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CHAPTER 13CHAPTER 13Properties of MaterialsProperties of Materials

Electrical PropertiesElectrical Properties

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13-I. ELECTRICAL CONDUCTION

A. OHM’S LAW

The ease with which a solid material transmits an electric current IRV (18.1)

V, I, and R: voltage in volts (J/C), current in amperes (C/s), and resistance in ohms (V/A). R is influenced by specimen configuration, resistivity is independent of specimen geometry

(18.2)

F18.1

/AR,R

RA

3

: ohm-meters (-m)

(18.3)

B. ELECTRICAL CONDUCTIVITY

1

(18.4)

Capability of conductiong an eletric current,

: [(-m)-1 , or mho/m], Ohm’s law may be expressed as J (18.5

)

1I IVVA A

I

VA

4

J: current density, the current per unit cross sectional area of specimen i.e., I/A,

ε: electric field intensity, or the voltage difference between two points divided by the distance

V

(18.6)

※ Conductors, semiconductors, and insulators

Conductors: e.g., metals, σ = ~ 107 (-m) –

1

Insulators: 10-20 (-m)-1

Semiconductors: 10-6 to 104 (-m)C. ELECTRONIC AND IONIC CONDUCTION

electronic conduction: electrons,

Ionic conduction: ions

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D. ENGERY BAND STRUCTRUES IN SOLIDS

D-1.Atomic Structure (single atoms)

◎ Shells: designated by integers (principle quantum number,I.e., 1,2,3, etc), subshells: by letters (s,p,d, and f)

◎ Each of s, p, d, and f subshells: one, three, five, and seven states

◎ Two electrons of opposite spin per state: Pauli exclusion principle

f2.2 T2.1 F2.2 F2.4 F2.3 T2.2

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D-2. Molecules and Solid Materials

◎ As the atoms come within close proximity of one another, electrons are acted upon, or perturbed, by the electrons and nuclei of adjacent atoms. Each distinct atomic state may split into a series of closely spaced electron states: electron energy band.

◎ At the equilibrium spacing , band formation may not occur for the electron subshells nearest the nucleus.

◎ The number of states within each band will equal the total of all states contributed by the N atoms. For example, an s band will consist of N states, and a p band of 3N states. Each energy state may accommodate two electrons, which must have oppositely directed spins.

F18.2 F18.3

f2.11

7

◎ The electrical properties are a consequence of its electron band structure: the arrangement of the

outermost electron bands and the way in which they are filled with electrons.( Eletrical conduction occurs only when there are available positions(empty states or holes) for electrons to

move.)

◎ Four different types of band structures are possible at 0 k:

• The first : partially filled(valence)band: conductor (Eg=0, i.e., no band gap), e.g., copper, one 4s electron(per atom), only half the available electorn positions within this 4S band are filled.

◎ For Solid ：

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• The second: overlap of an empty (conduction) band and a filled (valence) band: conductor (Eg=0, i.e., no band gap), e.g.,Mg, the 3s and 3p bands overlap.

• The final two: valence band (completely filled ) is separated from conduction band (empty) by a energy band gap. For materials that the band gap is relatively wide (Eg>3eV,Figure 18.4c): insulations; for Eg=0.02-3eV: semiconductors

(Figure 18.4d)

◎ The energy corresponding to the highest filled state at 0 k is called the Fermi energy Ef .

F18.4 t2.6f2.12 t2.7 Eg

9

Only electrons with energies greater than the Fermi energy may be acted on and accelerated in the presence of an electric field. These are the electrons that participate in the conduction process: free electrons. Another charged electronic entity: hole found in semiconductors

and insulators. Holes have energies less than Ef

and also participate in electronic conduction.

Distinction between conductors and nonconductors (insulators and semiconductors): numbers of these free electron and hole charge carriers.

E. CONDUCTION IN TERMS OF

BAND AND ATOMIC BONDING MODELS

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E-1. METALS

For an electron to become free, it must be excited or promoted into one of the empty and

available energy states above Ef (Figures 18.4a

and 18.4b). Generally, the energy provided by an electric field is sufficient to excite large numbers of electrons into these conducting states.( also thermal energy at room temperature)

For the metallic bonding model discussed in Section 2.6, although the valence electrons are not locally bound to any particular atom, they must experience some excitation to become conducting electrons that are truly free.

