516 • Chapter 12 / Electrical Properties

connecting wire nut is used, which employs a grease

that inhibits corrosion while maintaining a high elec-
trical conductivity at the junction.

Photograph courtesy of John Fernez

Insulated COPALUM
splice assemblies Aluminum
wire insulation
Typical
receptacle White aluminum
wire
Black aluminum
wire
Grounding
aluminum wire

Copper wire
Aluminum
pigtails
wire insulation

Figure 12.10 Schematic of a COPALUM connector Two copper wire–aluminum wire junctions (located
device that is used in aluminum wire electrical circuits. in a junction box) that experienced excessive heating.
(Reprinted by permission of the U.S. Consumer Product The one on the right (within the yellow wire nut) failed
Safety Commission.) completely.

Semiconductivity
The electrical conductivity of semiconducting materials is not as high as that of metals;
nevertheless, they have some unique electrical characteristics that render them especially
intrinsic useful. The electrical properties of these materials are extremely sensitive to the presence
semiconductor of even minute concentrations of impurities. Intrinsic semiconductors are those in which
the electrical behavior is based on the electronic structure inherent in the pure material.
extrinsic When the electrical characteristics are dictated by impurity atoms, the semiconductor is
semiconductor said to be extrinsic.

12.10 INTRINSIC SEMICONDUCTION

Intrinsic semiconductors are characterized by the electron band structure shown in Figure
12.4d: at 0 K, a completely filled valence band, separated from an empty conduction band
by a relatively narrow forbidden band gap, generally less than 2 eV. The two elemental
semiconductors are silicon (Si) and germanium (Ge), having band gap energies of approxi-
mately 1.1 and 0.7 eV, respectively. Both are found in Group IVA of the periodic table
(Figure 2.8) and are covalently bonded.5 In addition, a host of compound semiconducting
materials also display intrinsic behavior. One such group is formed between elements of
Groups IIIA and VA, for example, gallium arsenide (GaAs) and indium antimonide (InSb);
these are frequently called III–V compounds. The compounds composed of elements of
Groups IIB and VIA also display semiconducting behavior; these include cadmium sulfide
(CdS) and zinc telluride (ZnTe). As the two elements forming these compounds become
more widely separated with respect to their relative positions in the periodic table (i.e., the
electronegativities become more dissimilar, Figure 2.9), the atomic bonding becomes more
ionic and the magnitude of the band gap energy increases—the materials tend to become
more insulative. Table 12.3 gives the band gaps for some compound semiconductors.

5
The valence bands in silicon and germanium correspond to sp3 hybrid energy levels for the isolated atom; these
hybridized valence bands are completely filled at 0 K.
 12.10 Intrinsic Semiconduction • 517

Table 12.3
Band Gap Electron Mobility Hole Mobility Electrical Conductivity
Band Gap Energies, Material (eV ) (m2/V∙s) (m2/V∙s) (Intrinsic)(𝛀∙m)−1
Electron and Hole
Elemental
Mobilities, and
Intrinsic Electrical Ge 0.67 0.39 0.19 2.2
Conductivities at Si 1.11 0.145 0.050 3.4 × 10–4
Room Temperature III–V Compounds
for Semiconducting
Materials AlP 2.42 0.006 0.045 —
AlSb 1.58 0.02 0.042 —
GaAs 1.42 0.80 0.04 3 × 10–7
GaP 2.26 0.011 0.0075 —
InP 1.35 0.460 0.015 2.5 × 10–6
InSb 0.17 8.00 0.125 2 × 104
II–VI Compounds
CdS 2.40 0.040 0.005 —
CdTe 1.56 0.105 0.010 —
ZnS 3.66 0.060 — —
ZnTe 2.40 0.053 0.010 —
Source: This material is reproduced with permission of John Wiley & Sons, Inc.

Concept Check 12.3 Which of ZnS and CdSe has the larger band gap energy Eg? Cite
reason(s) for your choice.
(The answer is available in WileyPLUS.)

