Two-Dimensional Halide Perovskites: Tuning Electronic Activities of
Defects
Yuanyue Liu,
*
,
†
,
‡
Hai Xiao,
†
and William A. Goddard, III
*
,
†
†
Materials and Process Simulation Center and
‡
The Resnick Sustainability Institute, California Institute of Technology, Pasadena,
California 91125, United States
*
S
Supporting Information
ABSTRACT:
Two-dimensional (2D) halide perovskites are emerging as promising
candidates for nanoelectronics and optoelectronics. To realize their full potential, it
is important to understand the role of those defects that can strongly impact
material properties. In contrast to other popular 2D semiconductors (e.g., transition
metal dichalcogenides MX
2
) for which defects typically induce harmful traps, we
show that the electronic activities of defects in 2D perovskites are signi
fi
cantly
tunable. For example, even with a
fi
xed lattice orientation one can change the
synthesis conditions to convert a line defect (edge or grain boundary) from electron
acceptor to inactive site without deep gap states. We show that this di
ff
erence
originates from the enhanced ionic bonding in these perovskites compared with
MX
2
. The donors tend to have high formation energies and the harmful defects are
di
ffi
cult to form at a low halide chemical potential. Thus, we unveil unique
properties of defects in 2D perovskites and suggest practical routes to improve
them.
KEYWORDS:
Halide perovskites, two-dimensional materials, defects,
fi
rst-principle calculations
H
alide perovskites have attracted great interest due to their
low cost and high e
ffi
ciency for solar cell applications.
1
Recently, two-dimensional (2D) halide perovskites have been
realized experimentally and demonstrated to have attractive
properties. These materials have thicknesses of just one to few
unit-cell(s) with an A
2
BX
4
stoichiometry (where X = halides, B
= group-14 elements, and A = long-chain organic molecules
such as C
4
H
9
NH
3
) in contrast to ABX
3
for 3D perovskites.
2
−
5
The excellent properties of 2D perovskites combined with their
ease of fabrication render them promising for nanodevice
applications. For example, they exhibit strong light absorption
and photoluminescence at room temperature,
2
,
5
making them
interesting for photovoltaics and light emitters.
6
−
10
In addition,
the high mobility of charge carriers
11
−
15
in thin
fi
lm perovskites
renders them promising candidates for solution-processed
fi
eld-
e
ff
ect transistors.
12
,
13
,
15
To optimize the 2D perovskites, it is important to
understand the impact of defects on the material properties
and device performance. Although defects in 3D perov-
skites
16
−
19
and in other 2D materials (graphene,
20
,
21
boron
nitride,
22
,
23
transition metal dichalcogenides,
24
−
26
black phos-
phorus
27
) have been studied extensively, little is known about
defects in the emerging 2D perovskites. Here we report
fi
rst-
principles studies to answer such questions as the following:
•
What are the electronic properties of defects in 2D
perovskites?
•
How are they di
ff
erent from other 2D semiconductors
(especially transition metal dichalcogenides, which are also
heteroelemental semiconductors) and 3D perovskites?
•
How can we control defects to optimize the device
performance?
We performed density functional theory (DFT) using the
Vienna Ab-initio Simulation Package (VASP)
28
,
29
with
projector augmented wave (PAW) pseudopotentials.
30
,
31
We
employed the Perdew
−
Burke
−
Ernzerhof (PBE) exchange-
correlation functional
32
in most systems. For comparison, we
also calculated the band gap using the HSE functional
33
with
spin
−
orbit coupling (SOC). The plane-wave cuto
ff
energy is
400 eV, and the systems are fully relaxed until the
fi
nal force on
each atom becomes less than 0.01 eV/Å. In order to reduce
computational costs, we use Rb to represent the long-chain
organic molecules (A). This is based on the considerations that
the main role of A in the electronic structures of 3D perovskites
is to donate one electron into the host.
34
Although Rb has a
smaller size than A and hence leads to a di
ff
erent lattice
parameter, it does not a
ff
ect our main conclusions about the
defect properties, as explained below.
