Magnetotransport in the amorphous carbon films prepared from succinic anhydride

Article abstract of DOI:10.1016/j.physb.2005.08.009

In this paper, we report the low-temperature electrical conductivity of amorphous carbon films prepared from an organic precursor succinic anhydride at different pyrolysis temperatures (700-980 °C). The films prepared at low temperatures show activation behavior. The films prepared at 900 °C and above show metal-like behavior, with positive temperature coefficient and a resistivity hump below about 25 K in the R-T behavior. The metal-like behavior at low temperatures was suppressed by the application of a magnetic field. The magnetoconductance in the metal-like films at low and high field limits were analyzed in terms of weak localization and electron-electron interaction models. Negligible magnetoconductance was observed at higher temperatures.

Full text of DOI:10.1016/j.physb.2005.08.009

ARTICLE IN PRESS
Physica B 369 (2005) 168–176
www.elsevier.com/locate/physb
Magnetotransport in the amorphous carbon films
prepared from succinic anhydride
Ã
V. Prasad , S.V. Subramanyam1
Department of Physics, Indian Institute of Science, Bangalore 560 012, India
Received 5 November 2004; received in revised form 28 July 2005; accepted 11 August 2005
Abstract
In this paper, we report the low-temperature electrical conductivity of amorphous carbon films prepared from an
organic precursor succinic anhydride at different pyrolysis temperatures (700–980 1C). The films prepared at low
temperatures show activation behavior. The films prepared at 900 1C and above show metal-like behavior, with positive
temperature coefficient and a resistivity hump below about 25 K in the R–T behavior. The metal-like behavior at low
temperatures was suppressed by the application of a magnetic field. The magnetoconductance in the metal-like films at
low and high field limits were analyzed in terms of weak localization and electron–electron interaction models.
Negligible magnetoconductance was observed at higher temperatures.
r 2005 Elsevier B.V. All rights reserved.
PACS: 73.50; 71.30; 73.61; 71.55; 72.80.N
Keywords: Thin film; Amorphous carbon; Metal–insulator; Magnetoconductivity
1. Introduction
sp2/sp3 bond concentration. Diamond-like carbon,
tetrahedral carbon and glassy carbon are the few
non-graphitic disordered carbons having various
sp2=sp3 ratios. Disordered carbons show a variety
of electronic structures owing to the sp2 clustering
features and the absence of perfect graphitic
structure. The degree of clustering of sp2 carbons
is significant in determining the electronic proper-
ties of the disordered carbon systems. Amorphous
carbon is one such form of disordered structure
having clustering features. The studies on
the electrical properties are interesting in these
The two allotropes of carbon, diamond and
graphite, are found with either complete sp3 or sp2
bond configuration. Between these two, disordered
carbons spread in a wide range having arbitrary
Ã
Corresponding author. Tel.: +91 80 2293 2313;
fax: +91 80 2360 2602.
E-mail addresses: vishnu@physics.iisc.ernet.in (V. Prasad),
svs@physics.iisc.ernet.in (S.V. Subramanyam).
1Tel.: +91 80 2293 2315.
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.physb.2005.08.009

