Synthesis of Polycyclic Aromatic Hydrocarbons by Phenyl Addition–Dehydrocyclization: The Third Way

Article abstract of DOI:10.1002/anie.201909876

Polycyclic aromatic hydrocarbons (PAHs) represent the link between resonance-stabilized free radicals and carbonaceous nanoparticles generated in incomplete combustion processes and in circumstellar envelopes of carbon rich asymptotic giant branch (AGB) stars. Although these PAHs resemble building blocks of complex carbonaceous nanostructures, their fundamental formation mechanisms have remained elusive. By exploring these reaction mechanisms of the phenyl radical with biphenyl/naphthalene theoretically and experimentally, we provide compelling evidence on a novel phenyl-addition/dehydrocyclization (PAC) pathway leading to prototype PAHs: triphenylene and fluoranthene. PAC operates efficiently at high temperatures leading through rapid molecular mass growth processes to complex aromatic structures, which are difficult to synthesize by traditional pathways such as hydrogen-abstraction/acetylene-addition. The elucidation of the fundamental reactions leading to PAHs is necessary to facilitate an understanding of the origin and evolution of the molecular universe and of carbon in our galaxy.

Full text of DOI:10.1002/anie.201909876

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Thermal Transport in 2D Semiconductors—Considerations
for Device Applications
Yunshan Zhao, Yongqing Cai, Lifa Zhang, Baowen Li, Gang Zhang,*
and John T. L. Thong*
1. Introduction
The discovery of graphene has stimulated the search for and
investigations into other 2D materials because of the rich physics
and unusual properties exhibited by many of these layered materials.
Transition metal dichalcogenides (TMDs), black phosphorus, and SnSe
among many others, have emerged to show highly tunable physical and
chemical properties that can be exploited in a whole host of promising
applications. Alongside the novel electronic and optical properties of such
2D semiconductors, their thermal transport properties have also attracted
substantial attention. Here, a comprehensive review of the unique
thermal transport properties of various emerging 2D semiconductors
is provided, including TMDs, black- and blue-phosphorene among
others, and the different mechanisms underlying their thermal
conductivity characteristics. The focus is placed on the phonon-related
phenomena and issues encountered in various applications based
on 2D semiconductor materials and their heterostructures, including
thermoelectric power generation and electron–phonon coupling effect in
photoelectric and thermal transistor devices. A thorough understanding
of phonon transport physics in 2D semiconductor materials to inform
thermal management of next-generation nanoelectronic devices is
comprehensively presented along with strategies for controlling heat
energy transport and conversion.
Since the first discovery of monolayer
carbon atoms arranged in honeycomb
structures,[1,2] 2D graphene has inspired
the community of materials scientists
and opened up numerous competi-
tive applications in electronics,[3] spin-
tronics,[4] and valleytronics.[5] Due to its
strong in-plane covalent bonds formed
by sp2-hybridized carbon arrangement,
graphene exhibits many advantages
compared with traditional materials,
like super high electrical conductivity
(high mobility of charge carriers)[6]
and superior thermal conductivity.[7,8]
As a zero bandgap semimetal,[9,10] gra-
phene is limited for field-effect-transistor
(FET) applications since the carrier
channel cannot be fully closed by gate
voltage, resulting in a low working on/
off ratio (<10) that is typical for graphene-
channel FETs.[11] Following graphene,
there is an increasing abundance of other
members such as transition metal dichal-
cogenides (TMDs), black phosphorus (BP)
etc. that have joined the 2D family, which
also show excellent transport properties,
Dr. Y. Zhao, Prof. J. T. L. Thong
Department of Electrical and Computer Engineering
National University of Singapore
Singapore 117583, Republic of Singapore
E-mail: john_thong@nus.edu.sg
good mechanical flexibility and most importantly, interesting
layer-tunable bandgaps. Recent high-field measurements of
[12,13]
MoS2
and black phosphorus[14] show better performances
than silicon in terms of both critical field and saturation
velocity. Therefore, since discovery these kinds of 2D semicon-
ductors are believed to be good candidates for post-silicon semi-
conductor technology[15–17] due to their atomically thin channel
and freedom from surface dangling bonds.
Dr. Y. Cai, Dr. G. Zhang
Institute of High Performance Computing, Singapore
Singapore 138632, Republic of Singapore
E-mail: zhangg@ihpc.a-star.edu.sg
Prof. L. Zhang
For 2D semiconductors with a honeycomb lattice that
are noncentrosymmetric, such as TMDs, valley-contrasting
electronic physics has led to the emergence of valleytronics,
where the low-energy electronic states with handed-
ness properties have been proven to create chiral optical
excitations.[18,19] Recently, it has been theoretically predicted[20]
and then experimentally observed[21] that phonons in these
materials (WSe2) can have handedness or chirality as well.
Chiral phonons are also observed in graphene/hexagonal
boron nitride heterostructure,[22] where chiral phonons are
tunable and determine the selection rules of electronic inter-
valley scattering. This gives rise to potential applications in
NNU-SULI Thermal Energy Research Center (NSTER) & Center
for Quantum Transport and Thermal Energy Science (CQTES)
School of Physics and Technology
Nanjing Normal University
Nanjing 210023, China
Prof. B. Li
Department of Mechanical Engineering
University of Colorado
Boulder, Colorado 80309, USA
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/adfm.201903929.
DOI: 10.1002/adfm.201903929
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valleytronics and phonon-chirality-based phononics.[23] In
quantum dots of WSe2, the entanglement between chiral
phonons and optical excitation have also been reported very
recently.[24]
Yunshan Zhao is a Research
Fellow in the Department
of Electrical and Computer
Engineering, National
Alongside the novel phononics and electronic/optical prop-
erties of 2D semiconductors, their thermal transport proper-
ties have drawn considerable interest as well. They are ideal
platforms to study fundamental energy carrier transport and
provide new directions for thermal energy control and man-
agement. As atomically thin layered structures held together
by weak van der Waals forces, some 2D semiconducting mate-
rials show strong quantum confinement effect[25,26] while the
weak in-plane covalent bonds result in much lower thermal
conductivity compared with that of graphene,[7] which is ben-
eficial for thermoelectric (TE) energy conversion purposes,
where low thermal conductivity is needed to achieve high
efficiency.[27–29] On the other hand, with device scaling and
increasing integration in modern integrated circuits, the
power dissipation density has grown significantly, and high-
temperature hot spots can lead to performance degradation as
well as long-term reliability issues. Here a material with higher
thermal conductivity alleviates the dissipation of the Joule heat
originating from the active device, interconnects, and contacts.
Typically, for heat conduction, Fourier’s law is employed to
characterize the heat conduction ability of a solid, and can be
expressed as as J = −κ∇T, where J is the heat flux across the
system, κ is the thermal conductivity, and ∇T is the tempera-
ture gradient. A better understanding of phonon transport in
2D semiconductors would aid in the design of novel devices
that exploit such materials.
With increasing interest in new 2D materials, various fabri-
cation methods have been proposed, namely top-down methods
like mechanical/liquid exfoliation, and bottom-up methods
like chemical vapor deposition (CVD) and wet-chemical syn-
thesis.[30–32] Generally exfoliated specimens are of better quality
in terms of crystallinity that is consistent with their bulk coun-
terparts while synthesis approaches yield the quantity needed
for industrial applications.[33,34] Regarding to the thermal prop-
erties of 2D materials, many research papers and review articles
have been published. For theoretical calculation and simulation
modeling, the reader can refer to refs. [35,36]. For thermal meas-
urement methods, see refs. [37,38]. For a detailed survey of TE
applications of 2D materials, readers can refer to refs. [39,40].
