Dielectric response and structure of amorphous hydrogenated carbon �lms with
nitrogen admixture
Lenka Zajíčková a,
�, Daniel Franta a
, David NeÄŤas a
, Vilma Buršíková a
, Mihai Muresan a
,
Vratislav Peřina b
, Christoph Cobet c
a
Department of Physical Electronics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
b
Institute of Nuclear Physics, Academy of Science of the Czech Republic, �ež, Czech Republic
c
Institute for Analytical Sciences, Albert-Einstein-Str. 9, 12489 Berlin, Germany
a b s t r a c ta r t i c l e i n f o
Article history:
Received 31 August 2010
Received in revised form 26 January 2011
Accepted 3 February 2011
Available online 18 February 2011
Keywords:
Diamond-like carbon
Amorphous hydrogenated carbon
Optical properties
Band structure
The optical properties and structure of a-C:H �lms were modi�ed by addition of nitrogen into the CH4/H2
deposition mixture. Three �lms prepared in capacitively coupled rf discharge were compared:
(a) hydrogenated diamond like carbon �lm with hydrogen content of 34% and indentation hardness of
21.7 GPa, (b) hard a-C:H:N �lm with nitrogen content of 13% and indentation hardness of 18.5 GPa and
(c) soft a-C:H:N �lm with nitrogen content of 10% and indentation hardness of 6.7 GPa. It is shown how the
parametrized density of states model describing dielectric response of electronic interband transitions can be
applied to modi�ed a-C:H:N and how it can be combined with correct treatment of transmittance measured in
infrared range using additional Gaussian peaks in joint density of phonon states. This analysis resulted in
determination of �lm dielectric function in wide spectral range (0.045–30 eV) and provided also information
about the density of states of valence and conduction bands and lattice vibrations.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
There are many forms of amorphous carbon with great variety of
physical properties depending on the speci�c mixture of sp3
and sp2
sites. If they contain hydrogen its content additionally influences the
material structure and properties. An a-C or a-C:H of higher sp3
content belongs to the class of materials often called diamond-like
carbon (DLC). Casiraghi suggested more precise classi�cation of a-C:H
�lms into four types [1,2]: (a) polymer-like a-C:H (PLCH) with the
highest H content (40–60 at.%), up to 70% sp3
but soft and of low
density, (b) harder diamond-like a-C:H (DLCH) with intermediate H
content (20-40 at.%), (c) hydrogenated tetrahedral amorphous
carbon �lms (ta-C:H) in which the C–C sp3
content is increased
(as compared to DLCH) whilst keeping a �xed H content 25–30 at.% H
and (d) graphite-like a-C:H (GLCH) with less than 20 at.% of H, a high
sp2
content and sp2
clustering.
PLCH �lms are soft, have low density and the optical gap ranges from
2 to 4 eV. Even if DLCH �lms have lower overall sp3
content, they have
more C–C sp3
bonds than PLCH. Thus, they have better mechanical
properties. Their optical gap is between 1 and 2 eV. Films de�ned as
ta-C:H differ from DLCHs by their Raman spectra, higher density (up to
2.4 g/cm3
) and Young's modulus (up to 300 GPa) [3–5]. Their optical
gap can reach 2.4 eV [6]. The gap of GLCH is under 1 eV.
The optical gap in the above material classi�cation was determined
from the decrease of absorption coef�cient to 104
cm� 1
, so
called E04, or from Tauc plot. This approach provides information
about the �lm transparency but does not describe the nature of
sp3
/sp2
carbon materials because two different types of states in
valence and conduction bands form the density of states (DOS), the
states related to � and π electrons. Therefore, two different band gaps,
corresponding to �→�� and π→π� interband transitions, should be
distinguished. In this aspect a-C(:H) material differ from amorphous
semiconductors such as a-Si [7] and classi�cation using the optical gap
can be confusing.
The a-C(:H) coatings have wide range of applications but it is
necessary to optimize their adhesion to substrate material and decrease
intrinsic stress in the �lms. Approaches solving this problem include the
fabrication of an intermediate layer between the coating and substrate,
and the reduction of the internal stress of the coating. Intermediate
metal or compound layers such as Ti, Zr, W, Nb, or WC have shown
potential to improve the adhesive strength [8]. The great disadvantage
of this technique is that two or more steps, sometimes using different
deposition techniques, are necessary. A prospective trend is to use a
single step process by mixing some dopants into the structure of DLC.
The residual stress of the DLC coating has been reduced by including
additional elements. Positive results were achieved by Rabbani [9] for
nitrogen admixture.
Thin Solid Films 519 (2011) 4299–4308
� Corresponding author. Tel.: +420 54949 8217; fax: +420 541211214.
E-mail address: lenkaz@physics.muni.cz (L. Zajíčková).
0040-6090/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.tsf.2011.02.021
Contents lists available at ScienceDirect
Thin Solid Films
journal homepage: www.elsevier.com/locate/tsf
The optical properties and structure of a-C:H are modi�ed by
nitrogen addition. Hayashi [10] observed a decrease of the optical gap
with the increase of nitrogen content. Nitrogen addition decreased
refractive index due to lower density of the material [11]. Recently, we
have shown for DLCH �lms that optical measurement performed from
near infrared to extreme ultraviolet (NIR-XUV) range can be analyzed
using parametrization of DOS (PDOS) and, therefore, provide
information about valence and conduction bands [12,13]. This work
aims to show how the PDOS model can be applied to a-C:H:N and how
it can be combined with correct treatment of transmittance measured
in infrared range using additional Gaussian peaks in joint density of
states (JDOS). This approach results not only in the knowledge of �lm
dielectric function in wide spectral range but provides also information
about DOS of valence and conduction bands and lattice
vibrations.
2. Experimental details
Thin �lms were deposited in radio frequency (rf) capacitively
coupled discharge driven at the frequency of 13.56 MHz. A detailed
drawing of the plasma reactor can be found in Ref. [14]. Pumping system
consisted of turbo and rotary pumps. The reactor chamber was made of
stainless steel and equipped with two parallel plate electrodes. The
upper showerhead electrode, 380 mm in diameter, was grounded and
used for gas distribution. The bottom electrode, 420 mm in diameter,
was connected to an rf generator through a matching network. The
distance between the electrodes was 55 mm.