F18.4 F18.5 F2.11

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E-2. INSULATORS AND SEMICONDUCTORS

To become free, electrons must be promoted across the energy band gap and into empty states of the conduction band. This is possible only by supplying energy approximately equal to the band gap energy Eg. For many materials this band gap is several electron volts wide. Most often the excitation energy is from a nonelectrical source such as heat or light, usually the former.

The number of electrons excited thermally (by heat energy) into the conduction band depends on the energy band gap width as well as temperature.

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Distinction between semiconductors and insulators lies in the width of the band gap; semiconductors: narrow(0.03-3eV); insulating materials: wide(>3eV)

For electrically insulating materials, interatomic bonding is ionic or strongly covalent (Section 2.6).The bonding in semiconductors is covalent (or predominantly covalent) and relatively weak.F2.9 F2.10 F18.6

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F. ELECTRON MOBILTTY

According to quantum mechanics, there is no interaction between an accelerating electron and atoms in a perfect crystal lattice: as long as the electric field is applied, an electric current is continuously increasing with time. In fact, a current reaches a constant value the instant the a field is applied: there exist frictional forces, frictional forces: scattering of electrons by imperfections including impurity atoms, vacancies, interstitial atoms, dislocations, and even the thermal vibrations of the atoms themselves.

electric current: net electron motion

F18.7

14

Extent of this scattering: drift velocity and the mobility of an electron

Drift velocity, vd : average electron velocity in the direction of the force imposed by the applied field, ε

ed (18.7)

e: electron mobility

The conductivity of most materials:

(18.8)

/de

e

v

en

n: number of free or conducting electrons per unit volume

e : absolute magnitude of the electrical charge on an electron (1.6×10-19 C)

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G. ELECTRICAL RESISTIVITY OF MTALS

Most metals are extremely good conductors: because of the large numbers of free electrons that have been excited into empty states above the Fermi energy (n has a large value)Crystalline defects serve as scattering centers for conduction electrons it has been observed experimentally that the total resistivity total of a metal is the sum of the cotributions from thermal vibrations t impurities i, and platic deformation (d, cold work): ( scattering mechanisms act independently)

dittotal (18.9)Matthiessen’s rule

T8-1

1

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INFLUENCE OF TEMPERATUREaTt 0 (18.10

)

0 and a : constants

Dependence of the thermal resistivity on temperature: thermal vibrations( 熱振動 ) and other lattice irregularities ( 晶格不規整 , 即缺陷 ,e.g., vacancies) increase with temperature , which serve as electron-scattering centers.

F18.8

17

4.4 The equilibrium number of vacancies 4.4 The equilibrium number of vacancies NNvv

kT

QNN

vv exp

N is the total number of atomic sites, Qv is the energy required for the formation of a vacancy.T is the absolute temperature in kelvins, and k is the gas or Boltzmann’s constant. The value of k is 1.38 10-23 J/atom-K, or 8.6210-5 eV/atom-K.

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INFLUENCE OF IMPURITIES

For a solid solution

)1( iii cAc (18.11)A: composition-independent constant, ci: impurity

concentration

electrons are scattered by impurities.

Ci < 0.5 ： i is the minor phase

Ci > 0.5 ： i is the major phase

F18.8 F18.9

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For a two-phase alloy consisting of and phases

VVi (18.12)

V’s and ’s : volume fractions and individual resistivities

INELUENCE OF PLASTIC DEFORMATION

Electron-scattering by dislocations (which are increased in concentration due to deformation)

F18.8

F7.17

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H. ELECTRICAL CHARACTERISTICS OF

COMMERCIAL ALLOYS

Solid solution alloying (Section 7.9) and cold working (Section 7.10): improve strength at the expense of conductivity (due to increases in impurity and dislocation concentrations), a trade off must be made.

For some applications, such as furnace heating elements, a high electrical resistivity is desirable, an alloy instead of pure metal is used: e.g., a nickel-chromium alloy (Nichrome) is used as heating elements.

F7.14 F7.17

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SEMICONDUCTIVITY

The electrical properties of these materials are extremely sensitive to temperature( Intrinsic) or the presence of even minute concentrations of impurities( extrinsic).

I. INTRINSIC SEMICONDUCTION

Figure 18.4d: at 0K: a completely filled valence band, empty conduction band and relatively narrow band gap (<2 eV.) two elemental semiconductors: silicon (Si) germanium (Ge) 1.1 and 0.7 EV

T8-2

F18.4

22

Compound semiconducting materials: between elements of Groups IIIA and VA, e.g., gallium arsenide (GaAs) and indium antimonide (InSb); (III-V compounds). Groups IIB and VIA, e.g., 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 electrongegativities become more dissimilar, Figure 2.7). The atomic bonding becomes more ionic and the magnitude of the band gap energy increases-the materials tend to become more insulative.