Our review takes a perspective from the various thermally related
issues encountered in FETs based on 2D semiconductors, such
as thermal management in the active device regions and inter-
facial thermal resistance across various contacts and interfaces.
This article reviews phonon transport phenomena that are
relevant not only to FET applications, but also to various other
intriguing applications based on 2D semiconductor materials
and their heterostructures. Specifically, we will include a
discussion of several interesting works about functionalized
2D semiconductor materials for thermal transistor applications
that have been reported recently. Our review aims to provide a
thorough understanding of thermal transport issues in various
applications based on 2D semiconductor materials, to pave the
way for better thermal management and heat dissipation when
designing next-generation nanoelectronic and energy conver-
sion devices.
University of Singapore.
He received his B.S. from
Shandong University
and Ph.D. from National
University of Singapore.
His current research
mainly focuses on thermal/
thermoelectric transport in
low dimensional materials, such as nanowires and novel
2D materials.
Gang Zhang is a senior
scientist and capability group
manager at IHPC, Singapore.
He received his B.S. and Ph.D.
in physics from Tsinghua
University in 1998/2002,
respectively. His research
is focused on the energy
transfer and harvesting in
nanostructured materials. He is
a technical committee member
for the International Electron
Devices Meeting (IEDM).
John T. L. Thong obtained
his B.A. (1985) and Ph.D.
(1989) degrees from
Cambridge University. He
is currently a professor in
the Electrical and Computer
Engineering Department,
National University of
Singapore. His research
interests are 1D and 2D
materials, focusing on
their electrical and thermal
properties with a particular reference to electronic device
applications.
The outline of this review is as follows. A 2D semiconductor-
based FET is shown in Figure 1, where various elements consti-
tuting the 2D semiconductor family are represented, like 1T- and
2H-MoS2, BP, InSe, SnSe, and so on. Section 2 focuses on the
unique thermal transport properties of these 2D semiconduc-
tors. As a representative TMDs, MoS2 shows interesting thermal
transport along the in-plane and out-of-plane directions, and the
influence of layer-thickness and isotopes on its thermal transport
will be discussed. Discussions on the anisotropic thermal trans-
port behavior of BP and the ultralow thermal conductivity of
SnSe for TE applications are included in this section. Electrical
contacts to 2D semiconductor channels are typically made with
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Transition metal dichalcogenides having the chemical formula
of MX2, where M denotes a transition metal element and
X represents a chalcogen element as shown in Figure 2, are
promising candidates. With a reduction in the material thick-
ness from bulk to monolayer, TMDs show an indirect- to direct-
bandgap transformation, thus enabling potential applications
for electronic and optoelectronic devices. While monolayer
TMDs are semiconducting with bandgaps around 1–2 eV, the
corresponding bulk TMDs show quite diverse properties—
from insulators and semiconductors to semimetals and true
metals.[31]
Because of the difference in lattice structure of TMDs com-
pared with graphene, TMDs have different phonon trans-
port behaviors, and show much lower thermal conductivity in
theory and through experimental measurements. In contrast
to dimension-dependence of thermal conductivity in graphene,
thermal conductivity of TMDs typically shows near independ-
ence on size and roughness due to the very short intrinsic
phonon mean free path (MFP).[41] Moreover, compared to

the strong sp2 C C covalent bonds, the metal-chalcogen
bond is much weaker due to its special sandwich structure,
leading to variance in the phonon dispersions and Grüneisen
parameters.[41] All of these should be considered for thermal
management in the design of nanoelectronic devices based on
TMD materials.
Figure 1. Representative 2D semiconductors that have been applied to
FET devices. Various 2D semiconductors are shown, such as 1T- and
2H-MoS2, BP, InSe, and SnSe.
Among the semiconducting TMDs, the thermal properties
of Mo- and W-based materials are widely studied. Theoretically,
the transition metal atom has a minimal effect on thermal con-
ductivity for Mo- and W-based TMDs in the 2H structure and
the thermal conductivity is mainly dominated by the chalcogen
species, especially for the tellurides and selenides.[42] From high-
field electrical measurement and electrothermal modeling, the
thermal conductivity of semi-metallic WTe2 is 3 W m−1 K−1[43]
while density functional theory (DFT) calculation yields a
higher value of around 19 W m−1 K−1 for MoTe2 and WTe2. The
thermal conductivity of single-layer and bilayer MoSe2 is
59 18 and 42 13 W m−1 K−1, respectively, measured by opto-
thermal Raman technique,[44] which is comparable to the value
calculated by classical nonequilibrium molecular dynamics
(NEMD) simulations.[45] While WS2 shows a much larger
thermal conductivity estimated from first-principles calcula-
tions than other S-based TMDs, due to a relatively large atomic
weight difference induced phonon bandgap and suppressed
metals and transport across such interfaces, including MoS2/
contact and MoS2/substrate will be addressed in Section 3. In
addition to these primary considerations in FET thermal man-
agement, thermal phenomena related to other device applica-
tions of 2D materials, i.e., thermoelectrics, electron–phonon cou-
pling in photoelectric phenomena, effect of electrical field as well
as strain on thermal property and thermal functional devices,
like thermal transistor, are discussed in Section 4.
2. Thermal Properties in 2D Semiconductors
2.1. Transition Metal Dichalcogenides
Graphene is limited in its electronic device applications due to
its lack of an electrical bandgap[1] and this has prompted the
search for similar 2D materials with semiconducting properties.
Figure 2. Transition metals and chalcogen elements forming TMDs are highlighted in the periodic table. Reproduced with permission.[31] Copyright
2013, Nature Research.
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possibility of phonon–phonon scattering. This results in long
phonon relaxation time.[46]
As one of the most stable TMDs, MoS2 has been experi-
mentally fabricated by various approaches, and thermal trans-
port in this material has been widely explored. Nevertheless,
the thermal conductivity values reported by different research
groups diverge greatly. From ballistic NEGF calculations, the
thermal conductivity of MoS2 nanoribbons has been shown to
have a strong dependence on their orientation due to the dif-
ferent edge effect, and reported to be 673.6 and 841.1 W m−1 K−1
for armchair and zigzag directions, respectively.[47] Later on,
first-principles-based Peierls–Boltzmann transport equation
(PBTE) method predicted much lower thermal conductivity[48]
that is comparable to the experimental values. To further mini-
mize the thermal conductivity, Ding et al. proposed MoS2-
MoSe2 lateral superlattice structure,[49] which showed close
to 80% reduction in thermal conductivity compared with that
of individual single-layer due to the enhanced anharmonic
phonon scattering. On the other hand, even though it was the-
oretically predicted that the number of layers leads to different
thermal conductivity as a result of the change in phonon
dispersion and phonon scattering anharmonicity, the experi-
mental data show much weaker layer dependence (Figure 3).
Figure 3. Thermal conductivity of MoS2 as a function of layers numbers
at room temperature. The κ is measured by various experimental
techniques, including Raman spectrometer,[44,50,51,59] thermal bridge
method,[52] e-beam heating technique,[53] time-domain thermoreflectance
(TDTR),[54] and theoretical calculation by PBTE.[48]
The thermal conductivity is 34.5
4,[50] 77
25,[44] and
investigated,[57] where the thermal conductivity of isotopically
pure Mo 100MoS2 and 50% 100MoS2 was found to be higher by
50% and 30%, respectively, compared to that of natural MoS2
comprising naturally abundant isotopes of Mo of various
atomic masses of 92, 94, 95, 96, 97, 98, and 100.[57,58] Due to the
reduction of the isotopic disorder, the isotopically pure MoS2
shows less isotope-phonon scattering, which enhances the
phonon MFPs and thus the final thermal conductivity. These
results are shown in Figure 4.
