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Communication
Spatial-temporal imaging of anisotropic
photocarrier dynamics in black phosphorus
Bolin Liao, Huan Zhao, Ebrahim Najafi, Xiaodong Yan, He Tian,
Jesse Tice, Austin J. Minnich, Han Wang, and Ahmed H Zewail
Nano Lett.
,
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Spatial-Temporal Imaging of Anisotropic Photocarrie
r Dynamics in Black
Phosphorus
Bolin Liao
1,2
⊥
, Huan Zhao
3
⊥
, Ebrahim Najafi
1
, Xiaodong Yan
3
, He Tian
3
, Jesse Tice
4
,
Austin J. Minnich
2,5
*, Han Wang
3
* and Ahmed H. Zewail
1,2§
1
Division of Chemistry and Chemical Engineering, Cal
ifornia Institute of Technology,
Pasadena, CA 91125, USA
2
Kavli Nanoscience Institute, California Institute o
f Technology, Pasadena, CA 91125
3
Ming Hsieh Department of Electrical Engineering, Un
iversity of Southern California,
Los Angeles, CA 90089, USA
4
NG Next, Northrop Grumman, 1 Space Park, Redondo Be
ach, CA 90278, USA
5
Division of Engineering and Applied Science, Califo
rnia Institute of Technology,
Pasadena, CA 91125, USA
As an emerging single elemental layered material wi
th a low symmetry in-plane
crystal lattice, black phosphorus (BP) has attracte
d significant research interest
owing to its unique electronic and optoelectronic p
roperties, including its widely
tunable bandgap, polarization dependent photorespon
se and highly anisotropic in-
plane charge transport. Despite extensive study of
the steady-state charge transport
in BP, there has not been direct characterization a
nd visualization of the hot
carriers dynamics in BP immediately after photoexci
tation, which is crucial to
understanding the performance of BP-based optoelect
ronic devices. Here we use the
newly developed scanning ultrafast electron microsc
opy (SUEM) to directly
visualize the motion of photo-excited hot carriers
on the surface of BP in both space
and time. W
e observe highly anisotropic in-plane diffusion of
hot holes, with a 15-
times higher diffusivity along the armchair (x-) di
rection than that along the zigzag
(y-) direction. Our results provide direct evidence
of anisotropic hot carrier
transport in BP and demonstrate the capability of S
UEM to resolve ultrafast hot
carrier dynamics in layered two-dimensional materia
ls.
Keywords: Black Phosphorus, Anisotropy, Hot Carrier
Dynamics, Ultrafast
Electron Microscopy
⊥
These authors contributed equally.
*To whom correspondence should be addressed:
han.wang.4@usc.edu
(H.W.),
aminnich@caltech.edu
(A.J.M.)
§
Deceased
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With a widely tunable band gap from 0.3 eV in its b
ulk form to above 1.3 eV as a
single layer, black phosphorus (BP)
1–6
has recently emerged as a promising candidate
material for infrared optoelectronic applications
7–9
, due to its highly tunable and
customizable electronic and optical properties
10–14
. In addition, the relatively high charge
mobility of BP adds to its attractiveness for appli
cations that require efficient charge
transport
15
. One of the most intriguing features of BP, howeve
r, is its strong inGplane
anisotropy
3,4,16
, originating from the lowGsymmetry puckered orthor
hombic lattice
structure. The nearGequilibrium charge mobility alo
ng the armchair direction is known to
be higher than that along the zigzag direction, rev
ealed by both the fieldGeffect and Hall
measurements
2–4
. Due to the opposite trend in its thermal conducti
vity
17–19
,
the strong
anisotropy of BP is also believed to be promising f
or thermoelectric applications
20
.
Moreover, the inGplane anisotropy leads to strongly
polarizationGdependent optical
properties, rendering BP a suitable material for po
larizationGsensitive detectors
7,9
.
