S1
Supporting Information for
Schottky-barrier-free contacts with two-dimensional
semiconductors by sur-
face-engineered MXenes
Yuanyue Liu
1,2*
, Hai Xiao
1
, William A. Goddard III
1*
1
Materials and Process Simulation Center,
2
The Resnick Sustainability Institute
California Institute of Technology, Pasadena, Calif
ornia 91125, United States
*Email:
yuanyue.liu.microman@gmail.com
,
wag@wag.caltech.edu
1. Stacking order of the group-6 MXenes
Material
Stacking order of the T, M, X, M, T layers
Cr
2
C
ABC (no T layers)
Cr
2
CO
2
ABABA
Cr
2
C(OH)
2
ABCAB
Cr
2
CF
2
ABCAB
Mo
2
C
ABA (no T layers)
Mo
2
CO
2
ABABA
Mo
2
C(OH)
2
ABCBA
Mo
2
CF
2
ABCBA
Table S1.
The most stable stacking order of the group56 MXene
s
2. Electron density redistribution upon surface ter
mination
Figure S1
. The electron density (averaged over the xy plane;
arbitrary unit) of Hf
2
NT
2
, subtract5
ed by the electron density of the isolated Hf
2
N and the two T layers with the same coordinates as
those in the Hf
2
NF
2
. This reflects the electron redistribution on Hf
2
N and T after adsorption.
Note that the change of the electron density is non
5zero inside Hf
2
N; both T and N layers become
negatively charged while the surface Hf layers are
positively charged.
S2
3. Verification of SB-free contacts for electron/ho
le injection by the hybrid functional
B3PW91
It is well established that hybrid functionals are
superior to semilocal GGA functionals such as
PBE for describing band gaps of semiconductors. Con
sequently we used the hybrid functional
B3PW91, which we have shown to predict accurately b
oth band gaps
1, 2
and band offsets
3
, to val5
idate the absence of SB’s in two representative het
erojunctions, Hf
2
N(OH)
2
5WSe
2
and Nb
2
CO
2
5
WSe
2
, for electron and hole injection, respectively.
The B3PW91 calculations were performed using the CR
YSTAL14 package
4
, which uses local
atomic Gaussian5type basis sets. This enables fast
evaluation of the Hartree5Fock exchange terms
required for hybrid DFT method. We used the all5ele
ctron 65311G(
d
) basis sets of triple5ζ quality
for H, C, N and O, while for Se, Nb, Hf and W, we u
sed the SBKJC relativistic effective core
potentials and modified associated basis sets of tr
iple5ζ quality. An extra5large grid, consisting of
75 radial points and 974 angular points, was used f
or accurate integration, and the reciprocal
space was sampled by Γ5centered Monkhorst5Pack sche
me
5
with 12×12×1 and 5×5×1 grids for
Hf
2
N(OH)
2
5WSe
2
and Nb
2
CO
2
5WSe
2
, respectively.
The B3PW91 results confirm that for the Hf
2
N(OH)
2
5WSe
2
case, the CBM of WSe
2
at the K
point is below the Fermi level by 0.12 eV, i.e., el
ectron injection from the Hf
2
N(OH)
2
to the
WSe
2
takes place spontaneously; for the Nb
2
CO
2
5WSe
2
case, the VBM of WSe
2
at the Γ point is
above the Fermi level by 0.08 eV, i.e., hole inject
ion from the Nb
2
CO
2
to the WSe
2
takes place
spontaneously.
4. The stability of O and OH termination of V
2
C under applied potentials
To predict more accurately the electrochemical cond
itions for formation of V
2
C(OH)
2
, we used
the Grand Canonical constant potential formulation
with CANDLE implicit solvation model
6
as
implemented in the jDFTx software
759
to perform explicit constant electrochemical poten
tial (
μ
e
)
calculations
42
using a
√
3
×
√
3
supercell of V
2
C with various O/OH coverages, i.e., V
2
CO
2
,
V
2
C(OH
1/3
)
2
, V
2
C(OH
2/3
)
2
and V
2
C(OH)
2
. We used the GBRV ultrasoft pseudopotentials, with
a
plane wave cutoff of 544 eV (20 Hartree atomic unit
s). The reciprocal space was sampled by Γ5
centered Monkhorst5Pack scheme with an 8×8×1 grid.
