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680 Chapter 19 Electronic Materials 19-1 Ohm’s Law and Electrical Conductivity 681

S 19-1 Ohm’s Law and Electrical Conductivity

ilicon-based microelectronics are a ubiquitous part of modern life. With
microchips in items from laundry machines and microwaves to cell phones,
in MP3 players and from personal computers to the world’s fastest super Most of us are familiar with the common form of Ohm’s law,
computers, silicon was the defining material of the later 20th century and will
dominate computer-based and information-related technologies for the foresee- V 5 IR (19-1)
able future. where V is the voltage (volts, V), I is the current (amperes or amps, A), and R is the resis-
While silicon is the substrate or base material of choice for most devices, tance (ohms, V) to the current flow. This law is applicable to most but not all materials.
microelectronics include materials of nearly every class, including metals such as The resistance (R) of a resistor is a characteristic of the size, shape, and properties of the
copper and gold, other semiconductors such as gallium arsenide, and insulators such material according to
as silicon dioxide. Even semiconducting polymers are finding applications in such l l
R5 5 (19-2)
devices as light-emitting diodes. A A
In this chapter, we will discuss the principles of electrical conductivity in where l is the length (cm) of the resistor, A is the cross-sectional area (cm2) of the resistor,
metals, semiconductors, insulators, and ionic materials. We will see that a defining r is the electrical resistivity (ohm ? cm or V ? cm), and s, which is the reciprocal of r, is
difference between metals and semiconductors is that as temperature increases, the the electrical conductivity (ohm21 ? cm21). The magnitude of the resistance depends
resistivity of a metal increases, while the resistivity of a semiconductor decreases. upon the dimensions of the resistor. The resistivity or conductivity does not depend on
This critical difference arises from the band structures of these materials. The band the dimensions of the material. Thus, resistivity (or conductivity) allows us to compare
structure consists of the array of energy levels that are available to or forbidden different materials. For example, silver is a better conductor than copper. Resistivity is a
for electrons to occupy and determines the electronic behavior of a solid, such as microstructure-sensitive property, similar to yield strength. The resistivity of pure copper
whether it is a conductor, semiconductor, or insulator. is much less than that of commercially pure copper, because impurities in commercially
The conductivity of a semiconductor that does not contain impurities pure copper scatter electrons and contribute to increased resistivity. Similarly, the
generally increases exponentially with temperature. From a reliability standpoint, resistivity of annealed, pure copper is slightly lower than that of cold-worked, pure
an exponential dependence of conductivity on temperature is undesirable for copper because of the scattering effect associated with dislocations.
electronic devices that generate heat as they operate. Thus, semiconductors are In components designed to conduct electrical energy, minimizing power losses
doped (i.e., impurities are intentionally added) in order to control the conductivity is important, not only to conserve energy, but also to minimize heating. The electrical
of semiconductors with extreme precision. We will learn how dopants change the power P (in watts, W) lost when a current flows through a resistance is given by
band structure of a semiconductor so that the electrical conductivity can be tailored
P 5 VI 5 I2R (19-3)
for particular applications.
Metals, semiconductors, and insulators are all critical components of A high resistance R results in larger power losses. These electrical losses are known as
integrated circuits. Some features of integrated circuits are now approaching joule heating losses.
atomic-scale dimensions, and the fabrication of integrated circuits is arguably the A second form of Ohm’s law is obtained if we combine Equations 19-1 and
most sophisticated manufacturing process in existence. It involves simultaneously 19-2 to give
fabricating hundreds of millions, and even billions, of devices on a single microchip I V
and represents a fundamentally different manufacturing paradigm from that of 5
A l
any other process. We will learn about some of the steps involved in fabricating
integrated circuits, including the process of depositing thin films (films on the If we define I⁄A as the current density J (A⁄cm2) and V⁄l as the electric field E (V⁄cm), then
order of 10 Å to 1 mm in thickness).
J 5 E (19-4)
We will examine some of the properties of insulating materials. Insulators
are used in microelectronic devices to electrically isolate active regions from one The current density J is also given by
another. Insulators are also used in capacitors due to their dielectric properties. Finally, J 5 nqv
we will consider piezoelectric materials, which change their shape in response to an
applied voltage or vice versa. Such materials are used as actuators in a variety of where n is the number of charge carriers (carriers ycm3), q is the charge on each carrier
applications. (1.6 3 10219 C), and v is the average drift velocity (cm ys) at which the charge carriers
Superconductors comprise a special class of electronic materials. Super- move [Figure 19-1(a)]. Thus,
conductors are materials that exhibit zero electrical resistance under certain condi-
tions (which usually includes a very low temperature on the order of 135 K or less) E 5 nqv or 5 nq v
and that completely expel a magnetic field. A discussion of superconductivity is E
beyond the scope of this text.
Diffusion occurs as a result of temperature and concentration gradients, and drift occurs
as a result of an applied electric or magnetic field. Conduction may occur as a result of
diffusion, drift, or both, but drift is the dominant mechanism in electrical conduction.

1 2
cm2
The term vyE is called the mobility of the carriers (which in the case of
metals is the mobility of electrons): V?s

v
5
E

Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

76761_ch19.indd 680 24/10/14 7:56 PM 76761_ch19.indd 681 24/10/14 7:56 PM

682 Chapter 19 Electronic Materials 19-1 Ohm’s Law and Electrical Conductivity 683

Figure 19-1 (a) Charge carriers, Table 19-1 Electrical conductivity of selected
such as electrons, are deflected materials at T 5 300 K*
by atoms or defects and take an
irregular path through a conduc- Conductivity Conductivity
Material (ohm21 · cm21) Material (ohm21 · cm21)
tor. The average rate at which the
carriers move is the drift velocity v. Superconductors Semiconductors
(b) Valence electrons in metals Hg, Nb3Sn Group 4B elements
move easily. (c) Covalent bonds YBa2Cu3O72x Infinite (under certain conditions Si 4 3 1026
must be broken in semiconductors MgB2 such as low temperatures) Ge 0.02
and insulators that do not contain Metals Compound semiconductors
impurities for an electron to be
Alkali metals GaAs 2.5 3 1029
able to move. (d) Entire ions may AlAs 0.1
Na 2.13 3 105
diffuse via a vacancy mechanism SiC 10210
K 1.64 3 105
to carry charge in many ionically
bonded materials. Alkali earth metals Ionic Conductors
Mg 2.25 3 105 Indium tin oxide (ITO) ,104
Ca 3.16 3 105 Yttria-stabilized zirconia (YSZ) ,1014
Group 3B metals Insulators, Linear, and Nonlinear Dielectrics
Al 3.77 3 105
Hole Polymers
Ga 0.66 3 105 Polyethylene 10215
Transition metals Polytetrafluoroethylene 10218
Fe 1.00 3 105 Polystyrene 10217 to 10219
Ni 1.46 3 105 Epoxy 10212 to 10217
Group 1B metals Ceramics
Cu 5.98 3 105 Alumina (Al2O3) 10214
Ag 6.80 3 105 Silicate glasses 10217
Boron nitride (BN) 10213
Au 4.26 3 105 Barium titanate (BaTiO3) 10214
C (diamond) ,10218

*Unless specified otherwise, assumes high-purity material.

Finally,
5 nq (19-5a) Table 19-2 Some useful relationships, constants, and units
The charge q is a constant; from inspection of Equation 19-5a, we find that we can con-
Electron volt 5 1 eV 5 1.6 3 10219 joule 5 1.6 3 10212 erg
trol the electrical conductivity of materials by (1) controlling the number of charge carri-
1 amp 5 1 coulomb ∕ second
ers in the material or (2) controlling the mobility—or ease of movement—of the charge
carriers. The mobility is particularly important in metals, whereas the number of carriers 1 volt 5 1 amp · ohm
is more important in semiconductors and insulators. kBT at room temperature (300 K) 5 0.0259 eV
Electrons are the charge carriers in metals [Figure 19-1(b)]. Electrons are, of c 5 speed of light 2.998 3 108 m ∕ s
course, negatively charged. In semiconductors, electrons conduct charge as do positively ´0 5 permittivity of free space 5 8.85 3 10212 F ∕ m
charged carriers known as holes [Figure 19-1(c)]. We will learn more about holes in Section
q 5 charge on electron 5 1.6 3 10219 C
19-4. In semiconductors, electrons and holes flow in opposite directions in response to an
applied electric field, but in so doing, they both contribute to the net current. Thus, Equa- Avogadro constant NA 5 6.022 3 1023
tion 19-5a can be modified as follows for expressing the conductivity of semiconductors: kB 5 Boltzmann constant 5 8.617 3 1025 eV∕ K 5 1.38 3 10223 J ⁄ K
5 nqn 1 pqp (19-5b) h 5 Planck’s constant 6.63 3 10234 J ? s 5 4.14 3 10215 eV ? s
In this equation, mn and mp are the mobilities of electrons and holes, respectively. The terms
n and p represent the concentrations of free electrons and holes in the semiconductor.
In ceramics, when conduction does occur, it can be the result of electrons that Electronic materials can be classified as (a) superconductors, (b) conductors,
“hop” from one defect to another or the movement of ions [Figure 19-1(d)]. The mobil- (c) semiconductors, and (d) dielectrics or insulators, depending upon the magnitude of
ity depends on atomic bonding, imperfections, microstructure, and, in ionic compounds, their electrical conductivity. Materials with conductivity less than 10212 V21 ? cm21, or
diffusion rates. resistivity greater than 1012 V ? cm, are considered insulating or dielectric. Materials with
Because of these effects, the electrical conductivity of materials varies tremen- conductivity less than 103 V21 ? cm21 but greater than 10212 V21 ? cm21 are considered
dously, as illustrated in Table 19-1. These values are approximate and are for high-purity semiconductors. Materials with conductivity greater than 103 V21 ? cm21, or resistivity
materials at 300 K (unless noted otherwise). Note that the values of conductivity for less than 1023 V21 ? cm21, are considered conductors. (These are approximate ranges of
metals and semiconductors depend very strongly on temperature. Table 19-2 includes values.)
some useful units and relationships.

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19-2 Band Structure of Solids 685

5.98 3 105 V 21 ? cm21

684 Chapter 19 Electronic Materials 5 5
nq s8.466 3 1022 electrons/cm3ds1.6 3 10219Cd
We use the term “dielectric” for materials that are used in applications where the
dielectric constant is important. The dielectric constant (k) of a material is a microstruc- cm2 cm2
5 44.1 5 44.1
ture-sensitive property related to the material’s ability to store an electrical charge. We use V?C V?s
the term “insulator” to describe the ability of a material to stop the flow of DC or AC (b) The electric field is
current, as opposed to its ability to store a charge. A measure of the effectiveness of an
insulator is the maximum electric field it can support without an electrical breakdown. V 10 V
E5 5 5 0.1 Vycm
l 100 cm
Example 19-1 Design of a Transmission Line The mobility is 44.1 cm2y(V ? s); therefore,
2
Design an electrical transmission line 1500 m long that will carry a current of 50 A v 5 E 5 [44.1 cm ysV ? sd]s0.1 Vycmd 5 4.41 cmys
with no more than 5 3 105 W loss in power. The electrical conductivity of several
materials is included in Table 19-1.
Solution
Electrical power is given by the product of the voltage and current or
P 5 VI 5 I2R 5 s50d2R 5 5 3 105 W 19-2 Band Structure of Solids
R 5 200 ohms
From Equation 19-2, As we saw in Chapter 2, the electrons of atoms in isolation occupy fixed and discrete
l s1500 mds100 cm ymd 750
energy levels. The Pauli exclusion principle is satisfied for each atom because only two
A5 5 5 electrons, at most, occupy each energy level, or orbital. When N atoms come together to
R? s200 ohmsd
form a solid, the Pauli exclusion principle still requires that no more than two electrons
Let’s consider three metals—aluminum, copper, and silver—that have excellent electri- in the solid have the same energy. As two atoms approach each other in order to form a
cal conductivity. The table below includes appropriate data and some characteristics bond, the Pauli exclusion principle would be violated if the energy levels of the electrons
of the transmission line for each metal.
did not change. Thus, the energy levels of the electrons “split” in order to form new
energy levels.
s (ohm21 · cm21) A (cm2) Diameter (cm)
Figure 19-2 schematically illustrates this concept. Consider two atoms approach-
Aluminum 3.77 3 105 0.00199 0.050 ing each other to form a bond. The orbitals that contain the valence electrons are located
Copper 5.98 3 105 0.00125 0.040 (on average) farther from the nucleus than the orbitals that contain the “core” or inner-
Silver 6.80 3 105 0.00110 0.037 most electrons. The orbitals that contain the valence electrons of one atom thus interact

Any of the three metals will work, but cost is a factor as well. Aluminum will
likely be the most economical choice (Chapter 14), even though the wire has the largest
diameter. Other factors, such as whether the wire can support itself between transmis-
sion poles, also contribute to the final choice.

