04-03-2013, 10:58 AM
Electronic Structure of nanotubes.
[attachment=52501]
INTRODUCTION
The remarkable electrical properties of single wall carbon nanotubes stem from the unusual
electronic structure of “graphene”- the 2-D material from which they are made. (Graphene is
simply a single atomic layer of graphite.). The band structure of graphene is not same as that of a
metal or a semiconductor. Instead it is in between these two extremes. In most directions,
electrons moving at the Fermi energy are backscattered by atoms in the lattice whereas in some
others they don’t. Graphene therefore can be considered as a semi-metal, since it is metallic in
these special directions and semiconducting in the others. Thus a nanotube can be either a metal
or a semiconductor, depending on how the tube is rolled up.
Whereas the multiwall nanotubes were tens of nanometres across, the typical diameter of a
single-wall nanotube was just one or two nanometres. The past decade has seen an explosion of
research into both types of nanotube. The multi walled carbon nanotubes should behave slightly
different to their single walled relatives due to the interaction of the adjacent layers. Though
various theories can be incorporated, many of them may not hold true for such microscopic
materials.
Nanotubes as one dimensional metals
Solid –state devices in which electrons are confined to two-dimensional planes have provided
some of the exciting scientific and technological breakthroughs of the past many decades.
However, 1-D systems are also proving to be very exciting. Studies of quasi 1-D systems, such as
conducting polymers , study of ballistic systems, electron waveguides and many other fields that
may transform the face of electronics fall into this category. The 1-d systems on which these
phenomena can be studied have been limited by the fact that they are inherently complex to
make. What has been lacking is the perfect model system for exploring one dimensional transport
– a 1-d conductor that is cheap and easy to make. , can be individually manipulated and
measured, and has little structural disorder. Single walled carbon nanotubes fit this bill
remarkably well.
Nanotubes are ideal systems for studying the transport of electrons in one dimension, and have
commercial potential as nanoscale wires, transistors and sensors. For many years, studies of
quasi-one-dimensional systems, such as conducting polymers, have provided a fascinating insight
into the nature of electronic instabilities in one dimension. In addition, 1-D devices such as
"electron waveguides" - in which electrons propagate through a narrow channel of material - have
been created. Experiments on these devices have shown, for example, that the conductance of
"ballistic" 1-D systems - in which electrons travel the length of the channel without being
scattered - is quantized in units of the charge on the electron squared divided by the Planck
constant.
More on Electronic properties
Carbon nanotubes are giant molecular wires in which electrons can propagate freely, just as they
do in an ordinary metal. This contrasts strongly with conventional "conducting" polymers in
which the electrons are localized. These molecules are actually insulators and only become
conductors if they are heavily doped. Graphite, on the other hand, can conduct electricity because
one of the four valence electrons associated with each carbon atom is delocalized and can
therefore be shared by all the carbon atoms.
However, it turns out that a single sheet of graphite (also known as graphene) is an electronic
hybrid: although not an insulator, it is not a semiconductor or a metal either. Graphene is a
"semimetal" or a "zero-gap" semiconductor.
This peculiarity means that the electronic states of graphene are very sensitive to additional
boundary conditions, such as those imposed by rolling the graphene into a tube. It can be shown
that a stationary electron wave can only develop if the circumference of the nanotube is a multiple
of the electron wavelength. This boundary condition means that a nanotube is either a true metal
or a semiconductor - a fact that has been confirmed in experiments with single-wall nanotubes.
Field emission
The small diameter of carbon nanotubes is very favourable for field emission - the process by
which a device emits electrons when an electric field or voltage is applied to it. Field emission is
important in several areas of industry, including lighting and displays, and the relatively low
voltages needed for field emission in nanotubes could be an advantage in many applications.
However, as with all new technologies, there are formidable obstacles to be overcome.
To make a field-emission source with just one nanotube, individual multiwall nanotubes were
mounted onto a gold tip. The nanotubes were kept in place by van der Waals forces alone (i.e.
adhesive was not used). The field emissions from multiwall nanotubes with open and closed ends
were compared. Nanotubes grown in arc discharges are normally closed, but they can be opened
by applying a very large electric field, or by treating them with oxygen at high temperature. Field
emission occurred when a potential of a few hundred volts was applied to the gold tip. Both open
and closed nanotubes were capable of emitting currents as high as 0.1 mA, which represents a
tremendous current density for such a small object.
