of 17
Field Effect Optoelectronic Modulation of Quantum
-Confined Carriers in Black
Phosphorus
William
S. Whitney
1
ǂ
, Michelle C. Sherrott
2,3
ǂ
, Deep Jariwala
2,3
, Wei
-Hsiang Lin
2
, Hans
A. Bechtel
4
, George R. Rossman
5
, Harry A. Atwater
2,3
*
1. Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA
2. Thomas J. Watson Laboratory of Applied Physics, California Institute of Technology,
Pasadena, CA 91125, USA
3. Resnick Sustainability Institute, California Institute of T
echnology, Pasadena, CA
91125, USA
4.
Advanced Light Source,
Lawrence Berkeley National Laboratory
, Berkeley, CA 94720,
USA
5. Division of Geological and Planetary Sciences, California Institute of Technology,
Pasadena, CA 91125, USA
ǂ
Equal contributors
*Corresponding author: Harry
A.
Atwater (
haa@caltech.edu
)
Abstract
:
We report the infrared optical response of thin
black phosphorus under
field
-effect
modulation, and interpret the observed spectral shifts as a co
mbination of a
n ambipolar
Burstein
-Moss (BM)
bandgap shift due to band
-filling
and
Pauli
-blocking
under gate
control,
together with a quantum confined Franz
-Keldysh (QCFK) effect
, which
have
been proposed theoretically to occur for BP flakes under electric field modulation.
Modulation amplitudes as high as 15% are observed for 25 nm thick
layers, suggesting
the potential for use of black phosphorus as an active material in mid-
infrared
optoele
ctronic modulator applications.
Keywords:
Black phosphorus, tunable optical properties, mid-
infrared, Burstein
-Moss shift,
quantum
-confined Franz
-Keldysh
effect
, optical modulator
The emergence of a variety of two
-dimensional materials has spurred tremendous
research activity in the field of optoelectronics
1-4
. While
gapless
graphene
can in
principle exhibit an optoelectronic response
at wavelengths ranging
from the far
infrared
to the ultraviolet, its
optoelectronic
behavior is
limited by a lack of resonant absorption
and
poor
optical modulation in the absence of 1D confinement. On the other hand, the
semiconducting molybdenum
- and
tungsten-
based
transition metal dichalcogenides have
shown
considerable
prospects
for v
isible
frequency
optoelectronics
.
Yet while these
materials
promise exciting new directions for optoelectronics and nanophotonics
in
visible
, they
have limited response
for lower energy
, infrared light
.
The isolation of atomically thin black phosphorus in recent years has bridge
d the
wavelength
gap between graphene and
transition metal dichalcogenide
s, as black
phosphorus is an emerging two
-dimensional
semiconductor material with a
n infrared
energy
gap and typical carrier mobilities
between th
ose of
graphene
and transition metal
dichalcogenides
.
5-7
Since the
first
isolation
of black phosphorus
and demonstration of a
field effect device, numerous reports investigating the
synthesis and optoelectronic
properties of this material have emerged
, ap
propriately
summarized in recent
reviews.
5, 6, 8, 9
Likewise
a number of reports
have also appeared on the
applications
of
black phosphorus
in fast
photodetect
ors
10
, polar
ization sensitive
detectors
,
11
waveguide
integrated
devices
12
, multispectral photodetectors
13
, heterojunction
14
and split gate
p-
n
homojunction photovoltaics
15
, gate
-tunable van der Waals heterojunctions for digital
logic circuits
16
, 17
and
gigahertz frequency transistors in analog electron
ics
18
. A
majority
of the studies on both the fundamental optical properties of black phosphorus and
applications in optoelectronic devices have explored only the visible fre
quency range
19
-22
.
