The rapidly increasing number of 2-dimensional (2D) materials that have been isolated or synthesized provides an enormous opportunity to realize new device functionalities. Whereas their optical and electrical characterizations have been more readily reported, quantitative thermal characterization is more challenging due to the difficulties with localizing heat flow. Optical pump-probe techniques that are well established for the study of bulk materials or thin films have limited sensitivity to in-plane heat transport, and the characterization of the thermal anisotropy that is common in 2D materials is, therefore, challenging. Here, we present a new approach to quantify the thermal properties based on the magneto-optical Kerr effect that yields quantitative insight into cross-plane and in-plane heat transport. The use of a very thin magnetic material as heater/thermometer increases in-plane thermal gradients without complicating the data analysis in spite of the layer being optically semitransparent. The approach has the added benefit that it does not require the sample to be suspended, providing insight into thermal transport in supported, devicelike environments. We apply this approach to measure the thermal properties of a range of 2D materials, which are of interest for device applications, including single-layer graphene, few-layer hexagonal boron nitride, single- and few-layer MoS2, and bulk MoSe2 crystal. The measured thermal properties will have important implications for thermal management in device applications.

1.
K. S.
Novoselov
,
A.
Mishchenko
,
A.
Carvalho
, and
A. H. C.
Neto
, “
2D materials and van der Waals heterostructures
,”
Science
353
,
aac9439
(
2016
).
2.
A. K.
Geim
and
I. V.
Grigorieva
, “
Van der Waals heterostructures
,”
Nature
499
,
419
(
2013
).
3.
K. S.
Novoselov
 et al, “
A roadmap for graphene
,”
Nature
490
,
192
(
2012
).
4.
F.
Withers
 et al, “
Light-emitting diodes by band-structure engineering in van der Waals heterostructures
,”
Nat. Mater.
14
,
301
(
2015
).
5.
F.
Withers
 et al, “
Heterostructures produced from nanosheet-based inks
,”
Nano Lett.
14
,
3987
(
2014
).
6.
M.
Yankowitz
,
J.
Xue
, and
B. J.
LeRoy
, “
Graphene on hexagonal boron nitride
,”
J. Phys. Condens. Matter
26
,
303201
(
2014
).
7.
Z.
Zhang
,
S.
Hu
,
J.
Chen
, and
B.
Li
, “
Hexagonal boron nitride: A promising substrate for graphene with high heat dissipation
,”
Nanotechnology
28
,
225704
(
2017
).
8.
W.
Choi
 et al, “
Recent development of two-dimensional transition metal dichalcogenides and their applications
,”
Mater. Today
20
,
116
(
2017
).
9.
T.
Tian
,
P.
Rice
,
E. J. G.
Santos
, and
C.-J.
Shih
, “
Multiscale analysis for field-effect penetration through two-dimensional materials
,”
Nano Lett.
16
,
5044
(
2016
).
10.
K. F.
Mak
,
C.
Lee
,
J.
Hone
,
J.
Shan
, and
T. F.
Heinz
, “
Atomically thin MoS2: A new direct-gap semiconductor
,”
Phys. Rev. Lett.
105
,
136805
(
2010
).
11.
Y.
Zhao
,
W.
Wang
,
C.
Li
, and
L.
He
, “
First-principles study of nonmetal doped monolayer MoSe 2 for tunable electronic and photocatalytic properties
,”
Sci. Rep.
7
,
17088
(
2017
).
12.
C.
Jung
 et al, “
Highly crystalline CVD-grown multilayer MoSe2 thin film transistor for fast photodetector
,”
Sci. Rep.
5
,
15313
(
2015
).
13.
G. W.
Shim
 et al, “
Large-area single-layer MoSe2 and its van der Waals heterostructures
,”
ACS Nano
8
,
6655
(
2014
).
14.
N.
Peimyoo
 et al, “
Thermal conductivity determination of suspended mono- and bilayer WS2 by Raman spectroscopy
,”
Nano Res.