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V. Prasad, S.V. Subramanyam / Physica B 369 (2005) 168–176
169
carbons as the degree of disorder changes the
mode of conduction. The carbon, polymer and
doped semiconductors are interesting materials
that undergo metal–insulator (M–I) transitions.
Studying the behavior of electrical conductivity in
these disordered systems has been an active area of
research for many years. Various theories were
proposed to understand the phenomena as the
transition is approached from the metallic side to
the insulating side. The Mott [1] prediction for
variable-range hopping conductivity and the
Efros–Shklovskii [2] prediction for VRH in the
coulomb gap have appeared in the literature long
ago and were applicable for the samples in the
insulating regime. Castner [3] has summarized
some interesting predictions that describe the
cross over from Mott to Efros–Shklovskii VRH
conductivity. The crossover from Mott to Efros–
Shklovskii VRH conductivity was observed in
n-Cd Se crystal [4] indium oxide film [5] at low
temperatures. The transition from metallic to an
insulator state is associated with the carrier
localization at the Fermi level. In some cases, the
localization is induced by disorder. The extent of
disorder can be tuned by varying the preparation
temperature, application of a magnetic field,
pressure or impurity concentration. Such systems
show interesting features like weak localization [6]
and electron–electron (e–e) interaction [7].
Strongly doped semiconductors or heavily doped
conducting polymers are good candidates for the
study of M–I transition caused by disorder-
induced localization. Application of pressure,
magnetic field or impurity conduction can tune
the position of the mobility edge with respect to
the Fermi energy. The application of a magnetic
field in particular is of interest in carbon com-
pounds especially in graphite [8] pyrocarbons [9]
and conducting polymers [10].
initially evacuated to rotary vacuum level and
purged with argon gas. The films were deposited at
different temperatures on smoothened quartz
substrate from 700 to 980 1C at 50 1C step. The
substrate was placed at the high-temperature zone
of the furnace. The deposited carbon films were
black, shiny and reflecting in nature. The films
were annealed for 2–3 h after pyrolysis to release
the stresses. This improved the quality and
compactness of the film. The electrical contacts
were made with conducting silver epoxy paste and
the van-der-Pauw technique is applied for con-
ductivity measurements. The low-temperature
magnetoconductivity measurements were done
using a superconducting magnetic liquid helium
cryostat.
3. Results
The XRD pattern of the films prepared at
different pyrolysis temperatures showed amor-
phous character. Fig. 1 shows the XRD pattern
of the precursor and one such carbon film
prepared at 980 1C. A broad hump at 2y ¼ 22:2ꢀ
was observed, which is the characteristic of an
1000
400
22.2°
500
300
0
20
40
60
80
2θ
200
100
2. Experiment
The carbon films were prepared using a high-
temperature pyrolysis method. The organic pre-
cursor succinic anhydride ðC4H4O3Þ was taken at
one end-closed quartz tube and placed at the low-
temperature zone of the furnace. The tube was
20
40
60
80
2θ
Fig. 1. X-ray diffraction of the carbon film g deposited on
quartz substrate (inset shown is the XRD pattern of the
precursor).

