Anisotropic in-plane thermal conductivity of black phosphorus nanoribbons at temperatures higher than 100 K

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Received 24 Apr 2015 | Accepted 7 Sep 2015 | Published 16 Oct 2015 DOI: 10.1038/ncomms9573 OPEN
## Anisotropic in-plane thermal conductivity of black phosphorus nanoribbons at temperatures higher than 100 K

Sangwook Lee 1, - ,w, Fan Yang 2, *, Joonki Suh 1, Sijie Yang 3, Yeonbae Lee 1, Guo Li 2, Hwan Sung Choe 1, Aslihan Suslu 3,
Yabin Chen 1, Changhyun Ko 1, Joonsuk Park 4, Kai Liu 1,2, Jingbo Li 5, Kedar Hippalgaonkar 6, Jeffrey J. Urban 2,
Sefaattin Tongay 3 & Junqiao Wu 1,2

Black phosphorus attracts enormous attention as a promising layered material for electronic,

optoelectronic and thermoelectric applications. Here we report large anisotropy in in-plane

thermal conductivity of single-crystal black phosphorus nanoribbons along the zigzag and

armchair lattice directions at variable temperatures. Thermal conductivity measurements

were carried out under the condition of steady-state longitudinal heat flow using suspended
pad micro-devices. We discovered increasing thermal conductivity anisotropy, up to a factor

of two, with temperatures above 100 K. A size effect in thermal conductivity was also

observed in which thinner nanoribbons show lower thermal conductivity. Analysed with the

relaxation time approximation model using phonon dispersions obtained based on density

function perturbation theory, the high anisotropy is attributed mainly to direction-dependent

phonon dispersion and partially to phonon–phonon scattering. Our results revealing the

intrinsic, orientation-dependent thermal conductivity of black phosphorus are useful for

designing devices, as well as understanding fundamental physical properties of layered

materials.

1 Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA. 2 Materials Sciences Division, Lawrence
Berkeley National Laboratory, Berkeley, California 94720, USA. 3 School for Engineering of Matter, Transport, and Energy, Arizona State University, Tempe,
Arizona 85287, USA. 4 Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA. 5 State Key Laboratory of
Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China. 6 Institute of Materials Research and
Engineering, A*STAR (Agency for Science, Technology and Research), 3 Research Link, Singapore 117602, Singapore. * These authors contributed equally to
this work. w Present address: School of Materials Science and Engineering, Kyungpook National University, Daegu 41566, Korea. Correspondence and requests
for materials should be addressed to J.W. (email: [wuj@berkeley.edu).](mailto:wuj@berkeley.edu)

hermal transport in nanoscale materials attracts increasing
research attention because of both intriguing phonon
physics at the nanoscale as well as growing importance of
# T
heat management in nanoscale devices. Especially, layered
nanomaterials provide a new platform for fundamental study,
such as two-dimensional electronic effects at the mono- or
few-layer limit 1,2, as well as device applications derived from
their high flexibility and van der Waals nature of interlayer
coupling 3–6 . It is well known that thermal conductivity in these
layered nanomaterials is much lower along the cross-plane
direction than the in-plane direction 7–10 . It is also theoretically
predicted that additional anisotropy may exist in their
thermal conductivity along different lattice directions in the
basal plane 11–17 . Recent theoretical studies on few-layer graphene
nanoribbons expect anisotropic phonon transport along the
zigzag (ZZ) and armchair (AC) lattice directions of its
honeycomb structure. This anisotropy is not expected in the
bulk 11,12,17, because it arises mainly from different strengths of
boundary scattering at the nanoribbon edges with different
chiralities 11,17, that is, specular scattering at the ZZ edge while
angle-dependent scattering at the AC edge 17, an effect that is
reduced with increasing nanoribbon width as the material
approaches the bulk. However, experimental demonstration of
such in-plane anisotropy of thermal conductivity in thin layered
materials is lacking, due mostly to technical challenges in sample
preparation and measurements.

