1 K�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 6 0:3 W m�1 K�1. VC 2014 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4904513]

I. INTRODUCTION

Molybdenum disulfide (MoS2) has been extensively

studied in recent years for potential applications in two-

dimensional (2D) electronic devices.1–3 In contrast to gra-

phene, 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 ther-

mal conductivity of MoS2 has not yet been established. The

purpose of our study is to establish the baseline thermal con-

ductivity of bulk MoS2 that will serve as a point of compari-

son 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 meas-

ured 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 spec-

troscopy. Jo et al.6 measured the basal-plane thermal conduc-

tivity 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 fre-

quencies is used for lock-in detection of the thermoreflec-

tance signal and to generate useful heat accumulation

effects.10 The in-phase signal of lock-in amplifier Vin at posi-

tive delay time and high modulation frequencies is approxi-

mately 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 fre-

quency 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 ther-

mal 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 measure-

ments, 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 opti-

cally opaque to prevent the temperature dependence of the

a)Author to whom correspondence should be addressed. Electronic mail:

junliu@illinois.edu

0021-8979/2014/116(23)/233107/6/$30.00 VC 2014 AIP Publishing LLC116, 233107-1

JOURNAL OF APPLIED PHYSICS 116, 233107 (2014)

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optical properties of materials below the metal film trans-

ducer 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.

II. EXPERIMENTAL DETAILS

A. Analysis

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 Ra

for the FWHM of Vout with respect to beam offset x at nega-

tive delay time is defined by

Ra ¼@ ln FWHMð Þ½ �

@ ln að Þ½ � ; (1)

where the symbol a represents one of the geometrical factors

or thermal properties. Systematic errors in the experiment,

i.e., the propagation of errors from uncertainties in the prop-

erties 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 Sis 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 R is the sensitivity

parameters for the FWHM of Vout as defined by Eq. (1).)

In Figure 1, we plot the relative sensitivity jRa=RKj as a

function of film thickness d and the in-plane thermal conduc-

tivity of metal transducer Km. We use this analysis of the rel-

ative sensitivities to help us choose experimental parameters

that reduce error propagation in the measurement of K. Kwith no subscript is the in-plane thermal conductivity of the

sample. The sensitivity ratios plotted in Figure 1 are for a sin-

gle value of the modulation frequency (f ¼ 1 MHz), time

delay (t ¼ �100 ps), laser spot size (w0 ¼ 1:2 lm), heat

capacities (Cm ¼ 2:93 J cm�3 K�1 and C ¼ 1:89 J cm�3 K�1),

and through-plane thermal conductivity of the samples

(Kz ¼ 2 W m�1 K�1); two values of the thermal conductance

of metal-film/sample interface (G¼ 25 and 200 MW m�2

K�1); and three values of the in-plane thermal conductivity

of the sample (K¼ 10, 30, and 100 W m�1 K�1). Figure 1(a)

shows that jRa=RKj (both a ¼ w0 and a ¼ Km) decreases

with decreasing d, which indicates that a thinner metal trans-

ducer reduces the propagation of errors from uncertainties in

the laser spot size and thermal conductivity of the metal

transducer. Figure 1(b) shows that jRa=RKj (a ¼ Km)

decreases strongly with decreasing Km and jRa=RKj (a ¼ w0)

increases slightly with decreasing Km, with similar trends for

different values of K. To reduce the error propagation in

measuring K, 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).

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 contami-

nation of the signal by the temperature fields in other parts of

the sample. For an optically-thin magnetic layer with thick-

ness d, the complex Kerr rotation angle h is calculated by

dividing Eq. (21) by Eq. (20) in Ref. 18,

FIG. 1. The relative sensitivity jRa=RKj as a function of d and Km calculated

for a sample configuration of a metal transducer on an anisotropic bulk sub-

strate at measurement conditions t ¼ �100 ps, w0 ¼ 1:2lm, and f ¼ 1 MHz.

For the metal transducer: Cm ¼ 2:93 J cm�3 K�1; Km¼ 20 W m�1 K�1 for

(a) & (c), and d¼ 20 nm for (b) & (d). For the substrate: Kz ¼ 2 W m�1 K�1

and C ¼ 1:89 J cm�3 K�1. The interfacial thermal conductance between

metal transducer and substrate is G¼ 25 MW m�2 K�1 for (a) & (b), and

G¼ 200 MW m�2 K�1 for (c) & (d). The blue lines and red lines represent

a ¼ w0 and a ¼ Km, respectively. Solid lines, dash lines, and dot lines are

for K ¼ 100 W m�1 K�1, K ¼ 30 W m�1 K�1, and K ¼ 10 W m�1 K�1,

respectively. The lower the relative sensitivity jRa=RKj, the smaller the

errors due to parameter a propagated into systematic errors in measuring K.

