# Nanotechnology/Semiconducting Nanostructures#Semiconducting nanowires

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# Nanotubes

Certain compounds are capable of forming nanotubes where the tube
consists of round shell of a single layer of atoms in a cylindrical
lattice. Carbon nanotubes is the most famous example, but also other
materials can form nanotubes such as Boron-nitride, Molybdenum sulfide
and others.

Nanotubes can also be made by etching the core out of an shell
structured rod, but such tubes will normally contain many atomic layers
in the wall and have crystal facets on the sides.

# Carbon Nanotubes

Carbon nanotubes are fascinating nanostructures. A sheet of graphene as
in common graphite, but rolled up in small tubes rather than planar
sheets.

Carbon nanotubes have unique mechanical properties such as high
strength, high stiffness, and low density [^1] and also interesting
electronic properties. A single-walled carbon nanotube can be either
metallic or semiconducting depending on the atomic arrangement [^2].

This section is a short introduction to carbon nanotubes. For a broader
overview the reader is referred to one of the numerous review articles
or books on carbon nanotubes

[^3] [^4] [^5]

## Geometric Structure

The simplest type of carbon nanotube consists of just one layer of
graphene rolled up in the form of a seamless cylinder, known as a
single-walled carbon nanotube (SWCNT) with a typical diameter of just a
few nanometers. Larger diameter nanotube structures are nanotube ropes,
consisting of many individual, parallel nanotubes closed-packed into a
hexagonal lattice, and multi-walled carbon nanotubes (MWCNTs) consisting
of several concentric cylinders nested within each other.

! Multiwall carbon nanotube (MWCNT) sample made by a CVD process using
iron containing catalystic particles. The MWCNT are adhering in
mats. sample made by a CVD process using iron containing catalystic particles. The MWCNT are adhering in mats."){width="300"}

### Single walled Carbon Nanotube

The basic configuration is thus the SWCNT. Its structure is most easily
illustrated as a cylindrical tube conceptually formed by the wrapping of
a single graphene sheet. The hexagonal structure of the 2-dimensional
graphene sheet is due to the $sp^{2}$ hybridization of the carbon atoms,
which causes three directional, in-plane $\sigma$ bonds separated by an
angle of 120 degrees.

The nanotube can be described by a chiral vector $C$ that can be
expressed in terms of the graphene unit vectors $\textbf{a}_{1}$ and
$\textbf{a}_{2}$ as $\textbf{C}=n\textbf{a}_{1}+m\textbf{a}_{2}$ with
the set of integers $(n,m)$ uniquely identifying the nanotube. This
chiral vector or \'roll-up\' vector describes the nanotube circumference
by connecting two crystallographically equivalent positions i.e. the
tube is formed by superimposing the two ends of $\textbf{C}$.

Based on the chiral angle SWCNTs are defined as zig-zag tubes
($\theta =0 deg \leftrightarrow m=0$), armchair tubes
($\theta =30 deg \leftrightarrow n=m$), or chiral tubes
($0 deg < \theta  < 30 deg$).

### Multiwalled Carbon Nanotubes

MWCNTs are composed of a number of SWCNTs in a coaxial geometry. Each
nested shell has a diameter of
$d=\sqrt{3}a_{C-C}(m^{2}+n^{2}+mn)^{1/2}/\pi$ where $a_{C-C}$ is the
length of the carbon-carbon bond which is 1.42 Å. The difference in
diameters of the individual shell means that their chiralities are
different, and adjacent shell are therefore in general non-commensurate,
which causes only a weak intershell interaction.

The intershell spacing in MWCNTs is $\sim$ 0.34 nm - quite close to the
interlayer spacing in turbostratic graphite [^6]

## Electronic Structure

The electronic structure of a SWCNT is most easily described by again
considering a single graphene sheet. The 2-D, hexagonal-lattice graphene
sheet has a 2-D reciprocal space with a hexagonal Brillouin zone (BZ).

The $\sigma$ bonds are mainly responsible for the mechanical properties,
while the electronic properties are mainly determined by the $\pi$
bands. By a tight-binding approach the band structure of these $\pi$
bands can be calculated [^7]

Graphene is a zero-gap semiconductor with an occupied $\pi$ band and an
unoccupied $\pi^{*}$ band meeting at the Fermi level at six $K$ points
in the BZ, thus it behaves metallic, a so-called semimetal.