The ionic screening of net charges result5
ing from the constant
μ
e
condition was achieved with cation (0.1 M Na
+
) and anion (0.1 M Cl
−
)
components in the fluid model under the JDFT framew
ork. The algorithm employed by JDFTx
variationally minimizes the grand canonical free en
ergy at fixed electron chemical potential with
respect to Kohn5Sham orbitals, fluid bound charge a
nd an auxiliary Hamiltonian for the occupa5
tions. Previously we have found that the relative f
ree energies are linearly dependent on the ap5
plied potential U for |U| < ~2 V (vs standard hydrog
en electrode (SHE))
10
, so we assume the U5
dependence of free energy is linear between U = 0.0
and −1.2 V.
Zero5point energies (ZPE), enthalpy and entropy con
tributions to the free energies of V
2
C(OH
x
)
2
at room temperature (298.15 K) were calculated from
vibrational modes of O/OH surface termi5
S3
nation. The formation free energies of surface OH b
y electrochemical reduction using
H
+
(H
3
O
+
/H
2
O) +
e
5
were referenced to the free energy of H
2
(g), which was calculated including
the translational and rotational contributions assu
ming the ideal gas model, in addition to the vi5
brational contributions..
System
ZPE (H − TS)
vib
(,
rot
,
trans
)
H
2
(g) 0.2666
50.3131
V
2
C(OH
1/3
)
2
0.1958
50.0024
V
2
C(OH
2/3
)
2
0.3892
50.0054
V
2
C(OH)
2
0.5550
50.0111
Table S2.
The calculated enthalpy (H) and entropy (S) contrib
utions (in eV) to the free energies
of V
2
C(OH
x
)
2
(normalized to per formula unit) at room temperatu
re (T = 298.15 K).
Our results (Figure S2) allow us to conclude that t
he full surface OH coverage of V
2
C can be
achieved by applying potentials under −0.5 V. This
suggests that the desired V
2
C(OH)
2
can be
synthesized by applying a potential more negative t
han 50.5 V to a solution containing proton
sources.
Figure S2
. Calculated relative free energies (eV) of differe
nt OH coverages (w.r.t. V
2
CO
2
and
RHE).
U (V)
V
2
C(OH
1/3
)
2
V
2
C(OH
2
/3
)
2
V
2
C(OH)
2
0.0
50.1529
50.1080
0.1271
51.2
50.7698
51.3121
51.6938
Table S3
. Data used to plot Figure S2.
5. Work function (eV) of MXenes
S4
M
n
X
n+1
W
bare
(eV)
W
O
WHO
W
F
sc2c
-
4.02163
semiconductor
S
emiconductor
semiconductor
ti2c
-
4.0779
semiconductor
-
1.83103
-
5.04265
zr2c
-
3.91656
semiconductor
-
2.07189
-
3.98434
hf2c
-
4.47168
semiconductor
-
2.46955
-
3.55996
v2c
-
4.56658
-
6.6864
-
1.76566
-
5.52296
nb2c
-
4.53881
-
5.80539
-
2.15064
-
4.47982
ta2c
-
4.76506
-
5.43371
-
2.58449
-
3.75776
cr2c
-
4.69319
-
8.00915
S
emiconductor
semiconductor
mo2c
-
4.58759
-
7.39338
-
1.81619
-
5.73873
ti3c2
-
3.81906
-
6.15721
-
1.8106
-
4.98223
v3c2
-
4.58157
-
6.55148
-
1.83023
-
5.67346
ta3c2
-
4.90524
-
5.33699
-
2.49638
-
4.49258
ti4c3
-
3.81747
-
6.1264
-
2.09035
-
4.82451
v4c3
-
4.46816
-
6.63828
-
1.89568
-
5.82193
nb4c3
-
4.3696
-
5.76839
-
2.17737
-
4.96529
ta4c3
-
4.78514
-
5.34125
-
2.44412
-
4.32712
ti2n
-
4.54627
-
5.9911
-
2.1255
-
4.6798
zr2n
-
4.39661
-
4.99367
-
2.30219
-
3.70032
hf2n
-
4.55307
-
4.68043
-
2.75419
-
3.20681
v2n
-
4.69187
-
6.13505
-
1.89944
-
5.27783
ti4n3
-
4.49034
-
5.86673
-
2.35257
-
4.67932
Table S4.