This paper discusses two a-C:H:N �lms prepared from the mixture of
CH4/H2/N2, labeled CH16 and CH17, and one DLCH�lm (CH30)prepared
from CH4/H2 mixture for comparison. The flow rate of CH4 was 8.5 sccm.
The flow rate of H2 was 5 sccm in case of CH30 whereas 2.5 sccm of H2
and 2.5 sccm of N2 were used for CH17 and CH16. The total pressure was
12 Pa.
The substrates, double-side polished crystalline silicon (Si) pieces,
were placed on the rf electrode. This electrode was dc self-biased due
to a reactor asymmetry, i.e. smaller area of rf electrode as compared to
grounded surfaces, and different mobility of electrons and ions[15].
The bias Ub determined the energy of ions bombarding a growing �lm.
RF power and bias used for deposition of studied �lms are
summarized in Table 1.
The Si substrates were treated in H2/Ar plasma before the deposition.
The flow rate of H2 and Ar were 10 and 3 sccm, respectively. The total
pressure was 8 Pa. The discharge was operated at 100 W and
corresponding dc self-bias was �150V. The treatment time was 10 min.
The thin �lms on Si substrates were optically characterized as
follows:
� Ellipsometry in NIR-UV range (0.6–6.5 eV) measured with Jobin
Yvon UVISEL phase-modulated (PM) variable-angle spectroscopic
ellipsometer at �ve angles of incidence from 55�
to 75�
.
� Ellipsometry in UV–VUV range (5–9.6 eV) measured with BESSY II
synchrotron rotating-analyzer (RA) ellipsometer without retarder at
�xed angle of incidence. The angle of incidence was 67.5�
and the set of
two MgF2-Rochon prisms were used as polarizer and analyzer.
� Ellipsometry in XUV range (9–30 eV) measured with BESSY II
synchrotron ellipsometer with triple reflection polarizers at 45�
angle of incidence. This measurement was carried out only for DLCH
�lm CH30[13].
� Reflectance in NIR-UV range (1.24–6.5 eV) measured with PerkinElmer
Lambda 45 spectrophotometer with reflectance accessory at 6�
.
� Transmittance in IR range (0.045–0.93 eV, i.e. 370–7500 cm� 1
)
measured with Bruker Vertex 80v Fourier transform spectrophotometerequipped
witha parallelbeamtransmittance accessoryfor correct
absolute transmittance measurement.
The hardness and elastic modulus values were assessed from
depth sensing indentation tests using the Fischerscope H100 tester
with Berkovich indenter. The load and the corresponding indentation
depth were recorded as a function of time for both loading and
unloading processes. The desired material parameters were obtained
from analysis of loading and unloading curves. The indentation tests
were carried out for several different indentation depths (i.e. several
different applied loads) in order to map the mechanical properties of
the �lm/substrate system from near surface up to the �lm-substrate
interface. The applied load L ranged from 1 to 100 mN with the force
resolution of 0.04 mN. The accuracy of the indentation depth
measurement was ±1 nm. Each indentation test was repeated at
least 16 times.
The atomic composition was determined by Rutherford backscattering
(RBS) and elastic recoil detection (ERDA) methods using a INP
Van de Graaf generator and TANDETRON with a linear electrostatic
accelerators. The contents of C, N and O were measured by RBS using
1.74 MeV and 2.3 MeV protons and 3.04 MeV α-particles as projectiles.
Higher Rutherford cross-section values enhanced the backscattering
spectrometry sensitivity as follows: at 2.3 MeV protons for C approximately
sevenfold, for N sixfold, for O fourfold, at 1.74 MeV protons for C
by approximately 70× and at 3.04 MeV α-particles for O by 23×. A
surface barrier detector was used for the detection of particles scattered
under the laboratory scattering angle of 170�
. The particles impinging at
60�
to the surface normal were used for enhancement of measurement
sensitivity because studied �lms were quite thin. Anyway, the accuracy
of evaluation was not high especial as concerns �lm density. The depth
resolution was from some tens of nanometers due to the �nite energy
resolution of the detector.
The ERDA with an incident beam of 2.75 MeV α-particles at 75�
to the
surface normal was used for the measurement of H content. Hydrogen
atoms recoiled at 30�
were detected with a surface barrier detector
covered with a 12 μm thick mylar stopping foil. The foil �ltered out
reflected α-particles and protected the detector. The charge of
impinging α-particles was measured using beam chopper with Au
layer and monitored in RBS con�guration. For proper evaluation the
“dead time” is considered. The ERDA was calibrated using 11.9% H:Si
standard. The RBS and ERDA measurements were evaluated by
computer codes GISA 3 [16] and SIMNRA [17], respectively, using
cross-section values from a SigmaBase [18].
3. Results and discussion
Data measured with all optical instruments were �tted simultaneously
using a single, consistent structural and dispersion model.
The samples were modeled by the system consisting of Si substrate,
whose optical constants were determined with high precision in
previous experiments, an inhomogeneous transition layer and an
inhomogeneous anisotropic �lm. The transition layer originated from
interaction of plasma with Si substrate whose surface region is
modi�ed during a plasma pretreatment and the initial phase of the
Table 1
Summary of varying deposition parameters, i.e. power P and dc self-bias Ub, �lm
thickness d, elemental composition and mechanical properties (indentation hardness
HIT and indentation modulus EIT) of studied �lms.
Parameter/�lm CH30 CH16 CH17
P (W) 100 100 50
Ub (V) �80 �130 �50
d (nm) 101 114 216
C (%) 65 56 46
H (%) 34 28 38
N (%) 0 13 10
O (%) 1 3 6
HIT (GPa) 21.7 18.5 6.7
EIT (GPa) 155 130 68
4300 L. Zajíčková et al. / Thin Solid Films 519 (2011) 4299–4308
deposition. Dispersion models used for �tting were Kramers–Kronig
consistent. Optical measurements in NIR–XUV provided information
about electronic band structure of deposited �lms and transition
layers whereas phonon response in IR range revealed the presence of
chemical groups in studied materials.