For other members having semiconducting property, like
group IVB and VIII transition metal based TMDs, a much lower
thermal conductivity has been theoretically shown, which is
beneficial for TE applications.[60] Typically, the thermal conduc-
tivity of the TMDs from these groups has a similar dependence
on the chalcogen atom species and increases from selenides
to sulfides. The thermal conductivity of monolayer ZrSe2 and
HfSe2 at room temperature is 1.2 and 1.8 W m−1 K−1,[61] respec-
tively, which is lower than that of monolayer ZrS2, of around
52 W m−1 K−1,[51] for 1-layer (1-L), 2L, and 11L MoS2, meas-
ured by noncontact Raman spectrometry, where temperature-
sensitive Raman peaks are commonly employed to deduce the
thermal conductivity of 2D layered materials. Both thermal
bridge method[52] and e-beam technique[53] give similar thermal
conductivity values for 4L MoS2, which are much smaller than
that of bulk MoS2 obtained by time-domain thermoreflectance
(TDTR) technique.[54] These experimental discrepancies are
primarily attributed to the sample quality, such as extra PMMA
induced surface disorders, as well as experimental measure-
ment inaccuracies, which inevitably obfuscate the intrinsic
thermal conductivity of MoS2. For detailed descriptions of the
measurement setups, the reader may refer to other review
papers.[37,38]
Isotopic defects could affect the phonon transport by
increasing phonon scattering.[55,56] More recently, the iso-
tope effect on thermal transport in monolayer MoS2 has been
Figure 4. a) A sketch of different Mo isotoped-MoS2. b) The sample length-dependent thermal conductivity of natural-MoS2, 92MoS2, 96MoS2, and
100MoS2. Reproduced with permission.[57] Copyright 2019, American Chemical Society.
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3.2 W m−1 K−1.[62] Similarly, the thermal conductivity of
important consideration for potential candidates for modern
electronic applications, i.e., TE devices,[66,67] photodetectors,[68]
and field-effect transistors.[69,70] Phosphorene has two natural
allotropes–blue phosphorene and black phosphorene,[71,72]
which show different lattice structures and thus have different
phonon transport properties. Because of its special puckered
honeycomb structure, black phosphorene exhibits interesting
orientation-dependent phonon transport properties.[73] As blue
phosphorene is isotropic with a zigzag structure, phonon trans-
port in this material does not depend on the orientation in the
in-plane direction.[71]
Typically, few-layer phosphorene is exfoliated from crystal-
line phosphorus by means of mechanical cleavage, and other
techniques such as plasma-assisted process[74] and liquid-
phase fabrication technique[75] have been proposed as well.
Figure 5a shows the atomic structure of black phosphorene,
stacked together into black phosphorene by van der Waals
force, and each atom is bonded to three neighboring atoms in
sp[3] hybridization configuration.[76] Theoretically, it was pre-
dicted that phonon transport along zigzag (ZZ) direction is
preferred compared to armchair (AC) direction and many first
principles calculations have investigated this interesting ani-
sotropic thermal transport,[71,77–79] which is attributed to struc-
tural-asymmetry-induced phonon group velocity and relaxation
time. It was demonstrated as well that the strain would have
an inconsistent effect on the thermal transport along these two
[63]
monolayer PdS2
is much larger than that of monolayer
PdSe2.[64] It may be noticed that all these values are from the-
oretical calculations and more experimental work needs to be
carried out to further explore the thermal transport behaviors
of these TMDs.
More interestingly, unlikely the isotropic thermal transport
in the in-plane direction of most TMDs, ReS2 in a distorted 1T
phase shows strong anisotropic thermal conductivity along and
transverse Re-chains,[65] which is similar to the thermal trans-
port in puckered structures discussed below. Monolayer PdSe2,
due to its puckered morphology, shows direction-dependent
thermal transport along its in-plane direction as well and the
thermal conductivity of PdSe2 along the x- and y-directions is
3.7 (1.4) and 7.2 (2.7) W m−1 K−1 at 300 K (800 K), respectively.
This particular property could provide an additional degree of
freedom in the design of nanoscale thermal devices based on
these materials.
2.2. Phosphorene
Phosphorene, a single layer of phosphorus atoms arranged in
a honeycomb-like structure, has drawn a great deal of atten-
tion as a promising 2D semiconductor due to its layer-tunable
bandgap and high carrier (electron, hole) mobility, which is an
Figure 5. a) Atomic structure of multilayer black phosphorus with top view of monolayer phosphorene shown in the inset. Reproduced with permission.[76]
Copyright 2016, Wiley-VCH. b) A summary of thickness dependent thermal conductivity of black phosphorene with various dimensions, like black
phosphorene thin films, nanosheets and NRs. c) Thickness dependent Young’s modulus, including both theoretical calculations and experimental
measurement. Reproduced with permission.[91] Copyright 2018, Wiley-VCH. d) 3D sketch of b-As structures. e) Comparison of in-plane anisotropy
ratio of various properties along the AC and ZZ directions of b-As and other 2D materials. b-As has shown the maximum anisotropy ratio in both
electrical conductivity and mobility while comparable thermal conductivity with other materials. f) Temperature-dependent thermal conductivity of b-As
nanoribbons with dimension ≈124 nm along the ZZ and AC directions. Reproduced with permission.[93] Copyright 2018, Wiley-VCH.
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directions. By using nonequilibrium Green’s functions method
combined with first principles calculation, Ong et al.[80] showed
that the ZZ-oriented thermal conductance is increased when
a strain is applied along this direction and decreases when an
AC-oriented strain is applied; while the thermal conductance
in AC orientation is always reduced when a strain is applied to
either ZZ- or AC-directions. This inconsistent phonon response
to strain possibly explains the recent experimental observation
More recently, Zhao et al.[91] decoupled the dominant role
of phonon group velocity from phonon relaxation time by
linking the anisotropic phonon group velocity to anisotropic
sound velocity, as verified by measuring the Young’s modulus
of black phosphorene along both ZZ and AC directions using
method of three-point bending. It turns out that the anisotropy
ratio between κZZ and κAC is comparable to that of the Young’s
modulus value along these two directions. Considering the
fact that the speed of sound, vs2 is proportional to the Young’s
modulus E and that the phonon group velocity could be treated
as the speed of sound in the low frequency regime, the aniso-
tropic phonon dispersion relation therefore accounts for the
anisotropy observed in thermal transport between ZZ and AC
directions. Further change of anisotropy ratio of thermal con-
ductivity between ZZ and AC directions can be realized by
the introduction of “nonsquare” pores in a phononic crystal
(PnC),[92] where phonon group velocity along the direction
of more porous areas would be degraded more severely. This
adjustable anisotropic ratio of thermal transport is a unique
property of 2D phosphorene that can be exploited in thermal
management applications.