F2.7

23

Treating a missing electron as a positively charged particle called a hole ( 電洞 ). 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× 10-18 C). In the presence of an electric field, excited electrons and holes are scattered by lattice imperfections.

CONCEPT OF A HOLE

F18.10

f18.6

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INTRINSIC CONDUCTIVITY

Two types of charge carrier: free electrons( 自由電子 ) and holes( 電洞 ).

he epen (18.13)

P: number of holes per cubic meter, h: hole mobility; h is always less than e for semiconductors. For intrinsic semiconductors, n = p =

ni

(18.14)

)( heep )( hei en (18.1

5)

ni: intrinsic carrier concentration

T18.2

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J. EXTRINSIC SEMICONDUCTION

Electrical behavior is determined by impurites( in even minute concentrations): introduce excess electrons or holes

n-TYPE EXTRINSIC SEMICONDUCTION

Consider the elemental semiconductor silicon. An impurity atom with a valence of 5 is added as a substitutional impurity( Group VA, e.g., P, As, and Sb): The extra nonbonding electron is loosely bound by a weak electrostatic attraction, binding energy: on the order of 0.01 eV.

F18.11

F18.12

26

For each of the loosely bound electrons, its energy level, or energy state, is located within the forbidden band gap, just below the bottom of the conduction band. The electron binding energy corresponds to the energy required to excite the electron to the conduction band.

Each excitation event supplies or donates a single electron to the conduction band: an impurity of this type is termed a donor. No hole is created within the valence band.

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At room temperature, the thermal energy available is sufficient to excite large numbers of electrons from donor states; intrinsic valence -conduction band transitions is negligible, number of electrons in the conduction band far exceeds the number of holes in the valence band (or n >> p)

een (18.16)

A material of this type is said to be an n-type extrinsic semiconductor. Electrons: majority carriers; holes: minority charge carriers. For n-type semiconductors, the Fermi level is shifted upward to within the vicinity of the donor state.

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P-TYPE EXTRINSIC SEMICONDUCTION

addition to silicon or germanium of trivalent substitiutional impurities, e.g., aluminum, boron, and gallium from Group IIIA, each of these atoms is deficient( 欠缺 )in an electron: a hole that is weakly bound to the impurity atom. The electron and the hole exchange positions.

Each impurity atom of this type introduces an energy level within the band gap(acceptor state.), above yet very close to the top of the valence band (Figure 18.14a).

F18.13

F18.14

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A hole is imagined to be created in the valence band by the thermal excitation of an electron: one carrier is produced- a hole in the valence band.

An impurity of this type is called an acceptor because it is capable of accepting an electron from the valence band

For this type of extrinsic conduction p>>n, holes: majority carriers, electrons: minority concentrations hep

(18.17)

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The Fermi level is politioned 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 order of 10-7 at ％ .Donors or acceptors are then intentionally added: doping. In extrinsic semiconductiors, large numbers of charge carriesr either electrons or holes, are created at room temperature, electronic devices are to be operated at ambient conditions

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K. THE TEMPERATURE DEPENDENCE OF CARRIER CONCENTRATION

Intrinsic carrier concentration (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.

F18.15

)/exp( RTEgP )/exp( RTEgn

P n Eg T

－

－

“ －”： remains cm changedCarrier concentration in Ge is greater than for Si due to

germanium’s smaller band gap (0.67 versus 1.11 eV, Table 18.2).

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For an extrinsic semiconductor. For example, electron concentration versus temperature for silicon that has been doped with 1021 m-3

phosphorus atoms (Figure 18.16), three regions: At intermediate temperatures (between approximately 150kand 450k) electron concentration is constant: “extrinsic-temperature region” the electron concentration is approximately equal to the P content (1021 m-3); at low temperatures, (below about 100k), the thermal energy is insufficient to excite electrons from the P donor level into the conduction band: “freeze-out temperature region” ; at high temperature “intrinsic temperature region” the semiconductor becomes intrinsic.

