REPORT
◥THERMAL CONDUCTIVITY
Ultrahigh thermal conductivity in isotope-enriched
cubic boron nitride
Ke Chen^1 , Bai Song^1 †‡, Navaneetha K. Ravichandran^2 *, Qiye Zheng^3 §, Xi Chen^4 ¶, Hwijong Lee^4 ,
Haoran Sun^5 , Sheng Li^6 , Geethal Amila Gamage Udalamatta Gamage^5 , Fei Tian^5 , Zhiwei Ding^1 ,
Qichen Song^1 , Akash Rai^3 , Hanlin Wu^6 , Pawan Koirala^6 , Aaron J. Schmidt^1 , Kenji Watanabe^7 , Bing Lv^6 ,
Zhifeng Ren^5 , Li Shi4,8, David G. Cahill^3 , Takashi Taniguchi^7 , David Broido^2 †, Gang Chen^1 †
Materials with high thermal conductivity (k) are of technological importance and fundamental interest.
We grew cubic boron nitride (cBN) crystals with controlled abundance of boron isotopes and measured
k greater than 1600 watts per meter-kelvin at room temperature in samples with enriched^10 Bor^11 B.
In comparison, we found that the isotope enhancement ofk is considerably lower for boron phosphide
and boron arsenide as the identical isotopic mass disorder becomes increasingly invisible to phonons.
The ultrahighk inconjunctionwithitswidebandgap(6.2electronvolts)makescBNapromisingmaterialfor
microelectronics thermal management, high-power electronics, and optoelectronics applications.
U
ltrahigh thermal conductivity (k)mate-
rials are desirable for thermal manage-
ment and have long been a subject of
both fundamental and applied interest
( 1 ). Despite decades of effort, only a few
materials are known to have an ultrahigh ther-
mal conductivity, which we define as exceeding
1000 W m−^1 K−^1 at room temperature (RT) ( 2 ).
In metals, free electrons conduct both charge
and heat. Therefore, the best electrical con-
ductors, such as silver and copper, also have
the highestkfor metals. In semiconductors
and insulators, phonons carry the heat. The
intricate interplay between lattice dynamics,
anharmonicity, and defects dictates thermal
transport. Despite the large number of mate-
rials that have phonon-dominated heat tran-
sport, diamond has been recognized since
1953 as the most thermally conductive bulk
material at RT ( 3 ). Besides diamond, a set of
nonmetallic crystals with highkwas system-
atically identified by Slack in 1973 ( 4 ), includ-
ing silicon carbide (SiC), boron phosphide
(BP), and the cubic, zincblende polymorph of
boron nitride (cBN) ( 5 ). In addition, Slack ( 4 )
proposed guidelines for searching for crys-
tals with highk, suggesting that candidates
should be composed of a strongly bonded
light element or elements arranged in a sim-
ple lattice with low anharmonicity. These
guidelines were established with approximate
models but captured the essential need for
high-phonon group velocity and low-phonon
scattering rates.
Since Slack’swork,thekof diamond
(~2000 W m−^1 K−^1 with natural carbon iso-
topes at RT) ( 6 , 7 ) has not been surpassed
among bulk materials. High thermal conducti-
vities of up to 490 W m−^1 K−^1 and 768 W m−^1 K−^1
were reported for BP and cBN ( 8 – 12 ), respec-
tively, benefiting from progress in crystal growth
and thermal characterization techniques. Un-
like cBN and BP, boron arsenide (BAs) has the
much heavier arsenic element and was origi-
nally estimated to have a room-temperature
k(kRT) of 200 Wm−^1 K−^1 ( 4 ). In 2013, Lindsay,
Broido, and Reinecke ( 13 , 14 )showedwith
ab initio simulations that BAs should have
akRTrivaling that of diamond because of a
dramatic reduction in the strength of the
lowest-order processes giving intrinsic ther-
mal resistance, three-phonon scattering. Sev-
eral experiments in 2018 demonstrated akRT
of ~1200 W m−^1 K−^1 ( 11 , 15 , 16 ), making BAs
one of the most thermally conductive materials
and consistent with modified predictions that
included four-phonon scattering ( 16 , 17 ).