Figure 1
shows the atomic structure of 2D Rb
2
PbI
4
. The
octahedra are tilted, along both in-plane and out-of-plane
directions. Using the PBE functional without SOC, we calculate
a band gap of 2.22 eV, which is consistent with the band gap of
2.21 eV that we obtain from the more accurate HSE + SOC
method. This suggests that PBE is acceptable for studying
defect properties, as previously noted for 3D perovskites.
16
−
19
Received:
March 5, 2016
Revised:
April 13, 2016
Published:
April 21, 2016
Letter
pubs.acs.org/NanoLett
© 2016 American Chemical Society
3335
DOI:
10.1021/acs.nanolett.6b00964
NanoLett.
2016, 16, 3335
−
3340
This is an open access article published under an ACS AuthorChoice License, which permits
copying and redistribution of the article or any adaptations for non-commercial purposes.
The spatial distributions of the band edge states show that the
valence band maximum (VBM) is mainly composed of Pb and I
states, while the conduction band minimum (CBM) is
dominated by Pb states with Rb not contributing to the band
edges. This absence of Rb components near the band edges
further validates our choice of Rb to mimic A for studying the
defect electronic properties. These features are similar to those
of 3D perovskites,
34
indicating a similar electronic origin
despite the apparently di
ff
erent stoichiometry. On the other
hand, these band edge compositions are very di
ff
erent from 2D
MX
2
, whose VBM and CBM are both dominated by M d states
split in a ligand
fi
eld.
35
The spatial separation of VBM and
CBM onto anions and cations suggests that the 2D perovskites
possess more ionic bonding than MX
2
.
Defects in 2D MX
2
(point defects, edges, grain boundaries)
typically create deep electr
onic levels inside the band
gap,
24
−
26
,
36
which could trap/scatter/recombine charge carriers
making them generally harmful for many (opto)electronic
applications. These deep levels are di
ffi
cult to eliminate by local
structural variations without introducing additional chemical
species
26
,
37
−
39
due to the di
ffi
culty in restoring the original
ligand
fi
eld. However, for 2D perovskites it is possible to
recover the charge transfer characteristics of the ionic bonding
by manipulating the ratio of cations and anions at the defect
sites, thereby tuning their electronic levels.
Indeed, our study of the edges, an important type of line
defects, validates t
his speculation.
Figure 2
shows two
representative edge orientations: armchair (A) and zigzag (Z)
directions. The A edge orientation is along the axis of the
primitive cell, and the Z is along the diagonal direction. Each
edge orientation can have various structures, denoted by the
su
ffi
x (e.g.,
−
p,
−
N+,
−
N-). The A
−
p edge, which has the
same coordination of Pb and Rb as in the lattice (i.e., four I
atoms close to Pb with Rb atoms up and down in the centers of
the polygons), creates shallow acceptor levels located along the
edge, as shown by the band structure and the charge density
distribution in
Figure 2
a. These edge states can be partially
occupied by thermally ionized electrons from the lattice valence
band, generating free holes in the lattice (hence denoted as A
−
p).
The acceptor states originate from the nonfully
fi
lled valence
bands created by the surplus I atoms at the A
−
p type edge.
This can be understood by counting the charges for the local
stoichiometry. The I are distributed in three layers (
Figure 1
).
Figure 1.
Atomic structure (left) of 2D perovskite and charge density distributions (middle and right) of the band edge states, shown in both top
(upper panels) and side (lower panels) views. Blue, Pb; red, I; gray, Rb. The band gap is calculated to be
∼
2.2 eV with both PBE and HSE + SOC
fl
avors of DFT.
Figure 2.
Edges in 2D perovskite and their electronic structures.
“
A
”
indicates
“
armchair
”
orientation and
“
Z
”
indicates
“
zigzag
”
. The su
ffi
x
denotes the speci
fi
c structure:
“
−
p
”
indicates that the edge creates
acceptor levels, and
“
−
N
”
means that the edge is inactive (
“
neutral
”
).
