What You’ll Learn• You will be able to distinguish

among electric conductors,semiconductors, andinsulators.

• You will examine how puresemiconductors are modifiedto produce desired electricproperties.

• You will compare diodesand transistors.

Why It’s ImportantSemiconductors haveelectric properties thatallow them to act as one-way conductors to amplifyweak signals in manycommon electronic devices.

Fast Math Computers and electronic devices use the controlledmovement of electrons andholes in semiconductors to do quick calculations and logical operations.

Think About This �A silicon microchip mightbe small, but it may containthe equivalent of millions of resistors, diodes, andtransistors. How can thislevel of complexity beproduced in such a tiny structure?

774

physicspp.com

Larry Hamill, (inset)Getty Images

How can you show conduction in a diode?QuestionWhich 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 serieswith the AC source.

3. Be careful when plugging in the AC source soyou are not shocked. Do not touch theresistor as it may become hot. Plug the ACsource 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.

Analysis

What color was the LED after you plugged in the power supply? What color was the LED as

viewed through the stroboscopic disk?Critical Thinking Suggest a possibleexplanation for your observations.

29.1 Conduction in Solids

� Objectives• Describe electron

motion in conductors and semiconductors.

• Compare and contrastn-type and p-typesemiconductors.

� Vocabularysemiconductorsband theoryintrinsic semiconductorsdopantsextrinsic semiconductors

Electronic devices depend not only on natural conductors and insula-tors, 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 early1900s. In vacuum tubes, electron beams flow through space to amplifyand 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 amplifyand control very weak electric signals through the movement of electronswithin a tiny crystalline space. Because very few electrons flow in them andthey have no filaments, devices made from semiconductors operate with a low power input. They are very small, don’t generate much heat, and areinexpensive to manufacture. The estimated useful life of these devices is 20 years or more.

Section 29.1 Conduction in Solids 775Horizons Companies

Band Theory of SolidsYou have learned about electric conductors and insulators. In conduc-

tors, electric charges can move easily, but not in insulators. When youexamine these two types of materials at the atomic level, the difference inthe way they are able to carry charges becomes apparent.

You learned in Chapter 13 that crystalline solids consist of atoms boundtogether in regular arrangements. You also know from Chapters 27 and 28that an atom consists of a dense, positively charged nucleus surrounded bya cloud of negatively charged electrons. These electrons can occupy onlycertain allowed energy levels. Under most conditions, the electrons in anatom occupy the lowest possible energy levels. This condition is referred toas the ground state. Because the electrons can have only certain energies,any energy changes that occur are quantized; that is, the energy changesoccur in specific amounts.

Energy bands Suppose you could construct a solid by assembling atomstogether, one by one. You would start with an atom in the ground state. Atlarge interatomic spacings (� 0.8 nm) with no very near neighbors, thegraph in Figure 29-1 shows two discrete energy levels for the atom. As thesolid crystal forms by moving atoms closer to the atom, the electric fieldsof these other neighboring atoms affect the energy levels of its electrons. Inthe solid crystal, the result is that the ground state energy levels in eachatom are split into multiple levels by the electric fields of all of its neigh-bors. There are so many of these levels, and they are so close together, thatthey no longer appear as distinct levels, but as the energy bands shown inFigure 29-1. The lower energy or valence bands are occupied by bondingelectrons in the crystal, and the higher energy or conduction bands areavailable for electrons to move from atom to atom.

Notice in Figure 29-1 that the atomic separations for crystalline siliconand crystalline carbon (diamond) translate to valence bands and conduc-tion bands that are separated by energy gaps. These gaps have no energylevels available for electrons. They are called forbidden energy regions. Thisdescription of valence and conduction bands, separated by forbiddenenergy gaps, is known as the band theory of solids and can be used to better understand electric conduction. For example, the band diagram in

776 Chapter 29 Solid-State Electronics

Ener

gy

Atomic separation (nm)

0.2 0.4 0.6 0.8

C Si

Conduction band

Conduction band

Valence band

Valence band

E � 5.5 eV E � 1.1 eV

Carbon Silicon

■ Figure 29-1 Energy levels of anatom are split apart when otheratoms are brought closer, resultingin an energy gap between thevalence and conduction bands.

Figure 29-1 suggests that a lot more energy will be required to movevalence electrons from the valence band to the conduction band in thecase of crystalline carbon (diamond structure) compared to silicon.Carbon in graphite form is a much better conductor because the structureof the atom arrangement in graphite gives it a smaller energy gap than thatof diamond.

Crystalline silicon has a smaller energy gap than diamond does. Atabsolute zero, the valence band of silicon would be completely full andthe conduction band would be completely empty. At room temperature,some number of valence electrons have enough thermal energy to jumpthe 1.1-eV gap to the conduction band and serve as charge carriers. As the temperature increases and more electrons gain enough energy to jumpthe gap, the conductivity of silicon will increase. Germanium has anenergy gap of 0.7 eV, which is smaller than that of silicon. This means thatgermanium is a better conductor than silicon at any given temperature.However, it also means that germanium is too sensitive to heat for manyelectronic applications. Relatively small changes in temperature cause largechanges in the conductivity of germanium, making control and stability ofcircuits troublesome.

Lead has an interatomic spacing of 0.27 nm. Figure 29-1 shows that thiswould translate to a band-gap diagram in which the conduction bandoverlaps the valence band. One would, therefore, expect lead to be a goodconductor, and it is. Materials with overlapping, partially filled bands areconductors, as indicated in Figure 29-2.

ConductorsWhen a potential difference is placed across a material, the resulting

electric field exerts a force on the electrons. The electrons accelerate andgain energy and the field does work on them. If there are bands within thematerial that are only partially filled, then there are energy levels availablethat are only slightly higher than the electrons’ ground state levels. As a result, the electrons that gain energy from the field can move from oneatom to the next. Such movement of electrons from one atom to the nextis an electric current, and the entire process is known as electric conduc-tion. 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 ina random way, changing directions when they collide with the cores of theatoms. However, if an electric field is put across a length of wire, there willbe a net force pushing the electrons in one direction. Although their motionis not greatly affected, they have a slow overall movement dictated by theelectric field, as shown in Figure 29-3. Electrons continue to move rapidlywith speeds of 106 m/s in random directions, and they drift very slowly at speeds of 10�5 m/s or slower toward the positive end of the wire. Thismodel of conductors is called the electron-gas model. If the temperature is increased, the speeds of the electrons increase, and, consequently, theycollide more frequently with atomic cores. Thus, as the temperature rises,the conductivity of metals is reduced. Conductivity is the reciprocal ofresistivity. As conductivity is reduced, a material’s resistance rises.