Concept of a Hole
In intrinsic semiconductors, for every electron excited into the conduction band there
is left behind a missing electron in one of the covalent bonds, or in the band scheme, a
vacant electron state in the valence band, as shown in Figure 12.6b.6 Under the influence of
an electric field, the position of this missing electron within the crystalline lattice may be
thought of as moving by the motion of other valence electrons that repeatedly fill in the
incomplete bond (Figure 12.11). This process is expedited by treating a missing electron
from the valence band as a positively charged particle called a hole. A hole is considered
to have a charge that is of the same magnitude as that for an electron but of opposite
sign (+1.6 × 10–19 C). Thus, in the presence of an electric field, excited electrons and
holes move in opposite directions. Furthermore, in semiconductors both electrons and
holes are scattered by lattice imperfections.
Electrical
conductivity for Intrinsic Conductivity
an intrinsic
semiconductor— Because there are two types of charge carrier (free electrons and holes) in an intrinsic
dependence on semiconductor, the expression for electrical conduction, Equation 12.8, must be modified
electron/hole to include a term to account for the contribution of the hole current. Therefore, we write
concentrations and
electron/hole σ = n|e| μe + p|e| μh (12.13)
mobilities

6
Holes (in addition to free electrons) are created in semiconductors and insulators when electron transitions occur
from filled states in the valence band to empty states in the conduction band (Figure 12.6). In metals, electron
transitions normally occur from empty to filled states within the same band (Figure 12.5), without the creation of holes.
518 • Chapter 12 / Electrical Properties

Figure 12.11 Electron-bonding model of

electrical conduction in intrinsic silicon:
Si Si Si Si
(a) before excitation, (b) and (c) after excitation
(the subsequent free-electron and hole motions
in response to an external electric field).
Si Si Si Si

Si Si Si Si

(a)
ℰ Field ℰ Field

Si Si Si Si Si Si Si Si

Free electron
Hole Free electron

Si Si Si Si Si Si Si Si

Hole

Si Si Si Si Si Si Si Si

(b) (c)

where p is the number of holes per cubic meter and 𝜇h is the hole mobility. The mag-
nitude of 𝜇h is always less than 𝜇e for semiconductors. For intrinsic semiconductors,
every electron promoted across the band gap leaves behind a hole in the valence
band; thus,
n = p = ni (12.14)
where ni is known as the intrinsic carrier concentration. Furthermore,
For an intrinsic
semiconductor, σ = n|e| (μe + μh ) = p|e|(μe + μh )
conductivity in terms
of intrinsic carrier = ni|e| (μe + μh ) (12.15)
concentration
The room-temperature intrinsic conductivities and electron and hole mobilities for sev-
eral semiconducting materials are also presented in Table 12.3.

EXAMPLE PROBLEM 12.1

Computation of the Room-Temperature Intrinsic Carrier Concentration for
Gallium Arsenide
For intrinsic gallium arsenide, the room-temperature electrical conductivity is 3 × 10–7 (Ω∙m)–1;
the electron and hole mobilities are, respectively, 0.80 and 0.04 m2/V∙s. Compute the intrinsic
carrier concentration ni at room temperature.
 12.11 Extrinsic Semiconduction • 519

Solution
Because the material is intrinsic, carrier concentration may be computed, using Equation 12.15, as
σ
ni =
|e| (μe + μh )
3 × 10−7 (Ω∙m) −1
= −19
(1.6 × 10 C)[(0.80 + 0.04) m2/ V∙s]
= 2.2 × 1012 m−3

12.11 EXTRINSIC SEMICONDUCTION

Virtually all commercial semiconductors are extrinsic—that is, the electrical behavior is
determined by impurities that, when present in even minute concentrations, introduce
excess electrons or holes. For example, an impurity concentration of 1 atom in 1012 is
sufficient to render silicon extrinsic at room temperature.