Besides nearGequilibrium transport, another importa
nt aspect of charge transport is
the dynamics of photoGexcited hot carriers relevant
to the photoGdetection and
photovoltaic applications. Due to the initial high
temperature of the photoGexcited charge
carriers, the hotGcarrier dynamics can be drastical
ly different from nearGequilibrium
transport. Therefore, a thorough understanding in t
he motion of hot electrons and holes in
BP immediately after photoGexcitation is essential
for designing and improving BPGbased
optoelectronic devices. Previous studies
21–24
exclusively utilized ultrafast optical pumpG
probe spectroscopy to investigate the transient cha
nge of absorption or transmission of
BP induced by the pumping laser pulse, from which t
he dynamics of hot carriers could be
indirectly inferred. Restricted by the optical diff
raction limit, however, optical pumpG
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probe spectroscopy lacks the spatial resolution to
directly map out the diffusion process
of photoGexcited charge carriers.
Scanning ultrafast electron microscopy (SUEM)
25,26
is a newly developed
technique that can directly image the dynamics of p
hotoGexcited carriers in both space
and time, with subGpicosecond temporal resolution a
nd nanometer spatial resolution.
Details of the setup can be found elsewhere
25–29
and are briefly summarized here (also
illustrated in Figure 1a). Compared to optical pump
Gprobe spectroscopy, SUEM is a
photonGpumpGelectronGprobe technique, with subGpico
second electron pulses generated
by illuminating a photocathode (ZrOGcoated tungsten
tip) with an ultrafast ultraviolet
(UV) laser beam (wavelength 257 nm, pulse duration
300 fs, repetition rate 5 MHz,
fluence 300 IJ/cm
2
). A typical probing electron pulse consists of ten
s to hundreds of
electrons, estimated by measuring the beam current
through a Faraday cup, and is
accelerated to 30 keV before impacting the sample.
The probing electron pulses arrive at
the sample after the optical pump pulses (wavelengt
h 515 nm, fluence 80 IJ/cm
2
) by a
given time controlled by a mechanical delay stage (
G700 ps to 3.6 ns, with 1 ps
resolution). The probing electron pulses induce the
emission of secondary electrons from
the sample, which are subsequently collected by an
EverhartGThornley detector. To form
an image, the probing electron pulses are scanned a
cross the sample surface and the
secondary electrons emitted from each location are
counted. Since the yield of secondary
electrons depends on the local average electron ene
rgy, more/less secondary electrons are
emitted from regions of the sample surface where th
ere is a net accumulation of
electrons/holes
27
. Typically a reference SEM image is taken long bef
ore the pump optical
pulse arrives and is then subtracted from images ta
ken at other delay times to remove the
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background. In the resulting “contrast images”, bri
ght/dark contrasts are observed at
places with net accumulation of electrons/holes due
to higher/lower yield of secondary
electrons. In this fashion, the dynamics of electro
ns and holes after excitation by the
optical pump pulse can be monitored in real space a
nd time
26
. An alternative way of
visualizing hot carrier dynamics in space and time
was recently demonstrated using timeG
resolved photoemission electron microscopy (TRGPEEM
)
30
.
In this letter, we demonstrate the direct imaging o
f hotGcarrier dynamics in BP
with SUEM. Due to the presence of a surface potenti
al, we observe the motion of hot
holes on the surface of BP. With SUEM, we see strik
ing visualization of anisotropic
diffusion of hot holes after photoGexcitation, from
which quantitative transport
parameters can be extracted. Our results indicate a
15Gtimes higher diffusivity of hotG
holes moving along the armchair direction than that
along the zigzag direction, which is a
combined effect of anisotropic effective mass and d
irectionGindependent electronGphonon
scattering
31
.
Figure 1b displays a static SEM image of a typical
BP flake measured in this
work. BP flakes of 80 nm thickness were mechanicall
y exfoliated from a bulk crystal,
and subsequently transferred to an ITOGcoated glass
substrate to avoid charging of the
sample. The sample is exclusively handled in an arg
on glovebox before being
immediately loaded into the SUEM vacuum chamber. Th
e arrows in Figure 1b denote the
armchair (xG) and zigzag (yG) directions of the BP
crystal, determined optically by Raman
spectroscopy
32
. PolarizationGresolved Raman spectroscopy was perf
ormed after the
SUEM measurements using a 532 nm Nd:YAG laser in th
e LabRAM ARAMIS system.