Band gap, Eg
Example 19-2 Drift Velocity of Electrons in Copper

Electron energy
Assuming that all of the valence electrons contribute to current flow, (a) calculate the
mobility of an electron in copper and (b) calculate the average drift velocity for elec-
trons in a 100 cm copper wire when 10 V are applied.
Solution
(a) The valence of copper is one; therefore, the number of valence electrons equals
the number of copper atoms in the material. The lattice parameter of copper is
3.6151 3 1028 cm and, since copper is FCC, there are four atoms∕unit cell. From
Table 19-1, the conductivity s 5 5.98 3 105 V21 ? cm21
One Two Small number Large number
s4 atomsycellds1 electronyatomd
n5 5 8.466 3 1022 electronsycm3 atom atoms of atoms of atoms = solid
s3.6151 3 1028 cmd3ycell
Core level
q 5 1.6 3 10219 C n = (valence/atom * atom/cell)/(vol/cell)
electrons
Figure 19-2 The energy levels broaden into bands as the number of electrons grouped
together increases. (Courtesy of John Bravman)
Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

76761_ch19.indd 684 24/10/14 7:56 PM Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

76761_ch19.indd 685 24/10/14 7:56 PM

686 Chapter 19 Electronic Materials 19-2 Band Structure of Solids 687

with the orbitals that contain the valence electrons of the other atom first. Since the orbit- level at which half of the possible energy levels in the band are occupied by electrons. It is
als of these electrons have the same energy when the atoms are in isolation, the orbitals the energy level where the probability of finding an electron is 1y2. When electrons gain
shift in energy or “split” so that the Pauli exclusion principle is satisfied. As shown in energy, they are excited into the empty higher energy levels. The promotion of carriers to
Figure 19-2, when considering two atoms, each with one orbital of interest, one of the higher energy levels enables electrical conduction.
orbitals shifts to a higher energy level while the other orbital shifts to a lower energy level.
The electrons of the atoms will occupy these new orbitals by first filling the lowest energy
levels. As the number of atoms increases, so does the number of energy levels. A new Band Structure of Magnesium and Other Metals
orbital with its own energy is formed for each orbital of each atom, and as the number Magnesium and other metals in column 2A of the periodic table have two electrons
of atoms in the solid increases, the separation in energy between orbitals becomes in their outermost s band. These metals have a high conductivity because the p band
finer, ultimately forming what is called an energy band. For example, when N atoms come overlaps the s band at the equilibrium interatomic spacing. This overlap permits electrons
together to form a solid, the 2s energy band contains N discrete energy levels, one for each to be excited into the large number of unoccupied energy levels in the combined 3s and
atom in the solid since each atom contributes one orbital. 3p band. Overlapping 3s and 3p bands in aluminum and other metals in column 3B
In order for charge carriers to conduct, the carriers must be able to accelerate provide a similar effect.
and increase in energy. The energy of the carriers can increase only if there are available In the transition metals, including scandium through nickel, an unfilled 3d band
energy states to which the carriers can be promoted. Thus, the particular distribution of overlaps the 4s band. This overlap provides energy levels into which electrons can be
energy states in the band structure of a solid has critical implications for its electrical and excited; however, complex interactions between the bands prevent the conductivity from
optical properties. being as high as in some of the better conductors. In copper, the inner 3d band is full,
Depending on the type of material involved (metal, semiconductor, insulator), and the atom core tightly holds these electrons. Consequently, there is little interaction
there may or may not be a sizable energy gap between the energy levels of the orbitals between the electrons in the 4s and 3d bands, and copper has a high conductivity. A simi-
that shifted to a lower energy state and the energy levels of the orbitals that shifted to a lar situation is found for silver and gold.
higher energy state. This energy gap, if it exists, is known as the bandgap. We will discuss
the bandgap in more detail later.
Band Structure of Semiconductors and Insulators The
elements in Group 4—carbon (diamond), silicon, germanium, and tin—contain two
Band Structure of Sodium Sodium is a metal and has the electronic electrons in their outer p shell and have a valence of four. Based on our discussion in the
structure 1s22s22p63s1. Figure 19-3 shows a schematic diagram of the band structure previous section, we might expect these elements to have a high conductivity due to the
of sodium as a function of the interatomic separation. (Note that Figure 19-2 shows a unfilled p band, but this behavior is not observed!
general band diagram for a fixed interatomic separation.) The energies within the bands These elements are covalently bonded; consequently, the electrons in the outer
depend on the spacing between the atoms; the vertical line represents the equilibrium s and p bands are rigidly bound to the atoms. The covalent bonding produces a complex
interatomic spacing of the atoms in solid sodium. change in the band structure. The 2s and 2p levels of the carbon atoms in diamond can
Sodium and other alkali metals in column 1A of the periodic table have only one contain up to eight electrons, but there are only four valence electrons available. When
electron in the outermost s level. The 3s valence band in sodium is half filled and, at abso- carbon atoms are brought together to form solid diamond, the 2s and 2p levels inter-
lute zero, only the lowest energy levels are occupied. The Fermi energy (Ef ) is the energy act and produce two bands (Figure 19-4). Each hybrid band can contain 4N electrons.
Since there are only 4N electrons available, the lower (or valence) band is completely full,
whereas the upper (or conduction) band is empty at 0 k.
A large energy gap or bandgap (Eg) separates the valence band from the conduc-
tion band in diamond (Eg , 5.5 eV). Few electrons possess sufficient energy to jump
Figure 19-3 The simplified band
structure for sodium. The energy
levels broaden into bands. The 3s band,
which is only half filled with electrons, Figure 19-4 The band structure of
is responsible for conduction in carbon in the diamond form. The 2s
sodium. Note that the energy levels of and 2p levels combine to form two
the orbitals in the 1s, 2s, and 2p levels hybrid bands separated by an energy
do not split at the equilibrium spacing gap, Eg.
for sodium.

Equilibrium Distance
spacing between atoms

76761_ch19.indd 686 24/10/14 7:56 PM 76761_ch19.indd 687 24/10/14 7:56 PM

688 Chapter 19 Electronic Materials 19-3 Conductivity of Metals and Alloys 689

the forbidden zone to the conduction band. Consequently, diamond has an electrical
conductivity of less than 10218 ohm21 ? cm21. Other covalently and ionically bonded
19-3 Conductivity of Metals and Alloys
materials have a similar band structure and, like diamond, are poor conductors of elec- The conductivity of a pure, defect-free metal is determined by the electronic structure
tricity. Increasing the temperature supplies the energy required for electrons to overcome of the atoms, but we can change the conductivity by influencing the mobility, m, of the
the energy gap. For example, the electrical conductivity of boron nitride increases from carriers. Recall that the mobility is proportional to the average drift velocity, v . The
about 10213 at room temperature to 1024 ohm21 ? cm21 at 800°C. average drift velocity is the velocity with which charge carriers move in the direction
Figure 19-5 shows a schematic of the band structure of typical metals, semi- dictated by the applied field. The paths of electrons are influenced by internal fields due
conductors, and insulators. The differing temperature dependencies of the conductivi- to atoms in the solid and imperfections in the lattice. When these internal fields influence
ties of metals and semiconductors are a consequence of their different band structures. the path of an electron, the drift velocity (and thus the mobility of the charge carriers)
In a metal, there is a large supply of electrons available (roughly 1023 per cubic centi- decreases. The mean free path (e) of electrons is defined as
meter, or one per atom) at any temperature. An almost infinitesimally small amount
of energy supplied to the electrons will promote them to unoccupied states where e 5 tv (19-6)
they can participate in conduction. In a semiconductor at 0 K, the valence band is The average time between collisions is t. The mean free path defines the average dis-
completely full and the conduction band is completely empty; the semiconductor does tance between collisions; a longer mean free path permits higher mobilities and higher
not conduct. As temperature increases, the supply of electrons increases exponentially conductivities.
because the thermal energy frees an increasing number of electrons from the covalent
bonds, making the electrons available for conduction, and we find that the resistivity Temperature Effect When the temperature of a metal increases, thermal
of a semiconductor decreases with increasing temperature. In pure silicon, there are energy causes the amplitudes of vibration of the atoms to increase (Figure 19-6). This
about 1010 free electrons per cubic centimeter at room temperature, or about 1013 increases the scattering cross section of atoms or defects in the lattice. Essentially, the
times fewer than in a metal. Thus, an important distinction between metals and semi- atoms and defects act as larger targets for interactions with electrons, and interactions
conductors is that the conductivity of semiconductors increases with temperature, as occur more frequently. Thus, the mean free path decreases, the mobility of electrons
more and more electrons are promoted to the conduction band from the valence band.
The conductivity of most metals, on the other hand, decreases with increasing tem-
perature. This is because the number of electrons that are already available begin to
scatter more (i.e., increasing temperature reduces mobility). We will discuss this more
later in this chapter.
Although germanium, silicon, and a-Sn have the same crystal structure and
band structure as diamond, their energy gaps are smaller. In fact, the energy gap (Eg) in
a-Sn is so small (Eg 5 0.1 eV) that a-Sn behaves as a metal. The energy gap is somewhat
larger in silicon (Eg 5 1.1 eV) and germanium (Eg 5 0.67 eV)—these elements behave as
semiconductors. Typically, we consider materials with a bandgap greater than 4.0 eV as
insulators, dielectrics, or nonconductors; materials with a bandgap less than 4.0 eV are
considered semiconductors.

Partially filled
or empty Figure 19-6 Movement of an electron through (a) a perfect crystal, (b) a crystal
overlapping heated to a high temperature, and (c) a crystal containing atomic level defects.
conduction Scattering of the electrons reduces the mobility and conductivity.
band
4.0 eV 4.0 eV

Figure 19-7 The effect of temperature on the

electrical resistivity of a metal with a perfect
crystal structure.
RT R

Figure 19-5 Schematic of band structures for (a) metals, (b) semiconductors,
and (c) dielectrics or insulators. (Temperature is assumed to be 0 K.)

76761_ch19.indd 688 24/10/14 7:56 PM 76761_ch19.indd 689 24/10/14 7:56 PM

690 Chapter 19 Electronic Materials 19-3 Conductivity of Metals and Alloys 691

Table 19-3 The temperature resistivity coefficient aR for selected metals Figure 19-8 The electrical resistivity of a metal is due to a
constant defect contribution rd and a variable temperature
Room Temperature Resistivity Temperature Resistivity Coefficient contribution rT.
Metal (ohm · cm) (aR) [ohm/(ohm · °C)]

Be 4.0 3 1026 0.0250

Mg 4.45 3 1026 0.0037
Ca 3.91 3 1026 0.0042
Al 2.65 3 1026 0.0043
Cr 12.90 3 1026 (0°C) 0.0030
Fe 9.71 3 1026 0.0065
Co 6.24 3 1026 0.0053
Effect of Atomic Level Defects Imperfections in crystal structures
scatter electrons, reducing the mobility and conductivity of the metal [Figure 19-6(c)]. For
Ni 6.84 3 1026 0.0069
example, the increase in the resistivity due to solid solution atoms for dilute solutions is
Cu 1.67 3 1026 0.0043
d 5 bs1 2 xdx (19-8)
Ag 1.59 3 1026 0.0041
Au 2.35 3 1026 0.0035 where rd is the increase in resistivity due to the defects, x is the atomic fraction of the
impurity or solid solution atoms present, and b is the defect resistivity coefficient. In a
Pd 10.8 3 1026 0.0037
similar manner, vacancies, dislocations, and grain boundaries reduce the conductivity of
W 5.3 3 1026 (27°C) 0.0045
the metal. Each defect contributes to an increase in the resistivity of the metal. Thus, the
Pt 9.85 3 1026 0.0039 overall resistivity is
(Based on Handbook of Electromagnetic Materials: Monolithic and Composite Versions and Their 5 T 1 d (19-9)
Applications by P. S. Neelkanta, Taylor & Francis, 1995.)
where d equals the contributions from all of the defects. Equation 19-9 is known as
Matthiessen’s rule. The effect of the defects is independent of temperature (Figure 19-8).
is reduced, and the resistivity increases. The change in resistivity of a pure metal as a
function of temperature can be estimated according to Effect of Processing and Strengthening Strengthening mech-
5 RT s1 1 RDT d (19-7) anisms and metal processing techniques affect the electrical properties of a metal in dif-
ferent ways (Table 19-4). Solid-solution strengthening is not a good way to obtain high
where r is the resistivity at any temperature T, rRT is the resistivity at room temperature
(i.e., 25°C), DT 5 (T 2 TRT) is the difference between the temperature of interest and room Table 19-4 The effect of alloying, strengthening, and processing on the electrical
temperature, and aR is the temperature resistivity coefficient. The relationship between conductivity of copper and its alloys
resistivity and temperature is linear over a wide temperature range (Figure 19-7). Values
for the temperature resistivity coefficients for various metals are given in Table 19-3. alloy
Alloy Cu 3100 Remarks
The following example illustrates how the resistivity of pure copper can be
calculated. Pure annealed copper 100 Few defects to scatter electrons; the
mean free path is long.
Pure copper 98 Many dislocations, but because of the
deformed 80% tangled nature of the dislocation
Example 19-3 Resistivity of Pure Copper networks, the mean free path is still long.
Calculate the electrical conductivity of pure copper at (a) 400°C and (b) 2100°C. Dispersion-strengthened 85 The dispersed phase is not as closely
Cu-0.7% Al2O3 spaced as solid-solution atoms, nor is it
Solution coherent, as in age hardening. Thus, the
The resistivity of copper at room temperature is 1.67 3 1026 ohm · cm, and the effect on conductivity is small.
temperature resistivity coefficient is 0.0043 ohmy(ohm · °C). (See Table 19-3.) Solution-treated 18 The alloy is single phase; however,
(a) At 400°C: Cu-2% Be the small amount of solid-solution
strengthening from the supersaturated
5 RT s1 1 RDT d 5 s1.67 3 1026d[1 1 0.0043s400 2 25d] beryllium greatly decreases conductivity.

