Length dependence of current-induced breakdown in carbon nanofiber interconnects

Article abstract of DOI:10.1063/1.2918839

Current-induced breakdown is investigated for carbon nanofibers (CNF) for potential interconnect applications. The measured maximum current density in the suspended CNF is inversely proportional to the nanofiber length and is independent of diameter. This relationship can be described with a heat transport model that takes into account Joule heating and heat diffusion along the CNF, assuming that breakdown occurs when and where the temperature reaches a threshold or critical value.

Full text of DOI:10.1063/1.2918839

Length dependence of current-induced breakdown in carbon nanofiber
interconnects
Hirohiko Kitsuki, Toshishige Yamada, Drazen Fabris, John R. Jameson, Patrick Wilhite et al.
Citation: Appl. Phys. Lett. 92, 173110 (2008); doi: 10.1063/1.2918839
View online: http://dx.doi.org/10.1063/1.2918839
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Published by the American Institute of Physics.
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APPLIED PHYSICS LETTERS 92, 173110 ͑2008͒
Length dependence of current-induced breakdown in carbon
nanofiber interconnects
a͒
Hirohiko Kitsuki, Toshishige Yamada, Drazen Fabris, John R. Jameson, Patrick Wilhite,
Makoto Suzuki, and Cary Y. Yang
Center for Nanostructures, Santa Clara University, Santa Clara, California 95053, USA
͑
Received 14 March 2008; accepted 10 April 2008; published online 1 May 2008͒
Current-induced breakdown is investigated for carbon nanofibers ͑CNF͒ for potential interconnect
applications. The measured maximum current density in the suspended CNF is inversely
proportional to the nanofiber length and is independent of diameter. This relationship can be
described with a heat transport model that takes into account Joule heating and heat diffusion along
the CNF, assuming that breakdown occurs when and where the temperature reaches a threshold or
critical value. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2918839͔
Because of their high electrical and thermal conductivi-
down occurs due to Joule heating in the CNF bulk.
1
ties as well as current capacity, carbon nanotubes ͑CNTs͒
Systematic analysis using scanning transmission electron
microscopy ͑STEM͒ and in situ scanning electron micros-
copy ͑SEM͒ measurements has revealed the creation of void
and defective graphitic layers in the CNF induced by current
2
–5
and carbon nanofibers ͑CNFs͒ are being investigated for
high-performance device and interconnect applications.
Breakdown phenomena have been observed under high-
6
–12
14
current stress conditions for CNTs
and amorphous carbon
stress. This analysis suggests that the CNF resistance just
1
3
nanowires. Breakdown mechanisms generally depend on
the detailed carbon nanostructures. For CNFs, recent
before breakdown drastically increases due to severe degra-
dation of the nanofiber internal structure. The SEM image of
a CNF before current stress is shown in Fig. 3͑a͒. In all
experiments for suspended CNFs, we have confirmed that
breakdown always occurs near the middle of the nanofiber as
in Figs. 3͑b͒ and 3͑c͒. This is consistent with diffusive heat
5
,14,15
studies
suggest current-induced CNF breakdown to be
closely related to Joule heating, and thermal coupling be-
tween CNF and electrodes affects the maximum current den-
sity Jmax of CNF devices and their breakdown. Meanwhile,
current annealing has been reported to drastically reduce the
overall resistance and this may be attributed to significant
1
0
transport in CNTs at high bias, suggesting the importance
1
5
of Joule heating in breakdown.
1
6–18
To understand these experimental results, a one-
lowering of the contact resistances in CNT devices.
1
5,23
dimensional ͑1D͒ thermal transport model
is used. We
Therefore, one can assume that once the contact resistances
are reduced, the reliability of CNF interconnects becomes
largely dependent on the nanofiber resistance. In this work,
systematic characterization of CNFs under high-current
stress is performed to examine and to elucidate the CNF
breakdown phenomena.
define ⌬T͑x͒ as the difference between the local temperature
T͑x͒ and the temperature at infinity. ⌬T͑x͒ is determined
2
2
from the balance among heat diffusion ͑d ⌬T/dx ͒, heat dis-
2
sipation to the surroundings ͑a ⌬T͒, and heat generation due
to Joule heating ͑f͒ in
The CNF samples are grown using plasma-enhanced
d2⌬T
dx2
1
9,20
−
a2⌬T = − f.
͑1͒
chemical vapor deposition
with a Ni catalyst layer on a
Si substrate. A 30-nm-thick Ti adhesion layer is used be-
tween the 35-nm-thick Ni layer and Si, and a gas mixture of
2
2
Here, f =I /͑A ␴␬͒, where I is the current, A is the cross-
sectional area, ␴ is the electrical conductivity, and ␬ is the
CNF thermal conductivity. Also, a =w␥/A␬, where w is the
effective contact line width and ␥ is the coupling coefficient
for heat transport to the CNF surroundings ͑air and
2
1
NH :C H ͑4:1͒ at 4 Torr is used for the reaction. A solu-
3
2
2
tion of CNFs is drop-casted onto a substrate of prepatterned
gold electrodes on an oxidized silicon wafer. The structure