Therefore little is known about the intrinsic optical response of black phosphorus in the
infrared range. A
s a narrow band-
gap s
emiconduc
tor
, much of the
potential
for black
phosphorus
lies in these infrared optoelectronic applications
– r
anging from
tunable
infrared emitters
23
and absorbers for
waste heat management
/recovery
24
to
thermophotovoltaics
25
and optical modulators for telec
ommunications
26
. Th
eoretical
investigations of black phosphorus have suggested
novel infrared optical phenomena
,
such as anisotropic plasmons
27 , 28
, field
-effect tunable ex
citon stark shifts
29
, and strong
Burstein
-Moss
30
and quantum
-confined Franz
-Keldysh
effects
31
that promise to open new
directions for both fundamental nanophotonics research and applications
. In this work,
we report the first experimental observations of
the
infrared optical response of ultr
athin
BP samples
under field effect
modulation. We observe modulation of oscillati
ons in the
transmission spectra
which we attribute to a combin
ation of an ambipolar
Burstein
-Moss
shift / Pauli-
blocking effect
and quantum
-confined Franz
-Keldysh
behavior
. The large
modulation of transmittance (up to 15%) we observe in thicker BP (25 nm) suggests
promise
for BP as an
active material in
infrared optical modulator
s.
Measurements
were performed on black phosphorous flakes that were
mechanically exfoliated in a glove box on
to a 285
nm SiO
2
/Si substrate
. O
ptical
microscope images of these flakes are shown in Figure 1a and 1e. Raman spectroscopy
and atomic for
ce microscopy (AFM) (Figures 1b
- d and 1e
- g) were used to characterize
the quality and thicknesses of the samples. Crystal lattice orientations were determined
by polarized visible reflectance measurements, as in prior experiments an
d described in
detail in the Supporting I
nformation.
32
We analyzed two flakes of 6.5
nm and 25
nm
thickness with lateral dime
nsions of approximately 10
μ
m x 10
μ
m.
The observed
roughness in AFM scans is attributed primarily to the incomplete removal of a PMMA
capping layer prior to the measurement.
A schematic of our experimental setup is shown in Figure 2a. Standard electron
beam lithographic and metal deposition methods were used to define Ni/Au electrodes to
each exfoliated BP flake. The s
amples were
then
immediately coated in
PMMA
for
protection against environmental degradation.
Transmission measurements were obtained
using a Magna 760 (Nicolet) Fourier Transform Infrared (FTIR) Spectrometer coupled to
a NicPlan (Nicolet)
infrared microscope on infrared Beamline 1.4.3
at the Advanced
Light Source (ALS)
at Lawrence Berkeley National Laboratory. This allowed us to
perform measurements using a high brightness, diffraction-
limited infrared beam, which
is necessary for
accurately
analyzing the small-
area BP samples attainable by mechanical
exfoliation.
The incident light was ellipticall
y polarized due to the synchrotron source,
with
an
intensity ratio of two
to one
. The major axis and details of the polarization state
are
indicated and discussed in the Supporting I
nformation
. All measurements were done
in a Linkam cryo stage at a press
ure of 3
mTorr and a temperature of 80
K. First, a gate-
dependent source
-drain current was measured at 80
K
to extract approximate carrier
densities as a function of gate bias. Transmission spectra
were then gathered at different
gate voltages applied between the flake and lightly doped Si substrate.
We note that in
our setup, the silicon substrate is grounded and BP experiences the applied
voltage, so the
sign of the
applied
voltages is reversed fr
om that in some other works. In order to probe
the electric field
- and charge-
carrier
-dependent optical properties of the BP, all spectra
were normalized to the zero
-bias spectrum. The measured infrared optical properties
result primarily from the unique band structure of BP, schematically depict
ed
in Figure
2b.
Quantized
intersubband transitions provide the primary contribution to its zero-
field
optical conductivity.
Transport and infrared transmission results for the 6.5
nm thick flake are reported
in F
igure 3. Transport measurements taken at
80
K
and pressure of 3mTorr, shown in
Figure 3a, indicate that this sample was heavily hole-
doped, and only hole
-type transport
was observed throughout the voltage sweep of our field-
effect device. An on-
off ratio of
approximately 10
4
was attained, limited by the noise threshold of our measurement (a
Keithley 2400 SourceMeter), but consistent with literature values for similar thickness
devices
7
. Figure 3b shows the primary result of our experiment, which is the modulated
transmission of the sample at different voltages, normalized to the transmission spectrum
at zero bias. Three prominent features are observed in the
se spectra.