5 4.363 3 1026 ohm ? cm Aged Cu-2% Be 23 During aging, the beryllium leaves the
copper lattice to produce a coherent
5 1y 5 2.29 3 105 ohm21 ? cm21 precipitate. The precipitate does not
interfere with conductivity as much as
(b) At 2100°C: the solid-solution atoms.
5 s1.67 3 1026d[1 1 0.0043s2100 2 25d] 5 7.724 3 1027 ohm ? cm Cu-35% Zn 28 This alloy is solid-solution strengthened by
zinc, which has an atomic radius near that
5 1.29 3 106 ohm21 ? cm21 of copper. The conductivity is low, but not
as low as when beryllium is present.

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692 Chapter 19 Electronic Materials 19-4 Semiconductors 693

Table 19-5 Properties of commonly encountered semiconductors at room temperature

Mobility of Mobility of
Electrons (mn) Holes (mp) Density Melting
Bandgap Dielectric Resistivity g Temperature
1 Vs 2 1 Vs 2 1cm 2
cm2 cm2
Semiconductor (eV) Constant (k) (V · cm) 3 (°C)

Silicon (Si) 1.11 1350 480 11.8 2.5 3 105 2.33 1415
Amorphous 1.70 1 1022 ,11.8 1010 ,2.30 —
Silicon (a:Si:H)
Germanium (Ge) 0.67 3900 1900 16.0 43 5.32 936
SiC (a) 2.86 500 10.2 1010 3.21 2830
Gallium Arsenide 1.43 8500 400 13.2 4 3 108 5.31 1238
(GaAs)
Diamond ,5.50 1800 1500 5.7 . 1018 3.52 ,3550

Figure 19-9 (a) The effect of solid-solution strengthening and cold work on the elec-
trical conductivity of copper, and (b) the effect of the addition of selected elements on properties are stable with temperature and can be controlled using ion implantation or
the electrical conductivity of copper. diffusion of impurities known as dopants. Semiconductor materials, including silicon
and germanium, provide the building blocks for many electronic devices. These materials
have an easily controlled electrical conductivity and, when properly combined, can act as
strength in metals intended to have high conductivities. The mean free paths are short
switches, amplifiers, or information storage devices. The properties of some of the com-
due to the random distribution of the interstitial or substitutional atoms. Figure 19-9
monly encountered semiconductors are included in Table 19-5.
shows the effect of zinc and other alloying elements on the conductivity of copper; as the
As we learned in Section 19-2, as the atoms of a semiconductor come together
amount of alloying element increases, the conductivity decreases substantially.
to form a solid, two energy bands are formed [Figure 19-5(b)]. At 0 K, the energy levels
Age hardening and dispersion strengthening reduce the conductivity to an
of the valence band are completely full, as these are the lowest energy states for the elec-
extent that is less than solid-solution strengthening, since there is a longer mean free path
trons. The valence band is separated from the conduction band by a bandgap. At 0 K, the
between precipitates, as compared with the path between point defects. Strain hardening
conduction band is empty.
and grain-size control have even less effect on conductivity (Figure 19-9 and Table 19-4).
The energy gap Eg between the valence and conduction bands in semiconduc-
Since dislocations and grain boundaries are further apart than solid-solution atoms, there
tors is relatively small (Figure 19-5). As a result, as temperature increases, some electrons
are large volumes of metal that have a long mean free path. Consequently, cold working
possess enough thermal energy to be promoted from the valence band to the conduction
is an effective way to increase the strength of a metallic conductor without seriously
band. The excited electrons leave behind unoccupied energy levels, or holes, in the valence
impairing the electrical properties of the material. In addition, the effects of cold working
band. When an electron moves to fill a hole, another hole is created; consequently, the
on conductivity can be eliminated by the low-temperature recovery heat treatment in
holes appear to act as positively charged electrons and carry an electrical charge. When a
which good conductivity is restored while the strength is retained.
voltage is applied to the material, the electrons in the conduction band accelerate toward
the positive terminal, while holes in the valence band move toward the negative terminal
Conductivity of Alloys Alloys typically have higher resistivities than pure (Figure 19-10). Current is, therefore, conducted by the movement of both electrons and
metals because of the scattering of electrons due to the alloying additions. For example, holes in semiconductors.
the resistivity of pure Cu at room temperature is ,1.67 3 1026 V · cm and that of The conductivity is determined by the number of electrons and holes according to
pure gold is ,2.35 3 1026 V · cm. The resistivity of a 35% Au-65% Cu alloy at room 5 nqn 1 pqp (19-10)
temperature is much higher, ,12 3 1026 V · cm. Ordering of atoms in alloys by heat
where n is the concentration of electrons in the conduction band, p is the concentration
treatment can decrease their resistivity. Compared to pure metals, the resistivities of alloys
of holes in the valence band, and mn and mp are the mobilities of electrons and holes,
tend to be stable with regard to temperature variation. Relatively high-resistance alloys
respectively (Table 19-5). This equation is the same as Equation 19-5b.
such as nichrome (,80% Ni-20% Cr) can be used as heating elements. Certain alloys of
Bi-Sn-Pb-Cd are used to make electrical fuses due to their low melting temperatures.

19-4 Semiconductors
Elemental semiconductors are found in Group 4B of the periodic table and include
germanium and silicon. Compound semiconductors are formed from elements in
Groups 2B and 6B of the periodic table (e.g., CdS, CdSe, CdTe, HgCdTe, etc.) and
are known as II–VI (two–six) semiconductors. Compound semiconductors also can
be formed by combining elements from Groups 3B and 5B of the periodic table
(e.g., GaN, GaAs, AlAs, AlP, InP, etc.). These are known as III–V (three–five) semiconductors. Figure 19-10 When a voltage is applied to a semiconductor, the electrons move
An intrinsic semiconductor is one with properties that are not controlled by through the conduction band, while the holes move through the valence band in the
impurities. An extrinsic semiconductor (n- or p-type) is preferred for devices, since its opposite direction.

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694 Chapter 19 Electronic Materials 19-4 Semiconductors 695

Figure 19-11 The distribution Figure 19-12 The electrical conductivity

of electrons and holes in the versus temperature for intrinsic semiconduc-
valence and conduction bands tors compared with metals. Note the break
(a) at absolute zero and (b) at an in the vertical axis scale.
elevated temperature.

In intrinsic semiconductors, for every electron promoted to the conduction

band, there is a hole left in the valence band, such that
ni 5 pi
where ni and pi are the concentrations of electrons and holes, respectively, in an intrinsic
semiconductor. Therefore, the conductivity of an intrinsic semiconductor is

5 qni sn 1 pd (19-11)

In intrinsic semiconductors, we control the number of charge carriers and, hence,

the electrical conductivity by controlling the temperature. At absolute zero temperature,
all of the electrons are in the valence band, whereas all of the levels in the conduction band
are unoccupied [Figure 19-11(a)]. As the temperature increases, there is a greater probabil-
ity that an energy level in the conduction band is occupied (and an equal probability that Example 19-4 Carrier Concentrations in Intrinsic Ge
a level in the valence band is unoccupied, or that a hole is present) [Figure 19-11(b)]. The
number of electrons in the conduction band, which is equal to the number of holes in the For germanium at 25°C, estimate (a) the number of charge carriers, (b) the fraction of
valence band, is given by the total electrons in the valence band that are excited into the conduction band, and
(c) the constant n0 in Equation 19-12a.
1 2
2Eg
n(T) = p(T) n 5 ni 5 pi 5 n0 exp (19-12a) Solution
2kBT
From Table 19-5, 5 43 V · cm, ... 5 0.0233 V21 ? cm21
where n0 is given by Also from Table 19-5,

1 2
2kBT 3y2
n0 5 2 sm*n m*pd3y4 (19-12b) cm2 cm2
h2 Eg 5 0.67 eV, n 5 3900 , p 5 1900
V?s V?s
In these equations, kB and h are the Boltzmann and Planck’s constants and m*n and m*p 2kBT 5 2s8.617 3 1025 eVyKds273 K 1 25 Kd 5 0.05136 eV at T 5 258C
are the effective masses of electrons and holes in the semiconductor, respectively. The ef-
(a) From Equation 19-10,
fective masses account for the effects of the internal forces that alter the acceleration of
electrons in a solid relative to electrons in a vacuum. For Ge, Si, and GaAs, the room tem- 0.0233 electrons
n5 5 5 2.51 3 1013
perature values of ni are 2.5 3 1013, 1.5 3 1010, and 2 3 106 electronsycm3, respectively. qsn 1 pd s1.6 3 10219ds3900 1 1900d cm3
The ni pi product remains constant at any given temperature for a given semiconductor. There are 2.51 3 1013 electronsycm3 and 2.51 3 1013 holesycm3 conducting charge
This allows us to calculate ni or pi values at different temperatures. in germanium at room temperature.
Higher temperatures permit more electrons to cross the forbidden zone and,
hence, the conductivity increases: (b) The lattice parameter of diamond cubic germanium is 5.6575 3 1028 cm.
The total number of electrons in the valence band of germanium at 0 K is
1 2
2Eg
cond(T) 5 n0qsn 1 pd exp (19-13)
s8 atomsycellds4 electronsyatomd
2kBT
Total electrons 5
Note that both ni and s are related to temperature by an Arrhenius equation, s5.6575 3 1028 cmd3ycell
5 1.77 3 1023
1 RT 2. As the temperature increases, the conductivity of a semiconductor
2Q
rate 5 A exp
2.51 3 1013
also increases because more charge carriers are available for conduction. Note that as for Fraction excited 5 5 1.42 3 10210
1.77 3 1023
metals, the mobilities of the carriers decrease at high temperatures, but this is a much weaker
(c) From Equation 19-12a,
dependence than the exponential increase in the number of charge carriers. The increase
in conductivity with temperature in semiconductors sharply contrasts with the decrease n 2.51 3 1013 carriersycm3
n0 5 5
in conductivity of metals with increasing temperature (Figure 19-12). Even at high tem- exp [2Eg ys2kBTd] exp s20.67y0.05136d
peratures, however, the conductivity of a metal is orders of magnitudes higher than the
5 1.16 3 1019 carriersycm3
conductivity of a semiconductor. The example that follows shows the calculation for carrier
concentration in an intrinsic semiconductor.

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696 Chapter 19 Electronic Materials 19-4 Semiconductors 697

Extrinsic Semiconductors The temperature dependence of conductiv-

ity in intrinsic semiconductors is nearly exponential, but this is not useful for practical
applications. We cannot accurately control the behavior of an intrinsic semiconductor
because slight variations in temperature can significantly change the conductivity. By
intentionally adding a small number of impurity atoms to the material (called doping),
we can produce an extrinsic semiconductor. The conductivity of the extrinsic semicon-
ductor depends primarily on the number of impurity, or dopant, atoms and in a cer-
tain temperature range is independent of temperature. This ability to have a tunable yet
temperature-independent conductivity is the reason why we almost always use extrinsic
semiconductors to make devices.

n-Type Semiconductors Suppose we add an impurity atom such as

a ntimony (which has a valence of five) to silicon or germanium. Four of the electrons
from the antimony atom participate in the covalent-bonding process, while the extra
electron enters an energy level just below the conduction band (Figure 19-13). Since
the extra electron is not tightly bound to the atoms, only a small increase in energy,
Ed, is required for the electron to enter the conduction band. This energy level just Figure 19-14 When a dopant atom with a valence of less than four is substituted into
below the conduction band is called a donor state. An n-type dopant “donates” a the silicon structure, a hole is introduced in the structure and an acceptor energy level is
free electron for each impurity atom added. The energy gap controlling conductivity created just above the valence band.
is now Ed rather than Eg (Table 19-6). No corresponding holes are created when the
donor electrons enter the conduction band. It is still the case that electron-hole pairs
are created when thermal energy causes electrons to be promoted to the conduction Table 19-6 The donor and acceptor energy levels (in electron volts) when
band from the valence band; however, the number of electron-hole pairs is significant silicon and germanium semiconductors are doped
only at high temperatures.
Silicon Germanium

p-Type Semiconductors When we add an impurity such as gallium Dopant Ed Ea Ed Ea

or boron, which has a valence of three, to Si or Ge, there are not enough electrons to P 0.045 0.0120
complete the covalent bonding process. A hole is created in the valence band that can As 0.049 0.0127
be filled by electrons from other locations in the band (Figure 19-14). The holes act as
Sb 0.039 0.0096
“acceptors” of electrons. These hole sites have a somewhat higher than normal energy
and create an acceptor level of possible electron energies just above the valence band B 0.045 0.0104
(Table 19-6). An electron must gain an energy of only Ea in order to create a hole in the Al 0.057 0.0102
valence band. The hole then carries charge. This is known as a p-type semiconductor. Ga 0.065 0.0108
ln 0.160 0.0112

Charge Neutrality In an extrinsic semiconductor, there has to be overall

electrical neutrality. Thus, the sum of the number of donor atoms (Nd) and holes per unit
volume ( pext) (both are positively charged) is equal to the number of acceptor atoms (Na)
and electrons per unit volume (next) (both are negatively charged):
pext 1 Nd 5 next 1 Na
In this equation, next and pext are the concentrations of electrons and holes in an extrinsic
semiconductor.
If the extrinsic semiconductor is heavily n-type doped (i.e., Nd >> ni), then next , Nd.
Similarly, if there is a heavily acceptor-doped (p-type) semiconductor, then Na >> pi and
hence pext , Na. This is important, since this says that by adding a considerable amount of
dopant, we can dominate the conductivity of a semiconductor by controlling the dopant
concentration.
The changes in carrier concentration with temperature are shown in Figure 19-15.
From this, the approximate conductivity changes in an extrinsic semiconductor are easy
Figure 19-13 When a dopant atom with a valence greater than four is added to silicon, to follow. When the temperature is too low, the donor or acceptor atoms are not ionized
an extra electron is introduced and a donor energy state is created. Now electrons are and hence the conductivity is very small. As temperature begins to increase, electrons
more easily excited into the conduction band. (or holes) contributed by the donors (or acceptors) become available for conduction.