3.1. Analysis of interband transitions
Electronic dielectric responses of a-C:H(:N) �lms were constructed
using parametrization of density of states (PDOS) [12,19]. Schematic
diagram of the density of states (DOS) of a-C:H:N material is in Fig. 1. It is
similar to DOS of pure a-C:H, aside from the addition of nitrogen 1s core
level states, because 2s and 2p valence electrons of carbon and nitrogen
atoms form common valence and conduction bands of a-C:H:N material.
Since nitrogen and carbon can form multiple bonds two groups of
electron states, π and �, have to be considered. The valence bands
correspond to the π and � bonding states while the conduction bands to
the π and � antibonding states. The presence of hydrogen in the
material increases the density of � states but π states are not influenced
because hydrogen valence 1s electrons form only single bonds. Excited
levels, i.e. 2s, 2p etc. of H and 3s, 3p etc. of C and N, form higher excitation
bands ĂŽÄľ of the material.
Excitations of carbon and nitrogen core electrons contribute to the
dielectric response from energies 285 and 400 eV, respectively.
Therefore, only transitions from valence, π and �, to conduction, π
and ÄŽďż˝ , or higher excitation, ĂŽÄľ , bands contribute to the dielectric
response in NIR–XUV range. The contribution of electronic transitions to
the imaginary part of the dielectric function εi was, in our model,
calculated as a sum of three terms [20]
εi Eð Þ = εi;π→π� Eð Þ + εi;�→�� Eð Þ + εi;�→ξ� Eð Þ ð1Þ
where E is photon energy. The individual contributions can be
expressed as
εi;j→k� Eð Þ =
1
E2
Z �
��
Nj SĂ° ĂžN
k� S + Eð ÞdS; ð2Þ
where j,k=π,�,ξ. Density of states Nj and Nk
� were parametrized by
six parameters for π and � bands and three parameters for higher
excitation states ξ�, i.e. the 6+6+3 PDOS model [12] was used.
Dispersion model parameters found for all three �lms (one DLCH and
two a-C:H:N) are summarized in Table 2. Their physical meaning is
following: Q j is proportional to the product of electron density and
corresponding transition probability; Egj and Ehj represent the
minimum and maximum transition energy, respectively. Detailed
description of all the parameters can be found in [12].
The measurement of the DLCH �lm CH30 carried out up to 30 eV
was at �rst �tted independently. The data processing, data measured
by all the instruments and their agreement with the �t in entire
spectral range are discussed by Franta [13]. Afterwards, all the
samples were �tted simultaneously. The ellipsometric and reflectance
data in NIR–VUV compared with the �t are shown in Figs. 2 and 3.
Because of the shorter measurement range of CH16 and CH17 all the
parameters related to � and ξ� bands, except Eg� and Q�, were �xed at
the values found for CH30. The parameter Q ĂŽÄľ was set equal to Q ÄŽďż˝ for
all the �lms. Therefore, the total number of dispersion parameters in
Table 2 was 6+6+2=14.
The �nal values of the � band gap Eg� of the individual �lms differed
only slightly. The low energy �→�� transitions overlapped with π→π�
transitions (see Fig. 4) and, therefore, this value cannot be determined
directly from shape of dielectric function. The values of EgÄŽďż˝ follows from
the assumption of parabolic bands, i.e. square root-like shape of DOS in
vicinity of band edges. Still, the values of EgÄŽďż˝ were in the range
4.7–5.1 eV, i.e. in agreement with the band gap of crystalline diamond,
5.45–5.48 eV [21,22].
The changes of the parameters Q� and Qπ shown in Table 2 reflected
changes of the density of � and π electrons, i.e. changes of the bonding
con�guration in the �lms. The density of � electrons corresponded to
the density of strong bonds increasing the mechanical hardness. The
parameter Q � decreased from the maximum value in DLCH �lm, CH30,
to lower values in a-C:H:N. The hardness of the �lm CH16 was 18.5 GPa,
i.e. slightly decreased in comparison with 21.7 GPa of CH30, whereas
CH17 was quite soft polymeric �lm with the hardness of 6.7 GPa
(Table 1). Therefore, the decrease of QÄŽďż˝ between CH16 and CH17 was
surprisingly small. The parameter Q ÄŽďż˝ was probably not determined well
in case of CH16 and CH17 because the measurement range was
restricted to 10 eV and did not cover the full range of �→�� transitions
whose maximum energy was 28.1 eV.
In case of CH16 and CH17 the higher band gap EgÄŽďż˝ could suggest that
the ÄŽďż˝ bands are narrower and the density of ÄŽďż˝ electrons is, therefore,
overestimated.
The parameters describing the π→π� were all �tted independently
because the maximum energy of transitions was expected below 10 eV.
The π→π� band gap decreased from 0.752 eV for DLCH to 0.51–0.44 eV
for a-C:H:N. For all three samples the shape of the π and π� bands are
asymmetrical and their shape close to the band gap is evidently far from
square root-like form and it is more Gaussian-like (see Fig.4). It is
interesting that density of π electrons was higher in CH16 and lower in
CH17 compared to CH30 (see parameter Q π in Table 2). This is an
illustration that the concentration of π electrons is not correlated with
hardness of the material.
-400 -285 EF=0 eV
DOS
C
N
1s core levels valence
bands
conduction
bands
higher excitations
π π*
ÄŽďż˝ ÄŽďż˝*
ĂŽÄľ*
Fig. 1. Schematic diagram of the complete electronic structure of a-C:H:N. Shaded areas
depict occupied electronic states. Symbol EF denotes the Fermi energy.
Table 2
Summary of model parameters describing dielectric response of interband transitions
in the DLCH (�lm CH30) and a-C:H:N (�lms CH16 and CH17) �lms. Dispersion model
parameters are given in the �rst part of the table whereas the second part shows
parameters related to �lm inhomogeneity and anisotropy.
