Handout 8
Carbon nanotubes
8.1
Introduction
In the last lecture we started to look at bandstructure engineering and the construction of “artificial”
materials. In this section we will take a closer look at one particular nanostructure; the carbon nanotube,
which is currently the focus of intense research. This system also provides us with an opportunity apply
many of the techniques of bandstructure calculation that we have learnt so far.
Carbon nanotubes are single sheets of graphite (called graphene) rolled into cylinders. The diameter
of the tubes are typically of nanometer dimensions, while the lengths are typically micrometers. This
huge aspect ratio leads to unusual electrical transport. Notably some tubes behaving as metals and
others as semiconductors.
The bandstructure of graphite was first calculated by Wallace in 19471 , but it was not until 1991
that multi-walled nanotubes were discovered2 . We will concentrate on single walled nanotubes which
were discovered in 1993.
8.2
Reading
Since carbon nanotubes are currently an area of active research the books on the subject tend to be
aimed at a research audience. For those of you who would like to read more about carbon nanotubes I
can recommend two books:
1. Physical properties of carbon nanotubes by Saito, Dresselhaus and Dresselhaus (Imperial College
Press, 1998).
2. Carbon Nanotubes, basic concepts and physical properties by Reich, Thomsen and Maultzsch
(Wiley, 2004).
8.3
Lecture slides
The following 7 pages reproduce the slides shown in the lectures.
1 See
2 S.
P.R. Wallace Physical Review, 71: 622-634 (1947)
Iijima, Nature 354: 56-58 (1991)
61
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8.3. LECTURE SLIDES
Figure 8.1 shows the band gaps
69
70
HANDOUT 8. CARBON NANOTUBES
4
-5
Lattice mismatch to silicon (%)
5
10
15
0
20
0.4
3
ZnSe
AlP
CdS
AlAs
GaP
0.5
ZnTe
2
CdTe
AlSb
GaAs
1
Si
SLE
(Ge)
0
InP
1.0
Bulk
5.5
GaSb
Ge
InAs
6.0
º)
Lattice constant (A
Sn
Wavelength (¹m)
Minimum energy bandgap (eV)
ZnS
1.5
2.0
InSb
3.0
HgTe 5.0
6.5
Figure 8.1: Band gap versus lattice parameter for some of the more common semiconductors. The
curves indicate commonly-used alloys such as (Ga,Al)As, (Ga,In)As etc.; solid curves represent direct
gaps and dashed curves indirect gaps.