What You’ll Learn
• You will be able to distinguish
among electric conductors,
semiconductors, and
insulators.
• You will examine how pure
semiconductors are modified
to produce desired electric
properties.
• You will compare diodes
and transistors.
Why It’s Important
Semiconductors have
electric properties that
allow them to act as oneway conductors to amplify
weak signals in many
common electronic devices.
Fast Math Computers
and electronic devices
use the controlled
movement of electrons and
holes in semiconductors
to do quick calculations
and logical operations.
Think About This A silicon microchip might
be small, but it may contain
the equivalent of millions
of resistors, diodes, and
transistors. How can this
level of complexity be
produced in such a
tiny structure?
physicspp.com
774
How can you show conduction in a diode?
Question
Which way does a two-color light-emitting diode (LED) conduct?
Procedure
1. Obtain a bi-color (red-green) LED and a
9- to 12-V AC power supply or transformer.
2. Wire a 100-Ω resistor and the LED in series
with the AC source.
3. Be careful when plugging in the AC source so
you are not shocked. Do not touch the
resistor as it may become hot. Plug the AC
source into a GFCI receptacle.
4. Record your observations of the LED.
5. Hold a stroboscopic disk in front of the
LED and spin it. Record your observations
of the LED as viewed through the disk.
viewed through the stroboscopic disk?
Critical Thinking Suggest a possible
explanation for your observations.
Analysis
What color was the LED after you plugged in
the power supply? What color was the LED as
29.1 Conduction in Solids
E
lectronic devices depend not only on natural conductors and insulators, but also on materials that have been designed and produced by
scientists and engineers working together. This brief investigation into
electronics begins with a study of how materials conduct electricity.
All electronic devices owe their origins to the vacuum tubes of the early
1900s. In vacuum tubes, electron beams flow through space to amplify
and control faint electric signals. Vacuum tubes are big, require lots of
electric power, and generate considerable heat. They have heated filaments,
which require the replacement of the tubes after one to five years.
In the late 1940s, solid-state devices were invented that could do
the jobs of vacuum tubes. These devices are made of materials, such as
silicon and germanium, known as semiconductors. The devices amplify
and control very weak electric signals through the movement of electrons
within a tiny crystalline space. Because very few electrons flow in them and
they have no filaments, devices made from semiconductors operate with
a low power input. They are very small, don’t generate much heat, and are
inexpensive to manufacture. The estimated useful life of these devices is
20 years or more.
Objectives
• Describe electron
motion in conductors
and semiconductors.
• Compare and contrast
n-type and p-type
semiconductors.
Vocabulary
semiconductors
band theory
intrinsic semiconductors
dopants
extrinsic semiconductors
Section 29.1 Conduction in Solids
775
Horizons Companies
Band Theory of Solids
You have learned about electric conductors and insulators. In conductors, electric charges can move easily, but not in insulators. When you
examine these two types of materials at the atomic level, the difference in
the way they are able to carry charges becomes apparent.
You learned in Chapter 13 that crystalline solids consist of atoms bound
together in regular arrangements. You also know from Chapters 27 and 28
that an atom consists of a dense, positively charged nucleus surrounded by
a cloud of negatively charged electrons. These electrons can occupy only
certain allowed energy levels. Under most conditions, the electrons in an
atom occupy the lowest possible energy levels. This condition is referred to
as the ground state. Because the electrons can have only certain energies,
any energy changes that occur are quantized; that is, the energy changes
occur in specific amounts.
Carbon
Silicon
Energy
■ Figure 29-1 Energy levels of an
atom are split apart when other
atoms are brought closer, resulting
in an energy gap between the
valence and conduction bands.
Energy bands Suppose you could construct a solid by assembling atoms
together, one by one. You would start with an atom in the ground state. At
large interatomic spacings ( 0.8 nm) with no very near neighbors, the
graph in Figure 29-1 shows two discrete energy levels for the atom. As the
solid crystal forms by moving atoms closer to the atom, the electric fields
of these other neighboring atoms affect the energy levels of its electrons. In
the solid crystal, the result is that the ground state energy levels in each
atom are split into multiple levels by the electric fields of all of its neighbors. There are so many of these levels, and they are so close together, that
they no longer appear as distinct levels, but as the energy bands shown in
Figure 29-1. The lower energy or valence bands are occupied by bonding
electrons in the crystal, and the higher energy or conduction bands are
available for electrons to move from atom to atom.
Notice in Figure 29-1 that the atomic separations for crystalline silicon
and crystalline carbon (diamond) translate to valence bands and conduction bands that are separated by energy gaps. These gaps have no energy
levels available for electrons. They are called forbidden energy regions. This
description of valence and conduction bands, separated by forbidden
energy gaps, is known as the band theory of solids and can be used to
better understand electric conduction. For example, the band diagram in
Conduction band
C Si
Conduction band
E 5.5 eV
E 1.1 eV
Valence band
Valence band
0.2
0.4
0.6
0.8
Atomic separation (nm)
776
Chapter 29 Solid-State Electronics
■ Figure 29-2 In a material that is
a good conductor, the conduction
band is partially filled. The blueshaded area shows energies
occupied by electrons.
Conductor
Conduction band
Energy
Figure 29-1 suggests that a lot more energy will be required to move
valence electrons from the valence band to the conduction band in the
case of crystalline carbon (diamond structure) compared to silicon.
Carbon in graphite form is a much better conductor because the structure
of the atom arrangement in graphite gives it a smaller energy gap than that
of diamond.
Crystalline silicon has a smaller energy gap than diamond does. At
absolute zero, the valence band of silicon would be completely full and
the conduction band would be completely empty. At room temperature,
some number of valence electrons have enough thermal energy to jump
the 1.1-eV gap to the conduction band and serve as charge carriers. As
the temperature increases and more electrons gain enough energy to jump
the gap, the conductivity of silicon will increase. Germanium has an
energy gap of 0.7 eV, which is smaller than that of silicon. This means that
germanium is a better conductor than silicon at any given temperature.
However, it also means that germanium is too sensitive to heat for many
electronic applications. Relatively small changes in temperature cause large
changes in the conductivity of germanium, making control and stability of
circuits troublesome.
Lead has an interatomic spacing of 0.27 nm. Figure 29-1 shows that this
would translate to a band-gap diagram in which the conduction band
overlaps the valence band. One would, therefore, expect lead to be a good
conductor, and it is. Materials with overlapping, partially filled bands are
conductors, as indicated in Figure 29-2.
Valence band
Conductors
When a potential difference is placed across a material, the resulting
electric field exerts a force on the electrons. The electrons accelerate and
gain energy and the field does work on them. If there are bands within the
material that are only partially filled, then there are energy levels available
that are only slightly higher than the electrons’ ground state levels. As
a result, the electrons that gain energy from the field can move from one
atom to the next. Such movement of electrons from one atom to the next
is an electric current, and the entire process is known as electric conduction. Materials with partially filled bands, such as the metals aluminum,
lead, and copper, conduct electricity easily.
