Semiconduct
or
Carbon Nanotube Diode Design
Simulation
Gary Pennington and Neil Goldsman,Department of Electrical and Computer Engineering
Motivation:
Band edge of junction
CNT Y-junction array
Recently techniques for the production of junctions
between different carbon nanotubes (CNT) have been
developed. The experimental observation that these
contacts exhibit nonlinear IV characteristics leads to their
potential application as molecular nanoscale device
components.
Objective:
Develop tube-diameter dependent models for the effective
mass, doping, band offset, and dielectric constant of a
CNT and then, using standard heterojunction physics,
relate the physical properties of a y-junction array of
CNTs (diameters) to its electrical properties (IV).
Unit cell
Side 1
Side 2
• Electron orbital hybridization gives acceptor density:
β
(
)
(
)
ΔE v = γa cc 1 d2 − 1 d1
• Linear response approximation gives dielectric constant :
dN A
⎛
⎞⎟
ε ∝ ⎜
*
m ⎠
⎝
X (CNT number in array)
Effective mass averaged over indices (n,m)
*
(acc d )
= 1.3m
e
Effective mass with varying dr (gcd)
m e :Electron mass
IV plot for a y-junction array
-V
(N,β ) constants
N A ∝ N a cc d
• Average bond energy method gives band offset:
m
Laboratory
a cc:C bond length
Average effective mass
d :diameter
Upper valence bands of CNT
• Treating semiconducting CNT y-junction as a
thermionic emitter of holes, obtain the forward
bias current:
⎛
⎞
eV
+
γ
a
1
d
−
1
d
⎜
cc (
2
1 ) ⎟
I d d (V ) = I o (d1 , d 2 )exp
1 2
⎜ k T ⎛⎜ 1+8(d d )2 (β −2 ) ⎞⎟ ⎟
1 2
⎠ ⎠
⎝ b ⎝
2 ( β −2 ) ⎤
⎡
)⎥⎦
(β −3 2 )
⎢ (β −1 2 ) (1+8 (d1 d2 )
⎣
d
⎛ acc ⎞
⎛
⎞
2
⎟
⎜ (1 2 −β ) ⎟
I o = α ⎜
⎜ d ⎟
⎜ 2
d ⎟
⎝ 2 ⎠
⎝
1 ⎠
(
)
2
≈ eN2a cc
πk b T 10
• Comparison with experiments of:
[ C. Papadopoulos et al., Phy. Rev. Lett. 85, 3476 (2001). ]
α
β = 2.74
N 2 ≅ 3X10
28
cm
−3
Conclusion:
•  Theory for CNT diameter dependence of effective
mass, doping, band offset, and dielectric constant
useful in predicting electric properties of rectifying
junctions.
•  Comparison with limited data available gives a
donor level of about one in every 60 Carbon atoms
in the CNT.