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698 Chapter 19 Electronic Materials 19-5 Applications of Semiconductors 699

Assume that the lattice constant of Si remains unchanged as a result of doping:

s1 holeydopant atomdsx dopant atom ySi atomds8 Si atomsyunit celld
Na 5
s5.4307 3 1028 cmd3yunit cell
x 5 s1.30 3 1018ds5.4307 3 1028d3y8 5 26 3 1026 dopant atom ySi atom
next (cm–3)(log scale)

or 26 dopant atomsy106 Si atoms

Possible dopants include boron, aluminum, gallium, and indium. High-purity chemi-
cals and clean room conditions are essential for processing since we need 26 dopant
atoms per million silicon atoms.

( kB)
Many other materials that are normally insulating (because the bandgap is too large)
can be made semiconducting by doping. Examples of this include BaTiO3, ZnO, TiO2,
and many other oxides. Thus, the concept of n- and p-type dopants is not limited to Si,
Ge, GaAs, etc. We can dope BaTiO3, for example, and make n- or p-type BaTiO3. Such
materials are useful for many sensor applications such as thermistors.
Figure 19-15 The effect of temperature on the carrier concentration of an n-type
semiconductor. At low temperatures, the donor atoms are not ionized. As temperature
increases, the ionization process is complete, and the carrier concentration increases to
Direct and Indirect Bandgap Semiconductors In a direct
bandgap semiconductor, an electron can be promoted from the conduction band to
a level that is dictated by the level of doping. The conductivity then essentially remains
the valence band without changing the momentum of the electron. An example of a
unchanged until the temperature becomes too high and the thermally generated carriers
direct bandgap semiconductor is GaAs. When the excited electron falls back into the
begin to dominate. The effect of dopants is lost at very high temperatures, and the
valence band, electrons and holes combine to produce light. This is known as radiative
semiconductor essentially shows “intrinsic” behavior.
recombination. Thus, direct bandgap materials such as GaAs and solid solutions
of these (e.g., GaAs-AlAs, etc.) are used to make light-emitting diodes (LEDs) of
At sufficiently high temperatures, the conductivity is nearly independent of tempera- different colors. The bandgap of semiconductors can be tuned using solid solutions.
ture (region labeled as extrinsic). The value of conductivity at which the plateau occurs The change in bandgap produces a change in the wavelength [i.e., the frequency of the
depends on the level of doping. When temperatures become too high, the behavior color (v) is related to the bandgap Eg as Eg 5 hv, where h is Planck’s constant]. Since
approaches that of an intrinsic semiconductor since the effect of dopants essentially is an optical effect is obtained using an electronic material, often the direct bandgap
lost. In this analysis, we have not accounted for the effects of dopant concentration on materials are known as optoelectronic materials (Chapter 21). Many lasers and LEDs
the mobility of electrons and holes and the temperature dependence of the bandgap. At have been developed using these materials. LEDs that emit light in the infrared range
very high temperatures (not shown in Figure 19-15), the conductivity decreases again as are used in optical-fiber communication systems to convert light waves into electrical
scattering of carriers dominates. pulses. Different colored lasers, such as the blue laser using GaN, have been developed
using direct bandgap materials.
In an indirect bandgap semiconductor (e.g., Si, Ge, and GaP), the electrons
cannot be promoted to the valence band without a change in momentum. As a result,
Example 19-5 Design of a Semiconductor
in materials that have an indirect bandgap (e.g., silicon), we cannot get light emis-
Design a p-type semiconductor based on silicon, which provides a constant conductivity sion. Instead, electrons and holes combine to produce heat that is dissipated within
of 100 ohm21 ? cm21 over a range of temperatures. Compare the required concentration the material. This is known as nonradiative recombination. Note that both direct and
of acceptor atoms in Si with the concentration of Si atoms. indirect bandgap materials can be doped to form n- or p-type semiconductors.
Solution
In order to obtain the desired conductivity, we must dope the silicon with atoms hav-
ing a valence of 13, adding enough dopant to provide the required number of charge
carriers. If we assume that the number of intrinsic carriers is small compared to the
19-5 Applications of Semiconductors
dopant concentration, then We fabricate diodes, transistors, lasers, and LEDs using semiconductors. The p-n junction
5 Naqp is used in many of these devices, such as transistors. Creating an n-type region in a p-type
where s 5 100 ohm21 · cm21 and mp 5 480 cm2 ⁄(V · s). Note that electron and hole semiconductor (or vice versa) forms a p-n junction [Figure 19-16(a)]. The n-type region
mobilities are properties of the host material (i.e., silicon in this case) and not contains a relatively large number of free electrons, whereas the p-type region contains
the dopant species. If we remember that a coulomb can be expressed as ampere- a relatively large number of free holes. This concentration gradient between the p-type
seconds and voltage can be expressed as ampere-ohm, the number of charge carriers and n-type regions causes diffusion of electrons from the n-type material to the p-type
required is material and diffusion of holes from the p-type material to the n-type material. At the
junction where the p- and n-regions meet, free electrons in the n-type material recombine
100 ohm21 cm21 with holes in the p-type material. This creates a depleted region at the junction where the
Na 5 5 5 1.30 3 1018 acceptor atomsycm3
qp s1.6 3 10219 A ? sd[480 cm2ysA?ohm ? sd] number of available charge carriers is low, and thus, the resistivity is high. Consequently,

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700 Chapter 19 Electronic Materials 19-5 Applications of Semiconductors 701

V
+ −
pbase

p n

(a) (b) (c) Vdrain–source

Figure 19-16 (a) A p-n junction under forward bias. (b) The current–voltage characteristic for a p-n Vgate–source – +
junction. Note the different scales in the first and third quadrants. At sufficiently high reverse bias – +
voltages, “breakdown” occurs, and large currents can flow. Typically this destroys the devices. (c) If an
Gate
alternating signal is applied, rectification occurs, and only half of the input signal passes the rectifier.
(Based on Thomas L. Floyd, Electronic Devices (Conventional Flow Version), 6th, Pearson Education, n+ Oxide n+
2002.)
Source Drain
p
an electric field develops due to the distribution of exposed positive ions on the n-side of
the junction and the exposed negative ions on the p-side of the junction. The electric field
counteracts further diffusion.
Electrically, the p-n junction is conducting when the p-side is connected to a posi- Figure 19-17 (a) Sketch of the cross-section of the transistor. (b) A circuit for an n-p-n bipolar junction
tive voltage. This forward bias condition is shown in Figure 19-16(a). The applied voltage transistor. The input creates a forward and reverse bias that causes electrons to move from the emitter,
directly counteracts the electric field at the depleted region, making it possible for electrons through the base, and into the collector, creating an amplified output. (c) Sketch of the cross-section of a
from the n-side to diffuse across the depleted region to the p-side and holes from the p-side metal oxide semiconductor field effect transistor.
to diffuse across the depleted region to the n-side. When a negative bias is applied to the
p-side of a p-n junction (reverse bias), the p-n junction does not permit much current to flow.
The depleted region simply becomes larger because it is further depleted of carriers. When reverse bias is produced between the base and the collector (with the positive voltage
no bias is applied, there is no current flowing through the p-n junction. The forward current at the n-type collector). The forward bias causes electrons to leave the emitter and
can be as large as a few milli-amperes, while the reverse-bias current is a few nano-amperes. enter the base.
The current–voltage (I–V) characteristics of a p-n junction are shown in Figure Electrons and holes attempt to recombine in the base; however, if the base is
19-16(b). Because the p-n junction permits current to flow in only one direction, it passes exceptionally thin and lightly doped, or if the recombination time t is long, almost all of
only half of an alternating current, therefore converting the alternating current to direct the electrons pass through the base and enter the collector. The reverse bias between the
current [Figure 19-6(c)]. These junctions are called rectifier diodes. base and collector accelerates the electrons through the collector, the circuit is completed,
and an output signal is produced. The current through the collector (Ic) is given by
Bipolar Junction Transistors
1B 2
There are two types of transistors based VE
on p-n junctions. The term transistor is derived from two words, “transfer” and “resistor.” Ic 5 I0 exp (19-14)
A transistor can be used as a switch or an amplifier. One type of transistor is the bipolar
junction transistor (BJT). In the era of mainframe computers, bipolar junction transistors where I0 and B are constants and VE is the voltage between the emitter and the base. If
often were used in central processing units. A bipolar junction transistor is a sandwich the input voltage VE is increased, a very large current Ic is produced.
of either n-p-n or p-n-p semiconductor materials, as shown in Figure 19-17(a). There are
three zones in the transistor: the emitter, the base, and the collector. As in the p-n junction, Field Effect Transistors A second type of transistor, which is almost
electrons are initially concentrated in the n-type material, and holes are concentrated in universally used today for data storage and processing, is the field effect transistor
the p-type material. (FET). A metal oxide semiconductor (MOS) field effect transistor (or MOSFET)
Figure 19-17(b) shows a schematic diagram of an n-p-n transistor and its elec- consists of two highly doped n-type regions (n1) in a p-type substrate or two highly
trical circuit. The electrical signal to be amplified is connected between the base and doped p-type regions in an n-type substrate. (The manufacturing processes by which a
the emitter, with a small voltage between these two zones. The output from the tran- device such as this is formed will be discussed in Section 19-6.) Consider a MOSFET
sistor, or the amplified signal, is connected between the emitter and the collector and that consists of two highly doped n-type regions in a p-type substrate. One of the
operates at a higher voltage. The circuit is connected so that a forward bias is produced n-type regions is called the source; the second is called the drain. A potential is applied
between the emitter and the base (the positive voltage is at the p-type base), while a between the source and the drain with the drain region being positive, but in the

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702 Chapter 19 Electronic Materials 19-6 General Overview of Integrated Circuit Processing 703