Random motion The free electrons in conductors move about rapidly in
a random way, changing directions when they collide with the cores of the
atoms. However, if an electric field is put across a length of wire, there will
be a net force pushing the electrons in one direction. Although their motion
is not greatly affected, they have a slow overall movement dictated by the
electric field, as shown in Figure 29-3. Electrons continue to move rapidly
with speeds of 106 m/s in random directions, and they drift very slowly
at speeds of 105 m/s or slower toward the positive end of the wire. This
model of conductors is called the electron-gas model. If the temperature
is increased, the speeds of the electrons increase, and, consequently, they
collide more frequently with atomic cores. Thus, as the temperature rises,
the conductivity of metals is reduced. Conductivity is the reciprocal of
resistivity. As conductivity is reduced, a material’s resistance rises.
V
■ Figure 29-3 The electrons
move rapidly and randomly in
a conductor. If a field is applied
across the wire, the electrons
drift toward one end. Electron
flow is opposite in direction
to conventional current.
Section 29.1 Conduction in Solids
777
The Free-Electron Density of a Conductor How many free
electrons exist in a cubic centimeter of copper? Each atom
contributes one electron. The density, atomic mass, and number
of atoms per mole of copper can be found in Appendix D.
1
Cu
Cu
e
Analyze the Problem
Cu
e
e
• Identify the knowns using Appendix D.
2
Cu
Known:
Unknown:
For copper: 1 free e per atom
8.96 g/cm3
M 63.54 g/mol
NA 6.021023 atoms/mol
free e/cm3 ?
Cu
e
Cu
e
Cu
e
Solve for the Unknown
Cu
e
Cu
e
e
1
free e
(free e)
(NA ) ( )
M
cm3
atom
( )
e
8.96 g
1 mol
1 free
6.021023 atoms
3
(
1 atom
)(
1 mol
)(
63.54 g
8.491022 free e/cm3 in copper
3
)(
1 cm
)
Substitute free e/1 atom 1 free e/1 atom,
NA 6.021023 atoms/mol, M 63.54 g/mol,
8.96 g/cm3
Evaluate the Answer
• Are the units correct? Dimensional analysis on the units confirms
the number of free electrons per cubic centimeter.
• Is the magnitude realistic? One would expect a large
number of electrons in a cubic centimeter.
Math Handbook
Dimensional
Calculations
pages 846—847
1. Zinc, with a density of 7.13 g/cm3 and an atomic mass of 65.37 g/mol, has two free
electrons per atom. How many free electrons are there in each cubic centimeter of zinc?
2. Silver has 1 free electron per atom. Use Appendix D and determine the number of free
electrons in 1 cm3 of silver.
3. Gold has 1 free electron per atom. Use Appendix D and determine the number of free
electrons in 1 cm3 of gold.
4. Aluminum has 3 free electrons per atom. Use Appendix D and determine the number of
free electrons in 1 cm3 of aluminum.
5. The tip of the Washington Monument was made of 2835 g of aluminum because it was
a rare and costly metal in the 1800s. Use problem 4 and determine the number of free
electrons in the tip of the Washington Monument.
Insulators
In an insulating material, the valence band is filled to capacity and the
conduction band is empty. As shown in Figure 29-4, an electron must
gain a large amount of energy to go to the next energy level. In an insulator, the lowest energy level in the conduction band is 5–10 eV above the
highest energy level in the valence band, as shown in Figure 29-4a. There
is at least a 5-eV gap of energies that no electrons can possess.
778
Chapter 29 Solid-State Electronics
Although electrons have some kinetic energy as a result of their thermal
energy, the average kinetic energy of electrons at room temperature is not
sufficient for them to jump the forbidden gap. If a small electric field is
placed across an insulator, almost no electrons gain enough energy to
reach the conduction band, so there is no current. Electrons in an insulator
must be given a large amount of energy to be pulled into the conduction
band. As a result, the electrons in an insulator tend to remain in place, and
the material does not conduct electricity.
a
Insulator
Conduction band
E 5 eV
Forbidden gap
Valence band
Semiconductors
Electrons can move more freely in semiconductors than in insulators,
but not as easily as in conductors. As shown in Figure 29-4b, the energy
gap between the valence band and the conduction band is approximately
1 eV. How does the structure of a semiconductor explain its electronic
characteristics? Atoms of the most common semiconductors, silicon (Si)
and germanium (Ge), each have four valence electrons. These four electrons are involved in binding the atoms together into the solid crystal. The
valence electrons form a filled band, as in an insulator, but the forbidden
gap between the valence and conduction bands is much smaller than in an
insulator. Not much energy is needed to pull one of the electrons from a
silicon atom and put it into the conduction band, as illustrated in Figure
29-5a. Indeed, the gap is so small that some electrons reach the conduction band as a result of their thermal kinetic energy alone. That is, the random motion of atoms and electrons gives some electrons enough energy
to break free of their home atoms and wander around the silicon crystal.
If an electric field is applied to a semiconductor, electrons in the conduction band move through the solid according to the direction of
the applied electric field. In contrast to the effect in a metal, the higher the
temperature of a semiconductor, the more able electrons are to reach the
conduction band, and the higher the conductivity.
An atom from which an electron has broken free is said to contain a
hole. As shown in Figure 29-5b, a hole is an empty energy level in the
valence band. The atom now has a net positive charge. An electron from
the conduction band can jump into this hole and become bound to an
atom once again. When a hole and a free electron recombine, their opposite charges neutralize each other.
b
Semiconductor
Conduction band
E 1 eV
Forbidden gap
Valence band
■ Figure 29-4 Compare the
valence and conduction bands
in an insulator (a) and in
a semiconductor (b). Compare
these diagrams with the one
shown in Figure 29-2.
■ Figure 29-5 Some electrons in semiconductors have enough thermal kinetic energy to
break free and wander through the crystal, as shown in the crystal structure (a) and in
the bands (b).
a
b
e
Atom
core
Conduction band
e
Electron
Hole
e
Free
electron
Hole
Valence band
Section 29.1 Conduction in Solids
779
The electron, however, has left behind a hole at its previous location.
Thus, as in a game of musical chairs, the negatively charged, free electrons
move in one direction and the positively charged holes move in the opposite direction. Pure semiconductors that conduct as a result of thermally
freed electrons and holes are called intrinsic semiconductors. Because so
few electrons or holes are available to carry charge, conduction in intrinsic
semiconductors is very low, making their resistances very high.
Fraction of Free Electrons in an Intrinsic Semiconductor
Because of the thermal kinetic energy of solid silicon at room
temperature, there are 1.451010 free electrons/cm3. What
is the number of free electrons per atom of silicon at room
temperature?
1
Si
Si
Si
Atom
core
Electron
e
Analyze the Problem
• Identify the knowns and unknowns.
Known:
2.33 g/cm3
Si
Si
Si
Si
Si
Si
Unknown:
Hole
free e/atom of Si ?
M 28.09 g/mol
NA 6.021023 atoms/mol
For Si: 1.451010 free e/cm3
2
Si
e
Free
electron
Solve for the Unknown
1
free e
1
(M ) (1.451010 free e/cm3 for Si)
NA
atom
28.09 g 1 cm3 1.451010 free e
1 mol
23
6.0210 atoms
2.33 g
1 mol
cm3
( ) ()
(
)(
)(
)(
2.901013 free e/atom of Si
or, roughly 1 out of 3 trillion Si atoms has a free electron
3
)
Substitute NA 6.021023 atoms/mol,
M 28.09 g/mol, 2.33 g/cm3,
free e/cm3 Si 1.451010 free e/cm3
Evaluate the Answer
• Are the units correct? Using dimensional analysis confirms the
correct units.
