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Unformatted text preview: Week 8: Where Are We?
By now we should all know:
What holds atoms together in groups (bonding)
How atoms can group and form different structures
Key differences between structures of metals, ceramics
& polymers
The nature of imperfections (defects) in materials
How atoms can move (diffusion)
How materials interact with their environment
(corrosion & degradation) Next we will discuss:
Some important properties of different materials:
Electrical (3)
Magnetic (1.5)
Optical (1.5)
Web chapters will be posted (PDF) on BbVista
Chapter 18  1 Week 8: Where Are We?
Scores and Grades:
Completed 4 of 5/6 Quizzes
Completed inclass project (Wk 3)
Completed 2 x midterms (Wks 6 and 8):
Midterm 2 Average = TBD
HI = ??, LO = ??
These account for 250 out of 350 total points for course
Max score possible to date = 58.33 % (D)
Still to be Done:
1 Quiz (Week 9)
+ Attendance (= 1 Quiz)
Final Exam (35 % weighting)
Note: Monday, 5/31 is a holiday…no lectures!
Chapter 18  2 Chapter 18: Electrical Properties
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 Temp.? Chapter 18  3 ANNOUNCEMENTS
Reading:
Chapter 18: Sections 18.118.13 Week 8 Recitations:
Problems: 18.1, 18.7, 18.9, 18.12, 18.17, 18.19, 18.27,
18.29, 18.31, 18.D1
No Quiz – Midterm 2 this week Midterm 2:
Tuesday, May 18, 8:008:50 am, Main Auditorium
Accommodations: LeBow 348; 8:009:15 (1.5X) or
8:009:40 am (2X)
Chapters 12, 14, 17 + sprinkling of earlier topics Final Exam:
Friday, June 11, 1:003:00 pm
Accommodations: LeBow 348; 1:004:00 pm (1.5X) or
1:005:00 pm (2X)
Chapter 18  4 View of an Integrated Circuit
• Scanning electron microscope (SEM) images of an IC:
Al
Si
(doped) (d) (d) (a) 45 μm 0.5 mm • Dot map showing location of Si (a semiconductor):
 Si shows up as light regions. (b) • Dot map showing location of Al (a conductor):
 Al shows up as light regions. Fig. (d) from Fig. 18.27 (a), Callister 7e. (Fig. 18.27 is
courtesy Nick Gonzales, National Semiconductor Corp.,
West Jordan, UT.) (c) Fig. (a), (b), (c) from Fig. 18.0,
Callister 7e. Chapter 18  5 Measuring Electrical Conduction Chapter 18  6 Electrical Conduction
• Ohm's Law: V=IR Voltage drop (Volts = J/C)
C = Coulomb Resistance (Ohms)
Current (Amps = C/s) A e (crosssectional
area) I
V
L • Resistivity, and Conductivity, :  geometryindependent forms of Ohm’s Law
 Resistivity is a material property & is independent of sample
E: Electric
Field
intensity • Resistance:
R= V
I
=
L
A Resistivity
(Ohmm)
J: Current Density L
L
=
AA Conductivity = 1 Chapter 18  7 Electrical Properties
• Which wire will conduct more electricity?
D 2D • Analogous to flow of water in a pipe
• So resistance depends on sample
geometry, etc. = RA but since V = IR,
then, R = V/I, so
= VA
I Chapter 18  8 Example: Conductivity Problem
What is the minimum diameter (D) of the wire so that V < 1.5 V? e Cu wire  100 m
I = 2.5 A + V 100m D2
4 L
V
R=
=
A
I Solve to get: < 1.5 V
2.5 A 6.07 x 107 (Ohmm)1
D > 1.87 mm
Chapter 18  9 An Alternate Expression of Ohm’s Law
l Area = A = = RA RA V = IR
V
I=
R
I
Vl
lV
=
=
A AR l AR l
ll dV
J=
=
AR dx E  (I)
Chapter 18  10 Definitions
Therefore:
J= E an alternative way of stating Ohm’s law J = current density (A/m2) = current
I
=
and is indeed a flux
X  section area
A E = electric field potential = V/ or ( V/
J=
Electron flux ( V/ ) = V/m ) conductivity voltage gradient Charge (current) carriers:
• electrons in most solids
• ions can also carry  particularly in liquid solutions,
SOFCs
Chapter 18  11 Electron Scattering
• Efield exerts force on free e:
– Accelerated in direction opposite to Efield…
– e cannot accelerate indefinitely, otherwise I would
increase without limit over time
• I observed to reach constant value…so what’s going on?
