of 6
Supporting Information
Near-Unity Absorption in Van der Waals Semiconducto
rs
for Ultrathin Optoelectronics
Deep Jariwala,
1,2
Artur R. Davoyan,
1,2,3
Giulia Tagliabue,
1,4
Michelle C. Sherrott,
1,2
Joeson
Wong
1
and Harry A. Atwater
1,2,3,4*
1
Department of Applied Physics and Materials Science
, California Institute of Technology, Pasadena,
CA91125, USA
2
Resnick Sustainability Institute, California Instit
ute of Technology, Pasadena, CA91125, USA
3
Kavli Nanoscience Institute, California Institute o
f Technology, Pasadena, CA91125, USA
4
Joint Center for Artificial Photosynthesis, Califor
nia Institute of Technology, Pasadena, CA91125, US
A
*Corresponding author:
haa@caltech.edu
S1. Absorbance calculations:
Absorption in ultrathin TMDCs on metals was calcula
ted using the transfer matrix method.
1
The
optical constants used for the calculation are the
bulk crystal values for each TMDCs from
previously published reports.
2, 3
Permittivities of Ag and Au were taken from Jhonso
n and
Christie
4
.
The maximum integrated absorbance in ultrathin TMDC
s on a reflective metallic substrate is
only achieved for a critical TMDC thickness which l
ies somewhere between 1215 nm. Below
this critical thickness, the absorption in the red
part of the spectrum is reduced due to high
reflection from the underlying metal. Above this th
ickness, the absorption in the blue part of the
spectrum is reduced due to increased reflection fro
m the TMDC owing to the mismatch in
refractive index between air and the TMDC. Figure 2
cd in the manuscript can be seen for
experimental verification. The coupling of TMDCs wi
th reflective metals is crucial for this
resonantly enhanced absorption to occur. In case of
a free standing WSe
2
of similar thickness,
the total absorption is far lesser approaching ~40%
between 612 nm thickness before falling
down again due to increased reflection owing to ind
ex mismatch at the air /TMDC interface
(Figure S1).
Figure S1: Calculated absorption in free standing W
Se
2
with varying thickness. The total
absorption increases with increasing thickness upto
1214 nm and approaches ~40% following
which it steadily drops down with further increase
in the thickness.
S2. Absorption with Au back reflectors:
Figure S3 below shows calculated and measured absor
ption spectra for varying thicknesses of
WSe
2
and WS
2
on template stripped Au back reflectors. A good qu
alitative and quantitative
agreement between the measured and calculated spect
ra is apparent once again. However in Au,
interband absorption starts dominating below 550 nm
in wavelength. Therefore, the useful
absorption in the TMDC layer (dashed lines) drastic
ally reduces at λ < 500 nm. Ag back reflector
is thus more suitable from an optical standpoint of
maximizing useful absorption.
Figure S3: Calculated (left) and measured (right) a
bsorption spectra of WSe
2
on Au (ab) and
WS
2
on Au(cd).
S3. Estimation of minority carrier diffusion length
.
Minority carrier diffusion length can be estimated
from the spatial photocurrent profile. In cases
where the diffusion length is larger than the spot
size, a single exponential model
 


 /
where I is the photocurrent,


is the peak photocurrent,

is the distance and
is the diffusion length can explain the photocurren
t profile and provide an estimate of diffusion
length. Considering that we are using a 633 nm lase
r for spatially resolving the photocurrent, the
diffraction limited resolution (given by 0.61λ/N.A.
), where N.A. is the numerical aperture of the
objective, = 0.8 in our case) is
~
500 nm in our measurement. Based on that, we can fi
t our
photocurrent data to the above exponential decay eq
uation and extract minority carrier diffusion
lengths. We have estimated diffusion length varying
from about 1.35 μm in Figure S4 a to about
3 μm in Figure S4 b.
Figure S4. a. Photocurrent profile of device shown
in Figure 3 e of the manuscript with a
minority carrier diffusion length of
~
1.35 μm b. Photocurrent profile of another represen
tative
device (19 nm WSe
2
on Au) shown in Figure 4 e of the manuscript with
a minority carrier
diffusion length of
~
3 μm.
S4. Absorbance and EQE measurements:
A homebuilt optical setup was used for both the a
bsorption and EQE measurements. A
supercontinuum laser (Fianium) coupled to a monochr
omator was used to provide the
monochromated incident light. The collimated beam w
as focused onto the sample with a long
working distance (NA = 0.55) 50x objective in order
to achieve nearly normal illumination. The
reflection spectrum was measured with a Si photodet
ector. Low noise signals were obtained by
using a chopper and a lockin amplifier. The measur
ed reflection signal was then normalized to
the reflection from a silver mirror (Thorlabs) in o
rder to obtain the absolute reflection spectrum,
R(λ). In the absence of any transmission, the absor
ption spectrum can be obtained as A(λ) = 1
R(λ).
The same illumination configuration was used for th
e EQE measurements. The photocurrent
signal produced by the TMDC device was measured at
each wavelength by mean of the chopper
and lockin amplifier. In addition, the power spect
rum incident on the sample was later measured
by placing the Si photodetector in the same positio
n as the sample.
During all measurements, a small fraction of the il
lumination beam is deviated onto an optical
fiber and sent to a second lockin amplifier, also
driven at the same frequency of the chopper.
This reference signal is used to account for fluctu
ations of the illuminating beam over time
enabling accurate normalization of the reflection a
nd photocurrent signals.
S5. WS
2
/WSe
2
heterojunctions:
Heterojunctions of fewlayer WS
2
/WSe
2
on Au substrates can also be fabricated by exfolia
tion
and layer stacking using the dry transfer technique
.
5
As compared to individual TMDC layers,
heterojunctions show more enhanced, broadband absor
ption as shown below in Figure S5 below.
Further since WS
2
and WSe
2
are known to form a typeII junction,
6
it is expected that the
photocurrent collection efficiencies will also be e
nhanced in a optoelectronic device fabricated
out of such heterojunctions with optimized layer th
icknesses. Future work will involve
fabricating metal ring contacts on such heterostruc
tures and also fabricating graphene contacts to
understand and enhance the carrier collection and o
pencircuit voltage in the resulting devices.
Figure S5: a. Optical micrograph of a WS
2
/WSe
2
/Au heterostructure of varying thicknesses
(scale bar = 5 μm). The blue, red and green boundar
ies indicate the WS
2
/Au, WSe
2
/Au and
WS
2
/WSe
2
/Au heterostructures regions respectively. The blue
, red and green circles denote the
spots from where the absorption spectra were acquir
ed in b. b. Absorption spectra from the
correspondingly colored circles in a. The layer thi
cknesses were measured using AFM. A clear
increase in integrated absorption (area under the c
urve) is observed the case of heterojunction
(green) vs individual WS
2
(blue) and WSe
2
(red) layers. c. Corresponding calculated spectra
using the transfer matrix method in good agreement
with the measurements in b.
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