Supporting Information for: “Field Effect Optoelect
ronic Modulation of
Quantum-Confined Carriers in Black Phosphorus”
William S. Whitney
1ǂ
, Michelle C. Sherrott
2,3ǂ
, Deep Jariwala
2,3
, WeiHsiang Lin
2
, Hans
Bechtel
4
, George R. Rossman
5
, Harry A. Atwater
2,3*
1. Department of Physics, California Institute of T
echnology, 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 Ins
titute of Technology, Pasadena, CA
91125, USA
4. Lawrence Berkeley National Laboratories, Berkele
y, CA 94720, USA
5. Division of Geological and Planetary Sciences, C
alifornia Institute of Technology,
Pasadena, CA 91125, USA
ǂ
Equal contributors
*Corresponding author: Harry Atwater (haa@caltech.e
du)
I.
Extinction Modulation of 25 nm thick Flake
The infrared extinction results are shown in Figure
S1 normalized to the zero bias
extinction, and show significant modulation of a si
ngle 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 as a
n ambipolar BursteinMoss
shift. Because this flake exhibits ambipolar transp
ort, we can understand the primary
spectral feature as resulting from three separate r
egimes of charge carrier modulation. At
increasingly positive bias (ie: increased hole dopi
ng), Pauli blocking of optical transitions
is increased, resulting in higher infrared transmis
sion at lower photon energies. At
negative bias, transmission first decreases as we d
eplete the sample of holes and more
optical transitions are allowed, and then increases
as the sample becomes electrondoped
and a BursteinMoss effect of the opposite charge c
arrier type is introduced. This
ambipolar, gatecontrolled BursteinMoss shift is t
he first observed in a twodimensional
semiconductor, to the best of our knowledge. We not
e the presentation of this data in
arbitrary units, as further investigation of modula
tion strength in thick BP flakes is
needed to draw definitive, quantitative conclusions
.
Superimposed on this large modulation are small osc
illations that are most
evident at high applied field – particularly +120 V
. We suggest that these oscillations are
related to features in the quantized intersubband t
ransitions that occur in the BP optical
conductivity, as seen from the calculation in Figur
e S5d. 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 h
oledoped optical responses; however
further study would be required to draw definitive
conclusions about this. We further
note that transport measurements for this flake wer
e performed at 80 K, at a pressure of
3mTorr.
Figure S1:
Gate modulation of 25 nm flake.
a)
Sourcedrain current vs gate voltage.
Ambipolar conduction is seen. Inset: Optical micros
cope image of flake.
b)
FTIR e vs
photon energy normalized to zero bias.
c)
Schematic of electronic band structure and
allowed interband transitions at different voltages
.
d)
Calculated optical conductivity of
an intrinsic, 10 nm BP quantum well, normalized to
the universal conductivity of
graphene.
II.
Crystal Lattice Structure
The x (armchair) and y (zigzag) crystal lattice di
rections are determined by
polarizationdependent visible reflectance measurem
ents. At each angle of polarization
an image is recorded, and pixel RGB values are samp
led from both the BP flake and
nearby substrate. The ratio of green channel value
s from flake to substrate is averaged
over three sample positions, and plotted as a funct
ion of polarization angle in Figure S1.
Maxima and minima in green reflectance determine th
e armchair and zigzag directions,
respectively.
1
This characterization was not performed for the s
amples measured with
the internal FTIR globar source, as those measurem
ents are fundamentally unpolarized.
Figure S2:
Intensity of the green channel of light reflected f
rom 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 c
omponent of the pixel RGB of the flakes
is normalized to that of the adjacent substrate.
III.
Polarization State of Synchrotron FTIR Beam
The FTIR beam used in our final (Fig 4) measurement
and Supplement S1 has an
inherent elliptical polarization due to its synchro
tron source. The polarization state is
approximately two to one polarized along the major
and minor axes of this ellipse, which
are indicated in Figure S3. Due to the complicated
polarization state of incident light
from the synchrotron, and because a previous study
has extensively investigated this
effect experimentally
2
, 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 tw
o orders of
magnitude larger than the σ
yy
component, plotted in Figure S4, we argue that the
observed optical response derives almost entirely f
rom lightmaterial interactions along
the armchair direction. As a result, the only effe
ct of elliptically polarized light is to scale
down the observed modulation strength. Probing dev
ices with light of properly aligned
polarization – linear along the armchair direction
– would maximize this modulation
strength; however, the underlying physics would be
unchanged.
