Spatial
-
Temporal
Imaging
of Anisotropic Photo
c
arrier
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, California Institute of Technology,
Pasadena, CA 91125, USA
2
Kavli Nanoscience Institute, California Institute of Technology, Pasadena, CA 91125
3
Ming Hsieh Department of Electrical Engineering, University of Southern California,
Los
Angeles, CA 90089, USA
4
NG Next, Northrop Grumman, 1 Space Park, Redondo Beach, CA 90278, USA
5
Division of Engineering and Applied Science, California Institute of Technology,
Pasadena, CA 91125
, USA
As a
n emerging single elemental layered
material
with
a
low symmetry in
-
plane
crystal lattice
1
-
6
,
b
lack phosphorus
(BP)
has attracted significant research interest
owing to its unique electronic and optoe
lectronic properties, including
its
widely
tunable bandgap
7
-
9
, polarization dependent photoresponse
3
,
10
and highly anisotropic
in
-
plane charge transport
3
.
Despite extensive study of
the
steady
-
state charge
transport in BP
2
-
5
,
11
,
12
,
there has not been direct characterization
and visualization
of the
hot carriers
dynamics in BP immediately after
photoexcitation, which is
crucial to understanding the performance of BP
-
based optoelectronic devices. Here
we use
the newly developed
scanning ultrafast electron microscopy (SUEM)
13
,
14
to
directly
visualize the motion of photo
-
excited hot carriers on the surface of BP in
both space and time. We
observe highly anisotropic in
-
plane diff
usion of hot
holes
,
with a 15
-
times
higher diffusivity along the armchair
(x
-
)
direction than that along
the zigzag
(y
-
)
direction. Our results provide direct evidence of anisotro
pic hot
carrier transport in
BP
and demonstrate the capability of SUEM to resolve ultrafast
hot carrier dynamics in
layered
two
-
dimensional materials
.
⊥
These authors contributed equally.
*To whom correspondence should be addressed:
han.wang
.4@usc.edu
(H.W.),
aminnich@caltech.edu
(A.J.M.)
§
Deceased
With a widely tunable band g
ap from 0.3 eV in its bulk 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
application
s
,
10
,
15
,
16
due to its highly tunable and
customizable electr
onic
7
-
9
,
17
and optical properties.
In addition, the relatively high charge
mobility of BP adds to its attractiveness for applications that require efficient charge
transport.
18
One of the most intriguing features of BP, however, is it
s strong in
-
plane
anisotropy,
3
,
4
originati
ng from the
low
-
symmetry puckered orthorhombic
lattice structure.
The near
-
equilibrium charge mobility along the armchair direction is known to be higher
than that along the zigzag direction, revealed by both
the
field
-
effect and Hall
measurements.
2
-
4
Due to
the opposite trend in
its
thermal conductivity
,
19
-
21
th
e strong
anisotropy of BP is
also
believed to be promising for thermoele
ctric applications.
22
Moreover, the in
-
plane anisotropy leads to strongly polarization
-
dependent optical
properties, rendering BP a suitable material for polarization
-
sensitive detectors.
10
,
16
Besides near
-
equilibrium transport, ano
ther important aspect of charge transport is
the dynamics of photo
-
excited hot carriers
relevant to
the
photo
-
detection
and
photovoltaic
applications. Due to the
initial
high temperature of
the
photo
-
excited charge
carriers, the hot
-
carrier dynamics can be drastically different from near
-
equilibrium
transport
.
Therefore
, a thorough understanding
in
the motion of hot electrons and holes in
BP immediately after photo
-
excitation is essential for designing
and improving BP
-
based
optoelectronic devices.
Previous studies
23
-
26
exclusively utilized ultrafast optical pump
-
probe spectroscopy to investigate the transient change of absorption or transmission of
BP induced by the pumping laser pulse, from which the dynamics
of hot carriers
could
be
indirectly
inferred
. Restricted by the optical diffraction limit, however, optical pump
-
probe spectroscopy lacks the spatial resolution to directly map out the diffusion process
of photo
-
excited charge carriers.