First, u
nder negative
applied bias (i.e.: when the sample is being depleted of holes), a negative peak
(I) appears
in
transmission
near
0.45 eV, which grows in amplitude
and broadens to lower energies
as the magnitude of the bias increases.
Second, under positive applied bias (i.e.: when
the sample is being increasingly hole
-doped), a positive peak (II)
appears
in transmittance
near
0.5-
0.7
eV.
Lastly, these
carrier-
dependent effect
s are
superimposed with an
oscillatory feature (III) that varies with the magnitude of the applied field, but not its
polarity
, and
which is most
clearly visible in the negative bias spectra in the 0.5
-0.7
eV
range
, where no Burstein-
Moss shift should be seen.
Due to the distinct character of each feature, we can understand the overall
spectral shifts as arising from a combination of a Burstein
-Moss (BM) shift and the
quantum confined Franz
-Keldysh (QCFK) effect, as has been predicted theoretically in
BP flakes of this thickness.
31
Because our flake exceeds a thickness of ~4
nm, we can
neglect any excitonic effects and t
herefore do not consider the giant Stark effect or a
normal
-to-topological phase transition in our analysis.
21
, 22
We
suggest that peak (I) can be described by the
onset of
allo
wed
j = 1
intersubband transitions as the material is depl
eted of
holes at negative gate voltages
, in
agreement with our transport measurements.
We further suggest that peak (II) can be
described
primarily
by the suppression of j = 2 intersubband transitions as more holes are
accumulated in the flake at positive gate vo
ltages. This is sh
own schematically in Figure
3c. We additionally explain these results by calculating the optical conductivity of our BP
flakes at various doping levels, using the theoretical framework developed in
ref.
30
. T
he
band structure of thin BP is calculated for various thicknesses and carrier densities and
the Kubo formula is used to e
valuate the optical conductivity as a function of frequency,
shown in Figure 3d. Our experimental results correspond qualitatively
in this low energy
range to the optical
response obtained from our calculat
ions
. From these results, we may
assign
the band
gap energy of our flake as being E
g
~ 0.4
eV, consistent with theoretical
models that predict an increase in band gap energy from the bulk 0.3
eV value as the
material thickness decreases to several layer
s or thinner
.
21
The oscillatory feature (III)
, on the other hand, grow
s in magnitude as the local
field strength increases, likely
corresponding to a shift in the overlap of the first
conduction and valence subband
wavefunctions
as explained by the quantum
-confined
Franz
-Keldysh
effect, previously explored theoretically in
ref.
31
. In a bulk semiconductor
,
the Franz
-Keldysh effect introduces simple oscillatory perturbations to the absorption
edge, but in quantum well structures this behavior is modified.
33
Under a sufficiently
strong electric field, hybrid
optical transitions between subbands of different index (eg:
E
v1
to E
c2
) become allowed
, even though they
are predicted theoretically to
be
forbidden,
and
have zero oscillator strength
, in the a
bsence of a strong electrostatic field
. Notably,
recent experimental investigations
34
show evidence that these transitions may still occu
r
without the application of an electric field, and further theoretical and experimental
investigation of this phenomenon is needed to fully explain these results
. Nonetheless, we
suggest
that
the quantum
-confined Franz
-Keldysh
effect leads to the appearan
ce of the
additional oscillatory spectral features we observe, owing to the increased oscillator
strength making these transitions significantly more prominent. It is also worthwhile to
note that under a strong applied fie
ld, the optical band gap becomes l
ess sharply defined.
Interestingly, we see no evidence of a tunable plasma edge;
investigations in the long
-
wave infrared wavelength range with larger s
amples
would likely be needed to observe
this feature
.