Section 29.1 Conduction in Solids 777

Conduction band

Valence band

Ener

gy

Conductor

■ Figure 29-2 In a material that isa good conductor, the conductionband is partially filled. The blue-shaded area shows energiesoccupied by electrons.

��V

■ Figure 29-3 The electrons move rapidly and randomly in a conductor. If a field is appliedacross the wire, the electrons drift toward one end. Electron flow is opposite in direction to conventional current.

1. Zinc, with a density of 7.13 g/cm3 and an atomic mass of 65.37 g/mol, has two freeelectrons 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 freeelectrons in 1 cm3 of silver.

3. Gold has 1 free electron per atom. Use Appendix D and determine the number of freeelectrons in 1 cm3 of gold.

4. Aluminum has 3 free electrons per atom. Use Appendix D and determine the number offree 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 freeelectrons in the tip of the Washington Monument.

778 Chapter 29 Solid-State Electronics

The Free-Electron Density of a Conductor How many freeelectrons 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.

Analyze the Problem• Identify the knowns using Appendix D.

Known: Unknown:

For copper: 1 free e� per atom free e�/cm3 � ?� � 8.96 g/cm3

M � 63.54 g/molNA � 6.02�1023 atoms/mol

Solve for the Unknown

�fre

cem

e3

�� � �

(fraeteom

e�)�(NA)(�

M1�)( �)

� (��11fraeteom

e��)(�6.02�

110

m

23

olatoms

�)(��613.m54

olg

�)(��81.9c6m

g3�)

� 8.49�1022 free e�/cm3 in copper

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.

3

Substitute free e�/1 atom � 1 free e�/1 atom,NA � 6.02�1023 atoms/mol, M � 63.54 g/mol,� � 8.96 g/cm3

2

1 e�

e�

e�

e�

e�

e�

e�

e�

e�

Cu Cu Cu

Cu Cu Cu

Cu Cu Cu

InsulatorsIn an insulating material, the valence band is filled to capacity and the

conduction band is empty. As shown in Figure 29-4, an electron mustgain a large amount of energy to go to the next energy level. In an insula-tor, the lowest energy level in the conduction band is 5–10 eV above thehighest energy level in the valence band, as shown in Figure 29-4a. Thereis at least a 5-eV gap of energies that no electrons can possess.

Math Handbook

Dimensional Calculations

pages 846—847

Although electrons have some kinetic energy as a result of their thermalenergy, the average kinetic energy of electrons at room temperature is notsufficient for them to jump the forbidden gap. If a small electric field isplaced across an insulator, almost no electrons gain enough energy toreach the conduction band, so there is no current. Electrons in an insulatormust be given a large amount of energy to be pulled into the conductionband. As a result, the electrons in an insulator tend to remain in place, andthe material does not conduct electricity.

SemiconductorsElectrons can move more freely in semiconductors than in insulators,

but not as easily as in conductors. As shown in Figure 29-4b, the energygap between the valence band and the conduction band is approximately1 eV. How does the structure of a semiconductor explain its electroniccharacteristics? Atoms of the most common semiconductors, silicon (Si)and germanium (Ge), each have four valence electrons. These four elec-trons are involved in binding the atoms together into the solid crystal. Thevalence electrons form a filled band, as in an insulator, but the forbiddengap between the valence and conduction bands is much smaller than in aninsulator. Not much energy is needed to pull one of the electrons from asilicon atom and put it into the conduction band, as illustrated in Figure29-5a. Indeed, the gap is so small that some electrons reach the conduc-tion band as a result of their thermal kinetic energy alone. That is, the ran-dom motion of atoms and electrons gives some electrons enough energyto break free of their home atoms and wander around the silicon crystal.

If an electric field is applied to a semiconductor, electrons in the con-duction band move through the solid according to the direction of the applied electric field. In contrast to the effect in a metal, the higher thetemperature of a semiconductor, the more able electrons are to reach theconduction band, and the higher the conductivity.

An atom from which an electron has broken free is said to contain ahole. As shown in Figure 29-5b, a hole is an empty energy level in thevalence band. The atom now has a net positive charge. An electron fromthe conduction band can jump into this hole and become bound to anatom once again. When a hole and a free electron recombine, their oppo-site charges neutralize each other.

Section 29.1 Conduction in Solids 779

Conduction band

Valence band

Insulator

Conduction band

Valence band

Semiconductor

E � 5 eV Forbidden gap

Forbidden gapE � 1 eV

Conduction band

Valence band

e

Hole

Atomcore

Freeelectron

Electron

Hole

e�

e�

■ Figure 29-5 Some electrons in semiconductors have enough thermal kinetic energy tobreak free and wander through the crystal, as shown in the crystal structure (a) and inthe bands (b).

a b

a

b

■ Figure 29-4 Compare the valence and conduction bands in an insulator (a) and in a semiconductor (b). Comparethese diagrams with the oneshown in Figure 29-2.

6. In pure germanium, which has a density of 5.23 g/cm3 and an atomic mass of 72.6 g/mol,there are 2.25�1013 free electrons/cm3 at room temperature. How many free electronsare there per atom?

7. At 200.0 K, silicon has 1.89�105 free electrons/cm3. How many free electrons are thereper atom at this temperature? What does this temperature represent on the Celsius scale?

8. At 100.0 K, silicon has 9.23�10�10 free electrons/cm3. How many free electrons are thereper atom at this temperature? What does this temperature represent on the Celsius scale?

9. At 200.0 K, germanium has 1.16�1010 free electrons/cm3. How many free electrons arethere 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

Fraction of Free Electrons in an Intrinsic SemiconductorBecause of the thermal kinetic energy of solid silicon at roomtemperature, there are 1.45�1010 free electrons/cm3. What is the number of free electrons per atom of silicon at roomtemperature?

Analyze the Problem• Identify the knowns and unknowns.