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amorphous material. The scanning electron micro-
scopy (SEM) images of the films prepared at
various temperatures are shown in Fig. 2a–f. At a
low temperature of pyrolysis, (Fig. 2a) the globules
start forming at scattered nuclei centers on the
smoothened quartz substrate. With the increase of
pyrolysis temperature, the globules increase in
density and form clusters (Fig. 2b and c). Further
deposition of carbon on the already formed nuclei
centers leads to cluster formation. More and more
cluster formation can be seen at higher pyrolysis
temperatures (Fig. 2d and e). The size of a single
globule of film prepared at 850 1C (Fig. 2f) was
typically 1 mm. The surface morphology of these
films was different from that of glassy carbon. The
electrical conductivity is a function of the sp2 to
sp3 ratio, cluster size, density and orientation. The
room temperature conductivity of these films was
higher than that of any other amorphous carbon
structures. The conductivity was increased by two
orders of magnitude with the increase of the
pyrolysis temperature. Table 1 shows the resistiv-
ity of the a-carbon films prepared at different
pyrolysis temperatures. The films prepared at
different pyrolysis temperatures were labeled as
a—700 1C, b—750 1C, c—800 1C, d—850 1C, e—
900 1C, f—950 1C and g—980 1C. From the ratio
of the conductivity at the lowest to the highest
temperature, one can quantify the disorder. The
smaller the ratio, the lesser the disorder (Table 1).
For activation type of conduction, Eq. (2) reduces
to
log10 w ꢁ log10 xTx0 À xlog10 T.
(3)
For an activated type of the VRH regime, the
variable x lies between 0 and 1. The characteristic
temperature T0 can be found from the intercept of
Eq. (3). Fig. (3) shows the reduced activation
energy (w) vs. temperature (T) plot for the films
(a–g) on the logarithmic scale. The negative slope
of the films a, b shows that they were on the
insulating regime of the M–I transition. The value
of x obtained for the samples a and b are 0.56 and
0.5 and the corresponding T0’s calculated from
the intercepts are 208.4 and 80 K, respectively.
The films a; b at low temperatures showed Efros–
Shklovskii variable range-hopping conductivity,
which involves the Coulomb interaction between
hopping sites.
The Efros–Shklovskii theory predicts the fol-
lowing resistivity vs. temperature dependence for
all dimensions:
1=2
r ¼ r0 expðTES=TÞ
Fig. (4) shows the T
the films a, b.
.
(4)
À1/2
variation of resistivity of
The r0 values derived from the graphs for the
films a, b were 0.06664 and 0.04201 O cm, respec-
tively. The TES (77 K) for the film b extracted from
the graph was closer to the value obtained from
Eq. (3).
The T
–1/2
dependence on the conductivity for
3.1. Zero-field conductivity
the films a, b extends upto 6 and 30 K, respectively.
The hopping exponent x40.5 for the insulating
film a in the activated coulomb-gap regime is in
good agreement with the computational calcula-
The temperature dependence of the resistivity
was investigated by analyzing the temperature
dependence of the reduced activation energy of the
conductivity [11]
+
tions of Mobius and Richer [12].
The samples in the critical regime were analyzed
from the power law temperature dependence ðr /
TÀbÞ of resistivity [13,14].
The general expression is given by
x
rðTÞ / expðT0=TÞ .
(1)
Fig. (5) shows the r vs: T curves on the
logarithmic for the films c, d. The experimentally
observed exponent values of b at low temperatures
were 0.27 and 0.14, respectively. The critical
behavior with a low value of b has been reported
earlier in other systems [15–18] in compensated n-
doped polyaniline and carbon film. The b values
for the film d were 0.13, 0.1 in the temperature
By plotting reduced activation energy wðTÞ ¼
Àq ln r=ðq ln TÞvs: T on the logarithmic scale, one
can distinguish the insulating, critical and metallic
regimes of the resistive transition.
The temperature dependence of w is also given
by the equation:
x
wðTÞ ¼ m þ xðT0=TÞ .
(2)

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171
Fig. 2. (a) Formation of globules in the carbon film prepared at 700 1C. (b) Increase of globules in the carbon film prepared at 850 1C.
(c) Clustering of globules in the carbon film prepared at 850 1C. (d) Clustering of globules in the carbon film prepared at 950 1C. (e)
Clustering of globules in the carbon film prepared at 980 1C. (f) SEM image of a single globule prepared at 850 1C.

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Table 1
Resistivity data of the carbon films at 4.2 and 300 K
a
15
10
5
Linear fit
r4:2 K
r300 K
T (K)
r300 K (O cm)
r4.2 K (O cm)
973
1073
1173
1253
0.871
4377
5025.3
0.0561
0.0154
0.0082
0.12
0.0171
0.0087
2.14
1.11
1.06
b
102
0
a
b
100
10-2
10-4
10-6
c
d
0.0
0.2
0.4
T -0.5 (K -0.5
0.6
0.8
)
e
Fig. 4. ln r vs. TÀx (x ¼ 0:5) plots of the carbon films in the
f
insulating regime.
g
Linear fit
-2
β = -0.271
β = -0.157
1
10
100
T (K)
c
-3
Fig. 3. Reduced activation energy plots of the carbon films on
the logarithmic scale.
limits 4.5 and 87 K, respectively. The close value of
b for a wide temperature range was an indication
that the film d was more in the critical regime of
M–I transition. A low value of b indicates that the
film was close to the M–I boundary but on the
metallic side of the M–I transition. The carbon
films prepared at 900 1C and above showed a clear
metallic transition at low temperatures. This was
evident from the plots of temperature dependence
of the resistivity (see Fig. 6) in the films e–g. These
films showed positive temperature coefficient of
resistance and a resistivity hump at temperatures
about 25 K. With the increase of pyrolysis
temperature, the peak in the resistivity maximum
shifted to the high temperature side. A similar type
of behavior was reported [8,9,19,20] in other
-4
β = -0.134
β = -0.095
d
0
2
4
6
In T
Fig. 5. Power law behavior of the carbon films in the critical
regime.
carbon systems. In our films, this unusual behavior
may be due to the orientation of sp2-type clusters
in a preferred direction over small length scales
that may arise from the strains and form localized

