229
Electrical Properties
10
10.1
Fundamentals of Electric Conductivity; Diffusive versus Ballistic Conductivity
In a conventional metallic conductor, there is a huge number of electrons; after
connecting a voltage, they move slowly from one to the other end of the wire. This
is rather a drift than a directed movement. The electrons moving under the influence of an electrical field experience scattering processes leading to a change in
momentum by interactions with electrons, phonons, impurities, or other imperfections of the lattice. These processes are responsible for the electric losses.
Figure 10.1 displays these phenomena in a simplified way, where an Ohmic conductor, for example, a metallic wire, is connected to an electric circuit, electrons
are moving driven by the applied electric field.
The conventional process of electric conductivity called “diffusive conductance”
is ruled by Ohm’s law
V IR
I
G
G
I
V
=
=
=
or
.
(10.1)
In Eq. (10.1), the quantity V is the applied voltage, I the electrical current, R the
resistance, and G the electrical conductance. The validity of Ohm’s law implies
that the electrical resistance depends only on the geometry and material of
the conductor. The conductance G R
=
1 of a wire depends on the geometrical
parameters l, the length, and a, the cross section: G
l
a
= σ . The electric conductivity
σ is a material parameter. For metallic conductors the conductivity is independent
of the applied voltage and the electric current, for semiconductors or insulators,
the electric conductivity usually increases with increasing applied voltage. Wires
with dimensions in the nanometer range or molecular dimensions do not
follow Ohm’s law in any case. In particular, the strictly linear relation between
current and voltage is replaced by a nonlinear, non-Ohmic characteristic.
In metallic wires, electric conductivity is characterized by the mean free path of
the electrons, which is, in most well-crystallized metals, in the range of 50 nm.
When the geometric dimensions are in the range of or smaller than the mean free
Nanoparticles – Nanocomposites – Nanomaterials: An Introduction for Beginners, First Edition. Dieter Vollath.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.
Electrical Properties
10
10.1
Fundamentals of Electric Conductivity; Diffusive versus Ballistic Conductivity
In a conventional metallic conductor, there is a huge number of electrons; after
connecting a voltage, they move slowly from one to the other end of the wire. This
is rather a drift than a directed movement. The electrons moving under the influence of an electrical field experience scattering processes leading to a change in
momentum by interactions with electrons, phonons, impurities, or other imperfections of the lattice. These processes are responsible for the electric losses.
Figure 10.1 displays these phenomena in a simplified way, where an Ohmic conductor, for example, a metallic wire, is connected to an electric circuit, electrons
are moving driven by the applied electric field.
The conventional process of electric conductivity called “diffusive conductance”
is ruled by Ohm’s law
V IR
I
G
G
I
V
=
=
=
or
.
(10.1)
In Eq. (10.1), the quantity V is the applied voltage, I the electrical current, R the
resistance, and G the electrical conductance. The validity of Ohm’s law implies
that the electrical resistance depends only on the geometry and material of
the conductor. The conductance G R
=
1 of a wire depends on the geometrical
parameters l, the length, and a, the cross section: G
l
a
= σ . The electric conductivity
σ is a material parameter. For metallic conductors the conductivity is independent
of the applied voltage and the electric current, for semiconductors or insulators,
the electric conductivity usually increases with increasing applied voltage. Wires
with dimensions in the nanometer range or molecular dimensions do not
follow Ohm’s law in any case. In particular, the strictly linear relation between
current and voltage is replaced by a nonlinear, non-Ohmic characteristic.
In metallic wires, electric conductivity is characterized by the mean free path of
the electrons, which is, in most well-crystallized metals, in the range of 50 nm.
When the geometric dimensions are in the range of or smaller than the mean free
Nanoparticles – Nanocomposites – Nanomaterials: An Introduction for Beginners, First Edition. Dieter Vollath.
© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.