Known: Unknown:

� � 2.33 g/cm3 free e�/atom of Si � ?M � 28.09 g/molNA � 6.02�1023 atoms/molFor Si: 1.45�1010 free e�/cm3

Solve for the Unknown

�fraeteom

e�� � (�

N1

A�)(M )(�

1�

�)(1.45�1010 free e�/cm3 for Si)

� (�6.02�110

m23ol

atoms�)(�218.

m09

olg

�)(�21.3c3m

g

3�)(�1.45�1

c0m

10

3free e��)

� 2.90�10�13 free e�/atom of Sior, roughly 1 out of 3 trillion Si atoms has a free electron

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.

3

Substitute NA � 6.02�1023 atoms/mol, M � 28.09 g/mol, � � 2.33 g/cm3, free e�/cm3 Si � 1.45�1010 free e�/cm3

2

1

The electron, however, has left behind a hole at its previous location.Thus, as in a game of musical chairs, the negatively charged, free electronsmove in one direction and the positively charged holes move in the oppo-site direction. Pure semiconductors that conduct as a result of thermallyfreed electrons and holes are called intrinsic semiconductors. Because sofew electrons or holes are available to carry charge, conduction in intrinsicsemiconductors is very low, making their resistances very high.

e�

Si Si Si

Si

Si Si Si

Si Si Si

Atomcore

Freeelectron

Electron

Hole

e�

Math Handbook

Operations with Scientific Notationpages 842—843

Doped SemiconductorsThe conductivity of intrinsic semiconductors must be increased greatly

to make practical devices. Dopants are electron donor or acceptor atomsthat 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 calledan n-type semiconductor. Figure 29-6a shows a location in a silicon crys-tal where a dopant atom has replaced one of the silicon atoms. Four of the five As valence electrons bind to neighboring silicon. The fifth electronis called the donor electron. The energy of this donor electron is so closeto the conduction band that thermal energy can easily move the electronfrom the dopant atom into the conduction band, as shown in Figure 29-7a.Conduction in n-type semiconductors is increased by the availability ofthese extra donor electrons to the conduction band.

p-type semiconductors If an electron acceptor with three valence elec-trons, such as gallium (Ga), is used as a dopant for silicon, the product iscalled a p-type semiconductor. When a gallium atom replaces a siliconatom, one binding electron is missing, creating a hole in the silicon crys-tal, as shown in Figure 29-6b. Electrons in the conduction band can easilydrop into these holes, creating new holes. Conduction in p-type semicon-ductors is enhanced by the availability of the extra holes provided by theacceptor dopant atoms, as shown in Figure 29-7b.

Both p-type and n-type semiconductors are electrically neutral. Addingdopant atoms of either type does not add any net charge to a semicon-ductor. Both types of semiconductor use electrons and holes in conduction.Only a few dopant atoms per million silicon atoms are needed to increasethe conductivity of semiconductors by a factor of 1000 or more.

Silicon is doped by putting a pure silicon crystal in a vacuum with asample of the dopant material. The dopant is heated until it is vaporized,and the atoms condense on the cold silicon. The dopant diffuses into thesilicon on warming, and a thin layer of aluminum or gold is evaporatedonto the doped crystal. A wire is welded to this metal layer, allowing theuser to apply a potential difference across the doped silicon.

Section 29.1 Conduction in Solids 781

Excess holefree to move

Gallium Acceptor

Si Si Si

Si Ga Si

Si Si Si

Arsenic Donor

Excess electronfree to move

Si Si Si

Si As Si

Si Si Si

Acceptor levels

HoleHole

Forbidden gap

Donor levelsElectron

n-type p-type

Electron

Valence bands

Conduction bands

■ Figure 29-7 In an n-typesemiconductor (a), donor energylevels place electrons in theconduction band. In a p-typesemiconductor (b), acceptorenergy levels result in holes in the valence band.

■ Figure 29-6 A donor atom ofarsenic with five valence electronsreplaces a silicon atom andprovides an unbound electron inthe silicon crystal (a). An acceptoratom of gallium with three valenceelectrons creates a hole in thecrystal (b).

a b

a

b

782 Chapter 29 Solid-State Electronics

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.

a. What is the density of free electrons?

b. By what ratio is this density greater than that of intrinsic silicon with 1.45�1010 free e�/cm3?

c. Is conduction mainly by the electrons of the silicon or the arsenic?

Analyze the Problem• Identify the knowns and unknowns.

Known: Unknown:

1 As atom/106 Si atoms free e�/cm3 donated by 1 free e�/As atom As � ?4.99�1022 Si atoms/cm3 ratio of As-donated free e�

1.45�1010 free e�/cm3 to intrinsic free e� � ?in intrinsic Si

Solve for the Unknown

a. (�frecem

e3

�� from As) � (�Afrsee

ateo

�

m�)(�ASs

i aattoomm

ss

�)(�Sicamto

3ms

�)

(�frecem

e3

��) � (�11A

frseeat

eo

�

m�)(�1�

110

A6sSaitaotmoms

�)( )� 4.99�1016 free e�/cm3 from As donor in doped Si

b. Ratio � ( )� ( )� 3.44�106 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.

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.

3

Substitute 4.99�1016 free e�/cm3 in doped Si,1.45�1010 free e�/cm3 in intrinsic Si

4.99�1016 free e�/cm3 in doped Si����1.45�1010 free e�/cm3 in intrinsic Si

free e�/cm3 in doped Si���free e�/cm3 in intrinsic Si

Substitute free e�/As atom � 1 free e�/1 As atom, As atoms/Si atoms �1 As atom/1�106 Si atoms, Si atoms/cm3 � 4.99�1022 Si atoms/cm3

4.99�1022 Si atoms���

cm3

2

1

Thermistors The electric conductivity of intrinsic and extrinsic semicon-ductors is sensitive to both temperature and light. Unlike metals in whichconductivity is reduced when the temperature rises, an increase in temper-ature of a semiconductor allows more electrons to reach the conductionband, and conductivity increases and resistance decreases. One semicon-ductor device, the thermistor, is designed so that its resistance dependsvery strongly on temperature. The thermistor can be used as a sensitivethermometer and to compensate for temperature variations of other com-ponents in an electric circuit. Thermistors also can be used to detect radiowaves, infrared radiation, and other forms of radiation.

Arsenic Donor

Excesselectron freeto move

Si Si Si

Si As Si

Si Si Si

Personal Tutor For an online tutorial ondoped silicon, visit physicspp.com.

Section 29.1 Conduction in Solids 783

16. Carrier Mobility In which type of material, a conductor, a semiconductor, or an insulator, areelectrons most likely to remain with the same atom?