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173
1.15
0T
29.2
29.0
1T
3T
5T
7T
e
f
1.10
1.05
28.8
28.6
28.4
28.2
g
1.00
0
20
40
60
80
0
100
200
300
T (K)
T (K)
Fig. 7. Magnetic field-induced resistive transition in the film
f—950 1C.
Fig. 6. Normalized resistivity curves for the carbon films in the
metallic regime.
0T
states. The conduction mechanism in these dis-
ordered carbons has been classified as a metallic
behavior below a certain temperature, and acti-
1.08
7T
vated
character
at
higher
temperature.
1.06
1.04
1.02
1.00
s ¼ sM þ sH. This type of unusual behavior was
observed mostly in disordered carbons but until
now there was no well understood explanation for
the observed phenomena. The positive slope below
about 25 K is an indication of metal-like behavior
in these films.
3.2. Conductivity in the presence of magnetic field
The metallic behavior at low temperature was
suppressed with the application of the magnetic
field. The magnetic field-induced transition derived
from magnetoresistance data for the film f is
shown in Fig. 7. The R–T behavior of the film g in
the presence of 7 T magnetic fields for the entire
temperature range is shown in Fig. 8. In these
films, the temperature coefficient of resistance was
positive in the absence of the magnetic field and
turned to negative with the application of the
magnetic field. The slope of the reduced activation
energy plot (Fig. 9) changes sign at low tempera-
tures in the presence of the magnetic field. In the
0
100
200
300
T(K)
Fig. 8. Field-induced resistive transition in the carbon film
g—980 1C.
film g, the low b (0.016) value indicates that the
film was still on the metallic side of the M–I
transition. The film d, which was in the critical
regime in zero magnetic field has turned into the
insulating regime with the application of magnetic
field.

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0T
7T
10-1
10-2
10-3
10-4
10-5
-4.2
-4.4
0T
0.2
-4.6
7T
-4.8
10-1
0
2
4
6
10-2
10-3
In T
10-4
0.1
10-5
0.08
10
100
T (K)
1
10
100
1
10
100
T (K)
T (K)
Fig. 9. Reduced activation energy plots on a log scale of film g
at 7 T field (inset graph shown is for zero field and reproduced
from Fig. 3).
Fig. 10. Reduced activation energy plot of the carbon film d in
the presence of field (inset shown is the power law fit for the
same film).
This was evident from the reduced activation
energy plot (Fig. 10). The x values calculated by
using Eq. (3) were 0.55 in 7 T as compared to 0.28
in zero magnetic fields. This value was close to the
value obtained for the film a (x ¼ 0:54) that was
considered in the insulating regime. The b value
obtained in the presence of the magnetic
field by power law fit was 0.2, which was higher
than the value 0.13 obtained in the absence of the
magnetic field. The higher value of b indicates that
the film was on the insulator side of M–I
transition. Hence, the application of a magnetic
field pushes the film from the critical regime to the
insulating regime at low temperatures. The wave
functions near the mobility edge are more suscep-
tible to the localization by the magnetic field. The
induced localization by the magnetic field causes a
crossover from the metallic to critical or insulating
regime.
tance that may arise from e–e interaction (known
as spin contribution). A negative magnetoresis-
tance may arise from weak localization. In
amorphous materials, the weak localization and
e–e interaction, both affect low temperature
conductivity [6,7,21–25].
sðTÞ is given by the expression
sðTÞ ¼ s0 þ mT1=2 þ BTp=2
.
ð5Þ
The second term in Eq. (5) arises from e–e
interaction and the third term results from weak
localization contribution of electrons. In the
carbon films (e–g) that were considered in the
metallic regime T1=2 behavior extends down to
about 120 K. Thus, weak localization contribution
dominates at higher temperatures over e–e inter-
action contribution. The e–e interaction dominates
over the weak localization at low temperatures.
Both show T1=2 variation on conductivity and it is
rather difficult to separate them. The application
of a magnetic field reduces the weak localization of
electrons and decreases the resistance of the
material and hence the material shows positive
magnetoconductance. The e–e interaction in the
presence of the magnetic field leads to an increase
3.3. Magnetotransport
The magnetotransport measurements were
known to be sensitive to the structure and the
degree of crystallinity of carbons. Highly disor-
dered carbons have a weak positive magnetoresis-