Figure S3:
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 corre
spond to the armchair and zigzag
lattice directions, respectively, and the measureme
nt site, indicated by a red, dashed
circle.
Figure S4:
Calculated σ
yy
optical conductivities at different Fermi levels f
or
a)
the 6.5
nm flake,
b)
the 25 nm flake,
c)
the 7 nm flake and
d)
the 14 nm flake. In all 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 for measurements of the 6.5 nm and 25 nm flake
s effectively scales the gate
modulation as the strength of the interaction of th
e beam with the σ
xx
vs σ
yy
optical
conductivity components changes.
IV.
Carrier Concentration Determination
We estimate carrier concentration in our flakes fro
m gated resistance measurements by
noting the applied bias at which the flake is appro
ximately charge neutral – ie, least
conductive – and using a parallel plate capacitor m
odel to calculate the charge added
between that bias and 0 V. For 285 nm silicon oxid
e, the parallel plate model results in a
capacitance per unit area of c = ε/d = 12 nF/cm
2
. We then calculate ∆Q = C∆V.
V.
Accumulation/Depletion Length Determination
We estimate the screening length in our flakes usin
g the ThomasFermi method adopted
for black phosphorus by Tony Low, et al. The resul
t of this calculation is shown in
Figure S5, which describes band bending in the film
as a function of depth / thickness.
The screening length is of order 3 nm, indicating t
hat band bending yields modulation
that varies significantly along the depth axis of o
ur flakes.
Figure S5:
Calculated approximate voltage drop across the fl
ake using the Thomas
Fermi method. The screening length is of order 3 n
m.
VI.
Thickness Characterization
Atomic Force Microscopy (AFM) was used to determine
the nominal thickness of the
Black Phosphorus samples analyzed. Scans are shown
in Figure S6.
Figure S6:
AFM Scans of BP samples presented in the main tex
t and Supporting
Information. a) Fig. 2, indicating 7 nm thickness b
) Fig. 3, indicating 14 nm thickness, c)
Fig. 4, indicating 6.5 nm thickness, d) Figure S1,
indicating 25 nm thickness.
VII.
Raman Characterization
Raman spectroscopy was used to both compare results
to standard literature for black
phosphorus, and to characterize oxidation as a func
tion of time. No appreciable change
are seen in our encapsulated devices, suggesting th
at while oxide appears to form at some
point during fabrication, it does not continue to f
orm during our measurements.
Figure S7:
a)
Raman spectrum of a few layer BP flake using a 514
nm laser showing the
Ag
1
, B
2g
and Ag
2
peaks. The Ag
2
peak position suggests a flake thickness of 46 nm
.
Spectra acquired at times ranging from 0 to 1095 mi
ns are overlayed. No appreciable
shifts in peak in changes in peak magnitude are vis
ible as a function of time.
b)
Normalized intensity of Ag
1
and Ag
2
peaks as a function of time again suggesting no
signs of oxidation degradation or decay.
c)
Time evolution of ratio of Ag
1
/Ag
2
(known to
be a clear indicator of oxidation) suggesting no ap
preciable change over 1095 mins
further indication of no appreciable oxidation or d
egradation outside of the
initial/immediate oxide formation upon exfoliation.
1. Mao, N.; Tang, J.; Xie, L.; Wu, J.; Han, B.; Lin
, J.; Deng, S.; Ji, W.; Xu, H.; Liu,
K.; Tong, L.; Zhang, J.
Journal of the American Chemical Society
2016,
138, (1), 300
305.
2. Guowei Zhang, A. C., Shenyang Huang, Chaoyu Song
, Tony Low,; Yan, H.
arXiv:1607.08049
2016
.