Solid State Physics
275
conduction band and the valence band. Their conductivity is in-between that of
metals (~ 10
8
Ω
–1
m
–1
) and that of insulators (~ 10
–11
Ω
–1
m
–1
), and increases
with temperature. Because of the narrowness of the energy gap and the proximity
of the energy levels of the impurity to the valence and conduction bands,
semiconductors have rather striking electronic properties which make them very
useful in the development of sophisticated electronic equipment. Here the
positions and populations of the semiconductor energy levels which determine
their electronic properties are discussed.
It is useful to classify semiconductors into two categories. The class of
semiconductors which are pure, such as silicon, germanium (which are group
IV elements), GaAs, PbS, etc., are known as intrinsic semiconductors. In the
second class of semiconductors known as extrinsic (or impurity) semiconductors,
the properties of the semiconductors are modified by the introduction of carefully
controlled amounts of impurities.
To see how the impurities affect the properties of semiconductors, consider
the specific examples of silicon and germanium. These are group IV elements
which have diamond structure in which each atom has a covalent bond with
each of the four nearest neighbours at the corners of a tetrahedron. If a small
amount of a group V element, such as phosphorus, arsenic or antimony, is
introduced during the formation of the crystal, the group V atom will take the
place of one of the group IV atoms and form four covalent bonds with the
nearest neighbours. However, since it has five electrons in the valence shell,
the fifth electron is only weakly bound to the atom. They i.e., the ‘fifth’ electrons
occupy localized energy levels which are just below the conduction band [see
Fig. 8.8(a)]. The electrons in these levels are easily excited to the states in the
conduction band and serve as current carriers. Since group V atoms donate
electrons for conduction they are known as donors, and the new energy levels
just below the conduction band as donor levels. The charge carriers in this case
being negatively charged, the corresponding extrinsic semiconductors are known
as n-type semiconductors. Alternatively, if a small amount of a group III element
such as boron, aluminium or indium is introduced, the group III element will
form only three covalent bonds with the nearest neighbours. Thus, there is a
vacancy or a hole associated with each of these atoms. Since an electron in
these states would be fairly tightly bound, the vacant states provide localized
energy levels which lie just above the valence band [see Fig. 8.8(b)]. The
neighbouring electrons can easily be transferred to these levels, as a result of
which holes are created in the valence band. Since the states near the top of the
band have negative mass (see Sec. 8.3), these holes behave as positive mass,
positive charge carriers. The group III impurity atoms are known as acceptors
and the new energy levels just above the valence band as acceptor levels. The
charge carriers in this case being positively charged, the corresponding extrinsic
semiconductors are known as p-type semiconductors.
275
conduction band and the valence band. Their conductivity is in-between that of
metals (~ 10
8
Ω
–1
m
–1
) and that of insulators (~ 10
–11
Ω
–1
m
–1
), and increases
with temperature. Because of the narrowness of the energy gap and the proximity
of the energy levels of the impurity to the valence and conduction bands,
semiconductors have rather striking electronic properties which make them very
useful in the development of sophisticated electronic equipment. Here the
positions and populations of the semiconductor energy levels which determine
their electronic properties are discussed.
It is useful to classify semiconductors into two categories. The class of
semiconductors which are pure, such as silicon, germanium (which are group
IV elements), GaAs, PbS, etc., are known as intrinsic semiconductors. In the
second class of semiconductors known as extrinsic (or impurity) semiconductors,
the properties of the semiconductors are modified by the introduction of carefully
controlled amounts of impurities.
To see how the impurities affect the properties of semiconductors, consider
the specific examples of silicon and germanium. These are group IV elements
which have diamond structure in which each atom has a covalent bond with
each of the four nearest neighbours at the corners of a tetrahedron. If a small
amount of a group V element, such as phosphorus, arsenic or antimony, is
introduced during the formation of the crystal, the group V atom will take the
place of one of the group IV atoms and form four covalent bonds with the
nearest neighbours. However, since it has five electrons in the valence shell,
the fifth electron is only weakly bound to the atom. They i.e., the ‘fifth’ electrons
occupy localized energy levels which are just below the conduction band [see
Fig. 8.8(a)]. The electrons in these levels are easily excited to the states in the
conduction band and serve as current carriers. Since group V atoms donate
electrons for conduction they are known as donors, and the new energy levels
just below the conduction band as donor levels. The charge carriers in this case
being negatively charged, the corresponding extrinsic semiconductors are known
as n-type semiconductors. Alternatively, if a small amount of a group III element
such as boron, aluminium or indium is introduced, the group III element will
form only three covalent bonds with the nearest neighbours. Thus, there is a
vacancy or a hole associated with each of these atoms. Since an electron in
these states would be fairly tightly bound, the vacant states provide localized
energy levels which lie just above the valence band [see Fig. 8.8(b)]. The
neighbouring electrons can easily be transferred to these levels, as a result of
which holes are created in the valence band. Since the states near the top of the
band have negative mass (see Sec. 8.3), these holes behave as positive mass,
positive charge carriers. The group III impurity atoms are known as acceptors
and the new energy levels just above the valence band as acceptor levels. The
charge carriers in this case being positively charged, the corresponding extrinsic
semiconductors are known as p-type semiconductors.