Solid State Physics
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the hole states which are the dominant charge carriers and hence they have
positive Hall coefficients (see Example 3 in Sec. 8.8).
Metals, Insulators and Semiconductors
The existence of energy bands, i.e., the allowed bands consisting of allowed
energy levels and forbidden bands which are the gaps between the allowed
bands, provides a simple explanation for the general properties of metals,
insulators and semiconductors.
Consider the order in which the energy levels of the energy bands are filled.
To start with, the electrons in the inner shells fill the corresponding narrow
energy bands, and are not influential in determining the general properties of
the crystal. The relevant electrons are the valence electrons and they occupy
what is known as the valence band. At 0 K, the valence electrons occupy the
lower levels of the valence band. It is the position of the higher levels which
determines the conductivity properties of solids.
There are three important cases of the available higher energy levels, which
are shown in Fig. 8.7. In the first case the electrons fill only the lower half of the
valence band at 0 K. This happens for example, in the case of sodium for which
there are N electrons and 2N levels in the 3s band. At finite temperature some of
these electrons are excited to higher energy levels. In these cases of partially
filled valence bands, an external electric field will transfer some of these electrons
to the nearby higher energy vacant states and in addition provide additional
velocity in the direction of the field. Such crystals are good conductors of
electricity and are metals. It is worth noting that partial filling of the valence
band, which for metals is also the conduction band, is observed if there is an
odd number of electrons in the valence shell, e.g., sodium, or if the energy
bands overlap. Overlapping of bands is found, for example, in the case of Mg,
Zn, etc. which are good conductors.
In the second case [Fig. 8.7(b)], the valence electrons completely fill the
valence band which is separated by a large energy gap ∆E from the conduction
band. For example, the covalent bonding in diamond splits the 2s and 2p levels
into two bands (each of which is a mixture of 2s and 2p states) which are separated
by an energy gap ∆E of about 6 eV, with the valence electrons filling the lower
band. When an electric field is applied to such a crystal, there is no significant
change in the states of the valence electrons since a transition to an available
level requires an energy which is at least equal to the energy gap, which is
about 6 eV in the case of diamond. Such solids are insulators. The description
in terms of energy bands implies that if a radiation of high enough frequency is
incident on an insulator, the electrons in the valence band may absorb the
radiation and undergo transition to the conduction band. These excited electrons
can easily change their velocity since many states are available to them, and act
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the hole states which are the dominant charge carriers and hence they have
positive Hall coefficients (see Example 3 in Sec. 8.8).
Metals, Insulators and Semiconductors
The existence of energy bands, i.e., the allowed bands consisting of allowed
energy levels and forbidden bands which are the gaps between the allowed
bands, provides a simple explanation for the general properties of metals,
insulators and semiconductors.
Consider the order in which the energy levels of the energy bands are filled.
To start with, the electrons in the inner shells fill the corresponding narrow
energy bands, and are not influential in determining the general properties of
the crystal. The relevant electrons are the valence electrons and they occupy
what is known as the valence band. At 0 K, the valence electrons occupy the
lower levels of the valence band. It is the position of the higher levels which
determines the conductivity properties of solids.
There are three important cases of the available higher energy levels, which
are shown in Fig. 8.7. In the first case the electrons fill only the lower half of the
valence band at 0 K. This happens for example, in the case of sodium for which
there are N electrons and 2N levels in the 3s band. At finite temperature some of
these electrons are excited to higher energy levels. In these cases of partially
filled valence bands, an external electric field will transfer some of these electrons
to the nearby higher energy vacant states and in addition provide additional
velocity in the direction of the field. Such crystals are good conductors of
electricity and are metals. It is worth noting that partial filling of the valence
band, which for metals is also the conduction band, is observed if there is an
odd number of electrons in the valence shell, e.g., sodium, or if the energy
bands overlap. Overlapping of bands is found, for example, in the case of Mg,
Zn, etc. which are good conductors.
In the second case [Fig. 8.7(b)], the valence electrons completely fill the
valence band which is separated by a large energy gap ∆E from the conduction
band. For example, the covalent bonding in diamond splits the 2s and 2p levels
into two bands (each of which is a mixture of 2s and 2p states) which are separated
by an energy gap ∆E of about 6 eV, with the valence electrons filling the lower
band. When an electric field is applied to such a crystal, there is no significant
change in the states of the valence electrons since a transition to an available
level requires an energy which is at least equal to the energy gap, which is
about 6 eV in the case of diamond. Such solids are insulators. The description
in terms of energy bands implies that if a radiation of high enough frequency is
incident on an insulator, the electrons in the valence band may absorb the
radiation and undergo transition to the conduction band. These excited electrons
can easily change their velocity since many states are available to them, and act