Spin-polarized states are shown in di
ff
erent colors in the band
structures, and charge density distributions of the states indicated by
arrows are shown in the inset. (a) The cases of A
−
p and Z
−
p edges
are shown and (b) shows the rest. See
SI
for more edge structures.
Nano Letters
Letter
DOI:
10.1021/acs.nanolett.6b00964
NanoLett.
2016, 16, 3335
−
3340
3336
In the top and bottom layers of the ideal lattice, each I receives
1/4 electron per neighboring Rb from four Rb neighbors; thus
the charges are balanced. This is di
ff
erent from the middle
layer, where each I receives 1/2 electron per neighboring Pb
from two Pb neighbors, neutralizing the middle layer. However,
at the A
−
p edge, although the top and bottom layers are charge
balanced, the outmost I atoms in the middle layer lack 1/2
charge per I due to the missing Pb (
Figure 2
a), which gives rise
to the acceptor states. Although there are other ways to count
the charges, they all should lead to the same conclusion.
The above analysis suggests that adding one Rb atom to the
A
−
p edge might saturate the two outmost I. Indeed, our
calculations of band structure and charge density distribution
(
Figure 2
b, A
−
N+, where
“
N
”
denotes
“
neutral
”
, and + means
adding atoms to the previous A
−
p edge) show that the
acceptor levels disappear from the band gap, leading to the
absence of edge states. Therefore, this edge is relatively inactive
with regard to the lattice electronic properties. Alternatively,
removing the unsaturated I atoms, also results in an
electronically inactive edge A
−
N- (
Figure 2
b;
−
means
removing atoms from the previous A
−
p edge). We can
construct edges with even more cations or fewer anions (see
the
SI
for structures), that would create donor levels (hence
denoted as A
−
n) to generate free electrons in the lattice
conduction band. However, as shown below, we
fi
nd that these
edges are very unstable (very high formation energies).
Similarly, the
Z
edge provides opportunities, to stabilize
either electron acceptor (
Figure 2
a, Z
−
p) or inactive (
Figure
2
b, Z
−
N+, Z
−
N-) states, depending on the stoichiometry at
the edge. It is also unlikely to be donor due to the high
formation energies of the
Z
edge structures that could create
donor levels. These edge properties are very di
ff
erent from
those of MX
2
, which always exhibit deep levels independent of
structural variations,
36
demonstrating the unique electronic
structure of 2D perovskites. These observations suggest that,
Figure 3.
Gain boundaries in 2D perovskite and their electronic structures. The dashed line in the left panel shows the periodic length. The charge
density distributions of the acceptor levels are shown in the right panel. See
SI
for more grain boundary structures.
Figure 4.
Electronic levels of point defects in 2D perovskite. A long bar denotes two degenerate states, while a short bar stands for a single state. Spin
polarized states are shown in di
ff
erent colors, and the occupied states are marked by arrows.
Nano Letters
Letter
DOI:
10.1021/acs.nanolett.6b00964
NanoLett.
2016, 16, 3335
−
3340
3337
even for
fi
xed edge directions, the electronic activity can still be
tuned by varying synthesis conditions.
Grain boundaries provide another common type of line
defects, usually formed when the edges of two misorientated
grains join together during growth.
Figure 3
shows an example
grain boundary constructed by connecting two edges with a
shared I atom. We choose the kinked edges that contain both A
and Z segments to represent a general case. By varying the
number of Rb atoms, shallow acceptor levels can be created or
eliminated. It is energetically unfavorable to have surplus
cations (as shown below), so we expect the grain boundary is
unlikely to provide electron donor states. These grain boundary
properties are very di
ff
erent from those of MX
2
, which always
render deep levels regardless of structural variations.
