ECE 802-604: Nanoelectronics

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ECE 802-604Nanoelectronics

• Prof. Virginia Ayres
• Electrical Computer Engineering
• Michigan State University
• ayresv_at_msu.edu

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Lecture 19, 31 Oct 13
Carbon Nanotubes and Graphene Carbon
nanotube/Graphene physical structure Carbon
bond hybridization is versatile sp1, sp2, and
sp3 sp2 origin of CNT/Graphene mechanical and
electronic structures CNT/Graphene electronic
properties
R. Saito, G. Dresselhaus and M.S.
Dresselhaus Physical Properties of Carbon
Nanotubes Imperial College Press, London, 1998.
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Lecture 19, 31 Oct 13
Carbon Nanotubes and Graphene Carbon
nanotube/Graphene physical structure SWCNT
endcaps Carbon bond hybridization is versatile
sp1, sp2, and sp3 sp2 origin of mechanical
and electronic structures Carbon
nanotube/Graphene electronic structure
R. Saito, G. Dresselhaus and M.S.
Dresselhaus Physical Properties of Carbon
Nanotubes Imperial College Press, London, 1998.
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Lec 17 Introduction
Buckyball endcaps
Many different types of wrapping result in a
seamless cylinder. But The particular cylinder
wrapping dictates the electronic and mechanical
properties.
(10,10)
(9,0)
(7,4)
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Endcaps ½ stable buckyball C60
From Wikipedia C60 is very stable truncated
icosahedron 60 vertices with a carbon atom at
each vertex and 32 faces 20 hexagons and 12
pentagons where no pentagons share a vertex The
van der Waals diameter of a C60 molecule is about
1.1 nanometers (nm)
http//www.sesres.com/PhysicalProperties.asp C60
mean ball diameter  6.83 Å C60 ball outer
diameter  10.18 Å C60 ball inner diameter  3.48 Å
http//www.creative-science.org.uk/c60model.html
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Show same idea on a SWCNT
Outer (Van Der Waals)
Mean structure dt
Inner (repulsion)
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Endcaps ½ stable buckyball C60
From Wikipedia C60 is very stable truncated
icosahedron 60 vertices with a carbon atom at
each vertex and 32 faces 20 hexagons and 12
pentagons where no pentagons share a vertex The
van der Waals diameter of a C60 molecule is about
1.1 nanometers (nm)
http//www.sesres.com/PhysicalProperties.asp C60
mean ball diameter  6.83 Å C60 ball outer
diameter  10.18 Å C60 ball inner diameter  3.48 Å
Example which diameter should you use as an
estimate for matching a SWCNT diameter?
http//www.creative-science.org.uk/c60model.html
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Endcaps ½ stable buckyball C60
From Wikipedia C60 is very stable truncated
icosahedron 60 vertices with a carbon atom at
each vertex and 32 faces 20 hexagons and 12
pentagons where no pentagons share a vertex The
van der Waals diameter of a C60 molecule is about
1.1 nanometers (nm)
http//www.sesres.com/PhysicalProperties.asp C60
mean ball diameter  6.83 Å C60 ball outer
diameter  10.18 Å C60 ball inner diameter  3.48 Å
Example which diameter should you use as an
estimate for matching a SWCNT diameter? Answer
http//www.creative-science.org.uk/c60model.html
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Endcaps ½ stable buckyball C70
From Wikipedia C70 is also stable 70 vertices
with a carbon atom at each vertex 25 hexagons
and 12 pentagons The mean ball diameter is ?
LBL The structure of C70 molecule. Red atoms
indicate five hexagons additional to the C60
molecule.
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C60
Guess C70
Guess C36
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Endcaps ½ stable buckyball C36
http//www.lbl.gov/tt/techs/lbnl1366.html The
above image depicts the D6h isomer of the C36
molecule Piskoti C., Yarger J., Zettl A., "A New
Carbon Solid", Letters to Nature, v 393, 1997.
XZ Ke, et al, Physics Letters A 255 (1999) 294-300
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Endcaps ½ stable buckyball C20
The smallest possible buckyball is the
dodecahedral C20, a shape consisting of 12
pentagonal faces and no hexagonal faces.
4 angstroms
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Endcaps ½ stable buckyball C20 ? smallest SWCNT
inside MWCNT
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Example Problems

1. Based on dt 0.4 nm, what ultrasmall SWCNT
   structures (n.m) are possible?
2. What types of CNT are they?
3. What physical issues would be involved in the
   self-assembly of these SWCNTs?

HW04 Find Ch, Ch , cosq, q, T, T , and N for
the smallest SWCNT capped with a C20.
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Lecture 19, 31 Oct 13
Carbon Nanotubes and Graphene Carbon
nanotube/Graphene physical structure Carbon
bond hybridization is versatile sp1, sp2, and
sp3 sp2 origin of CNT/Graphene mechanical and
electronic structures CNT/Graphene electronic
properties
R. Saito, G. Dresselhaus and M.S.
Dresselhaus Physical Properties of Carbon
Nanotubes Imperial College Press, London,
1998. A. Beiser, Modern Physics, Chapter 13 E.
Anderson, Quantum Mechanics, Chapter 7
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diamond
Benzene/graphene/CNTs/buckyballs
polyacetylene
acetylene
alkane
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These are simulations of e- y2 with 1s, 2s, and
2p marked
Anderson, Quantum Mechanics
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The corresponding y are
3D in spherical coordinates
Anderson, Quantum Mechanics
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So all of the directional character must come
from 2p orbitals

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Beiser, Modern Physics Boundary surface
diagrams s-orbitals are all spherical no
preferred direction p-orbitals are highly
directional
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A carbon hybrid orbital comes from combining a 2s
and a 2p
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sp1 (sp) hybridization

• sp1 hybridization
• Use orthonormality

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Problem without hybridization

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sp1 hybridization
ONE

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sp1 hybridization
ONE

Warning watch axes, these directions have real
meaning
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sp1 hybridization

Warning watch axes, these directions have real
meaning
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sp1 hybridization
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sp1 hybridization
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sp1 hybridization
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sp1 hybridization
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sp1 hybridization
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sp1 hybridization
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sp1 hybridization
Can get the 4th equation for 4 unknowns from the
spherical character of the 2sgt components
Therefore
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sp1 hybridization

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sp1 hybridization

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sp1 hybridization

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Therefore acetylene is
sp1 hybridization