1. science
2. physics

Erik Jonsson School of Engineering and Computer Science
2015-1
Thickness Modulated MoS2 Grown by Chemical
Vapor Deposition for Transparent and Flexible
Electronic Devices
UTD AUTHOR(S): Gil Sik Lee
©2015 AIP Publishing, LLC
Park, Juhong, Nitin Choudhary, Jesse Smith, Gilsik Lee, et al. 2015. "Thickness modulated
MoS2 grown by chemical vapor deposition for transparent and flexible electronic
devices." Applied Physics Letters 106(1): doi:10.1063/1.4905476.
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APPLIED PHYSICS LETTERS 106, 012104 (2015)
Thickness modulated MoS2 grown by chemical vapor deposition for
transparent and flexible electronic devices
Juhong Park,1,a) Nitin Choudhary,1,a) Jesse Smith,1 Gilsik Lee,2 Moonkyung Kim,3
and Wonbong Choi1,b)
1
Department of Materials Science and Engineering, University of North Texas, Denton, Texas 76201, USA
Department of Electrical Engineering, University of Texas at Dallas, Richardson, Texas 75080-3021, USA
3
School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA
2
(Received 5 November 2014; accepted 22 December 2014; published online 6 January 2015)
Two-dimensional (2D) materials have been a great interest as high-performance transparent and flexible electronics due to their high crystallinity in atomic thickness and their potential for variety applications in electronics and optoelectronics. The present study explored the wafer scale production of
MoS2 nanosheets with layer thickness modulation from single to multi-layer by using two-step method
of metal deposition and CVD process. The formation of high-quality and layer thickness-modulated
MoS2 film was confirmed by Raman spectroscopy, AFM, HRTEM, and photoluminescence analysis.
The layer thickness was identified by employing a simple method of optical contrast value. The image
contrast in green (G) channel shows the best fit as contrast increases with layer thickness, which can
be utilized in identifying the layer thickness of MoS2. The presence of critical thickness of Mo for
complete sulphurization, which is due to the diffusion limit of MoS2 transformation, changes the linearity of structural, electrical, and optical properties of MoS2. High optical transparency of >90%, electrical mobility of 12.24 cm2 V1 s1, and Ion/off of 106 characterized within the critical thickness
make the MoS2 film suitable for transparent and flexible electronics as compared to conventional
amorphous silicon (a-Si) or organic films. The layer thickness modulated large scale MoS2 growth
method in conjunction with the layer thickness identification by the nondestructive optical contrast
will definitely trigger development of scalable 2D MoS2 films for transparent and flexible electronics.
C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4905476]
V
Two dimensional (2D) transition metal dichalcogenide
(TMD) materials have received considerable research interest in the past few years because of their unique properties
and wide applications in transparent and flexible electronics,
sensors, and sustainable energy.1–4 In particular, molybdenum dichalcogenide (MoS2), a 2D semiconductor material
has proven to be a very interesting material for future transparent and flexible optoelectronic device applications due to
its high mobility (200 cm2 V1 s1), high current on/off
ratio (108), and quantum confinement effects observed in
atomic layer thickness.5,6 Its layer thickness-dependent
band gap, for example, changing from 1.3 eV for bulk MoS2
(indirect bandgap) to 1.9 eV for single layer MoS2 (direct
band gap), opens avenues for highly efficient opto-electronic
devices.7–10 There have been considerable efforts for the
scalable synthesis and thickness control of MoS2 films that is
necessary for the development of practical and efficient devices. Most of the reports are dealing with the mechanical
exfoliation of bulk MoS2 as it is bonded with relatively weak
van der Waals force between each layer.11,12 However, this
method results in the formation of sub-micrometer size
MoS2 flakes with arbitrary distribution of film thickness.13,14
Recently, a direct growth method of MoS2 monolayer using
vapor-phase reaction of MoO3 and sulfur (S) powders in a
CVD furnace has been demonstrated.15–17 This method demonstrated the formation of small size single layer MoS2 with
a)
J. Park and N. Choudhary contributed equally to this work.
Electronic mail: wonbong.choi@unt.edu
b)
0003-6951/2015/106(1)/012104/5/$30.00
poor mobility and without a clear control over the film thickness. Besides this, the reaction of MoO3 with S results in the
formation of byproducts like MoO2, MoS2 nanoparticles, or
nanorod structures instead of forming continuous MoS2
layers during the synthesis.18 Lin et al.19 fabricated a waferscale few layer MoS2 on sapphire substrate by a two-step
thermal process on evaporated MoO3 layers in the presence
of sulfur. However, there still lacks of controlling the layer
thickness of MoS2 film. Therefore, it is imperative to develop a method that can precisely control the thickness of
MoS2 over a large scale to make it suitable for various electronic and optoelectronic applications via the band gap
engineering.