absence of a third component of the transistor (a conductor called the gate), electrons has required the commitment of enormous resources, both financial and human, as IC
cannot flow from the source to the drain under the action of the electric field through processing tools (and the physical environments in which they reside) have been serially
the low conductivity p-type region. The gate is separated from the semiconductor by developed to meet the challenges of reliably producing ever-smaller features.
a thin insulating layer of oxide and spans the distance between the two n-type regions. Fabrication of integrated circuits involves several hundred individual process-
In advanced device structures, the insulator is only several atomic layers thick and ing steps and may require several weeks to effect. In many instances, the same types of
comprises materials other than pure silica. processing step are repeated again and again, with some variations and perhaps with
A potential is applied between the gate and the source with the gate being pos- other processing steps interposed, to create the integrated circuit. These so-called “unit
itive. The potential draws electrons to the vicinity of the gate (and repels holes), but processes” include methods to deposit thin layers of materials onto a substrate, means to
the electrons cannot enter the gate because of the silica. The concentration of electrons define and create intricate patterns within a layer of material, and methods to introduce
beneath the gate makes this region (known as the channel) more conductive, so that a precise quantities of dopants into layers or the surface of the wafer. The length scales
large potential between the source and drain permits electrons to flow from the source involved with some of these processes are approaching atomic dimensions.
to the drain, producing an amplified signal (“on” state). By changing the input voltage The equipment used for these unit processes includes some of the most sophis-
between the gate and the source, the number of electrons in the conductive path changes, ticated and expensive instruments ever devised, many of which must be maintained in
thus also changing the output signal. When no voltage is applied to the gate, no electrons “clean rooms” that are characterized by levels of dust and contamination orders of mag-
are attracted to the region between the source and the drain, and there is no current flow nitude lower than that found in a surgical suite. A modern IC fabrication facility may
from the source to the drain (“off ” state). require several billion dollars of capital expenditure to construct and a thousand or more
people to operate.
Silicon wafers most often are grown using the Czochralski growth technique
[Figure 19-18(a)]. A small seed crystal is used to grow very large silicon single crystals. The
19-6 General Overview of Integrated Circuit seed crystal is slowly rotated, inserted into, and then pulled from a bath of molten silicon.
Silicon atoms attach to the seed crystal in the desired orientation as the seed crystal is
Processing retracted. Float zone and liquid encapsulated Czochralski techniques also are used. Single
crystals are preferred, because the electrical properties of uniformly doped and essentially
Integrated circuits (ICs, also known as microchips) comprise large numbers of electronic dislocation-free single crystals are better defined than those of polycrystalline silicon.
components that have been fabricated on the surface of a substrate material in the form Following the production of silicon wafers, which itself requires considerable
of a thin, circular wafer less than 1 mm thick and as large as 300 mm in diameter. Two expense and expertise, there are four major classes of IC fabrication procedures. The
particularly important components found on ICs are transistors, which can serve as first, known as “front end” processing, comprises the steps in which the electrical compo-
electrical switches, as discussed in Section 19-5, and capacitors, which can store data in a nents (e.g., transistors) are created in the uppermost surface regions of a semiconductor
digital format. Each wafer may contain several hundred chips. Intel’s well-known Xeon™ wafer. It is important to note that most of the thickness of the wafer exists merely as a
microprocessor is an example of an individual chip. mechanical support; the electrically active components are formed on the surface and typ-
When first developed in the early 1960s, an integrated circuit comprised just ically extend only a few thousandths of a millimeter into the wafer. Front-end processing
a few electrical components, whereas modern ICs may include several billion compo- may include a hundred or more steps. A schematic diagram of some exemplar front-end
nents, all within the area of a postage stamp. The smallest dimensions of IC components processing steps to produce a field-effect transistor are shown in Figure 19-18(b).
(or “devices”) now approach the atomic scale. This increase in complexity and sophistica- “Back end” processing entails the formation of a network of “interconnections”
tion, achieved simultaneously with a dramatic decrease in the cost per component, has on and just above the surface of the wafer. Interconnections are formed in thin films
enabled the entire information technology era in which we live. Without these achieve- of material deposited on top of the wafer that are patterned into precise networks; these
ments, mobile phones, the Internet, desktop computers, medical imaging devices, and serve as three-dimensional conductive pathways that allow electrical signals to pass
portable music systems—to name just a few icons of contemporary life—could not exist. between the individual electronic components, as required for the IC to operate and
It has been estimated that humans now produce more transistors per year than grains perform mathematical and logical operations or to store and retrieve data. Back-end
of rice. processing culminates with protective layers of materials applied to the wafers that
Since the inception of modern integrated circuit manufacturing, a reduction prevent mechanical and environmental damage. One feature of IC fabrication is that large
in size of the individual components that comprise ICs has been a goal of researchers numbers of wafers—each comprising several hundred to several thousand ICs, which in
and technologists working in this field. A common expression of this trend is known as turn may each include several million to several billion individual components—are often
“Moore’s Law,” named after Gordon Moore, author of a seminal paper published in fabricated at the same time.
1965. In that paper, Moore, who would go on to co-found Intel Corporation, predicted Once back-end processing has been completed, wafers are subjected to a num-
that the rapid growth in the number of components fabricated on a chip represented a ber of testing procedures to evaluate both the wafer as a whole and the individual chips.
trend that would continue far into the future. He was correct, and the general trends he As the number of components per chip has increased and the size of the components has
predicted are still in evidence four decades later. diminished, testing procedures have themselves become ever more complex and special-
As a result, for instance, we see that the number of transistors on a micropro- ized. Wafers with too small a fraction of properly functioning chips are discarded.
cessor has grown from a few thousand to several hundred million, while dynamic ran- The last steps in producing functioning ICs are collectively known as “packag-
dom access memory (DRAM) chips have passed the billion-transistor milestone. This ing,” during which the wafers are cut apart to produce individual, physically distinct
has led to enormous advances in the capability of electronic systems, especially on a chips. To protect the chips from damage, corrosion, and the like, and to allow electrical
per-dollar cost basis. During this time, various dimensions of every component on a chip signals to pass into and out of the chips, they are placed in special, hermetically sealed
have shrunk, often by orders of magnitude, with some dimensions now best measured in containers, often only slightly larger than the chip itself. A computer powered by a single
nanometers. This scaling, as it is called, drove and continues to drive Moore’s Law and microprocessor contains many other chips for many other functions.
plays out in almost every aspect of IC design and fabrication. Maintaining this progress

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704 Chapter 19 Electronic Materials 19-7 Deposition of Thin Films 705

19-7 Deposition of Thin Films

As noted in Section 19-6, integrated circuit fabrication depends in part on the deposition
of thin films of materials onto a substrate. This is similarly true for many technologies that
employ films, coatings, or other thin layers of materials, such as wear-resistant coatings on
cutting tools, anti-reflective coatings on optical components, and magnetic layers deposited
onto aluminum discs for data storage. Thin films may display very different microstructures
and physical properties than their bulk counterparts, features that may be exploited in a
number of ways. Creating, studying, and using thin films represents a tremendously broad
area of materials science and engineering that has enormous impact on modern technology.
Thin films are, as the name implies, very small in one dimension—especially in com-
parison to their extent in the other two dimensions. There is no well-defined upper bound on
what constitutes “thin,” but many modern technologies routinely employ thicknesses of sev-
eral microns down to just a few atomic dimensions. There are myriad ways by which thin films
can be deposited, but in general, any technique involves both a source of the material to be
deposited and a means to transport the material from the source to the workpiece surface upon
which it is to be deposited. Many deposition techniques require that the source and workpiece
be maintained in a vacuum system, while others place the workpiece in a liquid environment.
Physical vapor deposition (PVD) is one very important category of thin-film growth
techniques. PVD takes places in a vacuum chamber, and by one means or another creates a
low-pressure vapor of the material to be deposited. Some of this vapor will condense on the
workpiece and thereby start to deposit as a thin film. Simply melting a material in vacuum,
depending on its vapor pressure, may sometimes produce a useful deposit of material.
Sputtering is an example of physical vapor deposition and is the most impor-
n+ n+ tant PVD method for integrated circuit manufacturing. The interconnections that carry
electrical signals from one electronic device to another on an IC chip typically have been
made from aluminum alloys that have been sputter deposited. Sputtering can be used to
deposit both conducting and insulating materials.
As shown in Figure 19-19, in a sputtering chamber, argon or other atoms in a gas
are first ionized and then accelerated by an electric field towards a source of material to
n+ n+
be deposited, sometimes called a “target.” These ions dislodge and eject atoms from the
surface of the source material, some of which drift across a gap towards the workpiece;
those that condense on its surface are said to be deposited. Depending on how long the
process continues, it is possible to sputter deposit films that are many microns thick.
Chemical vapor deposition (CVD) represents another set of techniques that is
widely employed in the IC industry. In CVD, the source of the material to be depos-
ited exists in gaseous form. The source gas and other gases are introduced into a heated
vacuum chamber where they undergo a chemical reaction that creates the desired mate-
rial as a product. This product condenses on the workpiece (as in PVD processes) creat-
ing, over time, a layer of the material. In some CVD processes, the chemical reaction may
take place preferentially on certain areas of the workpiece, depending on the chemical
Figure 19-18 (a) Czochralski growth technique for growing single crystals of silicon. composition of these areas. Thin films of polycrystalline silicon, tungsten, and titanium
(Based on Microchip Fabrication, Third Edition, by P. VanZant, McGraw-Hill, 1997.) nitride are commonly deposited by CVD as part of IC manufacturing. Nanowire growth,
(b) Overall steps encountered in the processing of semiconductors. Production of a which was discussed in Chapter 11, also often proceeds via a CVD process.
FET semiconductor device: (i) A p-type silicon substrate is oxidized. (ii) In a process Electrodeposition is a third method for creating thin films on a workpiece.
known as photolithography, ultraviolet radiation passes through a photomask Although this is a very old technology, it has recently been adopted for use in IC manu-
(which is much like a stencil), thereby exposing a photosensitive material known facturing, especially for depositing the copper films that are replacing aluminum films
as photoresist that was previously deposited on the surface. (iii) The exposed in most advanced integrated circuits. In electrodeposition, the source and workpiece are
photoresist is dissolved. (iv) The exposed silica is removed by etching. (v) An n-type both immersed in a liquid electrolyte and also are connected by an external electrical
dopant is introduced to produce the source and drain. (vi) The silicon is again circuit. When a voltage is applied between the source and workpiece, ions of the source
oxidized. (vii) Photolithography is repeated to introduce other components, material dissolve in the electrolyte, drift under the influence of the field towards the
including electrical connections, for the device. (Based on Fundamentals of Modern workpiece, and chemically bond on its surface. Over time, a thin film is thus deposited.
Manufacturing, by M.P. Groover, John Wiley & Sons, Inc., 1996.) In some circumstances, an external electric field may not be required; this is called electro-
less deposition. Electrodeposition and electroless deposition are sometimes referred to as
“plating,” and the deposited film is sometimes said to be “plated out” on the workpiece.

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19-8 Conductivity in Other Materials 707

706 Chapter 19 Electronic Materials Example 19-6 Ionic Conduction in MgO

Suppose that the electrical conductivity of MgO is determined primarily by the
–
diffusion of the Mg21 ions. Estimate the mobility of the Mg21 ions and calculate
Vacuum chamber the electrical conductivity of MgO at 1800°C. The diffusion coefficient of Mg21
ions in MgO at 1800°C is 10210 cm2 ys.
Source “target”
Solution
(3) For MgO, Z 5 2yion, q 5 1.6 3 10219 C, kB 5 1.38 3 10223 J⁄K, and T 5 2073 K:
+ +
Ar Ar (2) ZqD s2ds1.6 3 10219 Cds10210 cm2ysd
+ + 5 5 5 1.12 3 1029 C ? cm2ysJ ? sd
Ar Ar kBT s1.38 3 10223 JyKds2073 Kd
(4) (1) Gas inlet
Ar
+
Ar Ar Ar Since one coulomb is equivalent to one ampere ? second, and one joule is equivalent
to one ampere ? second ? volt:
(5)
5 1.12 3 1029 cm2ysV ? sd
Workpiece MgO has the NaCl structure with four magnesium ions per unit cell. The
lattice parameter is 3.96 3 1028 cm, so the number of Mg21 ions per cubic centimeter is

+ s4 Mg21 ionsycelld
n5 5 6.4 3 1022 ionsycm3
s3.96 3 1028 cmd3ycell
Figure 19-19 Schematic illustration of sputtering. The workpiece and sputter target are placed in a
vacuum chamber. (1) An inlet allows a gas such as argon to enter at low pressure. In the presence of the
5 nZq 5 s6.4 3 1022ds2ds1.6 3 1029ds1.12 3 1029d
electric field across the target and workpiece, some of the argon atoms are ionized (2) and then acceler-
ated towards the target. By momentum transfer, atoms of the target are ejected (3), drift across the gap 5 23 3 1026 C ? cm2 yscm3 ? V ? sd
towards the workpiece (4), and condense on the workpiece (5), thereby depositing target atoms and
eventually forming a film. (Courtesy of John Bravman.) Since one coulomb is equivalent to one ampere ? second (A ? s) and one volt is
equivalent to one ampere ? ohm (A ? V),
5 2.3 3 1025 ohm21 ? cm21

19-8 Conductivity in Other Materials

Electrical conductivity in most ceramics and polymers is low; however, special materials
Applications of lonically Conductive Oxides The most widely
provide limited or even good conduction. In Chapter 4, we saw how the Kröger-Vink used conductive and transparent oxide is indium tin oxide (ITO), used as a transparent
notation can be used to explain defect chemistry in ceramic materials. Using dopants, it conductive coating on plate glass. Other applications of (ITO) include touch screen
is possible to convert many ceramics (e.g., BaTiO3, TiO2, ZrO2) that are normally insu- displays for computers and devices such as automated teller machines. Other conductive
lating into conductive oxides. The conduction in these materials can occur as a result of oxides include ytrria stabilized zirconia (YSZ), which is used as a solid electrolyte in solid
movement of ions or electrons and holes. oxide fuel cells. Lithium cobalt oxide is used as a solid electrolyte in lithium ion batteries.
It is important to remember that, although most ceramic materials behave as electrical
Conduction in lonic Materials Conduction in ionic materials often insulators, by properly engineering the point defects in ceramics, it is possible to convert
occurs by movement of entire ions, since the energy gap is too large for electrons to enter many of them into semiconductors.
the conduction band. Therefore, most ionic materials behave as insulators.
In ionic materials, the mobility of the charge carriers, or ions, is
Conduction in Polymers Because their valence electrons are involved in
ZqD
(19-15)
5 covalent bonding, polymers have a band structure with a large energy gap, leading to low-
kBT electrical conductivity. Polymers are frequently used in applications that require electrical
where D is the diffusion coefficient, kB is the Boltzmann constant, T is the absolute insulation to prevent short circuits, arcing, and safety hazards. Table 19-1 includes the
temperature, q is the electronic charge, and Z is the charge on the ion. The mobility is conductivity of four common polymers. In some cases, however, the low conductivity
many orders of magnitude lower than the mobility of electrons; hence, the conductivity is a hindrance. For example, if lightning strikes the polymer-matrix composite wing of
is very small:
an airplane, severe damage can occur. We can solve these problems by two approaches:
5 nZq (19-16)
(1) introducing an additive to the polymer to improve the conductivity, and (2) creating
For ionic materials, n is the concentration of ions contributing to conduction. Impurities polymers that inherently have good conductivity.
and vacancies increase conductivity. Vacancies are necessary for diffusion in substitution-
The introduction of electrically conductive additives can improve conductivity.
al types of crystal structures, and impurities can diffuse and help carry the current. High
temperatures increase conductivity because the rate of diffusion increases. The following For example, polymer-matrix composites containing carbon or nickel-plated carbon fibers
example illustrates the estimation of mobility and conductivity in MgO. combine high stiffness with improved conductivity; hybrid composites containing metal
fibers, along with normal carbon, glass, or aramid fibers, also produce lightning-safe
aircraft skins. Figure 19-20 shows that when enough carbon fibers are introduced to nylon
in order to ensure fiber-to-fiber contact, the resistivity is reduced by many orders of
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708 Chapter 19 Electronic Materials