Scanning ultrafast
electron microscopy (SUEM)
13
,
14
is a newly developed
technique that can directly image the dynamics of photo
-
excited carriers in both space
and time, with sub
-
picosecond temporal resolution and nanometer spatial resolution.
Details of t
he setup can be found elsewhere
13
,
14
,
27
-
29
and are briefly summarized here
(also illustrated in Fig
ure
1a). Compared to optical pump
-
probe spectroscopy, SUEM is a
photon
-
pump
-
electron
-
probe technique, with sub
-
picosecond electron pulses generated
by
illuminating a photocathode (ZrO
-
coated tungsten tip) with an ultrafast ultraviolet
(UV) laser beam (wavelength 257 nm, pulse duration 300 fs, repetition rate 5 MHz,
fluence 300 μJ/cm
2
). A typical probing electron pulse consists of tens to hundreds of
elec
trons, estimated by measuring the beam current through a Faraday cup. The probing
electron pulses arrive at the sample after the optical pump pulses (wavelength 515 nm,
fluence 80 μJ/cm
2
) by a given time controlled by a mechanical delay stage (
-
700 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 Everhart
-
Thornley
detector.
To form an image
, the probing electron pulses are sc
anned across the sa
mple
surface
and the secondary electrons emitted from each location
are counted
.
Since
the
yield of secondary electrons depends on the local average electron energy,
more/less
secondary electrons are emitted from regions of the sample surface where there i
s a net
accumulation of electrons/holes.
27
T
ypically a reference SEM image is taken long before
the pump optical pulse arrives
and
is
then
subtracted from images taken at other delay
times to remove the background. In the
resulting
“contrast images”, bright/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 electrons and holes after
excitation by the optical pump pulse can be monitored in real space and time.
14
An
alternative way of visualizing hot carrier dynamics in space and time was recently
demonstrated using time
-
resolved photoemission electr
on microscopy (TR
-
PEEM)
.
30
In this letter, we demonstrate the direct imaging of hot
-
carrier dynamics in BP
with SUEM. Due to the presence of a
surface potential, we observe the motion of hot
holes on the surface of BP. With SUEM, we see striking visualization of anisotropic
diffusion of hot holes after photo
-
excitation, from which quantitative transport
parameters can be extracted. Our results in
dicate a 15
-
times higher diffusivity of hot
-
holes moving along the armchair direction than that along the zigzag direction, which is a
combined effect of anisotropic effective mass and direction
-
independent electron
-
phonon
scattering
.
31
Figure 1b displays a static SEM
image
of a typical
BP flake measured in this
work. BP flakes
of 80 nm thick
ness
were mechanically exfoliated from a bulk crystal,
and subsequently transferred to an ITO
-
coated glass substrate
to avoid charging of the
sample
.
The sampl
e is exclusively handled in an a
r
gon
glovebox before being
immediately loaded into the S
U
EM vacuu
m chamber.
The arrow
s
in Fig
ure
1b denote the
armchair
(x
-
) and zigzag (y
-
) directions of the BP crystal
, determined optically by Raman
spectroscopy
.
32
Polarization
-
resolved Raman spectroscopy was performed
after the
SUEM measurements
using a 532 nm Nd:YAG laser in the LabRAM ARAMIS system.
A
100
×
microscope objective
was used
and the power incident on
the
BP
sample
was
kept below
500
μ
W to avoid sample damage.
Polarization resolved Raman spectroscopy
was con
ducted with a 532 nm laser with
different sample
rotating
angles.
The
dependence of the
Raman peaks
intensity on the
rotation angle of
the
sample basal plane
is shown in Fig
ure
1c
. T
he crystal orientation is determined specifically from the
intensity of the
A
g
1
peak
, which reaches
the mini
mal intensity when the laser polarization
is along
armchair
(x
-
)
direction
.
32
SUEM contrast images of the BP flake shown in Fig
ure
1b are presented in Fig
ure
2.