233107-2 Liu, Choi, and Cahill J. Appl. Phys. 116, 233107 (2014)

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h ¼ Qn2

k4pd

n2s � 1

� �þ i n2

s � n2� � ; (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

�� 0:02þ 0:02i); k is the laser wavelength. Whether dQ=dTdominates in dh=dT or not depends on the relative magnitudes

of jnsdQ=dTj and jQdns=dTj. For example, jdQ=dTj � 10�4

for CoPt multilayers and, for many dielectric or semiconduct-

ing materials, jdns=dTj � 10�5 to 10�4 at �800 nm.20

Therefore, typically jnsdQ=dTj � jQdns=dTj, and the TR-

MOKE signal is generated only by the change in temperature

of the magnetic layer.

B. Experimental setup

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 experi-

ment, 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 sepa-

rate the pump and probe beams at the back focal plane of the

objective.) Fortunately, recent advances in optical filter tech-

nology have made it possible to improve the spectral separa-

tion of the pump and probe in the two-tint approach. We use

optical filters with extremely sharp transitions (a Semrock

785 nm Razor EdgeVR

63 cm�1 transition long pass filter at

the pump path, a Semrock 785 nm Razor EdgeVR

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.

Transient changes in polarization are monitored by split-

ting the probe with a Wollaston prism and detecting the

changes in the relative intensities of the orthogonal polariza-

tion 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 bal-

anced 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.

C. Sample details

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 6 1 nm, was confirmed by X-ray reflectivity

measurement. We use volumetrically-averaged heat capacity

for the CoPt multilayer of Cm¼ 2:93 J cm�3 K�1. This metal-

lic multilayer is deposited by magnetron sputtering in a sys-

tem with a base pressure< 5� 10�8 Torr and a working

pressure of 3 mTorr. We flip the direction of the magnetiza-

tion 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 satu-

ration magnetization. All TR-MOKE measurements were

conducted at remanence, i.e., without an applied magnetic

field.

The MoS2 crystal was purchased from SPI suppliesVR

,

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.15 Km of the Al film is calculated by the

Wiedemann-Franz law from the electrical resistivity meas-

ured on the Al/SiO2/Si sample. Km of �65 nm NbV film is

18 W m�1 K�1 and Cm of NbV is 2:65 J cm�3 K�1 at room

temperature.15

III. RESULTS AND DISCUSSION

A. Through-plane thermal conductivity

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

FIG. 2. Schematic drawing of the detection scheme in TR-MOKE. The re-

mainder of the experimental setup is the same as the two-tint TDTR system

described in Ref. 21. Optical filters with extremely sharp transitions spec-

trally 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.

233107-3 Liu, Choi, and Cahill J. Appl. Phys. 116, 233107 (2014)

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of the CoPt layer is flipped from Mþ to M�. The ratio

�Vin=Vout ¼ �ðVMþin � VM�

in Þ=ðVMþout � VM�

out Þ is used as the

experimental signal for fitting. This approach of taking the

difference in the signals for positive and negative magnetiza-

tion removes any contribution to the signal from the thermor-

eflectance that remains because of imperfect nulling of the

balanced detector.

Figure 3(b) shows the data and fits of the data to the ther-

mal model9 using CoPt as the transducer and TR-MOKE for

detection. To minimize the in-plane heat spreading and facili-

tate an accurate measurement of the through-plane thermal

conductivity Kz, a modulation frequency of 10.7 MHz and a

relatively large beam spot size (5� microscope objective lens,

w0 ¼ 11:7 lm) was used. The best fit for Kz of SiO2 is Kz ¼1:3 6 0:1 W m�1 K�1 and the interfacial thermal conductance

between CoPt and SiO2 is G ¼ 180 6 20 MW m�2 K�1.

These measurement results by TR-MOKE agree with Kz ¼1:3 6 0:1 W m�1 K�1 and G ¼ 150 6 20 MW m�2 K�1 meas-

ured by TDTR at f ¼ 9:8 MHz and 5� objective lens, using

Al as the metal transducer. The error bars in the measure-

ments are calculated using the method described previously,17

with the assumption of a 5% uncertainty in w0, a 2% uncer-

tainty in C and Cm, a 5% uncertainty in Km and Kz, 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 ¼ 1:89 J cm�3 K�1.23 The best fit

for through-plane thermal conductivity of MoS2 and interface

conductance using TR-MOKE is Kz ¼ 2:0 6 0:2 W m�1 K�1

and G ¼ 26 6 2 MW m�2 K�1. These data agree with meas-

urements by conventional TDTR at f ¼ 9:8 MHz and 5�objective lens using an �80 nm Al transducer, Kz ¼ 2:06 0:2 W m�1 K�1 and G ¼ 20 6 4 MW m�2 K�1, and with a

�65 nm NbV transducer, Kz ¼ 2:0 6 0:2 W m�1 K�1 and

G ¼ 25 6 4 MW m�2 K�1. 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 6 5 MW m�2 K�1,

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.