Upon forming the tube by conceptually wrapping the graphene sheet, a
periodic boundary condition is imposed that causes only certain
electronic states of those of the planar graphene sheet to be allowed.
These states are determined by the tube\'s geometric structure, i.e. by
the indices $(n,m)$ of the chiral vector. The wave vectors of the
allowed states fall on certain lines in the graphene BZ.

Based on this scheme it is possible to estimate whether a particular
tube will be metallic or semiconducting. When the allowed states include
the $K$ point, the system will to a first approximation behave metallic.
However, in the points where the $\pi$ and the $\pi^{*}$ bands meet but
are shifted slightly away from the $K$ point due to curvature effects,
which causes a slight band opening in some cases [^8]

This leads to a classification scheme that has three types of nanotubes:

-   Metallic: These are the armchair tubes where the small shift of the
    degenerate point away from the $K$ point does not cause a band
    opening for symmetry reasons.

```{=html}
<!-- -->
```
-   Small-bandgap semiconducting: These are characterized by $n-m = 3j$
    with $j$ being an integer. Here, the wave vectors of the allowed
    states cross the $K$ point, but due to the slight shift of the
    degenerate point a small gap will be present, the size of which is
    inversely proportional to the tube diameter squared with typical
    values between a few and a few tens meV

[^9]

-   Semiconducting: In this case $n-m \neq 3j$. This causes a larger
    bandgap, the size of which is inversely proportional to the tube
    diameter: $E_{g}=k/d$ with experimental investigations suggesting a
    value of $k$ of 0.7-0.8 eV/nm

[^10]

Typically the bandgap of the type 2 nanotubes is so small that they can
be considered metallic at room temperature. Based on this it can be
inferred that 1/3 of all tubes should behave metallic whereas the
remaining 2/3 should be semiconducting. However, it should be noted that
due to the inverse proportionality between the bandgap and the diameter
of the semiconducting tubes, large-diameter tubes will tend to behave
metallic at room temperature. This is especially important in regards to
large-diameter MWCNTs.

From a electrical point of view a MWCNT can be seen as a complex
structure of many parallel conductors that are only weakly interacting.
Since probing the electrical properties typically involves electrodes
contacting the outermost shell, this shell will be dominating the
transport properties [^11] In a simplistic view, this can be compared to
a large-diameter SWCNT, which will therefore typically display metallic
behavior.

## Electrical and Electromechanical Properties

Many studies have focused on SWCNTs for exploring the fundamental
properties of nanotubes. Due to their essentially 1-D nature and
intriguing electronic structure, SWCNTs exhibit a range of interesting
quantum phenomena at low temperature [^12]

The discussion here will so far, however, primarily be limited to room
temperature properties.

The conductance $~G~$ of a 1-dimensional conductor such as a SWCNT is
given by the Landauer formula [^13]

$~G=G_{0}\sum_{i}T_{i}~$,

where $~G_{0}=2e^{2}/h = (12.9 \rm k\Omega)^{-1}$;\
$~1/G_{0}~$ is the conductance quantum;\
and $~T_{i}~$ is the transmission coefficient of the contributing
channel $~i~$.

## More information on nanotubes

-   Wikipedia  Carbon nanotubes
-   The nanotube site
-   Compiled overview of properties of carbon
    nanotubes

## Commercial suppliers of carbon nanotubes and related products

-   Nanoledge.com nanotubes and related
    products - fibers, pellets, resins and dispersions\...
-   Carbon Solution, Inc. Mainly
    SWCNT.
-   BuckyUSA Fullerens, SWCNT, MWCNT.
-   CNI
    HiPco Carbon nanotubes
-   Carbolex SWCNT,sub-gram quantities are
    sold via sigma aldric
-   Sigma-Aldrich
    SWCNT

## \"Buckyball\"

!C~60~ with isosurface of ground state electron density as calculated
with
DFT{width="160"}
!An w:association football is a
model of the Buckminsterfullerene
C~60~{width="160"}

**Buckminsterfullerene** (IUPAC name
**(C~60~-I~h~)\[5,6\]fullerene**) is the smallest fullerene molecule in
which no two pentagons share an edge (which can be destabilizing, as in
pentalene). It is also the most common in
terms of natural occurrence, as it can often be found in
soot.

