Ultralow thermal conductivity in disordered, layered WSe2 crystals.

Abstract

The cross-plane thermal conductivity of thin films of WSe2 grown from alternating W and Se layers is as small as 0.05 watts per meter per degree kelvin at room temperature, 30 times smaller than the c-axis thermal conductivity of single-crystal WSe2 and a factor of 6 smaller than the predicted minimum thermal conductivity for this material. We attribute the ultralow thermal conductivity of these disordered, layered crystals to the localization of lattice vibrations induced by the random stacking of two-dimensional crystalline WSe2 sheets. Disordering of the layered structure by ion bombardment increases the thermal conductivity.

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DOI: 10.1126/science.1136494
, 351 (2007);
315
Science
et al.Catalin Chiritescu,
Crystals2Layered WSe
Ultralow Thermal Conductivity in Disordered,

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financial support. Part of this work was also supported
by the Deutsche Forschungsgemeinschaft under grant
FA 453/1.
Supporting Online Material
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Materials and Methods
Figs. S1 to S3
References
23 October 2006; accepted 30 November 2006
10.1126/science.1136629
Ultralow Thermal Conductivity in
Disordered, Layered WSe2Crystals
Catalin Chiritescu,1David G. Cahill,1* Ngoc Nguyen,2David Johnson,2
Arun Bodapati,3Pawel Keblinski,3Paul Zschack4
The cross-plane thermal conductivity of thin films of WSe2grown from alternating W and Se layers
is as small as 0.05 watts per meter per degree kelvin at room temperature, 30 times smaller
than the c-axis thermal conductivity of single-crystal WSe2and a factor of 6 smaller than the
predicted minimum thermal conductivity for this material. We attribute the ultralow thermal
conductivity of these disordered, layered crystals to the localization of lattice vibrations induced
by the random stacking of two-dimensional crystalline WSe2sheets. Disordering of the layered
structure by ion bombardment increases the thermal conductivity.
M
andglasses.Inthesematerials,heatconductionis
adequately predicted by a simple phenomeno-
logical model, the minimum thermal conductiv-
ity, in which heat conduction is described by a
random walk of vibrational energy on the time
and length scales of atomic vibrations and inter-
atomic spacings (1). More sophisticated theories
of heat conduction in disordered materials sup-
port this description: A majority of the vibra-
tional modes [termed “diffusons” by Allen and
Feldman (2)] carry heat in this manner, and only
a small fraction of the vibrational modes prop-
agate as waves or are localized and therefore
unabletocontributetoheatconduction.Recently,
we (3) and others (4) have shown that the min-
imum thermal conductivity can be circumvented
in multilayer thin films of metals and oxides.
When the spacing between the interfaces is only
a few nanometers, the thermal resistance of the
interfaces reduces the thermal conductivity far
below the thermal conductivity of the homoge-
neous amorphous oxide.
Here, we demonstrated by both experiment
and computer simulation an alternative route for
achieving ultralow thermal conductivity in a
dense solid. The thermal conductivity of dis-
ordered thin films of the layered crystal WSe2
aterials with the lowest thermal con-
ductivity are typically found among
electrically insulating amorphous solids
can be as small as 0.05 W m−1K−1, a factor of 6
smaller than the predicted minimum thermal
conductivity and, to the best of our knowledge,
the lowest thermal conductivity ever observed in
a fully dense solid. Disruption of the layered
structure and the crystallinity of the WSe2sheets
by ion irradiation actually produces a marked
increase in the thermal conductivity of the thin
film. Thus, the lowest thermal conductivities
are not found in the fully amorphous form of
WSe2; rather, ultralow thermal conductivity is
achieved by controlling both order and disorder,
and hence the thermal pathways, in this aniso-
tropic material.
We synthesized WSe2thin films by the mo-
dulated elemental reactants method (5, 6). Se-
quential bilayers of W and Se were deposited in
an ultrahigh vacuum chamber onto unheated
Si (100) wafers with a stoichiometry of 1:2 and
then annealed for 1 hour at elevated temper-
atures in N2atmosphere to form the desired
layered structures (6). The microstructure of the
films was stable at room temperature. In the
WSe2structure, a hexagonal plane of Watoms is
bonded to two Se layers by strong covalent-ionic
bonds, and each two-dimensional (2D) WSe2
sheet is bonded to adjacent sheets by weaker van
der Waals forces (7, 8). We purchased a single
crystalofWSe2fromNanoscienceInstrumentsto
provide a baseline for comparisons. Thermal
conductivity was measured by time-domain ther-
moreflectance (TDTR) (6, 9–12). In our imple-
mentation of TDTR, we determine the thermal
conductivity by comparing the time dependence
of the ratio of the in-phase Vinand out-of-phase
Vout signals from the radio-frequency lock-in
amplifier to calculations made with the use of a
thermal model (11). The thermal model has
several parameters, but the thermal conductiv-
ity of the WSe2sample is the only important
unknown.