17. Semiconductors If the temperature increases,the number of free electrons in an intrinsic semi-conductor increases. For example, raising the temperature by 8°C doubles the number of freeelectrons in silicon. Is it more likely that an intrinsicsemiconductor or a doped semiconductor will havea conductivity that depends on temperature?Explain.

18. Insulator or Conductor? Silicon dioxide is widelyused in the manufacture of solid-state devices. Itsenergy-band diagram shows a gap of 9 eV betweenthe valence band and the conduction band. Is itmore useful as an insulator or a conductor?

19. Conductor or Insulator? Magnesium oxide hasa forbidden gap of 8 eV. Is this material a conduc-tor, an insulator, or a semiconductor?

20. Intrinsic and Extrinsic Semiconductors You aredesigning an integrated circuit using a single crystalof silicon. You want to have a region with relativelygood insulating properties. Should you dope thisregion or leave it as an intrinsic semiconductor?

21. Critical Thinking Silicon produces a doubling ofthermally liberated carriers for every 8°C increasein temperature, and germanium produces a dou-bling of thermally liberated carriers for every 13°Cincrease. It would seem that germanium would besuperior for high-temperature applications, but theopposite is true. Explain.

29.1 Section Review

physicspp.com/self_check_quiz

■ Figure 29-8 Photographers use light meters to measure theintensity of incident light on anobject.

11. If you wanted to have 1�104 as many electrons from arsenicdoping 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 5�103 as many electrons from arsenicdoping as thermally free electrons in the germanium semiconductordescribed in problem 6, how many arsenic atoms should there beper germanium atom?

13. Germanium at 400.0 K, has 1.13�1015 thermally liberated carriers/cm3.If it is doped with 1 As atom per 1 million Ge atoms, what is theratio of doped carriers to thermal carriers?

14. Silicon at 400.0 K, has 4.54�1012 thermally liberated carriers/cm3. If it is doped with 1 As atom per 1 million Si, what is the ratio ofdoped carriers to thermal carriers?

15. Based on problem 14, draw a conclusion about the behavior ofgermanium devices as compared to silicon devices at temperaturesin excess of the boiling point of water.

Light meters Other useful applications of semiconductors depend ontheir light sensitivity. When light falls on a semiconductor, the light canexcite electrons from the valence band to the conduction band in the sameway that other energy sources excite atoms. Thus, the resistance decreasesas the light intensity increases. Extrinsic semiconductors can be tailored torespond to specific wavelengths of light. These include the infrared and vis-ible regions of the spectrum. Materials such as silicon and cadmium sul-fide serve as light-dependent resistors in light meters used by lightingengineers to design the illumination of stores, offices, and homes; and byphotographers to adjust their cameras to capture the best images, as shownin Figure 29-8.

Laura Sifferlin

Forward-Biased Diode

R

I

n-typep-type

New holescreated

Electrons and holesrecombine at junction

New electronsadded

Reverse-Biased Diode

Holesfilled

n-type

I

R

p-type

Electronsleave

Metal

Junction

Junction Diode

Depletion layerElectrons

Metaln-typep-type

Holes

a

b c

784 Chapter 29 Solid-State Electronics

29.2 Electronic Devices

� Objectives• Describe how diodes limit

current to motion in only one direction.

• Explain how a transistor canamplify or increase voltagechanges.

� Vocabulary

diodedepletion layertransistormicrochip

■ Figure 29-9 A diagram of the pn-junction diode (a) showsthe depletion layer, where thereare no charge carriers. Comparethe magnitude of current in areverse-biased diode (b) and a forward-biased diode (c).

Today’s electronic instruments, such as radios, televisions, CD players,and microcomputers, rely on semiconductor devices that are com-

bined on chips of silicon a few millimeters wide. In these devices, currentand 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 andamplify voltages.

DiodesThe simplest semiconductor device is the diode. A diode consists of a

sandwich of p-type and n-type semiconductors. Rather than two separatepieces of doped silicon being joined, a single sample of intrinsic silicon istreated first with a p-dopant, then with an n-dopant. Metal contacts are coatedon 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 intothe 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 negativecharge. These charges produce forces in the opposite direction that stopfurther movement of charge carriers. The region around the junction is leftwith neither holes nor free electrons. This region, depleted of charge carri-ers, is called the depletion layer. Because it has no charge carriers, it is apoor conductor of electricity. Thus, a junction diode consists of relativelygood conductors at the ends that surround a poor conductor.

Interactive Figure To see an animation on diodes, visit physicspp.com.

Section 29.2 Electronic Devices 785

A Diode in a Simple Circuit A silicon diode, with I/V characteristics like those shown inFigure 29-10, is connected to a power supply through a 470-� resistor. The power supplyforward-biases the diode, and its voltage is adjusted until the diode current is 12 mA. What is the power supply voltage?

Analyze and Sketch the Problem• Draw a circuit diagram connecting a diode, a 470-� resistor,

and a power supply. Indicate the direction of current.

Known: Unknown:

I � 0.012 A Vb � ?Vd � 0.70 VR � 470 �

Solve for the UnknownThe voltage drop across the resistor is known from V � IR,and the power supply voltage is the sum of the resistor andthe 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

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.

3

2

1

�2 0 1�3 �1

20

15

10

5

0

�5

Cu

rren

t (m

A)

Voltage (V)

Diode Currentv. Voltage

R

I

Diode

Vd

Vb

Math Handbook

Order of Operationspage 843

■ Figure 29-10 The graphindicates current-voltagecharacteristics for a siliconjunction diode.

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 holesin the p-type semiconductor are attracted toward the battery. The width ofthe depletion layer is increased, and no charge carriers meet. Almost nocurrent passes through the diode: it acts like a very large resistor, almost aninsulator. 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 voltageof the battery is large enough—0.6 V for a silicon diode—electrons reachthe p-end and fill the holes. The depletion layer is eliminated, and a current passes through the diode. The battery continues to supply electronsfor the n-end. It removes electrons from the p-end, which is the same assupplying holes. With further increases in voltage from the battery, the cur-rent 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 silicondiode as a function of voltage across it. If the applied voltage is negative, thereverse-biased diode acts like a very high-value resistor and only a tiny currentpasses (about 10�11 A for a silicon diode). If the voltage is positive, the diodeis 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 voltageto DC voltage with only one polarity. When a diode is used in a circuit thatdoes this, it is called a rectifier. The arrow in the symbol for the diode, whichyou’ll see in Example Problem 4, shows the direction of conventional current.