n-Type Extrinsic Semiconduction

To illustrate how extrinsic semiconduction is accomplished, consider again the elemen-
tal semiconductor silicon. An Si atom has four electrons, each of which is covalently
bonded with one of four adjacent Si atoms. Now, suppose that an impurity atom with
a valence of 5 is added as a substitutional impurity; possibilities would include atoms
from the Group VA column of the periodic table (i.e., P, As, and Sb). Only four of five
valence electrons of these impurity atoms can participate in the bonding because there
are only four possible bonds with neighboring atoms. The extra, nonbonding electron is
loosely bound to the region around the impurity atom by a weak electrostatic attraction,
as illustrated in Figure 12.12a. The binding energy of this electron is relatively small (on
the order of 0.01 eV); thus, it is easily removed from the impurity atom, in which case it
becomes a free or conducting electron (Figures 12.12b and 12.12c).
The energy state of such an electron may be viewed from the perspective of the
electron band model scheme. For each of the loosely bound electrons, there exists a
single energy level, or energy state, which is located within the forbidden band gap just
below the bottom of the conduction band (Figure 12.13a). The electron binding energy
corresponds to the energy required to excite the electron from one of these impurity
states to a state within the conduction band. Each excitation event (Figure 12.13b)
supplies or donates a single electron to the conduction band; an impurity of this type is
aptly termed a donor. Because each donor electron is excited from an impurity level, no
corresponding hole is created within the valence band.
At room temperature, the thermal energy available is sufficient to excite large
donor state numbers of electrons from donor states; in addition, some intrinsic valence–conduction
band transitions occur, as in Figure 12.6b, but to a negligible degree. Thus, the number
of electrons in the conduction band far exceeds the number of holes in the valence band
For an n-type (or n >> p), and the first term on the right-hand side of Equation 12.13 overwhelms the
extrinsic second—that is,
semiconductor,
dependence of σ ≅ n|e|μe (12.16)
conductivity on
concentration and A material of this type is said to be an n-type extrinsic semiconductor. The electrons are
mobility of electrons majority carriers by virtue of their density or concentration; holes, on the other hand,
are the minority charge carriers. For n-type semiconductors, the Fermi level is shifted
upward in the band gap, to within the vicinity of the donor state; its exact position is a
function of both temperature and donor concentration.
520 • Chapter 12 / Electrical Properties

Figure 12.12 Extrinsic n-type semiconduc-

tion model (electron bonding). (a) An impurity Si Si Si Si
atom such as phosphorus, having five valence (4+) (4+) (4+) (4+)
electrons, may substitute for a silicon atom.
This results in an extra bonding electron, which
is bound to the impurity atom and orbits it. Si P Si Si
(4+) (5+) (4+) (4+)
(b) Excitation to form a free electron. (c) The
motion of this free electron in response to an
electric field.
Si Si Si Si
(4+) (4+) (4+) (4+)

(a)
ℰ Field ℰ Field

Si Si Si Si Si Si Si Si
(4+) (4+) (4+) (4+) (4+) (4+) (4+) (4+)

Free electron
Si P Si Si Si P Si Si
(4+) (5+) (4+) (4+) (4+) (5+) (4+) (4+)

Si Si Si Si Si Si Si Si
(4+) (4+) (4+) (4+) (4+) (4+) (4+) (4+)

(b) (c)

p-Type Extrinsic Semiconduction

An opposite effect is produced by the addition to silicon or germanium of trivalent substi-
tutional impurities such as aluminum, boron, and gallium from Group IIIA of the periodic
table. One of the covalent bonds around each of these atoms is deficient in an electron;
such a deficiency may be viewed as a hole that is weakly bound to the impurity atom. This
hole may be liberated from the impurity atom by the transfer of an electron from an ad-
jacent bond, as illustrated in Figure 12.14. In essence, the electron and the hole exchange
positions. A moving hole is considered to be in an excited state and participates in the con-
duction process, in a manner analogous to an excited donor electron, as described earlier.
Extrinsic excitations, in which holes are generated, may also be represented using
the band model. Each impurity atom of this type introduces an energy level within the

Figure 12.13 (a) Electron

Conduction

energy band scheme for a donor

band

impurity level located within the

band gap and just below the Free electron in
bottom of the conduction band. Donor state conduction band
Band gap

(b) Excitation from a donor state

in which a free electron is Eg
Energy

generated in the conduction band.