The structure of C~60~ is a truncated (T = 3)
icosahedron, which resembles a
soccer ball#Association_football "wikilink") of the
type made of twenty hexagons and twelve pentagons, with a carbon atom at
the vertices of each polygon and a bond along each polygon edge.

The w:van der Waals diameter of a
C~60~ molecule is about 1 nanometer (nm). The
nucleus to nucleus diameter of a C~60~ molecule is about 0.7 nm.

The C~60~ molecule has two bond lengths. The 6:6 ring bonds (between two
hexagons) can be considered \"double bonds\"
and are shorter than the 6:5 bonds (between a hexagon and a pentagon).
Its average bond length is 1.4 angstroms.

Silicon buckyballs have been created around metal ions.

### Boron buckyball

A new type of buckyball utilizing boron atoms
instead of the usual carbon has been predicted and described by
researchers at Rice University. The B-80 structure, with each atom
forming 5 or 6 bonds, is predicted to be more stable than the C-60
buckyball.[^14] One reason for this given by the researchers is that the
B-80 is actually more like the original geodesic dome structure
popularized by Buckminster Fuller which utilizes triangles rather than
hexagons. However, this work has been subject to much criticism by
quantum chemists[^15][^16] as it was concluded that the predicted Ih
symmetric structure was vibrationally unstable and the resulting cage
undergoes a spontaneous symmetry break yielding a puckered cage with
rare Th symmetry (symmetry of a
volleyball "wikilink"))[^17]. The number of six
atom rings in this molecule is 20 and number of five member rings is 12.
There is an additional atom in the center of each six member ring,
bonded to each atom surrounding it.

### Variations of buckyballs

Another fairly common buckminsterfullerene is C~70~,[^18] but fullerenes
with 72, 76, 84 and even up to 100 carbon atoms are commonly obtained.

In mathematical terms, the structure of a
**fullerene** is a trivalent "wikilink") convex
polyhedron with pentagonal and hexagonal
faces. In graph theory, the term
**fullerene** refers to any 3-regular,
planar graph with all faces of size 5 or 6
(including the external face). It follows from Euler\'s polyhedron
formula, \|V\|-\|E\|+\|F\| = 2,
(where \|V\|, \|E\|, \|F\| indicate the number of vertices, edges, and
faces), that there are exactly 12 pentagons in a fullerene and
\|V\|/2-10 hexagons.

+----------------+----------------+----------------+----------------+
| ![]            | ![]            | ![]            | ![]            |
| (Graph_of_20-f | (Graph_of_26-f | (Graph_of_60-f | (Graph_of_70-f |
| ullerene_w-nod | ullerene_5-bas | ullerene_w-nod | ullerene_w-nod |
| es.svg "Graph_ | e_w-nodes.svg  | es.svg "Graph_ | es.svg "Graph_ |
| of_20-fulleren | "Graph_of_26-f | of_60-fulleren | of_70-fulleren |
| e_w-nodes.svg" | ullerene_5-bas | e_w-nodes.svg" | e_w-nodes.svg" |
| ){width="200"} | e_w-nodes.svg" | ){width="200"} | ){width="200"} |
|                | ){width="200"} |                |                |
+----------------+----------------+----------------+----------------+
| 20-fullerene\  | 26-fullerene   | 60-fullerene\  | 70-fullerene   |
| (dodecahedral  | graph          | (truncated     | graph          |
| graph)         |                | icosahedral    |                |
|                |                | graph)         |                |
+----------------+----------------+----------------+----------------+

The smallest fullerene is the
w:dodecahedron\--the unique C~20~. There
are no fullerenes with 22 vertices.[^19] The number of fullerenes C~2n~
grows with increasing n = 12,13,14\..., roughly in proportion to n^9^.
For instance, there are 1812 non-isomorphic fullerenes C~60~. Note that
only one form of C~60~, the buckminsterfullerene alias w:truncated
icosahedron, has no pair of
adjacent pentagons (the smallest such fullerene). To further illustrate
the growth, there are 214,127,713 non-isomorphic fullerenes C~200~,
15,655,672 of which have no adjacent pentagons.

w:Trimetasphere carbon nanomaterials were
discovered by researchers at w:Virginia
Tech and licensed exclusively to w:Luna
Innovations. This class of novel
molecules comprises 80 carbon atoms (C80) forming a sphere which
encloses a complex of three metal atoms and one nitrogen atom. These
fullerenes encapsulate metals which puts them in the subset referred to
as w:metallofullerenes. Trimetaspheres
have the potential for use in diagnostics (as safe imaging agents),
therapeutics and in organic solar
cells.