Apart from controlling the layer thickness, it is required
to grow atomic-layer MoS2 in large area for its practical use
in electronic devices while keeping its compatibility with
standard micro-fabrication technology. Ma and Shi20
attempted to grow large area MoS2 by using thermal evaporation technique, but it resulted mainly in the island growth.
Similarly, Hu et al.21 reported the MoS2 nanoparticles formation by using pulsed laser deposition technique. Several
groups reported very poor mobility in large area MoS2 films
grown by CVD methods.22,23 However, they did not report
on the thickness modulation of MoS2 films. In this work, we
report on the synthesis of wafer scale (2 in.) layer
thickness-modulated MoS2 thin films and their thickness
identification. The layer thickness control from multi-layer
(12.20 nm) to single layer (0.72 nm) was achieved by controlling Mo deposition times. In order to identify the layer
106, 012104-1
C 2015 AIP Publishing LLC
V
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Park et al.
thickness of MoS2, we employed a simple and nondestructive method utilizing camera image of MoS2 films deposited
on glass substrates. Our method is better than the previously
reported white light contrast spectroscopy where continual
white light source, spectrometer, and expensive charged
coupled device (CCD) detectors are required.24 Furthermore,
the high field effect mobility in large-scale MoS2 film in
addition to its high optical transmittance (95%) and Ion/off
ratio will make it suitable candidate for future transparent
and flexible optoelectronic devices.
Large area growth and thickness modulated MoS2 films
were synthesized by using the two-step synthesis method.
First step involves the sputter deposition of Mo films on
(100)-oriented doped Si substrates with 300 nm thick SiO2
top layer. A high purity (99.99%) Mo target was sputtered at
different deposition times, such as 4 (L1), 10 (L2), 30 (L3),
60 (L4), and 180 (L5) s to control the Mo film thickness. second step involves the subsequent vapor phase sulfurization of
Mo films in a low pressure chemical vapor deposition
(LPCVD) system at 600 C, 5 Torr by using argon as a carrier
gas to convey sulfur vapor species to the downstream Mo
films. Thickness measurement of Mo and MoS2 films was
performed by an AFM (Parks NX-10) system and TECNAI
F20 S-Twin (FEI Co, The Netherland) Transmission Electron
Microscope (TEM). Raman spectra of MoS2 thin films were
collected in Almega XR Raman spectrometer equipped with
an Olympus BX51 microscope. The electrical measurements
were performed at room temperature by using an Agilent
B2912A precision source/measure unit connected to a probe
station. Room temperature photoluminescence (PL) and visible spectroscopy were employed to characterize the quality
and optical transmittance of MoS2 films.
Fig. 1(a) shows the Raman spectra corresponding to
samples L1L5 measured at 532 nm excitation laser line to
assess the presence and quality of the MoS2 films. Raman
peaks for the E12g and A1g vibration modes could be seen in
Appl. Phys. Lett. 106, 012104 (2015)
all the samples. A peak frequency difference (Dk) of
19.7 cm1 between two characteristic Raman modes E12g
(385.5 cm1) and A1g (405.2 cm1) in sample L1 indicates
the presence of single-layer MoS2.25 A gradual increase in
Dk from 19.7 cm1 (sample L1) to 27 cm1 (sample L5) represents an increase in the number of MoS2 layers from single
to bulk-like nature.26 Raman peak broadening is also
observed (Fig. 1(a)) when thickness is increased from SL
MoS2 (sample L1) to bulk MoS2 (sample L5). The increment
of lateral inhomogeneity present over the film with increasing film thickness is the major cause of the Raman peak
broadening.27 In order to assess the semiconducting phase
and optical quality of SL MoS2, we carry out PL spectroscopy on sample L1 as shown in the inset of Fig. 1(a). The
peak at photoluminescence energy of 1.89 eV at K point in
the visible region confirms the presence of single-layer
MoS2.28 However, two additional peaks in PL spectra with
smaller energies below the bandgap could be attributed to
the presence of trap levels between conduction and valence
band arising from imperfections of MoS2 lattice.29 The number
of MoS2 layers present in the MoS2 samples was also determined by AFM height profile measurement as shown in
Fig. 1(b). The thickness of MoS2 as estimated by AFM height
profiles was found to be 0.72, 3.01, 5.40, 7.16, and 12.69 nm
for L1, L2, L3, L4, and L5, respectively. Fig. 1(c) shows the photograph of MoS2 nanosheet transferred on the flexible polyethylene terephthalate (PET) substrate confirming its feasibility in
flexible and transparent electronic device applications.