Parameter/�lm CH30 CH16 CH17
QĎ€ (eV3/2
) 9.88 10.94 8.68
Egπ (eV) 0.752 0.509 0.440
Ehπ (eV) 9.03 8.70 8.70
C0Ď€ 0.966 1.000 1.000
E0Ď€ (eV) 6.44 12.49 8.23
B0Ď€ (eV) 1.29 2.80 1.58
Q� ≡Qξ (eV3/2
) 68.62 66.82 64.28
EgÄŽďż˝ (eV) 4.737 5.012 5.068
EhÄŽďż˝ (eV) 28.1 28.1 28.1
C0ÄŽďż˝ 0.694 0.694 0.694
E0ÄŽďż˝ (eV) 11.97 11.97 11.97
B0ÄŽďż˝ (eV) 3.26 3.26 3.26
EgĂŽÄľ (eV) 12.14 12.14 12.14
EhĂŽÄľ (eV) 39.3 39.3 39.3
pπ 1.158 1.438 1.070
pÄŽďż˝ 0.930 0.854 0.851
a 0.989 0.996 0.978
4301L. Zajíčková et al. / Thin Solid Films 519 (2011) 4299–4308
3.2. Effect of �lm inhomogeneity, anisotropy and transition layer on NIR–XUV
analysis
The �lm inhomogeneity brings another two parameters to the
model, pπ and p�. They represent squared ratio of densities at the top,
Q j
top
, and bottom, Q j
bot
, interface of the �lms as
pj =
Qtop
j
 2
Qbot
j
 2
: Ă°3Ăž
The parameter Q j, given in Table 2, is the mean squared density
Q
2
j =
Qtop
j
 2
+ Qbot
j
 2
2
: Ă°4Ăž
Real and imaginary parts of the dielectric function of a-C:H(:N) �lms
at the top and bottom interfaces are compared in Fig. 5. The ratio pπ/p�
higher than one means that the �lms contain more π electrons, i.e. more
sp2
bonded atoms, in their top regions. It can be probably explained by
longer exposure of the bottom region to ion bombardment during �lm
growth. Another possible explanation is photosensitivity of the material
to VUV light that has relatively small penetration depth. The
synchrotron measurement was carried out after the table-top measurement
and VUV light could modify the material. The CH16 table-top
and synchrotron ellipsometric measurements were less compatible
than in case of other two �lms. This caused worse agreement between
-1.00
-0.50
0.00
0.50
1.00
ellipsometry,Is
CH30
CH16
CH17
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
ellipsometry,IcIIellipsometry,IcIII
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
1 2 3 4 5 6
reflectance,R
photon energy, E (eV)
Fig. 2. Spectral dependencies of the associated ellipsometric parameters Is, Ic, II, Ic, III and
reflectance R of samples CH30, CH16 and CH17 measured with table-top instruments:
the lines and symbols denote theoretical and experimental data, respectively.
The ellipsometric data correspond to the incidence angle of 65�
.
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
ellipsometry,C2ellipsometry,S2
CH30
CH16
CH17
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
5 5.5 6 6.5 7 7.5 8 8.5 9 9.5
photon energy, E (eV)
Fig. 3. Spectral dependencies of the second harmonic components C2 and S2 measured
with BESSY II synchrotron ellipsometer at 67.5�
in VUV spectral range for samples CH30,
CH16 and CH17: the lines and symbols denote theoretical and experimental data,
respectively.
0
2
4
6
8
CH30 ÄŽďż˝, ÄŽďż˝*
π, π*
ĂŽÄľ*
0
2
4
6
8
CH16
0
2
4
6
8
-15 -10 -5 0 5 10 15 20
DOS,N(eV1/2
)DOS,N(eV1/2
)DOS,N(eV1/2
)
electron state energy, S (eV)
CH17
Fig. 4. DOS of electronic states of �lms CH30, CH16 and CH17 calculated from the best
�t parameters. The DOS normalization corresponds to formula (2).
4302 L. Zajíčková et al. / Thin Solid Films 519 (2011) 4299–4308
the synchrotron data and the �t (Fig. 3). Therefore, the combination of
both above effects probably took place in CH16. This �lm exhibited the
highest inhomogeneity of π electrons, pπ =1.4.
A weak stress-induced anisotropy of the �lms was introduced in the
model similarly as in [12]. The anisotropy is parametrized by a single
parameter a determining the ordinary, ˆεo, and extraordinary, ˆεe,
dielectric functions:
ˆεo = a ˆ�1ð Þ + 1 ˆεe =
1
a2 ˆ�1ð Þ + 1 ð5Þ
where ˆε is the mean dielectric function.
The dielectric function of transition layers was modeled by
parametrized JDOS model described in [19]. It resembled amorphous
silicon or SiC material in the NIR–XUV region. Consistent understanding
of transition layer band structure and inhomogeneity would require a
specialized study using a set of samples with very thin a-C:H(:N) �lms.
Here studied samples with the �lms having thickness 100–200 nm
provide mostly information about dielectric response of a-C:H(:N) �lms
and the influence of the transition layer on the measured quantities is
hidden by the complexity of effects related to relatively thick �lms.
3.3. Analysis of optical measurement in IR region
A correct analysis of �lm absorption peaks in the measured
transmittance of a thin �lm on absorbing substrate is not as simple as
usually performed. Many authors use the Lambert–Beer law describing
an attenuation of light intensity in homogeneous absorbing material.
Since the substrate is absorbing the measured transmittance T is, in this
approach, divided by the transmittance of substrate Tsub in order to
“remove” the substrate absorption peaks:
Trel = T = Tsub: Ă°6Ăž
This relative transmittance is then used to calculate the �lm
absorbance Af which is assumed proportional to the �lm absorption
coef�cient, i.e. the Lambert–Beer law is applied to the system with
interfaces. Since the reflections at interfaces are usually non-negligible
this approach has several weaknesses. The absorption peaks in the
substrate, supposedly removed, can still appear in the analyzed �lm
absorbance. Moreover, the analyzed �lm absorbance is influenced by
the dispersion of the real part of refractive index. Therefore, the
Lambert–Beer law based approximation is applicable only to weak
absorption peaks or weak reflections at interfaces. Furthermore, the
signi�cant dispersion of real part of refractive index in the vicinity of
strong absorption peaks causes peak asymmetry and shift of their
positions.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5 top CH30
CH16
CH17
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5 bottom
0.0
0.5
1.0
1.5
2.0
2.5 top
0.0
0.5
1.0
1.5
2.0
2.5
0 5 10 15 20 25 30
bottom
photon energy, E (eV)
εiεiεrεr
Fig. 5. Real and imaginary parts of the dielectric function of the DLCH �lm, CH30, and
a-C:H:N �lms, CH16 and CH17, at their top and bottom interfaces.