Figure 19-20 Effect of carbon fibers on the

electrical resistivity of nylon. 19-10 Polarization in Dielectrics 709

Any separation of charges (e.g., between the nucleus and electron cloud) or
any mechanism that leads to a change in the separation of charges that are already
present (e.g., movement or vibration of ions in an ionic material) causes polarization.
There are four primary mechanisms causing polarization: (1) electronic polarization,
(2) ionic polarization, (3) molecular polarization, and (4) space charge (Figure 19-21).
Their occurrence depends upon the electrical frequency of the applied field, just like
the mechanical behavior of materials depends on the strain rate (Chapters 6 and 8). If
we apply a very rapid rate of strain, certain mechanisms of plastic deformation are not
activated. Similarly, if we apply a rapidly alternating electric field, some polarization
mechanisms may be unable to induce polarization in the material.
Polarization mechanisms play two important roles. First, if we make a capacitor
from a material, the polarization mechanisms allow charge to be stored, since the dipoles
created in the material (as a result of polarization) can bind a certain portion of the charge
on the electrodes of the capacitor. Thus, the higher the dielectric polarization, the higher
the dielectric constant (k) of the material. The dielectric constant is defined as the ratio
magnitude. Conductive fillers and fibers are also used to produce polymers that shield of capacitance between a capacitor filled with dielectric material and one with vacuum
against electromagnetic radiation. between its electrodes. This charge storage, in some ways, is similar to the elastic strain in a
Some polymers inherently have good conductivity as a result of doping
or processing techniques. When acetal polymers are doped with agents such as arsenic
pentafluoride, electrons or holes are able to jump freely from one atom to another along
the backbone of the chain, increasing the conductivity to near that of metals. Some poly- E
mers, such as polyphthalocyanine, can be cross-linked by special curing processes to raise
the conductivity to as high as 102 ohm21 ⋅ cm21, a process that permits the polymer to
behave as a semiconductor. Because of the cross-linking, electrons can move more easily
from one chain to another. Organic light-emitting diodes are fabricated from semicon-
ducting polymers including polyanilines.

19-9 Insulators and Dielectric Properties

Materials used to insulate an electric field from its surroundings are required in a large
number of electrical and electronic applications. Electrical insulators obviously must
have a very low conductivity, or high resistivity, to prevent the flow of current. Insula-
tors must also be able to withstand intense electric fields. Insulators are produced from
ceramic and polymeric materials in which there is a large energy gap between the valence
and conduction bands; however, the high-electrical resistivity of these m aterials is not
always sufficient. At high voltages, a catastrophic breakdown of the insulator may occur,
and current may flow. For example, the electrons may have kinetic energies sufficient to
ionize the atoms of the insulator, thereby creating free electrons and generating a current
at high voltages. In order to select an insulating material properly, we must understand
how the material stores, as well as conducts, electrical charge. Porcelain, alumina, cordi-
erite, mica, and some glasses and plastics are used as insulators. The resistivity of most of
these is . 1014 V ⋅ cm, and the breakdown electric fields are ,5 to 15 kV⁄mm.

19-10 Polarization in Dielectrics

Figure 19-21 Polarization mechanisms in materials: (a) electronic, (b) atomic or ionic,
When we apply stress to a material, some level of strain develops. Similarly, when we (c) high-frequency dipolar or orientation (present in ferroelectrics), (d) low-frequency
dipolar (present in linear dielectrics and glasses), (e) interfacial-space charge at
subject materials to an electric field, the atoms, molecules, or ions respond to the applied
electrodes, and (f) interfacial-space charge at heterogeneities such as grain boundaries.
electric field (E). Thus, the material is said to be polarized. A dipole is a pair of opposite (Based on Principles of Electronic Ceramics, L. L. Hench and J. K. West, Wiley Inter-
charges separated by a certain distance. If one charge of 1q is separated from another science, John Wiley & Sons, Inc., 1990.)
charge of 2q (q is the electronic charge) and d is the distance between these charges, the
dipole moment is defined as the product of q and d. The magnitude of polarization is given
by P 5 zqd, where z is the number of charge centers that are displaced per cubic meter.
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76761_ch19.indd 708 24/10/14 7:57 PM

710 Chapter 19 Electronic Materials

material subjected to stress. The second important role played by polarization mechanisms
is that when polarization sets in, charges move (ions or electron clouds are displaced). 19-10 Polarization in Dielectrics 711
If the electric field oscillates, the charges move back and forth. These displacements are
extremely small (typically , 1 Å); however, they cause dielectric losses. This energy is lost Capacitance C is the ability to store charge and is defined as
as heat. The dielectric loss is similar to the viscous deformation of a material. If we want Q
C5 (19-17)
to store a charge, as in a capacitor, dielectric loss is not good; however, if we want to use V
microwaves to heat up our food, dielectric losses that occur in water contained in the food where Q is the charge on the electrode plates of a capacitor and V is the applied
are great! The dielectric losses are often measured by a parameter known as tan d. When voltage [Figure 19-22(a)]. Note that a voltage must be applied to create the charge on the
we are interested in extremely low loss materials, such as those used in microwave com- electrodes, but that the charge is “stored” in the absence of the voltage until an external
munications, we refer to a parameter known as the dielectric quality factor (Qd , 1⁄tan d). circuit allows it to dissipate. In microelectronic devices, this is the basis for digital data
storage. If the space between two parallel plates (with surface area A and separated by
The dielectric constant and dielectric losses depend strongly on electrical frequency and
a distance t) is filled with a material, then the dielectric constant k, also known as the
temperature. relative permittivity ´r, is determined according to
Electronic polarization is omnipresent since all materials contain atoms. The
k 0A
electron cloud gets displaced from the nucleus in response to the field seen by the atoms. C5 (19-18)
t
The separation of charges creates a dipole moment [Figure 19-21(a)]. This mechanism
can survive at the highest electrical frequencies (,1015 Hz) since an electron cloud can The constant ´0 is the permittivity of a vacuum and is 8.85 3 10212 Fym. As the
material undergoes polarization, it can bind a certain amount of charge on the elec-
be displaced rapidly, back and forth, as the electrical field switches. Larger atoms and
trodes, as shown in Figure 19-22(b). The greater the polarization, the higher the dielectric
ions have higher electronic polarizability (tendency to undergo polarization), since the constant, and therefore, the greater the bound charge on the electrodes.
electron cloud is farther away from the nucleus and held less tightly. This polarization The dielectric constant is the measure of how susceptible the material is to the
mechanism is also linked closely to the refractive index of materials, since light is an applied electric field. The dielectric constant depends on the composition, microstruc-
electromagnetic wave for which the electric field oscillates at a very high frequency ture, electrical frequency, and temperature. The capacitance depends on the dielectric
(,1014 2 1016 Hz). The higher the electronic polarizability, the higher the refractive constant, area of the electrodes, and the separation between the electrodes. Capacitors in
index. We use this mechanism in making “lead crystal,” which is really an amorphous parallel provide added capacitance (just like resistances add in series). This is the reason
glass that contains up to 30% PbO. The large lead ions (Pb12) are highly polarizable why multi-layer capacitors consist of 100 or more layers connected in parallel. These are
due to the electronic polarization mechanisms and provide a high-refractive index when typically based on BaTiO3 formulations and are prepared using a tape-casting process.
high enough concentrations of lead oxide are present in the glass. This high-refractive Silver-palladium or nickel is used as electrode layers.
For electrical insulation, the dielectric strength (i.e., the electric field value that
index causes more light to be reflected than by a glass with a lower refractive index,
can be supported prior to electrical breakdown) is important. The dielectric properties of
thereby enhancing its appearance for aesthetic purposes. some materials are shown in Table 19-7

Linear and Nonlinear Dielectrics The dielectric constant, as expected,

is related to the polarization that can be achieved in the material. We can show that the
Example 19-7 Electronic Polarization in Copper dielectric polarization induced in a material depends upon the applied electric field and the
dielectric constant according to
Suppose that the average displacement of the electrons relative to the nucleus in a P 5 sk 2 1d0E sfor linear dielectricsd (19-19)
copper atom is 1028 Å when an electric field is imposed on a copper plate. Calculate where E is the strength of the electric field (Vym). For materials that polarize easily, both
the electronic polarization. the dielectric constant and the capacitance are large and, in turn, a large quantity of
Solution charge can be stored. In addition, Equation 19-19 suggests that polarization increases, at
least until all of the dipoles are aligned, as the voltage (expressed by the strength of the
The atomic number of copper is 29, so there are 29 electrons in each copper atom. The
lattice parameter of copper is 3.6151 Å. Thus,
s4 atomsycellds29 electronsyatomd
z5 5 2.455 3 1030 electronsym3
s3.6151 3 10210 md3ycell

P 5 zqd 5 2.455 3 1030 1 electrons

m3 2 11.6 3 10 219 C
electron 2
s1028Ads10210 m /Ad
8 8
t

5 3.93 3 1027 Cym2

Frequency and Temperature Dependence of the Figure 19-22 (a) A charge can be stored on the conductor plates in a vacuum.
Dielectric Constant and Dielectric Losses A capacitor is a (b) When a dielectric is placed between the plates, the dielectric polarizes, and
device that is capable of storing electrical charge. It typically consists of two electrodes additional charge is stored.
with a dielectric material situated between them. The dielectric may or may not be a solid;
even an air gap or vacuum can serve as a dielectric. Two parallel, flat-plate electrodes
represent the simplest configuration for a capacitor.
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76761_ch19.indd 710 24/10/14 7:57 PM

712 Chapter 19 Electronic Materials 19-11 Electrostriction, Piezoelectricity, and Ferroelectricity 713

Table 19-7 Properties of selected dielectric materials

Dielectric Constant Dielectric
Strength tan d Resistivity
Material (at 60 Hz) (at 106 Hz) (106 V/m) (at 106 Hz) (ohm · cm)

Polyethylene 2.3 2.3 20 0.00010 . 1016

Teflon 2.1 2.1 20 0.00007 1018
Polystyrene 2.5 2.5 20 0.00020 1018
PVC 3.5 3.2 40 0.05000 1012 Figure 19-23 The (a) direct and (b) converse piezoelectric effect. In the direct piezoelec-
Nylon 4.0 3.6 20 0.04000 1015 tric effect, applied stress causes a voltage to appear. In the converse effect (b), an applied
Rubber 4.0 3.2 24 voltage leads to the development of strain.
Phenolic 7.0 4.9 12 0.05000 1012
Epoxy 4.0 3.6 18 1015
Paraffin wax 2.3 10 1013–1019 Conversely, when an electrical voltage is applied, a piezoelectric material shows
Fused silica 3.8 3.8 10 0.00004 1011–1012 the development of strain. This is known as the converse or generator piezoelectric
Soda-lime glass 7.0 7.0 10 0.00900 1015 effect. This effect is used in making actuators. For example, this movement can be used to
Al2O3 9.0 6.5 6 0.00100 1011–1013 generate ultrasonic waves that are used in medical imaging, as well as such applications as
ultrasonic cleaners or toothbrushes. Sonic energy can also be created using piezoelectrics
TiO2 14–110 8 0.00020 1013–1018
to make the high-fidelity “tweeter” found in most speakers. In addition to Pb(ZrxTi12x)O3
Mica 7.0 40 1013
(PZT), other piezoelectrics include SiO2 (for making quartz crystal oscillators), ZnO, and
BaTiO3 2000–5000 12 ,0.0001 108–1015 polyvinylidene fluoride (PVDF). Many naturally occurring materials such as bone and
Water 78.3 1014 silk are also piezoelectric.
The “d” constant for a piezoelectric is defined as the ratio of strain () to electric
field:
electric field) increases. The quantity (k21) is known as dielectric susceptibility (xe). The 5d ?E (19-20)
dielectric constant of vacuum is one, or the dielectric susceptibility is zero. This makes The “g” constant for a piezoelectric is defined as the ratio of the electric field generated
sense since a vacuum does not contain any atoms or molecules. to the stress applied (X):
In linear dielectrics, P is linearly related to E and k is constant. This is similar to
E5g?X (19-21)
how stress and strain are linearly related by Hooke’s law. In linear dielectrics, k (or xe)
remains constant with changing E. In materials such as BaTiO3, the dielectric constant The d and g piezoelectric coefficients are related by the dielectric constant as:
changes with E, and hence, Equation 19-19 cannot be used. These materials in which d
P and E are not related by a straight line are known as nonlinear dielectrics or ferroelec- g5 (19-22)
k0
trics. These materials are similar to elastomers for which stress and strain are not linearly
related and a unique value of the Young’s modulus cannot be assigned. We define ferroelectrics as materials that show the development of a spon-
taneous and reversible dielectric polarization (Ps). Examples include the tetragonal
polymorph of barium titanate. Lead zirconium titanate is both ferroelectric and piezo-
electric. Ferroelectric materials show a hysteresis loop (i.e., the induced polarization is
not linearly related to the applied electric field) as seen in Figure 19-24. Ferroelectric
19-11 Electrostriction, Piezoelectricity, materials exhibit ferroelectric domains in which the region (or domain) has uniform
and Ferroelectricity polarization (Figure 19-25.) Certain ferroelectrics, such as PZT, exhibit a strong piezo-
electric effect, but in order to maximize the piezoelectric effect (e.g., the development of
When any material undergoes polarization, its ions and electron clouds are displaced, strain or voltage), piezoelectric materials are deliberately “poled” using an electric field
causing the development of a mechanical strain in the material. This effect is seen in all to align all domains in one direction. The electric field is applied at high temperature and
materials subjected to an electric field and is known as electrostriction. maintained while the material is cooled.
Of the total 32 crystal classes, eleven have a center of symmetry. This means The dielectric constant of ferroelectrics reaches a maximum near a tem-
that if we apply a mechanical stress, there is no dipole moment generated since ionic perature known as the Curie temperature. At this temperature, the crystal structure
movements are symmetric. Of the 21 that remain, 20 point groups, which lack a center acquires a center of symmetry and thus is no longer piezoelectric. Even at these high
of symmetry, exhibit the development of dielectric polarization when subjected to stress. temperatures, however, the dielectric constant of ferroelectrics remains high. BaTiO3
These materials are known as piezoelectric. (The word piezo means pressure.) When these exhibits this behavior, and this is the reason why BaTiO3 is used to make single and
materials are stressed, they develop a voltage. This development of a voltage upon the multi-layer capacitors. In this state, vibrations and shocks do not generate spurious
application of stress is known as the direct or motor piezoelectric effect (Figure 19-23). voltages due to the piezoelectric effect. Since the Curie transition occurs at a high
This effect helps us make devices such as spark igniters, which are often made using lead temperature, use of additives in BaTiO3 helps to shift the Curie transition temperature
zirconium titanate (PZT). This effect is also used, for example, in detecting submarines to lower temperatures. Additives also can be used to broaden the Curie transition.
and other objects under water. Materials such as Pb(Mg1⁄3Nb2⁄3)O3 or PMN are known as relaxor ferroelectrics.