A 100× microscope objective was used and the power
incident on the BP sample was
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kept below 500 μW to avoid sample damage. Polarizat
ion resolved Raman spectroscopy
was conducted with a 532 nm laser with different sa
mple rotating angles. The
dependence of the Raman peaks intensity on the rota
tion angle of the sample basal plane
is shown in Figure 1c. The crystal orientation is d
etermined specifically from the
intensity of the
A
g
1
peak, which reaches the minimal intensity when the
laser polarization
is along armchair (xG) direction
32
.
SUEM contrast images of the BP flake shown in Figur
e 1b are presented in Figure
2. A lowGpass Gaussian filter is used to suppress t
he noise of the images for presentation,
while raw images are used for quantitative analysis
shown later. Images displayed in the
first row were taken when the flake is oriented as
shown in Figure 1b, whereas images in
the second row were taken when the flake is rotated
by 90 degree. Firstly, only dark
contrast is observed in the region of the sample ex
cited by the pump laser. The initial
shape of the excited spot is elliptical as expected
because the pump laser is incident on
the sample at an angle. Since secondary electrons a
re typically emitted only from the top
few nanometers of the sample, the observation of on
ly dark contrast indicates that the
electrons and holes are separated vertically after
photoGexcitation, and the holes are
accumulated near the sample surface while the elect
rons are drawn away from the
surface. This separation is most likely due to the
existence of a surface potential on the
BP sample (we observed the same behavior in heavily
doped nGtype silicon with SUEM
also caused by a surface potential), which arises d
ue to the formation of an atomically
thin phosphorus oxide layer
33
on the BP surface when the samples are briefly exp
osed to
air (<30 seconds) during their loading into the vac
uum chamber of the SUEM. The
vertical transport process associated with the surf
ace potential is also reflected in the
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observation that the intensity of the dark contrast
reaches a maximum around 40 ps after
the optical pump pulse arrives. At 40 ps delay time
, the profile of the spatial distribution
of holes follows approximately the shape of the pum
p beam. As the time progresses, it is
clearly observed that the holes preferentially diff
use along the armchair (xG) direction,
denoted by the orange arrow, regardless of the rela
tive orientation of the BP flake and the
optical pump beam. In this measurement the polariza
tion of the optical pump beam is not
specifically chosen. Although it is known that the
absorption of BP is strongly dependent
on the light polarization
7
, we verified experimentally that the light polariz
ation does not
affect the dynamics of the hot holes after photoGex
citation, as shown in Supplementary
Figure 2.
In addition to the direct and intuitive visualizati
on of the highly anisotropic
transport of photoGexcited hot holes in BP provided
by the SUEM contrast images in
Figure 2, numerical values of transport parameters
can be extracted through quantitative
analysis of the contrast images. A convenient param
eter to describe the spatial
distribution of particles is the variance
σ
, which in this case is angleGdependent, defined
as
σ θ
,
t
( )
=
ρ
r
,
t
( )
r
⋅
ˆ
θ
(
)
2
d
2
r
∫∫
ρ
r
,
t
( )
∫∫
d
2
r
−
ρ
r
,
t
( )
r
⋅
ˆ
θ
(
)
d
2
r
∫∫
ρ
r
,
t
( )
∫∫
d
2
r
2
,
(1)
where
ρ
r
,
t
(
)
is the local carrier concentration, and
ˆ
θ
is a unit vector pointing to a
certain angle
θ
. Here we approximate
ρ
r
,
t
(
)
with the measured local intensity
I
r
,
t
(
)
of
the SUEM contrast images, assuming a linear relatio
n between them. This assumption
should hold here since the optical excitation is we
ak and the measurement works in the
linear response regime. Figure 3a shows the calcula
ted
σ
θ
,
t
(
)
from the images at
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different delay times in the first row of Figure 2,
normalized by
σ
θ
,
t
(
)
at 40 ps. It is
clear that the variance of the spatial distribution
increases significantly along the armchair
direction, while its change along the zigzag direct
ion is hardly discernible.
