of 31
A new metal transfer process for van der Waals contacts to vertical Schottky
-
junction
transition metal dichalcogenide photovoltaics
Cora M. Went
1,2
, Joeson Wong
3
, Phillip R. Jahelka
3
, Michael Kelzenberg
3
, Souvik Biswas
3
, Harry
A. Atwater
2,3,4
*
1
. Departm
ent of Physics, California Institute of Technology, Pasadena, CA 91125, USA
2. Resnick Sustainability Institute, California Institute of Technology, Pasadena, CA 91125, USA
3
. Thomas J. Watson Laboratory of Applied Physics, California Institute of Technolo
gy, Pasadena,
CA 91125, USA
4
. Joint Center for Artificial Photosynthesis, California Institute of Technology, Pasadena, CA
91125, USA
*Corresponding author: Harry A. Atwater (
haa@caltech.edu
)
Abstract
Two
-
dimensio
nal transition metal dichalcogenides are promising candidates for ultrathin
optoelectronic devices due to their high absorption coefficients and intrinsically passivated
surfaces. To maintain these near
-
perfect surfaces, recent research has focused on fabr
icating
contacts that limit Fermi
-
level pinning at the metal
-
semiconductor interface. Here, we develop a
new, simple procedure for transferring metal contacts that does not require aligned lithography.
Using this technique, we fabricate vertical Schottky
-
j
unction WS
2
solar cells with Ag and Au as
asymmetric work function contacts. Under laser illumination, we observe rectifying behavior and
open
-
circuit voltage above 500 mV in devices with transferred contacts, in contrast to resistive
behavior and open
-
cir
cuit voltage below 15 mV in devices with evaporated contacts. One
-
sun
measurements and device simulation results indicate that this metal transfer process could enable
high
-
specific
-
power vertical Schottky
-
junction transition metal dichalcogenide photovolt
aics, and
we anticipate that this technique will lead to advances for two
-
dimensional devices more broadly.
Two
-
dimensional (2D) semiconducting transition metal dichalcogenides (TMDs),
including MoS
2
, WS
2
, MoSe
2
, and WSe
2
, are promising for many optoel
ectronic applications,
including high
-
specific
-
power photovoltaics
1
4
. With absorption coefficients 1
2 orders of
magnitude higher than conventional semiconductors, monolayer (<1 nm thick) TMDs can absorb
as much visible light as about 15 nm of GaAs or 50 nm of Si
5
. Both multilayer and monolayer
TMDs can achieve near
-
unity broadband absorption in the visible range
6,7
. Due to their layered
structure and out
-
of
-
plane van der Waals bonding, TMDs have intrinsically passivated s
urfaces
with no dangling bonds and can form heterostructures without the constraint of lattice matching.
To take advantage of the intrinsically passivated surfaces of TMDs, gentle fabrication
techniques are needed to form metal contacts without damaging t
he underlying semiconductor. A
number of new contact techniques have been presented recently, including one
-
dimensional edge
contacts
8
, via contacts embedded in hBN
9
, slowly
-
deposited In/Au contacts
10
, and 2D metals
11
.
Recently, Liu
et al
have shown that tran
sferring rather than evaporating metal contacts onto TMDs
can yield interfaces with no Fermi
-
level pinning, where the Schottky barrier height can be
predicted by the ideal Schottky
-
Mott rule
12
. Their work demonstrates the utility of transferring an
arbitrary three
-
dimensional metal onto a 2D
material, forming a nondamaging van der Waals
contact. However, this technique requires a final aligned lithography step to expose the contact
under the polymer used for transfer, which limits its scalability
12
.
To date, the above techniques for gentle contact fabrication have been applied
to device
geometries where carriers are collected laterally rather than vertically. Though laterally
-
contacted
devices are important for electronic applications, such as field
-
effect transistors, vertically
-
contacted devices are necessary for optoelectron
ic applications that require scalable photoactive
areas, such as solar cells. Van der Waals contacts could have an even greater advantage for these
vertical device geometries, where the ratio of contact area to device area is often higher than in
lateral d
evice geometries.
