Lecture 14

Chapter 18: Electrical Properties

Mechanical properties - strength, hardness, ductility - depend on atomic movements (ex. dislocations)

Electrical properties - depend of movement of small charged particles (electrons, ions)

in the atomic structure

Conduction and Carriers

Ohm’s Law V = IR

where V = voltage (volts, V)

I = current (amps, A)

R = resistance (Ohms, )depends on material,size of material

Resistivity- independent of material geometry- constant at particular temperature

- measures the resistance a particular material has to current flow

= R A (-m) l

where R = resistance A = cross-sectional area of conductor (ex. wire) l = length across which voltage is measured

Conductivity- measures ease at which current flows through a material

= 1 = l (-m)-1

RA

~ 107 metals ~ 10-15 ceramics (insulators) ~ 10-6 - 104 semiconductors

Conductivity depends on:

number of charge carriers (n) charge per carrier (e) mobility of each carrier ()

mobility is affected by crystal defects andthermal vibrations (anything that scatterselectrons)

= n e

Example18.1 (a) Compute the electrical conductivity of a 7.0 mm diameter cylindrical silicon specimen 57 mm long in which a current of 0.25 A passes in an axial direction. A voltage of 24 V is measured across two probes that areseparated by 45 mm.(b) Compute the resistance over the entire 57 mm of the specimen.

Example18.11 At room temperature the electrical conductivity and the electron mobility for aluminum are 3.8 x 107 (-m)-1 and 0.0012 m2/Vs, respectively.(a) Compute the number of free electrons per cubic meter for aluminum at room temperature.(b) What is the number of free electrons per aluminum atom?Assume a density of 2.7 g/cm3.

Factors affecting resistivity of metals:

total = t + i + d

1. temperature

metals: ( ) as T

t = 0 + aT where 0, a = constants T = temperature

higher T increases number of collisions between conduction electrons and atoms (decreases )

ceramics and semiconductors: ( ) as T(thermally activated)

2. chemical composition- solid solution alloying increases (decreases )

distortion in the lattice impedes mobilityof charge carriers

single phase

wt% B0 100

Tm (B)

Tm (A)L

+ L

wt% B0 100

A

B

complete solid solubility

A = composition-independent constant that is a function of host and impurity atomsci = impurity concentration

i = Aci(1-ci)

multiphase

V = volume fraction

rule of mixtures

3. deformation (d)- plastic deformation (cold working) increases resistivity because dislocations aid in electron scattering (decreases )

( ) as %CW

i = V+ V

Figure 18.8: Effects of temperature, impurities,and deformation on resistivity of copper

Types of carriers

1. electron (e = 1.602 x 10-19 C)

2. electron hole - electron jumps from ion to ion, leaving behind a hole

(e = 1.602 x 10-19 C)

3. positive and negative ions- ion jumps from one lattice position to another, made possible by vacancies (e = n x 1.602 x10-19 C, where n = valence)

Conduction in metals

metallic bonds - free electrons wander throughout material

an applied voltage causes electrons to move in direction opposite direction of electric field

electric current flows

Band model - used for determining electrical properties - based on quantum mechanics

Consider Na (Z = 11)

single atom

1s2

2s2

2p6

3s1

energy

single energy level

group of atoms

1s2

2s2

2p6

3s

energy

band of energy levelsof 3s electrons(each energy level iscalled a state)

Example: 4 Na atoms

3sbandenergy

applied voltage excites electrons from lowerenergy states to higher energy states(these act as charge carriers)

Electron Energy Band Structure (Fig. 18.3)

• Valence band – filled – highest occupied energy levels• Conduction band – empty – lowest unoccupied energy levels

valence band

Conduction band

Conventional electron band structure representation

energy

filled states

empty states

band gap

empty band

Efvalence band

Ef - Fermi energy - energy level of highest filled state - only electrons with energy above Ef

participate in conduction

Metal with partially filledvalence band (ex. Cu, Ag,Au all good conductors)

Conduction in insulators (ex. ceramics)

- insulators have full valence band, so e- must be excited to conduction band

energy

filled valenceband

empty conduction

band

band gap Eg

Eg = energy gap between valence and conduction bands

need to supply energy of ~Eg to excite electronfrom valence band to conduction band (where itcan act as a charge carrier)

Eg ~ 6-7 eV

(energy ~ kT) - thermally activated

Ionic materials also have ionic conduction

total = ionic + electronic

temperature dependence i = ni e Di

kT

where i = mobility of ionDi = diffusion coefficient of ion (dependent on T)ni = valence of ion

ionic as T

Conduction in semiconductors

Group IV Si, GeIII - V GaAs, AlPII-VI CdS, ZnTe

Electron band structure:

energy

filled valenceband

empty conduction

band

band gap Eg ~ 1 eV(much smaller than Eg ofinsulators)

What helps e- jump energy gap?

electric field (voltage)electromagnetic radiationheatmagnetic fields

Intrinsic semiconductors

- only valence band and conduction band are involved in charge transport- each electron that jumps to the conduction band leaves an electron hole in the valence band

= n e e + p e h

e = mobility of electronsh = mobility of holesn = # of electrons/m3

p = # of holes/m3

n = p

Extrinsic semiconductors

- conduction characteristics due to controlled presence of impurity atoms (doping)

0.0001 to 0.01 wt% impurities (1 to 100 ppm)

2 types:

1. n-type (negatively charged carriers)

- addition of Group V elements (P, As, Sb) to Si or Ge

ex. P in Si

Si 4 e-

P 5 e-

- only 4 of the 5 e- in P participate in bonding- 5th valence e- can be easily excited to conduction band (no hole is produced)

impurity atom in n-type is called a donor (donates e-

to conduction band)

dominates, n > p

= n e e + p e h

Extrinsic n-type semiconductor model (Figure 18.12)

2. p-type (positively charged carriers)

- addition of group III elements (B, Al) to Si or Ge

ex. B in Si

Si 4 e-

B 3 e-

- one bond deficient in e-, so hole is formed

impurity atom in p-type is called an acceptor (accepts e-)

dominates, p > n

= n e e + p e h

Extrinsic p-type semiconductor model (Figure 18.14)

Example18.29 (a) The room temperature electrical conductivity of a silicon specimen is 500 (-m)-1. The hole concentration is known to be 2.0 x 1022 m-3. Using the electron and hole mobilities for silicon in table 18.3, compute the electron concentration. (b) On the basis of the result in part (a), is the specimen intrinsic,n-type extrinsic, or p-type extrinsic? Why?

Example18.31 The following electrical characteristics have been determined for both intrinsic and p-type extrinsic gallium antimonide (GaSb) at room temperature. Calculate the electron and hole mobilities.

  (-m)-1 n (m-3) p (m-3)Intrinsic 8.9 x 104 8.7 x 1023 8.7 x 1023

Extrinsic(p-type) 2.3 x 105 7.6 x 1022 1.0 x 1025