In the case when the diffusivity is a constant, the
variance of the spatial
distribution should be a linear function of time. I
n the current experiment, however, the
diffusivity changes with time due to a decreasing t
emperature of the hot carriers. As a
firstGorder approximation, we assume the temperatur
e of the hot carriers decays
exponentially
T t
(
)
=
T
0
exp
−
t
τ
T
(
)
, with a time constant
τ
T
controlled mainly by
inelastic electronGphonon scatterings
34
. We further apply the Einstein relation
D
=
k
B
T
(
)
q
, where
D
is the diffusivity and
is the mobility, and argue that
D t
(
)
=
D
0
exp
−
t
/
τ
T
(
)
, where
D
0
is the diffusivity right after photoGexcitation, b
ecause
immediately after photoGexcitation, the lattice is
still cold so that the mobility limited by
electronGphonon interaction is not largely affected
. In this case the time dependence of
the variance is:
σ θ
,
t
( )
=
2
D
0
θ
( )
τ
T
1
−
exp
−
t
τ
T
+
σ
0
θ
( )
.
(2)
Fits of Eq. (2) to experimentally measured variance
s along the armchair and zigzag
directions are plotted in Figure 3b. From the fitti
ngs, the parameters can be extracted as
τ
T
≈
150 ps
,
D
0,armchair
≈
1.3
×
10
4
cm
2
s
,
D
0,zigzag
≈
870 cm
2
s
,
σ
0,armchair
≈
216.7
m
2
and
σ
0,zigzag
≈
405.8
m
2
. The ratio between the diffusivities along the two
directions is
approximately 15. This ratio is much higher than th
at measured by steadyGstate transport
experiments
4
and calculated by firstGprinciples simulations ass
uming nearGequilibrium
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transport
31
, but close to the value inferred from an optical p
umpGprobe measurement
24
.
This observation demonstrates the significant diffe
rence between hotGcarrier dynamics
and nearGequilibrium dynamics, and the fact that th
e measured hotGcarrier diffusivity ratio
is on the same order of the effective mass ratio
35
indicates that the transport of photoG
excited hot carriers is likely more affected by the
effective mass of the carriers than their
scattering properties. This can be qualitatively un
derstood in the following way: due to
the initial high temperature of the photoGexcited c
harge carriers, they carry high kinetic
energies and can travel a long distance between con
secutive electronGphonon scattering
events. In this regime, the transport process of th
e hot carriers is essentially controlled by
the velocity of the “free flight” between scatterin
g events, which in turn depends on the
effective mass given the same temperature (and thus
kinetic energy). Furthermore, the
timescale of carrier recombination can be inferred
from the timeGdependence of the
average intensity of the dark contrast, as shown in
Fig. 3c. Data collected from three
different BP samples are compiled here, each coveri
ng a different range of delay time to
avoid sample degradation due to longGtime exposure
to laser and electron pulses (see
Supplementary Figure 2), and the exponential fit gi
ves a recombination lifetime
τ
R
~550
ps. Possibly due to the small band gap and recombin
ation at the surface oxide sites, this
recombination time is much shorter than that in con
ventional semiconductors such as
silicon and gallium arsenide, which could limit the
charge collection efficiency of BP
based photoGdetection devices. Within this recombin
ation time, the average diffusion
length of holes can be estimated, using Eq. (2), to
be 9.7 Im along the armchair direction
and 0.6 Im along the zigzag direction, which sets t
he relevant length scale for designing
BPGbased optoelectronic devices.
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To further examine the validity of the extracted mo
del parameters, here we
simulate the SUEM contrast images by numerically so
lving the twoGdimensional
diffusion equation with timeGdependent anisotropic
diffusivities and a recombination
term:
∂
ρ
r
,
t
(
)
∂
t
=
D
x
t
( )
∂
2
ρ
r
,
t
(
)
∂
x
2
+
D
y
t
( )
∂
2
ρ
r
,
t
(
)
∂
y
2
−
ρ
r
,
t
(
)
τ
R
,
(3)
where
x
and
y
directions are the armchair and zigzag directions,
respectively, and
D
x
and
D
y
are timeGdependent diffusivities along the two dir
ections, with values as
discussed in the previous sections. The simulated i
mages are shown in Figure 4. The
intensity of these simulated images represents the
spatial concentration of holes
normalized to the maximum value (at the center) of
the initial distribution. The timeG
dependence of the distribution profile of hot holes
in the simulation is in good agreement
with the experimental images shown in the first row
of Fig. 2, justifying the transport
parameters extracted from our analysis of the exper
imental SUEM images.
