3.

SEMICONDUCTOR DEVICES

The versatility inherent in nonlinear electronic components is enhanced

immeasurably by the capability to influence current in the device in accordance
with signals introduced at a control electrode.

Both the older vacuum triode (so named because of the third electrode) and the
modern transistor exhibit this feature.

These are considered to be active devices, rather than passive components, because
the control electrode permits active interaction with signal currents in the device.

Electrical properties of active devices are described by current-voltage

characteristics as for other nonlinear components.

It is often useful to develop an appreciation for the origin of these current-voltage

characteristics in terms of basic physical processes.

In this way it is possible to optimize performance of a nonlinear element in any

application, and also to design improved components having desirable electrical
features.

It turns out that the current-voltage characteristics of electronic devices depend

primarily upon the motions of free electrons in them.

The electronic functions of transistors take place within solid materials called
semiconductors. Accordingly, the properties of transistors and other semiconductor
devices, such as the junction diode, stem directly from the behavior of electrons in
semiconductor crystals. The great variety of semiconductor devices that have been
developed since the discovery of the transistor are possible because of the
versatility of semiconductor materials.

3.1 Energy Bands

Properties of any solid material, including semiconductors, depend upon the nature
of the constituent atoms and upon the way in which the atoms are grouped together.

That is, the properties are a function of both the atomic structure of the atoms and
the crystal structure of the solid.
Experiments have shown that an atom consists of a positively charged nucleus
surrounded by electrons located in discrete orbits.

Actually electrons can exist in stable orbits near nucleus only for certain discrete
values of energy called energy levels of the atom.

The allowed energies of electrons in an atom are depicted by horizontal lines on an

energy-level diagram.

In figures below (Fig.3.1), the curved lines in the diagram represent the potential
energy of an electron near the nucleus. As a consequence of the Pauli exclusion
principle, only a certain maximum number of electrons can occupy a given energy
level and the result is that in any atom, electrons fill up the lowest possible levels
first.

When atoms come close together to form a solid crystal, electrons in the upper
levels of adjacent atoms interact to bind the atoms together. Because of the strong
interaction between these outer, or valence, electrons, the upper energy levels are
drastically altered. This can be illustrated by an energy-level diagram for the entire
crystal.

Consider first two isolated atoms, each with an energy-level diagram pertaining to
the outer electrons as in Fig. 3.1a.

When these are brought close together, Fig. 3.1b, the valence electrons in both
atoms are attracted by both nuclei.

The result is that the energy required to remove an electron from one nucleus and
place it on the other is reduced.

This means that an outer electron is equally likely to be located near either nucleus.

The appropriate energy-level diagram for the combination of two atoms has two
energy levels near each atom core.

The higher, unoccupied, levels are similarly split, indicating that these levels, too,
can each contain two electrons.

When three atoms are brought together, Fig. 3.1b, the outer electrons of all three
atoms can be associated with any of the three nuclei. Consequently, three energy
levels are available.

Even the tiniest crystal contains many hundreds of millions of atoms, so that very
many energy levels are associated with each nucleus and the energy-level diagram
appropriate for the entire crystal is a band of levels. The lowest energy band, called
the valence hand (Fig. 3.1c), is completely filled with electrons for there is one
electron for each of the available energy levels. Conversely, the upper energy band
is empty of electrons because it corresponds to the unoccupied higher levels in the
isolated atom. It is called the conduction band, for reasons explained below. The
energy region between the valence band and the conduction band is called the
forbidden energy gap since no electrons with such energies exist in the crystal. The
forbidden energy gap corresponds to the energy region between energy levels in the
isolated atom, as can be seen by comparing the energy-level diagrams in Fig. 3.1.

This picture of the electronic energy levels in a crystal is known as the energy-band
model of a crystal. It is very useful in determining the electrical properties of any
solid, since it shows how electrons can move in the crystal. While the general
features of the band model for any solid are as described, many important details
depend upon the specific atomic and crystal structure. In particular, the differences
between metals, semiconductors, and insulators are reflected in their energy-band
models.