786 Chapter 29 Solid-State Electronics

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 wereconnected in series but with improper polarity.

26. A germanium diode has a voltage drop of 0.40 V when 12 mApasses through it. If a 470-� resistor is used in series, what batteryvoltage is needed?

Approximations often are used in diode circuits because diode resistance is not constant. For diode circuits, the firstapproximation ignores the forward voltage drop across thediode. The second approximation takes into account a typicalvalue for the diode voltage drop. A third approximation usesadditional 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-voltage curve for the diode. Thestraight line shows current-voltage conditions for all possiblediode 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 oneend, to a 1.8-V drop, 0.0 mA at the other end.

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 using the accompanying diode graph.

4. Estimate the error for all three approximations, ignoring thebattery and resistor. Discuss the impact of greater battery voltages on the errors.

1.81.41.00.60.2

14.0

12.0

10.0

8.0

6.0

4.0

2.0

Cu

rren

t (

mA

)

Voltage (V)

0.0

Graphic solution

Diode Current v. Voltage

■ Figure 29-11 Diode lasers areused as both light emitters anddetectors in bar-code scanners.

Light-emitting diodes Diodes made from combinations of gallium andaluminum with arsenic and phosphorus emit light when they are forward-biased. When electrons reach the holes in the junction, they recombineand release the excess energy at the wavelengths of light. These diodes arecalled light-emitting diodes, or LEDs. Some LEDs are configured to emit anarrow beam of coherent, monochromatic laser light. Such diode lasersare compact, powerful light sources. They are used in CD players, laserpointers, 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 areverse-biased pn-junction diode creates electrons and holes, resulting in acurrent that depends on the light intensity.

Getty Images

Transistors and Integrated CircuitsA transistor is a simple device made of doped semiconductor material.

An npn-transistor consists of layers of n-type semiconductor on either sideof a thin p-type layer. The central layer is called the base and the regions oneither side are the emitter and the collector. The schematic symbols for thetwo transistor types are shown in Figure 29-12. The arrow on the emittershows the direction of conventional current.

The operation of an npn-transistor is illustrated in Figure 29-13. The twopn-junctions in the transistor can be thought of as initially forming twoback-to-back diodes. The battery on the right, VC, keeps the collector morepositive than the emitter. The base-collector diode is reverse-biased, with awide 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 positivethan the emitter. That makes the base-emitter diode forward-biased, allow-ing current IB from the base to the emitter.

The very thin base region is part of both diodes in the transistor. Thecharges injected by IB reduce the reverse bias of the base-collector diode,permitting charge to flow from the collector to the emitter. A small changein IB thus produces a large change in IC.

The collector current causes a voltage drop across resistor RC. Smallchanges in the voltage, VB, applied to the base produce large changes in thecollector current and thus changes in the voltage drop across RC. As aresult, the transistor amplifies small voltage changes into much largerchanges. If instead the center layer is an n-type region, then the device iscalled a pnp-transistor. A pnp-transistor works the same way, except that thepotentials of both batteries are reversed.

Current gain The current gain from the base circuit to the collector circuitis a useful indicator of the performance of a transistor. Although the basecurrent is quite small, it is dependent on the base-emitter voltage that iscontrolling the collector current. For example, if VB in Figure 29-13 isremoved, the collector current will drop to zero. If VB is increased, the basecurrent, IB, increases. The collector current, IC, will also increase, but manytimes more (perhaps 100 times or so). The current gain from the base tothe collector ranges from 50 to 300 for general-purpose transistors.

Section 29.2 Electronic Devices 787

npn-transistor

E

C

n

p

n

B

B B � base

C � collector

E � emitter

C

E

pnp-transistor

Circuitsymbols

Transistors

C

E

E

C

p

n

p

B

B

RB

VC

RC

B

IB

IC

VB

■ Figure 29-12 Compare thecircuit symbols used to representa pnp-transistor (a) and an npn-transistor (b).

■ Figure 29-13 A circuit using annpn-transistor demonstrates howvoltage can be amplified.

a b

� Diode Laser A typical diodelaser emits light at 800 nm, whichis the near infrared. The beam isoutput from a small spot on aGaAlAs chip, and when poweredby 80 mA, the diode has a forwardvoltage drop of about 2 V. Diodelasers commonly are used inoptical fiber transmissions. �

Interactive Figure To see an animation on transistors, visitphysicspp.com.

In a tape player, the small voltage variations from the voltage induced ina coil by magnetized regions on the tape are amplified to move the speakercoil. 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 operationsor to add numbers together. In these cases, they act as fast switches ratherthan as amplifiers.

Microchips An integrated circuit, called a microchip, consists of thou-sands of transistors, diodes, resistors, and conductors, each less than amicrometer across. All these components can be made by doping siliconwith donor or acceptor atoms. A microchip begins as an extremely puresingle crystal of silicon, 10–30 cm in diameter and 1–2 m long, as shownin Figure 29-14. The silicon is sliced by a diamond-coated saw into wafersless than 1-mm thick. The circuit is then built layer by layer on the surfaceof this wafer.

By a photographic process, most of the wafer’s surface is covered by aprotective layer, with a pattern of selected areas left uncovered so that theycan 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 inthe unprotected regions. By controlling the amount of exposure, the engi-neer can control the conductivity of the exposed regions of the chip. Thisprocess creates resistors, as well as one of the two layers of a diode or oneof the three layers of a transistor. The protective layer is removed, andanother one with a different pattern of exposed areas is applied. Then thewafer is exposed to another dopant, often gallium, producing pn-junctions.If a third layer is added, npn-transistors can be formed. The wafer also maybe exposed to oxygen to produce areas of silicon dioxide insulation. Alayer exposed to aluminum vapors can produce a pattern of thin conduct-ing pathways among the resistors, diodes, and transistors.

788

■ Figure 29-14 A technicianprepares a large silicon crystal to be sliced into wafers formicrochips.

Red LightMake a series circuit with a DCpower supply, a 470-� resistor,and a red LED. Connect the shortlead of the LED to the negativeside of the power supply which isplugged into a GFCI-protectedreceptacle. Attach the other leadto the resistor. Connect theremaining resistor lead to thepositive side of the power supply.Slowly increase the voltage untilthe LED glows. Note the voltagesetting on the power supply.1. Hypothesize what will happenif you reverse the direction ofcurrent. 2. Experiment by reversing theconnections to the battery.

