Copyright WILEY-VCH Verlag GmbH & Co
. KGaA, 69469 Weinheim, Germany, 2013.
Supporting Information
for
Adv. Mater.
,
DOI: 10.1002/ad
ma. 201304473
Bandgap Tunability in Zn(Sn,
Ge)N 2 Semiconductor Alloys
Prineha Narang, Shiyou Chen,* Naomi C. Coronel, Sheraz
Gul, Junko Yano, Lin-Wang Wang, Nathan S. Lewis, and
Harry A. Atwater*
Copyright WILEY
-
VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany,
2013
.
Supporting Information
for
Adv. Mater.
,
DOI: 10.1002/
adma.
20130
4473
Band
G
ap Tunability in
Zn
(
Sn
,
Ge
)
N
2
S
emiconductor
Alloy
s
Prineha Narang
1,3
,
†
, Shiyou Chen
3,5
,
†
, Naomi C. Coronel
1
†
, Sheraz Gul
4
, Junko Yano
3,4
, Lin
-
Wang
Wang
3,5
, Nathan S. Lewis
2,3
and Harry A. Atwater
1,3
X
-
ray Absorption
Fine Structure
Spectroscopy Experimental Details
Curve fitting was performed with Artemis and IFEFFIT software using
ab initio
-
calculated
phases and amplitudes from the program FEFF
8.2.
These
ab initio
phases and amplitudes were
used in the EXAFS equation:
(
k
)
S
0
2
N
j
k
R
j
2
j
f
e f
f
j
(
,
k
,
R
j
)
e
2
j
2
k
2
e
2
R
j
/
j
(
k
)
s i n (
2
kR
j
ij
(
k
))
(Equation
S1)
The neighboring atoms to the central atom(s)
were
divided into
j
shells, with all atoms with the
same atomic number and distance from the central atom grouped into a single shell. Within each
shell, the coordination number
N
j
denote
d
the number of neig
hboring atoms in shell
j
at a
distance of
R
j
from the central atom.
f
e f f
j
(
,
k
,
R
j
)
is the
ab initio
amplitude function for shell
j
,
and the Debye
-
Waller term
e
–
2σ
j
2
k
2
account
ed
for damping due to static and thermal disorder in
absorber
-
backscatterer
distances. The mean free path term
e
–
2R
j
/ λ
j
(k)
reflects losses due to inelastic
scattering, where
λ
j
(
k
) is the electron mean free path. The oscillations in the EXAFS spectrum
are reflected in the sinusoidal term, sin(2
kR
j
+ φ
ij
(
k
)) where φ
ij
(
k
) is the
ab
initio
phase function
for shell
j
.
S
0
2
is an amplitude reduction factor due to shake
-
up/shake
-
off processes at the central
atom(s). The EXAFS equation was used to fit the experimental data using
N
,
R
, and the EXAFS
Debye
-
Waller factor (
σ
2
)
as variable par
ameters. For
conversion
of
the energy (eV) to wave
vector (
k
, Å
–
1
) axis, E
0
was defined as 11111.0 eV and the S
0
2
value was fixed
at
1.0. All fits
were performed in the R space.
Figure S1:
EXAFS curve
-
fitting results
for
ZnSn
1
-
x
Ge
x
N
2
alloys
with
the fitti
ng parameters
summarized in
Table
S
1
.
Table S1: Ge K
-
edge EXAFS curve fitting parameters.
Path
R ( Å)
N
σ
2
( Å
2
)
R
f
(%)
EXAFS
XRD
Ge
-
N
1.86 (0.03)
1.84
4.0
0.004 (0.002)
2.7
ZnGeN
2
Ge
-
Zn
3.23 (0.08)
3.14
8.0
0.011 (0.001)
Δ
E
0
(eV)=2.3
Ge
-
Ge
3.20 (0.04)
3.11
–
3.20
4.0
0.015 (0.005)
Ge
-
N
1.88 (0.09)
4.0
0.004 (0.008)
1.6
ZnGeSnN
2
Ge
-
Zn
3.26 (0.14)
8.0
0.012 (0.013)
Δ
E
0
=4.3
(Ge:Sn=2:1)
Ge
-
Ge
3.34 (0.01)
3.0
0.020 (0.001)
Ge
-
Sn
3.28 (0.60)
1.0
0.016 (0.020)
Ge
-
N
1.88 (0.08)
4.0
0.003 (0.007)
1.7
ZnGeSnN
2
Ge
-
Zn
3.28 (0.14)
8.0
0.020 (0.002)
Δ
E
0
=4.3
(Ge:Sn=1:1)
Ge
-
Ge
3.24 (0.10)
2.0
0.020 (0.001)
Ge
-
Sn
3.29 (0.44)
2.0
0.020 (0.003)
Ge
-
N
1.87 (0.12)
4.0
0.002 (0.011)
1.4
ZnGeSnN
2
Ge
-
Zn
3.29 (0.01)
8.0
0.020 (0.012)
Δ
E
0
=3.7
(Ge:Sn=1:2)
Ge
-
Ge
3.23 (0.01)
1.7
0.020 (0.012)
Ge
-
Sn
3.33 (0.30)
2.3
0.020 (0.002)
N is the number of neighboring atoms, R, the atomic distance, σ
2
, the Debye
-
Waller factor, and
Δ
E
0
, the EXAFS threshold energy. Bold letters are the fixed parameters. The number in the
parenthesis shows uncertainty in the variables. The goodness of the fit was evaluated by the
EXAFS R
-
factor (R
f
, %) that represents the absolute difference (least
-
squa
re fit) between theory
and data.