Schottky
-
junction solar cells represent one specific device geometry where van der Waals
metal contacts could enable high performance in vertical devices. Although vertical
-
junction solar
cells are more aligned with conventional photovolt
aics
13
, most Schottky
-
junction TMD solar cells
studied have been lateral
-
junction devices
12,14,15
. Vertical Schottky
-
junction TMD solar cells have
been limited by ohmic I
-
V behavior, low external quantu
m efficiencies, and low open
-
circuit
voltages, likely due to Fermi
-
level pinning induced by contact evaporation
6,16
. New gentle contact
fabrication tech
niques have the potential to eliminate this Fermi
-
level pinning, enabling high
-
efficiency vertical TMD solar cells in the Schottky
-
junction geometry.
Here, we develop a simple technique for transferring metal contacts, where all lithographic
patterning is
done on a donor substrate rather than on the active device. We apply this technique
to vertical Schottky
-
junction solar cells with multilayer TMD absorber layers. Due to the tradeoff
between bandgap energy and photoluminescence quantum yield, the theoreti
cal maximum power
conversion efficiency achievable for multilayer and monolayer single
-
junction solar cells is
similar
4,17
, and further, tunneling limits transport in monolayer vertical devices
18
, so we focus on
multilayer devices in this work. Ultrathin (10
20 nm) WS
2
forms the absorber layer, while Ag and
Au form the asymmetric
-
work
-
function contacts. Devices made with transfer
red metal contacts
show diode
-
like I
-
V behavior with a near
-
unity ideality factor and high V
OC
, while similar devices
made with evaporated metal contacts show ohmic I
-
V behavior and near
-
zero V
OC
. We
demonstrate peak external quantum efficiency (EQE) of >4
0% and peak active
-
layer internal
quantum efficiency (IQE
active
) of >90% in transferred
-
contact devices. Using a solar simulator, we
measure a photovoltaic power conversion efficiency of 0.46%, comparable to what has been seen
in other ultrathin vertical T
MD photovoltaics
19
. Device simulations of further
-
optimized
geometries suggest that this new metal transfer process has the potential to enable Schottky
-
junction TMD solar cells with power conversion efficiencies greater
than 8% and specific powers
greater than 50 kW/kg.
Results
& Discussion
Fabrication of vertical WS
2
Schottky
-
junction solar cells
.
We prepare vertical WS
2
Schottky
-
junction solar cells made from 16
-
nm
-
thick WS
2
absorber layers, with Ag (
f
Ag
»
4.3 eV) a
nd Au
(
f
Au
»
5.1 eV)
as asymmetric work function contacts (Fig. 1
a
)
12
. Template
-
stripped Ag, which
exhibits an RMS roughness <0.5 nm, forms both the electron
-
collecting bottom contact and back
reflector for all devices
20
. We mechanically exfoliate WS
2
directly onto the Ag substrate. The
subwavelength
-
thick WS
2
achieves broadband, angle
-
insensitive absorption on top of the highly
reflective Ag, giving the WS
2
a de
ep purple color as illustrated in Fig. 1
b
6,21
. For transferred
-
contact devices, we trans
fer thin Au disks from a thermally
-
oxidized Si donor substrate to form
the semi
-
transparent hole
-
collecting top contact, using the process described in the following
section. Both the top surface of the template
-
stripped Ag and the bottom surface of the tr
ansferred
Au inherit the smoothness of the SiO
2
/Si donor substrate, leading to near atomically
-
sharp metal
-
WS
2
interfaces
12,20
. For comparison, we also fabricate devices by d
irect evaporation of thin Au
disks onto the WS
2
using standard photolithography techniques.
The ideal band diagram of this Schottky
-
junction solar cell is shown in Fig. 1
c
. We assume
a doping concentration of 10
14
cm
-
3
for WS
2
, as provided by the bulk cry
stal vendor. Since the
length of the depletion region at a Schottky junction between bulk WS
2
and either Au or Ag is on
the order of 1
μ
m, the device is fully depleted. We measure the final thicknesses of the WS
2
and
the Au to be 16 nm and 19 nm, respectiv
ely, using atomic force microscopy (Fig. 1
d
).
Metal transfer process
.
We develop a new, simple process for transferring metal contacts onto
TMDs (Fig. 2). This process relies on a self
-
assembled monolayer (SAM) to reduce the adhesion
between the Au and th
e SiO
2
/Si
donor substrate
22
, a thermoplastic polyme
r to preferentially pick
up or drop down the metal
23
, and a variable peeling rate to tune the velocity
-
dependent adhesion
between a metal and a viscoelastic stamp
22
.