• Is the magnitude realistic? In an intrinsic semiconductor, such as
silicon at room temperature, very few atoms have free electrons.
Math Handbook
Operations with
Scientific Notation
pages 842—843
6. In pure germanium, which has a density of 5.23 g/cm3 and an atomic mass of 72.6 g/mol,
there are 2.251013 free electrons/cm3 at room temperature. How many free electrons
are there per atom?
7. At 200.0 K, silicon has 1.89105 free electrons/cm3. How many free electrons are there
per atom at this temperature? What does this temperature represent on the Celsius scale?
8. At 100.0 K, silicon has 9.231010 free electrons/cm3. How many free electrons are there
per atom at this temperature? What does this temperature represent on the Celsius scale?
9. At 200.0 K, germanium has 1.161010 free electrons/cm3. How many free electrons are
there per atom at this temperature?
10. At 100.0 K, germanium has 3.47 free electrons/cm3. How many free electrons are there
per atom at this temperature?
780
Chapter 29 Solid-State Electronics
Doped Semiconductors
The conductivity of intrinsic semiconductors must be increased greatly
to make practical devices. Dopants are electron donor or acceptor atoms
that can be added in low concentrations to intrinsic semiconductors.
Dopants increase conductivity by making extra electrons or holes available.
The doped semiconductors are known as extrinsic semiconductors.
n-type semiconductors If an electron donor with five valence electrons,
such as arsenic (As), is used as a dopant for silicon, the product is called
an n-type semiconductor. Figure 29-6a shows a location in a silicon crystal where a dopant atom has replaced one of the silicon atoms. Four of
the five As valence electrons bind to neighboring silicon. The fifth electron
is called the donor electron. The energy of this donor electron is so close
to the conduction band that thermal energy can easily move the electron
from the dopant atom into the conduction band, as shown in Figure 29-7a.
Conduction in n-type semiconductors is increased by the availability of
these extra donor electrons to the conduction band.
p-type semiconductors If an electron acceptor with three valence electrons, such as gallium (Ga), is used as a dopant for silicon, the product is
called a p-type semiconductor. When a gallium atom replaces a silicon
atom, one binding electron is missing, creating a hole in the silicon crystal, as shown in Figure 29-6b. Electrons in the conduction band can easily
drop into these holes, creating new holes. Conduction in p-type semiconductors is enhanced by the availability of the extra holes provided by the
acceptor dopant atoms, as shown in Figure 29-7b.
Both p-type and n-type semiconductors are electrically neutral. Adding
dopant atoms of either type does not add any net charge to a semiconductor. Both types of semiconductor use electrons and holes in conduction.
Only a few dopant atoms per million silicon atoms are needed to increase
the conductivity of semiconductors by a factor of 1000 or more.
Silicon is doped by putting a pure silicon crystal in a vacuum with a
sample of the dopant material. The dopant is heated until it is vaporized,
and the atoms condense on the cold silicon. The dopant diffuses into the
silicon on warming, and a thin layer of aluminum or gold is evaporated
onto the doped crystal. A wire is welded to this metal layer, allowing the
user to apply a potential difference across the doped silicon.
a
Electron
n-type
b
Donor levels
a
Arsenic Donor
Si
Si
Si
Si
As
Si
Si
Si
Si
Excess electron
free to move
b
Gallium Acceptor
Si
Si
Si
Si
Ga
Si
Si
Si
Si
Excess hole
free to move
■ Figure 29-6 A donor atom of
arsenic with five valence electrons
replaces a silicon atom and
provides an unbound electron in
the silicon crystal (a). An acceptor
atom of gallium with three valence
electrons creates a hole in the
crystal (b).
p-type
Acceptor levels
Conduction bands
Forbidden gap
Electron
Hole
Hole
Valence bands
■ Figure 29-7 In an n-type
semiconductor (a), donor energy
levels place electrons in the
conduction band. In a p-type
semiconductor (b), acceptor
energy levels result in holes in
the valence band.
Section 29.1 Conduction in Solids
781
Thermistors The electric conductivity of intrinsic and extrinsic semiconductors is sensitive to both temperature and light. Unlike metals in which
conductivity is reduced when the temperature rises, an increase in temperature of a semiconductor allows more electrons to reach the conduction
band, and conductivity increases and resistance decreases. One semiconductor device, the thermistor, is designed so that its resistance depends
very strongly on temperature. The thermistor can be used as a sensitive
thermometer and to compensate for temperature variations of other components in an electric circuit. Thermistors also can be used to detect radio
waves, infrared radiation, and other forms of radiation.
The Conductivity of Doped Silicon Silicon is doped with arsenic so that one in every million
silicon atoms is replaced by an arsenic atom. Each arsenic atom donates one electron to the
conduction band.
Arsenic Donor
a. What is the density of free electrons?
b. By what ratio is this density greater than that of intrinsic
silicon with 1.451010 free e/cm3?
c. Is conduction mainly by the electrons of the silicon or
Si
Si
Si
the arsenic?
1
Analyze the Problem
• Identify the knowns and unknowns.
Known:
Unknown:
free e/cm3 donated by
As ?
ratio of As-donated free e
to intrinsic free e ?
1 As atom/106 Si atoms
1 free e/As atom
4.991022 Si atoms/cm3
1.451010 free e/cm3
in intrinsic Si
2
Si
As
Si
Si
Si
Si
Excess
electron free
to move
Solve for the Unknown
a.
free e As atoms Si atoms
free e
from As 3
As atom Si atoms
cm
cm3
(
) (
)(
)(
1 free e
1 As atom
free e
3
1 As atom 1106 Si atoms
cm
(
) (
)(
)(
)
4.991022 Si atoms
cm3
)
4.991016 free e/cm3 from As donor in doped Si
(
(
3
free e /cm in doped Si
b. Ratio 3
free e /cm in intrinsic Si
Substitute free e/As atom 1 free
e/1 As atom, As atoms/Si atoms 1 As atom/1106 Si atoms,
Si atoms/cm3 4.991022 Si atoms/cm3
)
4.991016 free e/cm3 in doped Si
1.451010 free e/cm3 in intrinsic Si
)
Substitute 4.991016 free e/cm3 in doped Si,
1.451010 free e/cm3 in intrinsic Si
3.44106 As-donated electron per instrinsic Si electron
c. Because there are over 3 million arsenic-donated electrons
for every intrinsic electron, conduction is mainly by the
arsenic-donated electrons.
3
Math Handbook
Evaluate the Answer
• Are the units correct? Using dimensional analysis confirms the correct units.
• Is the magnitude realistic? The ratio is large enough so that intrinsic electrons
make almost no contribution to conductivity.
782
Chapter 29 Solid-State Electronics
Ratios
page 838
11. If you wanted to have 1104 as many electrons from arsenic
doping as thermally free electrons in silicon at room temperature,
how many arsenic atoms should there be per silicon atom?
12. If you wanted to have 5103 as many electrons from arsenic
doping as thermally free electrons in the germanium semiconductor
described in problem 6, how many arsenic atoms should there be
per germanium atom?
13. Germanium at 400.0 K, has 1.131015 thermally liberated carriers/cm3.
If it is doped with 1 As atom per 1 million Ge atoms, what is the
ratio of doped carriers to thermal carriers?