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714 Chapter 19 Electronic Materials Summary 715

P(C/m2) Figure 19-24 The ferroelectric Thus, the capacitance per layer will be
hysteresis loop for a single-domain
single crystal of BaTiO3. (From s3000ds8.85 3 10212 Fymds10 3 1023 mds5 3 1023 md
Clayer 5
Electroceramics: Material, Properties, 10 3 1026 m
Applications, by A. J. Moulson and Clayer 5 13.28 3 1028
J. M. Herbert, Chapman and Hall,
Kluwer Academic Publishers, 1990.) We have 100 layers connected in parallel. Capacitances add in this arrangement. All
layers have the same geometric dimensions in this case.
Ctotal 5 snumber of layersd ? scapacitance per layerd

E(MV/m)
Ctotal 5 s100ds13.28 3 1028 Fd 5 13.28 F

Summary
●● Electronic materials include insulators, dielectrics, conductors, semiconductors,
and superconductors. These materials can be classified according to their band
structures. Electronic materials have enabled many technologies ranging from
Figure 19-25 high-voltage line insulators to solar cells, computer chips, and many sensors and
Ferroelectric domains can actuators.
be seen in the microstructure ●● Important properties of conductors include the conductivity and the temperature
of polycrystalline BaTiO3.
dependence of conductivity. In pure metals, the resistivity increases with temperature.
(Courtesy of Professor Chris
Resistivity is sensitive to impurities and microstructural defects such as grain
Bowen)
boundaries. Resistivity of alloys is typically higher than that of pure metals.
●● Semiconductors have conductivities between insulators and conductors and are much
poorer conductors than metals. The conductivities of semiconductors can be altered
by orders of magnitude by minute quantities of certain dopants. Semiconductors can
be classified as elemental (Si, Ge) or compound (GaN, InP, GaAs). Both of these can
be intrinsic or extrinsic (n- or p-type). Some semiconductors have direct bandgaps
(e.g., GaAs), while others have indirect bandgaps (e.g., Si).
●● Creating an n-type region in a p-type semiconductor (or vice versa) forms a p-n
junction. The p-n junction is used to make diodes and transistors.
●● Microelectronics fabrication involves hundreds of precision processes that can produce
hundreds of millions and even a billion transistors on a single microchip.
These materials show very high dielectric constants (up to 20,000) and good piezo-
electric behavior, so they are used to make capacitors and piezoelectric devices.
●● Thin films are integral components of microelectronic devices and also are used for
wear-resistant and anti-reflective coatings. Thin films can be deposited using a variety
of techniques, including physical vapor deposition, chemical vapor deposition, and
electrodeposition.
Example 19-8 Design of a Multi-Layer Capacitor ●● Ionic materials conduct electricity via the movement of ions or electrons and holes.
A multi-layer capacitor is to be designed using a BaTiO3 formulation containing ●● Dielectrics have large bandgaps and do not conduct electricity. With insulators,
SrTiO3. The dielectric constant of the material is 3000. (a) Calculate the capacitance the focus is on breakdown voltage or field. With dielectrics, the emphasis is on the
of a multi-layer capacitor consisting of 100 layers connected in parallel using nickel dielectric constant, frequency, and temperature dependence. Polarization mechanisms
electrodes. The area of each layer is 10 mm 3 5 mm, and the thickness of each layer in materials dictate this dependence.
is 10 mm. ●● In piezoelectrics, the application of stress results in the development of a voltage; the
Solution application of a voltage causes strain.
(a) The capacitance of a parallel plate capacitor is given by ●● Ferroelectrics are materials that show a reversible and spontaneous polarization.
k0A BaTiO3, PZT, and PVDF are examples of ferroelectrics. Ferroelectrics exhibit a large
C5 t
dielectric constant and are often used to make capacitors.

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716 Chapter 19 Electronic Materials Problems 717

Glossary Linear dielectrics Materials in which the dielectric polarization is linearly related to the electric
field; the dielectric constant is not dependent on the electric field.
Matthiessen’s rule The resistivity of a metal is given by the addition of a base resistivity that
Bandgap A range of energy values in which there are no allowed electron energy levels (except
accounts for the effect of temperature and a temperature independent term that reflects the effect
those attributed to the presence of impurities). These values fall between the top of the valence
of atomic level defects, including solutes forming solid solutions.
band and the bottom of the conduction band.
Mean free path The average distance that electrons move without being scattered by other
Band structure The band structure consists of the array of energy levels that are available to
atoms or lattice defects.
or forbidden for electrons to occupy and determines the electronic behavior of a solid, such as
whether it is a conductor, semiconductor, or insulator. Microstructure-sensitive property Properties that depend on the microstructure of a
material (e.g., conductivity, dielectric constant, or yield strength).
Capacitor A device that is capable of storing electrical charge. It typically consists of two
electrodes with a dielectric material situated between them, but even an air gap can serve as a Mobility The ease with which a charge carrier moves through a material.
dielectric. A capacitor can be a single layer or multi-layer device. Nonlinear dielectrics Materials in which dielectric polarization is not linearly related to the
Chemical Vapor Deposition A thin-film growth process in which gases undergo a reaction in a electric field (e.g., ferroelectric). These have a field-dependent dielectric constant.
heated vacuum chamber to create the desired product on a substrate. Nonradiative recombination The generation of heat when an electron loses energy and falls
Conduction band The unfilled energy levels into which electrons are excited in order to from the conduction band to the valence band to occupy a hole; this occurs mainly in indirect
conduct. bandgap materials such as Si.
Curie temperature The temperature above which a ferroelectric is no longer piezoelectric. p-n junction A device made by creating an n-type region in a p-type material (or vice versa). A p-n
junction behaves as a diode and multiple p-n junctions function as transistors. It is also the basis
Current density Current per unit cross-sectional area. of LEDs and solar cells.
Dielectric constant The ratio of the permittivity of a material to the permittivity of vacuum, Permittivity The ability of a material to polarize and store a charge within it.
thus describing the relative ability of a material to polarize and store a charge; the same as relative
permittivity. Physical Vapor Deposition A thin-film growth process in which a low-pressure vapor supplies
the material to be deposited on a substrate. Sputtering is one example of PVD.
Dielectric loss A measure of how much electrical energy is lost due to motion of charge entities
that respond to an electric field via different polarization mechanisms. This energy appears as heat. Piezoelectrics Materials that develop voltage upon the application of a stress and develop strain
when an electric field is applied.
Dielectric strength The maximum electric field that can be maintained between two conductor
plates without causing a breakdown. Polarization Movement of charged entities (i.e., electron cloud, ions, dipoles, and molecules) in
response to an electric field.
Doping Deliberate addition of controlled amounts of other elements to increase the number of
charge carriers in a semiconductor. Radiative recombination The emission of light when an electron loses energy and falls from
the conduction band to the valence band to occupy a hole; this occurs in direct bandgap materials
Drift velocity The average rate at which electrons or other charge carriers move through a such as GaAs.
material under the influence of an electric or magnetic field.
Rectifier A p-n junction device that permits current to flow in only one direction in a circuit.
Electric field The voltage gradient or volts per unit length.
Reverse bias Connecting a junction device so that the p-side is connected to a negative terminal;
Electrodeposition A method for depositing materials in which a source and workpiece are very little current flows through a p-n junction under reverse bias.
connected electrically and immersed in an electrolyte. A voltage is applied between the source and
workpiece, and ions from the source dissolve in the electrolyte, drift to the workpiece, and gradually Sputtering A thin-film growth process by which gas atoms are ionized and then accelerated by
deposit a thin film on its surface. an electric field towards the source, or “target,” of material to be deposited. These ions eject atoms
from the target surface, some of which are then deposited on a substrate. Sputtering is one type of
Electrostriction The dimensional change that occurs in any material when an electric field a physical vapor deposition process.
acts on it.
Superconductor A material that exhibits zero electrical resistance under certain conditions.
Energy gap A range of energy values in which there are no allowed electron energy levels (except
those attributed to the presence of impurities). These values fall between the top of the valence Thermistor A semiconductor device that is particularly sensitive to changes in temperature,
band and the bottom of the conduction band. permitting it to serve as an accurate measure of temperature.
Thin film A coating or layer that is small or thin in one dimension. Typical thicknesses range from
Extrinsic semiconductor A semiconductor prepared by adding dopants, which determine the
10 Å to a few microns depending on the application.
number and type of charge carriers. Extrinsic behavior can also be seen due to impurities.
Transistor A semiconductor device that amplifies or switches electrical signals.
Fermi energy The energy level at which the probability of finding an electron is 1y2.
Valence band The energy levels filled by electrons in their lowest energy states.
Ferroelectric A material that shows spontaneous and reversible dielectric polarization.
Forward bias Connecting a p-n junction device so that the p-side is connected to a positive
terminal, thereby enabling current to flow. Problems
Holes Unfilled energy levels in the valence band. Because electrons move to fill these holes, the
holes produce a current. Section 19-1 Ohm’s Law and Electrical Con- 19-2 Find the resistance of a fiber with a cross-
Hysteresis loop The loop traced out by the nonlinear polarization in a ferroelectric material as ductivity sectional area of 1.34 mm2 and length
the electric field is cycled. A similar loop occurs in certain magnetic materials. of 10 cm that is subjected to a voltage
Section 19-2 Band Structure of Solids of 225 V for which the current density
Integrated circuit An electronic package that comprises large numbers of electronic devices
fabricated on a single chip. is 1.25 A⁄cm2. Assume the resistor is
Section 19-3 Conductivity of Metals and
Intrinsic semiconductor A semiconductor in which properties are controlled by the element or uniform in material and properties.
Alloys
compound that is the semiconductor and not by dopants or impurities. 19-3 A wire two microns in diameter is made
19-1 Of the metals listed in Table 19-1, which from 10 cm silver, 0.1 cm gallium, and
are the most and least conductive?