# Semiconducting nanowires

Semiconducting nanowires can be made from most semiconducting materials
and with different methods, mainly variations of a chemical vapor
deposition process (CVD).

There are many different semiconducting materials, and heterosrtuctures
can be made if the lattice constants are not too incompatible.
Heterostructures made from combinations of materials such as GaAs-GaP
can be used to make barriers and guides for electrons in electrical
systems.

Low pressure metal organic vapor phase epitaxy (MOVPE) can be used to
grow III-V nanowires epitaxially on suitable crystalline substrates,
sucha s III-V materials or silicon with a reasonably matching lattice
constant.

!Low pressure metal organic vapor phase epitaxy (MOVPE) can be used to
grow III-V nanowires epitaxially on suitable crystalline substrates,
sucha s III-V materials or silicon with a reasonably matching lattice
constant. Nanowire growth is catalyzed by various nanoparticles, which
are deposited on the substrate surface, typically gold nanoparticles
with a diameter of 20-100nm.
 can be used to grow III-V nanowires epitaxially on suitable crystalline substrates, sucha s III-V materials or silicon with a reasonably matching lattice constant. Nanowire growth is catalyzed by various nanoparticles, which are deposited on the substrate surface, typically gold nanoparticles with a diameter of 20-100nm. "){width="300"}

Nanowire growth is catalyzed by various nanoparticles, which are
deposited on the substrate surface, typically gold nanoparticles with a
diameter of 20-100nm.

To grow for instance GaP wires, the sample is typically annealed at 650C
in the heated reactor chamber to form an eutectic with between the gold
catalyst and the underlying substrate.

Then growth is done at a lower temperature around 500C in the presence
of the precursor gasses trimethyl gallium and phosphine. By changing the
precursor gasses during growth, nanowire heterostructures with varying
composition can be made

!SEM image of epitaxial nanowire heterostructures grown from catalytic
gold
nanoparticles{width="400"}

## Resources

-   wikipedia  Semiconducting nanowires
-   IOFFE semiconductor physical
    properties

# Nanoparticles

-    Nanoparticles
-    Quantum dots

## Catalytic particles

-    Catalyst
-    Catalysis
-    Haber process

## Commercial suppliers of nanoparticles

-   Reade has a wide selection of
    nanoparticles
-   sigma-aldrich
    has dispersions of
    nanoparticles
-   nanophase

# Contributors and Acknowledgements

-   Jakob Kjelstrup Hansen

# References

See also notes on editing this book about how to add references
Nanotechnology/About#How_to_contribute.

```{=html}
<references />
```

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[^1]: qian2002

[^2]: hamada1992

[^3]: avouris2003

[^4]: dresselhaus2001

[^5]: saito1998

[^6]: dresselhaus2001

[^7]: saito1998

[^8]: hamada1992.

[^9]: zhou2000

[^10]: wildoer1998,odom1998

[^11]: frank1998

[^12]: nygard1999,dresselhaus2001

[^13]: datta1995

[^14]: *Bucky\'s brother \-- The boron buckyball makes its début* Jade
    Boyd April **2007**
    eurekalert.orgLink

[^15]: *The boron buckyball has an unexpected Th symmetry* G. Gopakumar,
    Nguyen, M. T., Ceulemans, Arnout, Chem. Phys. lett. 450, 175,
    2008.1&_cdi=5231&_sort=d&_docanchor=&view=c&_ct=53&_acct=C000024498&_version=1&_urlVersion=0&_userid=4466739&md5=2e8f3b9eacbc9a4b9a3dbd42fdbf2826)

[^16]: \"Stuffing improves the stability of fullerenelike boron
    clusters\" Prasad, DLVK; Jemmis, E. D.; Phys. Rev. Lett. 100,
    165504,
    2008.2

[^17]:

[^18]: Buckminsterfullerene: Molecule of the
    Month

[^19]: Goldberg Variations Challenge: Juris Meija, Anal. Bioanal. Chem.
    2006 (385)
    6-7