We observed that Mo films were fully sulfurized into
MoS2 only up to a critical thickness in our CVD process. The
extent of sulfurization in Mo films was performed by a simple
calculation based on the lattice parameters of Mo (bcc) and
MoS2 (hcp) materials. Theoretically, when Mo films are com˚ )30 of Mo crystal
pletely sulfurized, lattice constant (3.147 A
˚ ),31 as shown
is changed into MoS2 lattice constant (12.29 A
in the inset of Fig. 2(a). The expected thickness change during Mo to MoS2 transformation can be estimated by
TMo 3:91 ¼ TMoS2 ;
FIG. 1. (a) Raman spectra of MoS2 thin films for different layered samples
of L1–L5. The peak frequency differences (Dk) are 19.7, 21.2, 23.4, 24.7,
and 27 cm1 for samples L1, L2, L3, L4, and L5, respectively. Inset shows
the PL spectra of single layer MoS2 on Si/SiO2. (b) AFM height profiles of
samples L1 (inset) and L2–L5. (c) Photograph of SL MoS2 film transferred
on a flexible (PET) substrate demonstrating flexibility and transparency.
(1)
where TMo and TMoS2 are the thicknesses of Mo and MoS2
films, respectively. Fig. 2(a) compares the theoretically
(Eq. (1)) and experimentally measured (AFM) thickness of
MoS2 films corresponding to samples L1L5. It is evident
from the figure that up to sample L3, the MoS2 thicknesses
are in agreement with the theoretical calculations demonstrating that the Mo films are completely transformed into
MoS2. However, a significant deviation is observed for samples L4 and L5. It could be explained that during sulfurization, sulfur vapor diffusion is the rate-limiting process.
Hence, the sulfur atom could not react with Mo molecules
beyond a certain thickness of MoS2 film at given temperature
and time. Therefore, the thicknesses for L4 and L5 were
lower than the calculated values. Figs. 2(b)–2(d) show the
cross-sectional HRTEM images for samples L1, L2, and L4,
respectively. The thickness of MoS2 film for sample L1, as
determined by HRTEM, was 0.69 nm, which is in agreement with our AFM results. The inset of Fig. 2(b) clearly
shows the formation of SL MoS2. The HRTEM image of
sample L2 shows the formation of 3–4 layers of MoS2. It is
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Park et al.
FIG. 2. (a) Theoretical and experimental thickness values of Mo and MoS2
thin films corresponding to samples L1–L5. Inset shows the crystal structure
and lattice constants of Mo and MoS2. Cross-sectional HRTEM images of
MoS2 films for samples (b) L1, (c) L2, and (d) L4.
worth noting that the cross-sectional HRTEM image of sample L4 shows the presence of two different materials (different contrasts in Fig. 2(d)) with a wavy type layered structure
of MoS2 on top-section while a thin interfacial structure on
the bottom-section. It seems that the interfacial structure is
not fully sulfurized and affects its electrical and optical properties. A similar image was observed in case of sample L5.