Work function (eV) of MXenes
6. Surface dipole moment density (e/Å) of MXenes
O
OH
F
sc2c
--
--
ti2c
--
-
0.0239
0.00817
zr2c
--
-
0.02669
4.88694E
-
4
hf2c
--
-
0.02776
-
0.00618
v2c
0.01653
-
0.02665
0.00652
nb2c
0.01121
-
0.02609
-
0.00239
ta2c
0.00522
-
0.02561
-
0.00733
cr2c
0.01988
--
--
mo2c
0.0187
-
0.02796
0.00432
S5
ti3c2
0.01976
-
0.0334
0.00388
v3c2
0.02138
-
0.02232
0.02122
ta3c2
0.00156
-
0.0347
-
0.00552
ti4c3
0.02892
-
0.05002
0.00984
v4c3
0.02415
-
0.04035
0.01501
nb4c3
0.01415
-
0.04724
0.00621
ta4c3
0.00667
-
0.04805
-
0.00263
ti2n
0.01466
-
0.02462
0.00183
zr2n
0.00761
-
0.02045
-
0.00485
hf2n
0.00517
-
0.01815
-
0.01182
v2n
0.00918
-
0.03034
0.00223
ti4n3
0.0198
-
0.04569
0.00261
Table S5.
Surface dipole moment density (e/Å) of MXenes
7. Formation free energies (eV/T) of surface termin
ations
O (0) OH (0) F (0) O (1.23) OH
(1.23)
F (1.23)
sc2c
-
2.07321
-
2.43849
-
3.17374
-
4.53321
-
3.66849
-
4.40374
ti2c
-
2.35893
-
1.99019
-
2.51438
-
4.81893
-
3.22019
-
3.74438
zr2c
-
2.90636
-
2.16382
-
2.7231
-
5.36636
-
3.39382
-
3.9531
hf2c
-
3.34228
-
2.24923
-
2.69881
-
5.80228
-
3.47923
-
3.92881
v2c
-
1.50419
-
1.31173
-
1.74068
-
3.96419
-
2.54173
-
2.97068
nb2c
-
1.92688
-
1.35809
-
1.78263
-
4.38688
-
2.58809
-
3.01263
ta2c
-
2.33209
-
1.29844
-
1.61751
-
4.79209
-
2.52844
-
2.84751
cr2c
-
1.09838
-
1.01356
-
1.46056
-
3.55838
-
2.24356
-
2.69056
mo2c
-
1.50958
-
0.53261
-
0.95134
-
3.96958
-
1.76261
-
2.18134
S6
ti3c2
-
2.21363
-
1.92019
-
2.4598
-
4.67363
-
3.15019
-
3.6898
v3c2
-
1.33075
-
0.9898
-
1.44549
-
3.79075
-
2.2198
-
2.67549
ta3c2
-
2.28017
-
1.09102
-
1.38181
-
4.74017
-
2.32102
-
2.61181
ti4c3
-
2.24001
-
1.9051
-
2.44317
-
4.70001
-
3.1351
-
3.67317
v4c3
-
1.30069
-
1.03147
-
1.47778
-
3.76069
-
2.26147
-
2.70778
nb4c3
-
1.68681
-
1.08836
-
1.5104
-
4.14681
-
2.31836
-
2.7404
ta4c3
-
2.13313
-
1.05909
-
1.3885
-
4.59313
-
2.28909
-
2.6185
ti2n
-
2.47362
-
1.95239
-
2.44429
-
4.93362
-
3.18239
-
3.67429
zr2n
-
2.99264
-
2.0722
-
2.57936
-
5.45264
-
3.3022
-
3.80936
hf2n
-
3.34632
-
1.99737
-
2.34293
-
5.80632
-
3.22737
-
3.57293
v2n
-
1.58514
-
1.22403
-
1.67618
-
4.04514
-
2.45403
-
2.90618
ti4n3
-
2.42895
-
1.8124
-
2.30364
-
4.88895
-
3.0424
-
3.53364
Table S6.