14. Silicon at 400.0 K, has 4.541012 thermally liberated carriers/cm3.
If it is doped with 1 As atom per 1 million Si, what is the ratio of
doped carriers to thermal carriers?
■ Figure 29-8 Photographers
use light meters to measure the
intensity of incident light on an
object.
15. Based on problem 14, draw a conclusion about the behavior of
germanium devices as compared to silicon devices at temperatures
in excess of the boiling point of water.
Light meters Other useful applications of semiconductors depend on
their light sensitivity. When light falls on a semiconductor, the light can
excite electrons from the valence band to the conduction band in the same
way that other energy sources excite atoms. Thus, the resistance decreases
as the light intensity increases. Extrinsic semiconductors can be tailored to
respond to specific wavelengths of light. These include the infrared and visible regions of the spectrum. Materials such as silicon and cadmium sulfide serve as light-dependent resistors in light meters used by lighting
engineers to design the illumination of stores, offices, and homes; and by
photographers to adjust their cameras to capture the best images, as shown
in Figure 29-8.
29.1 Section Review
16. Carrier Mobility In which type of material, a
conductor, a semiconductor, or an insulator, are
electrons most likely to remain with the same atom?
17. Semiconductors If the temperature increases,
the number of free electrons in an intrinsic semiconductor increases. For example, raising the
temperature by 8°C doubles the number of free
electrons in silicon. Is it more likely that an intrinsic
semiconductor or a doped semiconductor will have
a conductivity that depends on temperature?
Explain.
18. Insulator or Conductor? Silicon dioxide is widely
used in the manufacture of solid-state devices. Its
energy-band diagram shows a gap of 9 eV between
the valence band and the conduction band. Is it
more useful as an insulator or a conductor?
physicspp.com/self_check_quiz
19. Conductor or Insulator? Magnesium oxide has
a forbidden gap of 8 eV. Is this material a conductor, an insulator, or a semiconductor?
20. Intrinsic and Extrinsic Semiconductors You are
designing an integrated circuit using a single crystal
of silicon. You want to have a region with relatively
good insulating properties. Should you dope this
region or leave it as an intrinsic semiconductor?
21. Critical Thinking Silicon produces a doubling of
thermally liberated carriers for every 8°C increase
in temperature, and germanium produces a doubling of thermally liberated carriers for every 13°C
increase. It would seem that germanium would be
superior for high-temperature applications, but the
opposite is true. Explain.
Section 29.1 Conduction in Solids
783
29.2 Electronic Devices
T
oday’s electronic instruments, such as radios, televisions, CD players,
and microcomputers, rely on semiconductor devices that are combined on chips of silicon a few millimeters wide. In these devices, current
and voltage vary in more complex ways than are described by Ohm’s law.
As a result, semiconductor devices can change current from AC to DC and
amplify voltages.
Objectives
• Describe how diodes limit
current to motion in only
one direction.
• Explain how a transistor can
amplify or increase voltage
changes.
Vocabulary
Diodes
diode
depletion layer
transistor
microchip
The simplest semiconductor device is the diode. A diode consists of a
sandwich of p-type and n-type semiconductors. Rather than two separate
pieces of doped silicon being joined, a single sample of intrinsic silicon is
treated first with a p-dopant, then with an n-dopant. Metal contacts are coated
on each region so that wires can be attached, as shown in Figure 29-9a.
The boundary between the p-type and the n-type regions is called the junction.
The resulting device, therefore, is called a pn-junction diode.
The free electrons on the n-side of the junction are attracted to the
positive holes on the p-side. The electrons readily move into the p-side
and recombine with the holes. Holes from the p-side similarly move into
the n-side, where they recombine with electrons. As a result of this flow,
the n-side has a net positive charge, and the p-side has a net negative
charge. These charges produce forces in the opposite direction that stop
further movement of charge carriers. The region around the junction is left
with neither holes nor free electrons. This region, depleted of charge carriers, is called the depletion layer. Because it has no charge carriers, it is a
poor conductor of electricity. Thus, a junction diode consists of relatively
good conductors at the ends that surround a poor conductor.
■ Figure 29-9 A diagram of
the pn-junction diode (a) shows
the depletion layer, where there
are no charge carriers. Compare
the magnitude of current in a
reverse-biased diode (b) and
a forward-biased diode (c).
a
Junction Diode
Metal
p-type
Holes
b
Reverse-Biased Diode
n-type
Depletion layer
c
Holes
filled
784
R
n-type
I
Chapter 29 Solid-State Electronics
Junction
p-type
Electrons
leave
Electrons
Forward-Biased Diode
R
p-type
Metal
New holes
created
Electrons and holes
recombine at junction
n-type
I
New electrons
added
When a diode is connected into a circuit in the way shown in Figure
29-9b, both the free electrons in the n-type semiconductor and the holes
in the p-type semiconductor are attracted toward the battery. The width of
the depletion layer is increased, and no charge carriers meet. Almost no
current passes through the diode: it acts like a very large resistor, almost an
insulator. A diode oriented in this manner is a reverse-biased diode.
If the battery is connected in the opposite direction, as shown in
Figure 29-9c, charge carriers are pushed toward the junction. If the voltage
of the battery is large enough—0.6 V for a silicon diode—electrons reach
the p-end and fill the holes. The depletion layer is eliminated, and a
current passes through the diode. The battery continues to supply electrons
for the n-end. It removes electrons from the p-end, which is the same as
supplying holes. With further increases in voltage from the battery, the current increases. A diode in this kind of circuit is a forward-biased diode.
The graph shown in Figure 29-10 shows the current through a silicon
diode as a function of voltage across it. If the applied voltage is negative, the
reverse-biased diode acts like a very high-value resistor and only a tiny current
passes (about 1011 A for a silicon diode). If the voltage is positive, the diode
is forward-biased and acts like a low-value resistor, but not, however, one
that obeys Ohm’s law. One major use of a diode is to convert AC voltage
to DC voltage with only one polarity. When a diode is used in a circuit that
does this, it is called a rectifier. The arrow in the symbol for the diode, which
you’ll see in Example Problem 4, shows the direction of conventional current.
Diode Current
v. Voltage
Current (mA)
20
15
10
5
0
5
3
2
1
0
1
Voltage (V)
■
Figure 29-10 The graph
indicates current-voltage
characteristics for a silicon
junction diode.
A Diode in a Simple Circuit A silicon diode, with I/V characteristics like those shown in
Figure 29-10, is connected to a power supply through a 470- resistor. The power supply
forward-biases the diode, and its voltage is adjusted until the diode current is 12 mA.
What is the power supply voltage?
1
R
Analyze and Sketch the Problem
• Draw a circuit diagram connecting a diode, a 470- resistor,
and a power supply. Indicate the direction of current.
2
Known:
Unknown:
I 0.012 A
Vd 0.70 V
R 470 Vb ?
I
Diode
Vb
Vd
Solve for the Unknown
The voltage drop across the resistor is known from V IR,
and the power supply voltage is the sum of the resistor and
the diode voltage drops.
Vb IR Vd
(0.012 A)(470 ) 0.70 V Substitute I 0.012 A, R 470 , Vd 0.70 V
6.3 V
3
Evaluate the Answer
• Are the units correct? The power supply’s potential difference
is in volts.
• Is the magnitude realistic? It is in accord with the current and
the resistance.