A low
-
pass Gaussian filter is used to suppre
ss the 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 Fig
ure
1b, whereas images in
the second row were taken when th
e flake is rotated by 90 degree. Firstly,
only
dark
contrast
is observed in the region of the sample excited 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 are typically emitted only from the top
few nanometers of the sample, the observation of only dark contrast indicates that
the
electrons and holes are separated vertically after photo
-
excitation, and
the
holes are
accumulated near
the sample surface while
the
electrons 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 n
-
type silicon with SUEM
also caused by a s
urface potential)
,
which arises
due to the formation of
an
atomically
thin phosphorus oxide layer
33
on the BP surface
when the
samples
are briefly exposed to
air
(<30 seconds
)
during
their
loading
into the vacuum chamber of the SUEM.
The
vertical transport process associated with the surface potential is also reflected in the
observation that the intensity of the dark contrast reaches
a
maximum around 40 ps after
the optical pump pulse arrives.
A
t 40 ps delay time, the profile of the spatial distribution
of holes follows approximately the shape of the pump beam.
As the time progresses
, it is
clearly
observed
that
the
holes preferentially
diffuse along the armchair
(x
-
)
direction,
denoted by the
orange
arrow, regardless of the relative orientation of the
BP flake and the
optical pump beam. In this measurement the polarization 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,
10
we verified experimentally that the light polarization does not
affect t
he dynamics of the hot holes after photo
-
excitation, as shown in Supplementary
Figure 2.
In addition to the direct and intuitive visualization of the highly anisotropic
transport of photo
-
excited hot holes in BP provided by the SUEM contrast images in
Fig
ure
2, numerical values of transport parameters can be extracted through quantitative
analysis of the contrast images. A convenient parameter to describe the spatial
distribution of particles is the variance
σ
,
which
in this case
is
angle
-
dependent, 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 re
lation between them. This assumption
should hold here since the optical excitation is weak and the measurement works in the
linear response regime. Figure 3a shows the calculated
σ
θ
,
t
(
)
from the images at
different delay times in the fi
rst row of Fig
ure
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 direction is hardly discernible.
In t
he case when the diffusivity is a constant, the variance of the spatial
distribution should be a linear function of time. In the current experiment, however, the
diffusivity changes with time due to a decreasing temperature of the hot carriers. As a
first
-
order approximation, we assume the temperature of the hot carriers decays
exponentially
T
t
(
)
=
T
0
e
xp
−
t
τ
T
(
)
, with a time constant
τ
T
controlled mainly by
inelastic electron
-
phonon scatterings
.
34
We further apply the Einstein relation
D
=
k
B
T
μ
(
)
q
, where
D
is the diffusivity and
μ
is the mobility, and argue that
D
t
(
)
=
D
0
e
xp
−
t
/
τ
T
(
)
,
where
D
0
is the diffusivity right after photo
-
excitation,
because
immediately after photo
-
excitation, the lattice is still cold so that the mobility limited by
electron
-
phonon 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
−
e
xp
−
t
τ
T
⎛
⎝
⎜
⎞
⎠
⎟
⎡
⎣
⎢
⎤
⎦
⎥
+
σ
0
θ
(
)
.
(
2
)
Fits of Eq. (2) to experimentally measured variances along the armchair and zigzag
directions are plotted in Fig
ure
3b. From the fitting
s
,
the parameters can be extracted as
τ
T
≈
150
ps
,
D
0
,
a
r
m
c
ha
i
r
≈
1.3
×
10
4
c
m
2
s
,
D
0
,
z
i
gz
a
g
≈
870
c
m
2
s
,
σ
0,
a
r
m
c
ha
i
r
≈
216.7
μ
m
2
and
σ
0,
z
i
gz
a
g
≈
405.8
μ
m
2
.
The ratio between the diffusivities along the two directions is
approximately 15. This ratio is much higher than that measured by steady
-
state transport
experiments
4
and calculated by first
-
principles simulations assuming near
-
equilibrium
transport
,
31
but close to the value inferred from an optical pump
-
probe measurement
.
26
This observation demonstrates
the significant
difference between hot
-
carrier dynamics
and near
-
equilibrium dynamics
, and the fact that t
he measured hot
-
carrier diffusivity ratio
is on the same order of the effective mass ratio
35
indicates that the transport of
photo
-
excited hot carriers is likely more affected by the effective mass of the carriers than their
scattering properties.
