Magnetotransport in the amorphous carbon films near the metal-insulator transition

Article abstract of DOI:10.1016/j.ssc.2007.10.027

The low temperature electrical conductivity behavior of the amorphous carbon films in the non-metallic regime of the metal-insulator transition is studied in magnetic fields up to 7?T. The films are prepared from the pyrolysis of succinic anhydride in the temperature range 700-980?^{{ring operator}}C. A positive magnetoresistance (MR) is observed in films that are in the insulating regime and follows the variable range hopping (VRH) mechanism of conduction. In the VRH regime, at low temperatures B² dependence on the magnetoresistance is observed. The conductivity of the films in the critical regime follows the power law behavior. The MR is positive both at low and high field limits. At high fields the magnetoconductance is proportional to B^{1 / 2} and is negligible at high temperatures.

Full text of DOI:10.1016/j.ssc.2007.10.027

Solid State Communications 145 (2008) 186–191
www.elsevier.com/locate/ssc
Magnetotransport in the amorphous carbon films near the
metal–insulator transition
Vishnubhotla Prasad∗
Department of Physics, Indian Institute of Science, Bangalore, 560 012, India
Received 10 April 2007; received in revised form 14 October 2007; accepted 20 October 2007 by S. Miyashita
Available online 26 October 2007
Abstract
The low temperature electrical conductivity behavior of the amorphous carbon films in the non-metallic regime of the metal–insulator transition
◦
is studied in magnetic fields up to 7 T. The films are prepared from the pyrolysis of succinic anhydride in the temperature range 700–980 C. A
positive magnetoresistance (MR) is observed in films that are in the insulating regime and follows the variable range hopping (VRH) mechanism
2
of conduction. In the VRH regime, at low temperatures B dependence on the magnetoresistance is observed. The conductivity of the films in the
critical regime follows the power law behavior. The MR is positive both at low and high field limits. At high fields the magnetoconductance is
1/2
proportional to B
and is negligible at high temperatures.
c
ꢀ 2007 Elsevier Ltd. All rights reserved.
PACS: 73.43.Qr; 73.50.-h; 72.20Ee; 71.35.+h
Keywords: A. Disordered systems; A. Thin films; B. Chemical synthesis; D. Electronic transport
1. Introduction
that arise purely as a consequence of disorder in the system.
He established that in a disordered system if the randomness of
the potential exceeds a critical value, the wave functions of all
the states up to the mobility edge are localized and such states
are referred to as localized states. A localized system exhibits
metallic or insulating behavior depending upon whether the
Fermi energy lies above or below the mobility edge. Later N.F.
Mott showed that this kind of localization necessarily occurs
at the bottom of the conduction band and at the top of the
valence band of any disordered material. The conduction occurs
in the localized states by a thermally assisted hopping process
also known as variable range hopping conduction (VRH).
Mott’s T −1/4 law for low-T variable range hopping (VRH)
conduction for constant density of states at the Fermi level is
very popular. The Efros–Shklovskii VRH conduction accounts
for the Coulomb interactions between the hopping sites that
create a gap (Coulomb gap) in the density of states near the
Fermi level. The transition from a metallic to an insulating state
is associated with the carrier localization at the Fermi level. In
many systems a transition from Mott VRH to Efros–Shklovskii
VRH is observed at sufficiently low temperatures. In some
cases like strongly doped semiconductors or heavily doped
conducting polymers the carrier localization is induced by
The metal–insulator transition is one of the subjects of
research interest all over the world for many decades [1–6].
It is observed in many systems such as carbon, polymers and
doped semiconductors [7–10]. Recently it is observed in carbon
nanotubes and transition metal doped ZnO films [11,12]. This
transition is more prominent in disordered systems and the
disorder can be tuned by changing various parameters like
temperature, pressure, magnetic field or impurity concentration
etc. The electrical property studies on graphitic carbons in
particular are interesting due to the fact that the degree of
disorder changes the mode of electrical conduction. Starting
from pure diamond (sp3) to graphite (sp2) there are many
other graphitic systems that are amorphous and show different
electrical and thermal properties depending on the extent of
disorder (sp3 to sp2 ratio). Among the numerous theoretical
explanations on metal–insulator transitions, the most prominent
one is Anderson’s gapless model on the localization of states
∗
Tel.: +91 80 22933461; fax: +91 80 23602602.
E-mail address: vishnu@physics.iisc.ernet.in.
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doi:10.1016/j.ssc.2007.10.027