Formation free energies (eV/T) of surface terminat
ions
1.
Xiao, H.; Tahir-Kheli, J.; Goddard, W. A.
J. Phys. Chem. Lett.
2011,
2, 212-217.
2.
Crowley, J. M.; Tahir-Kheli, J.; Goddard, W. A.
J. Phys. Chem. Lett.
2016,
7, 1198-1203.
3.
Xiao, H.; Goddard, W. A.
J. Chem. Phys.
2014,
141, 094701.
4.
Dovesi, R.; Orlando, R.; Erba, A.; Zicovich-Wilso
n, C. M., et al.
International Journal of Quantum
Chemistry
2014,
114, 1287-1317.
5.
Monkhorst, H. J.; Pack, J. D.
Phys. Rev. B
1976,
13, 5188-5192.
6.
Sundararaman, R.; Goddard, W. A.
J. Chem. Phys.
2015,
142, 064107.
7.
Arias, T. A.; Payne, M. C.; Joannopoulos, J. D.
Phys. Rev. Lett.
1992,
69, 1077-1080.
8.
Ismail-Beigi, S.; Arias, T. A.
Comput. Phys. Comm.
2000,
128, 1-45.
9.
Sundararaman, R.; Gunceler, D.; Letchworth-Weave
r, K.; Schwarz, K., et al.
JDFTx
.
10. Xiao, H.; Cheng, T.; Goddard, W. A.; Sundararam
an, R.
J. Am. Chem. Soc.
2016,
138, 483-486.
1. Xiao, H.; Tahir5Kheli, J.; Goddard, W. A.
J. Phys. Chem. Lett.
2011,
2, 2125217.
2. Crowley, J. M.; Tahir5Kheli, J.; Goddard, W. A.
J. Phys. Chem. Lett.
2016,
7, 119851203.
3. Xiao, H.; Goddard, W. A.
J. Chem. Phys.
2014,
141, 094701.
4. Dovesi, R.; Orlando, R.; Erba, A.; Zicovich5Wils
on, C. M.; Civalleri, B.; Casassa, S.;
Maschio, L.; Ferrabone, M.; De La Pierre, M.; D'Arc
o, P.; Noël, Y.; Causà, Mauro; Rérat, M.;
Kirtman, B.
International Journal of Quantum Chemistry
2014,
114, 128751317.
5. Monkhorst, H. J.; Pack, J. D.
Phys. Rev. B
1976,
13, 518855192.
6. Sundararaman, R.; Goddard, W. A.
J. Chem. Phys.
2015,
142, 064107.
S7
7. Arias, T. A.; Payne, M. C.; Joannopoulos, J. D.
Phys. Rev. Lett.
1992,
69, 107751080.
8. Ismail5Beigi, S.; Arias, T. A.
Comput. Phys. Comm.
2000,
128, 1545.
9. Sundararaman, R.; Gunceler, D.; Letchworth5Weave
r, K.; Schwarz, K.; Arias, T. A.
JDFTx
, available from http://jdftx.sourceforge.net (2012
).
10. Xiao, H.; Cheng, T.; Goddard, W. A.; Sundararam
an, R.
J. Am. Chem. Soc.
2016,
138,
4835486.