Math Handbook
Order of Operations
page 843
Section 29.2 Electronic Devices
785
22. What battery voltage would be needed to produce a current
of 2.5 mA in the diode in Example Problem 4?
23. What battery voltage would be needed to produce a current
of 2.5 mA if another identical diode were added in series with
the diode in Example Problem 4?
24. Describe how the diodes in the previous problem should
be connected.
25. Describe what would happen in problem 23 if the diodes were
connected in series but with improper polarity.
26. A germanium diode has a voltage drop of 0.40 V when 12 mA
passes through it. If a 470- resistor is used in series, what battery
voltage is needed?
■
Figure 29-11 Diode lasers are
used as both light emitters and
detectors in bar-code scanners.
Light-emitting diodes Diodes made from combinations of gallium and
aluminum with arsenic and phosphorus emit light when they are forwardbiased. When electrons reach the holes in the junction, they recombine
and release the excess energy at the wavelengths of light. These diodes are
called light-emitting diodes, or LEDs. Some LEDs are configured to emit a
narrow beam of coherent, monochromatic laser light. Such diode lasers
are compact, powerful light sources. They are used in CD players, laser
pointers, and supermarket bar-code scanners, as shown in Figure 29-11.
Diodes can detect light as well as emit it. Light falling on the junction of a
reverse-biased pn-junction diode creates electrons and holes, resulting in a
current that depends on the light intensity.
Use the diode circuit in Example Problem 4 with Vb 1.8 V,
but with R 180 :
1. Determine the diode current using the first approximation.
2. Determine the diode current using the second approximation
and assuming a 0.70-V diode drop.
3. Determine the diode current using the third approximation by
Diode Current v. Voltage
14.0
12.0
Current (mA)
Approximations often are used in diode circuits because
diode resistance is not constant. For diode circuits, the first
approximation ignores the forward voltage drop across the
diode. The second approximation takes into account a typical
value for the diode voltage drop. A third approximation uses
additional information about the diode, often in the form of
a graph, as shown in the illustration to the right. The curve
is the characteristic current-volatage curve for the diode. The
straight line shows current-voltage conditions for all possible
diode voltage drops for a 180- resistor, a 1.8-V battery, and
a diode, from a zero diode voltage drop and 10.0 mA at one
end, to a 1.8-V drop, 0.0 mA at the other end.
10.0
8.0
Graphic solution
6.0
4.0
2.0
0.0
0.2
using the accompanying diode graph.
4. Estimate the error for all three approximations, ignoring the
battery and resistor. Discuss the impact of greater battery voltages on the errors.
786
Getty Images
Chapter 29 Solid-State Electronics
0.6
1.0
1.4
Voltage (V)
1.8
a
pnp-transistor
b
C
Circuit
symbols
B
C
B
E
E
C
C
p
Transistors
■ Figure 29-12 Compare the
circuit symbols used to represent
a pnp-transistor (a) and an npntransistor (b).
npn-transistor
n
B
n
B
p
E
E
p
B base
n
C collector
E emitter
Transistors and Integrated Circuits
A transistor is a simple device made of doped semiconductor material.
An npn-transistor consists of layers of n-type semiconductor on either side
of a thin p-type layer. The central layer is called the base and the regions on
either side are the emitter and the collector. The schematic symbols for the
two transistor types are shown in Figure 29-12. The arrow on the emitter
shows the direction of conventional current.
The operation of an npn-transistor is illustrated in Figure 29-13. The two
pn-junctions in the transistor can be thought of as initially forming two
back-to-back diodes. The battery on the right, VC, keeps the collector more
positive than the emitter. The base-collector diode is reverse-biased, with a
wide depletion layer, so there is no current from the collector to the base.
When the battery on the left, VB, is connected, the base is more positive
than the emitter. That makes the base-emitter diode forward-biased, allowing current IB from the base to the emitter.
The very thin base region is part of both diodes in the transistor. The
charges injected by IB reduce the reverse bias of the base-collector diode,
permitting charge to flow from the collector to the emitter. A small change
in IB thus produces a large change in IC.
The collector current causes a voltage drop across resistor RC. Small
changes in the voltage, VB, applied to the base produce large changes in the
collector current and thus changes in the voltage drop across RC. As a
result, the transistor amplifies small voltage changes into much larger
changes. If instead the center layer is an n-type region, then the device is
called a pnp-transistor. A pnp-transistor works the same way, except that the
potentials of both batteries are reversed.
Current gain The current gain from the base circuit to the collector circuit
is a useful indicator of the performance of a transistor. Although the base
current is quite small, it is dependent on the base-emitter voltage that is
controlling the collector current. For example, if VB in Figure 29-13 is
removed, the collector current will drop to zero. If VB is increased, the base
current, IB, increases. The collector current, IC, will also increase, but many
times more (perhaps 100 times or so). The current gain from the base to
the collector ranges from 50 to 300 for general-purpose transistors.
Diode Laser A typical diode
laser emits light at 800 nm, which
is the near infrared. The beam is
output from a small spot on a
GaAlAs chip, and when powered
by 80 mA, the diode has a forward
voltage drop of about 2 V. Diode
lasers commonly are used in
optical fiber transmissions. ■
Figure 29-13 A circuit using an
npn-transistor demonstrates how
voltage can be amplified.
IC
RC
RB
B
IB
VB
Section 29.2 Electronic Devices
VC
787
Red Light
Make a series circuit with a DC
power supply, a 470- resistor,
and a red LED. Connect the short
lead of the LED to the negative
side of the power supply which is
plugged into a GFCI-protected
receptacle. Attach the other lead
to the resistor. Connect the
remaining resistor lead to the
positive side of the power supply.
Slowly increase the voltage until
the LED glows. Note the voltage
setting on the power supply.
1. Hypothesize what will happen
if you reverse the direction of
current.
2. Experiment by reversing the
connections to the battery.
Analyze and Conclude
3. Explain your observations in
terms of LED characteristics.
■ Figure 29-14 A technician
prepares a large silicon crystal
to be sliced into wafers for
microchips.
788
In a tape player, the small voltage variations from the voltage induced in
a coil by magnetized regions on the tape are amplified to move the speaker
coil. In computers, small currents in the base-emitter circuits can turn
on or turn off large currents in the collector-emitter circuits. In addition,
several transistors can be connected together to perform logic operations
or to add numbers together. In these cases, they act as fast switches rather
than as amplifiers.
Microchips An integrated circuit, called a microchip, consists of thousands of transistors, diodes, resistors, and conductors, each less than a
micrometer across. All these components can be made by doping silicon
with donor or acceptor atoms. A microchip begins as an extremely pure
single crystal of silicon, 10–30 cm in diameter and 1–2 m long, as shown
in Figure 29-14. The silicon is sliced by a diamond-coated saw into wafers
less than 1-mm thick. The circuit is then built layer by layer on the surface
of this wafer.
By a photographic process, most of the wafer’s surface is covered by a
protective layer, with a pattern of selected areas left uncovered so that they
can be doped appropriately. The wafer is then placed in a vacuum chamber.
Vapors of a dopant such as arsenic enter the machine, doping the wafer in
the unprotected regions. By controlling the amount of exposure, the engineer can control the conductivity of the exposed regions of the chip. This
process creates resistors, as well as one of the two layers of a diode or one
of the three layers of a transistor. The protective layer is removed, and
another one with a different pattern of exposed areas is applied. Then the
wafer is exposed to another dopant, often gallium, producing pn-junctions.