As a cousin of black phosphorene, black arsenic (b-As) has
just been fabricated and shows interesting anisotropic trans-
port behaviors in electrical and thermal properties.[93,94] Its
puckered atomic structure, shown in Figure 5d, is similar to
that of black phosphorene. Among the materials with puck-
ered lattice structures, such as black phosphorene and other
puckered materials, b-As has the greatest anisotropy in both
electrical conductance and carrier mobility as shown in
Figure 5e. For b-As, the electrical transport is more favorable in
the AC direction than that in ZZ direction while thermal con-
ductance just behaves in the opposite trend, similar to that of
black phosphorene, which thus enables the implementation of
novel transverse TE devices.[93] Nevertheless, unlike BP which
easily oxidizes, b-As demonstrates good resistance to ambient
degradation.[94]
1
2
that Raman sensitive peak Ag , B2g, and Ag modes could have
opposite responses for tensile strain ZZ- and AC-directions.[81]
By using a polymeric low-k dielectric to stretch the substrate, a
high tensile strain of more than 7% was achieved in ref. [81],
which nonetheless is still short of the theoretical predication
of the high strain limit for ZZ and AC directions of 27% and
30%,[82] respectively. Interestingly, the in-plane modes, B2g and
2
Ag , show a red/blue shift when a strain is introduced along the
ZZ and AC directions, respectively, due to the special in-plane
puckered structure of BP. Even though the out-of-plane mode,
1
Ag , remains unchanged for ZZ direction strain, it shows red
shifting for AC direction strain. This study of strained BP pro-
vides insight into strain engineering of BP for electronic and
optical devices.[83,84]
Experimentally, different measurement techniques have
been employed to explore the thermal transport anisotropy
behaviors in black phosphorene, such as the use of sus-
pended-pad thermal bridge,[85,86] TDTR[87,88] and micro-Raman
spectroscopy,[89] and the measurement results and sample
dimensions are summarized in Table 1, where the anisotropy
ratio are compared for different techniques as well. According
to Zhu et al.,[90] the strong anisotropy of thermal transport in
black phosphorene is attributed to both group velocity variations
and relaxation time variations along different crystalline orien-
tations. The role of phonon relaxation time for thermal trans-
port anisotropy is doubtful since dominant direction-dependent
phonon dispersion[85] and similar intrinsic phonon scat-
tering rate along ZZ and AC directions[89] were demonstrated.
Table 1. Thermal conductivity of BP at room temperature.
κ [W m−1 K−1] [300 K]
Dimension
Method
Anisotropy ratio
AC
4.59
ZZ
15.33
ZZ/AC
3.34
Monolayer[95]
First-principles calculations
First-principles calculations
First-principles calculations
MD simulation
Monolayer[71]
36
110
3.06
Monolayer[78]
27.8
48.9
1.76
Monolayer[96]
63.6
110.7
1.74
Monolayer[73]
MD simulation
33.0
152.7
4.63
Monolayer[77]
First-principles calculations
Suspended-pad microdevices
Suspended-pad microdevices
Micro-Raman spectroscopy
Four-probe measurement
E-beam technique
24.3
83.5
3.44
Film (13–48 nm)[86]
NRs (60–300 nm)[85]
Film (9–30 nm)[89]
Film (39–277 nm)[97]
NRs (106–220 nm)[91]
Film (138–552 nm)[87]
Bulk[88]
5.8–9.6
5.4–15.5
12.4–22
17.3–24.5
13.5–20.6
26.4–33.9
7.8–13.2
11.7–27
18.2–45.1
64.9
1.34–1.36
1.74–2.17
1.5–2
≈3
30.5–38.6
63–86.4
83 10
84–101
1.99–2.33
2.39–2.55
≈2.96
≈3
TDTR
TDTR
28
5
Bulk[90]
TR-MOKE
26–36
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[107]
2.3. Other 2D Semiconductors
their ultralow thermal conductivity, such as GeAs2
and
SnSe.[108] Since the dimensionless figure of merit ≈2.62 was
experimentally reported,[109] layered SnSe has been considered
as an excellent candidate for commercial development. Natural
SnSe has a layered orthorhombic crystal structure and its mon-
olayer has a highly puckered structure, very similar to that of
puckered BP.[109–111] Zhang et al. proposed a phase-controlled
method to synthesize SnSe nanosheets[112] and a single-crystal-
line SnSe nanosheet with thickness of ≈1.0 nm and lateral size
of ≈300 nm was synthesized experimentally.[113] Using density
functional theory combined with Boltzmann transport theory,
Wang et al. studied thermal and thermoelectric properties of
single-layered SnSe.[108] It was demonstrated that anharmonic
phonon–phonon interaction is dominant in the phonon scat-
tering process, because of the remarkable overlapping between
low frequency optical branches with the acoustic branches, as
a consequence of the heavy atomic masses, weak interatomic
bonds and the low atomic coordination. At room temperature,
in addition to the contributions of acoustic branches to thermal
conductivity, the low frequency optical modes also have non-
trivial contributions. Thus, due to an anomalously high Grü-
neisen value and high anharmonicity of chemical bonds, there
is strong anharmonicity in phonon–phonon scattering process,
which leads to a low thermal conductivity (3.0 W m−1 K−1 for
ZZ direction and 2.6 W m−1 K−1 for AC direction) in monolayer
SnSe according to first-principles calculations.[114] This strong
phonon anharmonicity is theoretically attributed to the long-
range interaction driven by the resonant bonding.[95,115–117] The
thermal conductivity of bulk SnSe is smaller than that of mon-
olayer SnSe possibly due to the smaller interlayer interactions
induced smaller phonon group velocity, as shown in Figure 6b,
which thus contributes to better TE property considering
its ultralow thermal conductivity (experimentally measured
≈0.25–0.28 W m−1 K−1 at 773 K).[109] The strong phonon anhar-
monicity was later demonstrated by inelastic neutron scattering
(INS) measurement,[118] where a softer transverse acoustic
(TA) and transverse optic (TO) mode along Γ-Χ direction was
observed than that of Γ-Υ direction and this accounts for its
anisotropic thermal transport as well.[110] Unlike the weak direc-
tion dependence in thermal conductivity of SnSe, anisotropic
and low thermal conductivity was presented in GeAs2, a semi-
conductor formed from group IV and V elements. At room
Other than the TMDs and BP discussed above, the elements in
Groups III to VI have drawn a lot of interest as well for inter-
esting 2D layered semiconducting materials. Among them,
the compounds of indium selenide, such as InSe and InSe2
and compounds of bismuth telluride, such as Bi2Te3, Bi2Se3,
and Sb2Te3 are the representative ones in various applica-
tions in optoelectronic devices,[98] high-mobility filed-effect
transistors,[99] phase-change memory,[100] single-mode phonon
laser,[101] and TE.[102] The thermal transport in these materials
has been studied quite recently. From EMD calculation, Bi2Te3
exhibits bulk-like thermal conductivity value when its thickness
is around 5 nm, and the thermal conductivity has a nonmono-
tonic dependence on its thickness due to the interplay between
Umklapp scattering and boundary scattering.[103] Later experi-
mental work by suspended pads measurement shows that the
thermal conductivity increases with the thickness,[102] as shown
in Figure 6a, where the phonon-boundary scattering is domi-
nant in the phonon transport.
Different from Bi2Te3 that has shorter phonon MFPs, InSe
has relatively larger MFPs. The multiple crystalline phases
of few-layered In2Se3 sheets are stable under experimental
conditions,[104] which provides the possibility of conducting
further experimental study on other physical properties. In
2016, Zhou et al. measured the thermal conductivity of single-
crystal In2Se3 sheets.[105] In2Se3 powders were used in the CVD
growth of 2D In2Se3 sheets, and H2 was used as the carrier gas.
Through the temperature dependence of the phonon modes,
thermal conductivity was measured using micro-Raman spec-
troscopy method. In general, in-plane thermal conductivity of
In2Se3 sheets suspended across holes increases with increasing
layer thickness in the range from 5 to 35 nm. Specifically, in
this range of thickness, in-plane thermal conductivity increases
from ≈4 to ≈60 W m−1 K−1. This thickness dependence is sim-
ilar to that observed in supported graphene, but opposite that
in suspended graphene sheets[106] as shown in Figure 6a. This
suggests the dominant role of phonon-boundary scattering in
the thermal transport process in In2Se3, instead of phonon–
phonon anharmonic scattering.