We used synchrotron x-ray diffraction to char-
acterize the microstructure of a typical WSe2
film (Fig. 1). Data for (0 0 L) reflections (6)
showed that the layering of the 2D WSe2sheets
was very precise; the surface normal to each
sheet (hexagonal c axis) was well aligned with
the surface normal of the substrate, and the spac-
ing between the centers of WSe2sheets was
highlyuniformat0.66nm.Thesehighlytextured
films had completely random crystalline orienta-
tion in the a-b plane. We examined the crys-
talline structure of the film by scanning the
diffraction intensity through reciprocal space
where the (1 0 3) reflection intersected the Ewald
sphere. The relatively narrow line width (0.06 in
reciprocal lattice units) in the direction parallel
to the surface, [h 0 3], gave a lateral coherence
length of 23 nm (Fig. 1C). Scans through the
1Department of Materials Science and Engineering, Frederick
Seitz Materials Research Laboratory, University of Illinois,
Urbana, IL 61801, USA.2Department of Chemistry, University
of Oregon, Eugene, OR 97403, USA.3Department of Ma-
terials Science and Engineering, Rensselaer Polytechnic In-
stitute, Troy, NY 12180, USA.
Argonne National Laboratory, Argonne, IL 60439, USA.
*To whom correspondence should be addressed. E-mail:
d-cahill@uiuc.edu
4Advanced Photon Source,
Fig. 1. X-ray diffraction data for a 32.5-nm-thick
WSe2film collected at the 33–bending magnet
beamline of the Advanced Photon Source with the
useof18.5-keVphotons.Afterdeposition,theWSe2
film was annealed for 1 hour at 650°C in a N2
atmosphere. (A) False-color depiction of the x-ray
diffraction intensities collected by the area detector
in the vicinity of the (1 0 3) and (1 0 5) reflections.
Theverticaldirectionisnormaltothesamplesurface
and the horizontal direction is in the plane of the
sample. (B) Scan of the x-ray diffraction intensities
along the surface normal. The scan direction is
shown as the vertical red line in (A). (C) Scan of the
x-ray diffraction in the in-plane direction. The scan
direction is shown as the horizontal red line in (A).
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intersection of (1 0 L) reflections with the
Ewald sphere probed the coherence of the
crystal structure along the direction normal to
the WSe2sheets. The large line widths (Fig.
1B) indicated that crystallographic ordering
in the stacking of the WSe2sheets was limited
to <2 nm.
We next compared the thermal conductivity
of annealed WSe2films to the conductivity of a
single crystal of WSe2and the predicted min-
imum thermal conductivity (Fig. 2). The thermal
conductivity of single-crystal WSe2was approx-
imately proportional to 1/T (the reciprocal of
absolute temperature), as expected for a di-
electric or semiconductor in which heat trans-
port is dominated by phonons with mean-free
paths limited by anharmonicity. Calculations of
the minimum thermal conductivity require
knowledge of the number density of atoms and
the speed of sound (1). We used picosecond
acoustics to measure the longitudinal speed of
soundinthecross-planedirectionofnominal360-
nm-thick films and found that vL= 1.6 nm ps−1
(13, 14). This measurement is in good agreement
with an independent measurement of the same
film (vL= 1.7 nm ps−1) with the use of pico-
second interferometry (15) and an index of
refraction at the laser wavelength of 800 nm
of n = 4.13. If we use the average of these val-
ues, vL= 1.65 nm ps−1, and a mass density of
r = 9.2 g cm−3, we obtain an elastic constant
C33=25 GPa,which isapproximately a factor of
2 smaller than C33for single crystals of NbSe2
and TaSe2measured by neutron scattering (16)
andsingle-crystalWSe2measuredbypicosecond
interferometry. The transverse speed of sound vT
is not accessible to the standard methods of
picosecond acoustics; instead, we estimated vT=
1.15 based on our measurement of vLand the
ratio C44/C33previously measured for NbSe2
and TaSe2(16).
Thelowestthermalconductivity,L,measured
at 300 K is L = 0.048 W m−1K−1for a 62-nm-
thick WSe2film, 30 times smaller than the cross-
plane thermal conductivity of a single-crystal
sample of WSe2(Fig. 2) and a factor of 6 smaller
than the predicted minimum thermal conductiv-
ity. This degree of deviation from the predicted
minimum thermal conductivity in a homoge-
neous material is unprecedented (17). Notably,
the conductivity of the 62-nm-thick film is
smaller than the conductivity of a thinner film
(24 nm) or a thicker film (343 nm). The reasons
for these differences are not understood in detail,
but we speculate that variations in the degree of
crystallographic ordering along the thickness of
the films are playing an important role.