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175
in resistance and the material shows negative
magnetoconductance.
0
-1
-2
-3
The temperature dependence as well as the
magnetic field dependence is similar in both the
low-field limit and the high-field limit [24,26,27].
In the low-field limit ðgmBB5kBTÞ, the expres-
sions are given by
1.3K
2.5K
4.2K
3=2
2
DsðBÞL ¼ ðe2=12p2_ÞðDtinÞ ðeB=_Þ
ðWeak localizationÞ,
6K
8K
2
DsðBÞspin ¼ Àðe2=4p2_ÞFÃð0:056gmBB=kBTÞ
ðe2e interactionÞ.
10K
0
20
40
2
2
(a)
B (T
)
In the high-field limit ðgmBBbkBTÞ, the expres-
sions are given by
1=2
DsðBÞL ¼ ð0:605e2=12p2_ÞðeB=_Þ
0
-1
-2
-3
ðWeak localizationÞ,
1=2
DsðBÞspin ¼ Àðe2=4p2_ÞFÃðkT=2_DÞ
1.3K
1=2
2.5K
4.2K
 ½ðgmBB=kBTÞ À 1:294ꢂ
ðe2e interactionÞ.
6K
8K
In the above equations, tin is the inelastic mean
free time, B is the field, g is the Zeeman splitting
factor, D is the diffusion coefficient and F* is the
coupling strength in the Hatree process.
10K
0
1
2
3
1/2 1/2
(T
Magnetoconductivity was measured in metallic
films at low temperatures up to 7 T. The data for
the film g were analyzed at the both low-field and
high-field limits. In a low-field regime and at low
temperatures, B2 dependence on magnetoconduc-
tance was observed as shown in Fig. 11a. As the
temperature increases, the dependence shifted to
higher fields. Fig. 11b shows the magnetoconduc-
tance fit in the high-field limit. At high fields, the
magnetoconductance was positive and propor-
tional to B1/2. As the temperature falls, this trend
extends to low fields. The magnetoconductance
became negligible at high temperatures. For the
film g, the magnetoconductance has fallen from
À2.6% at 1.3 K to À0.5% at 4.2 K in 7 T field. The
magnetoconductance was negative below 6 K and
positive above 6 K as shown in the Fig. 11c. At
6 K, magnetoconductance was negative at low
fields and attained minimum value on the same
side at 1.5 T. It further increases with the increase
(b)
B
)
0
-1
0.05
0.00
-2
-3
-0.05
-0.10
-0.15
0
2
4
6
8
B (T)
0
2
4
6
8
(c)
B (T)
Fig. 11. (a) B2 dependence on magnetoconductance of the
carbon film g in the low-field region. (b) Low-field dependence
on magnetoconductance in the carbon film g. (c) Low-
temperature magnetoconductance of the carbon film g (&
J
1.3 K, 2.5 K, n 4.2 K, $ 6 K, } 8 K, v 10 K). Inset shown
is the magnetoconductance of the same film at 6 K.