On the materials side, a new member, black phosphorus (BP),
recently joins the family of layered nanomaterials as a promising
candidate for electronic, optical and optoelectronic applications.
BP has been shown to have some remarkable properties
compared with other two-dimensional materials, such as high
hole mobility (B1,000 cm 2 V � 1 s � 1 in field-effect transistors) 6,18,19 and tunable direct bandgap from 0.3 eV (bulk) to
41.4 eV (monolayer) 20–23 . In addition, BP is considered to be a
potentially good thermoelectric material 24–27 . It has been
theoretically predicted that BP has opposite anisotropy in
thermal and electrical conductivities: electrical conductivity is
higher along the AC direction, while thermal conductivity is
higher along the ZZ direction 24,25,28–30 . The anisotropic in-plane

thermal transport in BP, in stark contrast to few-layer graphene,
is believed to be an intrinsic property 28–31, that is, caused by
anisotropic phonon dispersion and phonon–phonon scattering
rate along the ZZ and the puckered AC directions (Fig. 1a).
Therefore, the anisotropy exists not only in the monolayer limit
or ribbons but also in multilayer or bulk BP. However,
experimental demonstration of this intrinsically anisotropic
thermal transport is lacking, owing mostly to the highly
preferential growth of single-crystal BP only along the ZZ
direction. There exists only one report on the directional thermal
conductivity of BP, which was measured at room temperature by
Raman thermography 32 .

In this work, we directly measured the in-plane thermal
conductivity of single-crystal BP nanoribbons along the ZZ and
AC lattice directions. The measurements were carried out in the
condition of steady-state longitudinal heat flow, using suspendedpad micro-devices (Fig. 1b), over a wide temperature range from
30 to 350 K. Our results reveal a high anisotropy in thermal
conductivity up to a factor of two at temperatures greater than
B 100 K. The high anisotropy is attributed mainly to the
anisotropic phonon dispersion, and partially to the phonon–
phonon scattering. A size effect in the thermal conductivity was
also observed from B50- to B 300-nm-thick BP nanoribbons in
which thinner nanoribbons show lower thermal conductivity.
These discoveries not only shed light on phonon physics in this
interesting material but also provide important design guidelines
in its device applications.

Results
Synthesis and characterization of BP crystals. BP bulk
crystals were synthesized following a well-developed process, as
described in Supplementary Note 1. The synthesized bulk BP
(Supplementary Fig. 1a, inset) is comprised of bundles of long
crystallites. Powder X-ray diffraction taken from exfoliated BP
flakes on a slide glass confirms orthorhombic (Cmca) crystal
structure (Supplementary Fig. 1b,c) 33 without any other phases.
Energy dispersive X-ray spectroscopic elemental analysis
(Supplementary Fig. 1d) shows only phosphorous element from

Ag2

b BP e
nanoribbon

Suspended
pads

(002)
(200)

Laser // AC

B2g

Laser // ZZ

350 400 450 500

Raman shift (cm –1 )

Figure 1 | Crystal structure of BP and device structure for the thermal transport experiment. (a) Illustration of the crystal structure of BP showing the ZZ
and AC axes. ZZ and AC axes correspond to the [100] and [001] direction of the orthorhombic unit cell, respectively (Supplementary Fig. 1a). (b) Scanning
electron microscopic image of a micro-device consisting of two suspended pads and a bridging BP nanoribbon. Thermal conductivity is measured by
transporting heat from the Joule-heated pad to the other pad through the nanoribbon. (c) High-resolution transmission electron microscopy lattice image
of a BP flake. (d) Selected area electron diffraction pattern taken from the area shown in c. (e) Micro-Raman spectra of a BP flake with laser polarized in
parallel to the ZZ and AC axis, respectively. Scale bars, 50 mm (b); 10 nm (c); 20 nm � 1 (d).

the crystals. The X-ray diffraction shows exclusively the planes
oriented to the [010] direction, proving the layered nature of the
crystals. Exfoliated BP flakes were also analysed using a highresolution transmission electron microscopy with the [010] zone
axis (out-of-plane direction), as shown in Fig. 1c. Each flake has
identical lattice structure with identical selected area electron
diffraction pattern showing the ZZ and AC planes (Fig. 1d),
confirming that each flake is a single crystal. The crystallographic
orientations agree well with Raman analysis, which utilizes
intensity ratio between the Raman peaks of Ag 1 and Ag 2 phonon
modes (Fig. 1e). It is well known that the intensity ratio of the Ag 2
mode to the Ag 1 mode is the maximum when the laser is polarized
in parallel to the AC direction, because the Ag 1 and Ag 2 modes
correspond to atomic vibration along the [010] (out of plane) and

[001] (AC, in-plane) directions, respectively 19,34 .