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718 Chapter 19 Electronic Materials Problems 719

10 cm silver all joined end to end (i.e., in 0.1 in., and the average diameter of the 19-22 Find the resistivity of palladium at 443°C beryllium contained 10 at% of the alloying
series). Assume the joints are perfect and arc is about 0.18 in. Calculate the cur- if it has a defect contribution of 1.02 3 element at 200°C?
have no additional resistance. What is the rent density in the arc, the electric field 1027 ohm · cm.
Section 19-4 Semiconductors
total resistance of the wire? across the arc, and the electrical conduc- 19-23 (a) Copper and nickel form a complete solid
19-4 A current of 10 A passes through a 1-mm- tivity of the hot gases in the arc during solution. Draw a schematic diagram il- Section 19-5 Applications of Semiconductors
diameter wire 1000 m long. Calculate the welding. lustrating the resistivity of a copper and
power loss if the wire is made from 19-14 Draw a schematic of the band structures nickel alloy as a function of the atomic Section 19-6 General Overview of Integrated
(a) aluminum and of an insulator, a semiconductor, and a percent nickel. Comment on why the Circuit Processing
(b) silicon (see Table 19-1). metal. Use this to explain why the con- curve has the shape that it does.
19-5 A 0.5-mm-diameter fiber, 1 cm in length, ductivity of pure metals decreases with (b) Copper and gold do not form a com- Section 19-7 Deposition of Thin Films
made from boron nitride is placed in a increasing temperature, while the opposite plete solid solution. At the compo- 19-25 Explain the following terms: semicon-
120-V circuit. Using Table 19-1, calculate is true for semiconductors and insulators. sitions of 25 and 50 atomic percent ductor, intrinsic semiconductor, extrinsic
(a) the current flowing in the circuit; and 19-15 A typical thickness for a copper conductor gold, the ordered phases Cu3Au and semiconductor, elemental semiconductor,
(b) the number of electrons passing through (known as an interconnect) in an integrated CuAu form, respectively. Do you ex- compound semiconductor, direct band-
the boron nitride fiber per second. circuit is 250 nm. The mean free path of pect that a plot of the resistivity of a gap semiconductor, and indirect bandgap
(c) What would the current and number electrons in pure, annealed copper is about copper and gold alloy as a function semiconductor.
of electrons be if the fiber were made 40 nm. As the thickness of copper intercon- of the atomic percent gold will have 19-26 What is radiative and nonradiative recom-
from magnesium instead of boron nects approaches the mean free path, how a shape similar to the plot in part (a)? bination? What types of materials are used
nitride? do you expect conduction in the intercon- Explain. to make LEDs?
19-6 The power lost in a 2-mm-diameter copper nect is affected? Explain. 19-24 The electrical resistivity of a beryllium alloy 19-27 Report the temperature range (in °C) for
wire is to be less than 250 W when a 5 A 19-16 Calculate the resistivities of cobalt and containing 5 at% of an alloying element is which the sample in Figure 19-15 behaves
current is flowing in the circuit. What is beryllium at 505 K. found to be 50 3 1026 ohm · cm at 400° C. as an extrinsic semiconductor.
the maximum length of the wire? 19-17 Calculate the electrical conductivity of Determine the contributions to resistivity 19-28 For germanium and silicon, compare,
19-7 A current density of 100,000 A⁄cm2 flows platinum at 2200°C. due to temperature and due to impurities at 25°C, the number of charge carriers
through a gold wire 50 m in length. The 19-18 Calculate the electrical conductivity of by finding the expected resistivity of pure per cubic centimeter, the fraction of the
resistance of the wire is found to be 2 ohm. nickel at 250°C and at 1500°C. beryllium at 400°C, the resistivity due to im- total electrons in the valence band that are
Calculate the diameter of the wire and the 19-19 The electrical resistivity of pure chromium purities, and the defect resistivity coefficient. excited into the conduction band, and the
voltage applied to the wire. is found to be 18 3 1026 ohm . cm. Estimate What would be the electrical resistivity if the constant n0.
19-8 We would like to produce a 5000-ohm the temperature at which the resistivity mea-
resistor from boron-carbide fiber having a surement was made.
diameter of 0.1 mm. What is the required 19-20 After finding the electrical conductivity
length of the fiber? of cobalt at 0°C, we decide we would like
19-9 Ag has an electrical conductivity of 6.80 to double that conductivity. To what tem-
3 105 V21 · cm21. Au has an electrical perature must we cool the metal?
conductivity of 4.26 3 105 V21 · cm21. 19-21 From Figure 19-9(b), estimate the defect

next (cm–3)(log scale)

Calculate the number of charge carriers resistivity coefficient for tin in copper.
per unit volume and the electron mobility
in each in order to account for this differ-
ence in electrical conductivity. Comment
on your findings.
19-10 If the current density is 1.25 A⁄cm2 and
the drift velocity is 107 cm⁄s, how many
charge carriers are present? ( kB)
19-11 A current density of 5000 A⁄cm2 flows
through a magnesium wire. If half of the
valence electrons serve as charge carriers,
calculate the average drift velocity of the
electrons.
19-12 We apply 10 V to an aluminum wire 2 mm Figure 19-15 The effect of temperature on the carrier concentration of an n-type
in diameter and 20 m long. If 10% of semiconductor. At low temperatures, the donor or acceptor atoms are not ionized. As
the valence electrons carry the electrical temperature increases, the ionization process is complete, and the carrier concentration
charge, calculate the average drift velocity increases to a level that is dictated by the level of doping. The conductivity then
of the electrons in km⁄h and miles⁄h. essentially remains unchanged until the temperature becomes too high and the
19-13 In a welding process, a current of 400 A Figure 19-9(b) The effect of the addition of thermally generated carriers begin to dominate. The effect of dopants is lost at very
flows through the arc when the voltage selected elements on the electrical conductivity high temperatures, and the semiconductor essentially shows “intrinsic” behavior.
is 35 V. The length of the arc is about of copper. (Repeated for Problem 19-9.) (Repeated for Problem 19-27.)

76761_ch19.indd 718 24/10/14 7:57 PM 76761_ch19.indd 719 24/10/14 7:57 PM

720 Chapter 19 Electronic Materials Problems 721

19-29 For germanium and silicon, compare trend will continue to be followed in the required to produce a polarization of P(C/m2)
the temperatures required to double the future using established microelectronics 5 3 1027 Cym2.
electrical conductivities from the room fabrication techniques? If not, what are 19-51 Suppose we are able to produce a
temperature values. some of the alternatives currently being polarization of 5 3 1028 Cym2 in a cube
19-30 Determine the electrical conductivity considered? Provide a list of the references (5 mm side) of barium titanate. Assume a
of silicon when 0.0001 at% antimony is or websites that you used. dielectric constant of 3000. What voltage
added as a dopant and compare it to the 19-41 Silicon is the material of choice for the is produced?
electrical conductivity when 0.0001 at% substrate for integrated circuits. Explain 19-52 For the 14 materials with both a dielectric
indium is added. why silicon is preferred over germanium, strength and resistivity listed in Table 19-7,
19-31 We would like to produce an extrinsic ger- even though the electron and hole mo- plot the dielectric strength as a function of
manium semiconductor having an electrical bilities are much higher and the bandgap resistivity. Assume log average values for E(MV/m)
conductivity of 2000 ohm21 · cm21. Deter- is much smaller for germanium than for the resistivity ranges.
mine the amount of phosphorus and the silicon. Provide a list of the references or 19-53 What polarization mechanism will be pres-
amount of gallium required to make n- and websites that you used. ent in (a) alumina; (b) copper; (c) silicon;
p-type semiconductors, respectively. and (d) barium titanate?
Section 19-8 Conductivity in Other Materials
19-32 Estimate the electrical conductivity of Section 19-11 Electrostriction, Piezoelec-
silicon doped with 0.0002 at% arsenic at 19-42 If we want the resistivity of a nylon to be
tricity, and Ferroelectricity
600°C, which is above the plateau in the 104 ohm · cm, what weight percent carbon
fibers should be added? 19-54 Define the following terms: electrostric-
conductivity-temperature curve.
19-43 Calculate the electrical conductivity of a tion, piezoelectricity (define both its direct Figure 19-24 The ferroelectric hysteresis loop
19-33 Determine the amount of arsenic that must
fiber-reinforced polyethylene part that is and converse effects), and ferroelectricity. for a single-domain single crystal of BaTiO3.
be combined with 1 kg of gallium to pro-
reinforced with 20 vol % of continuous, 19-55 Calculate the capacitance of a parallel- (From Electroceramics: Material, Properties,
duce a p-type semiconductor with an elec-
aligned nickel fibers. plate capacitor containing five layers of Applications, by A. J. Moulson and J. M. Herbert,
trical conductivity of 500 ohm21 · cm21
19-44 What are ionic conductors? What are their mica for which each mica sheet is 1 cm 3 Chapman and Hall, Kluwer Academic Publishers,
at 25°C. The lattice parameter of GaAs
applications? 2 cm 3 0.005 cm. The layers are connected 1990.) (Repeated for Problem 19-58.)
is about 5.65 Å, and GaAs has the
19-45 How do the touch screen displays on some in parallel.
zincblende structure.
computers work? 19-56 A multi-layer capacitor is to be designed us-
19-34 Calculate the intrinsic carrier concentra-
19-46 Can polymers be semiconducting? What ing a relaxor ferroelectric formulation based
tion for GaAs at room temperature. Given
that the effective mass of electrons in would be the advantages in using these on lead magnesium niobate (PMN). The ap- Computer Problems
instead of silicon? parent dielectric constant of the material is
GaAs is 0.067me, where me is the mass of
20,000. Calculate the capacitance of a multi- 19-62 Design of Multi-layer Capacitors. Write
the electron, calculate the effective mass Section 19-9 Insulators and Dielectric Prop- layer capacitor consisting of ten layers con- a computer program that can be used to
of the holes. erties nected in parallel using Ni electrodes. The calculate the capacitance of a multi-layer
19-35 Calculate the electrical conductivity of sili-
Section 19-10 Polarization in Dielectrics area of the capacitor is 10 mm 3 10 mm, capacitor. The program, for example,
con doped with 1018 cm23 boron at room
and the thickness of each layer is 20 mm. should ask the user to provide values of
temperature. Compare the intrinsic carrier 19-47 With respect to mechanical behavior, we 19-57 A force of 20 lb is applied to the face of the dielectric constant and the dimensions
concentration to the dopant concentration. have seen that stress (a cause) produces a 0.5 cm 3 0.5 cm 3 0.1 cm thickness of the layer. The program should also
19-36 At room temperature, will the conductivity strain (an effect). What is the electrical of quartz crystal. Determine the voltage be flexible in that if the user provides an
of silicon doped with 1017 cm23 of arsenic analog of this? produced by the force. The modulus of intended value of capacitance and other
be greater than, about equal to, or less 19-48 With respect to mechanical behavior, elasticity of quartz is 10.4 3 106 psi. dimensions, the program should provide
than the conductivity of silicon doped elastic modulus represents the elastic 19-58 For the example hysteresis loop in Figure the required dielectric constant.
with 1017 cm23 of phosphorus? energy stored, and viscous dissipation 19-24, what is the polarization (Cym2)
19-37 When a voltage of 5 mV is applied to the represents the mechanical energy lost in if the electric field starts at 0.2 MV⁄m and
emitter of a transistor, a current of 2 mA
is produced. When the voltage is increased
deformation. What is the electrical ana-
log of this?
drops to zero? Knovel® Problems
to 8 mV, the current through the collector 19-49 Calculate the displacement of the electrons
rises to 6 mA. By what percentage will the or ions for the following conditions: Design Problems K19-1 Calculate the resistivity of pure iridium
at 673 K using its temperature resistivity
collector current increase when the emitter (a) electronic polarization in nickel of
voltage is doubled from 9 mV to 18 mV? 19-59 We would like to produce a 100-ohm coefficient.
2 3 1027 Cym2;
19-38 Design a light-emitting diode that will emit (b) electronic polarization in aluminum of resistor using a thin wire of a material. K19-2
Electrical conductivity is sometimes
at 1.12 micrometers. Is this wavelength 2 3 1028 Cym2; Design such a device. given in the units of %IACS. What does
in the visible range? What is a potential (c) ionic polarization in NaCl of 4.3 3 19-60 Design a capacitor that is capable of IACS stand for? Define the unit using the
application for this type of LED? 1028 Cym2; and storing 1 mF when 100 V is applied. information found.
19-39 How can we make LEDs that emit white (d) ionic polarization in ZnS of 5 3 19-61 Design an epoxy-matrix composite that K19-3 Can organic materials such as polymers
light (i.e., light that looks like sunlight)? 1028 Cym2. has a modulus of elasticity of at least and carbon nanotubes be semiconduc-
19-40 Investigate the scaling relationship known 19-50 A 2-mm-thick alumina dielectric is used 35 3 106 psi and an electrical conductivity tors? If they are, what determines their
as Moore’s Law. Is it expected that this in a 60 Hz circuit. Calculate the voltage of at least 1 3 105 ohm21 · cm21. semiconducting properties?

76761_ch19.indd 720 24/10/14 7:57 PM 76761_ch19.indd 721 24/10/14 7:57 PM

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1 - Fismat X 1

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680 Chapter 19 Electronic Materials 19-1 Ohm’s Law and Electrical Conductivity 681

S 19-1 Ohm’s Law and Electrical Conductivity

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*Unless specified otherwise, assumes high-purity material.

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 5.98 3 105 V 21 ? cm21

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Figure 19-7 The effect of temperature on the

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Be 4.0 3 1026 0.0250

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Table 19-5 Properties of commonly encountered semiconductors at room temperature

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Figure 19-11 The distribution Figure 19-12 The electrical conductivity

In intrinsic semiconductors, for every electron promoted to the conduction

 5 qni sn 1 pd (19-11)

In intrinsic semiconductors, we control the number of charge carriers and, hence,

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Extrinsic Semiconductors The temperature dependence of conductiv-

n-Type Semiconductors Suppose we add an impurity atom such as

p-Type Semiconductors When we add an impurity such as gallium Dopant Ed Ea Ed Ea

Charge Neutrality In an extrinsic semiconductor, there has to be overall

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Assume that the lattice constant of Si remains unchanged as a result of doping:

or 26 dopant atomsy106 Si atoms

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(a) (b) (c) Vdrain–source

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19-7 Deposition of Thin Films

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706 Chapter 19 Electronic Materials Example 19-6 Ionic Conduction in MgO

19-8 Conductivity in Other Materials

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Figure 19-20 Effect of carbon fibers on the

19-9 Insulators and Dielectric Properties

19-10 Polarization in Dielectrics

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Linear and Nonlinear Dielectrics The dielectric constant, as expected,

P 5 zqd 5 2.455 3 1030 1 electrons

5 3.93 3 1027 Cym2

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Table 19-7 Properties of selected dielectric materials

Polyethylene 2.3 2.3 20 0.00010 . 1016

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next (cm–3)(log scale)

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5.98 3 105 V 21 ? cm21

5 qni sn 1 pd (19-11)