Special Quasi
-
random Structures of the
ZnSn
1
-
x
Ge
x
N
2
alloys:
The structural details of the
SQS models used in our calculation are given in Table S2, with the corresponding atomic
correlation functions listed in Table S3.
Table S2
: Basis vectors (in Angstrom) and atomic coordinates (relative to the basis vectors) of
the SQS used in our calculation for the ZnSn
1
-
x
Ge
x
N
2
alloys at concentration x=0.25, 0.50. For
clarity, only the cation coordinates are shown.
x=0.50
x=0.25
a
-
6.72
-
5.81 5.47
a
-
6.72
-
5.81 5.47
b
6.72
-
5.81 5.47
b
6.72
-
5.81 5.47
c
0.00 0.00 10.94
c
0.00 5.81 5.47
Zn
0.5000000 0.5000000 0.1875
Zn
1.09375000 0.09375000 0.1875000
Zn
0.1250000 0.3750000 0.1875
Zn
-
0.15625000 0.09375000 0.4375000
Zn
1.0833335 0.5833335 0.4375
Zn
0.88541675 0.38541675 0.6041665
Zn
0.7083335 0.4583335 0.4375
Zn
0.63541675 0.38541675 0.8541665
Zn
1.0000000 0 0.1875
Zn
0.59375000 0.59375000 0.1875000
Zn
0.6250000 0.8750000 0.1875
Zn
0.34375000 0.59375000 0.4375000
Zn
0.5833335 0.0833335 0.4375
Zn
0.38541675 0.88541675 0.6041665
Zn
0.2083335 0.9583335 0.4375
Zn
0.13541675 0.88541675 0.8541665
Zn
0.5000000 0.5000000 0.6875
Zn
0.34375000 0.34375000 0.6875000
Zn
0.1250000 0.3750000 0.6875
Zn
0.09375000 0.34375000
-
0.0625000
Zn
1.0833335 0.5833335 0.9375
Zn
1.13541675 0.63541675 1.1041665
Zn
0.7083335 0.4583335 0.9375
Zn
-
0.11458325 0.63541675 0.3541665
Zn
1.0000000 0 0.6875
Zn
0.84375000
-
0.15625000 0.6875000
Zn
0.6250000 0.8750000 0.6875
Zn
0.59375000 0.84375000
-
0.0625000
Zn
0.5833335 0.0833335 0.9375
Zn
0.63541675 0.13541675 1.1041665
Zn
0.2083335 0.9583335 0.9375
Zn
0.38541675 1.13541675 0.3541665
Sn
0.2500000 0.7500000 0.1875
Sn
0.84375000 0.34375000 0.1875000
Sn
0.3333335 0.3333335 0.4375
Sn
0.13541675 0.13541675 0.6041665
Sn
0.8750000 0.6250000 0.1875
Sn
0.59375000 0.34375000 0.4375000
Sn
0.9583335 0.2083335 0.4375
Sn
0.88541675 0.13541675 0.8541665
Sn
0.3750000 0.1250000 0.1875
Sn
0.34375000 0.84375000 0.1875000
Sn
0.4583335 0.7083335 0.4375
Sn
0.63541675 0.63541675 0.6041665
Sn
0.2500000 0.7500000 0.6875
Sn
0.38541675 0.63541675 0.8541665
Sn
0.3333335 0.3333335 0.9375
Sn
0.09375000 0.59375000 0.6875000
Ge
0.7500000 0.2500000 0.1875
Sn
0.38541675 0.38541675 0.1041665
Ge
0.8333335 0.8333335 0.4375
Sn
0.84375000 0.59375000 0.9375000
Ge
0.8750000 0.6250000 0.6875
Sn
0.13541675 0.38541675 0.3541665
Ge
0.9583335 0.2083335 0.9375
Sn
0.59375000 0.09375000 0.6875000
Ge
0.7500000 0.2500000 0.6875
Ge
0.09375000 0.84375000 0.4375000
Ge
0.8333335 0.8333335 0.9375
Ge
0.88541675 0.88541675 0.1041665
Ge
0.3750000 0.1250000 0.6875
Ge
0.34375000 0.09375000 0.9375000
Ge
0.4583335 0.7083335 0.9375
Ge
0.63541675 0.88541675 0.3541665
Table S3:
Atomic correlation functions for the atomic clusters (
k
,
m)
with
k
vertices and up to the
m
-
th neighbor
of the SQS used in our calculation, at the alloy concentration
x
=0.25, 0.5, and
compared with the ideal values
of the random alloy.
(m,k)
(2,1)
(2,2)
(2,3)
(2,4)
(3,2)
(3,3)
(3,4)
(4,3)
(4,4)
x
=0.50
R
andom
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
SQS
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-
1.0
x
=0.25
R
andom
0.25
0.25
0.25
0.25
-
0.125
0.125
0.0625
0.0625
SQS
0.25
0.25
0.25
0.25
-
0.000
0.250
0.0000
0.2500
Calculated density of states of
ZnSnN
2
and ZnGeN
2
:
The
calculated density of states for
ZnSnN
2
and ZnGeN
2
is given in Figure S2
, with the energy relative to the valence band
maximum (VBM) eigen
-
energy.
Figure S2
:
Calculated total and partial density of states of (a) ZnSnN
2
and (b) ZnGeN
2
. The
partial density of states is projected on Zn, Sn, Ge
and N s, p, and d orbitals respectively.