• “Frictional forces” counter e acceleration:
– Scattering of e by lattice imperfections:
• impurities, vacancies, interstitials, dislocations, thermal
vibrations – e lose KE & change direction
– But, net e motion opposite to Efield…current flow Chapter 18  12 Electron Scattering
• Drift Velocity & Mobility:
describe extent of escattering
vd = average e vel. in
direction of force due to
applied Efield vd = eE e= electron mobility…
fn. (frequency of scattering
events), units of m2/Vs Chapter 18  13 If n electrons flow thru a wire with an average drift velocity
vd then the current density, Ji, passing through the wire is: Ji = e v d n  (II) WIRE n = concentration of mobile carriers, (m3)
vd = average drift velocity of mobile carriers (m/s)
Electron mobility is defined as: vd
vd drift velocity drift velocity
μe =
=
=
=
dV dx E driving force electric field
v Average drift
velocity, vd
vd
time (III) For any given solid
and temperature, e
is constant!
Chapter 18  14 Combine Eqs. I, II and III and Show that:‡ J= E J = evdn vd = e E = n e μe
Most important equation in this chapter!
The link between the macro, i.e. , and the micro, i.e. n and
e In order to understand we need to understand how n and
vary with composition, temperature and defects. ‡ Better to do it here and now than in the final! Chapter 18  15 Conductivity: Comparisons
• Room T values (Ohmm)1 = ( m)1
METALS
Conductors CERAMICS
10
Silver
6.8 x 10 7
Sodalime glass 10 1011
Copper
6.0 x 10 7
Concrete
10 9
Iron
1.0 x 10 7
Aluminum oxide <1013 POLYMERS
SEMICONDUCTORS
Polystyrene
Silicon
4 x 10 4
Polyethylene
Germanium 2 x 10 0
GaAs
10 6
Semiconductors 14 <10
10 151017
Insulators Huge range! And this does not include superconductors
Chapter 18  16 What Accounts for This Huge Range?
Let’s look at the KEY equation for this chapter and decide: = n e μe
It certainly doesn’t come from e, it also does not stem from
So the KEY is n…to understand n, we need to understand
band theory in solids… Chapter 18  17 e Band Theory: Background
Most Conductors, Insulators, Semiconductors:
Conduction due to e alone
Magnitude of depends on n
Not all e will move under applied electric field
n related to e states (levels), their energy & how filled
• Quantum Mechanics…
Quantum Mechanics Revisited:
e energy states (Ch. 2)
discrete energy levels occupied by earranged in shells (1, 2, 3 etc.) & subshells (s, p, d &
f), latter with 1, 3, 5, 7 states
e fill states with lowest energies, 2 per state, ±1/2 spins
e configuration for 1 atom
e arrangement in allowed
states
Chapter 18  18 Band Theory: Background
Consider Solids:
Comprise large # (N) atoms, initially well separated
Brought together when crystalline solid formed
At large separations, each atom independent
At close separations, e acted on by e & nuclei of
adjacent atoms
Atomic states “split” into series of closely spaced estates…electron energy band Chapter 18  19 Electronic Band Structures
Level of splitting:
fn. (interatomic separation)
begins with outermost e shells. Why?
Energy states discrete within each band; differences v. small Adapted from Fig. 18.2, Callister 7e. Chapter 18  20 Band Structure
At =m atom spacing, bands do not form for subshells nearest nucleus
•
• Valence Band – filled – highest occupied energy levels
Conduction Band – empty – lowest unoccupied energy levels Conduction
Band Adapted from Fig. 18.3, Callister 7e. Valence band Gaps between adjacent bands.
Energies within band gaps not
available for e to occupy Chapter 18  21 ...
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This note was uploaded on 07/27/2011 for the course ENGR 134 taught by Professor Marks during the Spring '11 term at Drexel.
 Spring '11
 Marks
 Ceramics

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