The electrical properties of MoS2 films were determined
by characterizing MoS2-field effect transistor (FET) devices
using 50 nm thick Au as source and drain electrodes, 300 nm
thick SiO2 served as dielectric layer, and doped silicon as the
back gate. Electrical measurements on sample L1 showed a
very high resistance without an indication of FET behavior
or gate biasing effect. It could be attributed to the large spatial constraints imposed by the substrates for very thin layers
of MoS2 and/or grain discontinuity across the film. The electrical characterization (Id-Vg curve) of MoS2 thin film corresponding to samples L2 and L3 (Fig. 3(a)) exhibits p-type
conductance which could be attributed to the presence of
localized trap states at the interface of Si/SiO2 substrate and
MoS2 film.32 The inset of Fig. 3(a) shows the Id-Vg curves of
Appl. Phys. Lett. 106, 012104 (2015)
L2 on L3 on logarithmic scale. The field effect mobility is
calculated using formula: l ¼ (L/WCox)DG/DVg,33 where
G ¼ IDS/VDS is the conductance, L ¼ 10 lm is the length,
and 30 lm is the width of the MoS2 channel. DG/DVG
¼ (1/VDS)(DIDS/DVG) is determined from the slope of a
linear-fit of the data ranging from Vg ¼ þ15 V to Vg
¼ 15 V. Cox ¼ e0er/d is the capacitance per unit area, where
the thickness of the SiO2 layer d ¼ 300 nm, the free-space
permittivity e0 ¼ 8.854 1012 F m1, and the relative permittivity of Si er ¼ 3.9. The average value of field effect mobility (l) and current on/off (Ion/off) ratio for sample L2, as
determined from Fig. 3(a), is 12.24 6 0.741 cm2 V1 s1 and
1.57 106, respectively. It is important to note that the measured mobility in our sample is higher than the previous
reports of exfoliated single-crystal MoS2 and CVD grown
MoS2, and it is comparable with the mobility of amorphous
silicon (a-Si) and organic materials.34,35 For sample L3, the
values for l and Ion/off are 0.44 6 0.062 cm2 V1 s1 and
5.7 104, respectively. However, samples L4 and L5 show a
conducting nature of MoS2 films with very low resistance
(102 X), which could be attributed to the presence of
un-transformed interfacial layer at the bottom of film. The
spectral transmission for the MoS2 films with different thicknesses, samples L1L5, was also measured over the wavelength range of 300–800 nm (Fig. 3(b)). An average optical
transmittance value up to 95% was observed in the single
layer MoS2 film and the value was decreased with increasing
film thickness. The very low transmittance from L4 and L5
MoS2 film is attributed to the presence of the interfacial layer
as explained above. The high optical transmittance with high
field effect mobility and Ion/off ratio in sample L2 makes it
suitable for optoelectronic devices.
To identify the number of layers in thickness-modulated
CVD grown MoS2, we introduced a method of using the
contrast of a photographic image, which is a simple and nondestructive characterization method. Fig. 4(a) shows a typical camera image of the MoS2 films (L1L5) on glass. The
photographic image (Fig. 4(a)) was decomposed into its red
(R), green (G), and blue (B) channels shown in Figs.
4(b)4(d) by using scientific python, which allows to determine the contrast of each channel.36 The contrast of MoS2
films on glass/paper can be calculated using the following
equation:24
C¼
I0 I
;
I0
(2)
where I0 and I are the reflected light intensities from the airglass (substrate) interface and air-MoS2 interface, respectively. Our definition of contrast (Eq. (2)) is modified slightly
to instantiate a definition for the contrast of each separate
channel (R, G, and B)
CRGB ¼
FIG. 3. (a) Electric charge transfer characteristics (Id-Vg curve) for samples
L2 and L3 at Vd ¼ 0.5 V. Inset shows the corresponding curves on logarithmic scale. (b) UV-vis optical transmittance spectra of MoS2 films corresponding to samples L1 (0.72 nm)–L5 (12.69 nm).
I0;RGB IRGB
;
I0;RGB
(3)
where I0;RGB and IRBG are the channel intensities of either
red, green, or blue channel from light that interacts with substrate and MoS2, respectively. The calculated results by
using Eq. (3) for all three channels, R, G, and B, across the
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Park et al.
Appl. Phys. Lett. 106, 012104 (2015)
substituting the green configuration of Eq. (3) into Eq. (4),
and solving for x
I0;G IG
þ 0:0259
I0;G
x¼
;
(5)
0:06894
FIG. 4. (a) Photographic camera image of MoS2 films with different number
of layers (L1L5). The (b) red (c) green, and (d) blue channel images of the
original camera image, obtained using matplotlib module for scientific
python. The rectangles in 4(c) show examples of domains where Io and I
were taken to calculate the contrast. (e) Contrast values of MoS2 films for R,
G, and B channels as a function of thickness. (f) Three-dimensional contrast
image of the green channel of samples L1–L5 calculated by Eq. (5), demonstrating the variation of MoS2 thickness.