V. Prasad / Solid State Communications 145 (2008) 186–191
187
disorder. Such systems show features like weak (electron)
The reduced activation energy is defined as
localization, electron–electron interaction etc. Application of
pressure and magnetic field can tune the position of the mobility
edge with respect to the Fermi energy. This is of particular
interest in carbon compounds such as graphite, pyrocarbons and
conducting polymers.
We have earlier [10] reported the metal–insulator transition
in the amorphous carbon films prepared from succinic
anhydride by the pyrolysis method. This paper deals with the
magnetoresistance properties of the amorphous carbon films
which are in the non-metallic regime (critical or insulating) of
the M–I transition.
d ln ρ(T )
W(T ) = −
.
(1)
d ln T
The low temperature behavior of W can be used to identify
the various transport regimes. In the insulating regime of the
metal–insulator transition, W has a negative temperature coef-
ficient and the resistivity has strong temperature dependence. In
the critical regime, the parameter W is temperature independent
at low temperatures. In the metallic regime (W → 0 as T → 0)
of the M–I transition the sign of dW/dT is positive.
In the insulating regime, the films showed an activated
behavior and the temperature dependence of conductivity
followed variable range hopping conduction. The charge
carriers at the Fermi surface are strongly localized in the
insulating regime. The resistivity in the strongly localized
regime is given by the equation
2. Experimental — Details
The amorphous carbon films are prepared by the high
temperature pyrolysis method. The carbon rich precursor
succinic anhydride is pyrolyzed at different temperatures
ranging from 700–980 ◦C in a one end closed fused silica
tube. The carbon films are deposited on smoothened quartz
substrate and showed amorphous nature as revealed from
X-ray diffraction. The scanning electron microscopy on the
film surface revealed the spherical globule formation that
led to cluster formation at higher pyrolysis temperatures.
The electrical contacts are made with conducting silver paste
and a standard four-probe technique is used for conductivity
measurements. The low temperature magnetotransport studies
are performed using a liquid helium superconducting magnet
cryostat down to 1.3 K and magnetic fields up to 7 T.
ꢀꢁ ꢂ ꢃ
p
T0
ρ(T ) = ρ0 exp
.
(2)
T
1
d+1
For d-dimensional Mott VRH, p =
.
By plotting the logarithm of resistivity against the powers of
the reciprocal temperature (1/T ), the p value can be extracted.
p = 1/4 in 3D and in 2D, p = 1/3.
In the Coulomb-gap (CG) Efros–Shklovskii VRH regime the
temperature dependence of conductivity changes from 1/4
ꢀ
ꢃ
ꢄ
ꢅ
0.5
T0
T
to 1/2 and is given by σ = σ0 exp −
. This is
3. Results
due to the fact that the Fermi level lies in the region of
localized states. The low temperature dc conduction is due
to hopping of charge carriers between such localized states
inside an energy band that is localized near the Fermi level.
The width of the band decreases when the temperature is
◦
The amorphous carbon films prepared at 700 and 750 C
are more disordered and are on the insulating side of the
metal–insulator transition. The films prepared at 800 and
◦
850 C are in the critical regime of the M–I transition. Above
◦
lowered. The a-C films prepared at 700 and 750 C (Fig. 1),
that temperature the films are less disordered and are on the
metallic side of the M–I transition. The room temperature
conductivity of the films varies from 1–120 S/cm depending
on the pyrolysis temperature.
showed insulating behavior at◦low temperatures whereas the
films prepared at 800 and 850 C (Fig. 2) are semiconducting
with a weak temperature dependence of resistivity. In the films
prepared at low temperature (700 ◦C), there is a variation
of six orders of change in the resistivity. On the other hand
the variation is only 1.85 times at the lowest temperature
3.1. Zero field conductivity
◦
(1.3 K) in the films prepared at 850 C. The films that are
Materials are classified as metals, semiconductors and
insulators in terms of their resistivity and its temperature
dependence. The temperature coefficient of resistance (TCR)
concept is valid generally for crystalline systems in which the
wave functions of the charge carriers extend over the entire
crystal. This picture breaks down in a disorder system. The
temperature coefficient of resistance (TCR) is not a proper
parameter and can be positive or negative for a number of
amorphous metallic systems (Mooji correction).
The most authentic way of identifying the various regimes
(metallic, critical and insulating) in the disordered systems is
through Zabroskii plots of the logarithmic derivative of the
conductivity [13]. This plot facilitates the identification of the
various regimes of the electrical transport.
in the critical regime showed power law behavior and the
conductivity is given by [σ(T ) ∝ T β]. The films prepared
at higher pyrolysis temperatures show less disorder and are
in the metallic regime of the metal–insulator transition. Fig. 3
shows the normalized resistivity versus temperature curve on
the logarithmic scale. From these graphs it is evident that as
the preparation temperature is increased the extent of disorder
decreases for these films.
In non-crystalline systems, the resistivity ratio is another
parameter to quantify the disorder in various regimes. The
smaller the resistivity ratio the less is the disorder in the
system. The disorder in different samples is quantified from the
h
i
ρ
4.2K
resistivity and ratio
to sort out the various regimes in the
ρ
300K