Other layered semiconducting materials belonging to these
families have been proposed for TE applications considering
[105]
[102]
Figure 6. a) Thickness dependent thermal conductivities of In2Se3
and Bi2Te3
by experimental measurement. A weak dimension dependent
for Bi2Te3 is shown. b) Temperature-dependent thermal conductivity of monolayer GeS, GeSe, SnS and SnSe, and bulk SnSe. Reproduced with
permission.[114] Copyright 2016, Royal Society of Chemistry.
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temperature, thermal conductivity of 6.03 W m−1 K−1 is reported
along a-axis, while a much lower value of 0.68 W m−1 K−1 along
the b-axis.[107]
Similar to the role of transition metal in thermal conduc-
tivity of TMDs, the thermal conductivity of InSe was calculated
to be lower than that of GaSe due to the enhancement in
acoustic phonon velocity and in the reduction of scattering
between acoustic and optical phonons.[119–121] Moreover GaS
has an overall larger thermal conductivity considering its even
higher acoustic phonon velocity and weaker coupling of optical
phonon modes with acoustic phonons.
layered materials. The Raman-sensitive peaks of the meas-
ured sample would serve as a temperature thermometer
while the incident heat source is from the heating by either
electrical[133] or optical[134,135] means. A sketch of a Raman
laser heating setup is shown in Figure 7a, where the interface
thermal transport across monolayer MoS2 and SiO2/AlN sub-
strate is measured.[136] For MoS2, the positions of E1 and A1g
2g
show redshift with increasing temperature, which works as a
temperature indicator, and its absorption power is obtained
from the absorbed incident laser power of one free-standing
monolayer MoS2 by considering the substrate enhancement
effect. Although MD simulations[124] show that the interface
thermal conductance of MoS2 on Au substrate is as high as
135–221MWm−2K−1,theresultsobtainedbytheRamantechnique
are considerably lower–0.44 0.07 MW m−2 K−1 for MoS2-Au,[44]
1.94 MW m−2 K−1 for MoS2-SiO2,[59] 17.0 MW m−2 K−1
for MoS2-h-BN,[137] and 15 MW m−2 K−1 for MoS2-AlN.[136] The
variations in the measured interface thermal conductance pro-
bably originate from the different interface quality prepared
by the wet transfer method.[138] Higher values obtained are
possibly due to the better interface quality in the absence of
polymeric residues.[139] Temperature also affects the interface
thermal transport as shown in Figure 7b, where the thermal
boundary conductance (TBC) of MoS2-SiO2 exhibits a T0.65
dependence. This temperature dependent interface thermal
conductance agrees well with that of MoS2-graphene interfaces
simulated by MD calculation,[140] which is theoretically attrib-
uted to the higher temperature-induced strong scattering of
inelastic phonons and the presence of excited phonons.
By changing the thickness of the channel and increasing
the spacing between the sample and substrate, the interface
thermal transport could be tuned significantly. Layer-dependent
interface thermal conductance of MoS2 with c-Si substrate
was measured by means of micro-Raman spectroscopy, which
increases monotonically with the number of layers.[138] Typi-
cally, the interface spacing leads to a higher Raman intensity
and disturbs the local interface thermal transport as well. With
decreasing number of layers, the Raman intensity difference
between measured and theoretical values increases, implying
a higher interface spacing, on the assumption that there is no
spacing for the thickest MoS2 (75 layers) for the theoretical
Raman intensity calculation, which is shown in Figure 7c. The
interface spacing would impair the interatomic forces between
MoS2 and substrates. Therefore, due to the higher interfacial
energy coupling, thicker MoS2 usually shows a better interface
contact and the interface thermal conductance increases from
0.974 to 68.6 MW m−2 K−1 with increasing number of MoS2
layers.[138] The thickness-dependence of interface thermal con-
ductance is shown in Figure 7d. A similar trend of interface
thermal conductance on thickness was shown between WSe2
and SiO2 in ref. [141]. The layer-controllable interface thermal
conductance of 2D semiconductors is favorable for FET appli-
cations considering the improved heat dissipation to the
substrates without degrading the channel electrical transport.
3. Interface Thermal Resistance in 2D Devices
3.1. Interface Thermal Resistance (ITR) between 2D Materials
and Dielectric Contacts
The thermal conductance at interfaces is a critical consideration
for heat management in the scaling down of modern nanoe-
lectronics devices, at length scales that are comparable to the
MFP of energy carriers. This interfacial thermal resistance, or
thermal boundary resistance (Kapitzal resistance) was initially
discovered for helium-solid system[122] and two theoretical
models were accordingly developed, which are the acoustic
mismatch model (AMM) and the diffusive mismatch model
(DMM),[123] depending on whether the heat carriers (phonons)
are specularly scattered (AMM) or randomly and elastically
scattered (DMM) at the interface. Therefore, the interfacial
thermal resistance could be influenced by many factors, such
as the interface roughness, chemical bonding and the atomic
defects.[124,125] For a more detailed theoretical modeling of heat
transfer across interfacial boundaries, readers can refer to the
review papers.[126,127]
For 2D based semiconductor devices, thermal transport at
interfaces normally dominates in energy dissipation as well
as in thermal management and thus understanding and char-
acterization of interface heat transfer is necessary. Interface
conditions also dominate the functionalities of these nanoelec-
tronic devices. For example, trapped-charge induced Coulomb
potential at the interface between the MoS2 channel and the
dielectric substrate is the dominant cause for the low carrier
mobility in MoS2 field-effect devices.[128] Just from a funda-
mental study point of view, 2D materials and especially their
heterostructures provide an ideal platform to study interfacial
heat transport along the cross-plane direction as a function of
quantum-well exfoliation-controlled thickness. This has given
rise to numerous studies in the past few years and this section is
mainly focused on this topic. Modern advanced fabrication
techniques have also enabled the realization of in-plane het-
erostructures[129,130] with atomically sharp interfaces. However,
interfacial thermal resistance measurement of such small lat-
eral interfaces is much more challenging compared to more
popular interface measurements between different materials in
the cross-plane direction.
Besides TDTR[131] and different 3ω techniques,[132] which
are preferred for bulk interface measurement, noncontact
Raman thermometry is an attractive technique to charac-
terize atomic interface thermal transport, especially for 2D
3.2. ITR between 2D Materials and Metal Contact
Electrical contacts to devices are usually made using metals.
Thus the interfacial thermal resistance between metal and
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Figure 7. a) Sketch of monolayer MoS2 on substrate and Raman thermometry measurement setup. b) Temperature dependent thermal boundary con-
ductance (TBC) across MoS2-SiO2, which follows trend of T0.65. The graphs are from paper. Reproduced with permission.[136] Copyright 2017, American
Chemical Society. c) Change of measured- and theoretical calculated- Raman peak intensity of A1g mode for MoS2 samples. d) Layer-dependent inter-
face thermal conductance of MoS2-c-Si deduced from Raman sensitive E2g1 and A1g modes. Reproduced with permission.[138] Copyright 2017, Elsevier.