24
We
fi
nd a similar charge-balance-controlled electronic
activity for point defects in 2D perovskites, as shown in
Figure
4
. Although a Rb vacancy (V
Rb
) creates an acceptor level, a
neighboring V
I
(hence converting it to V
RbI
) could eliminate
this gap state. Similarly, V
PbI2
does not exhibit deep levels. Such
defects have also been found to be electronically inactive in 3D
perovskites.
19
Most of point defects have the electronic
behavior expected for a typical ionic semiconductor. For
example, cation vacancies/anion interstitials usually generate
acceptor levels, while anion vacan
cies/cation interstitials
typically create donor states. These point defect properties
are very di
ff
erent from those of MX
2
, In the latter case, a cation
vacancy (V
M
) generates deep acceptor levels, while the
stoichiometric vacancies (V
MX2
) produce more gap states.
25
In order to identify optimal conditions for growth of
materials that suppress harmful defects, we examine the
formation energies (
E
f
) following the method used for 3D
perovskites.
16
Thermodynamic equilibrium condition requires
μμμμ
++=
2
4
Rb
Pb
I
Rb PbI
2
4
(1)
where
μ
is the chemical potential. To avoid phase separation,
the following constraints must be satis
fi
ed
μ
μ
<
−
Rb
Rb bulk
(2)
μ
μ
<
−
Pb
Pb bul
k
(3)
μ
μ
<
2
I
I2
(4)
μ
μμ
+<
Rb
I
Rb
I
(5)
μ
μμ
+<
2
Pb
I
PbI2
(6)
Substituting eq
1
into eqs
2
and
5
, we get
μ
μμμ
+>
−
−
42
Pb
I
Rb PbI
Rb bul
k
24
(7)
μ
μμμ
+>
−
22
Pb
I
Rb PbI
Rb
I
24
(8)
where
μ
Rb
2
PbI
4
,
μ
PbI
2
,
μ
RbI
,
μ
Rb
‑
bulk
,
μ
Pb
‑
bulk
. and
μ
I2
can be
approximated by the internal energies of the corresponding
condensed phases. We
fi
nd that eq
7
or eq
2
is automatically
satis
fi
ed when eqs
3
,
4
,
6
, and
8
are met. Hence eqs
3
,
4
,
6
, and
8
together de
fi
ne a range of (
μ
Pb
,
μ
I
) where the 2D perovskite is
thermodynamically stable. Because the
E
f
depends linearly on
μ
,
the maximum and minimum of
E
f
should fall on the corners of
the phase boundaries. Therefore,
Figure 5
shows
E
f
along the
two boundary lines:
μ
Pb
+2
μ
I
=
μ
PbI2
, and
μ
Pb
+2
μ
I
=
μ
Rb2PbI4
−
2
μ
RbI
(or
μ
Rb
+
μ
I
=
μ
RbI
).
The thermodynamic equilibrium concentration of defects (
n
)
in the materials can be estimated by
∼−
∧
n
EkT
e( / )
fB
S
(9)
where
S
is the area of the primitive cell, and
T
is temperature.
The experimentally grown 2D perovskites typically exhibit sizes
less than 10
μ
m, and
T
is usually below 100
°
C.
2
Based on eq
9
,
we estimate that defects with
E
f
< 0.62 eV would likely form
under these experimental growth conditions. Therefore, we use
this value as a criterion to judge if
E
f
is
“
high
”
or
“
low
”
.
Although V
RbI
and V
PbI2
generally have a low
E
f
(
Figure 5
a),
they are electronically inactive and hence have limited impact
on the lattice properties. The dominating defects at high
μ
I
are
those with surplus anions or de
fi
cient cations, such as I
Rb
,I
i
, and
I
Pb
(
Figure 5
a). These defects create deep levels (
Figure 4
) and
hence are harmful to many applications. Fortunately, their
E
f
increase to a high level as
μ
I
decreases. On the other hand, the
E
f
for defects with surplus cations/de
fi
cient anions still remains
high at low
μ
I
. Therefore, using synthesis conditions that lower
μ
I
, should reduce the total concentration of harmful defects.
We
fi
nd that the line defects exhibit a similar behavior for
E
f
.