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of field and becomes positive above 4.8 T. The
change of sign in magnetoconductance may be due
to the interplay between the weak localization and
the e–e interaction contributions. At low fields, the
negative magnetoconductance was due to domina-
tion of e–e interaction over weak localization. The
positive but weak magnetoconductance at higher
fields was due to weak localization contribution.
[3] T.G. Castner, in: M. Pollak, B.I. Shklovskii (Eds.),
Hopping Transport in Solids, Elsevier/North-Holland,
Amsterdam, 1990, p. 1.
[4] Youzhu Zhang, Peihua Dai, Miguel Levy, M.P. Sarachik,
in: H. Fritzsche, M. Pollak (Eds.), Hopping and Related
Phenomena, World Scientific Publishing Company, Singa-
pore, 1990, p. 85.
[5] Ralph Rosenbaum, Phys. Rev. B 44 (1991) 3599.
[6] E. Abrahams, P.W. Anderson, D.C. Liccardello, T.V.
Ramakrishnan, Phys. Rev. Lett. 42 (1979) 673.
[7] B.L. Altshuler, A.G. Arnov, in: A.L. Effros, M. Pollak
(Eds.), Electron–Electron Interactions in Disordered Sys-
tems, North-Holland, Amsterdam, 1985, p. 1.
[8] H. Kempa, P. Esquinazi, Y. Kopelevich, Phys. Rev. B 65
(2002) 241101.
4. Conclusion
We have measured the electrical transport
properties of amorphous carbon films prepared
from succinic anhydride by the pyrolysis method.
Depending on the temperature of preparation, the
samples showed different conduction mechanisms.
The samples prepared at low temperatures showed
variable hopping conduction and the samples
prepared at higher temperatures showed metal-
like behavior with very low temperature coefficient
of resistance. The disorder in the films can be
tuned by thermal energy and changes with
pyrolysis temperature thereby influencing their
conductivity. The observation of the resistivity
maximum around 25 K in the amorphous carbon
films that showed metal-like transition and its
suppression by the application of a magnetic field
was typical of some other similar disordered
carbon systems. The e–e interaction and the weak
localization influence the magnetotransport prop-
erties in these amorphous carbon films.
[9] A. FaiXt, H.V. Loneysen, Carbon 40 (2002) 321.
[10] M. Reghu, et al., Synthet. Met. 65 (1994) 167.
[11] A.G. ZabrodskII, K.N. Zinov’eva, Sov. Phys. JETP 59 (2)
(1984) 425.
+
[12] A. Mobius, M. Richer, J. Non-Cryst. Solids 97 and 98
(1987) 483.
[13] W.L. McMillan, Phys. Rev. B 24 (1981) 2739.
[14] A.I. Larkin, D.E. Khmelnitskii, Sov. Phys. JETP 56 (1982)
647.
[15] G. ZabrodskII, Sov. Phys. Semicond. 11 (1977) 345.
[16] M. Reghu, et al., Phys. Rev. B 47 (1993) 1758.
[17] M. Raghu, et al., Phys. Rev. B 48 (1993) 817.
[18] A. Sayeed, Doctoral Thesis, Indian Institute of Science,
1998.
[19] C. Uher, L.M. Sander, Phys. Rev. B 27 (1983) 1326.
[20] I.L. Spain, et al., Solid State Commun. 45 (1983) 817.
[21] P.A. Lee, T.V. Ramakrishnan, Rev. Mod. Phys. 57 (1985)
287.
[22] P. Dai, Y. Zhang, M.P. Sarachik, Phys. Rev. B 45 (1992)
3984.
[23] D.J. Thouless, Phys. Rep. 13 (1974) 93.
[24] A. Howson, B.L. Gallagher, Phys. Rep. 170 (1988) 265.
[25] H. Fukuyama, in: A.L. Effros, M. Pollak (Eds.),
Electron–Electron Interactions in Disordered Systems,
Elsevier Science Publishers B.V., Amsterdam, 1985.
[26] B.J. Hickey, D. Greig, M.A. Hawson, Phys. Rev. B 36
(1987) 3074.
References
[1] N.F. Mott, J. Non-Cryst. Solids 1 (1968) 1.
[2] A.L. Efros, B.I. Shklovskii, J. Phys. C 8 (1975) L49.
[27] J.S. Dugdale, The Electrical Properties of Disordered
Metals, Cambridge University Press, Cambridge, 1995.