Equation (10.12) leads, for large values of the applied voltage, to a saturation
current of I 0 and this has interesting consequences for the conductance:
G ¼
I
V
¼
1
R 0 þ
V
j j
I 0
) lim
V !1
G ¼ 0
ð10: 13aÞ
Having this limiting value for the conductivity in mind, one may ask for the electrical
current under the conditions:
I j V !1 ¼ I saturation ¼ lim
V !1
V
R 0 þ
V
j j
I 0
¼ I 0
ð10: 13bÞ
Fo r i n finite voltages, the conductance vanishes and this saturation current was
observed experimentally. Experiments led to a value of 25 m A for the saturation
current I 0 , which is independent of the individual nanotube and is expected from
theory. Specifically, the value is independent of the nanotube length but, when
considering this saturation current and the dimensions, a single-wall nanotube can
carry a current density in the range of 10
13 A m
À2 (10
7 A mm
À2 ).
When comparing Figures 10.14 and 10.15 with Figures 10.16 and 10.17, as
expressed by Eqs. (10.10) and (10.12), an almost inverse I– V (respectively, R–V )
behavior between single-wall and multiwall nanotubes is apparent. It is important to
note again that isolated graphene layers behave like multiwall nanotubes.
Potentially, one of the most important applications of carbon nanotubes lies in
electronics, as it is possible to produce a field-effect transistor (FET) with just one
carbon nanotube, which lies between two gold contacts (that act as the source and
drain) and is in touch with the gate insulator. The set-up of such an FET, as first
realized at the IBM laboratories, is shown in Figure 10.18. Whilst it is astonishing
that this simple device will act as a transistor, it is equally surprising that the voltages
and currents controlled by such a nanotube FET (see Figure 10.19) are within a
Figure 10.18 Metal oxide FET made from a carbon nanotube [10] (www.research.ibm.com/
nanoscience/fet.html). Such a simple device shows much promise as it is operated with voltages
and currents that can be handled without major problems.
282j 10 Electrical Properties of Nanoparticles
current of I 0 and this has interesting consequences for the conductance:
G ¼
I
V
¼
1
R 0 þ
V
j j
I 0
) lim
V !1
G ¼ 0
ð10: 13aÞ
Having this limiting value for the conductivity in mind, one may ask for the electrical
current under the conditions:
I j V !1 ¼ I saturation ¼ lim
V !1
V
R 0 þ
V
j j
I 0
¼ I 0
ð10: 13bÞ
Fo r i n finite voltages, the conductance vanishes and this saturation current was
observed experimentally. Experiments led to a value of 25 m A for the saturation
current I 0 , which is independent of the individual nanotube and is expected from
theory. Specifically, the value is independent of the nanotube length but, when
considering this saturation current and the dimensions, a single-wall nanotube can
carry a current density in the range of 10
13 A m
À2 (10
7 A mm
À2 ).
When comparing Figures 10.14 and 10.15 with Figures 10.16 and 10.17, as
expressed by Eqs. (10.10) and (10.12), an almost inverse I– V (respectively, R–V )
behavior between single-wall and multiwall nanotubes is apparent. It is important to
note again that isolated graphene layers behave like multiwall nanotubes.
Potentially, one of the most important applications of carbon nanotubes lies in
electronics, as it is possible to produce a field-effect transistor (FET) with just one
carbon nanotube, which lies between two gold contacts (that act as the source and
drain) and is in touch with the gate insulator. The set-up of such an FET, as first
realized at the IBM laboratories, is shown in Figure 10.18. Whilst it is astonishing
that this simple device will act as a transistor, it is equally surprising that the voltages
and currents controlled by such a nanotube FET (see Figure 10.19) are within a
Figure 10.18 Metal oxide FET made from a carbon nanotube [10] (www.research.ibm.com/
nanoscience/fet.html). Such a simple device shows much promise as it is operated with voltages
and currents that can be handled without major problems.
282j 10 Electrical Properties of Nanoparticles