B. In-plane thermal conductivity of CoPt transducer

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� objec-

tive lens, w0 � 1:2lm), and a low modulation frequency of 2

MHz. Figure 4 shows the beam-offset TR-MOKE measure-

ment 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 (f¼ 9.8 MHz) at

small positive delay time (t¼ 50 ps). The laser spot

size was extracted by fitting Vin to a Gaussian function,

Vin � expð�x2=w20Þ. Then, we measured the FWHM of the

out-of-phase beam-offset signal Vout at low modulation

frequency (f¼ 2 MHz) at small negative delay time

(t¼�100 ps). By simulating the FWHM as a function of Km

and comparing to the measured FWHM, the Km of the CoPt

multilayer can be determined: Km ¼ 27 6 4 W m�1 K�1.

The in-plane electrical resistivity of the CoPt layer,

measured using a four-point probe, was 340 6 17 nX m. The

Wiedemann-Franz law and the Sommerfeld value of the

FIG. 3. Example TR-MOKE signals used for measuring the through-plane

thermal conductivity using 10.7 MHz modulation frequency and 5� objec-

tive lens. (a) The in-phase Vin (blue) or out-of-phase Vout (red) signal meas-

ured for a CoPt/SiO2/Si sample. Filled circles (Mþ) 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. 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 (t¼ 50 ps) and high modulation frequency

(f¼ 9.8 MHz) used to measure the beam spot size. Red color: �Vout at nega-

tive time delay (t¼�100 ps) and low modulation frequency (f¼ 2 MHz for

CoPt/SiO2/Si and f¼ 1 MHz for CoPt/MoS2), used to extract the FWHM.

233107-4 Liu, Choi, and Cahill J. Appl. Phys. 116, 233107 (2014)

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Lorenz number predicts an electrical component to the ther-

mal conductivity of the CoPt film of 21 6 2 W m�1 K�1.

C. In-plane thermal conductivity of MoS2 crystal

The same beam-offset TR-MOKE measurement proce-

dure was applied to the MoS2 sample. We calculated RFWHMa

for all of the geometrical factors and thermal properties a for

20 nm CoPt film on bulk MoS2 at td ¼ �100 ps using a modu-

lation frequency of 1 MHz and 20� objective (w0 ¼ 2:7 lm).

RFWHMK � �RFWHM

C , indicating that the FWHM is sensitive to

the in-plane thermal diffusivity, K=C. Moreover, FWHM is

more sensitive to the laser spot size w0 than any other parame-

ter: precise measurement of w0 is critical for accurately deter-

mining 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 measure-

ment 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.

The in-plane thermal conductivity K decreases from

110 6 20 W m�1 K�1 (measured using the 10� objective) to

85 6 6 W m�1 K�1 (measured using the 50� objective) with

decreasing w0. A similar phenomenon is also found in TDTR

measurements of Si and Si:B with w0 < 5lm, 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 Kdecreases� 25% from 2w0 � 12lm (using 10� objective

lens) to 2w0 � 2lm (using 50� objective lens). The connec-

tion between the spot-size dependence of the thermal con-

ductivity 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 lm in the a-b plane of MoS2.

Our measurement values agree with the ab initio calcula-

tions by Li et al.,25 which calculated the basal-plane thermal

conductivity of monolayer MoS2 using the single-mode relax-

ation 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; sam-

ple length L varies from 50 nm to 10 lm. 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 isotopi-

cally pure and natural isotope abundance MoS2 were com-

pared. For an L¼ 1 lm sample, the isotope effect is

approximately 10%. We are not aware of calculations for the

thermal conductivity of bulk MoS2 crystals. We believe, how-

ever, 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 con-

ductivities for the reasons discussed briefly below.

In graphene, calculations27,28 and some experiments8

suggest that the in-plane thermal conductivity of a mono-

layer 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 conductiv-

ity of MoS2 should be much lower compare to that in gra-

phene. This conclusion is supported by the ab initiocalculations of Gu et al.26

Our data for the in-plane thermal conductivity of the

MoS2 crystal (85–112 W m�1 K�1) are much higher than

recently reported data for exfoliated monolayer5 (�35

W m�1 K�1), exfoliated few-layer MoS2 (44

�52 W m�1 K�1), 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 or-

ganic 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

FIG. 5. The beam-offset TR-MOKE (red filled circle) and beam-offset

TDTR (blue filled triangle) measurement results of the in-plane thermal con-

ductivity K of the MoS2 crystal using three different beam spot sizes w0.

The ab initio calculations of K 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 ¼ 2w0.

233107-5 Liu, Choi, and Cahill J. Appl. Phys. 116, 233107 (2014)

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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 com-

pared 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 ther-

mal 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 ox-

ide layer.

IV. CONCLUSION

In summary, we developed an ultrafast-laser pump-

probe technique based on TR-MOKE to improve measure-

ments 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.

ACKNOWLEDGMENTS

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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