five thicknesses are shown in Fig. 4(e). These contrast values
were calculated by taking the statistical mean of I0;RGB and
IRGB across rectangular domains from the substrate and each
MoS2 film to account for variations (see Fig. 4(c)) for an
example of the rectangular domains. This data is plotted as a
function of MoS2 thickness (measured from AFM) so that a
linear regression (solid lines) can be fit to the experimental
data. The linear regression then provides the link between
contrast and expected thickness. It is clear from Fig. 4(e) that
blue channel has the largest range with the worst linear fit of
R2 ¼ 0:7237. The green channel has the best linear fit of
R2 ¼ 0:996 making it the most accurate channel for thickness identification. The corresponding linear regression of
the green channel is
CG ¼ 0:06894x 0:0259;
(4)
where CG is the contrast of the green channel and x is the
MoS2 thickness. This yields the critical link between the
layer thickness of the MoS2 layer, x, and the contrast of the
green channel, CG . Thus, an explicit relationship between x
and the green intensities, IG and I0;G , can be acquired by
with this Eq. (5), the MoS2 thickness can be predicted by
simply knowing the I0;G and IG values, which can be easily
determined from any color image by using its green channel.
We found that the image contrast in green (G) channel shows
the best fit as contrast increases with layer thickness, which
can be utilized for identifying the layer thickness simply by
taking an optical image of MoS2. Fig. 4(f) shows the three
dimensional thickness distribution of MoS2 samples (L1L5)
obtained by iterating Eq. (5). Contrast differences for the
MoS2 samples with different thicknesses can clearly be seen
in this figure.
We report the synthesis of layer-thickness modulated
MoS2 film from multilayers to single layer and its optical
and electrical properties towards its application in transparent and flexible electronics. The formation of high quality
and layer thickness modulated MoS2 film was confirmed by
Raman spectroscopy, AFM, HRTEM, and PL analysis. The
characterized high optical transparency of >90%, electrical
mobility of 12.24 cm2 V1 s1, and Ion/off of 106 of the
large scale MoS2 film are suitable for transparent and flexible
electronics as compared to conventional amorphous silicon
(a-Si) or organic films. We observed the presence of critical
thickness of MoS2 over which Mo film was not fully sulfurized due to its diffusion limit in phase transformation. A simple layer thickness identification method based on calculated
contrast values in green channel is very well matched with
the experimental data confirming its utilization in layerthickness identification in CVD grown MoS2 film. The layerthickness modulated MoS2 growth in conjunction with the
layer-thickness identification method will definitely trigger
development of scalable 2D MoS2 films for transparent and
flexible electronics.
This work was supported by a start-up fund from
University of North Texas. J. S. acknowledges a partial
support from the I-GRO program, University of North Texas.
1
S. Das, M. Kim, J. Lee, and W. Choi, Crit. Rev. Solid State Mater. Sci. 39,
231 (2014).
2
H. Qiu, L. Pan, Z. Yao, J. Li, Y. Shi, and X. Wang, Appl. Phys. Lett. 100,
123104 (2012).
3
S. M. Tabatabaei, M. Noei, K. Khaliji, M. Pourfath, and M. Fathipour,
J. Appl. Phys. 113, 163708 (2013).
4
N. Choudhary, S. Hwang, and W. Choi, Handbook of Nanomaterials
Properties (Springer, USA, 2014), p. 709.
5
R. Fivaz and E. Mooser, Phys. Rev. 163, 743 (1967).
6
B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, and A. Kis, Nat.
Nanotechnol. 6, 147 (2011).
7
G. L. Frey, S. Elani, M. Homyonfer, Y. Feldman, and R. Tenne, Phys.
Rev. 57, 6666 (1998).
8
K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Phys. Rev. Lett. 105,
136805 (2010).
9
M. R. Islam, N. Kang, U. Bhanu, H. P. Paudel, M. Erementchouk, L.
Tetard, M. N. Leuenberger, and S. I. Khondaker, Nanoscale 6, 10033
(2014).
10
W. Bao, X. Cai, D. Kim, K. Sridhara, and M. S. Fuhrer, Appl. Phys. Lett.
102, 042104 (2013).
012104-5
11
Park et al.