Preparation of BP nanoribbons and suspended-pad micro-devices.
The thermal conductivity of BP was measured by a steady-state
longitudinal heat flow method, using suspended-pad micro-devices

as described in Supplementary Note 2 with Supplementary Figs 2–3,
as well as in previous reports 35,36 . Each pad has two Pt electrodes for
four-probe electrical conduction measurements, and a Pt microheater/thermometer to control/sense the temperature for thermal
conduction measurements. To make BP nanoribbons with proper
geometries to bridge the two suspended pads, a top–down microfabrication process was used as shown in Fig. 2a–e. First, crystal
orientation of BP flakes was identified using Raman analysis; they
were then micro-patterned into nanoribbons with desired widths and
lengths using electron beam lithography (EBL) and followed by
reactive ion etching (see the Method section). Afterwards, a second
EBL was applied to define four openings on each BP nanoribbon,
followed by in situ Ar þ milling and Ti/Au deposition with electron
beam evaporation. The Ar þ milling is essential to remove the
surface oxidized layer, which is well known to quickly form when BP
is exposed to ambient air. Very mild milling to remove o1nm of the
BP surface was sufficient to obtain a good thermal/electrical contact
between the contact metal and the BP nanoribbons. Such contactready BP nanoribbons were manually, individually picked up using a
sharp probe tip with the aid of a micro-manipulator 37, and dry

a
Exfoliated BP

BP flake

b c
1 st lithography Dry etching/PMMA removal

BP
PMMA
Substrate NRs

e Transfer/FIB Pt deposition

d
2 nd lithography/Ar + milling/deposition

Electrodes
BP NRs

Suspended pads

f 2.5 g

Transfer
using a sharp tip

–5

Ti/Au

2.0

1.5

1.0

0.5

0.0
0 5 10 15 20

Length (µm)

–10
–4 –2 0 2 4

Voltage (mV)

Figure 2 | Preparation of BP nanoribbons and nanoribbon-bridged micro-devices. (a–e) Illustration of the fabrication process. (a) Exfoliation of BP flakes
onto a SiO2 substrate. Crystal directions are identified by Raman analysis. (b) Formation of PMMA stripes on the BP flake by the first electron beam
lithography (EBL). (c) Removal of the exposed BP by dry etching, and removal of the PMMA protecting stripes with acetone, to form BP nanoribbons (NRs).
(d) Opening up the contact area via the second EBL, Ar þ milling of the exposed contact area and electron beam deposition of Ti/Au and lift-off. The Ti/Au
layer offers good thermal/electrical contact with BP nanoribbon. Inset shows optical image of BP nanoribbons coated with four Ti/Au contacts resting on
the SiO2 substrate. (e) Dry transfer of a BP nanoribbon onto the micro-device to bridge two suspended pads, and connection of the Ti/Au to the metal
electrodes on the pads using FIB Pt bonding. (f) Plot of total thermal resistance (1/K) at room temperature multiplied by cross-sectional area (A) as a
function of the nanoribbon length. Error bars include the errors (B8%) from thermal conductance and sample size measurements. These ribbons have
similar thicknesses. The linear relationship extrapolating to nearly zero indicates negligible thermal contact resistance for both ZZ and AC oriented
nanoribbons. (g) Linear electrical current–voltage curves of the ZZ and AC oriented nanoribbons, measured on the micro-devices. All the measured devices
(six devices) show linear I–V curves.