Analyze and Conclude3. Explain your observations interms of LED characteristics.

Science Photo Library/Photo Researchers

Section 29.2 Electronic Devices 789

27. Transistor Circuit The emitter current in a tran-sistor circuit is always equal to the sum of the basecurrent and the collector current: IE � IB IC. If thecurrent 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 characterizedin Figure 29-10 is forward-biased by a battery anda series resistor so that there is more than 10 mAof 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 diodeor the voltage across the resistor increase?

b. By how much does the current through theresistor increase?

29. Diode Resistance Compare the resistance of apn-junction diode when it is forward-biased andwhen it is reverse-biased.

30. Diode Polarity In a light-emitting diode, whichterminal should be connected to the p-end to makethe diode light?

31. Current Gain The base current in a transistor circuit measures 55 A and the collector currentmeasures 6.6 mA. What is the current gain frombase to collector?

32. Critical Thinking Could you replace an npn-transistor with two separate diodes connected bytheir p-terminals? Explain.

29.2 Section Review

physicspp.com/self_check_quiz

■ Figure 29-15 Microchips formthe heart of the central processingunit of computers. A penny isshown in the picture to representscale.

Thousands of identical circuits, usually called chips, are produced at onetime on a single wafer. The chips are then tested, sliced apart, and mountedin a carrier; wires are attached to the contacts; and the final assembly isthen sealed into a protective plastic body. The tiny size of microchips,shown in Figure 29-15, allows the placement of complicated circuits in asmall space. Because electronic signals need only travel tiny distances, thisminiaturization has increased the speed of computers. Chips now are usedin appliances and automobiles as well as in computers.

Semiconductor electronics requires that physicists, chemists, and engi-neers work together. Physicists contribute their understanding of themotion of electrons and holes in semiconductors. Physicists and chemiststogether add precisely controlled amounts of dopants to extremely puresilicon. Engineers develop the means of mass-producing chips containingthousands of miniaturized diodes and transistors. Together, their effortshave brought our world into this electronic age.

Horizons Companies

790

Diode Current and VoltageSemiconductor devices, such as diodes and transistors, are fabricated using asemiconductor that is made of partly p-type material and partly n-type material. Asemiconductor doped with donor atoms is called an n-type semiconductor, whilea semiconductor doped with an element leaving a vacancy or a hole in the latticestructure 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 characteristicsof a diode that is placed in a direct current circuit and compare the response withyour knowledge of resistors.

QUESTIONHow do the current-voltage characteristics of a diode, an LED, and a resistor compare?

Alternate CBL instructionscan be found on the Web site.

physicspp.com

■ Collect and organize data of voltage drop andcurrent for a diode and an LED.

■ Measure the current passing through a diodeand an LED as a function of voltage drop.

■ Compare and contrast the current-voltagecharacteristics of a resistor with diodes.

■ Use caution with electric connections.Avoid contact with the resistor, which maybecome hot.

■ Plug power supplies into only GFCI-protectedreceptacles to prevent shock hazard.

DC power supply, variable, 0–12 VDC100-Ω resistor, �

12

�- or 1-W 1N4002 diode LED, red ammeter, DC, 0–100 mAvoltmeter, 0–5 VDChook-up wire

1. Prepare a data table similar to the one shownon page 791.

2. As indicated on the schematic diagram below,wire the negative terminal of the power supplyto the negative side of the ammeter using thehook-up wire provided.

3. Locate the end of the diode with the silver bandaround it. Attach this end to the positive side ofthe ammeter.

4. Attach one end of the 100-Ω resistor to the freeend of the diode.

Procedure

Materials

Safety Precautions

Objectives

DiodeV

mA

100 �

0�12 VDC

LED

��

�

�

a

b

5. Attach a wire from the free end of the 100-Ωresistor to the positive lead on the power supply.

6. As shown in the schematic, the voltmeter is inparallel with the diode. Attach a wire from thepositive side of the voltmeter to the end of thediode attached to the resistor. Connect thenegative side of the voltmeter to the end of thediode 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 isturned to zero and plug it in. Slowly turn up the power supply to increase the voltage dropacross the diode from 0 up to 0.8 V, in 0.1-Vincrements. Record the corresponding currentat each voltage. CAUTION: If your currentgoes higher than the capacity of yourammeter, do not increase the voltage anyhigher, and discontinue taking readings.Turn the power supply to zero and unplug it.

8. Observe the LED leads. One should be shorterthan the other. Replace the 1N4002 diode withthe LED so that it corresponds with part b ofthe schematic.

9. Connect the shorter lead on the LED to thepositive side of the ammeter (negative side ofthe voltmeter) where the silver banded end ofthe diode had been connected. Connect thelonger lead of the LED to the resistor and tothe positive side of the voltmeter.

10. Plug in the power supply. Slowly turn up thepower supply to increase the voltage dropacross the LED from 0 up to 2.0 V, in 0.1-Vincrements. Record the corresponding currentat each voltage. Additionally, observe the LEDand record your observations of it.

1. Make and Use Graphs On one chart, sketchand label graphs of current versus voltage dropfor both the diode and the LED. Place currenton the y-axis and voltage on the x-axis. Whatare the shapes of these curves?

2. Formulate Models Using Ohm’s law, computeand plot on the same graph the voltage-currentrelationship for a 100-Ω resistor from 0 to 2 V.Label this line 100 Ω. What is the form of this plot?

1. Compare and Contrast How do the current-voltage 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 describedas having a turn-on voltage. What is the turn-on voltage for a silicon diode? For the LED youused?

4. Explain Why would the specifications for anLED give a light output at a specific current,such as 20 mA?

What could be done to get better measurements ofcurrent for the diode?

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?

Real-World Physics

Going Further

Conclude and Apply

Analyze

791

To find out more about solid-state electronics,visit the Web site: physicspp.comphysicspp.com

1.7 ————

1.8 ————

1.9 ————

2.0 ————

Data TableVoltage (V)

Drop Across DiodeDiode Current (mA) LED Current (mA)

0

0.1

0.2

0.3

792 Extreme Physics

1. Debate the Issue Are there ethicallimits to the development of artificialintelligence?

2. Recognize Cause and Effect Whatproblems might cause an expert systemto make a poor decision?

3. Critical Thinking In what situationsmust artificial intelligence be absolutelyrational, and in what situations should it include human biases?