Furthermore, the timescale of carrier recombination can be inferred
from the time
-
dependence of the average intensity of the dark con
trast, as shown in Fig.
3
c
. Data collected from three different
BP samples
are compiled here,
each covering a
different range
of delay time
,
and the exponential fit gives a recombination lifetime
τ
R
~550 ps.
Within this recombination time, the average diffusion length of holes can be
estimated, using
E
q
.
(2), to be 9.7 μm along the armchair direction and 0.6 μm along the
zigzag direction.
To further examine the validity of the extracted model parameters, here
we
simulate the SUEM contrast images by numerically solving the two
-
dimensional
diffusion equation with time
-
dependent 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 time
-
dependent diffusivities along the two directions, with values as
discussed in the previous section
s
.
The simula
ted images are shown in Fig
ure
4.
The
intensity of these simulated images represents the spatial concentration of holes
normalized to t
he maximum value (at the center) of the initial distribution.
The time
-
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
parame
ters extracted from our analysis of the experimental SUEM images.
In summary, we use SUEM to directly visualize the dynamics of photo
-
excited
hot holes on the surface of black phosphorus. The highly anisotropic in
-
plane charge
transport of black phosphorus
is confirmed in our experiment, 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
-
equilibrium conditions, illustrating the
drastic diff
erence between hot carrier dynamics and near
-
equilibrium carrier dynamics.
This study demonstrates the capability of SUEM in deepening our understanding of hot
carrier dynamics in
low
-
symmetry layered
materials.
Author contributions
B.L., H.Z. and H.W.
conceived the project. H.Z. prepared the BP samples. H.Z. and J.T.
performed the Raman characterization. B.L. and E.N. carried out the SUEM
mea
surements. 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
manus
cript
.
A.H.Z.
led the 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 Science Foundation (DMR
-
0964886)
and the Air Force Office of Scientific Research (FA9550
-
11
-
1
-
0055) in the Gordon and
Betty Moore Center for Physical Biology at the California Institute of Technology.
The
work is also supported by
the Army Resea
rch Office (
W911NF
-
16
-
1
-
0435
),
the
Air
Force Office of Scientific Research FATE MURI program (FA9550
-
15
-
1
-
0514)
and the
Northrop Grumman Institute
of Optical Nanomaterials and Nanophotonics (NG
-
ION
2
) at
University of Southern California
.
B.
L. is grateful for
the financial support from the KNI
Prize Postdoctoral Fellowship in Nanoscience at the Kavli Nanoscience Institute of
California Institute of Technology.
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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 flake
used for
the SUEM
measurements
. The
orange and yellow
arrow
s
denote the armchair
(x
-
) and zigzag (y
-
)
direction
s of the BP crystal, respectively,
as
determined by optical Raman measurement.
Scale bar: 100 μm. (c) Raman characterization of the BP flake in (b). Left:
the Raman
spectra
measured with the incident laser at
different polarization
angles
. x denotes the
armchair
direction and y denotes the
zigzag
direction. Right: the intensity of the
A
g
1
peak
with the incident laser at different
polarization
angles
.
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 degree
s
. The arrows denote the armchair direction. Scale bar
: 60 μm.
The
orange and
yellow
arrow
s
shown in the two left images
denote the armchair
(x
-
) and zigzag (y
-
)
direction
s of the BP crystal for the original sample orientation (first row) and after the
sample is rotated by 90 degrees (second row), respectivel
y. A low
-
pass Gaussian filter is
used to suppress the noise in the images for presentation.
The dashed
red
ellipses are to
guide the eye.
Figure 3. Analysis of the SUEM images and hot carrier transport.
(a) The
variance
of
hole
-
distribution along different
directions, normalized by that of the initial distribution.
(b) The
variation
of hole distribution along
the
armchair and zigzag directions versus
time delay. Dashed lines represent fit with an exponentially decaying diffusivity due to
the cooling process
of
the
holes. (c) The average intensity of the hole
-
distribution versus
time delay, indicating the time scale of the carrier 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 in BP.
These images are simulated
by numerically integrating Eq. (3) in the main text up to the corresponding delay ti
me.
Scale bar: 60 μm. 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 the maximum value (at the
center) of the
initial distribution.