Figure 5
b shows the
E
f
for various edge structures along A
orientation, with respect to that of A
−
N+ (the
E
f
for edges
along
Z
orientation and grain boundaries can be found in the
SI
). At high
μ
I
, the edge that creates acceptor levels, with
surplus I (A
−
p), possesses an
E
f
comparable with those of
inactive edges (A
−
N+ and
A
−
N-). However, it becomes
unfavorable at low
μ
I
. In contrast, the edges that create donor
levels with surplus cations/de
fi
cient anions (A
−
n+ and A
−
n-,
see structures in the
SI
), exhibit a high
E
f
in the whole range of
μ
I
, and therefore are unlikely to form (as mentioned above).
To check whether the trends of
E
f
can be generalized to
other 2D perovskites with di
ff
erent chemical compositions, we
calculate the
E
f
for point defects in (CH
3
NH
3
)
2
SnBr
4
as a test
Figure 5.
Formation energies of point defects (a) and line defects (b) in 2D perovskite, as a function of I chemical potential (with respect to that of
I
2
molecule) along phase boundaries (see the text). For line defects, edges along A orientation are shown here as an example, and the rest can be
found in the
SI
; the energies are referred to that of A
−
N+. Shadowed regions mark the point defects that would likely form in a 10
μ
m size square
sheet grown at 100
°
C in thermodynamic equilibrium.
Nano Letters
Letter
DOI:
10.1021/acs.nanolett.6b00964
NanoLett.
2016, 16, 3335
−
3340
3338
example. As shown in
Figure S6
,we
fi
nd again that a low
μ
Br
can decrease the total concentration of harmful defects,
therefore con
fi
rming the generality of the trends.
The behavior of
E
f
in 2D perovskites is di
ff
erent from that in
3D perovskites, where point defects with surplus cations/
de
fi
cient anions can have a low
E
f
at low
μ
I
, rendering n-doping
of the host.
16
,
17
This n-doping is unlikely to exist in 2D case,
because of the high
E
f
for donors across the whole range of
chemical potential. Note that the same calculation methods
were used to study the defects in 3D case, that is, PBE
functional with plane-wave basis sets, allowing for direct
comparison. For grain boundaries in 3D perovskites, theoretical
analyses suggested that they do not create deep levels, due to
the strong coupling between Pb s orbitals and I p orbitals and
the large atomic size of Pb.
17
,
18
We show here that these
previous results arose because the grain boundary models
chosen were all neutral (charge balanced), making them
electronically inactive as explained above for 2D cases.
Considering that both donor- and acceptor-like point defects
can form in 3D perovskites, we anticipate that the grain
boundaries can also have surplus/de
fi
cient cations/anions,
making them donors/acceptors depending on the
μ
I
. This is
di
ff
erent from the grain boundaries in our 2D case, which are
unlikely to be donors. In addition, theoretical analyses
suggested that deep-level defects are di
ffi
cult to from in 3D
perovskites and the dominating defects all have shallow
states;
16
,
17
this contrasts with defects in 2D perovskites,
where deep-level defects (e.g., I
i
,I
Rb
) can form easily at high-
μ
I
conditions.
This study demonstrates that defects in ionic semiconductors
can be tuned to be less harmful in general, providing a guideline
to design new 2D semiconductors. It also explains the
experimental observation of relatively high quantum e
ffi
ciency
in 2D perovskites, and suggests ways to further improve it. A
common way to adjust the chemical potential is to change the
concentration of reactants. For example, recent experiments use
PbX
2
and Cs-oleate to synthesize CsPbX
3
nanostructures,
creating a Pb-rich (or I-poor) environment.
40
,
41
Besides the
intrinsic defects which are the focus of this work, extrinsic
defects would also play an important role in the electronic
properties. A major source is the solvent residues adsorbed on
the surface. The ionic contaminants could induce n- or p-
doping, while neutral adsorbates should have less impact. Given
that 3D perovskite is not very stable in the ambient conditions,
one would expect a similar issue for 2D perovskite. Particularly,
humidity could have a strong e
ff
ect on the material. This could
be mitigated by using encapsulation techniques (e.g., using h-
BN to seal the material/device
42
), or choosing hydrophobic
organic cations.