Briefly, we create a SAM on clean thermally
-
oxidized Si chips in a vacuum desiccator
22
.
We then deposit 20
nm of Au via electron beam evaporation. Using photolithography, we define
the contact areas with
positive photoresist and a positive photomask. We etch the Au outside the
masked contact areas, then dissolve the remaining photoresist in acetone, leaving Au disks on the
SAM
-
coated SiO
2
/Si substrates. We prepare a polydimethylsiloxane (PDMS) stamp coate
d with
the thermoplastic polymer polypropylene carbonate (PPC) on a glass slide
23
. In a 2D transfer setup,
we align and slowly lower the stamp onto a contact at 60ºC. We set the temperature to 40ºC, and
once the stage reaches that temperature, we raise the transfer ar
m rapidly to peel the stamp and
pick up the contact. We align the contact with the target TMD and slowly lower the stamp down
at 60ºC, and then slowly peel it away immediately after contact at the same temperature. The
contact delaminates from the PDMS/PPC
stamp and sticks to the TMD. Further details of the
procedure are provided in Supplementary Note 1.
This metal transfer technique has worked in 15 out of 16 devices fabricated thus far (94%
yield). It works for both 20
-
nm
-
thick and 100
-
nm
-
thick Au, and ca
n likely be extended to other
metals and to larger
-
scale contacts (i.e. for contacts to CVD
-
grown TMDs). A substantial
advantage of this technique is that, whereas prior metal transfer techniques require a final aligned
electron
-
beam lithography step to ex
pose the contact area
12
, this techni
que only utilizes unaligned
photolithography to define the initial contacts on the SiO
2
/Si donor substrate. This allows for
batch
-
fabrication of an array of contacts that can then be picked up, aligned, and printed to form
multiple devices. Further, this m
etal transfer process could enable van der Waals contacts to air
-
and moisture
-
sensitive nanomaterials, such as lead halide perovskites or black phosphorus, to be
formed without removing the sample from an inert environment.
Comparison of transferred and
evaporated metal contacts
.
We measure I
-
V curves under
illumination with a 633 nm laser focused to a ~1
μ
m
2
spot in a confocal microscope at room
temperature. In devices with transferred metal contacts, we observe rectifying I
-
V curves and a
pronounced pho
tovoltaic effect (Fig. 3
a
). We measure a V
OC
of 510
mV under the maximum laser
excitation. Short
-
circuit current follows a power law as a function of incident power, I
SC
= P
inc
a
,
with
a
close to 1 (Fig. 3
c
). According to the diode equation, V
OC
scales line
arly with ln(I
SC
) and
can be fit with an ideality factor n = 1.2 (Fig. 3
d
). This near
-
unity ideality factor confirms the high
interface and material quality in these devices. The ideality factor, diode
-
like behavior and high
open
-
circuit voltage suggest th
at a Schottky junction is successfully formed in devices with
transferred contacts.
In contrast, we observe resistive behavior and a small photovoltaic effect in devices with
evaporated top metal contacts (Fig. 3
b
). I
SC
vs. P
inc
follows a power law with
a
less than 1 (Fig.
3
e
). As shown in Fig. 3
f
, this device behaves as a resistor with R = 3.1
k
W
. At comparable laser
powers, V
OC
is around 4 mV in evaporated contact devices and 400 mV in transferred contact
devices, and J
SC
is three to four times higher fo
r transferred contacts than for evaporated contacts.
Previous work demonstrates that due to Fermi
-
level pinning, evaporated Au and transferred Ag
have effectively the same barrier height for electrons and holes
12
. Assuming an effective work
function difference between Au and Ag of 50
meV, de
vice simulations can predict the purely
resistive behavior in an evaporated
-
contact Schottky
-
junction device (Supplementary Fig. 1). This
evidence points to strong Fermi
-
level pinning in devices with evaporated contacts due to interface
states induced by t
he Au evaporation.
In devices with transferred contacts, the slope of the I
-
V curve at short
-
circuit increases
linearly with increasing laser power, corresponding to a decreasing shunt resistance
(Supplementary Fig. 2
a
). This photoshunting effect occurs i
n solar cells without perfectly selective
contacts due to increased minority carrier conductivity across the device under illumination
24,25
.
Device simulations can replicate this photoshunt pathway without the addition of any external
shunt resistance (Supplementary Fig. 2
b
). In future devices, the introduction
of contacts with
greater carrier selectivity could reduce or eliminate the photoshunting observed here.