transferred onto a suspended-pad micro-device, with careful
alignment of the four Ti/Au metal contacts to the four electrodes
on the pads. The aligned nanoribbon was subsequently bonded to the
electrodes with Pt deposition using a focused ion beam (FIB).
Microscopic images for a target BP flake before and after the
micro-patterning, and nanoribbons before and after the metal
(Ti/Au and Pt) deposition are shown in Supplementary Fig. 4. We
note that direct FIB deposition of Pt on the BP, without the
pre-formed Ti/Au metal contacts, failed to yield good electrical
contacts. To minimize possible damage by the FIB, the Pt deposition
was conducted only for connecting the Ti/Au metal contacts to the
device electrodes, rather than covering and bonding the entire
nanoribbon onto the electrodes. Between each step of the fabrication
processes, the BP samples were stored in dry N2 atmosphere to
maximally prevent surface oxidation. Accumulated time period of
exposure to ambient air during the entire fabrication process was
estimated to be o15min, which warrants minimum oxidation of the
BP surface, as evidenced by the nano-Auger electron spectroscopic
surface analysis (Supplementary Fig. 5). All the thermal and electrical
measurements were performed in vacuum (o10 � 6 torr). Figure 2f
shows the measured thermal resistance as a function of the length of
the BP nanoribbons. The linear fitting and extrapolation yield
negligible contact thermal resistance (y intercept) between the
nanoribbon and the suspended pads for both the ZZ and AC
oriented ribbons. Moreover, the Ti/Au/Pt layers make good
Ohmic electrical contacts with the nanoribbons, as evidenced by
the linear I–V curves (Fig. 2g).

Thermal conductivity of BP nanoribbons. We first note that
the measured total thermal conductivity (k) in this study is
dominated by the lattice (phonon) contribution. Electronic
contribution to the thermal conductivity (ke) is estimated to be
negligible (o0.1% of total) in the measured temperature range.
This is calculated from the electrical conductivity (s) measured
with four-probe I–V and converted using the Wiedemann–Franz
law, ke ¼ L0sT, where L0 is the Sommerfeld value of the Lorenz
number (Supplementary Fig. 6). We also note that our device
geometry and configuration guarantee that the electrical and
thermal currents flow along the same crystal direction in the
material along the nanoribbon length, which is important to
apply the Wiedemann–Franz law.

The measured k along the ZZ and AC crystal orientations is
compared with each other in Fig. 3a using ZZ and AC

is used, where B1 and B2 are fitting parameters and - is phonon
frequency. For the impurity scattering, the Klemens’ expression
ti � 1 ¼ Aio 4 is used, where Ai is a parameter that can also be

nanoribbons with the same thickness and similar widths
(o10% difference). It is evident that the ZZ nanoribbon
has a higher k than the AC nanoribbon, by as much as
B7 Wm � 1 K � 1 at temperatures above B100 K, while both have
similar k at lower temperatures between 30 and 100 K. The
anisotropy in k, that is, the ratio of k along the ZZ and AC
directions, increases with temperature, reaching up to B2 at
B300 K. The increasing anisotropy ratio is attributed to increased
contribution from phonon–phonon (Umklapp) scattering,
which becomes the dominating scattering mechanism at high
temperatures.

The temperature dependency is also observed from other BP
nanoribbons that have different dimensions, as shown in
Fig. 3b,c. To investigate the anisotropic effect of phonon
scattering on the thermal transport in the high-temperature
regime, we evaluate scattering times using the relaxation time
approximation model with phonon dispersions obtained using
the force constants calculated from density function perturbation
theory, as detailed in the Methods part and Supplementary Note
3. The branch-dependent group velocities are extracted from the
phonon dispersions (Supplementary Fig. 7). The sound velocities
are summarized in Supplementary Table 1.

In general, the lattice k along the temperature gradient
direction can be expressed as 38

cqðuq � ^ tÞ 2 tq; ð1Þ

k ¼

where cq is the specific heat contributed by the mode with the
wavevector q, u is phonon group velocity, ^ t is the unit vector in
the direction of temperature gradient, t is the phonon relaxation
time and the summation is over the first Brillouin zone of all q
modes.