2D materials plays a critical role in thermal management of
future 2D devices. There are two types of interface geometry:
side contact and edge contact. Side contact can be made by con-
tacting the metal surface with the plane of 2D materials. How-
ever, large contact resistance, for both electron and phonon,
usually exists at the interface which drastically restrains the
device current.[142] Mao et al. studied interfacial thermal resist-
ance in the side contact configuration between MoS2 and Sc
(Ru) through chemical bonding, and that between MoS2 and
Au (Pd) via weak physical bonding.[143] As expected, the phys-
isorbed case with a weaker bonding results in a much larger
interfacial thermal resistance than the chemisorbed case. Com-
pared with graphene/metal chemisorbed system, the metal/
MoS2 chemisorbed contact is significantly more resistive, with
almost 10-times higher thermal resistance. Therefore, for MoS2
devices with side contact to metal electrodes, the interfacial
thermal resistance is an impediment to heat dissipation.
On the other hand, for edge contacts, strong overlapping of
electronic orbitals between the 2D material and metal electrode
in most cases can lead to a substantial reduction in electron
tunnel barrier and a great increase in electrical transport, which
has been experimentally reported for both graphene[144] and
MoS2 devices.[145] By using molecular dynamics simulations,
Liu et al. studied the interfacial thermal transport across the
monolayer MoS2 and Au electrode, where an edge contact was
formed.[124] The effect of surface orientation of the crystal gold
electrode is also considered. As shown in Figure 8, although
there is a remarkable dependence of interfacial thermal con-
ductance on the interfacial structure, overall, the interfacial
thermal conductance is large. For example, the largest value
of interfacial thermal conductance occurs when θ = 0 at the
(110) surface, about 2.21 × 108 W m−2 K−1. This is comparable
to many commonly studied contact in semiconductor devices,
for example, the Si/Ge (3 × 108 W m−2 K−1),[146] Au–Si (1.88 ×
108 W m−2 K−1),[147] Al–Si (4.5 × 108 W m−2 K−1),[148] and Cu–Si
(4 × 108 W m−2 K−1)[149] interfaces. It is worth emphasizing that
although the thermal conductivity of graphene is nearly two
orders higher than that of monolayer MoS2, the contact thermal
conductance of monolayer MoS2 with metal contact is compa-
rable to that of metal–graphene interfaces with a chemically
bonded structure (2.5 × 108 W m−2 K−1).[150] Thus edge contact
between MoS2 and metal electrodes has advantages in thermal
management, in addition to the larger electrical current, com-
pared to the side contact configuration.
In addition, the interfacial thermal conductance also depends
on the interface configuration. At the MoS2/Au (001) con-
tact, the interfacial thermal conductance is robust and weakly
dependent of the orientation angle. On the other side, for both
MoS2/Au (111) and MoS2/Au (110) contacts, the interfacial
thermal conductance decreases markedly when θ increases
from 0° to 30°. For all the considered contacts, the interfacial
thermal conductance decreases with the number of S vacan-
cies, following a linear dependence.
4. Phonon-Driven Emerging Applications
of 2D Semiconductors
4.1. Thermoelectric
The thermoelectric effect describes the conversion between
heat and electrical energy.[29,151,152] Heat is directly converted
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contributions and phonon (κL) contributions. Thus, a higher
ZT factor follows from a low thermal conductivity to generate
a large temperature gradient, and high electrical conductivity to
conduct electricity efficiently–desirable TE materials are those
that behave like a phonon-glass electron-crystal.[29,155] Typically,
optimizing the material parameters is an exercise in compro-
mise since they are correlated to each other. For example, the
electrical conductivity of a material increases with increasing
carrier concentration while the Seebeck coefficient decreases
as it is physically related to the average entropy per charge
carrier. Meanwhile, the carrier concentration induces a larger
electrical thermal conductivity as related by the Wiedemann–
Franz law.[156,157] Therefore, good TE materials are typically
degenerate semiconductors, as shown in Figure 9. According to
Hicks and Dresselhaus,[25,158] low dimensional nanostructures
perform favorably for TE applications due to quantum confine-
ment. Considering the staircase-like energy dependent density
of states (DOS) of 2D materials shown in Figure 9b, 2D mate-
rials show better TE properties than those of bulk ones.
By electrolyte gating method, Pu et al. measured carrier density-
dependent TE properties of monolayer MoS2 and WSe2.[159]
In this work, the authors fabricated the electric double-layer
transistors based on centimeter-scale MoS2, MoSe2, and WSe2
monolayers. In electric double-layer transistors, the dielectric
layers of transistors are replaced with electrolytes. Therefore,
it is possible to continuously increase the carrier density up to
5 × 1013 cm−2 and realize precise control of the Fermi level and
Seebeck coefficient, owing to the high specific capacitance of
electric double-layer. As shown in Figure 10, the absolute value
of Seebeck coefficient of the monolayer samples is comparable
with that of the bulk samples. However, at a similar Seebeck
coefficient, the electrical conductivity of the 2D monolayers is a
few orders of magnitude higher than that of the bulk samples.
It turns out that the power factor of monolayer MoS2 and WSe2
is nearly one order of magnitude higher than that of their bulk
materials counterparts, which provides direct evidence for the
advantage of 2D monolayer sheets in thermoelectric applica-
tion. Figure 10a,b compares the Seebeck coefficient and power
factor of monolayers and their 3D bulk counterparts.
Figure 8. a–c) MoS2 on (001), (110), and (111) Au surfaces, respectively. Mo
and S atoms are shown in purple and yellow color, and Au atoms in the first,
second, and third layers are shown in cyan, brown, and red color, respec-
tively. d) Interfacial thermal conductance on Au crystal surfaces with different
contacting cases. Reproduced with permission.[124] Copyright 2016, Springer.
into electricity through the Seebeck effect, and an electric cur-
rent flow would lead to heat absorption and release, which is
known as Peltier effect.[153] The reversible generation of heat
flow when an electric current passes through a conductor with
a temperature gradient is called the Thomson effect.[154] The
efficiency of TE devices is normally characterized by a dimen-
sionless figure of merit ZT = (S2T)/(ρκ), where S is the Seebeck
coefficient, T is the temperature, ρ is the electrical resistivity,
and κ is the thermal conductivity, including both electron (κe)
Given the combination of field-effect doping that can be well
controlled, atomically clean surfaces, and quantum-well thick-
ness variation, 2D semiconductors provide a versatile platform
Figure 9. a) Figure of merit as a function of reduced Fermi level η[151] and η is defined as η = (EF − E0)/kBT, where EF is the Fermi energy, kB is the
Boltzmann constant, and T is temperature. b) DOS, g(E), for bulk materials (3D), quantum well (2D), and quantum wire (1D). 2D is favorable for high
power factor due to its staggered DOS. Reproduced with permission.[151] Copyright 2010, Elsevier.
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Figure 10. Comparison of electrical conductivity-dependent Seebeck coefficient a) and power factor b) for various TMDs, including bulk and monolayer
MoS2, MoSe2, MoTe2, WS2, and WSe2. Reproduced with permission.[159] Copyright 2016, American Physical Society.
to study the TE effect. MoS2, as a representative 2D semicon-
ductor, has shown attractive thermal as well as thermoelectric
properties. Numerous theoretical papers[160,161] have predicted
its superior TE properties while spin-dependent thermal
transport has been studied for sandwiched S–Mo–Se struc-
ture (Janus SMoSe).[162] Earlier TE measurements focused on
its photo-thermoelectric effect[163] and the measured Seebeck
coefficient value of single layer MoS2 was between −4 × 102 to
−1 × 105 µV K−1. Wu et al.[164] later measured the Seebeck coef-
ficient of monolayer CVD grown MoS2 with values ≈30 mV K−1,
even though the conductivity was low and the authors dem-
onstrated that the transport was dominated by variable-range
hopping (VRH). Kayyalha et al.[165] reported the thermoelec-
tric transport properties of MoS2 with different number of
layers and it was shown that both electrical conductivity and
Seebeck coefficient demonstrate a strong dependence on thick-
ness (Figure 11a,b). With reducing thickness, the thermoelec-
tric power factor (PF) keeps increasing until a peak, where a
high ≈50 µW cm−1 K−2 PF was shown for two-layer MoS2
sample in its ON state, before dropping greatly for the mono-
layer, which was theoretically attributed to a difference in the
energy dependence of the electron MFP. A similar thickness-
dependent PF trend was reported in paper,[166] where a rela-
tively higher PF of two-layer MoS2 was demonstrated due to
the better conductivity in the degenerate metallic regime and
a large Seebeck coefficient due to the high valley degenera-
cies and large effective masses. Quite recently, Wu et al.[167]
showed that the PF of layered MoS2 can be even enhanced
by a strong interaction of electrons at the Fermi level with a
local magnetic impurity (i.e., sulfur vacancy) and this so-
called magnetic impurity-induced Kondo effect leads to a new
record PF around 50 mW m−1 K−2, as shown in Figure 11d.