F18.16F18.6 F18.12 F18.14

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L. FACTORS THAT AFFECT CARRIER MOBILITY

Electron and hole mobilities are affected by: crystalline defects (same are responsible for the scattering electrons in metals): thermal vibrations (i.e., temperature) and impurity atoms.INFLUENCE OF DOPANT CONTENT

At dopant concentrations less than about 1020 m -3, both carrier mobilities are at their maximum levels and independent of the doping concentration. Both mobilities decrease with increasing impurity content. The mobility of electrons is always larger than the mobility of holes.

F18.17

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INFLUENCE OF TEMPERATURE

For dopant concentrations of 1024 m-3 and below, both electron and hole mobilities decrease in magnitude with rising temperature. For both electrons and holes, and dopant levels less than 1020 m -3, mobility is independent of acceptor/donor concentration

When dopant conc. 1024m-3, both dopant conc. and temp effect are evident (important).

When dopant conc, > 1024m-3, dopant conc. effect is evident (important), but temp effect is not.

F18.18

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M. SEMICONDUCTOR DEVICES

Two familiar examples: diodes( 二極體 ) and transistors ( 電晶體 , replaced old-fashioned vacuum tubes). Advantages of semiconductor devices (sometimes termed solid-state devices): small size, low power consumption, and no warmup time.

THE p-n RECTIFYING JUNCTION

F18.19

F18.20

F18.21

A rectifier( 整流器 ), or diode: allows the current to flow in one direction only; e.g., transforms an alternating current into direct current. Before, vacuum tube diode.

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Forward bias: Large numbers of charge carriers flow across the semiconductor as evidenced by an appreciable current and a low resistivity.

Electron + hole

Reverse bias: The junction region is relatively free of mobile charge carriers, the junction is highly insulative.

At high reverse bias voltages, order of several hundred volts, large numbers of charge carriers (electrons and holes) are generated. A very abrupt increase in current: breakdown.

energy

(18.18)

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THE TRANSISTOR Two primary types of function: First, the triode( 三極體 ): amplify an electrical signal; Second, serve as switching devices in computers for the processing and storage of information. Two major types:junction (or bimodal) transistor and metal-oxide-semiconductor field-effect transistor MOSFET)

JUNCTION TRANSISTORS

A very thin n-type base region is sandwiched in between p-type emitter and collector regions. The emitter is p-type and junction 1 is forward biased, large numbers of holes enter the base region.

F18.22 F18.23

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A small increase in input voltage within the emitter-base circuit produces a large increase in current across junction 2. Thus, a voltage signal that passes through a junction transistor experiences amplification.

Similar reasoning, n-p-n transistor: electrons instead of holes are injected across the base and into the collector

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The MOSFETOne variety of MOSFET: two small islands of p-type semiconductor that are created within a substrate of n-type silicon. Appropriate metal connections (source and drain) are made to these islands; an insulating layer of silicon dioxide is formed by the surface oxidation of the silicon. A final connector (gate) is then fashioned onto the surface of this insulating layer. A positive field on the gate will drive charge carriers (in this case holes) out of the channel, thereby reducing the electrical conductivity. Thus, a small alteration in the field (negative) at the gate will produce a relatively large variation in current between the source and the drain.

F18.24

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Semiconductors in ComputersTransistors and diodes may also act as switching de

vices: for arithmetic and logical operation and for information storage. Computer numbers and functions are expressed in terms of a binary code (desinated 0 and 1) transistors and diodes also have two states-on and off, (or conducting and nonconducting)

The process begins with the growth of relatively large cylindrical single crystals of high-purity silicon from which thin circular wafers( 晶圓 ) are cut.

MICROELECTRONIC CIRCUITRYF18.25

41

A chip( 晶片 ) is rectangular, typically on the order of 6 m

m (¼ in.) on a side and contains thousands of circuit ele

ments: diodes, transistors, resistors, and capacitors.

At this time, microprocessor chips containing 500 million transistors are being produced, and this number doubles about every 18 months. Microelectronic circuits consist of many layers. Using photolithographic techniques( 微影技術 ). Circuit elements are constructed by the selective introduction of specific materials (by diffusion( 擴散 ) or ion implantation( 離子佈植 )) into unmasked regions to create localized n-type, p-type, high-resistivity, or conductive areas.

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ELECTRICAL CONDUCTION IN IONIC CERAMICS AND IN POLYMERS

Most polymers and ionic ceramics are insulating materials at room temperature: (Figure 18.4c) a filled valence band is separated from an empty conduction band with a band gap greater than 2 eV.