Going Further

Artificial intelligence also is used to createexpert systems in computers that are pro-grammed with knowledge about specific topics.Humans can tell the computer the details of aspecific situation, and the computer calculatesthe most logical course of action. In a medicalenvironment, an expert system can be used toaccurately diagnose disorders. Artificial intelli-gence weighs the facts of the situation and theninfers which actions are most appropriate.However, artificial intelligence can operate only with facts that have been taught to thecomputer. Users must constantly be aware ofthis limitation of expert systems.

Artificial IntelligenceThe phrase artificial intelligence was firstused in 1955. It is defined as “the scientificunderstanding of the mechanisms underlyingthought and intelligent behavior and theirembodiment in machines.” Sometimes, a taskneeds artificial intelligence to be very logical.At other times, it may need artificial intelli-gence to think and behave with human biases.The goals in the field of artificial intelligenceare to develop systems that can do both.

Applications Artificial intelligence alreadyis used in many areas, and it will do even morefor us in the future. When a computer playschess, it searches through hundreds of thou-sands of possible moves before selecting thebest one. Research is being done to improvethe efficiency of search algorithms.

Artificial intelligence currently is used forspeech recognition to allow hands-free dialing ofcell phones and for some interactive telephonetransactions. It is not yet fully capable of under-standing natural language, but that is a goal.

Three-dimensional computer vision isanother future application. To mimic the sensory input and behaviors of humans, com-puters need to extract three-dimensional realityfrom two-dimensional images. Progress hasbeen made, but humans are still much betterthan computers at this. With improved vision,artificial intelligence may control automobileson Earth, or robots exploring another planet,with no human navigators needed.

Careers Studying mathematics, mathematicallogic, and computer programming languages is important for developing systems that canmake rational decisions. Knowledge of psy-chology assures that these decisions also canhave a human character.

A prototype Mars rover decides how tonavigate obstacles.

The robot, Kismet, displays human facial expressions.

(l)NASA, (r)Sam Ogden/Photo Researchers

29.1 Conduction in Solids

Vocabulary• semiconductors (p. 775)

• band theory (p. 776)

• intrinsic semiconductors (p. 780)

• dopants (p. 781)

• extrinsic semiconductors (p. 781)

29.2 Electronic Devices

Vocabulary• diode (p. 784)

• depletion layer (p. 784)

• transistor (p. 787)

• microchip (p. 788)

Key Concepts• Electric conduction may be explained by the band theory of solids.

• In solids, the allowed energy levels for outer electrons in an atom are spreadinto 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 conductionband is partially filled.

• Electrons in metals have a fast random motion. A potential difference acrossthe metal causes a slow drift of electrons, called an electric current.

• In insulators, more energy is needed to move electrons into the conductionband than is generally available.

• Conduction in semiconductors is enhanced by doping pure crystals withsmall amounts of other kinds of atoms, called dopants.

• n-type semiconductors are doped with electron donor atoms, and they conductby 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 theyconduct by making holes available to electrons in the conduction band.

• Gallium, with three valence electrons, is an example of an acceptor atom.

Key Concepts• 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 rectifiercircuits to convert AC to DC.

• Electrons and holes near either side of the diode junction combine toproduce a region without charge carriers known as the depletion layer.

• Applying a potential difference of the proper polarity across the diode makesthe depletion layer even wider, no current is observed, and the diode is saidto be reverse-biased.

• Reversing the polarity of the applied potential across the diode greatlyreduces 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 thincompared to the other layers, the emitter and collector.

• A transistor can act as an amplifier to convert a weak signal into a muchstronger one.

• The ratio of the collector-emitter current to the base current is known as thecurrent gain and is a useful measure of transistor amplification.

• Conductivity of semiconductors increases with increasing temperature orillumination, making them useful as thermometers or light meters. Diodesthat emit light when a potential is applied are used in optical devices.

793physicspp.com/vocabulary_puzzlemaker

33. Complete the concept map using the followingterms: transistor, silicon diode, emits light, conductsboth ways.

Mastering Concepts 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-typesemiconductor? (29.1)

37. An ohmmeter is an instrument that places apotential 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 onwhich end of the diode was connected to thepositive terminal of the ohmmeter? Explain. (29.2)

38. What is the significance of the arrowhead at theemitter in a transistor circuit symbol? (29.2)

39. Describe the structure of a forward-biased diode,and explain how it works. (29.2)

Applying Concepts 40. For the energy-band diagrams shown in Figure 29-16,

which one represents a material with an extremelyhigh resistance?

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?

43. The resistance of graphite decreases as temperaturerises. Does graphite conduct electricity more likecopper or more like silicon does?

44. Which of the following materials would make abetter insulator: one with a forbidden gap 8-eVwide, one with a forbidden gap 3-eV wide, or onewith no forbidden gap?

45. Consider atoms of the three materials in problem44. From which material would it be most difficultto remove an electron?

46. State whether the bulb in each of the circuits ofFigure 29-17 (a, b, and c) is lighted.

47. In the circuit shown in Figure 29-18, state whetherlamp L1, lamp L2, both, or neither is lighted.

48. Use the periodic table to determine which of thefollowing elements could be added to germaniumto 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 apn-junction diode is forward-biased or reverse-biased?

50. If the ohmmeter in problem 49 shows the lowerresistance, is the ohmmeter lead on the arrow sideof the diode at a higher or lower potential than thelead connected to the other side?

51. If you dope pure germanium with gallium alone, do you produce a resistor, a diode, or a transistor?

L1 L2

794 Chapter 29 Solid-State Electronics For more problems, go to Additional Problems, Appendix B.

■ Figure 29-16

■ Figure 29-18

a b c

a b c

Concept Mapping

■ Figure 29-17

LEDcopper

wire

conductsone way

amplifies

CircuitComponents

Chapter 29 Assessment 795physicspp.com/chapter_test

52. Draw the time-versus-amplitude waveform for pointA in Figure 29-19a assuming an input ACwaveform, as shown in Figure 29-19b.

Mastering Problems 29.1 Conduction in Solids

53. How many free electrons exist in a cubic centimeterof sodium? Its density is 0.971 g/cm3, its atomicmass is 22.99 g/mol, and there is 1 free electron per atom.

54. At a temperature of 0°C, thermal energy frees1.55�109 e�/cm3 in pure silicon. The density of silicon is 2.33 g/cm3, and the atomic mass ofsilicon is 28.09 g/mol. What is the fraction of atomsthat have free electrons?