8
,
1210
(
2015
).
15.
Y.
Wang
,
N.
Xu
,
D.
Li
, and
J.
Zhu
, “
Thermal properties of two dimensional layered materials
,”
Adv. Funct. Mater.
27
,
1604134
(
2017
).
16.
D. G.
Cahill
, “
Analysis of heat flow in layered structures for time-domain thermoreflectance
,”
Rev. Sci. Instrum.
75
,
5119
(
2004
).
17.
J. P.
Feser
and
D. G.
Cahill
, “
Probing anisotropic heat transport using time-domain thermoreflectance with offset laser spots
,”
Rev. Sci. Instrum.
83
,
104901
(
2012
).
18.
A. J.
Schmidt
,
X.
Chen
, and
G.
Chen
, “
Pulse accumulation, radial heat conduction, and anisotropic thermal conductivity in pump-probe transient thermoreflectance
,”
Rev. Sci. Instrum.
79
,
114902
(
2008
).
19.
M.
Rahman
 et al, “
Measuring the thermal properties of anisotropic materials using beam-offset frequency domain thermoreflectance
,”
J. Appl. Phys.
123
,
245110
(
2018
).
20.
A. J.
Schmidt
,
R.
Cheaito
, and
M.
Chiesa
, “
A frequency-domain thermoreflectance method for the characterization of thermal properties
,”
Rev. Sci. Instrum.
80
,
094901
(
2009
).
21.
J.
Yang
,
C.
Maragliano
, and
A. J.
Schmidt
, “
Thermal property microscopy with frequency domain thermoreflectance
,”
Rev. Sci. Instrum.
84
,
104904
(
2013
).
22.
D.
Rodin
and
S. K.
Yee
, “
Simultaneous measurement of in-plane and through-plane thermal conductivity using beam-offset frequency domain thermoreflectance
,”
Rev. Sci. Instrum.
88
,
014902
(
2017
).
23.
K. T.
Regner
,
S.
Majumdar
, and
J. A.
Malen
, “
Instrumentation of broadband frequency domain thermoreflectance for measuring thermal conductivity accumulation functions
,”
Rev. Sci. Instrum.
84
,
064901
(
2013
).
24.
M.
Shahzadeh
,
M.
Rahman
,
O.
Hellwig
, and
S.
Pisana
, “
High-frequency measurements of thermophysical properties of thin films using a modified broad-band frequency domain thermoreflectance approach
,”
Rev. Sci. Instrum.
89
,
084905
(
2018
).
25.
J.
Yang
 et al, “
Thermal conductance imaging of graphene contacts
,”
J. Appl. Phys.
116
,
023515
(
2014
).
26.
D. G.
Cahill
 et al, “
Nanoscale thermal transport
,”
J. Appl. Phys.
93
,
793
(
2003
).
27.
D. G.
Cahill
 et al, “
Nanoscale thermal transport. II. 2003–2012
,”
Appl. Phys. Rev.
1
,
011305
(
2014
).
28.
J.
Liu
,
G.-M.
Choi
, and
D. G.
Cahill
, “
Measurement of the anisotropic thermal conductivity of molybdenum disulfide by the time-resolved magneto-optic Kerr effect
,”
J. Appl. Phys.
116
,
233107
(
2014
).
29.
C.
Casiraghi
,
S.
Pisana
,
K. S.
Novoselov
,
A. K.
Geim
, and
A. C.
Ferrari
, “
Raman fingerprint of charged impurities in graphene
,”
Appl. Phys. Lett.
91
,
233108
(
2007
).
30.
A. C.
Ferrari
 et al, “
Raman spectrum of graphene and graphene layers
,”
Phys. Rev. Lett.
97
,
187401
(
2006
).
31.
R.
Ghosh
 et al, “
Large area chemical vapor deposition growth of monolayer MoSe2 and its controlled sulfurization to MoS2
,”
J. Mater. Res.
31
,
917
(
2016
).
32.
