Electrical properties • • • • • • • •

ELECTRICAL CONDUCTION ENERGY BAND STRUCTURE IN SOLIDS INSULATORS AND SEMICONDUCTORS METALS: ELECTRON MOBILITY INFLUENCE OF TEMPERATURE INFLUENCE OF IMPURITY SEMICONDUCTORS P-N RECTIFYING JUNCTION

M Medraj / PM Wood-Adams

Mech. Eng. Dept. - Concordia University

MECH 221 fall 2008/1

ELECTRICAL CONDUCTION A

• Ohm's Law:

e-

(cross sect. area)

R depends on specimen geometry

I ΔV L

ΔV = I R voltage drop (volts)

resistance (Ohms) current (amps)

• Resistivity, ρ and Conductivity, σ: Æ geometry-independent forms of Ohm's Law E: electric field intensity

• Resistance: M Medraj / PM Wood-Adams

ΔV I = ρ L A

resistivity (Ohm-m) J: current density

Conductivity:

I σ= ρ

ρL L = R= A Aσ Mech. Eng. Dept. - Concordia University

MECH 221 fall 2008/2

CONDUCTIVITY: COMPARISON • solid materials exhibit a very wide range of electrical conductivity – widest range compared to other phys. properties. Æ Materials can be classified according to their electrical conductivity.

Conductivity values (Ohm-m)-1 at room temp. METALS Silver Copper Iron

conductors 6.8 x 107 6.0 x 107 1.0 x 107

CERAMICS Soda-lime glass 10-10 Concrete 10-9 Aluminum oxide > p)

• P-type Extrinsic: (p >> n) Boron atom

Phosphorus atom

4+ 4+ 4+ 4+

4+ 5+ 4+ 4+

hole conduction electron

4+ 4+ 4+ 4+

valence electron

4+ 4+ 4+ 4+

4+ 4+ 4+ 4+

no applied electric field

Si atom

σ ≈ n e μe M Medraj / PM Wood-Adams

4+ 3+ 4+ 4+

no applied electric field

σ ≈ p e μh Mech. Eng. Dept. - Concordia University

MECH 221 fall 2008/14

INTRINSIC VS EXTRINSIC CONDUCTION Donor impurities → n-type (negative) conductivity: by electrons

(a) Donor impurity energy level located just below the bottom of the conduction band. (b) Excitation from a donor state in which a free electron is generated in the conduction band.

Acceptor impurities → p-type (positive) conductivity: by holes

(a) Acceptor impurity level just above the top of the valence band. (b) Excitation of an electron into the acceptor level, leaving behind a hole in the valence band.

‰ Can control concentration of donors/acceptors ⇒ concentration of charge

•

carriers ⇒ control conductivity Materials with desired conductivities can be manufactured

M Medraj / PM Wood-Adams

Mech. Eng. Dept. - Concordia University

MECH 221 fall 2008/15

Semiconductors: Summary ƒ Intrinsic conductivity (pure materials): electronhole pairs • Conductivity: Si 4×10-4 (Ωm)-1 vs. Fe 1×107 (Ωm)-1 • Electron has to overcome the energy gap Eg Intrinsic conductivity strongly depends on temperature and as-present impurities • Extrinsic Conductivity • Doping: substituting a Si atom in the lattice by an impurity atom (dopant) that has one extra or one fewer valence electrons • Donor impurities have one extra electron (group V: P, As, Sb), donate an electron to Si. • Acceptor impurities have one fewer electrons (group III: B, Al, In, Ga), accept electrons from Si which creates holes. M Medraj / PM Wood-Adams

Mech. Eng. Dept. - Concordia University

MECH 221 fall 2008/16

electrical conductivity, σ (Ohm-m)-1

104 103 102

0.0052at%B

1

intrinsic

2

extrinsic

3

0 0

200 400 600 T(K)

Adapted from Fig. 18.16, Callister 6e.

• Intrinsic vs Extrinsic conduction:

doped 0.0013at%B

- extrinsic doping level:

101 100 10-1

doped undoped freeze-out

• Doped Silicon: - Dopant concentration ↑ - σ ↑ - Reason: imperfection sites lower the activation energy to produce mobile electrons.

conduction electron concentration (1021/m3)

CONDUCTIVITY VS T FOR EXTRINSIC SEMICOND.

pure (undoped)

10-2 50 100

Adapted from Fig. 19.15, Callister 5e.

M Medraj / PM Wood-Adams

1000 T(K)

1021/m3 of a n-type donor impurity (such as P). freeze-out - for T < 100K: “………….." thermal energy insufficient to excite electrons. extrinsic - for 150K < T < 450K: “…………" intrinsic - for T >> 450K: “…………."

Mech. Eng. Dept. - Concordia University

MECH 221 fall 2008/17

SUMMARY • Electrical resistance is: - a geometry and material dependent parameter. • Electrical conductivity and resistivity are: - material parameters and geometry independent.

• Conductors, semiconductors, and insulators... - different in whether there are accessible energy states for electrons.

• For metals, conductivity is increased by - reducing deformation - reducing imperfections - decreasing temperature.

• For pure semiconductors, conductivity is increased by - increasing temperature - doping (e.g., adding B to Si (p-type) or P to Si (n-type). M Medraj / PM Wood-Adams

Mech. Eng. Dept. - Concordia University

MECH 221 fall 2008/18