Valence
band

(a) (b)
 12.11 Extrinsic Semiconduction • 521

ℰ Field

Si Si Si Si Si Si Si Si
(4 +) (4 +) (4 +) (4 +) (4 +) (4 +) (4 +) (4 +)

Si Si B Si Si Si B Si
(4 +) (4 +) (3 +) (4 +) (4 +) (4 +) (3 +) (4 +)

Hole
Si Si Si Si Si Si Si Si
(4 +) (4 +) (4 +) (4 +) (4 +) (4 +) (4 +) (4 +)

(a) (b)
Figure 12.14 Extrinsic p-type semiconduction model (electron bonding). (a) An impurity atom such as boron,
having three valence electrons, may substitute for a silicon atom. This results in a deficiency of one valence electron,
or a hole associated with the impurity atom. (b) The motion of this hole in response to an electric field.

band gap, above yet very close to the top of the valence band (Figure 12.15a). A hole is
imagined to be created in the valence band by the thermal excitation of an electron from
the valence band into this impurity electron state, as demonstrated in Figure 12.15b.
With such a transition, only one carrier is produced—a hole in the valence band; a free
electron is not created in either the impurity level or the conduction band. An impurity
of this type is called an acceptor because it is capable of accepting an electron from the
valence band, leaving behind a hole. It follows that the energy level within the band gap
acceptor state introduced by this type of impurity is called an acceptor state.
For this type of extrinsic conduction, holes are present in much higher concentra-
tions than electrons (i.e., p >> n), and under these circumstances a material is termed
p-type because positively charged particles are primarily responsible for electrical con-
duction. Of course, holes are the majority carriers, and electrons are present in minority
For a p-type concentrations. This gives rise to a predominance of the second term on the right-hand
extrinsic side of Equation 12.13, or
semiconductor,
dependence of σ ≅ p|e|μh (12.17)
conductivity on
concentration and
mobility of holes For p-type semiconductors, the Fermi level is positioned within the band gap and near
to the acceptor level.
Extrinsic semiconductors (both n- and p-type) are produced from materials that
are initially of extremely high purity, commonly having total impurity contents on the

Figure 12.15 (a) Energy band

Conduction

scheme for an acceptor impurity level

band

located within the band gap and just

above the top of the valence band.
(b) Excitation of an electron into the
Band gap

acceptor level, leaving behind a hole

Eg in the valence band.
Energy

Acceptor Hole in
state valence band
Valence
band

(a) (b)
522 • Chapter 12 / Electrical Properties

order of 10–7 at%. Controlled concentrations of specific donors or acceptors are then
intentionally added, using various techniques. Such an alloying process in semiconduct-
doping ing materials is termed doping.
In extrinsic semiconductors, large numbers of charge carriers (either electrons or
holes, depending on the impurity type) are created at room temperature by the available
thermal energy. As a consequence, relatively high room-temperature electrical conduc-
tivities are obtained in extrinsic semiconductors. Most of these materials are designed
for use in electronic devices to be operated at ambient conditions.

Concept Check 12.4 At relatively high temperatures, both donor- and acceptor-doped
semiconducting materials exhibit intrinsic behavior (Section 12.12). On the basis of discussions of
Section 12.5 and this section, make a schematic plot of Fermi energy versus temperature for an
n-type semiconductor up to a temperature at which it becomes intrinsic. Also note on this plot energy
positions corresponding to the top of the valence band and the bottom of the conduction band.
Concept Check 12.5 Will Zn act as a donor or as an acceptor when added to the com-
pound semiconductor GaAs? Why? (Assume that Zn is a substitutional impurity.)
(The answers are available in WileyPLUS.)