If a third layer is added, npn-transistors can be formed. The wafer also may
be exposed to oxygen to produce areas of silicon dioxide insulation. A
layer exposed to aluminum vapors can produce a pattern of thin conducting pathways among the resistors, diodes, and transistors.
■ Figure 29-15 Microchips form
the heart of the central processing
unit of computers. A penny is
shown in the picture to represent
scale.
Thousands of identical circuits, usually called chips, are produced at one
time on a single wafer. The chips are then tested, sliced apart, and mounted
in a carrier; wires are attached to the contacts; and the final assembly is
then sealed into a protective plastic body. The tiny size of microchips,
shown in Figure 29-15, allows the placement of complicated circuits in a
small space. Because electronic signals need only travel tiny distances, this
miniaturization has increased the speed of computers. Chips now are used
in appliances and automobiles as well as in computers.
Semiconductor electronics requires that physicists, chemists, and engineers work together. Physicists contribute their understanding of the
motion of electrons and holes in semiconductors. Physicists and chemists
together add precisely controlled amounts of dopants to extremely pure
silicon. Engineers develop the means of mass-producing chips containing
thousands of miniaturized diodes and transistors. Together, their efforts
have brought our world into this electronic age.
29.2 Section Review
27. Transistor Circuit The emitter current in a transistor circuit is always equal to the sum of the base
current and the collector current: IE IB IC. If the
current gain from the base to the collector is 95,
what is the ratio of emitter current to base current?
28. Diode Voltage Drop If the diode characterized
in Figure 29-10 is forward-biased by a battery and
a series resistor so that there is more than 10 mA
of current, the voltage drop is always about 0.70 V.
Assume that the battery voltage is increased by 1 V.
a. By how much does the voltage across the diode
or the voltage across the resistor increase?
b. By how much does the current through the
resistor increase?
physicspp.com/self_check_quiz
29. Diode Resistance Compare the resistance of a
pn-junction diode when it is forward-biased and
when it is reverse-biased.
30. Diode Polarity In a light-emitting diode, which
terminal should be connected to the p-end to make
the diode light?
31. Current Gain The base current in a transistor
circuit measures 55 A and the collector current
measures 6.6 mA. What is the current gain from
base to collector?
32. Critical Thinking Could you replace an npntransistor with two separate diodes connected by
their p-terminals? Explain.
Section 29.2 Electronic Devices
789
Horizons Companies
Diode Current and Voltage
Alternate CBL instructions
can be found on the
Web site.
physicspp.com
Semiconductor devices, such as diodes and transistors, are fabricated using a
semiconductor that is made of partly p-type material and partly n-type material. A
semiconductor doped with donor atoms is called an n-type semiconductor, while
a semiconductor doped with an element leaving a vacancy or a hole in the lattice
structure is referred to as a p-type semiconductor. A diode is made by doping
adjacent regions of a semiconductor with donor and acceptor atoms, forming a
p-n junction. In this lab, you will investigate the voltage and current characteristics
of a diode that is placed in a direct current circuit and compare the response with
your knowledge of resistors.
QUESTION
How do the current-voltage characteristics of a diode, an LED, and a resistor compare?
Objectives
Materials
■ Collect and organize data of voltage drop and
DC power supply, variable, 0–12 VDC
100-Ω resistor, 12- or 1-W
1N4002 diode
LED, red
ammeter, DC, 0–100 mA
voltmeter, 0–5 VDC
hook-up wire
current for a diode and an LED.
■ Measure the current passing through a diode
and an LED as a function of voltage drop.
■ Compare and contrast the current-voltage
characteristics of a resistor with diodes.
Safety Precautions
Procedure
■ Use caution with electric connections.
Avoid contact with the resistor, which may
become hot.
■ Plug power supplies into only GFCI-protected
receptacles to prevent shock hazard.
1. Prepare a data table similar to the one shown
on page 791.
2. As indicated on the schematic diagram below,
wire the negative terminal of the power supply
to the negative side of the ammeter using the
hook-up wire provided.
100 Diode
012 VDC
a
b
V
LED
mA
3. Locate the end of the diode with the silver band
around it. Attach this end to the positive side of
the ammeter.
4. Attach one end of the 100-Ω resistor to the free
end of the diode.
790
Data Table
Voltage (V)
Drop Across Diode
Diode Current (mA)
LED Current (mA)
0
0.1
9. Connect the shorter lead on the LED to the
positive side of the ammeter (negative side of
the voltmeter) where the silver banded end of
the diode had been connected. Connect the
longer lead of the LED to the resistor and to
the positive side of the voltmeter.
10. Plug in the power supply. Slowly turn up the
power supply to increase the voltage drop
across the LED from 0 up to 2.0 V, in 0.1-V
increments. Record the corresponding current
at each voltage. Additionally, observe the LED
and record your observations of it.
0.2
0.3
1.7
————
Analyze
1.8
————
1.9
————
2.0
————
1. Make and Use Graphs On one chart, sketch
and label graphs of current versus voltage drop
for both the diode and the LED. Place current
on the y-axis and voltage on the x-axis. What
are the shapes of these curves?
5. Attach a wire from the free end of the 100-Ω
resistor to the positive lead on the power supply.
6. As shown in the schematic, the voltmeter is in
parallel with the diode. Attach a wire from the
positive side of the voltmeter to the end of the
diode attached to the resistor. Connect the
negative side of the voltmeter to the end of the
diode with the silver band, which is attached
to the ammeter.
7. The diode circuit should look like part a of
the schematic. Make sure the power supply is
turned to zero and plug it in. Slowly turn up
the power supply to increase the voltage drop
across the diode from 0 up to 0.8 V, in 0.1-V
increments. Record the corresponding current
at each voltage. CAUTION: If your current
goes higher than the capacity of your
ammeter, do not increase the voltage any
higher, and discontinue taking readings.
Turn the power supply to zero and unplug it.
8. Observe the LED leads. One should be shorter
than the other. Replace the 1N4002 diode with
the LED so that it corresponds with part b of
the schematic.
2. Formulate Models Using Ohm’s law, compute
and plot on the same graph the voltage-current
relationship for a 100-Ω resistor from 0 to 2 V.
Label this line 100 Ω. What is the form of
this plot?
Conclude and Apply
1. Compare and Contrast How do the currentvoltage curves for a diode, an LED, and a
resistor compare?
2. Which of these devices follow Ohm’s law?
3. Analyze and Conclude Diodes are described
as having a turn-on voltage. What is the turnon voltage for a silicon diode? For the LED you
used?
4. Explain Why would the specifications for an
LED give a light output at a specific current,
such as 20 mA?
Going Further
What could be done to get better measurements of
current for the diode?
Real-World Physics
To find out more about solid-state electronics,
visit the Web site: physicspp.com
Small incandescent lightbulbs typically draw
75–150 mA of current at a particular voltage.
Why might manufacturers prefer using LEDs in
a battery-powered CD or MP3 player?
791
Artificial Intelligence
The phrase artificial intelligence was first
used in 1955. It is defined as “the scientific
understanding of the mechanisms underlying
thought and intelligent behavior and their
embodiment in machines.” Sometimes, a task
needs artificial intelligence to be very logical.
At other times, it may need artificial intelligence to think and behave with human biases.