Measuring Conductance of nanotubes
Before we can measure the conducting properties of a nanotube, we have to wire up the tube by
attaching metallic electrodes to it. The electrodes, which can be connected to either a single tube
or a bundle of tubes, are usually made using electron-beam lithography. This can be done in many
ways and many others are on the way to becoming feasible in the lab. These include the
possibility of growing the tubes between electrodes, or by attaching the tubes to the surface in a
controllable fashion using either electrostatic or chemical forces. Other relatively conventional
methods include the making of the electrodes and dropping the nanotubes onto them. Another is
to deposit the tubes on the substrate, locate them with a scanning probe microscope, and then
attach leads to the tubes using lithography.
The “source” and the “drain “ electrodes allow the conducting properties to be measured. In
addition a third terminal –“gate” is often used. The gate and the tube act like the two plates of a
capacitor, which means that the gate can be used to electrostatically induce carriers on the tube.
When the conductance of the tubes are measured as a function of the gate voltage, two types of
behaviour are observed, corresponding to metal and semiconductor tubes.
Nanotube rectifier
It is created by the intersection of two nanotubes such as a metallic tube crossing over a
semiconducting tube. The metallic tube locally depletes the holes in the underlying p-type
semiconductor tube. That is an electron traversing the semiconducting tube must overcome the
barrier created by this metal tube. Biasing one end of the semiconducting tube relative to the
metal tube leads to rectifying behaviour.
Nanotubes as model 1-Dimensional systems
The conductance of some nanotubes are near room temperature are not noticeably affected by the
addition of a few carriers. This behaviour is typical of metals which have a large number of
carriers and have conducting properties that are not significantly affected by the addition of a few
more carriers. The conductances of these metallic nanotubes are much larger than the
semiconducting nanotubes. It implies that electrons can travel for distances of several microns
down a tube before they are scattered. The experiments also showed that electrons can travel for
long distances in nanotubes without being backscattered. Whereas in striking contrast is the
behaviour of metals in which scattering length from lattice vibrations are typically only several
nanometers at room temperature.The main reason for this difference is that an electron in a 1-D
system can only scatter by completely reversing its direction whereas electrons in a 2-D or 3-D
material can scatter by simply changing changing direction through a tiny angle.
[attachment=52501]
INTRODUCTION
The remarkable electrical properties of single wall carbon nanotubes stem from the unusual
electronic structure of “graphene”- the 2-D material from which they are made. (Graphene is
simply a single atomic layer of graphite.). The band structure of graphene is not same as that of a
metal or a semiconductor. Instead it is in between these two extremes. In most directions,
electrons moving at the Fermi energy are backscattered by atoms in the lattice whereas in some
others they don’t. Graphene therefore can be considered as a semi-metal, since it is metallic in
these special directions and semiconducting in the others. Thus a nanotube can be either a metal
or a semiconductor, depending on how the tube is rolled up.
Whereas the multiwall nanotubes were tens of nanometres across, the typical diameter of a
single-wall nanotube was just one or two nanometres. The past decade has seen an explosion of
research into both types of nanotube. The multi walled carbon nanotubes should behave slightly
different to their single walled relatives due to the interaction of the adjacent layers. Though
various theories can be incorporated, many of them may not hold true for such microscopic
materials.
Nanotubes as one dimensional metals
Solid –state devices in which electrons are confined to two-dimensional planes have provided
some of the exciting scientific and technological breakthroughs of the past many decades.
However, 1-D systems are also proving to be very exciting. Studies of quasi 1-D systems, such as
conducting polymers , study of ballistic systems, electron waveguides and many other fields that
may transform the face of electronics fall into this category. The 1-d systems on which these
phenomena can be studied have been limited by the fact that they are inherently complex to
make. What has been lacking is the perfect model system for exploring one dimensional transport
– a 1-d conductor that is cheap and easy to make. , can be individually manipulated and
measured, and has little structural disorder. Single walled carbon nanotubes fit this bill
remarkably well.
Nanotubes are ideal systems for studying the transport of electrons in one dimension, and have
commercial potential as nanoscale wires, transistors and sensors. For many years, studies of
quasi-one-dimensional systems, such as conducting polymers, have provided a fascinating insight
into the nature of electronic instabilities in one dimension. In addition, 1-D devices such as
"electron waveguides" - in which electrons propagate through a narrow channel of material - have
been created. Experiments on these devices have shown, for example, that the conductance of
"ballistic" 1-D systems - in which electrons travel the length of the channel without being
scattered - is quantized in units of the charge on the electron squared divided by the Planck
constant.