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1000 1500 2000 2500 3000 3500 4000
wavenumber, ĂŽËť (cm-1)
wavenumber, ĂŽËť (cm-1
)
wavenumber, ĂŽËť (cm-1
)
(a)
1.12
1.14
1.16
1.18
1.20
1.22
1.24
1000 1050 1100 1150 1200 1250 1300
relativetransmittance,Trel
(b)
0.0
0.1
0.2
0.3
0.4
0.5
2000 2500 3000 3500 4000
filmabsorbance,Af
(c)
transmittance,T
Fig. 6. Illustration of artifacts caused by naive evaluation of IR transmittance data:
(a) simulated transmittance of a simple �lm-substrate system and “background”
transmittance; (b)residuum of supposedly removed substrate absorption peak in the
relative transmittance; (c)influence of peak position with respect to the interference
minima and maxima on its apparent height and shape.
4303L. Zajíčková et al. / Thin Solid Films 519 (2011) 4299–4308
The weaknesses of the Lambert–Beer law approximation are
demonstrated in Fig. 6 for a simpli�ed system of a thin �lm exhibiting
three identical Gaussian absorption peaks at 2000, 3000 and 4000 cm� 1
on a substrate with one absorption peak at 1100 cm� 1
. The mean
refractive indices of the model �lm with the thickness of 680 nm and the
substrate, 380 ÎĽm thick, correspond approximately to DLCH and silicon,
respectively. The calculated transmittance T of this system is in Fig. 6a.
Note that its overall shape is given by interference in the �lm
(see dashed line, i.e. “background” transmittance Tbg). A “parasitic”
peak obtained in relative transmittance Trel at the position of substrate
absorption is shown in Fig. 6b. Fig. 6c shows comparison of three peaks
at different positions with respect to the interference maxima and
minima after “background” interference was subtracted in �lm
absorbance
Af = 1�T�R�As�
Tbg
Tsub
�Trel; ð7Þ
where As is substrate absorbance. Although thesepeaks were identicalin
extinction coef�cient they appear with different intensity. The effect of
peak asymmetry can be seen, especially for a peak in sloping part of
transmission, also from Fig. 6c.
Because of theabove described effects measured IRtransmittances of
studied samples were �tted together with other optical data using a
Kramers–Kronig consistent model. Within this model the joint density
of states J(E) correspondingto phonon absorption wasdescribed bya set
of Gaussian peaks [19]:
J Eð Þ = �i
Ai
������
2Ď€
p
Bi
exp �
E�Eið Þ2
2B2
i
" #
�exp �
E + EiĂ° Ăž2
2B2
i
" #( )
; Ă°8Ăž
where Ai, Bi and Ei are the strength, broadening and position of i-th peak.
Note that the positions of the Gaussian peaks are not the same as the
positions of absorption peaks in imaginary part of dielectric function εi
(E), extinction coef�cient k(E) and absorption coef�cient α(E) because
of following relations:
εi Eð Þ =
J EĂ° Ăž
E2
= 2n EĂ° Ăžk EĂ° Ăž =
ħc
E
α Eð Þn Eð Þ; ð9Þ
where E is the energy in Joules, n(E) denotes refractive index, h and c are
Planck constant and vacuum light velocity, respectively. The peak
position mismatch increases with increasing ratio of peak width to peak
position or with strong dispersion of refractive index in the vicinity of
absorption peak. Therefore, the comparison of peak positions among
different authors has to be carefully performed taking into account
Eq. (9) and effects of the Lambert–Beer law approximation discussed
above. Parameter Bi is related to the peak full-width at half-maximum
(FWHM) as follows:
FWHM = 2
����������
2ln2
p
Bi�2:35Bi: ð10Þ
Since peak widths are commonly given as FWHMs we will follow
this convention below to ease comparison with other works.
All the samples were �tted simultaneously using the multi-sample
method. The advantage of this method consisted in better stability of
�tting, especially in case of many free parameters. The positions and
widths of the Gaussian absorption peaks were chosen as common
multi-sample parameters. The strengths of the Gaussian peaks were
searched separately for each sample.
The measured IR transmittance is shown in Fig. 7 for all three
samples. The noticeably different values for the sample CH17 are caused
by its different thickness. It can be seen that the transmittance below
1200 cm� 1
is dominated by absorption in the Si substrate. This region
was not suitable for precise �tting of �lm peaks because the dielectric
function of the substrate was determined from measurement of an
arbitrarily chosen Si piece and not by measuring of each Si substrate
prior to the �lm deposition. Even though the substrate is cut from the
same wafer as the reference the thickness can slightly differ leading to
only partial compensation of substrate peaks. Additionally, different Si
pieces can differ slightly in the amount of impurities that correspond to
some absorption peaks. Therefore, a good agreement of the �t and the
interpretation of �tted absorption peaks was sought only in the region
above 1240 cm� 1
.
Note that since IR transmittance is not sensitive to where in the �lm
the absorption takes place the phonon contribution to εi was assumed to
be homogeneous even though pπ/p� differed from unity, indicating
different composition at the top and bottom of the �lm. The
inhomogeneity of εr in IR region is thus given only by inhomogeneity
of contributions of interband transitions. Both parts of the dielectric
function are shown in Fig. 8.
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0 1000 2000 3000 4000 5000 6000 7000 8000
CH30
CH16
CH17
wavenumber, ĂŽËť (cm-1)
transmittance,T
Fig. 7. Measured transmittances of the �lms CH30, CH16 and CH17 on Si substrates in
the complete range of Bruker Vertex 80v spectrometer.
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0 top CH30
CH16
CH17
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0 bottom
0.0
0.1
0.2
0.3
0.4
0.5
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
wavenumber, ĂŽËť (cm-1
)
εiεrεr
Fig. 8. Real and imaginary part of the dielectric function of all three �lms in IR region.