Total effects of the phonon–phonon scattering, impurity
scattering and boundary scattering are commonly summed up
by the Matthiessen’s rule, t � 1 ¼ tu � 1 þ ti � 1 þ tbd � 1. For the

phonon–phonon relaxation time (tu), the common expression 39,40

u � 1 þ ti � 1

i � 1 þ tbd � 1

u � 1 ¼ B1o 2 T exp - B T 2

tu � 1

-
 - B2 ð2Þ

a b 50 c

ZZ
AC

_t_ = 170 nm _t_ = 170 nm ZZ _t_ = 170 nm AC

40 310 nm 40 270 nm

Fit 10
Fit

0 100 200 300 400 10 1 10 2 10 3 10 1 10 2 10 3

_T_ (K) _T_ (K) _T_ (K)

Figure 3 | Temperature-dependent thermal conductivity of BP nanoribbons. (a) Thermal conductivity (k) versus temperature (T) plot of BP nanoribbons
axially oriented to the ZZ and AC directions, respectively. Thickness (t)/width (W) of the ZZ and AC nanoribbons are 170/540 nm and 170/590 nm,
respectively. Error bars include the errors (B8%) from thermal conductance and sample size measurements. (b) k versus T plots (on logarithmic scale) of
ZZ nanoribbons with different dimensions; 170 (t)/540 nm (W) and 310 (t)/540 nm nm (W). (c) k versus T plots (on logarithmic scale) of AC nanoribbons
with different dimensions; 170 (t)/590 nm (W) and 270 (t)/420 nm (W). The solid lines in b and c are fitted lines by taking into account various phonon
scattering mechanisms (phonon–phonon, impurity and boundary). Lengths of the nanoribbons all exceed 10 mm.

evaluated from the density and species of impurities (generally
point defects including native defects such as vacancies and
interstitials) 41 . The boundary scattering is determined by a
characteristic size and surface roughness of the specimen.

The unknown scattering parameters are usually obtained
from fitting k of the bulk, but the bulk k of BP specifically
along the ZZ or AC direction has not been reported. Therefore,
we first obtain these parameters by fitting k of the nanoribbon
with the largest thicknesses in our measurements. This
corresponds to 310- and 270-nm thick for the ZZ and AC,
respectively. The fitting is validated by the fact that in fitting to
the measured k of thinner nanoribbons, good agreements can be
obtained by fixing the Ai, B1 and B2 at the same values and
adjusting only the boundary size Lbdð¼ u�tbdÞ for the thinner
ribbons, as shown in Fig. 3b,c. We obtain the following
best-fit parameters: B1,ZZ ¼ 5.1 � 10 � 19 sK � 1, B2,ZZ ¼ 326 K
and Ai,ZZ ¼ 1.0 � 10 � 43 s 3 for ZZ nanoribbons, and B1,AC ¼ 7.8

- 10 � 19 sK � 1, B2,AC ¼ 390 K and Ai,AC ¼ 1.0 � 10 � 43 s 3 for AC
nanoribbons. Among these, the anharmonicity parameter B1,
which is the important parameter at high temperatures, is
discussed in the next section. Discussion of the other parameters
is presented in Supplementary Note 3.

The minimum flake thickness suitable for our fabrication
process is B50 nm due to challenges in dry transferring the
ultrathin ribbons. BP nanoribbons thinner than 50 nm were not
able to be picked up, due to limitation in the sharpness of probe
tip. Figure 4 plots room temperature k of the BP nanoribbons as a
function of ribbon thickness. k shows a clear thickness
dependence along both ZZ and AC directions, decreasing
from B27 to B12 Wm � 1 K � 1 in ZZ, and from B15 to
B5 Wm � 1 K � 1 in the AC direction, as the thickness
varying from B300 to B50 nm. The anisotropy of k is about 2
over this thickness range. The thickness dependence implies that
in this thickness range, surface or boundary scattering is effective
even at such a high temperature. The k values measured in this
study may differ from predicted k of few-layer BP, due to
different heat transport factors, such as evolution of flexural (ZA,
out of plane) phonon mode, or more specular boundary
scattering with smooth surface in theoretical simulations of
few-layer BP. However, the k anisotropy, that is, larger k along
the ZZ direction than the AC direction, is in agreement with
predictions of monolayer (or few layer) BP. For an example, a
recent theoretical work predicts k B110 and B36 Wm � 1 K � 1
at room temperature along the ZZ and the AC direction in
monolayer BP 31 .