Apart from the unusual BAs, cBN was pre-
dicted to have akRTexceeding 2000 W m−^1 K−^1
upon isotopic enrichment of the boron atoms
by using theories that ignored four-phononscattering ( 13 , 18 , 19 ). We combined experimen-
tal characterizations with ab initio simulations
that include four-phonon scattering to revisit
heat transport in cBN, using synthetic crystals
with natural (natB)andcontrolledabundanceof
boron isotopes. We demonstrated experimen-
tally that cnatBN crystals can have akRTover
850 W m−^1 K−^1 and that enriched c^10 B(or^11 B)
N can reach over 1600 W m−^1 K−^1 .Theultrahigh
kwe measured was consistent with our first-
principles calculations, which showed rela-
tively weak effects of higher-order anharmonic
phonon-phonon interactions onkin cBN. Fur-
thermore, the ~90% enhancement ofkRT
upon boron isotope enrichment qualitatively
supported prior calculations ( 13 , 18 , 19 ) and
represents a very large RT isotope effect. For
isotope-controlled BP and BAs, we only calcu-
lated a 31 and 12% increase inkRT, respec-
tively, which agreed with the small isotope
effect we measured. We used simulations to
discover the differences between these boron
pnictides which can only be understood by
considering the subtle interplay between the
mutual interactions involving phonons and
isotopic disorder.
We prepared four sets of cBN crystals com-
bining natural nitrogen (99.6%^14 N and 0.4%(^15) N) with different boron isotope composi-
tions, includingnatB(21.7%^10 Band78.3%^11 B),
enriched (99.3%)^10 B, enriched (99.2%)^11 B,
and a roughly equal mix of^10 B and^11 B(eqB,
53.1%^10 B and 46.9%^11 B). The cnatBN crystals
were obtained by means of a conventional
process by using commercial hexagonal boron
nitride (hBN, withnatB) crystals as a starting
material ( 20 – 22 ). Because no boron isotope–
controlled hBN crystals were commercially
available, we grew the other cBN crystals with
a metathesis reaction of NamBH 4 +NH 4 Cl un-
der high pressure, wheremBis^10 Bor^11 B( 22 ).
By controlling the mixing ratio of Na^10 BH 4
and Na^11 BH 4 , we achieved the desired boron
isotope ratios. We obtained nearly colorless
cnatBN crystals with the conventional process,
whereas the isotope-controlled cBN crystals
from the metathesis reaction generally were
a light amber color (Fig. 1A and fig. S1). We
made single-crystal x-ray diffraction (XRD)
measurements on a c^10 BN sample (Fig. 1B and
fig. S1) and found a cubic structure with the
F 43 mspace group with a refined lattice con-
stant of 3.6165 ± 0.0005 Å, which is in good
agreement with literature values ( 5 ). We ob-
served peaks corresponding to different crystal-
lographic directions, indicating the presence
of multiple crystallites ( 22 ). We measured the
isotope compositions of the cBN crystals using
time-of-flight secondary ion mass spectrome-
try (TOF-SIMS) (Fig. 1C). We also character-
ized impurities using TOF-SIMS (fig. S2) and
found that they mainly consisted of carbon
and oxygen, which is consistent with previ-
ous results ( 21 ). In addition, we used Raman
RESEARCH
Chenet al.,Science 367 , 555–559 (2020) 31 January 2020 1of5
(^1) Department of Mechanical Engineering, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA.
(^2) Department of Physics, Boston College, Chestnut Hill, MA
02467, USA.^3 Department of Materials Science and
Engineering and Materials Research Laboratory, University of
Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
(^4) Materials Science and Engineering Program, Texas Materials
Institute, The University of Texas at Austin, Austin, TX 78712,
USA.^5 Department of Physics and Texas Center for
Superconductivity, University of Houston, Houston, TX
77204, USA.^6 Department of Physics, The University of
Texas at Dallas, Richardson, TX 75080, USA.^7 National
Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki
305-0044, Japan.^8 Department of Mechanical Engineering,
The University of Texas at Austin, Austin, TX 78712, USA.
*These authors contributed equally to this work.
†Corresponding author. Email: [email protected] (B.S.);
[email protected] (D.B.); [email protected] (G.C.)‡Present address:
Department of Energy and Resources Engineering, and Beijing
Innovation Center for Engineering Science and Advanced Technol-
ogy, Peking University, Beijing 100871, China. §Present address:
Lawrence Berkeley National Laboratory, and Department of
Mechanical Engineering, University of California, Berkeley, CA 94720,
USA. ¶Present address: Department of Electrical and Computer
Engineering, University of California, Riverside, CA 92521, USA.