More on Electronic properties
Carbon nanotubes are giant molecular wires in which electrons can propagate freely, just as they
do in an ordinary metal. This contrasts strongly with conventional "conducting" polymers in
which the electrons are localized. These molecules are actually insulators and only become
conductors if they are heavily doped. Graphite, on the other hand, can conduct electricity because
one of the four valence electrons associated with each carbon atom is delocalized and can
therefore be shared by all the carbon atoms.
However, it turns out that a single sheet of graphite (also known as graphene) is an electronic
hybrid: although not an insulator, it is not a semiconductor or a metal either. Graphene is a
"semimetal" or a "zero-gap" semiconductor.
This peculiarity means that the electronic states of graphene are very sensitive to additional
boundary conditions, such as those imposed by rolling the graphene into a tube. It can be shown
that a stationary electron wave can only develop if the circumference of the nanotube is a multiple
of the electron wavelength. This boundary condition means that a nanotube is either a true metal
or a semiconductor - a fact that has been confirmed in experiments with single-wall nanotubes.
Field emission
The small diameter of carbon nanotubes is very favourable for field emission - the process by
which a device emits electrons when an electric field or voltage is applied to it. Field emission is
important in several areas of industry, including lighting and displays, and the relatively low
voltages needed for field emission in nanotubes could be an advantage in many applications.
However, as with all new technologies, there are formidable obstacles to be overcome.
To make a field-emission source with just one nanotube, individual multiwall nanotubes were
mounted onto a gold tip. The nanotubes were kept in place by van der Waals forces alone (i.e.
adhesive was not used). The field emissions from multiwall nanotubes with open and closed ends
were compared. Nanotubes grown in arc discharges are normally closed, but they can be opened
by applying a very large electric field, or by treating them with oxygen at high temperature. Field
emission occurred when a potential of a few hundred volts was applied to the gold tip. Both open
and closed nanotubes were capable of emitting currents as high as 0.1 mA, which represents a
tremendous current density for such a small object.
Measuring Conductance of nanotubes
Before we can measure the conducting properties of a nanotube, we have to wire up the tube by
attaching metallic electrodes to it. The electrodes, which can be connected to either a single tube
or a bundle of tubes, are usually made using electron-beam lithography. This can be done in many
ways and many others are on the way to becoming feasible in the lab. These include the
possibility of growing the tubes between electrodes, or by attaching the tubes to the surface in a
controllable fashion using either electrostatic or chemical forces. Other relatively conventional
methods include the making of the electrodes and dropping the nanotubes onto them. Another is
to deposit the tubes on the substrate, locate them with a scanning probe microscope, and then
attach leads to the tubes using lithography.
The “source” and the “drain “ electrodes allow the conducting properties to be measured. In
addition a third terminal –“gate” is often used. The gate and the tube act like the two plates of a
capacitor, which means that the gate can be used to electrostatically induce carriers on the tube.
When the conductance of the tubes are measured as a function of the gate voltage, two types of
behaviour are observed, corresponding to metal and semiconductor tubes.
Nanotube rectifier
It is created by the intersection of two nanotubes such as a metallic tube crossing over a
semiconducting tube. The metallic tube locally depletes the holes in the underlying p-type
semiconductor tube. That is an electron traversing the semiconducting tube must overcome the
barrier created by this metal tube. Biasing one end of the semiconducting tube relative to the
metal tube leads to rectifying behaviour.
Nanotubes as model 1-Dimensional systems
The conductance of some nanotubes are near room temperature are not noticeably affected by the
addition of a few carriers. This behaviour is typical of metals which have a large number of
carriers and have conducting properties that are not significantly affected by the addition of a few
more carriers. The conductances of these metallic nanotubes are much larger than the
semiconducting nanotubes. It implies that electrons can travel for distances of several microns
down a tube before they are scattered. The experiments also showed that electrons can travel for
long distances in nanotubes without being backscattered. Whereas in striking contrast is the
behaviour of metals in which scattering length from lattice vibrations are typically only several
nanometers at room temperature.The main reason for this difference is that an electron in a 1-D
system can only scatter by completely reversing its direction whereas electrons in a 2-D or 3-D
material can scatter by simply changing changing direction through a tiny angle.