R. A. Bromley, A. D. Yoffe, and R. B. Murray, J. Phys. C: Solid State
Phys. 5, 759 (1972).
12
L. F. Mattheiss, Phys. Rev. 8, 3719 (1973).
13
R. Coehoorn, C. Haas, J. Dijkstra, and C. J. F. Flipse, Phys. Rev. 35, 6195
(1987).
14
H. Li, J. Wu, Z. Yin, and H. Zhang, Acc. Chem. Res. 47, 1067 (2014).
15
J. Mann, D. Sun, Q. Ma, J. R. Chen, E. Preciado, T. Ohta, B. Diaconescu,
K. Yamaguchi, T. Tran, M. Wurch, K. M. Magnone, T. F. Heinz, G. L.
Kellogg, R. Kawakami, and L. Bartels, Eur. Phys. J. B 86, 226 (2013).
16
S. Najmaei, Z. Liu, W. Zhou, X. Zou, G. Shi, S. Lei, B. I. Yakobson, J. C.
Idrobo, P. M. Ajayan, and J. Lou, Nat. Mater. 12, 754 (2013).
17
S. Balendhran, J. Z. Ou, M. Bhaskaran, S. Sriram, S. Ippolito, Z. Vasic, E.
Kats, S. Bhargava, S. Zhuiykovd, and K. Kalantar-zadeh, Nanoscale 4,
461 (2012).
18
X. L. Li and Y. D. Li, Chem. - Eur. J. 9, 2726 (2003).
19
Y. C. Lin, W. Zhang, J. K. Huang, K. K. Liu, Y. H. Lee, C. T. Liang, C.
W. Chu, and L. J. Li, Nanoscale 4, 6637 (2012).
20
X. Ma and M. Shi, Nano-Micro Lett. 5, 135 (2013).
21
J. J. Hu, J. S. Zabinski, J. E. Bultman, J. H. Sanders, and A. A. Voevodin,
Cryst. Growth Des. 8, 2603 (2008).
22
Y. F. Yu, C. Li, Y. Liu, L. Q. Su, Y. Zhang, and L. Y. Cao, Sci. Rep. 3,
1866 (2013).
23
Y. Zhan, Z. Liu, S. Najmaei, P. M. Ajayan, and J. Lou, Small 8, 966
(2012).
Appl. Phys. Lett. 106, 012104 (2015)
24
Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng,
and Z. X. Shen, Nano Lett. 7, 2758 (2007).
H. Li, Q. Zhang, C. C. R. Yap, B. K. Tay, T. H. T. Edwin, A. Olivier, and
D. Baillargeat, Adv. Funct. Mater. 22, 1385 (2012).
26
B. Chakraborty, H. S. S. Ramakrishna Matte, A. K. Sooda, and C. N. R.
Rao, J. Raman Spectrosc. 44, 92 (2013).
27
C. Lee, H. Yan, L. Brus, T. Heinz, J. Hone, and S. Ryu, ACS Nano 4,
2695 (2010).
28
A. Splendiani, L. Sun, Y. B. Zhang, T. S. Li, J. Kim, C. Y. Chim, G. Galli,
and F. Wang, Nano Lett. 10, 1271 (2010).
29
S. Tongay, J. Suh, C. Ataca, W. Fan, A. Luce, J. S. Kang, J. Liu, C. H. Ko,
R. Raghunathanan, J. Zhou, F. Ogletree, J. Li, J. C. Grossman, and J. Wu,
Sci. Rep. 3, 2657 (2013).
30
R. G. Ross and W. Hume-Rothery, J. Less-Common Met. 5, 258 (1963).
31
W. O. Winer, Wear 10, 422 (1967).
32
K. Dolui, I. Rungger, and S. Sanvito, Phys. Rev. 87, 165402 (2013).
33
A. Ayari, E. Cobas, O. Ogundadegbe, and M. S. Fuhrer, J. Appl. Phys.
101, 014507 (2007).
34
L. Han, P. Mandlik, K. H. Cherenack, and S. Wagner, Appl. Phys. Lett.
94, 162105 (2009).
35
J. Poortmans and V. Arkhipov, Thin Film Solar Cells: Fabrication,
Characterization and Applications (John Wiley and Sons Ltd., 2006), p.
181.
36
J. D. Hunter, Comput. Sci. Eng. 9, 90 (2007).
25