ZZ

0
0 100 200 300

Thickness, _t_ (nm)

Figure 4 | Thickness and orientation-dependent thermal conductivity of
BP nanoribbons. Thermal conductivity of ZZ and AC nanoribbons, at
300 K, as a function of thickness. Error bars include the errors (B8%) from
thermal conductance and sample size measurements. The lines show linear
fitting of the data to guide the eye.

Discussion
Compared with the k (B12 Wm � 1 K � 1 at 293 K) of bulk BP
reported by Slack in 1965 (ref. 42), our thickest samples have
slightly higher values. This is understandable given the fact that
their bulk BP was polycrystalline, which can significantly reduce k
by grain boundary scattering, cross-layer scattering and averaging
of the anisotropy. The crystallite size of the bulk in that work,
obtained from fitting to the temperature dependent k below 10 K,
is only 10% of the visual crystallite size of the crystal. Therefore, it
is reasonable that our thick crystal BP nanoribbons have a higher
k. We note that the absolute value of k measured in our study
also can be different from a BP single crystal due to possible
damage caused during the device fabrication process 43 .

At high temperatures, most acoustic phonon states are excited,
which leads to the saturation of specific heat at the Dulong–Petit
limit. If the phonon–phonon scattering rate is the same
(scattering rate difference will be discussed later), k / u 2 . Thus,
k in ZZ direction is higher than AC direction (Fig. 3a) due to the
higher group velocities (Supplementary Table 1). If we compare
the group velocities of TA1 modes (uTA1; ZZ ¼ 2,126 m s � 1 and
uTA1; AC ¼ 1,567 m s � 1, which are close to the results from
ultrasonic experiments in literature 44 ), we obtain a k
anisotropic ratio of 1.85, which is close to our experimental
result of B2 at high temperatures.

When the temperature drops below 100 K, k becomes close to
each other and has a crossover at B40 K. The main physical
picture for this crossover is freezing out of phonons when
temperature drops 45 . At the low-temperature limit, the excited
phonon wavevectors (q) are small, where the Debye
approximation is valid such that j q j - o=u. Comparing the
same phonon branch in the ZZ direction to that in the AC
direction, the group velocities are all higher in the ZZ direction.
Thus, when counting the phonon states in reciprocal q-space, the
higher group velocity would lead to lower density of states in ZZ
direction. Thus, k in the ZZ direction could possibly be lower
than k in the AC direction. Thus, in the intermediate
temperature, such as between 30 and 75 K, there is a transition
regime that the thermal conductivities are close to each other
along these two directions.

To investigate which phonons contribute the most to the heat
conduction, we evaluated the contributions of two TA branches
(out-of-plane TA1, and in-plane TA2) and LA branch in the
170-nm-thick nanoribbons. We find that the TA1 mode
contributes the most to the heat conduction among the three
acoustic modes. It contributes 53% (48%) of the total k of
19.0 Wm � 1 K � 1 (13.5 Wm � 1 K � 1 ) in the ZZ (AC) nanoribbon
(Supplementary Table 2). The TA2 mode and LA mode
contribute 24% (19%) and 23% (33%), respectively, to the total
k in the ZZ (AC) direction for these nanoribbons. In addition, k
of TA1 and TA2 branches in the ZZ direction are B1.6 and B1.8
times of those in the AC direction, respectively, which contributes
significant to the anisotropy.

The phonon–phonon scattering, which is the dominant
scattering mechanism at high temperatures, are compared by
calculating the tu in ZZ and AC directions using the fit
parameters. From equation (2), tu, ZZ is B1.25 times of tu, AC
at room temperature for the identical phonon frequency.
Therefore, the different phonon–phonon scattering also contributes in part to the k anisotropy. However, compared with the
difference caused by the group velocities (that is,
ðu u TA1 TA1 ; ; AC ZZ ~~Þ~~ 2 � 1:85, Supplementary Table 1), the difference in tu

is small. Therefore, we attribute the high anisotropy in k mostly
to the anisotropic phonon dispersion, and partially to the
anisotropic phonon–phonon scattering. In addition, it would
also be interesting to know the anharmonic difference, such as the
Gru¨neisen number (g). In general, the anharmonic parameter B1

is given by B1 - M‘ug 22 y (ref. 39), where M is the average mass of
atoms in the crystal, and y is the Debye temperature, which is
proportional to group velocity u. As only g and u are directionsensitive parameters, the ratio of B1,ZZ and B1,AC is
BB11;; AC ZZ �ð g g AC ZZ ~~Þ~~ 2 ~~ð~~ u u AC ZZ ~~Þ~~ 3, where uZZ and uAC are the group velocities

