Download - Lecture 14
![Page 1: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/1.jpg)
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
![Page 2: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/2.jpg)
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
![Page 3: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/3.jpg)
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
![Page 4: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/4.jpg)
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
![Page 5: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/5.jpg)
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
![Page 6: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/6.jpg)
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.
![Page 7: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/7.jpg)
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.
![Page 8: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/8.jpg)
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)
![Page 9: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/9.jpg)
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)
![Page 10: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/10.jpg)
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
![Page 11: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/11.jpg)
Figure 18.8: Effects of temperature, impurities,and deformation on resistivity of copper
![Page 12: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/12.jpg)
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)
![Page 13: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/13.jpg)
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
![Page 14: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/14.jpg)
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)
![Page 15: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/15.jpg)
Example: 4 Na atoms
3sbandenergy
applied voltage excites electrons from lowerenergy states to higher energy states(these act as charge carriers)
![Page 16: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/16.jpg)
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
![Page 17: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/17.jpg)
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)
![Page 18: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/18.jpg)
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
![Page 19: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/19.jpg)
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
![Page 20: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/20.jpg)
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
![Page 21: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/21.jpg)
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)
![Page 22: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/22.jpg)
What helps e- jump energy gap?
electric field (voltage)electromagnetic radiationheatmagnetic fields
![Page 23: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/23.jpg)
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
![Page 24: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/24.jpg)
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
![Page 25: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/25.jpg)
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
![Page 26: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/26.jpg)
Extrinsic n-type semiconductor model (Figure 18.12)
![Page 27: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/27.jpg)
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
![Page 28: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/28.jpg)
Extrinsic p-type semiconductor model (Figure 18.14)
![Page 29: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/29.jpg)
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?
![Page 30: Lecture 14](https://reader033.vdocument.in/reader033/viewer/2022061122/54703ff8b4af9fa4038b464b/html5/thumbnails/30.jpg)
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