Transcript
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
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