Physica B 165&166
North-Holland
(1990)
299-300
CONDUCTION MECHANISM IN GRANULAR Ru02-BASED
THICK-FILM RESISTORS
Wilfried
SCHOEPE
Institut
fiir Angewandte
The conductivity
up to 7 Tesla.
the density
strongly
Physik,
Universitit
of a commercial
thick-film
The
of states.
localized
Commercial
processes.
models
devices,
systems
however,
is lacking.
tion which is affected
by temperature
from
10 kR resistors
of Siegert
GmbH
layer.
chamber
A magnetic
Fig.
0.48 K. (The deviation
(l-4).
An
conducfield
semiconductor.
a batch
(5).
or parallel
3o-d
It was mounted
dilution
re-
to the conductive
dependence
current
is observed
in
del is valid only for ?’ <
(6).
Strictly,
Z’, but no deviation
up to 4 K. From 7’, N e2 /4?rc,kca (where t is the dielectric constant
ta - 3 10-s
and a the radius of localisation)
m. Assuming
which corresponds
is negative
usual
case of a large positive
localized
the wavefunction
effect indicates,
vefunction
in a magnetic
by orbital
field.
that the long-range
is not relevant
0921-4526/90/$03.50 @
contrast
magnetoresistance
regime caused
heating
0
R(OI
a.
by the measuring
1
of the wa-
1990 -El sevier Science Publishers
current
of 15 pA.
0.669
L.2
I
-4
TIK).Cl177a2L8
0
50
2
L
0
of
in this case.
law
below 20 mK is due to
-2 -
-6
this
in zero field.
a exp(T,,/T)i
HO-3I
in the
shrinking
-.
.
to the
The absence
behaviour
for transport
Joule
grains.
at all temperatures
and fields, see Fig. 2. This is in striking
strongly
m,
-.
J&is
indicates
with To = 0.48 K. The deviation
one finds
c N 10 gives a N 3. lo@
to the size of the metallic
The magnetoresistance
line behaviour
A!3_.
is visible
8
The straight
to
the mo-
6
FIGURE
1
dependence of the resistance
often in gra-
to variable-range
L
T-l/2 (K-l/2)
Temperature
ef-
was reduced
rather
and may be attributed
interaction
2
of commercial
law below 4 K with Z’,, =
the measuring
with Coulomb
T (Kl
in this work
below 20 mK is due to heating
15 pA.) This behaviour
hopping
effects in the
of theoretical
1 shows that the temperature
systems
fields
gap in
Conduction
of a home-made
zero field follows a exp(Z’,/T):
nular
ex-
field up to 7 Tesla could be ap-
perpendicular
fects even though
with a Coulomb
to quantum-interference
are use-
and magnetic
localized
was taken
plied either
mechanism
for doped semiconductors
sample
frigerator.
may be attributed
of their
in terms of a hopping
for a strongly
inside the mixing
4 K and 15 mK and in magnetic
hopping
by manufacturing
The data obtained
can be described
The
between
W.Germany
and field dependen-
the applicability
developped
is still under discussion.
as expected
resistors
because
may be affected
Furthermore,
originally
actually
magnetoresistance
thick-film
thermometers
of the temperature
ces of these
is measured
by the variable-range
and small magnetoresistance
understanding
in granular
The negative
Ru02-based
stability
resistor
can be described
8400 Regensburg,
regime.
ful low-temperature
cellent
data
Regensburg,
Magnetoresistance
Except
nearly
at
6
ITI
FIGURE
various
2
constant
temperatures.
for small fields the magnetoresistance
as B/B,.
B.V. (North-Holland)
varies li-
300
PI. Schoepe
A negative magnetoresistance
of the hopping mechanism has recently been calculated on the basis of quantum interference effects of the tunneling electron (7-9).
The magnetic field dependence
is predicted to be linear except for very small fields where it should increase
quadratically.
This is in agreement with the data of
Fig. 2. The temperature
dependence of the linear part
should scale as r-g, where r cc (T,/T))
is the temperature dependent hopping length (9). Therefore, the inverse of the slopes of the straight lines should vary as
Tf . The experimental results, see Fig. 3, are approximately described by a T2 law for T 5 To and tend to
saturate above 1 K. This is consistent with the above
mechanism.
A more detailed analysis requires a calculation of the prefactor which is not yet available.
10 0.l
1
5
T (Kl
FIGURE 3
The temperature
dependence of B, (i.e. of the inverse
of the slopes in Fig. 2).
ACKNOWLEDGEMENTS
It is a pleasure to thank W. Pfab of Siegert GmbH
for supplying the sample. I have had very helpful discussions on the theory with W. Schirmacher and B.
Shklovskii. Similar experiments
were performed simultaneously and independently
by K. Neumaier and I am
grateful to him for cummunicating
his results prior to
publication.
REFERENCES
(1) H. Doi, Y. Narahara, Y. Oda and H. Nagano, Proceedings LT 17, eds. U. Eckern et al. (North
Holland, Amsterdam,
1984) p. 405.
(2) W.A. Bosch, F. Mathu, H.C. Meijer and R.W. Willekers, Cryogenics 26 (1986) 3.
(3) Q. Li, C.H. Watson, R.G. Goodrich, D.G. Haase
and H. Lukefahr, Cryogenics 26 (1986) 467.
(4) M.W. Meisel, G.R. Stewart and E.D. Adams, Cryogenics 29 (1989) 1168.
(5) Siegert GmbH, D-8501 Cadolzburg, W.Germany.
(6) B.I. Shklovskii and A.L. Efros, Electronic
properties of doped semiconductors
(Springer-Verlag,
Berlin, 1984).
(7) V.L. Nguen, B.Z. Spivak and B.I. Shklovskii, Zh.
Eksp. Teor. Fiz 89 (1985) 1770 (English translation Sov. Phys. JETP 62 (1985) 1021).
(8) U. Sivan, 0. Entin-Wohlman
and Y. Imry, Phys.
Rev. Letters 60 (1988) 1566.
(9) W. Schirmacher, Phys. Rev. B., to be published.