Inductive Peaking Technology for Bandwidth
Enhancement in Carbon Nanotube Bundle Interconnect
Songjie Zhao and Zhongliang Pan*
Based on transmission line modeling, this paper proposes an inductive
peaking technology to improve the bandwidth of single-walled carbon
nanotube interconnect. And the transfer function of the equivalent model is
derived to obtain the frequency response of the interconnect according to
ABCD parameter matrix approach. Considering the effects of temperature,
length, load resistance, and driver size, the 3-dB bandwidth of the
interconnect for 14 nm technology node at global level versus the peaking
inductance has been obtained. The results show an increase of the peaking
inductance can improve the bandwidth effectively. However, the increase is
not boundless for higher inductances. The bandwidth will roughly maintain a
steady level when the value of the inductance reaches a certain degree.
Moreover, overshoot phenomenon will occur and the crosstalk is increased
for larger inductance. On the other hand, as the length, temperature, and
load resistance increase, 3-dB bandwidth decreases correspondingly. Whereas
it increases with the increase of the driver size.
With integrated circuits shrinking into the nanometer scale, the
performance degradation and reliability problems for traditional
copper interconnects have emerged in recent years.
As one of
the most promising candidate materials in nanometer regime,
carbon nanotubes (CNTs) have received a number of scholars’
attention in view of unique mechanical, electrical, and thermal
Compared with copper material, CNTs have longer
mean free path (MFP) which can reach several micrometers. So
it can provide ballistic transport for shorter interconnects,
which leads to the lower resistivity in CNT interconnects.
Furthermore, current carrying density of CNTs can exceed
without any damage,
which greatly alleviates the
electro-migration problem induced by surface scattering and
grain-boundary scattering and thus improves the reliability of
integrated circuit. CNTs can be either metallic or semiconduct-
ing in the light of their chirality.
Nevertheless, only metallic
CNTs are preferred for interconnect.
To reduce the resistance
of isolated CNT, a great quantity of CNTs
need to be in parallel to form CNT bundle
interconnects in practical applications.
On account of so many advantages,
plenty of meaningful explorations about
CNT interconnects have been made, in-
cluding theoretical investigations and ex-
equivalent model of the traditional inter-
connect mainly includes the lumped model
and distributed model, which are used for
the modeling of the longer and shorter
interconnects, respectively. Considering
the effect of the resistance and capacitance
of the interconnect, the lumped RC model
was proposed in order to investigate the
performance of the interconnect.
However, the lumped RC model will be
inaccurate when the interconnect gets
longer. The distributed RC model for
current-mode signaling interconnect was
used to obtain the delay and power.
Moreover, the inductance effects cannot be neglected and need
to be considered in the delay and crosstalk models with the
increase of the operating frequency. Then the distributed RLC
models for the analysis of delay in a single transmission line and
a pair of coupled transmission lines were presented, respec-
Different from the modeling of the conventional
copper interconnect, the electrical equivalent circuit model of an
individual CNT was ﬁrstly proposed by Burke based on Lüttinger
which consists of the lumped and distributed
parts owing to its unique property. The multiconductor
transmission line (MTL) model for SWCNT bundle and
MWCNT interconnects was developed.
analysis based on the MTL method could be complex and
computationally expensive. As a result, in Refs. [19,20], the
equivalent single conductor (ESC) model was proposed and
widely applied, where all nanotubes or shells were assumed to be
parallel connected at both ends. From then on, many researchers
have deeply investigated the performance and application of
CNT bundle interconnects. In Refs. [21,22], Fathi et al. took
advantage of ABCD parameter matrix method to analyze the step
response, delay and relative stability of CNT interconnects.
However, the induced crosstalk badly affects the signal integrity
of circuit. In Ref. , coupling capacitance and mutual
inductance were taken into consideration for the transient
response and delay analyses. Besides the performances in the
time domain, bandwidth also plays an important role in the
performance of integrated circuits. A higher bandwidth for
interconnects can effectively decrease the total time to transmit a
Dr. S. Zhao, Prof. Z. Pan
School of Physics and Telecommunication Engineering
South China Normal University
Guangzhou 510006, China
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/pssa.201700459.
Carbon Nanotubes www.pss-a.com
Phys. Status Solidi A 2018, 215, 1700459 © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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