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R
QP/2
L
KP
Outermost shell
R
QP
/2
R
SP
L
MP
P
C
QP
C
sp-1
G
Tp
-1
R
mc
/2
R
mc
/2
M
1P
R
Q2
/2
R
S2
L
K2
L
M2
C
Q2
R
Q2/2
M
12
G
T1
C
s1
L
M1
R
Q1/2
L
K1
R
S1
C
Q1
R
Q1/2
1 ,
Innermost shell
C
E
Distributed Elements
Fig. 2.
Equivalent
RLC
model of MWCNT having
p
number of shells
Since all the interconnect parasitics of different shells vary in MWCNTs, the
potentials of different shells cannot be assumed to be equal as in the case of SWCNT
bundle. Therefore, a shell-to-shell coupling capacitance is introduced that arises due
to the small separation between two adjacent shells. The per unit length (
p.u.l.
) shell-
to-shell coupling capacitance (
C
S
) can be expressed as [13]
2
πε
2
πε
(6)
C
S
=
=
ln(
DD
)
ln
DD
(
−
2
δ
)
p
pp
p
−
1
Based on the aforementioned analysis, Li
et al
. [13] proposed a distributed
RLC
model for MWCNT interconnects as presented in Fig. 2. The resistance of each shell
in Fig. 2 can be defined as (1) quantum resistance
R
Q
, (2) scattering resistance
R
S
and
(3) imperfect metal-nanotube contact resistance
R
mc
. The scattering resistance (
R
S
)
occurs if the length of the nanotube is larger than the mean free path (
mfp
) of
electrons.
R
Q
and
R
S
are intrinsic, and the value of
R
mc
depends on the fabrication
process. The interconnect parasitics of MWCNT bundle is calculated using the
equivalent
RLC
model of Fig. 2 where each parasitic is modeled using the total
number of conducting channels in MWCNT. Therefore, the total resistance (
R
total
) can
be determined as [13]
h
h
(7)
R
=+=
R
QS
+
total
2
2
2
eN
2
eN
mfp
λ
2~ .9
where
he k
Ω
,
ʻ
mfp
and
N
are the
mfp
and total number of conducting channels
respectively. The
mfp
is calculated using the diameter of each shell in MWCNT.
Apart from this, the imperfect metal-nanotube contact resistance
R
mc
exhibits a value
ranging from zero to hundreds of kΩ depending on the different growth process [13].
Moreover, the tunneling conductance (
G
T
) depends on the diameter of each shell in
MWCNT [13].
