Supporting Information Anisotropic Quantum Well Electro
-
Optics in Few
-
Layer Black
Phosphorus
Michelle C. Sherrott
1,2ǂ
, William S. Whitney
3ǂ
, Deep Jariwala
1,2,^
, Souvik Biswas
1
, Cora M.
Went
2,3
, Joeson Wong
1
, George R. Rossman
4
, Harry A. Atwater*
1,2,5
1. Thomas J. Watson Laboratory of Applied Physics, California Institute of Technology,
Pasadena, CA 91125, USA
2. Resnick Sustainability Institute, California Institute of Technology, Pasadena, CA 91125, USA
3. Department of Physics, California Institute o
f Technology, Pasadena, CA 91125, USA
4. Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena,
CA 91125, USA
5. Joint Center for Artificial Photosynthesis, California Institute of Technology, Pasadena, CA
91125, USA
ǂ
Equal contributors
^ Current affiliation, Department of Electrical and Systems Engineering, University of
Pennsylvania, Philadelphia, PA, 19104, USA
*Corresponding author: Harry A. Atwater (
haa@caltech.edu
)
S1. Id
entification of Crystal Axes:
To identify the principal crystal axes of the BP flakes, cross
-
polarization microscopy was used.
Incident light passes through a linear polarizer, then the sample, and finally through a second,
orthogonal linear polarizer. Th
is technique has been previously described
[
1
]
. By rotating the
sample, the fast and slow optical axes (and hence crystal axes) are identified.
S2. AFM Characterization of
Flake Thickness:
To characterize the thickness of the BP flakes, AFM measurements are made of the entire
device stack. Cross
-
cuts of AFM images of the flakes are shown in Figure S1. We note that, as
previously described, AFM measures a thickness 2
–
3 nm
larger than the true value, due to the
presence of thin phosphorus oxide layers at each interface
[
2
]
. Moreover, we note that the
presence of the top oxide and nickel coatings prevent perfectly
accurate determination of
thickness, and therefore we additionally determine thickness based on the energy levels of the
band gap and intersubband transitions.
Figure S1
AFM
Characterization of Flake Thickness
. a) AFM crosscut of ‘3.5 nm’ thick
flake,
showing measured thickness of 6.5 nm. b) AFM crosscut of ‘8.5 nm’ thick flake, showing
measured thickness of 11.5 nm. c) AFM crosscut of ‘20 nm’ thick flake, showing measured
thickness of 20 nm. Thicknesses have some uncertainty due to Ni/Al
2
O
3
top
layers.
S3. Tunability for 8.5 nm Flake along Zigzag Axis:
Fourier transform infrared spectroscopy is used to measure electrical tunability of extinction for
light polarized along the zig
-
zag
crystal axis of the 8.5 nm flake, as with the 3.5 nm flake. The
corresponding spectra for tunability of the floating device under an applied field and contacted
device under direct gating are shown in Fig. S2a and S2b, respectively. No tunability is see
n for
this polarization, as with the 3.5 nm flake.
Figure S2.
Tunability for 8.5 nm Flake along Zigzag Axis
. a)
Tunability of BP oscillator strength
with field applied to floating device, for light polarized along the ZZ axis. b) Tunability of BP
oscill
ator strength with gating of contacted device, for light polarized along the ZZ axis.
S4. Tunability for 8.5 nm Flake at Lower Energies:
To better understand the behavior of the QCSE at the band edge of the 8.5 nm flake, a second
measurement was made of e
lectrical tunability of extinction for light polarized along the
armchair crystal axis of the 8.5 nm flake using a KBr beamsplitter instead of CaF
2
. With better
resolution at lower photon energies, clear QCSE redshifting of intersubband transitions can be
seen at the lowest transition energies. The tunability strength is plotted in arbitrary units, since
the extinction tunability is still normalized to the CaF
2
extinction / oscillator strength maximum.
Figure S3.
Tunability for 8.5 nm Flake at Lower Ene
rgies
.
Tunability of BP oscillator strength
with field applied to floating device,
for light polarized along the AC
axis, measured at lower
photon energies.
S5. Optical Response of Top Contact Material:
In order to verify that no interference effects or s
purious absorption features are present in the
fabricated device for visible measurements, we performed full wave Finite Difference Time
Domain (FDTD) simulations using the Lumerical software package. We verify that the
transmittance through 5 nm Ni/90 nm
Al
2
O
3
/5 nm Ni/0.5 mm SrTiO
3
is featureless, and
therefore we can be confident that all tunability is due to the BP. For this reason, we select Ni
as the semi
-
transparent top and bottom
-
contact and 45 nm thick top and bottom gate
dielectrics of Al
2
O
3
.
Figure S4.
Optical Response of Top Contact Material.
FDTD simulation results of transmittance
through Ni/Al
2
O
3
/Ni/SrTiO
3
superstrate/substrate for visible BP measurements. No features are
observed.
S6. High reflectance modulation of 6 nm BP flake:
In
order to demonstrate that thin BP films can generate technologically compelling absolute
modulation depths, we present armchair
-
axis FTIR reflectance data for a 6 nm flake. This data,
for which reflectance at 100 V is normalized to reflectance at zero bia
s, is presented in Figure
S5. The device structure consists of 6 nm BP on 285 nm SiO
2
on Si, with a 10 nm Al
2
O
3
cap.
Further, the observed modulation depth can be dramatically enhanced by integrating the BP
into a resonant optical cavity, as described in
Fig. 5 in the main text.
Figure S5.
High reflectance modulation of 6 nm BP flake.
Armchair
-
axis FTIR reflectance is
shown for 100 V bias, normalized to the zero bias reflectance. Data taken at room temperature
under ambient conditions.
S7.
Comparison of Extinction Modulation to Theory
We have used theory results for the tunable complex refractive index of black phosphorus to
calculate the extinction modulation predicted for a device like those presented in Fig. 2 and Fig.
3, to allow us to c
ompare our results to available theory. This theory work treats the quantum
-
confined Stark effect and band filling effects for a 5 nm black phosphorus flake using a self
-
consistent Schrödinger
-
Poisson model in combination with a Kubo formula to arrive at
a charge
density dependent optical conductivity.
3
We use those reported optical constants and a
transfer matrix model to calculate extinction modulation, which we present in Fig. S6 in the
same units of modulation strength that we use in the main text. We see a predicted
modulation strength and tre
nds that qualitatively match those seen in experiment: redshifting
optical transition energies, and the appearance of absorption consistent with a “forbidden”
optical transition between conduction and valence subbands with different quantum numbers.
More
details on the energies of these transitions are available in Lin, et al.
3
Figure S6.
Predicted modulation strength for a device like those in Fig. 2 and Fig. 3, with a 5 nm
black phosphorus flake, based on a transfer matrix calculation and theoretical treatment of the
electrically tunable complex
refractive index of black phosphorus. The predicted modulation
strength and trends qualitatively match those seen in experiment.
References:
(
1)
Whitney, W. S.; Sherrott, M. C.; Jariwala, D.; Lin, W.
-
H.; Bechtel, H. A.; Rossman, G. R.;
Atwater, H. A.
Nano Letters
2017,
17, 78
-
84.
(2)
Tian, H.; Guo, Q.; Xie, Y.; Zhao, H.; Li, C.; Cha, J. J.; Xia, F.; Wang, H.
Advanced Materials
2016,
28, 4991
-
4997.
(3)
Lin, C.; Grassi, R.; Low, T.; Helmy, A. S.
Nano Letters
2016,
16, 1683
-
1689.