43
In summary, we use
fi
rst-principles calculations to predict
unique properties of defects in 2D perovskites. The line defects
with
fi
xed orientation can be tuned from electron acceptors to
inactive sites by varying synthesis conditions, while donors are
energetically unfavorable. This is consistent with the trends of
point defects formation. The optimal synthesis conditions are
also identi
fi
ed.
■
ASSOCIATED CONTENT
*
S
Supporting Information
The Supporting Information is available free of charge on the
ACS Publications website
at DOI:
10.1021/acs.nano-
lett.6b00964
.
Computational details, more line defect structures,
energies of
Z
edges and grain boundaries, energies of
point defects in 2D MA
2
SnBr
4
.(
PDF
)
■
AUTHOR INFORMATION
Corresponding Authors
*
E-mail:
yuanyue.liu.microman@gmail.com
.
*
E-mail:
wag@wag.caltech.edu
.
Notes
The authors declare no competing
fi
nancial interest.
■
ACKNOWLEDGMENTS
Y.L. thanks discussions with Professor Wan-Jian Yin and
acknowledges the support from Resnick Prize Postdoctoral
Fellowship at Caltech. H.X. and W.A.G. were supported by the
Joint Center for Arti
fi
cial Photosynthesis, a DOE Energy
Innovation Hub, supported through the O
ffi
ce of Science of the
U.S. DOE under Award No. DE-SC0004993. This research was
also supported by NSF (CBET-1512759, program manager:
Robert McCabe), DOE (DE FOA 0001276, program manager:
James Davenport). This work used computational resources of
National Energy Research Scienti
fi
c Computing Center, a DOE
O
ffi
ce of Science User Facility supported by the O
ffi
ce of
Science of the U.S. DOE under Contract DE-AC02-
05CH11231, and the Extreme Science and Engineering
Discovery Environment (XSEDE), which is supported by
NSF Grant ACI-1053575.
■
REFERENCES
(1) Stranks, S. D.; Snaith, H. J.
Nat. Nanotechnol.
2015
,
10
, 391
−
402.
(2) Dou, L.; Wong, A. B.; Yu, Y.; Lai, M.; Kornienko, N.; Eaton, S.
W.; Fu, A.; Bischak, C. G.; Ma, J.; Ding, T.; Ginsberg, N. S.; Wang, L.-
W.; Alivisatos, A. P.; Yang, P.
Science
2015
,
349
, 1518
−
1521.
(3) Niu, W.; Eiden, A.; Vijaya Prakash, G.; Baumberg, J. J.
Appl. Phys.
Lett.
2014
,
104
, 171111.
(4) Yaffe, O.; Chernikov, A.
; Norman, Z. M.; Zhong, Y.;
Velauthapillai, A.; van der Zande, A.; Owen, J. S.; Heinz, T. F.
Phys.
Rev. B: Condens. Matter Mater. Phys.
2015
,
92
, 045414.
(5) Cao, D. H.; Stoumpos, C. C.; Farha, O. K.; Hupp, J. T.;
Kanatzidis, M. G.
J. Am. Chem. Soc.
2015
,
137
, 7843
−
7850.
(6) Cheng, H.-C.; Wang, G.; Li, D.; He, Q.; Yin, A.; Liu, Y.; Wu, H.;
Ding, M.; Huang, Y.; Duan, X.
Nano Lett.
2016
,
16
, 367
−
373.
(7) Dou, L.; Yang, Y.; You, J.; Hong, Z.; Chang, W.-H.; Li, G.; Yang,
Y.
Nat. Commun.
2014
,
5
, 5404.
(8) Fang, Y.; Dong, Q.; Shao, Y.; Yuan, Y.; Huang, J.