BB11;; AC ZZ �ð g g AC ZZ ~~Þ~~ 2 ~~ð~~ u u AC ZZ ~~Þ~~ 3, where uZZ and uAC are the group velocities

in ZZ and AC directions. Using the extracted group velocities of
TA1 modes ~~(~~ u u TA1 TA1 ; ; AC ZZ � 1:36) from the calculated dispersion (the

TA1 branch that contributes the most to total k), we obtain
ggACZZ � 1:90. To the best of our knowledge, this is the first
experimental evidence of orientation-dependent anharmonicity
in BP.

Due to the relevance of BP for thermoelectrics, we have also
measured electrical conductivity (s) and Seebeck coefficient (S)
along the AC and the ZZ directions, as presented in
Supplementary Fig. 8. The room temperature Seebeck coefficients
in the AC and ZZ directions are B320 and B270 mV K � 1
(p-type conductivity), and close to that of the bulk
(B330 mV K � 1 ) 26,46 . The power factor ( ¼ S 2 s) of the AC
nanoribbon is three times larger than that of the ZZ
nanoribbon. ZT ( ¼ S 2 sT/k) of the AC nanoribbon (t ¼ 170 nm)
and the ZZ nanoribbon (t ¼ 200 nm) are B0.0036 and B0.0006,
respectively, at room temperature. This low ZT is obviously due
to the relatively high k (single-crystalline samples) and low s
(undoped samples).

In summary, we discovered a strong in-plane anisotropy in
thermal conductivity, up to a factor of two, along the ZZ and AC
directions of single-crystal black phosphorous. The BP was
prepared in the nanoribbon geometry via a top–down microfabrication and the measurements were performed with steadystate longitudinal heat flow using suspended-pad micro-devices.
At 300 K, the thermal conductivity decreases as the nanoribbon
thickness is reduced from B300 to B50 nm, but the anisotropy
ratio stays around two within the thickness range. Detailed
analysis from the relaxation time approximation model shows
that the anisotropy in the thermal conductivity originates mostly
from phonon dispersion, and partially from phonon–phonon
scattering rate, that are both orientation dependent. Our results
reveal the intrinsic, orientation-dependent thermal conductivity
of BP, which would be important for developing highperformance electronic, optoelectronic and thermoelectric devices
using BP, as well as for understanding fundamental physical
properties of layered materials approaching the few- or monolayer limit.

Methods
Materials preparation and characterization. BP bulk crystals were synthesized
from red phosphorus powders with SnI4 (American Elements, electronic grade
99.995%) and Sn ingot (Sigma Aldrich) promoters. Please see Supplementary Note
1 for more details. BP flakes were mechanically exfoliated from the synthesized BP
bulk crystal, and transferred onto SiO2 substrates, using a polydimethylsiloxane
stamp (thickness: 1 cm). The morphology and size, crystal structure, composition,
phase and crystal orientation of BP flakes were characterized by optical microscopy, SEM, X-ray diffraction, TEM, Energy dispersive X-ray spectroscopic, Auger
electron spectroscopic and Raman spectroscopy (with 488 nm laser). For the TEM
analysis, selected flakes were transferred from the SiO2 substrate to TEM grid using
a sharp probe tip by the aid of a micromanipulator.

Device fabrication for thermal transport experiments. The fabrication of the BP
nanoribbons with Ti/Au metal contacts are well described in the main text
(Fig. 2a–e). We use the term nanoribbon based on the geometry of the BP samples.
For each EBL, PMMA (C4 950) was spin-coated (4,000 r.p.m., 1 min) onto the BP
flakes (on SiO2 substrate), and baked at 120 �C for 5 min. After the first EBL, dry
etching to remove the exposed BP stripes was conducted via reactive ion etching
(in mixed gas, 90% SF6 and 10% O2). The Ti/Au metal was deposited via in situ
Ar þ milling and Ti (10 nm)/Au (70 nm) deposition via electron beam evaporation.
Lift-off process was conducted with a gentle shaking in acetone, to avoid fracture of
nanoribbons. The final nanoribbons were rinsed thoroughly using isopropyl
alcohol.