12.12 THE TEMPERATURE DEPENDENCE OF CARRIER CONCENTRATION

Figure 12.16 plots the logarithm of the intrinsic carrier concentration ni versus tempera-
ture for both silicon and germanium. A couple of features of this plot are worth noting.
First, the concentrations of electrons and holes increase with temperature because, with
rising temperature, more thermal energy is available to excite electrons from the valence
to the conduction band (per Figure 12.6b). In addition, at all temperatures, carrier con-
centration in Ge is greater than in Si. This effect is due to germanium’s smaller band gap
(0.67 vs. 1.11 eV; Table 12.3); thus, for Ge, at any given temperature more electrons will
be excited across its band gap.
However, the carrier concentration–temperature behavior for an extrinsic semicon-
ductor is much different. For example, electron concentration versus temperature for
silicon that has been doped with 1021 m–3 phosphorus atoms is plotted in Figure 12.17.
[For comparison, the dashed curve shown is for intrinsic Si (taken from Figure 12.16)].7
Noted on the extrinsic curve are three regions. At intermediate temperatures (between
approximately 150 K and 475 K) the material is n-type (inasmuch as P is a donor im-
purity), and electron concentration is constant; this is termed the extrinsic-temperature
region.8 Electrons in the conduction band are excited from the phosphorus donor state
(per Figure 12.13b), and because the electron concentration is approximately equal to
the P content (1021 m–3), virtually all of the phosphorus atoms have been ionized (i.e.,
have donated electrons). Also, intrinsic excitations across the band gap are insignificant
in relation to these extrinsic donor excitations. The range of temperatures over which
this extrinsic region exists depends on impurity concentration; furthermore, most solid-
state devices are designed to operate within this temperature range.
At low temperatures, below about 100 K (Figure 12.17), electron concentration
drops dramatically with decreasing temperature and approaches zero at 0 K. Over these
temperatures, the thermal energy is insufficient to excite electrons from the P donor
7
Note that the shapes of the Si curve of Figure 12.16 and the ni curve of Figure 12.17 are not the same, even though
identical parameters are plotted in both cases. This disparity is due to the scaling of the plot axes: temperature (i.e.,
horizontal) axes for both plots are scaled linearly; however, the carrier concentration axis of Figure 12.16 is logarithmic,
whereas this same axis of Figure 12.17 is linear.
8
For donor-doped semiconductors, this region is sometimes called the saturation region; for acceptor-doped materials,
it is often termed the exhaustion region.
 12.13 Factors That Affect Carrier Mobility • 523

1028

1026
Temperature (°C)
1024 –200 –100 0 100 200 300
Ge 3 × 1021
1022
Si
Intrinsic carrier concentration (m–3)

20
10
Intrinsic

Electron concentration (m–3)

region
18
10
2 × 1021

1016

1014 Freeze-out
region
Extrinsic region
1012 1 × 1021

1010
ni
108

106 0
0 200 400 600 800 1000 1200 1400 1600 1800 0 100 200 300 400 500 600
T (K) Temperature (K)

Figure 12.16 Intrinsic carrier concentration Figure 12.17 Electron concentration versus tempera-
(logarithmic scale) as a function of temperature ture for silicon (n-type) that has been doped with 1021 m–3
for germanium and silicon. of a donor impurity and for intrinsic silicon (dashed line).
(From C. D. Thurmond, “The Standard Thermodynamic Freeze-out, extrinsic, and intrinsic temperature regimes
Functions for the Formation of Electrons and Holes in Ge, Si, are noted on this plot.
GaAs, and GaP,” Journal of the Electrochemical Society, 122, (From S. M. Sze, Semiconductor Devices, Physics and Technology.
[8], 1139 (1975). Reprinted by permission of The Electro- Copyright © 1985 by Bell Telephone Laboratories, Inc. Reprinted
chemical Society, Inc.) by permission of John Wiley & Sons, Inc.)

level into the conduction band. This is termed the freeze-out temperature region inas-
much as charged carriers (i.e., electrons) are “frozen” to the dopant atoms.
Finally, at the high end of the temperature scale of Figure 12.17, electron concentra-
tion increases above the P content and asymptotically approaches the intrinsic curve as
temperature increases. This is termed the intrinsic temperature region because at these
high temperatures the semiconductor becomes intrinsic—that is, charge carrier concen-
trations resulting from electron excitations across the band gap first become equal to
and then completely overwhelm the donor carrier contribution with rising temperature.