Nat. Photonics
2015
,
9
, 679
−
686.
(9) Tan, Z.-K.; Moghaddam, R. S.; Lai, M. L.; Docampo, P.; Higler,
R.; Deschler, F.; Price, M.; Sadhanala, A.; Pazos, L. M.; Credgington,
D.; Hanusch, F.; Bein, T.; Snaith, H. J.; Friend, R. H.
Nat. Nanotechnol.
2014
,
9
, 687
−
692.
(10) Cho, H.; Jeong, S.-H.; Park, M.-H.; Kim, Y.-H.; Wolf, C.; Lee,
C.-L.; Heo, J. H.; Sadhanala, A.; Myoung, N.; Yoo, S.; Im, S. H.;
Friend, R. H.; Lee, T.-W.
Science
2015
,
350
, 1222
−
1225.
(11) Brenner, T. M.; Egger, D. A.; Kronik, L.; Hodes, G.; Cahen, D.
Nature Reviews Materials
2016
,
1
, 15007.
(12) Chin, X. Y.; Cortecchia, D.; Yin, J.; Bruno, A.; Soci, C.
Nat.
Commun.
2015
,
6
, 7383.
(13) Mei, Y.; Zhang, C.; Vardeny, Z. V.; Jurchescu, O. D.
MRS
Commun.
2015
,
5
, 297
−
301.
(14) Stoumpos, C. C.; Malliakas, C. D.; Kanatzidis, M. G.
Inorg.
Chem.
2013
,
52
, 9019
−
9038.
(15) Li, F.; Ma, C.; Wang, H.; Hu, W.; Yu, W.; Sheikh, A. D.; Wu, T.
Nat. Commun.
2015
,
6
, 8238.
(16) Yin, W.-J.; Shi, T.; Yan, Y.
Appl. Phys. Lett.
2014
,
104
, 063903.
(17) Yin, W.-J.; Shi, T.; Yan, Y.
Adv. Mater.
2014
,
26
, 4653
−
4658.
Nano Letters
Letter
DOI:
10.1021/acs.nanolett.6b00964
NanoLett.
2016, 16, 3335
−
3340
3339
(18) Yin, W.-J.; Chen, H.; Shi, T.; Wei, S.-H.; Yan, Y.
Advanced
Electronic Materials
2015
,
1
, 1500044.
(19) Kim, J.; Lee, S.-H.; Lee, J. H.; Hong, K.-H.
J. Phys. Chem. Lett.
2014
,
5
, 1312
−
1317.
(20) Liu, Y.; Yakobson, B. I.
Nano Lett.
2010
,
10
, 2178
−
2183.
(21) Vicarelli, L.; Heerema, S. J.; Dekker, C.; Zandbergen, H. W.
ACS
Nano
2015
,
9
, 3428
−
3435.
(22) Liu, Y.; Zou, X.; Yakobson, B. I.
ACS Nano
2012
,
6
, 7053
−
7058.
(23) Wong, D.; Velasco, J., Jr; Ju, L.; Lee, J.; Kahn, S.; Tsai, H.-Z.;
Germany, C.; Taniguchi, T.; Watanabe, K.; Zettl, A.; Wang, F.;
Crommie, M. F.
Nat. Nanotechnol.
2015
,
10
, 949
−
953.
(24) Zou, X.; Liu, Y.; Yakobson, B. I.
Nano Lett.
2013
,
13
, 253
−
258.
(25) Zhou, W.; Zou, X.; Najmaei, S.; Liu, Z.; Shi, Y.; Kong, J.; Lou, J.;
Ajayan, P. M.; Yakobson, B. I.; Idrobo, J.-C.
Nano Lett.
2013
,
13
,
2615
−
2622.
(26) Liu, Y.; Stradins, P.; Wei, S.-H.
Angew. Chem., Int. Ed.
2016
,
55
,
965
−
968.
(27) Liu, Y.; Xu, F.; Zhang, Z.; Penev, E. S.; Yakobson, B. I.
Nano
Lett.