4304 L. Zajíčková et al. / Thin Solid Films 519 (2011) 4299–4308
3.4. Chemical structure and lattice vibrations of the �lms
Information about chemical composition of the �lms was obtained
using the combination of RBS and ERDA methods. It provided complete
atomic composition of the �lms including the hydrogen content. Traces
of argon (below 0.3%) were attributed to the incorporation of argon into
the Si substrate during plasma pretreatment. The �lms were mainly
composed of hydrogenated carbon as summarized in Table 1. The �lms
CH16 and CH17, deposited from CH4/H2/N2 mixture, contained 13 and
10% of nitrogen, respectively. All the �lms contained a small amount of
oxygen. The base pressure in the reactor chamber was below 10� 3
Pa
and the leak/desorption rate was below 0.02 sccm. Therefore, oxygen
had to be incorporated into the �lm structure after exposure to
atmosphere. This can also explain the different amounts of oxygen in the
�lms because vacuum conditions during the deposition were similar but
post-deposition oxygen incorporation depended on the material
chemical structure that was affected by differing deposition conditions.
Namely, the oxygen content increased for nitrogen containing �lms and
soft polymer-like �lm CH17.
The analysis of lattice vibrations provides more detail information
about the chemical structure of the �lms. It starts in following text from
the high frequency part of measured IR transmittance – region of group
frequencies. Absorption peaks attributed to C�H stretching of hydrocarbon
groups are generally found in the region 2850–3100 cm�1
. The peaks
below 3000 cm�1
are mostly related to vibration modes present in
saturated hydrocarbons, i.e. sp3
C�Hx (x=1,2,3). These group frequencies
are similar for different compounds because of little coupling to the
rest of molecular system and can be, therefore, predicted quite exactly.
Stretching of sp2
C�Hx (x=1,2) can be found above 3000 cm�1
[23].
The C�H stretching peaks strongly overlapped and formed a distinct
absorption band (Figs. 7 and 9). The absorption above 3000 cm�1
, related
tosp2
C, was a weakshoulder of the band (Fig. 9b,d).The positionsof �tted
peaks were �xed at following values: 2915 cm�1
assigned as C�H
stretching in sp3
C�H, 2855, 2925, 2870 and 2960 cm�1
assigned as
symmetric and antisymmetric stretching in sp3
C�H2 and sp3
C�H3,
respectively [23,24], 3000 and 3080 cm�1
associated with symmetric and
asymmetric stretch of ole�nic sp2
C�H2, 3030 and 3050 cm�1
associated
with stretch of ole�nic sp2
C�H and aromatic sp2
C�H, respectively [23].
The widths of C�H stretching peaks were kept as an identical �tting
parameter for sp3
C�Hx and sp2
C�Hx separately. The previously
published FWHMs were in the range 70–90 cm�1
[24]. Our best �t
corresponded to 60 and 44 cm�1
of peak FWHM, respectively. The
agreement between the measured and theoretical transmittances is
shown for the sample CH30 in Fig. 9b. The imaginary part of dielectric
function, εi, of all three �lms and contribution of the C�H stretching to εi
are depicted in Fig. 9c and d. The summary of �tting results and peak
assignment are in Table 3.
The �lms deposited with nitrogen addition were characterized by
wide absorption peaks in the range 2950–3500 cm� 1
. Their parameters,
i.e. position, width and strength, were set free, however, the position
and width were kept identical for both CH16 and CH17. The resulting
peak parameters are summarized in Table 3 and their contribution to
the imaginary part of dielectric function is shown in Fig. 10d, e. Since the
peaks were wide their positions in JDOS and εi(E) differed. The FWHM of
the JDOS peak at 3372 cm� 1
was 136 cm� 1
and its position in εi was
shifted to lower frequencies by 2 cm� 1
. However, the widest peak at
2949 cm� 1
was shifted by as much as 64 cm� 1
.
The peak strengths were higher for the �lm CH17 that contained
more oxygen with the exception of the peak at 3372 cm� 1
. This
relatively narrow peak(compare FWHMof 136 cm� 1
to167–713 cm� 1
in Table 3) could be perhaps assigned to NH stretching because it was
slightly stronger in the �lm CH16 containing more nitrogen. Rodil [25]
assumed that the peaks related to the NH or OH bonds formed during
the deposition are narrower and this argument also justi�es the
assignment of the NH bonds. The other peaks were attributed to OH
groups. The incorporation of oxygen containing groups into a-C:H and
especially a-C:H:N �lms have been already observed by other authors
too and its assumed to take place in case of soft, rough or porous �lms
[26]. The optical measurements con�rmed that the �lms do not exhibit
any roughness but the �lm with the most of OH groups, CH17, was
indeed soft, polymer-like material in which adsorption of water can
easily take place by formation of hydrogen bonds.
The absorption peak observed at 2100 cm�1
in the transmittances of
all samples was assigned to Si–H stretching (Fig. 7b). It was attributed to
the transition layer created by plasma modi�cation of Si substrate. Its
position, width and strength were set identical for all the samples. In spite
of this restriction the agreement between the measurement and the �t
was satisfactory (shown for an arbitrary chosen sample CH16 in Fig. 10b).
It con�rmed that this peak can be really attributed to the transition layer
that was similar for all three samples. The peak at 2205 cm�1
was
observed only in a-C:H:N and, therefore, the assignment to nitrile �C≡N,
isonitrile �N≡C and/or carbodi-imide �N=C=N� [23,25,27] is
clearly justi�ed.
Additional �lm absorption peaks were observed in low frequency
region (Figs. 11 and 12). According to the above discussion of the Si
substrate effect the detailed analysis is restricted to the peaks from
1240 cm� 1
. Note that two broad peaks positioned at 720 and
1212 cm� 1
were necessary for good agreement with measured data
(Fig. 12b). Their contribution to εi is shown in Fig. 12d.
0.54
0.55
0.56
0.57
0.58
0.59
0.60 (a)CH30
CH16
CH17
0.54
0.55
(b)CH30, exp.
CH30, fit
0.00
0.02
0.04
0.06
0.08
0.10 (c)CH30
CH16
CH17
0.00
0.02
0.04
0.06
0.08
0.10
2750 2800 2850 2900 2950 3000 3050 3100 3150
contributiontoεi
(d)
only CHx
CH30
CH16
CH17
transmittance,Ttransmittance,T
wavenumber, ĂŽËť (cm-1
)
εi
Fig. 9. Infrared spectra in range 2750–3150 cm� 1
: (a) measured transmittances of all
three samples; (b) comparison of the measurement and �t for the sample CH30;
(c) imaginary part of dielectric function εi of all three �lms (d) contribution of the C�H
stretching.