We note that because of the complicated
polarization state of incident light
from
the synchrotron,
and because previous studies
have extensively studied this effect
experimentally
30
, 35
, we do not study
in detail
the anisotropic optical properties of BP.
However, due to the primary contribution to the optical conductivity arising from the σ
xx
component, we argue that the
only effect of
elliptically
pola
rized light
is to scale the
observed modulation, as discussed in the
Supporting Information.
Results for
the
25
nm thick BP flake are shown in Figure 4.
Unlike
the 6.5
nm
thick flake, we observe ambipolar transport at a temperature of 80
K and a pressure of 3
mTorr, as shown in Figure 4a. Similar results have been shown in the literature with
on/off ratios of ~10
4
for flakes
thinner
than
the one considered here;
it is likely that the
low operation temperature and strong gate bias
conditions used i
n our experiments
, as
well as the nearly intrinsic doping of the flake
at zero bias
enable us to observe strong
conductance modulation.
14
The
infrared
transmission results are
shown in Figure 4b,
normalized to the zero bias tra
nsmission,
and
show significant modulation of a single
broad feature. This feature is strongest at positive bias, and reverses sign twice: it changes
polarity as the bias crosses 0
V, and again between -
60 V and -
120 V.
We interpret our
results for the 25
nm sample
using a combination of a Burstein-
Moss sh
ift and quantum
-confined Franz
-Keldysh effect. Because this flake exhibits
ambipolar transport, we can understand the primary
spectral
feature as resulting from
three separate regimes of charge carrier modulation. At increasingly positive bias (ie:
increased hole doping), Pauli blocking of optical transitions is increased, resulting in
higher
infrared
transmission at low
er photon
energies. At negative bias, transmission first
decreases as we deplete the sample of holes and more optical transitions are allowed, and
then increases
as the sample becomes electron
-doped and a Bur
stein
-Moss effect of the
opposite charge carrier type is introduced.
This ambipolar, gate
-controlled Burstein
-
Moss shift is the first observed in a two
-dimensional
semiconductor, to the best of our
knowledge. We further highlight the significant modulation strength of this effect –
a
relative change in transmission of up to 15% despite background signal
s from the PMMA
capping layer an
d SiO
2
/Si substrate.
Superimposed on this large modulation are small oscillations that are most
evident at high applied field –
particularly
+12
0 V
. We suggest that these oscillations are
related to features in the quantized intersubband transitions
that
occur
in the
BP optical
conductivity, as seen from
the calculation in Figure 4d.
A further, larger oscillation
appears in the -
120 V transmittance spectrum near 0.3 eV.
We speculate that this feature
may
result from
distinctions between electron and hole
-doped optical responses; however
further study would be required to draw definit
ive
conclusions about this.
In conclusion, we have demonstrated experimentally that ultra
-thin black
phosphorus exhibits widely tunable optical properties at
mid
-infrare
d wavelengths
. We
find that in 6.5 nm thick BP, modulation of infrared transmission takes place as a result of
both a Burstein-
Moss shift and quantum confined Franz
-Keldysh effect. In thicker 25 nm
BP
, we observe for the first time an ambipolar Burstein
-Mo
ss shift, with modulation
strengths up to 15%. While our results verify some of the theoretical predictions about
the
electro
-optical effects in few
-layer BP
, more work is needed
to further understand the
BP optical response
as function of sample thickness, in addition to the field effect
mediated infrared response
in the few
-layer
(< 3
nm) limit. O
ur results indicate that BP
is both an interesting system for exploring the fundamental behavior of quantum confined
carriers in
two
-dimensional semiconductors under field-
effect modulation, and a
promising candidate for tunable mid
-infrared
optical devices
.
Methods:
BP flakes were exfoliated in a glove box from crystals grown by HQ Graphene. After
fabrication
of Ni/Au (20
nm
/ 130 nm)
electrodes by electron beam lithography and
electron beam evaporation, 90 nm PMMA 950 A2 was spin-
coated as an encapsulation
layer. Electron beam lithography was
again used to expose the contacts for wire bonding.