The atomic and crystal structures of metals are such that the valence and
conduction bands overlap, as indicated in the conventional energy-band model for a
metal, Fig. 3.2c. Since there is no forbidden energy gap in a metal crystal, any of
the many valence electrons are free to roam throughout the solid and to move in
response to an electric field. Therefore, metals are excellent electric conductors.
Figure 3.1. Energy-level diagram for (a) isolated atom, (b) two and three atoms close together, (c)
solid crystal. In the crystal, energy levels are broadened into bands.

Fig.3.2. Energy-band models for (a) an insulator, (b) semiconductor and (c) metal

An insulating crystal has a wide forbidden energy gap, Fig. 3.2a. The valence band
is completely filled with electrons and the conduction band is completely empty.
Obviously the upper band cannot contribute to electric conductivity since no
electrons are present to act as carriers. It may seem paradoxical at first, but
electrons in the completely filled valence band also cannot conduct electricity.
When an electron moves in response to an electric field, it must move slightly
faster than before. Consequently, it has greater energy and must find an empty level
at a slightly higher energy. Every nearby level is filled, however, so that it is
impossible for any electron in the filled valence band to be accelerated by the
electric field and the crystal is therefore an insulator.

The energy-band model of a semiconductor, Fig. 3.2b, is similar to that of an

insulator except that the forbidden energy gap is comparatively narrow. A few
electrons can be promoted from the valence band to the conduction band across the
forbidden energy gap by virtue of the thermal energy of the crystal at room
temperature. Electrons promoted to the conduction band can conduct electricity.
The corresponding electron vacancies in the valence band make it possible for
electrons in this band to contribute to conductivity as well. Since the number of
carriers is much fewer than in the case of a metal, semiconductors are poorer
conductors than metals but better than insulators.

Fig. 3.3. Energy-band models for (a) an insulator, (b) semiconductor and (c) metal

Fig.3.4 Energy-band diagram (a) insulator (silicon dioxide 9eV) (b) semiconductors (silicon 1.12
eV) (c) conductors (0 eV)
Fig.3.5. Electron movement (a) electron receives energy (b) energized electron has a higher orbit
(c) electron emits energy (d) returns to original orbit.

Free (conduction band) electrons can move readily under the influence of an
external electric field.

Fermi level is simply a reference energy level or average energy level of the
electrons.

The width of the forbidden energy gap of semiconductors is of the order of 1

electronvolt, eV as shown in Table 1 for several typical semiconductor crystals.

Table 1. Forbidden energy gaps for typical semiconductors.

The electronvolt is equal to the kinetic energy gained by an electron in traversing a
potential difference of 1 V. It is a convenient energy unit in semiconductor studies.

In general, materials with wider forbidden energy gaps are desirable for
semiconductor devices.

The number of electrons promoted to the conduction band at high

temperatures is smaller, and the change in device characteristics with
temperature is less severe when the forbidden energy gap is wide. For this
reason, silicon crystals are more widely used than germanium crystals.

3.2. Electrons and Holes

According to the preceding discussion, the net current resulting from electrons in a
filled valence band is zero.

Electrons in the valence band of a semiconductor at room temperature can conduct

current, however, because of the few vacant levels left behind by electrons excited
to the conduction band.

The vacant levels in the valence band are called holes. It turns out that holes in the
valence band can be treated as positively charged carriers fully analogous to the
negatively charged electrons in the conduction band.

Fig. 3.6 refers to a perfect crystal structure which contains no chemical impurities
and in which no atoms are displaced from their proper sites. The properties of the
solid are therefore characteristic of an ideal structure, and the crystal is called an
intrinsic semiconductor. Although it is not possible to achieve perfect structures in
real crystals, this ideal may be approached, and intrinsic behavior is observed
experimentally.
 Fig. 3.6. Two-dimensional illustration of a semiconductor crystal lattice

3.3 Conductivity of Intrinsic Semiconductors

All the valence electrons are tied in covalent bonds. A silicon monocrystal would
appear to be an ideal insulator at –273 oC (or 0 K), since no thermal energy exists.