g g AC ZZ ~~Þ~~ 2 ~~ð~~ u u AC ZZ

Suspended-pad micro-devices were used to simultaneously measure the thermal
and electrical transport properties of the nanoribbons. Pt lines were patterned on
SiNx based, suspended pads and flexural arms. Each pad has two arms to measure
the electrical conductance of the nanoribbon bridging the two pads, and four arms
to measure the electrical conductance of pre-patterned Pt micro-heater/
thermometers on the pads for thermal conductivity measurements. A prepared
nanoribbon was transferred to bridge the suspended pads using a sharp probe tip.
Pt/C composite was deposited using FIB to bond the Ti/Au coat of the nanoribbon
onto the Pt electrode lines for securing the thermal and electrical contacts. To
further secure the contacts, the devices were annealed at B370 K for 1 h in vacuum
chamber before measurements. To minimize the surface oxidation, all the pristine
and fabricated BP samples were stored in a desiccator in dry nitrogen stream with
over pressure.

Density functional theory calculation for phonon dispersion. To obtain the
phonon dispersion of black phosphorous, we first calculate its atomic structure and
the Hessian matrix using the Vienna ab initio simulation package 47,48 . The
projector augmented-wave potentials are used for the ion-electron interactions 49,50,
the optB88-vdW exchange-correlation potential is adopted to include long-range
dispersion forces 51,52, and the energy cutoff is set to 350 eV. In the density
functional theory calculation of the bulk structure, a 10 � 14 � 4 k-mesh is used,
and the coordinates are fully relaxed until the forces at each atom are
o0.001 eV Å � 1 . The calculated lattice constants of the conventional cell are
a ¼ 4.348, b ¼ 3.329 and c ¼ 10.495 Å, respectively, consistent with experimental
values 53 . In the following density functional perturbation theory calculation 54, the
Hessian matrix is calculated with a 3 � 3 � 3 supercell of the primitive cell and a
5 � 4 � 3 k-mesh. On the basis of this Hessian matrix, we extract the force
constants and calculate the phonon dispersion using Phonopy 55 .

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Acknowledgements
This work was supported by the US Department of Energy Early Career Award
DE-FG02-11ER46796. J.W. acknowledges support from the Tsinghua-Berkeley Fund.
S.T. acknowledges ASU start-up funding and Origami Engineering Initiative Seeding
funding. C. K., J. J. U and F. Y. acknowledge the Molecular Foundry supported by the
Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under
Contract No. DE-AC02-05CH11231. Part of the materials processing and characterization used facilities in the Electronic Materials Program at the Lawrence Berkeley National
Laboratory, which is supported by the Office of Science, Office of Basic Energy Sciences,
of the US Department of Energy under Contract No. DE-AC02-05CH11231. We thank
Dr D. Frank Ogletree for technical assistance in nano-Auger analysis, and Professor
Baowen Li and Alan McGaughey for helpful discussion.

Author contributions
J.W. and S.T. conceived the project, S.L. performed the thermal and electrical measurements, F.Y., G.L. and S.L. performed computational analysis, S.L. and Y.L. set up the
thermal and electrical measurement system, S.L., S.J., Y.C. and K.L. fabricated the devices,
H.S.C. fabricated the suspended-pad micro-devices, S.Y., and A.S. synthesized the
materials, C.K. performed the Auger electron spectroscopic, J.P. performed TEM, F.Y.,
G.L., J.L., K.H. and J.J.U. helped with data analysis and theoretical understanding, and
S.L., F.Y. and J.W. wrote the manuscript.

Additional information
Supplementary Information accompanies this paper at [http://www.nature.com/](http://www.nature.com/naturecommunications)
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Competing financial interests: The authors declare no competing financial interests.

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How to cite this article: Lee, S. et al. Anisotropic in-plane thermal conductivity of
black phosphorus nanoribbons at temperatures higher than 100K. Nat. Commun. 6:8573
doi: 10.1038/ncomms9573 (2015).

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