4305L. Zajíčková et al. / Thin Solid Films 519 (2011) 4299–4308
The measured transmittances in the range 1200–1850 cm� 1
are
shown for all three samples in Fig. 11a. Three absorption bands at about
1300, 1375 and 1450 cm� 1
were well separated in the region of C�H
deformations, i.e. below 1500 cm� 1
. They were�tted byfour peaks with
their positions �xed at 1300, 1375, 1450 and 1460 cm� 1
. The FWHMs of
the peaks were assumed to be identical and the best �t corresponded to
64 cm� 1
. The contribution of these peaks to the imaginary part of
dielectric function is shown in Fig. 11d. The selection and assignment of
the peak positions are discussed below on the basis of previously
published papers.
Antisymmetric bending of methyl, sp3
C�H3, was previously
observed from 1460 cm� 1
[23,28] to 1490 cm� 1
[29]. The scissoring
of methylene, sp3
C�H2, was positioned at 1450 cm� 1
[23,28,29] and
the symmetric bending of sp3
C�H3 at 1375 cm� 1
[23,28]. As for the
C �H stretching, only a little coupling of these deformations to the rest
of material is expected. Wagging and twisting modes of methylene at
around 1300 cm� 1
are usually weak in infrared spectra and their
positions are coupled to chemical environment [23]. The relatively
strong peak at 1300 cm� 1
was, therefore, assigned rather to the
collective vibration of carbon skeleton following Theye [30,31].
Deformations of sp2
C�Hx either strongly overlapped with sp3
C�H2
[29] or, if positioned at about 1400 cm� 1
[28], they were too weak.
In a-C:H �lms, a well-de�ned peak found in the region
1580–1640 cm�1
have been already unambiguously attributed to the
stretching modes of sp2
C double bonds in aromatic or ole�nic con�gurations
[30,32]. Its position shifted to higher frequencies for chain structures
of ole�ns observed in polymeric �lms whereas frequency below
1600 cm�1
was assigned to ring structure of sp2
clusters in hard �lms
Table 3
Parameters of Gaussian peaks describing �lm dielectric response in IR range, i.e. peak
positions, FWHMs and strengths, found by multi-sample �tting the optical data of
CH30, CH16 and CH17 �lms on Si substrate. The position and FWHM of the peaks were
kept identical for all three samples whereas the strengths were independent
parameters.
Position
(cm� 1
)
FWHM
(cm� 1
)
Strength Vibration mode
CH30 CH16 CH17
CH stretching
3080 44 38 44 31 sp2
C�H2 olef. sym.
3050 44 26 0 29 sp2
C�H arom.
3030 44 81 89 53 sp2
C�H olef.
3000 44 197 52 69 sp2
C�H2 olef. asym.
2960 60 512 363 452 sp3
C�H3 asym.
2925 60 19 240 324 sp3
C�H2 asym.
2915 60 764 277 122 sp3
C�H
2870 60 0 117 243 sp3
C�H3 sym.
2855 60 494 246 68 sp3
C�H2 sym.
OH/NH/CN
3493 167 0 154 927 O�H
3372 136 0 848 625 N�H
3281 320 0 1625 2836 O�H
2949 713 0 1856 2971 O�H
2205 102 0 227 93 C≡N/N≡C/�N=C=N�
CC/CO/OH
1732 19 0 65 31 C=O
1695 106 0 57 1328 C=O/N-induced sp2
C
1680 64 45 42 181 sp2
C
1652 111 0 773 0 N-induced sp2
C/O�H
1638 45 0 180 158 N-induced sp2
C/O�H
1600 64 128 655 542 sp2
C
1553 57 0 456 218 N-induced sp2
C
1513 38 0 217 69 N-induced sp2
C
1300 64 56 68 52 sp2
C
1248 441 0 3766 2573 N-induced sp2
C
CH deformation
1460 64 0 177 0 sp3
C�H3 asym. bend.
1450 64 119 346 287 sp3
C�H2 scissoring
1375 64 29 233 199 sp3
C�H3 sym. bend.
Unidenti�ed peaks below 1240 cm� 1
1212 737 1402 0 346
720 508 671 2188 747
0.54
0.55
0.56
0.57
0.58
0.59
0.60
0.61
0.62
transmittance,Ttransmittance,T
(a)CH30
CH16
CH17
0.54
0.55
0.56
(b)CH16, exp.
CH16, fit
0.00
0.02
0.04
0.06
0.08
0.10
0.12
εiεi
(c)CHx
NH, OH
CN
CH30
CH16
CH17
0.00
0.01
0.02
0.03
0.04
0.05
contributiontoεi
(d)
only OH
CH16
CH17
0.00
0.01
0.01
0.01
0.02
0.03
0.03
contributiontoεi
(e)
only CN and NH
CH16
CH17
0.00
0.05
0.10
0.15
0.20
0.25
0.30
2000 2500 3000 3500
wavenumber, ĂŽËť (cm-1
)
(f)
SiHx in transition layer
Fig. 10. Infrared spectra in range 1800–3800 cm� 1
: (a)measured transmittances of
all three samples; (b)comparison of the measurement and �t for the sample CH16;
(c)imaginary part of dielectric function εi (d) contribution of OH; (e)contribution
CN and NH; (f)εi corresponding to the Si-H stretching peak in the transition layer.
4306 L. Zajíčková et al. / Thin Solid Films 519 (2011) 4299–4308
[30,31]. In this work, two peaks with �xed positions at 1600 and
1680 cm�1
were included in JDOS of all the �lms. The corresponding
absorption peaks in transmittance of DLCH were very weak, especially in
case of the peak at 1680 cm�1
.
The above discussed peaks centered in the region 1375–1600 cm� 1
were much stronger for a-C:H:N �lms as shown in Fig. 11d. Moreover,
the a-C:H:N �lms required addition of a strong wide peak at 1248 cm� 1
(FWHM 442 cm� 1
), two weaker sharper peaks at 1513 and 1553 cm� 1
and several peaks in the region above 1600 cm� 1
(Table 3). The
contribution of these peaks is depicted in Fig. 11e. The peaks at 1513 and
1553 cm� 1
formed one broad flat or asymmetric band. The peaks at
1638, 1652 and 1695 cm� 1
composed a broad band centered at 1632
and 1683 cm� 1
for CH16 and CH17, respectively. The peak at
1732 cm� 1
was well separated from this band in case of CH16.