29.2 Electronic Devices

55. LED The potential drop across a glowing LED isabout 1.2 V. In Figure 29-20, the potential dropacross the resistor is the difference between thebattery voltage and the LED’s potential drop. Whatis the current through each of the following?

a. the LEDb. the resistor

56. Jon wants to raise the current through the LED in problem 55 up to 3.0�101 mA so that it glowsbrighter. Assume that the potential drop across theLED is still 1.2 V. What resistor should be used?

57. Diode A silicon diode with I/V characteristics, asshown in Figure 29-10, is connected to a batterythrough a 270-� resistor. The battery forward-biasesthe diode, and the diode current is 15 mA. What isthe battery voltage?

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.

59. Assume that the switch shown in Figure 29-21 is on, and that there is a 0.70-V drop across the base-emitter junction and a current gain from base tocollector of 220.

a. Determine the base current.b. Determine the collector current.c. Determine the voltmeter reading.

Mixed Review60. The forbidden gap in silicon is 1.1 eV.

Electromagnetic waves striking the silicon causeelectrons to move from the valence band to theconduction band. What is the longest wavelength of radiation that could excite an electron in thisway? Recall that E � 1240 eV�nm/�.

61. Si Diode A particular silicon diode at 0°C shows acurrent of 1.0 nA when it is reverse-biased. Whatcurrent can be expected if the temperature increasesto 104°C? Assume that the reverse-bias voltageremains constant. (The thermal carrier productionof silicon doubles for every 8°C increase intemperature.)

62. Ge Diode A particular germanium diode at 0°Cshows a current of 1.5 A when it is reverse-biased.What current can be expected if the temperatureincreases to 104°C? Assume that the reverse-biasingvoltage remains constant. (The thermal charge-carrierproduction of germanium doubles for every 13°Cincrease in temperature.)

120,000 �

1500 �

15 V

3.5 V

A

A

V

1.2 VBatteryV � 6.0 V

R � 240 �

LED

A

Time

AC

vo

ltag

e

■ Figure 29-19

■ Figure 29-20

■ Figure 29-21

a

b

63. LED A light-emitting diode (LED) produces greenlight with a wavelength of 550 nm when an electronmoves from the conduction band to the valenceband. Find the width of the forbidden gap in eV in this diode.

64. Refer to Figure 29-22.

a. Determine the voltmeter reading.

b. Determine the reading of A1.

c. Determine the reading of A2.

Thinking Critically65. Apply Concepts A certain motor, in Figure 29-23,

runs in one direction with a given polarity appliedand reverses direction with the opposite polarity.

a. Which circuit (a, b, or c) will allow the motorto run in only one direction?

b. Which circuit will cause a fuse to blow if theincorrect polarity is applied?

c. Which circuit produces the correct direction ofrotation regardless of the applied polarity?

d. Discuss the advantages and disadvantages of all three circuits.

66. Apply Concepts The I/V characteristics of twoLEDs that glow with different colors are shown inFigure 29-24. Each is to be connected through aresistor to a 9.0-V battery. If each is to be run at a current of 0.040 A, what resistors should bechosen for each?

67. Apply Concepts Suppose that the two LEDs inproblem 66 are now connected in series. If the same battery is to be used and a current of 0.035 Ais desired, what resistor should be used?

Writing in Physics68. Research the Pauli exclusion principle and the

life of Wolfgang Pauli. Highlight his outstandingcontributions to science. Describe the application of the exclusion principle to the band theory ofconduction, especially in semiconductors.

69. Write a one-page paper discussing the Fermi energylevel as it applies to energy-band diagrams forsemiconductors. Include at least one drawing.

Cumulative Review70. An alpha particle, a doubly ionized (2) helium

atom, has a mass of 6.7�10�27 kg and isaccelerated by a voltage of 1.0 kV. If a uniformmagnetic field of 6.5�10�2 T is maintained on thealpha particle, what will be the particle’s radius ofcurvature? (Chapter 26)

71. What is the potential difference needed to stopphotoelectrons that have a maximum kinetic energyof 8.0�10�19 J? (Chapter 27)

72. Calculate the radius of the orbital associated with the energy level E4 of the hydrogen atom.(Chapter 28)

0.5 2.51.51 2

0.02

0.04

Cu

rren

t (A

)Voltage (V)

0

LED Current v. Voltage

�

�

�

�

�

�

�

�

M M

M

V

A1 A2

220 �

10.0 V

All diodesare silicon.

796 Chapter 29 Solid-State Electronics For more problems, go to Additional Problems, Appendix B.

■ Figure 29-23

■ Figure 29-22

■ Figure 29-24

c

a b

1. Which statement about diodes is false? Diodes can ___________.

amplify voltage emit light

detect light rectify AC

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.

1.24�1021 9.26�1024

9.26�1022 1.17�1027

3. The base current in a transistor circuit measures45 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 currentincreased?

5 A 10 mA

1 mA 190 A

5. A transistor circuit shows a collector current of4.75 mA, and the base to collector current gainis 250. What is the base current?

1.19 A 4.75 mA

18.9 A 1190 mA

6. Which line in the following table best describesboth n- and p-type silicon semiconductors?

7. Which line in the following table best describesthe behavior of intrinsic silicon semiconductors to increasing temperature?

8. Thermal electron production in silicon doublesfor every 8°C increase in temperature. A silicondiode at 0°C shows a current of 2.0 nA whenreverse-biased. What will be the current at112°C if the reverse-bias voltage is constant?

11 A 44 A

33 A 66 A

Extended Answer9. A silicon diode is connected in the forward-

biased direction to a power supply though a485-� resistor, as shown below. If the diodevoltage drop is 0.70 V, what is the power supplyvoltage when the diode current is 14 mA?

I � 14 mA

R � 485 �

VbVd � 0.70 V

Multiple Choice

Focus

If students near you are talking during a test, you should move. Respond only to the instructorwhen 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 797physicspp.com/standardized_test

Effect of Increasing Temperature on Intrinsic Silicon Semiconductors

Conductivity Resistance

Increases

Increases

Decreases

Decreases

Increases

Decreases

Increases

Decreases

n-type p-type

Gallium-doped

Added electrons

Arsenic-doped

Added holes

Added electrons

Arsenic-doped

Added holes

Gallium-doped