The single-atom sulfur vacancy in naturally grown MoS2, con-
firmed by low-temperature scanning tunneling microscopy
(STM) induces magnetic states, which further leads to a sig-
nificant band splitting of ≈50 5 meV at the conduction sub-
band adjacent to the sulfur vacancy. The Kondo effect induced
by magnetic impurities is seen to be an effective way to tune
the Seebeck coefficient and ZT value for 2D semiconductor
materials. Different from n-type MoS2, WSe2 shows interesting
p-typed transport behavior. By means of gate-controlled surface
carrier doping, Yoshida et al.[168] showed that the optimization
of power factor is possible in WSe2 single crystals and the opti-
mized values are comparable to those of a popular TE material,
bismuth telluride, which is measured as 37 and 32 µW cm−1 K−2
for p- and n- type conduction transport, respectively.
Like TMDs that have high mobility and tunable bandgap,
layered black phosphorus has also been studied for its TE proper-
ties. As discussed in Section 2.2, BP exhibits unique anisotropic
transport for both electrons and phonons, which is benefi-
cial for TE performance, since the high electrical and thermal
conductance directions are orthogonal to each other, enabling
values of ZT above 1 for monolayer BP at a doping density of
≈2 × 1020 cm−2 along the AC orientation.[169] Later experimental
work was carried out on thicker material and it was found that
Seebeck coefficient could reach up to +510 µV K−1 in the hole
depleted state at 210 K by using an EDLT configuration.[66]
Thickness-dependent thermoelectric characteristics of thick BP
was studied as well,[170] where Mott’s VRH model was demon-
strated to be the dominant mechanism in the TE and electrical
transport of BP,[170,171] as for the case of MoS2.
Other 2D semiconducting materials, like n-type TiS2
[172]
and
InSe[173] have been recently explored as well for TE applications.
As mentioned earlier, due to their weak interlayer van der Waals
force, 2D layered semiconductors can be mechanically exfoli-
ated into well-defined thickness down to single layer of a few
angstroms thickness.[174,175] By measuring thickness dependent
TE properties in InSe, Zeng et al.[176] have recently shown that
the power factor increases greatly due to the sharper edge of the
conduction-band DOS caused by quantum confinement and a
Seebeck coefficient up to 570 µV K−1 in 7 nm InSe sample has
been reported. Further analysis shows that power factor in InSe
would be increased significantly when the confined dimension
is smaller than the thermal de Broglie wavelength, a scenario
estimated by theoretical calculation.[177] When the confined
length increases beyond than the thermal de Broglie wave-
length, the power factor decreases gradually toward the value
for bulk InSe,[178] which is shown in Figure 12.
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Figure 11. a) Back-gate voltage (Vg-Vth) dependent thermoelectric power factor (PF) for different layers of MoS2. b) PF versus the number of layers at
different Vg-Vth. All the PF values are for room temperature. Reproduced with permission.[165] Copyright 2016, American Institute of Physics. c) PF as
a function of back-gate voltage. The bilayer MoS2 shows a maximum PF with a larger electrical mobility. Reproduced with permission.[166] Copyright
2017, American Physical Society. d) PF versus measured temperature for different back-gate voltages. An abnormal increase of PF is exhibited due to
the Kondo effect. Reproduced with permission.[167] Copyright 2019, arXiv.
4.2. Photoelectric (Electron–Phonon Coupling)
can be estimated to be 1 ns,[181] which is in contrast to direct
excitons with lifetime of around 100 ps and a higher quantum
yield.[182] Similarly, by using femtosecond time-resolved
photoemission electron microscopy, the carrier dynamics
property of monolayer WSe2 on SiO2/Si substrate has been
studied to uncover the role of the intervalley electron–phonon
scattering of electrons.[183]
In monolayer or few-layer TMDs energy dissipation during
nonradiative emission plays a vital role in the ultrafast pro-
cesses of the carriers. Generally, two pathways of nonradiative
energy channels exist after photoexcitation of layered TMDs[184]
(see Figure 13): 1) ultrafast cooling of hot carriers via electron–
phonon scattering and subsequent formation of excitons, and
2) nonradiative recombination of excitons at the surface. While
thermalization of the MoS2 leads to a redshift of the exciton
resonance energy due to electron–phonon scattering, the excess
energy released from the cooling of hot carriers can be dissi-
pated and transferred to the phonons within ≈2 ps for pathway
1), while process 2) is a Shockley–Read–Hall recombination
responsible for energy dissipation from surfaces to external
phonons within ≈9 ps.
In addition to the direct effect to heat-to-electric energy con-
version, phonons also play important roles in other energy
conversion mechanisms, such as the photoelectric effect.
Light–matter interaction is highly sensitive to the thermal
environment of the material during the measurement. The
coupling of the phonon and electron can renormalize the
electronic structure, which can affect the light emission and
absorption. Photocarriers, electrons and holes, can be scat-
tered through a series of phonon coupling mechanisms sat-
isfying the selection rules subject to energy and momentum
conservation. In addition, thermal vibration distorts the ideal
atomic positions and scatters the light-triggered electron–hole
pairs. Specifically, acoustic phonons are involved in the car-
rier relaxation process via deformation potential interaction[179]
while optical/homopolar phonons are through Fröhlich inter-
action. For instance, TMDs such as MoS2 and WS2 show a
strong absorption of visible light due to the “band nesting”
effect. Photocarriers produced in the band-nesting part (located
훬
midway between the Γ and points) drifts toward their imme-
훬
diate band extrema: valley and Γ hill for electrons and holes,
In addition, phonons are also found to be important for
the production of the excitons, a type of quasiparticle playing
a significant role in the optical properties of layered semi-
conducting materials. The strength of the exciton-phonon
can be obtained by experimentally measuring the dephasing
respectively.[180] These electron–hole pairs are separated in the
k-space and their radiative recombination requires either emis-
sion or absorption of single or multiple phonons. This indirect
emission process results in low yield and the carrier lifetime
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derive the formation dynamics of excitons from free carriers in
TMDs.[189] Depending on the density of the electrons and holes,
nonzero momentum excitons could be generated from free
electron–hole pairs in layered materials via the longitudinal
optical phonons coupling of charge carriers at high tempera-
ture (≈120 K). On the other hand, in monolayer TMDs, excitons
can be relaxed by phonons by means of the deformation poten-
tial or in the process of piezoelectric coupling. This relaxation
effect could be as important as those by defect-assisted scat-
tering or trapping effect by the surface states.[190] Photolumi-
nescence study of monolayer MoS2 highlighted the importance
of exciton-phonon coupling.[191]
In addition to phonon–phonon, phonon-boundary and
phonon-defect scattering, the phonon lifetime can be modu-
lated by other factors as well. In particular, due to their atomic
thickness, the phonon properties of 2D materials are extremely
sensitive to environment, including substrate, electrical field,
etc. One example is for free-standing and supported graphene.