shown in Fig. 1͑a͒ is a model of an on-chip interconnect
configuration, where the CNF sidewall is in contact with
2
2
2
the electrodes. Constant-current stress or anneal is applied
in ambient ͓Fig. 1͑b͔͒ for 13 samples, ranging from
1
00 to 200 nm in diameter and 1.5 to 6 ␮m in length.
The progression of constant-current stress cycles ͑at
80 s each͒ is illustrated in Fig. 2͑a͒. At the end of each
1
cycle, I-V characteristics are obtained around V=0. Increas-
ing the annealing current results in a gradual decrease in the
differential resistance R at V=0 before the nanofiber breaks
down at 700 ␮A ͓Fig. 2͑b͔͒. Since R consists of bulk and
contact contributions, and the CNF consistently breaks near
the middle away from the contacts, current annealing likely
reduces the contact resistances significantly, while break-
FIG. 1. Setup for current-stressing experiments. ͑a͒ SEM image of a CNF
sample suspended between gold electrodes at 75° tilted-angle view. High-
resolution STEM images of CNFs can be seen in Ref. 14. ͑b͒ Schematic of
electrical measurement.
a͒The author to whom correspondence should be addressed. Electronic mail:
tyamada@scu.edu.
0003-6951/2008/92͑17͒/173110/3/$23.00
92, 173110-1
© 2008 American Institute of Physics
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173110-2
Kitsuki et al.
Appl. Phys. Lett. 92, 173110 ͑2008͒
FIG. 2. Resistance reduction of CNF device due to current annealing. ͑a͒
Schematic of successive current annealing cycles using stepwise increment
of stressing current. ͑b͒ Resistance of the CNF device at V=0 obtained after
each annealing cycle. The inset shows the current-voltage behavior at the
end of one of the anneal cycles.
substrate͒. We impose ⌬T=0 at the two ends where
2
x= ϮL/2 and x=0 is the midpoint. Thus, ⌬T͑x͒=͑f /a ͓͒1
−
cosh͑ax͒/cosh͑aL/2͔͒ results, with the maximum at x=0.
We assume that, in general, breakdown occurs when T
reaches a threshold ͑critical͒ temperature Tmax, which is com-
mon for all CNFs with any diameters or lengths, prepared
using the same growth process. Then, the maximum current
density Jmax can be expressed as
FIG. 4. ͑a͒ Maximum current density as a function of reciprocal CNF length
for thirteen devices. The line shows a linear fit predicted by our heat trans-
port model. ͑b͒ Resistance of CNF device as a function of annealing current
after each annealing cycle for the same thirteen devices. The line approxi-
mates the resistance just before breakdown.
Jmax = ͓͑Tmax − T ͒␴␥w/A͔1/2͓1 − 1/cosh͑aL/2͔͒−1/2. ͑2͒
ϱ
In the suspended case, heat dissipation is expected to be
the aLӶ1 limit of Eq. ͑2͒. This excellent agreement con-
firms that for a suspended CNF, heat dissipation to its sur-
roundings is, in fact, small and heat diffusion along the CNF
leads to the highest temperature in the middle of the nanofi-
ber. Moreover, Jmax scales with 1/L, which is consistent with
the peak current behavior of suspended single-walled
negligible, or aLӶ1, yielding JmaxϷ2ͱ2͑T −T ͒␴␬/L.
max
ϱ
Figure 4͑a͒ shows the experimental results ͑dots͒ for
Jmax versus 1/L for 13 devices. The behavior is consistent
2
4
with current-induced breakdown in single-walled CNTs or
gold nanowires fabricated using conventional lithography
2
5
24
techniques. The same behavior is predicted in our model in
CNTs.
From the fitted result of Jmax=5.39/L in Fig. 4͑a͒, Tmax
1260 K. This is comparable to the CNF synthesis tempera-
=
ture, estimated to be in the 1000 K range. Here, a CNF ther-
2
6
mal conductivity of 12 W/m K and the maximum electri-
cal conductivity from the present data are used. Having no
radiative heat transfer and in the limit of no coupling with
the substrate, the temperature estimate is only an indication
of CNF durability and points to the need for systematic local
temperature measurement.
1
4
ͱ
Our previous work showed a Jmaxϰ1/ L behavior,
based on the assumption that CNF was a long 1D thermal
conductor with an exponential decay of temperature beyond
the CNF/electrode contacts. In the present work, the heat
dissipation to the substrate is weak over the suspended dis-
tance, while the nanofiber coupling with the electrodes is
relatively strong, where ⌬T=0 is assumed. The difference in
boundary conditions leads to Jmax scaling with 1/L as veri-
fied by the present experimental results.
FIG. 3. ͑a͒ SEM images of a CNF suspended gold electrode before current
stressing. ͑b͒ CNF after breakdown ͑top view͒ and ͑c͒ at 75° tilted-angle
view.
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173110-3
Kitsuki et al.
Appl. Phys. Lett. 92, 173110 ͑2008͒
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Figure 4͑b͒ shows a plot of R measured at the end of
each current annealing cycle as a function of annealing cur-
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different diameter and length, with different contact proper-
ties. For this reason, one can expect that well before break-
down when Jmax is reached, R significantly deviates from
sample to sample partly due to large contact resistances, up
to a factor of 20 in our case. However, after successive cur-
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