The absorption bands in the region 1000–1700 cm� 1
for a-C:H and
especially a-C:H:N �lms were matter of a long term discussion and very
different assignments can be found in previously published papers. Theye
[30] shifted deformation modes of C�H bonds to lower frequencies by
replacing H by D and observed two broad bands centered at 1300–1350
and 1580–1630 cm�1
assigned to carbon skeletal vibrations. A weak
absorption at the positions 1300, 1600 and 1680 cm�1
was observed also
in here studied DLCH �lm CH30 (discussed above). The approach of
Theye was adopted by Ferrari [33] for a-C(:H):N �lms. They assumed that
major absorption band observed in the 1000–1650 cm�1
region was due
to sp2
C vibrations and not due to speci�c CH, CN, NH and NN vibrations.
The increase of absorption in case of increased nitrogen content was
explained by polarization of sp2
C phase induced by the terminal N atoms.
The shape of this band changed with the type of the �lms. Accordingly,
increased strength and addition of some peaks in case of the �lms CH16
and CH17 was attributed to sp2
C phase vibrations. Part of this absorption
at higher frequencies can be, however, also assigned to the bending
mode of water observed in a-C:N(:H) �lms at about 1610–1640 cm� 1
[26] and stretching of carbonyl group whose typical frequency is around
1720 cm� 1
[23]. The carbonyl frequency is quite variable depending on
the chemical surrounding. Indeed, the absorption at frequencies above
1650 cm� 1
was higher in the �lm CH17 that contained more oxygen
than CH16 and had more polymeric character.
It is worth noting that the assignment of increased absorption in the
range 1200–1650 cm� 1
to increased optical activity of sp2
C phase
induced by the presence of nitrogen corresponded to the results from
0.52
0.53
0.54
0.55
0.56
0.57
(a)CH30
CH16
CH17
0.53
0.54
0.55
0.56
(b)CH17, exp.
CH17, fit
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
(c)CH30
CH16
CH17
0.00
0.05
0.10
0.15
0.20 (d)CH30
CH16
CH17
0.00
0.05
0.10
0.15
0.20
1200 1300 1400 1500 1600 1700 1800
(e)CH16
CH17
wavenumber, ĂŽËť (cm-1
)
contributiontoεicontributiontoεi
transmittance,Ttransmittance,Tεi
Fig. 11. Infrared spectra in range 1200–1850 cm� 1
: (a)measured transmittances of all
three samples; (b)comparison of the measurement and �t for the sample CH17;
(c) imaginary part of dielectric function εi; (d)contributions related to the peaks found in
all three �lms; (e)contributions of the peaks found solely in a-C:H:N, i.e. CH16 and CH17.
0.35
0.40
0.45
0.50
0.55
0.60
(a)CH30
CH16
CH17
0.35
0.40
0.45
0.50
0.55
0.60
(b)CH16, exp.
CH16, fit
0.00
0.10
0.20
0.30
0.40
0.50 (c)CH30
CH16
CH17
0.00
0.10
0.20
0.30
0.40
0.50
400 600 800 1000 1200 1400 1600
(d)CH30
CH16
CH17
wavenumber, ĂŽËť (cm-1
)
contributiontoεi
transmittance,Ttransmittance,Tεi
Fig. 12. Infrared spectra in range 360–1600 cm� 1
: (a)measured transmittances of all
three samples; (b)comparison of the measurement and �t for the sample CH16;
(c) imaginary part of dielectric function εi of all three �lms (d) contribution of the broad
peaks.
4307L. Zajíčková et al. / Thin Solid Films 519 (2011) 4299–4308
NIR–VUV region because the density of π electrons, obtained from
NIR–VUV measurement, as well as the infrared absorption in
1200–1650 cm� 1
was higher in CH16 than in CH17.
4. Conclusion
The combination of measurements carried out with two spectrophotometers,
synchrotron and table-top ellipsometers provided optical
data in a wide spectral range (IR–XUV) that were simultaneously �tted by
the Kramers–Kronig consistent model taking into account electronic
interband transitions and lattice vibrations. This unique approach
provided parameters describing DOS of valence and conduction bands,
i.e. bonding structure, and revealed complicated infrared absorption
induced by nitrogen incorporation. Three broad peaks in range 2950–
3500 cm�1
corresponded to increased incorporation of oxygen containing
groups especially in polymer-like a-C:H:N �lms. The increased
absorption in the range 1000–1700 cm�1
for a-C:H:N mainly corresponded
to polarization of sp2
C phase induced by nitrogen and its shape
changed with the �lm hardness. The density of � electrons decreased with
decreasing hardness for both the a-C:H:N �lms as compared to the
hydrogenated diamond like carbon (DLCH) �lm with hydrogen content of
34% and indentation hardness of 21.7 GPa. The density of π electrons
increased for the hard a-C:H:N �lm (13% of nitrogen, hardness 18.5 GPa)
and decreased for the soft a-C:H:N �lm (10% of nitrogen, hardness
6.7 GPa). Therefore, the soft �lm prepared at lower dc self-bias had a
considerably lower electron density. The results were in agreement with
the expected correlations between the material bonding structure and
hardness, con�rming the correctness of the applied model. However, the
a-C:H:N �lms were not measured in the spectral range covering all �→�
transitions and, therefore, parameters of ÄŽďż˝ bands might not be reliably
determined. Parameters of π→π transitions were more reliable because
the maximum energy of transitions was about 10 eV. Considering these
issues the described approach could utilize table-top ellipsometers
working in VUV range (up to 10 eV) instead of synchrotron ellipsometry
and, therefore, be applied to a wider group of a-C:H:N �lms.
Acknowledgements
This work was supported by the Czech Science Foundation 202/07/
1669 and 104/09/H080; by the EC under BESSY II IA-SFS Contract RII
3-CT-2004-506008 (BESSY-BM.08.2.80317 and 09.1.80896); by the
Czech Ministry of Education MSM 0021622411; and by the Czech
Ministry of Trade FT-TA5/114.
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