2014
,
14
, 6782
−
6786.
(28) Kresse, G.; Hafner, J.
Phys. Rev. B: Condens. Matter Mater. Phys.
1993
,
47
, 558
−
561.
(29) Kresse, G.; Furthmu
̈
ller, J.
Phys. Rev. B: Condens. Matter Mater.
Phys.
1996
,
54
, 11169
−
11186.
(30) Blo
̈
chl, P. E.
Phys. Rev. B: Condens. Matter Mater. Phys.
1994
,
50
,
17953
−
17979.
(31) Kresse, G.; Joubert, D.
Phys. Rev. B: Condens. Matter Mater. Phys.
1999
,
59
, 1758
−
1775.
(32) Perdew, J. P.; Burke, K.; Ernzerhof, M.
Phys. Rev. Lett.
1996
,
77
,
3865
−
3868.
(33) Paier, J.; Marsman, M.; Hummer, K.; Kresse, G.; Gerber, I. C.;
A
́
ngya
́
n, J. G.
J. Chem. Phys.
2006
,
124
, 154709.
(34) Yin, W.-J.; Yang, J.-H.; Kang, J.; Yan, Y.; Wei, S.-H.
J. Mater.
Chem. A
2015
,
3
, 8926
−
8942.
(35) Chhowalla, M.; Shin, H.; Eda, G.; Li, L.; Loh, K.; Zhang, H.
Nat.
Chem.
2013
,
5
, 263
−
275.
(36) Lauritsen, J. V.; Kibsgaard, J.; Helveg, S.; Topsoe, H.; Clausen,
B. S.; Laegsgaard, E.; Besenbacher, F.
Nat. Nanotechnol.
2007
,
2
,53
−
58.
(37) Amani, M.; Lien, D.-H.; Kiriya, D.; Xiao, J.; Azcatl, A.; Noh, J.;
Madhvapathy, S. R.; Addou, R.; KC, S.; Dubey, M.; Cho, K.; Wallace,
R. M.; Lee, S.-C.; He, J.-H.; Ager, J. W.; Zhang, X.; Yablonovitch, E.;
Javey, A.
Science
2015
,
350
, 1065
−
1068.
(38) Yu, Z.; Pan, Y.; Shen, Y.; Wang, Z.; Ong, Z.-Y.; Xu, T.; Xin, R.;
Pan, L.; Wang, B.; Sun, L.; Wang, J.; Zhang, G.; Zhang, Y. W.; Shi, Y.;
Wang, X.
Nat. Commun.
2014
,
5
, 5290.
(39) Meng, Y.; Ling, C.; Xin, R.; Wang, P.; Song, Y.; Bu, H.; Gao, S.;
Wang, X.; Song, F.; Wang, J.; Wang, X.; Wang, B.; Wang, G. 2016,
arXiv:1601.05534 [cond-mat.mes-hall].
(40) Bekenstein, Y.; Koscher, B. A.; Eaton, S. W.; Yang, P.; Alivisatos,
A. P.
J. Am. Chem. Soc.
2015
,
137
, 16008
−
16011.
(41) Protesescu, L.; Yakunin, S.; Bodnarchuk, M. I.; Krieg, F.;
Caputo, R.; Hendon, C. H.; Yang, R. X.; Walsh, A.; Kovalenko, M. V.
Nano Lett.
2015
,
15
, 3692
−
3696.
(42) Chen, X.; Wu, Y.; Wu, Z.; Han, Y.; Xu, S.; Wang, L.; Ye, W.;
Han, T.; He, Y.; Cai, Y.; Wang, N.
Nat. Commun.
2015
,
6
, 7315.
(43) Yang, S.; Wang, Y.; Liu, P.; Cheng, Y.-B.; Zhao, H. J.; Yang, H.
G.
Nature Energy
2016
,
1
, 15016.
Nano Letters
Letter
DOI:
10.1021/acs.nanolett.6b00964
NanoLett.
2016, 16, 3335
−
3340
3340