Chapter -3. Electrical Properties

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ISSUES TO ADDRESS...

• How are electrical conductance and resistance

characterized?

• What are the physical phenomena that distinguish

conductors, semiconductors, and insulators?

• For metals, how is conductivity affected by

imperfections, temperature, and deformation?

• For semiconductors, how is conductivity affected

by impurities (doping) and temperature?

View of an Integrated Circuit

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• Scanning electron micrographs of an IC:

Fig. (d) from Fig. 12.27(a), Callister & Rethwisch 3e.

(Fig. 12.27 is courtesy Nick Gonzales, National Semiconductor Corp., West Jordan, UT.)

Electrical Conduction

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• Ohm's Law:

V = I R

voltage drop (volts = J/C)

C = Coulomb

resistance (Ohms)

current (amps = C/s)

Electrical Properties

• Which will have the greater resistance?

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​

​

​

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• Analogous to flow of water in a pipe
• Resistance depends on sample geometry and size.

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D

2D

2

Definitions

Further definitions

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J = σ ε <= another way to state Ohm’s law

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J ≡ current density

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ε ≡ electric field potential = V/

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Conductivity: Comparison

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• Room temperature values (Ohm-m)^-1 = (Ω - m)^-1

Selected values from Tables 18.1, 18.3, and 18.4, Callister & Rethwisch 8e.

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Silver

6.8 x 10

7

Copper

6.0 x 10

7

Iron

1.0 x 10

7

METALS

conductors

Example: Conductivity Problem

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What is the minimum diameter (D) of the wire so that V < 1.5 V?

Cu wire

I = 2.5 A

-

+

V

Solve to get D > 1.87 mm

Electron Energy Band Structures

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Adapted from Fig. 18.2, Callister & Rethwisch 8e.

Band Structure Representation

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Adapted from Fig. 18.3, Callister & Rethwisch 8e.

Conduction & Electron Transport

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• Metals (Conductors):

-- for metals empty energy states are adjacent to filled states.

-- two types of band � structures for metals

-- thermal energy � excites electrons � into empty higher � energy states.

- partially filled band

- empty band that � overlaps filled band

Energy Band Structures: Insulators & Semiconductors

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• Insulators:

-- wide band gap (> 2 eV)

-- few electrons excited � across band gap

Energy

filled

band

filled

valence

band

filled states

GAP

Metals: Influence of Temperature and Impurities on Resistivity

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• Presence of imperfections increases resistivity

-- grain boundaries

-- dislocations

-- impurity atoms

-- vacancies

These act to scatter

electrons so that they

take a less direct path.

Estimating Conductivity

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Adapted from Fig. 7.16(b), Callister & Rethwisch 8e.

• Question:

-- Estimate the electrical conductivity σ of a Cu-Ni alloy

that has a yield strength of 125 MPa.

Charge Carriers in Insulators and Semiconductors

Two types of electronic charge carriers:

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Free Electron

– negative charge

– in conduction band

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Hole

– positive charge� – vacant electron state in � the valence band

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Adapted from Fig. 18.6(b), Callister & Rethwisch 8e.

Move at different speeds - drift velocities

Intrinsic Semiconductors

• Pure material semiconductors: e.g., silicon & germanium
• Group IVA materials

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• Compound semiconductors
• III-V compounds
• Ex: GaAs & InSb
• II-VI compounds
• Ex: CdS & ZnTe
• The wider the electronegativity difference between � the elements the wider the energy gap.

Intrinsic Semiconduction in Terms of Electron and Hole Migration

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Adapted from Fig. 18.11, Callister & Rethwisch 8e.

electric field

electric field

electric field

Number of Charge Carriers

Intrinsic Conductivity

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Intrinsic Semiconductors: �Conductivity vs T

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• Data for Pure Silicon:

-- σ increases with T

-- opposite to metals

Adapted from Fig. 18.16, Callister & Rethwisch 8e.

material

Si

Ge

GaP

CdS

band gap (eV)

1.11

0.67

2.25

2.40

Selected values from Table 18.3, Callister & Rethwisch 8e.

Intrinsic vs Extrinsic Conduction

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• Intrinsic:

-- case for pure Si

-- # electrons = # holes (n = p)

• Extrinsic:

-- electrical behavior is determined by presence of impurities � that introduce excess electrons or holes

-- n ≠ p

Extrinsic Semiconductors: Conductivity vs. Temperature

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• Data for Doped Silicon:

-- σ increases doping

-- reason: imperfection sites

lower the activation energy to

produce mobile electrons.

• Comparison: intrinsic vs

extrinsic conduction...

-- extrinsic doping level:

10²¹/m³ of a n-type donor

impurity (such as P).

-- for T < 100 K: "freeze-out“,

thermal energy insufficient to

excite electrons.

-- for 150 K < T < 450 K: "extrinsic"

-- for T >> 450 K: "intrinsic"

p-n Rectifying Junction

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• Allows flow of electrons in one direction only (e.g., useful

to convert alternating current to direct current).

• Processing: diffuse P into one side of a B-doped crystal.

-- No applied potential:

no net current flow.

-- Forward bias: carriers

flow through p-type and

n-type regions; holes and

electrons recombine at

p-n junction; current flows.

-- Reverse bias: carriers

flow away from p-n junction;

junction region depleted of � carriers; little current flow.

p-type

n-type

Adapted from Fig. 18.21 Callister & Rethwisch 8e.

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Properties of Rectifying Junction

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Fig. 18.22, Callister & Rethwisch 8e.

Fig. 18.23, Callister & Rethwisch 8e.

Junction Transistor

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Fig. 18.24, Callister & Rethwisch 8e.

MOSFET Transistor �Integrated Circuit Device

• Integrated circuits - state of the art ca. 50 nm line width
• ~ 1,000,000,000 components on chip
• chips formed one layer at a time

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Fig. 18.26, Callister & Rethwisch 8e.

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• MOSFET (metal oxide semiconductor field effect transistor)

Ferroelectric Ceramics

• Experience spontaneous polarization

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Fig. 18.35, Callister & Rethwisch 8e.

BaTiO₃ -- ferroelectric below its Curie temperature (120ºC)

Piezoelectric Materials

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Adapted from Fig. 18.36, Callister & Rethwisch 8e. (Fig. 18.36 from Van Vlack, Lawrence H., Elements of Materials Science and Engineering, 1989, p.482, Adapted by permission of Pearson Education, Inc., Upper Saddle River, New Jersey.)

Piezoelectricity � – application of stress induces voltage

– application of voltage induces dimensional change

Summary

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• Electrical conductivity and resistivity are:

-- material parameters

-- geometry independent

• Conductors, semiconductors, and insulators...

-- differ in range of conductivity values

-- differ in availability of electron excitation states

• For metals, resistivity is increased by

-- increasing temperature

-- addition of imperfections

-- plastic deformation�• For pure semiconductors, conductivity is increased by

-- increasing temperature

-- doping [e.g., adding B to Si (p-type) or P to Si (n-type)]

• Other electrical characteristics

-- ferroelectricity

-- piezoelectricity