188
V. Prasad / Solid State Communications 145 (2008) 186–191
Fig. 3. Resistivity versus temperature plots of the carbon films on the log scale.
Fig. 1. Normalized resistivity versus temperature plots of the carbon films
prepared at 700 and 750 C.
◦
Fig. 4. The resistivity ratio versus the pyrolysis temperature plot of the carbon
films.
Fig. 2. Normalized resistivity versus temperature plots of the carbon films
prepared at 800 and 850 C.
◦
above 800 ◦C, an indication that the samples prepared at higher
pyrolysis temperatures tend to be on the metallic side of the
M–I transition.
disordered system. Fig. 4 shows the resistivity ratio versus the
pyrolysis temperature curve of the samples on the logarithmic
scale. The ratio falls drastically for the samples pyrolysed

V. Prasad / Solid State Communications 145 (2008) 186–191
189
Fig. 5. Magnetoresistance plots of the amorphous carbon films prepared at
750 C.
2
Fig. 6. B dependence of the magnetoresistance in the carbon film prepared at
750 C.
◦
◦
√
3.2. Magnetotransport
where λ = hc/eH is the magnetic field length, ξ is the
¯
localization length of the wave function, p = 2 and t is
typically of the order of 0.0015 which is p dependent.
Fig. 6 shows the B2 dependence of the magnetoresistance for
the film prepared at 750 ◦C. All the MR curves follow quadratic
field dependence at low magnetic fields. The magnitude of
MR increases with the decreasing temperature. The magnetic
field value for the onset of deviation from the quadratic field
dependence decreases with the decrease of temperature.
At low fields, VRH can also lead to negative MR. The
mechanism is similar to weak localization, except the magnetic
flux is enclosed by a loop formed by the hopping path and
the relevant length scale is the hopping distance R instead of
Lφ [21,22]
Magnetoresistance measurement is a sensitive tool in
investigating the various scattering process in the disordered
systems and they are closely related to the low temperature
conductivity behavior in the presence of magnetic field. The
temperature and field dependence of MR are sensitive to
disorder and electron interactions. Highly disordered carbons
show a weak positive magnetoresistance that may arise from
electron–electron interactions. The negative MR is observed
in pregraphitic carbons, pitch derived carbon fibers and heat-
treated activated carbon fibers [8,14–17] in the metallic regime.
In the strongly localized regime in which transport is via
variable range hopping, both experiments and theories predict
that the insulating phase yields positive MR in the presence of
spin–orbit scattering.
Fig. 5 shows the MR plots of the films at different
temperatures in the insulating regime. The MR is positive and
about 19% at the lowest temperature of 1.3 K in 7 T magnetic
field. The positive MR gradually decreases with the increase
of temperature and becomes negligible at high temperatures.
The MR data fits well to quadratic magnetic field dependence.
The positive MR for the strongly disordered systems is due to
the wave function shrinkage effect in the presence of magnetic
field. Accompanying the reduced wave-function overlap is a
decrease in the probability of tunneling and hence an increase
in the resistance.
In such cases, one predict linear and the other quadratic
magnetic field dependence at low fields. The MR data for the
insulating samples support the latter. But there is no simple
correspondence between the data and the theories available
right now to explain this type of behavior.
The MR curves for the films prepared at 800 and 850 ◦C are
given in Figs. 7 and 10. The samples fall in the critical regime
of the metal–insulator transition. The highest positive MR
observed at the lowest measured temperature in these samples
is 6.4% and 5.4% respectively. The zero field conductivity is
fitted well to the power law behavior with β values 0.27 and
◦
0.14 respectively for the films prepared at 800 and 850 C.
These reported low values of β for these films compared to
the theoretically predicted value of 0.33 < β < 1 [19,
20] is an indication that the films fall close to the M–I
boundary but on the metallic side of the M–I transition.
The magnetoconductivity in the critical region near the M–I
The theory [18] predicts a temperature and field dependence
of MR in the Mott VRH regime and is given by
ꢀ
ꢃ
ꢁ ꢂ ꢁ
ꢂ
4
3/p
ρ(B)
ρ(0)
ξ
T0
T
ln
= t
≡ AH2,
λ