PMMA
8
and other encapsulation layers
including ALD grown dielectrics,
36
, 37
polymers
38
,
39
, covalent surface funct
ionalization
40
and atomically thin hexagonal boron nitride
41
have
been
shown in the past to successfully protect BP devices again
st ambient degradation.
Acknowledgments
:
This work was supported by the U.S. Department of Energy (DOE) Office of Science,
under grant DE
-FG02
-07ER46405. The authors gratefully acknowledge use of the
facilities of beam
line 1.4.3 at the
Advanced Light Source which is supported by the
Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of
Energy under Contract No. DE
-AC02
-05CH11231. M.C. Sherrott
and D. Jariwala
acknowledge
s upport by the Resnick Institute and W.S. Whitney acknowledges support
by the National Defense Science and Engineering Graduate Fellowship.
This research
used resources of the National Energy Research Scientific Computing Center, a DOE
Office of
Science User Facility supported by the Office of Science of the U.S.
Department of Energy under Contract No. DE
-AC02
-05CH11231. The authors are
grateful to Victor Brar for helpful discussions.
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8, (6), 597-
602.
41.
Doganov, R. A.; O/'Farrell, E. C. T.; Koenig, S. P.; Yeo, Y.; Ziletti, A.; Carvalho,
A.; Campbell, D. K.; Coker, D. F.; Watanabe, K.; Taniguchi, T.; Neto, A. H. C.;
Ozyilmaz, B.
Nat Commun
2015,
6.
Figure 1
: Few
-layer black phosphorus sample characterization.
a), e)
Optical image of
6.5 nm and 25 nm black phosphorus flakes, respectively, with red circles
indicating the
location
s of Raman measurement
s, and white axes indicating directions of the armchair
(x) and zig
-zag (y) crystal axes
.
b), f)
Raman spectrum with characteristic bla
ck
phosphorus and silicon modes.
c), g)
Large area AFM scan
s with corresponding cross
-
cut
s
d), h)
Cross
-cuts indicating flake thicknesses
Figure 2: a)
Schematic illustration of FTIR transmission modulation experiment.
Diffraction
-limited IR beam from synchrotron is transmitted through black phosphorus
sample. Variable gate voltage applied across SiO
2
modulates transmittance.
b)
Schematic
band diagram of few
-layer black phosphorus with subbands arising from vertical
quantum confinement
Figure 3:
Gate modulation of 6.5 nm flake.
a)
Source
-drain current vs gate voltage.
Only hole
-type conduction is seen.
b)
FTIR transmittance vs photon energy, normalized
to zero bias
. Peak I
noted
at E = 0.45 eV, II at 0.6
eV, and III the oscillatory behavior
most notable at large biases
.
c)
Schematic of electronic band structure and allowed
intersubband transitions at different voltages.
d)
Calculated optical conductivity of a 6.5
nm BP flake for different Fermi levels
, normalized to the universal conductivity of
graphene.
Color coding to part (
b)
indicates that the BP is moderately hole doped at zero
bias. At negative gate voltages, the previously Pauli
-blocked E
c1
-E
v1
transition becomes
allowed, and at positive gate voltages, the previously allowed E
c2
-E
v2
transition is Pauli-
blocked. This behavior is superimposed with a field magnitude
-dependent effect, which
we suggest to be the predicted QCFK effect
, and which is clearly visible in the negative
voltage spectra abov
e the E
c1
-E
v1
transition
.
Figure 4:
Gate modulation of 25 nm flake.
a)
Source-
drain current vs gate voltage.
Ambipolar conduction is seen.
b)
FTIR transmittance vs photon energy normalized to
zero bias.