In summary, we use SUEM to directly visualize the d
ynamics of photoGexcited
hot holes on the surface of black phosphorus. The h
ighly anisotropic inGplane charge
transport of black phosphorus is confirmed in our e
xperiment, and we further find that the
ratio between the diffusivities of hot holes along
the armchair direction and the zigzag
direction is much larger than that measured at near
Gequilibrium conditions, illustrating the
drastic difference between hot carrier dynamics and
nearGequilibrium carrier dynamics.
This study demonstrates the capability of SUEM in d
eepening our understanding of hot
carrier dynamics in lowGsymmetry layered materials.
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Author contributions
B.L., H.Z. and H.W. conceived the project. H.Z. pre
pared the BP samples. H.Z. and J.T.
performed the Raman characterization. B.L. and E.N.
carried out the SUEM
measurements. B.L., H.Z., X.Y., H.T., A.J.M. and H.
W. analyzed the data. B.L., H.Z.,
A.J.M. and H.W. wrote the manuscript. A.H.Z. led th
e development of the SUEM
technique and supervised the research effort during
the initial stage of the project.
Competing financial interests
Authors declare no competing financial interests.
Acknowledgement
This work is partially supported by the National Sc
ience Foundation (DMRG0964886)
and the Air Force Office of Scientific Research (FA
9550G11G1G0055) in the Gordon and
Betty Moore Center for Physical Biology at the Cali
fornia Institute of Technology. The
work is also supported by the Army Research Office
(W911NFG16G1G0435), the Air
Force Office of Scientific Research FATE MURI progr
am (FA9550G15G1G0514) and the
Northrop Grumman Institute of Optical Nanomaterials
and Nanophotonics (NGGION
2
) at
University of Southern California. B. L. is gratefu
l for the financial support from the KNI
Prize Postdoctoral Fellowship in Nanoscience at the
Kavli Nanoscience Institute of
California Institute of Technology.
Supporting Information
Hot hole dynamics in BP within a broad time range,
lightGpolarization dependence of the
hot hole dynamics in BP.
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Figure Captions
Figure 1. SUEM setup and BP sample.
(a) Schematic of the experimental setup. SE:
secondary electron. (b) SEM image of a typical BP f
lake used for the SUEM
measurements. The orange and yellow arrows denote t
he armchair (xG) and zigzag (yG)
directions of the BP crystal, respectively, as dete
rmined by optical Raman measurement.
Scale bar: 100 Im. (c) Raman characterization of th
e BP flake in (b). Left: the Raman
spectra measured with the incident laser at differe
nt polarization angles. x denotes the
armchair direction and y denotes the zigzag directi
on. Right: the intensity of the
A
g
1
peak
with the incident laser at different polarization a
ngles.
Figure 2. SUEM imaging of hole diffusion on the BP
surface.
First row: the sample
orientation is the same as that shown in Fig. 1(b).
Second row: the sample is rotated by
90 degrees. The arrows denote the armchair directio
n. Scale bar: 60 Im. The orange and
yellow arrows shown in the two left images denote t
he armchair (xG) and zigzag (yG)
directions of the BP crystal for the original sampl
e orientation (first row) and after the
sample is rotated by 90 degrees (second row), respe
ctively. A lowGpass Gaussian filter is
used to suppress the noise in the images for presen
tation. The dashed red ellipses are to
guide the eye.
Figure 3. Analysis of the SUEM images and hot carri
er transport.
(a) The variance of
holeGdistribution along different directions, norma
lized by that of the initial distribution.
(b) The variation of hole distribution along the ar
mchair and zigzag directions versus
time delay. Dashed lines represent fit with an expo
nentially decaying diffusivity due to
the cooling process of the holes. (c) The average i
ntensity of the holeGdistribution versus
time delay, indicating the time scale of the carrie
r recombination process. Data collected
from three different BP samples are compiled here,
each covering a different range of
delay time. Dashed line is an exponential fit with
a recombination time of 550 ps.
Figure 4. Simulated anisotropic carrier diffusion i
n BP.
These images are simulated
by numerically integrating Eq. (3) in the main text
up to the corresponding delay time.
Scale bar: 60 Im. The initial distribution at 40 ps
is assumed to be a Gaussian of radius
set by the incident pump laser beam. The intensity
of these simulated images represents
the spatial concentration of holes normalized to th
e maximum value (at the center) of the
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initial distribution.
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