Quantum efficiency and photocurrent generation
.
Light
-
beam induced current (LBIC, or
photocurrent) maps, acquired with a 633
nm laser in a confocal mi
croscope, show uniform current
generation under the entire Au disk contact, except where shaded by the contact probe (Fig. 4
a
).
The uniformity of the photocurrent demonstrates that the Au is homogeneously semitransparent
and in good contact with the TMD. I
mportantly, this indicates that the area of the Au disk can be
used to accurately define the device active area (Supplementary Fig. 3) and suggests that one
-
dimensional device simulations are sufficient to describe the behavior in these vertical devices
26
.
Further, it demonstrates that there are no visible bubbles created during the metal transfer process.
The measured total
absorption (Fig. 4
c
) matches well with the absorption calculated using
the transfer matrix method (Fig. 4
b
), as has been previously demonstrated in TMD solar cells
6,16
.
To calculate the active
-
layer absorption in the experimental WS
2
devices, we subtract the
simulated parasitic absorption (the sum of the Au and Ag curves in Fig. 4
b
) from the
experimentally measured total absorption in Fig. 4
c
. The mean a
ctive
-
layer absorption from
450
nm to 650
nm is 39%. The reduced absorption in our devices relative to what has been
previously demonstrated in WS
2
on a metal back
-
reflector (~80% over this wavelength range)
6
is
due to parasitic absorption and reflection losses from the 19
-
nm
-
thick Au top contact. Using a
more transparent top contact could double our photogenerated c
urrent, assuming identical work
function and conductivity.
The external quantum efficiency (EQE) of the device follows the spectral shape of
absorption well, averaging 28% from 450
nm to 650
nm and reaching a peak of above 40% around
550
nm (Fig. 4
d
). To
accurately determine EQE, we multiply by a shading factor of 1.39 to correct
for shading from the probes (see Methods). Internal quantum efficiency (IQE) remains relatively
flat across all wavelengths above the bandgap, averaging 49% from 450
nm to 650
nm
(Fig. 4
e
).
IQE
active
, calculated by dividing EQE by the active
-
layer absorption rather than the total absorption,
is greater than 90% at its peak, and averages 74% between 450
nm and 650
nm (Fig. 4
f
). This high
IQE
active
suggests efficient collection of p
hotogenerated carriers in transferred
-
contact devices.
Performance under one
-
sun illumination
.
Vertical Schottky
-
junction WS
2
solar cells with
transferred top contacts achieve reasonable photovoltaic performance when measured under
simulated AM1.5G illum
ination. Fig. 5 shows the AM1.5G I
-
V behavior of a representative
device. We divide the measured current by the device active area to yield current density, then
then further divide by a factor of 0.67 to account for spectral mismatch between our solar sim
ulator
calibration point and the true AM1.5G spectrum (see Methods; Supplementary Fig.
4)
27
. The
spectral mismatch correction leads to a 50% increase in short
-
circuit current, so the V
OC
and powe
r
conversion efficiency of the device are likely underestimated here. We measure a V
OC
of 256
mV,
a corrected J
SC
of 4.10
mA/cm
2
, a fill factor (FF) of
0.44, and a power conversion efficiency (PCE)
of 0.46%. This efficiency is in the range of what others h
ave reported for ultrathin TMD
photovoltaics
15,16,19
. Using the densities of Au, WS
2
, and Ag, we estimate a specific pow
er of
3
kW/kg for this device.
By fitting the one
-
sun I
-
V curve using the diode equation with series and shunt resistances,
we estimate a shunt resistance (R
SH
) of 231
W
cm
2
and a negligible series resistance (R
S
), as shown
in Supplementary Fig. 5. The
shunt resistance is likely due to the photoshunting behavior discussed
above, and could be reduced by design and realization of contacts that are more carrier
-
selective.
This photovoltaic performance is consistent among multiple measurements and devices.
The J
SC
of 4.10
mA/cm
2
that we measure with the solar simulator is within 10% of the J
SC
that we
calculate by integrating the EQE over the solar spectrum (4.55
mA/cm
2
). We believe that probe
shading, which we correct for in EQE measurements but not in sol
ar simulator measurements,
accounts for the 10% discrepancy. Though the J
SC
varies due to differences in thickness and
therefore absorption in exfoliated flakes, the V
OC
is replicable across all devices fabricated for this
work. As shown in Supplementary F
igs. 6 and 7, V
OC
is between 220
mV and 260
mV in all four
devices measured under one
-
sun illumination, and V
OC
is greater than 220
mV in
six different
devices measured under illumination with a halogen lamp (~20 suns power density). The I
-
V
curves show no
hysteresis when swept in the forwards and backwards directions (Supplementary
Fig. 8).