Gate modulation of up to 15 percent is seen
. Small ripples in transmittance are
observed, reflecting the quantized optical conductivity.
c)
Schematic of electronic band
structure and allowed interband transitions at different voltages.
d)
Calculated optical
conductivity of
a 25
nm BP flake for different Fermi levels
, normalized to the universal
conductivity of graphene. Color coding to part (
b)
indicates that the BP is least doped at
small negative gate voltage. At larger negative gate voltages, Pauli-
blocking reduces the
optical conductivity nea
r the band edge, increasing transmittance. At positive gate
voltages, Pauli
-blocking again reduces the band edge optical conductivity. This behavior
suggests an ambipolar Burstein-
Moss shift.
Supporting Information for: “Field Effect Optoelectronic Mod
ulation of Quantum
-
Confined Carriers in Black Phosphorus”
William S
. Whitney
, Michelle C. Sherrott
2,3ǂ
, Deep Jariwala
2,3
, Wei
-Hsiang Lin
2
, Hans
Bechtel
4
, George R. Rossman
5
, Harry A. Atwater
2,3*
1. Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA
2. Thomas J. Watson Laboratory of Applied Physics, California Institute of Technology,
Pasadena, CA 91125, USA
3. Resnick Sustainability Institute, California Institute of Technology, Pasadena, CA
91125, USA
4. Lawrence Berkeley National Laboratories, Berkeley, CA 94720, USA
5. Division of Geological and Planetary Sciences, California Institute of Technology,
Pasadena, CA 91125, USA
ǂ
Equal contributors
*Corresponding author: Harry Atwater (haa@caltech.edu)
I.
Crystal Latt
ice Structure
The x (armchair) and y (zig
-zag) crystal lattice directions are determined by
polarization
-dependent visible reflectance measurements. At each angle of polarization
an image is recorded, and pixel RGB values are sampled from both the BP flake and
nearby substrate. The ratio of green channel values from flake to substrate is averaged
over three sample positions, and plotted as a function of polarization angle in Figure S1.
Maxima and minima in green reflectance determine the armchair and
zig
-zag directions,
respectively.
32
Figure S1:
Intensity of the green channel of light reflected from BP flakes as the linear
polarization of the incident light is rotated for
a)
the 6.5 nm flake and
b)
the 25 nm flake.
In both cases, the polarization angle is defined as the angle between the x (armchair)
crystal axis and the linear polarizer. The green component of the pixel RGB of the flakes
is normalized to that of the adjacent substrate.
II.
Polarization State of FTIR Beam
The FTIR beam used in all transmittance measurements has an inherent elliptical
polarization due to its synchrotron source. The polarization s
tate is approximately two to
one polarized along the major axis of this ellipse, which is indicated in Figure S2. Due to
the complicated polarization state of incident light from the synchrotron, and because
previous studies have extensively investigated this effect experimentally
30
, 35
, we do not
study in detail the anisotropic optical properties of BP. However,
since the σ
xx
component of the optical conductivity is one to two orders of magnitude larger than the
σ
yy
component, plotted in Figure S3, we argue that the observed optical response derives
almost entirely from light-
material interactions along the armch
air direction. As a result,
the only effect of elliptically polarized light is to scale down the observed modulation
strength. Probing devices with light of properly aligned polarization – linear along the
armchair direction – would maximize this modulat
ion strength; however, the underlying
physics would be unchanged.
Figure S2:
Polarization states of FTIR light. The synchrotron infrared source is
inherently polarized at ALS beamline 1.4.3, with a roughly
2:1 elliptical polarization in
the direction indicated here in red for
a)
the 6.5 nm flake and
b)
the 25 nm flake. Also
indicated are the crystal axes, where x and y correspond to the armchair and zig
-zag
lattice directions, respectively
, and the measurement site, indicated by a red, dashed
circle.
Figure S3:
Calculated
σ
yy
optical conductivities at different Fermi levels for
a)
the 6.5
nm flake and
b)
the 25 nm flake. In both cases,
σ
yy
is one to two orders of magnitude
smaller than
σ
xx
, implying that the interaction of the FTIR beam with the flake is
dominated by the
σ
xx
. As a result, any polarization of the FTIR beam effectively scales
the gate modulation as the strength of the interaction of the beam with the
σ
xx
vs
σ
yy
optical conductivity components changes.