The data shown in Figs. 1 and 2 lead us to
conclude that the ultralow thermal conductiv-
ities are produced by random stacking of well-
crystallized WSe2sheets. To test this idea, we
used irradiation by energetic heavy ions to dis-
rupt the crystalline order in the thin film samples
(Fig. 3). Because our TDTR measurements re-
quire knowledge of the thermal conductivity of
the substrate, bare silicon substrates were ir-
radiated with the same range of ion fluences and
measured by TDTR (6). At the highest ion dose,
3 × 1015ions cm−2, we observed a factor of 5
increase in the thermal conductivity of the WSe2
film. This increase in thermal conductivity with
ion beam damage is also unprecedented. We
inferred from these experiments that ion-induced
damage introduces disorder that reduces local-
ization of vibrational energy and enhances the
transfer of vibrational energy in the material.
To gain further insight and confidence in our
experimental results, we performed molecular
dynamics (MD) simulations on model structures.
For simplicity and computational efficiency, the
atomic interactions in our model compound are
described by 6-12 Lennard-Jones potentials:
?
UðrÞ ¼ 4e
s
r
? ?12
−
s
r
? ?6
?
ð1Þ
where e is the energy scale and s is the length
scale. Two sets of e and s parameters were used:
For interactions within a single WSe2sheet, e =
0.91 eVand s = 2.31 A˚, and for the interaction
betweenlayers,e =0.08eVands =3.4A˚.These
parameters achieved a good fit to WSe2crystal
structureandtheC11(200GPa)andC33(50GPa)
elastic constants. For computation efficiency, a
cutoff of 5.4 A˚was used, with both energy and
forces shifted such that they were zero at the
Fig. 2. Summary of measured thermal conductiv-
ities of WSe2films as a function of the measure-
ment temperature. Each curve is labeled by the
film thickness. Data for a bulk single crystal are
included for comparison. Error bars are the
uncertainties propagated from the various exper-
imental parameters used to analyze the data (6).
The ion-irradiated sample (irrad) was subjected to
a 1-MeV Kr+ion dose of 3 × 1015cm−2. The
dashed line marked Lmin is the calculated
minimum thermal conductivity for WSe2films in
the cross-plane direction.
Fig. 3. Thermal conductivity versus irradiation
dose for WSe2films 26 nm thick. Samples were
irradiatedwith1-MeVKr+ionstothedoseindicated
on the x axis of the plot. Error bars are the uncer-
tainties propagated from the various experimental
parameters used to analyze the data (6).
Fig. 4. (A) Atomic positions in a model WSe2
structure showing stacking disorder. The positions
of the heat sink and sourceseparatedby 8 nm are
indicated. (B) The steady-state temperature pro-
fileobtainedfromthenonequilibrium,heatsource–
sinkmethod.Thesolidlinedepictsalinearfittothe
central region between the heat source and sink.
The dashed line is an analogous fit but for the
structure with doubled size along the z direction
withthecorrespondingseparationbetweentheheat
source and sink of 16 nm.
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cutoff (18). The cross-sectional area of the sim-
ulation cell is 15.3 × 13.3 Å. Along the (001) di-
rection, two sizes were selected: 160 and 320 A˚.
Periodic boundary conditions were used for all
directions. Newton’s equations of motions were
solved by the fifth-order predictor corrector algo-
rithm(18)withanMDtimestep,Dt=1.8×10−15s.
The simulation cell for the thermal transport
measurement is depicted in Fig. 4. To calculate
the thermal conductivity, the we first equilibrated
the structure at T = 300 K for 100,000 MD time
steps. Next, the global thermostat was turned off
andthermalenergywasaddedtooneWSe2sheet
and removed from a second sheet, which was
located at a distance from the first sheet equal to
one-half of the size of the simulation cell along
the (001) direction (19, 20). Atomic velocities
were scaled such that heat was added or sub-
tracted at a constant rate, 10−6eV per MD time
step (21). We monitored the temperature profile
by averaging the kinetic energy of atoms in each
WSe2sheet. Because of the small energy barrier
for shearing of the WSe2structure and the small
cross-sectional area of the simulation cell, our
modelstructuresexhibitedthermallyexcitedlocal
shearingeventsleadingtodisorderinthestacking
of the WSe2sheets (Fig. 4).
After5to20millionMDsteps(dependingon
the system size), a steady-state temperature dis-
tribution was established (Fig. 4). The temper-
ature gradient, and thus the thermal conductivity,
of 16- and 32-nm-long simulation cells were es-
sentially the same within the statistical standard
deviation of 10%, L = 0.06 W m−1K−1. Given
the approximate form of the potentials used in
our computational work, the agreement between
the measured and calculated thermal conductiv-
ities was better than we expected. Nevertheless,
the low thermal conductivity of the model struc-
ture suggests that the ultralow thermal conduc-
tivity in disordered, layered crystals is a general
phenomenon and not restricted to WSe2.