As the temperature is raised from absolute zero, more and more heat energy
available, and an occasional covalent bond will be broken. At the room
temperature, there is enough heat energy so that many electrons are set free from
their covalent bonds. Therefore, the semiconductor crystal will have enough free
electrons to transport current through it (Fig. 3.7).

Fig. 3.7. a) Silicon crystal lattice, b) a hole is formed.

3.4 Electron-Hole Movement in a semiconductor crystal

When an electron is set free, there remains a broken covalent bond, which is called
a ‘HOLE’.

The hole lacks a negative charge, and will therefore attract electrons. It should be
noted that since the parent atom has become deficient by one electron, it has
become a positive ion.

The electrons that are attracted to the hole may come from one of two sources.
They may be other free electrons that lose energy and fall into the hole, or they may
be electrons from a neighboring atom. The latter case is more likely. When a hole
captures an electron from a neighboring atom, the neighboring atom will then have
a hole (Fig.3.8).

Figure 3.8. Electron-hole movement in a semiconductor crystal.

In fact, under the influence of an electric field, the free electrons (and to some
extent, the valence electrons) will move toward the plus pole, and the holes will
effectively move toward the minus pole. Hence it can be said that the holes behave
as positive charges. This electron-hole movement is illustrated in Fig. 3.9.

Fig. 3.9. Electron-hole movement in a semiconductor crystal.

Recalling the energy diagram, we can conclude that a free electron jumps from the
valance band to the conduction band, whereas a hole remains in the valence band.

In other words, electron flow requires electrons with conduction band energies, but
hole flow requires electrons with lower (valence band) energies.

The electron and the hole from the broken covalent bond form an electron-hole
pair.

Since each time a free electron is produced, a hole is formed, we have an equal
number of holes and electrons in an intrinsic semiconductor.

As mentioned earlier, if a free electron wanders (travels) near a hole, it may fall
into it. This is referred to as recombination.

As it turns out, the probability of recombination occurring in regions where the

crystal is perfect is small. Consequently, the probability of recombination is much
higher in regions where the crystal has imperfections such as impurities.
These regions are referred to as recombination centers. To promote recombination
in silicon crystals, impurity atoms, such as gold, may be built into the crystal to
increase the recombination rate.

3.5 Movement of the Charge Carriers

There are two mechanisms by which holes and electrons move through a
semiconductor crystal:
(1) diffusion
(2) drift.

Diffusion is a process. Specifically, a mixture of easily flowing materials (such as a

drop of ink in a glass of water) will ultimately reach a final blend that is uniform in
composition. This is precisely what happens in a semiconductor material. In this
case concentrations of charge carriers (either holes or electrons) will tend to
distribute themselves uniformly throughout a semiconductor crystal. The charge
carrier movement that results is called diffusion current.

Drift current results when available charges move under the influence of an applied
electric field. Drift and diffusion occur simultaneously in a semiconductor.

3.6 Extrinsic Semiconductors

In intrinsic semiconductors there are an equal number of holes and electrons. In

extrinsic semiconductors, impurities are added to increase the number of holes, or
to increase the number of free electrons.

Semiconductors that have had impurities added are referred to as doped semi-
conductors. If the semiconductor has been doped to have additional free electrons,
it is called n-type. If the semiconductor has been doped to have additional holes, it
is called p-type. These p- and n-type semiconductors are found in almost all solid-
state devices. Understanding the characteristics of these two types of
semiconductor materials is instrumental to our future studies.
In an n-type semiconductor, the electrons are called the majority carriers and the
holes are called the minority carriers. The reverse is true for p-type
semiconductors.

Donor impurities are pentavalent elements such as arsenic (group V). Donor
impurities are added to semiconductors to give them an excess of electrons.

Since pentavalent elements have five outer-shell electrons, one of them will not be
taken up in a covalent bond.

This is true because in the crystal lattice structure there are only four neighboring
atoms. This is illustrated in Fig. 3.10.

Fig. 3.10. N-type semiconductor

As shown in the figure, the unbound electron will remain near its parent atom.