190
V. Prasad / Solid State Communications 145 (2008) 186–191
Fig. 7. Magnetoresistance plots of the amorphous carbon films prepared at
800 C.
1/2
◦
dependence of the film prepared at 800 C.
Fig. 9. B
◦
2
◦
Fig. 8. Magnetoresistance versus B plots of the film prepared at 800 C.
√
transition is proportional to
H and the proportionality
constant does not depend on the proximity to the mobility
edge [23].
Fig. 10. Magnetoresistance plots of the amorphous carbon films prepared at
850 C.
◦
For both the films in the critical regime, at low temperatures,
the magnetoconductance data is fitted well to B1/2 dependence
at higher fields (Figs. 9 and 12).
This is due to the shifting of the mobility edge in the
presence of the magnetic field.
Increasing the magnetic field tends to cause a trajectory from
the metallic side towards the insulating side resulting a positive
MR for the samples in the critical regime at low temperatures.
A similar thing is observed in the polymers [24]. The plots for

V. Prasad / Solid State Communications 145 (2008) 186–191
191
Table 1
Resistivity ratio at different temperatures
◦
◦
◦
C
Temperature (K)
750
h
C
800
h
C
850
h
i
i
i
ρ
ρ
ρ
1.3K
1.3K
1.3K
(%)
(%)
(%)
ρ
ρ
ρ
300K
300K
300K
1.3
2.4
4.2
10
20
50
18.7
12
6.4
6.2
3.8
1
5.4
5.1
3.3
0.7
0.2
0.1
0.06
3.9
2
1.5
1.1
0.6
0.3
0.2
0.003
77
In both the regimes MR is positive but higher values are
observed for more disordered samples.
4. Conclusions
The amorphous carbon films prepared at lower pyrolysis
temperatures show positive magnetoresistance both in the
insulating and critical regimes and is proportional to B2 at
low fields. In the strongly localized or insulating regime the
films show higher MR due to wave-function shrinkage effects
and its magnitude decreases with the increase of temperature.
The shifting of mobility edge in the presence of magnetic field
drives the sample from the metallic side of the M–I transition
into the insulating side.
2
◦
Fig. 11. Magnetoresistance versus B plots of the film prepared at 850 C.
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Fig. 12. B
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B2 dependence of magnetoresistance for the films in the critical
regime are shown in Figs. 8 and 11. The magnetoresistance is
quite linear up to 4.2 K. Below that temperature the initial linear
behavior at low fields is followed by a saturating trend at high
fields.
The magnetoresistance values of the films both in the
insulating and critical regimes at different temperatures are
given in Table 1.