Our WSe2films are poor electrical conduc-
tors in the cross-plane direction; however, if
semiconductors with similar structural features
and good electrical mobility can be identified,
disorderedlayeredcrystalsmayofferapromising
route to improved materials for thermoelectric
energy conversion.
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22. Supported by Office of Naval Research grant nos. N00014-
05-1-0250 and N00014-96-0407. Research for this work
wasperformedintheLaserandSpectroscopyFacilityandthe
Center for Microanalysis of Materials of the Frederick Seitz
Materials Research Laboratory, University of Illinois, which is
partially supported by the U.S. Department of Energy under
grant DEFG02-91-ER45439. Use of the Advanced Photon
Source was supported by the U.S. Department of Energy,
Office of Science, Office of Basic Energy Sciences, under
contract no. W-31-109-ENG-38.
Supporting Online Material
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Materials and Methods
Figs. S1 to S5
References
19 October 2006; accepted 4 December 2006
Published online 14 December 2006;
10.1126/science.1136494
Include this information when citing this paper.
Organic Glasses with Exceptional
Thermodynamic and Kinetic Stability
Stephen F. Swallen,1Kenneth L. Kearns,1Marie K. Mapes,1Yong Seol Kim,1
Robert J. McMahon,1M. D. Ediger,1* Tian Wu,2Lian Yu,2Sushil Satija3
Vapor deposition has been used to create glassy materials with extraordinary thermodynamic and
kinetic stability and high density. For glasses prepared from indomethacin or 1,3-bis-(1-naphthyl)-5-
(2-naphthyl)benzene, stability is optimized when deposition occurs on substrates at a temperature of
50 K below the conventional glass transition temperature. We attribute the substantial improvement in
thermodynamic and kinetic properties to enhanced mobility within a few nanometers of the glass
surfaceduringdeposition.Thistechniqueprovidesanefficientmeansofproducingglassymaterialsthat
are low on the energy landscape and could affect technologies such as amorphous pharmaceuticals.
G
tems can be described in terms of a potential
energy landscape, with thermodynamics and
kinetics controlled by the minima and barriers
on the landscape, respectively (1–3). Many im-
lassy materials combine the disordered
structure of a liquid with the mechanical
properties of a solid. Amorphous sys-
portant issues could be addressed if liquids or
glasses with very low energies could be created
(2, 4–6). For example, it might be possible to
definitively understand the Kauzmann entropy
crisis, an area of intense recent interest (1, 7–11).
Kauzmann observed that if the entropy of many
supercooled liquids is extrapolated to low tem-
perature,theamorphousstateispredictedtohave
a lower entropy than that of the highly ordered
crystal well above absolute zero (5, 6).
Glasses are usually prepared by cooling a
liquid, but accessing low energy states by this
route is impractically slow (4, 12). If a liquid
avoids crystallization as it is cooled, molecular
motion eventually becomes too slow to allow the
molecules to find equilibrium configurations.
This transition to a nonequilibrium state defines
the glass transition temperature Tg. Glasses are
“stuck” in local minima on the potential energy
landscape (2, 3). Because glasses are thermody-
namically unstable, lower energies in the land-
scape are eventually achieved through molecular
rearrangements. However, this process is so slow
that itisgenerallyimpossible to reach states deep
in the landscape by this route.
Wehavediscoveredthatvapordepositioncan
bypass these kinetic restrictions and produce
glassy materials that have extraordinary en-
ergetic and kinetic stability and unusually high
densities. We demonstrate this for two mo-
lecular glass formers: 1,3-bis-(1-naphthyl)-5-(2-
naphthyl)benzene (TNB) (Tg = 347 K) and
indomethacin (IMC) (Tg= 315 K). For these
systems,themoststableglassesareobtainedwhen
vapor is deposited onto a substrate controlled
near Tg– 50 K. We argue that surface mobility
during the deposition process is the mechanism
of stable glass formation.
Differential scanning calorimetry (DSC)
was used to examine the kinetics and thermo-
dynamics of vapor-deposited samples created
by heating crystalline TNB or IMC in a vacu-
um. Figure 1A shows DSC data for TNB vapor-
deposited (blue) onto a substrate held at 296 K.
1Department of Chemistry, University of Wisconsin–
Madison, Madison, WI 53706, USA.2School of Pharmacy,
University of Wisconsin–Madison, Madison, WI 53705,
USA.3Center for Neutron Research, National Institute of
Standards and Technology, Gaithersburg, MD 20899, USA.
*To whom correspondence should be addressed. E-mail:
ediger@chem.wisc.edu
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