The goals in the field of artificial intelligence
are to develop systems that can do both.
A prototype Mars rover decides how to
navigate obstacles.
Artificial intelligence also is used to create
expert systems in computers that are programmed with knowledge about specific topics.
Humans can tell the computer the details of a
specific situation, and the computer calculates
the most logical course of action. In a medical
environment, an expert system can be used to
accurately diagnose disorders. Artificial intelligence weighs the facts of the situation and then
infers which actions are most appropriate.
However, artificial intelligence can operate
only with facts that have been taught to the
computer. Users must constantly be aware of
this limitation of expert systems.
The robot, Kismet, displays human facial
expressions.
Applications Artificial intelligence already
Careers Studying mathematics, mathematical
is used in many areas, and it will do even more
for us in the future. When a computer plays
chess, it searches through hundreds of thousands of possible moves before selecting the
best one. Research is being done to improve
the efficiency of search algorithms.
Artificial intelligence currently is used for
speech recognition to allow hands-free dialing of
cell phones and for some interactive telephone
transactions. It is not yet fully capable of understanding natural language, but that is a goal.
Three-dimensional computer vision is
another future application. To mimic the
sensory input and behaviors of humans, computers need to extract three-dimensional reality
from two-dimensional images. Progress has
been made, but humans are still much better
than computers at this. With improved vision,
artificial intelligence may control automobiles
on Earth, or robots exploring another planet,
with no human navigators needed.
logic, and computer programming languages
is important for developing systems that can
make rational decisions. Knowledge of psychology assures that these decisions also can
have a human character.
792
Extreme Physics
(l)NASA, (r)Sam Ogden/Photo Researchers
Going Further
1. Debate the Issue Are there ethical
limits to the development of artificial
intelligence?
2. Recognize Cause and Effect What
problems might cause an expert system
to make a poor decision?
3. Critical Thinking In what situations
must artificial intelligence be absolutely
rational, and in what situations should
it include human biases?
29.1 Conduction in Solids
Vocabulary
Key Concepts
• semiconductors (p. 775)
• band theory (p. 776)
• intrinsic semiconductors
•
•
(p. 780)
• dopants (p. 781)
• extrinsic semiconductors
(p. 781)
•
•
•
•
•
•
•
•
•
Electric conduction may be explained by the band theory of solids.
In solids, the allowed energy levels for outer electrons in an atom are spread
into broad bands by the electric fields of electrons on neighboring atoms.
The valence and conduction bands are separated by forbidden energy gaps;
that is, by regions of energy levels that electrons may not possess.
In conductors, electrons can move through the solid because the conduction
band is partially filled.
Electrons in metals have a fast random motion. A potential difference across
the metal causes a slow drift of electrons, called an electric current.
In insulators, more energy is needed to move electrons into the conduction
band than is generally available.
Conduction in semiconductors is enhanced by doping pure crystals with
small amounts of other kinds of atoms, called dopants.
n-type semiconductors are doped with electron donor atoms, and they conduct
by the response of these donor electrons to applied potential differences.
Arsenic, with five valence electrons, is an example of a donor atom.
p-type semiconductors are doped with electron acceptor atoms, and they
conduct by making holes available to electrons in the conduction band.
Gallium, with three valence electrons, is an example of an acceptor atom.
29.2 Electronic Devices
Vocabulary
Key Concepts
•
•
•
•
•
diode (p. 784)
depletion layer (p. 784)
transistor (p. 787)
microchip (p. 788)
•
•
•
•
•
•
•
•
A pn-junction diode consists of a layer of a p-type semiconductor joined with
a layer of an n-type semiconductor.
Diodes conduct charges in one direction only. They can be used in rectifier
circuits to convert AC to DC.
Electrons and holes near either side of the diode junction combine to
produce a region without charge carriers known as the depletion layer.
Applying a potential difference of the proper polarity across the diode makes
the depletion layer even wider, no current is observed, and the diode is said
to be reverse-biased.
Reversing the polarity of the applied potential across the diode greatly
reduces the depletion layer, current is observed, and the diode is said to
be forward-biased.
A transistor is a sandwich of three layers of semiconductor material,
configured as either npn- or pnp-layers. The center base layer is very thin
compared to the other layers, the emitter and collector.
A transistor can act as an amplifier to convert a weak signal into a much
stronger one.
The ratio of the collector-emitter current to the base current is known as the
current gain and is a useful measure of transistor amplification.
Conductivity of semiconductors increases with increasing temperature or
illumination, making them useful as thermometers or light meters. Diodes
that emit light when a potential is applied are used in optical devices.
physicspp.com/vocabulary_puzzlemaker
793
Concept Mapping
33. Complete the concept map using the following
terms: transistor, silicon diode, emits light, conducts
both ways.
41. For the energy-band diagrams shown in Figure 29-16,
which have half-full conduction bands?
42. For the energy-band diagrams shown in Figure 29-16,
which ones represent semiconductors?
Circuit
Components
43. The resistance of graphite decreases as temperature
rises. Does graphite conduct electricity more like
copper or more like silicon does?
copper
wire
44. Which of the following materials would make a
LED
conducts
one way
better insulator: one with a forbidden gap 8-eV
wide, one with a forbidden gap 3-eV wide, or one
with no forbidden gap?
amplifies
45. Consider atoms of the three materials in problem
44. From which material would it be most difficult
to remove an electron?
46. State whether the bulb in each of the circuits of
Mastering Concepts
Figure 29-17 (a, b, and c) is lighted.
34. How do the energy levels in a crystal of an element
differ from the energy levels in a single atom of
that element? (29.1)
35. Why does heating a semiconductor increase
its conductivity? (29.1)
36. What is the main current carrier in a p-type
semiconductor? (29.1)
37. An ohmmeter is an instrument that places a
potential difference across a device to be tested,
measures the current, and displays the resistance
of the device. If you connect an ohmmeter across
a diode, will the current you measure depend on
which end of the diode was connected to the
positive terminal of the ohmmeter? Explain. (29.2)
a
b
c
■
Figure 29-17
47. In the circuit shown in Figure 29-18, state whether
lamp L1, lamp L2, both, or neither is lighted.
38. What is the significance of the arrowhead at the
emitter in a transistor circuit symbol? (29.2)
L1
L2
39. Describe the structure of a forward-biased diode,
and explain how it works. (29.2)
■
Applying Concepts
Figure 29-18
48. Use the periodic table to determine which of the
40. For the energy-band diagrams shown in Figure 29-16,
which one represents a material with an extremely
high resistance?
following elements could be added to germanium
to make a p-type semiconductor: B, C, N, P, Si, Al,
Ge, Ga, As, In, Sn, or Sb.
49. Does an ohmmeter show a higher resistance when a
pn-junction diode is forward-biased or reverse-biased?
50. If the ohmmeter in problem 49 shows the lower
resistance, is the ohmmeter lead on the arrow side
of the diode at a higher or lower potential than the
lead connected to the other side?
a
■
794
b
Figure 29-16
Chapter 29 Solid-State Electronics
c
51. If you dope pure germanium with gallium alone,
do you produce a resistor, a diode, or a transistor?
For more problems, go to Additional Problems, Appendix B.
52. Draw the time-versus-amplitude waveform for point
A in Figure 29-19a assuming an input AC
waveform, as shown in Figure 29-19b.