Concept Check 12.6 On the basis of Figure 12.17, as dopant level is increased, would
you expect the temperature at which a semiconductor becomes intrinsic to increase, to remain
essentially the same, or to decrease? Why?
(The answer is available in WileyPLUS.)

12.13 FACTORS THAT AFFECT CARRIER MOBILITY

The conductivity (or resistivity) of a semiconducting material, in addition to being de-
pendent on electron and/or hole concentrations, is also a function of the charge carriers’
mobilities (Equation 12.13)—that is, the ease with which electrons and holes are trans-
ported through the crystal. Furthermore, magnitudes of electron and hole mobilities are
influenced by the presence of those same crystalline defects that are responsible for the
scattering of electrons in metals—thermal vibrations (i.e., temperature) and impurity
524 • Chapter 12 / Electrical Properties

Figure 12.18 For silicon, dependence of

room-temperature electron and hole mobilities
(logarithmic scale) on dopant concentration
0.1
(logarithmic scale). Electrons
(Adapted from W. W. Gärtner, “Temperature

Mobility (m2/V.s)
Dependence of Junction Transistor Parameters,”
Proc. of the IRE, 45, 667, 1957. Copyright © 1957 Holes
IRE now IEEE.)
0.01

0.001
1019 1020 1021 1022 1023 1024 1025
Impurity concentration (m–3)

atoms. We now explore the manner in which dopant impurity content and temperature
influence the mobilities of both electrons and holes.
Influence of Dopant Content
Figure 12.18 represents the room-temperature electron and hole mobilities in silicon as
a function of the dopant (both acceptor and donor) content; note that both axes on this
plot are scaled logarithmically. At dopant concentrations less than about 1020 m–3, both
carrier mobilities are at their maximum levels and independent of the doping concentra-
tion. In addition, both mobilities decrease with increasing impurity content. Also worth
noting is that the mobility of electrons is always larger than the mobility of holes.
Influence of Temperature
The temperature dependences of electron and hole mobilities for silicon are presented in
Figures 12.19a and 12.19b, respectively. Curves for several impurity dopant contents are
shown for both carrier types; note that both sets of axes are scaled logarithmically. From
these plots, note that, for dopant concentrations of 1024 m–3 and less, both electron and hole
mobilities decrease in magnitude with rising temperature; again, this effect is due to enhanced
thermal scattering of the carriers. For both electrons and holes and dopant levels less than
1020 m–3, the dependence of mobility on temperature is independent of acceptor/donor
concentration (i.e., is represented by a single curve). Also, for concentrations greater than
1020 m–3, curves in both plots are shifted to progressively lower mobility values with increasing
dopant level. These latter two effects are consistent with the data presented in Figure 12.18.

These previous treatments discussed the influence of temperature and dopant

content on both carrier concentration and carrier mobility. Once values of n, p, 𝜇e, and
𝜇h have been determined for a specific donor/acceptor concentration and at a specified
temperature (using Figures 12.16 through 12.19), computation of σ is possible using
Equation 12.15, 12.16, or 12.17.

Concept Check 12.7 On the basis of the electron-concentration–versus–temperature

curve for n-type silicon shown in Figure 12.17 and the dependence of the logarithm of electron
mobility on temperature (Figure 12.19a), make a schematic plot of logarithm electrical conduc-
tivity versus temperature for silicon that has been doped with 1021 m–3 of a donor impurity. Now,
briefly explain the shape of this curve. Recall that Equation 12.16 expresses the dependence of
conductivity on electron concentration and electron mobility.
(The answer is available in WileyPLUS.)