Simulated performance of optimized devices
.
To examine and further optimize the performance
of these devices, we simulate a variety of device geometries. The assumed m
aterial parameters of
the WS
2
are detailed in Supplementary Table 1. Simulating the same device geometry as our
experimental device yields the I
-
V curve in Fig. 6
a
. The simulated J
SC
of 5.7
mA/cm
2
is consistent
with our measured active
-
layer IQE of 74% and
the J
SC
of 4.55
mA/cm
2
estimated from the EQE.
The simulated V
OC
of 646
mV and R
SH
of 2240
W
cm
2
are considerably higher than the V
OC
of
256
mV and R
SH
of 231
W
cm
2
observed in our one
-
sun measurements. This demonstrates that
with further optimization, ou
r device geometry could achieve higher voltages and less shunting
than we currently see (Supplementary Fig. 9). As a first improvement, we suggest replacing Au
with a different high
-
work
-
function metal, as Au is known to form thiol bonds with sulfides that
could affect the quality of the van der Waals contact
12,28
.
To identify a pot
ential path towards high
-
efficiency vertical Schottky
-
junction WS
2
solar
cells, we simulate a series of optimized devices (Fig. 6
b
). Using an optimized thickness of WS
2
(26 nm) for maximum absorption under 20
nm of Au increases the J
SC
to
7.1 mA/cm
2
. The J
SC
can
be further increased to 12.5
mA/cm
2
by replacing Au with a transparent top contact, assuming an
identical work function to Au and no parasitic absorption or reflection. By selecting metal work
functions that are optimally aligned to the conduction a
nd valence bands of WS
2
, we predict a V
OC
increase of 230
mV. Combining transparent top contacts and optimized metal work functions
yields the device shown in Fig. 6
c
, with a V
OC
of 898
mV, a J
SC
of 12.7
mA/cm
2
, a fill factor of
0.78, and a power conversio
n efficiency of 8.9%. This simulated power conversion efficiency in a
device with a thickness <150 nm represents a specific power of 58
kW/kg, demonstrating that this
metal transfer process has the potential to enable devices with an unprecedented power
-
pe
r
-
unit
-
weight ratio for transportation and aerospace applications.
Conclusion
We develop here a process for transferring metal contacts with near
-
atomically smooth
interfaces that has high
-
yield, allows for batch fabrication, and eliminates aligned litho
graphy. We
expect that this procedure will be highly relevant and useful to the 2D community, as well as to
researchers working on air
-
sensitive nanomaterials, as it allows all processing to be done on the
contacts rather than the device. By applying this
new technique to vertical Schottky
-
junction TMD
solar cells, we demonstrate that transferred contacts are particularly advantageous for vertical
device geometries, which are important for photovoltaic and other optoelectronic applications due
to their scal
able active areas.
The rectifying I
-
V curves shown in transferred
-
contact devices and resistive I
-
V curves
shown in evaporated
-
contact devices support the hypothesis that transferring contacts can reduce
Fermi
-
level pinning and allow the work function asy
mmetry between the contacts to define the
maximum achievable V
OC
. We observe active
-
layer absorption >55%, EQE >40%, and active
-
layer IQE >90% in these devices, demonstrating efficient collection of photogenerated carriers.
Under one
-
sun illumination, we m
easure a V
OC
of 256
mV, a J
SC
of 4.10
mA/cm
2
, a fill factor of
0.44, and a power conversion efficiency of 0.46%. We highlight areas for improvement by
simulating the behavior of optimized devices based on this architecture and show 8.9% simulated
efficienc
y and 58
kW/kg simulated specific power in a device with transparent top contacts,
optimized thickness, and ideal metal work functions for carrier extraction.
Given the proof
-
of
-
concept performance and the clear pathways for improvement
presented here for
devices less than 150
nm
thick, ultrathin vertical Schottky
-
junction TMD solar
cells with transferred contacts are promising candidates for high
-
specific
-
power photovoltaic
applications. We anticipate that this new metal transfer process will enable simil
ar advances for
2D TMD devices beyond Schottky
-
junction solar cells, as well as for nanomaterial
-
based devices
more broadly.