C.
Lee
 et al, “
Anomalous lattice vibrations of single- and few-layer MoS2
,”
ACS Nano
4
,
2695
(
2010
).
33.
H.
Li
 et al, “
From bulk to monolayer MoS2: Evolution of Raman scattering
,”
Adv. Funct. Mater.
22
,
1385
(
2012
).
34.
I.
Stenger
 et al, “
Low frequency Raman spectroscopy of few-atomic-layer thick hBN crystals
,”
2D Mater.
4
,
031003
(
2017
).
35.
R.
Cheaito
 et al, “
Thermal boundary conductance accumulation and interfacial phonon transmission: Measurements and theory
,”
Phys. Rev. B
91
,
035432
(
2015
).
36.
R. B.
Wilson
and
D. G.
Cahill
, “
Anisotropic failure of Fourier theory in time-domain thermoreflectance experiments
,”
Nat. Commun.
5
,
5075
(
2014
).
37.
C.
Hua
and
A. J.
Minnich
, “
Heat dissipation in the quasiballistic regime studied using the Boltzmann equation in the spatial frequency domain
,”
Phys. Rev. B
97
,
014307
(
2018
).
38.
S. M.
Oommen
and
S.
Pisana
, “
Role of the electron-phonon coupling in tuning the thermal boundary conductance at metal-dielectric interfaces by inserting ultrathin metal interlayers
,” e-print arXiv:1910.05893.
39.
H.
Zobeiri
 et al, “
Frequency-domain energy transport state-resolved Raman for measuring the thermal conductivity of suspended nm-thick MoSe2
,”
Int. J. Heat Mass Transfer
133
,
1074
(
2019
).
40.
D. O.
Lindroth
and
P.
Erhart
, “
Thermal transport in van der Waals solids from first-principles calculations
,”
Phys. Rev. B
94
,
115205
(
2016
).
41.
Z.
Chen
,
Z.
Wei
,
Y.
Chen
, and
C.
Dames
, “
Anisotropic Debye model for the thermal boundary conductance
,”
Phys. Rev. B
87
,
125426
(
2013
).
42.
J. H.
Seol
 et al, “
Two-dimensional phonon transport in supported graphene
,”
Science
328
,
213
(
2010
).
43.
M.-H.
Bae
 et al, “
Ballistic to diffusive crossover of heat flow in graphene ribbons
,”
Nat. Commun.
4
,
1734
(
2013
).
44.
E. K.
Sichel
,
R. E.
Miller
,
M. S.
Abrahams
, and
C. J.
Buiocchi
, “
Heat capacity and thermal conductivity of hexagonal pyrolytic boron nitride
,”
Phys. Rev. B
13
,
4607
(
1976
).
45.
I.
Jo
 et al, “
Thermal conductivity and phonon transport in suspended few-layer hexagonal boron nitride
,”
Nano Lett.
13
,
550
(
2013
).
46.
H.
Zhou
 et al, “
High thermal conductivity of suspended few-layer hexagonal boron nitride sheets
,”
Nano Res.
7
,
1232
(
2014
).
47.
X.
Zhang
 et al, “
Measurement of lateral and interfacial thermal conductivity of single- and bilayer MoS2 and MoSe2 using refined optothermal Raman technique
,”
ACS Appl. Mater. Interfaces
7
,
25923
(
2015
).
48.
X.
Gu
,
B.
Li
, and
R.
Yang
, “
Layer thickness-dependent phonon properties and thermal conductivity of MoS2
,”
J. Appl. Phys.
119
,
085106
(
2016
).
49.
R.
Yan
 et al, “
Thermal conductivity of monolayer molybdenum disulfide obtained from temperature-dependent Raman spectroscopy
,”
ACS Nano
8
,
986
(
2014
).
50.
A.
Taube
 et al, “
Temperature-dependent thermal properties of supported MoS2 monolayers
,”
ACS Appl. Mater. Interfaces
7
,
5061
(
2015
).
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