As well known, there are three acoustic phonon modes in
monolayer freestanding graphene, the in-plane longitudinal
acoustic mode (LA), in-plane transverse acoustic mode and
out-of-plane flexural mode (ZA), and at Brillouin zone center,
the energy of these acoustic modes is zero. However, for sup-
ported graphene, while the in-plane LA and TA modes are
slightly influenced, the ZA mode is flattened and shifted.
Obviously, a new flexural mode, called ZA’ mode appears with
energy of 6 THz at Γ point. This is because the substrate can
break the translational invariance at the out-of-plane direction.
The mismatch in flexural modes can induce significant resist-
ance for heat flow through boundary between free-standing
and supported graphene.[192] Furthermore, due to the different
lattice constant between the supported 2D materials and sub-
strate, there exists strain (stress) in the 2D materials. Usually,
tensile strain results in softening of the bonds, reducing the
phonon group velocity and enhancing the phonon–phonon
anharmonic scattering strength. The combination of all these
factors will reduce the thermal conductivity of 2D mate-
rials.[193] However, for thermal conductance of certain 2D
materials, for example, borophene, tensile strain may increase
its thermal conductance along certain crystal axis, because of
Figure 12. Power factor dependence on h0/ξ at different carrier
concentration.[176] h0 is the quantum confinement length and ξ the de
Broglie wavelength. Power factor becomes saturated to bulk value when
h0/ξ is far large than 1. When the sample thickness is much smaller than
the de Broglie wavelength, there is significant increase in thermal power
due to quantum confinement. Reproduced with permission.[176] Copyright
2018, American Chemical Society.
times,[185] exciton linewidths and mobility,[186] and photolumi-
nescence.[187] Different from excitons in bulk GaAs materials
where the excitons are predominantly located at the center of
the Brillouin zone thus carrying zero momentum, excitons in
TMDs are formed at the noncentral points in the momentum
space.[188] This induces dramatic differences in the pathways
of the exciton creation between GaAs and TMDs. For these
nonzero wavevector excitons, the subsequent relaxation to the
zero wavevector momentum involves emission of acoustic
phonons or longitudinal optical (LO) phonons. A model within
the framework of Fermi’s Golden rule was established to
Figure 13. a) Schematic for visible (vis), near-infrared (NIR), and mid-infrared (MIR) detection irradiation in MoS2. Possible optical transitions are
marked by dashed and solid straight arrows caused by the pump pulse and probe pulse. b) Sketch of nonradiative energy channels that follow the
ultrafast excitation. Reproduced with permission.[184] Copyright 2018, American Chemical Society.
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the change in the bond environment[194] and
for monolayer silicene, tensile strain would
greatly increase its thermal conductivity due
to the enhancement in the acoustic phonon
lifetime.[195]
Moreover, the interactions between electron
and phonon would affect the thermal trans-
port property of 2D materials as well. In elec-
tronic devices based on 2D materials an elec-
tric field always exists. For some polar mate-
rials, the electric field may have a direct influ-
ence on their phonon vibrational modes, con-
sequently affecting the thermal conductivity.
For nonpolar materials, electric field may
provide indirect effect on thermal conductivity
through electron–phonon coupling.[196] Using
fully first-principles calculations, Liao et al.[197]
studied the effect of electron–phonon inter-
action on phonon transport, and compared
this effect with the intrinsic phonon–phonon
anharmonic interaction. Using silicon as
an example, they found a significant reduc-
tion in the lattice thermal conductivity due to
Figure 14. a) Illustration of the thermal transistor under operation. b) The MoS2 working electrode
VWE measured during the electrochemical cycle. c) Cross-plane thermal conductance during the
electrochemical cycle. Reproduced with permission.[206] Copyright 2018, Nature Research.
electron–phonon interaction when the carrier density exceeded
1019 cm−3. It is worth mentioning that for p-type silicon with
hole density of 1021 cm−3, electron–phonon coupling can induce
45% reduction in its room temperature thermal conductivity.
Considering the fact that this is a typical range of carrier concen-
tration in the electronic devices and thermoelectric devices, the
electron–phonon coupling cannot be ignored in a study of
thermal conductivity of semiconductors. The impact of elec-
tron–phonon interaction on thermal conduction of 2D materials
deserves future studies.
decreases as Li ions enter the MoS2 films. Consequently,
the cross-plane thermal conductivity decreases from about
15 to 1.6 MW m−2 K−1 as shown in Figure 14c. When the cur-
rent is reversed during the delithiation step, Li ions are removed
from the MoS2 film, and the cross-plane thermal conductance
increases back to the pre-lithiation value. The on/off ratio is
about 10 times between the lithiated and delithiated states.
The underlying mechanism was examined using first-prin-
ciples calculations. The pre-lithiation MoS2 film is in 2H phase
with ABAB stacking sequence. Upon intercalation, Li ions
occupy the octahedral sites inside the interlayer gap, forming
2H-Li1MoS2 phase and mixed with 1T-Li1MoS2 phase with
stacking sequence AA. As shown in Figure 15a–c, lithiation
4.3. Thermal Transistor Devices
Engineering the physical characteristics of phonons provides
a powerful way to realize designable thermal functional mate-
rials. Furthermore, achieving active control of heat flow in a
manner analogous to electronic circuits represents a game
changer in engineering energy transport. Theoretical models
to realize various types of thermal devices have been devel-
oped.[198,199] Because of the advantages of high thermal conduc-
tivity, single-atom thickness and tunable shape, graphene-based
thermal rectifier[200–204] and thermal modulator[205] have been
explored both theoretically and experimentally.
Recently, Sood et al. demonstrated experimentally a thermal
transistor based on MoS2 thin film actuated by reversible electro-
chemical intercalation of Li ions.[206] Conceptually, thermal tran-
sistor is a device whose thermal conductance can be modulated
via an external stimulus, such as electrical voltage. For the MoS2
based thermal transistor, the on-state corresponds to the pristine
MoS2 and the off-state corresponds to the Li-intercalated MoS2.
Figure 14a shows the schematic of the device under operation.
It is a 10 nm thick few-layer MoS2 film, and LiPF6 in ethylene
carbonate/diethyl carbonate serves as the liquid electrolyte.
Charging/discharging the cell is controlled by electrical current
in a manner of real-time modulation. As shown in Figure 14b,
during the lithiation step, the MoS2 working electrode
Figure 15. Phonon dispersions along the cross-plane direction.
a) 2H-MoS2, b) 1T-Li1MoS2, and c) 2H-Li1MoS2. Blue curves show
the contribution from MoS2 and red curves show that from Li atoms.
Reproduced with permission.[206] Copyright 2018, Nature Research.
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gives rise to several flat bands, results in decreased group
velocity and increased phonon scattering rates according to
phonon rattling effect,[207] and consequently leads to a reduction
in thermal conductivity. Moreover, lithiation may induce disor-
dered stacking among MoS2 film, lead to significant reduction
in cross-plane thermal conductivity. Thus the observed thermal
transistor is due to lithiation induced phonon scattering, reduc-
tion in group velocity and stacking disorder.
Keywords
2D semiconductors, interface thermal resistance, phonon transport,
thermal functional device
Received: May 16, 2019
Revised: August 2, 2019
Published online:
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Conflict of Interest
The authors declare no conflict of interest.
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