N. CONDUCTION IN INOIC MATERIALSBoth cations and anions are capable of migration or diffusion when an electric field is present. The total conductivity of an ionic material total is thus equal to the sum of both electronic and ionic contributions.

ionicelectronictotal (18.19)

F18.4 T2.6 T18.3 T18.1

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Mobility I

kT

eDn III (18.20)

nI and DI : valence and diffusion coefficeient of particular ion; the ionic contribution to the total conductivity increases with increasing temperature. However most ionic materials remain insulative, even at elevated temperatures.Except those doped with small ions.

18.17 ELECTRICAL PROPERTIES OF POLYMERS

Most polymeric materials are poor conductors of electricity (unavailability of free electrons)

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CONDUCTING POLYMERS

Conductivities as high as 1.5×107 (-m) -1 have been achieved in these materials; (on a volume basis, one-fourth of the conductivity of copper, or twice its conductivity on the basis of weight) e.g., polyacetylene, polyparaphenylene, polypyrrole, and polyaniline that have been doped with appropriate impurities. As is the case with semiconductors, these polymers may be made either n-type (i.e., free-electron dominant) or p-type (i.e., hole dominant) depending on the dopant. However, unlike semiconductors, the dopant atoms or molecules do not subsitute for or replace any of the polymer atoms.

45

High purity polymers have electron band structures characteristic of electrical insulators. The mechanism by which large numbers of free electrons and holes are generated in these conducting polymers is complex and not well understood. It appears that the dopant atoms lead to the formation of new energy bands that overlap the valence and conduction bands of the intrinsic polymer, giving rise to a partially filled band, and the production at room temperature of a high concentration of free electrons or holes.

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Applications (low densities, highly flexible( 可彎曲 ), easy to produce): rechargeable batteries( 可充電式電池 ): employ polymer electrodes( 高分子電極 ); wiring in aircraft and aerospace components, antistatic coatings( 防靜電塗料 ) for clothing, electromagnetic screening materials( 電磁波遮蔽材料 ), electronic devices (e.g., transistors and diodes).

Orienting the polymer chains, either mechanically (Section 15.7) or magnetically, during synthesis results in a highly anisotropic material having a maximum conductivity along the direction of orientation.

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OTHER ELECTRICAL CHARACTERISTICS OF MATERIALS

O. FERROFLECTRICITYThe group of dielectric materials: ferroelectrics, exhibit spontaneous polarization-that is, polarization in the absence of an electric field. Permanent electric dipoles,e.g., barium

titanate(BaTiO3): one of the most common

ferroelectrics Ba2+ ions are located at the corners of the unit cell, which is of tetragonal symmetry (a cube that has been elongated slightly in one direction). The dipole moment results from the relative displacements of the O2- and Ti4+ ions from their symmetrical positions

F18.26

48

A permanent ionic dipole moment is associated with each unit cell. When barium titanate is heated above its ferroelectric Curie temperature [120℃ (250℉)], the unit cell becomes cubic, and all ions assume symmetric positions.

The material now has a perovskite crystal structure (Section 12.2), and the ferroelectric behavior ceases. The telative displacements of O2- and Ti4+ ions are in the same direction for all the unit cells within some volume region of these specimen.

49

Other materials display ferroelectricity: Rochelle s

alt (NaKC4H4O6.4H2O), potassium dihydrogen p

hosphate (KH2PO4), potassium niobate (KNbO3),

and lead zirconate-titanate (pb[ZrO3, TiO3]). Ferr

oelectrics have extremely high dielectric constant

s, capacitors made from these materials can be si

gnificantly smaller than capacitors made from oth

er dielectric materials. f11.3-1

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P. PIEZOELECTRICITY

Piezoelectric materials( 壓電材料 ) are utilized in transducers, which are devices that convert electrical energy into mechanical strains, or vice versa. Applications phonograph cartridges, microphones, speakers( 擴音器 ), audible alarms and ultrasonic imaging( 超音波顯影 ).

F18.27 f13.43

+Z -Z d

Strength of dipole Z and d

51

Piezoelectric materials: titanates of barium and lead, lead zirconate (pbZrO3), ammonium dihydrogen phosphate (NH4H2PO4), and quartz. (crystal structures with a low degree of symmetry). The pizeoelectric behavior of a polycrystalline specimen may be improved by heating above its Curie temperature and then cooling to room temperature in a strong electric field.

100

Energy states of

individual atoms

a precise level

Energy band of

solid (particle)

a band with a width

Interaction

Interaction Energy band widthbandgap

Valence electrons at a more outer shell doping of impurity others

higher extent Of

interaction

smaller band gap