Methods
Device fabrication.
Template
-
stripped silver substrates are prepared as described previously
16,20
.
WS
2
is mechanically exfoliated directly onto template
-
stripped silver from the bulk crystal (HQ
Graphene) using Scotch tape. For transferred contact devices, Au top contacts are prepare
d and
transferred using the metal transfer technique summarized in the main text, and described in detail
in Supplementary Note 1. The SAM used is trichloro(1H,1H,2H,2H
-
perfluorooctyl)silane
(PFOTS, Sigma Aldrich), the photoresist used is S1813, and the Au
etchant used is Transene Gold
Etchant TFA. For evaporated contact devices, Au top contacts are patterned using standard
photolithography techniques as described previously
16
. Contacts are fabricated on WS
2
within 12
hours of exfoliation. Final WS
2
and Au thicknesses are confirme
d using atomic force microscopy
(Asylum Research).
Photocurrent
and
power
-
depend
ent I
-
V.
Photocurrent and power
-
dependent IV are measured
on a scanning confocal microscope (Zeiss Axio Imager 2) using a long working distance objective
(50x, NA = 0.55). De
vices are contacted using piezoelectrically controlled micromanipulators
(MiBots, Imina Technologies). I
-
V curves are measured with a Keithley 236 Source
-
Measure Unit
using custom LabView programs. Laser powers are measured using a USB power meter
(ThorLab
s). All measurements are performed under ambient temperature and pressure.
Absorption
and
EQE.
Absorption and EQE are measured using a home
-
built optical setup with
a long working distance objective (50x, NA = 0.55). A supercontinuum laser (Fianium) is co
upled
to a monochromator to produce a tunable, monochromatic light source. A chopper and lock
-
in
detection are used for all measurements. For absorption, the sample reflectance is measured using
a NIST
-
calibrated photodetector (Newport 818
-
ST2
-
UV/DB) with
a beamsplitter. A protected
silver mirror (Thorlabs) is used to calibrate the reflectance based on its reported reflectance curve,
and a dark background is subtracted from both measurements. For EQE, the current generated by
the sample is probed using MiBo
ts and compared to the current collected by the NIST calibrated
photodetector when placed at the sample position, corrected by the photodetector’s responsivity.
Absorption and EQE measurements are both corrected by a shading factor of 1.39 that corrects fo
r
the shading of the MiBot tips, which is calculated by comparing absorption with and without the
tips in place and averaging over the spectral range 450 nm
650 nm.
Solar simulator.
One
-
sun I
-
V curves are measured using a 1 kW Xenon arc lamp (Newport Ori
el)
with an
AM1.5G filter (ABET Technologies). To ensure 100
mW/cm
2
incident power, the lamp
power is adjusted to generate the correct current on a Si reference cell placed at the same location
as the sample. MiBots are used to contact the device, and I
-
V
curves are measured with a Keithley
2425 SourceMeter using custom LabView programs. The current density is divided by a spectral
mismatch factor to account for the difference in bandgap between our WS
2
sample and our Si
reference cell and the difference in
spectrum between our solar simulator and AM1.5G
27
. As no
EQE data was available for our device below 400
nm, linear extrapolation was used, leading to
about a 5% error in the spectral mismatch
factor and the reported J
SC
values. The device area was
assumed to be that of the Au disk, which has a diameter of 28
μ
m.
Device simulations.
Absorption and generation are calculated using the transfer matrix method,
with optical constants for WS
2
taken f
rom literature
29
. All other device simulations are performed
using Lumerical Device. The WS
2
doping was specified by the bulk crystal vendor (HQ
Graphene). Other WS
2
parameters, including bandgap
30
, work function
31
, DC permittivity
32
,
effec
tive mass
33
, out
-
of
-
plane mobility
34
36
, and photoluminescence quan
tum yield
37
39
are taken
from literature and listed in Supplementary Table 1. The radiative recombination coefficient is
calculated using the Roosbroeck
-
Shockley relation
40
, and the Shockley
-
Read
-
Hall lifetime for
minority carriers is then estimated using the photoluminesce
nce quantum yield.
Data availability
All data supporting the findings of this study are available from the corresponding author upon
request.
References
1.
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