This occurs because the impurity atom has a proton in its nucleus which attracts the
unbound electron.

However, due to the geometry involved, the electron is partially

shielded from its parent atom and the attractive force between them will be
somewhat reduced.
As can be seen in Fig. 3.11, the energy level of this unbound electron is not far
below the semiconductor's conduction energy band. Note that the Fermi level is
slightly raised because the average energy level of the electrons is higher. Also
recall that the hole is a minority carrier. Observe in Fig. 3.11 that the energy
required to ionize a donor atom is only 0.05 eV, whereas the energy required to
ionize a silicon atom is 1.12 eV (0.7 eV for Ge). As before, when a silicon atom is
ionized, a hole is left in the valence energy band.

Fig. 3.11. Energy diagram for a silicon n-type semiconductor.

Acceptor impurities are trivalent elements such as boron (group III). Acceptor
impurities are added to semiconductors to give them an excess of holes. Since
trivalent elements have only three outer-shell electrons, one of its four neighboring
semiconductor atoms will be lacking a covalent bond (see Fig. 3.12).
 Fig. 3.12 P-type semiconductor
 As discussed previously, a hole is the absence of an electron required to
complete a covalent bond.

 A hole will capture a nearby electron. However, if the electron is

a free electron, it must lose energy to fall into a hole.

 In general, an electron with only about 0.08 eV above the valence band may
be captured by a hole. As a final point, when an electron is captured by a
hole, the associated acceptor impurity atom will become a negative ion.

 It will have a net negative charge since it will not have enough positive
protons in its nucleus to compensate an additional orbital electron.

 The energy diagram for p-type semiconductor is shown in Fig. 3.13. Observe
that the Fermi level is slightly lowered by adding the acceptor impurity. The
free electron is a minority carrier
 Fig.3.13 Energy diagram for a p-type semiconductor

The electrical properties of a semiconductor are drastically altered when foreign, or

impurity, atoms are incorporated (introduced) into the crystal. Since the properties
now depend strongly upon the impurity content, the solid is called an extrinsic
semiconductor.

 Consider, for example, a single crystal of the important semiconductor

material silicon.

 Each silicon atom has four valence electrons that are part of the filled
valence band of a silicon crystal.

 Suppose now a pentavalent atom, such as phosphorus, arsenic, or antimony,

substitutes for a silicon atom in the crystal.

 Four of the impurity atom's electrons play the same role as the four valence
electrons of the replaced silicon atom and become part of the valence band.

 The fifth valence electron is easily detached by thermal energy and moves
freely in the conduction band.
Phosphorus, arsenic, or antimony impurity atoms in silicon donate electrons to
the conduction band and are called donor impurities. One electron is present in the
conduction band for each donor atom in the crystal; note that there is not an
equivalent number of holes in the valence band. The crystal conducts electricity
mainly by virtue of electrons in the conduction band, and such a crystal is called an
n-type semiconductor because of the negative charge on the current carriers.

By comparison, a trivalent atom like boron, aluminum, gallium, or indium

substituted for a silicon atom produces a hole in the valence band. Since only three
electrons are available, an electron from an adjacent silicon atom transfers to the
impurity atom. The foreign atom is said to have accepted a valence electron, and
such impurities are termed acceptors. Acceptors in a crystal create holes in the
valence band and produce a p-type semiconductor because of the effective
positive charge on each hole.

A crystal containing both donor and acceptor impurities is either n-type or p-type,
depending upon which impurity concentration is greater, because electrons from
donor atoms fill up all available acceptor levels.

Intrinsic crystals can be produced by including concentrations of donor and

acceptor impurities and such crystals are said to be compensated. Note that a few
holes are present in the valence band of an n-type crystal since some electrons are
thermally excited across the forbidden energy gap. These holes are called minority
carriers and the electrons are called majority carriers because of their relative
concentration. Conversely, holes are majority carriers in a p-type semiconductor,
while electrons in the conduction band are minority carriers.
Intentionally introducing impurity atoms in semiconductors to obtain a desired
concentration of majority carriers is called doping.