57. Diode A silicon diode with I/V characteristics, as
shown in Figure 29-10, is connected to a battery
through a 270- resistor. The battery forward-biases
the diode, and the diode current is 15 mA. What is
the battery voltage?
a
58. Assume that the switch shown in Figure 29-21 is off.
a. Determine the base current.
b. Determine the collector current.
c. Determine the voltmeter reading.
A
b
AC voltage
A
■
Time
1500 15 V
120,000 Figure 29-19
A
Mastering Problems
V
3.5 V
29.1 Conduction in Solids
■
Figure 29-21
53. How many free electrons exist in a cubic centimeter
of sodium? Its density is 0.971 g/cm3, its atomic
mass is 22.99 g/mol, and there is 1 free electron
per atom.
54. At a temperature of 0°C, thermal energy frees
1.55109 e/cm3 in pure silicon. The density
of silicon is 2.33 g/cm3, and the atomic mass of
silicon is 28.09 g/mol. What is the fraction of atoms
that have free electrons?
59. Assume that the switch shown in Figure 29-21 is
on, and that there is a 0.70-V drop across the baseemitter junction and a current gain from base to
collector of 220.
a. Determine the base current.
b. Determine the collector current.
c. Determine the voltmeter reading.
29.2 Electronic Devices
Mixed Review
55. LED The potential drop across a glowing LED is
60. The forbidden gap in silicon is 1.1 eV.
about 1.2 V. In Figure 29-20, the potential drop
across the resistor is the difference between the
battery voltage and the LED’s potential drop. What
is the current through each of the following?
a. the LED
b. the resistor
R 240 Battery
V 6.0 V
1.2 V
LED
Electromagnetic waves striking the silicon cause
electrons to move from the valence band to the
conduction band. What is the longest wavelength
of radiation that could excite an electron in this
way? Recall that E 1240 eVnm/.
61. Si Diode A particular silicon diode at 0°C shows a
current of 1.0 nA when it is reverse-biased. What
current can be expected if the temperature increases
to 104°C? Assume that the reverse-bias voltage
remains constant. (The thermal carrier production
of silicon doubles for every 8°C increase in
temperature.)
62. Ge Diode A particular germanium diode at 0°C
■
Figure 29-20
56. Jon wants to raise the current through the LED
in problem 55 up to 3.0101 mA so that it glows
brighter. Assume that the potential drop across the
LED is still 1.2 V. What resistor should be used?
physicspp.com/chapter_test
shows a current of 1.5 A when it is reverse-biased.
What current can be expected if the temperature
increases to 104°C? Assume that the reverse-biasing
voltage remains constant. (The thermal charge-carrier
production of germanium doubles for every 13°C
increase in temperature.)
Chapter 29 Assessment
795
63. LED A light-emitting diode (LED) produces green
light with a wavelength of 550 nm when an electron
moves from the conduction band to the valence
band. Find the width of the forbidden gap in eV
in this diode.
66. Apply Concepts The I/V characteristics of two
LEDs that glow with different colors are shown in
Figure 29-24. Each is to be connected through a
resistor to a 9.0-V battery. If each is to be run at
a current of 0.040 A, what resistors should be
chosen for each?
64. Refer to Figure 29-22.
a. Determine the voltmeter reading.
LED Current v. Voltage
b. Determine the reading of A1.
Current (A)
c. Determine the reading of A2.
220 All diodes
are silicon.
0.04
0.02
0
V
0.5
1
10.0 V
2
2.5
Voltage (V)
A1
■
1.5
A2
■
Figure 29-24
67. Apply Concepts Suppose that the two LEDs in
Figure 29-22
problem 66 are now connected in series. If the
same battery is to be used and a current of 0.035 A
is desired, what resistor should be used?
Thinking Critically
65. Apply Concepts A certain motor, in Figure 29-23,
runs in one direction with a given polarity applied
and reverses direction with the opposite polarity.
a. Which circuit (a, b, or c) will allow the motor
to run in only one direction?
b. Which circuit will cause a fuse to blow if the
incorrect polarity is applied?
c. Which circuit produces the correct direction of
rotation regardless of the applied polarity?
d. Discuss the advantages and disadvantages of
all three circuits.
M
c
b
M
■
796
Figure 29-23
Chapter 29 Solid-State Electronics
life of Wolfgang Pauli. Highlight his outstanding
contributions to science. Describe the application
of the exclusion principle to the band theory of
conduction, especially in semiconductors.
69. Write a one-page paper discussing the Fermi energy
level as it applies to energy-band diagrams for
semiconductors. Include at least one drawing.
70. An alpha particle, a doubly ionized (2) helium
M
68. Research the Pauli exclusion principle and the
Cumulative Review
a
Writing in Physics
atom, has a mass of 6.71027 kg and is
accelerated by a voltage of 1.0 kV. If a uniform
magnetic field of 6.5102 T is maintained on the
alpha particle, what will be the particle’s radius of
curvature? (Chapter 26)
71. What is the potential difference needed to stop
photoelectrons that have a maximum kinetic energy
of 8.01019 J? (Chapter 27)
72. Calculate the radius of the orbital associated
with the energy level E4 of the hydrogen atom.
(Chapter 28)
For more problems, go to Additional Problems, Appendix B.
Multiple Choice
1. Which statement about diodes is false?
Diodes can ___________.
amplify voltage
emit light
detect light
rectify AC
7. Which line in the following table best describes
the behavior of intrinsic silicon semiconductors
to increasing temperature?
Effect of Increasing Temperature
on Intrinsic Silicon Semiconductors
2. Cadmium has two free electrons per atom.
How many free electrons are there per cm3
of cadmium? The density of cadmium is
8650 kg/m3.
1.241021
9.261024
9.261022
1.171027
3. The base current in a transistor circuit measures
45 A and the collector current measures 8.5 mA.
What is the current gain from base to collector?
110
205
190
240
4. In problem 3, if the base current is increased
by 5 A, how much is the collector current
increased?
5 A
10 mA
1 mA
190 A
4.75 mA
18.9 A
1190 mA
Resistance
Increases
Increases
Increases
Decreases
Decreases
Increases
Decreases
Decreases
8. Thermal electron production in silicon doubles
for every 8°C increase in temperature. A silicon
diode at 0°C shows a current of 2.0 nA when
reverse-biased. What will be the current at
112°C if the reverse-bias voltage is constant?
11 A
33 A
44 A
66 A
Extended Answer
9. A silicon diode is connected in the forwardbiased direction to a power supply though a
485- resistor, as shown below. If the diode
voltage drop is 0.70 V, what is the power supply
voltage when the diode current is 14 mA?
R 485 5. A transistor circuit shows a collector current of
4.75 mA, and the base to collector current gain
is 250. What is the base current?
1.19 A
Conductivity
I 14 mA
Vb
Vd 0.70 V
6. Which line in the following table best describes
both n- and p-type silicon semiconductors?
n-type
p-type
Gallium-doped
Added electrons
Added electrons
Arsenic-doped
Arsenic-doped
Added holes
Added holes
Gallium-doped
physicspp.com/standardized_test
Focus
If students near you are talking during a test,
you should move. Respond only to the instructor
when taking a test. Talking is a distraction and
the instructor might think that you are cheating.
Don’t take the chance. Focus on the test.
Chapter 29 Standardized Test Practice
797