slide1
Download
Skip this Video
Download Presentation
Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected]

Loading in 2 Seconds...

play fullscreen
1 / 29

Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected] - PowerPoint PPT Presentation


  • 123 Views
  • Uploaded on

Engineering 45. Electrical Properties-1. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected] Learning Goals – Elect. Props. How Are Electrical Conductance And Resistance Characterized?

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected]' - cardea


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

Engineering 45

ElectricalProperties-1

Bruce Mayer, PE

Licensed Electrical & Mechanical [email protected]

learning goals elect props
Learning Goals – Elect. Props
  • 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, Temp, and Deformation?
  • For Semiconductors, How Is Conductivity Affected By Impurities (Doping) And Temp?
electrical conduction
Georg Simon Ohm (1789-1854) First Stated a Relation for Electrical Current (I), and Electrical Potential (V) in Many Bulk Materials

()

Volt Meter

Bulk Matl

AmpMeter

I

Battery

Electrical Conduction
  • The Constant of Proportionality, R, is
    • Called the Electrical RESISTANCE
    • Has units of Volts/Amps, a.k.a, Ohms (Ω)
  • This Expression is known as Ohm’s Law
electrical conduction cont
Fluid↔Current Flow AnalogsElectrical Conduction cont.
    • Current as the “Electrical Fluid”
    • Wire as the “ Electrical Pipe”
  • Just as a Small Pipe “Resists” Fluid Flow, A Small Wire “Resists” current Flow
    • Thus Resistance is a Function of GEOMETRY and MATERIAL PROPERTIES
      • Next Discern the Resistance PROPERTY
  • Think of
    • Voltage as the “Electrical Pressure”
electrical resistivity
Consider a Section of Physical Material, and Measure its

Resistance

Geometry

Length

X-Section Area

Resistance, R

Matl Prop → “”

Area, A

Length, L

Electrical Resistivity
  • R↑ as L↑
    • R  L
  • R↑ as A↓
    • R  1/A
  • Thinking Physically, Since R is the Resistance to Current Flow, expect
electrical resistivity cont
Thus Expect

Resistance, R

Matl Prop → “”

Area, A

Length, L

Electrical Resistivity cont.
  • This is, in fact, found to be true for many Bulk Materials
  • Convert the Proportionality () to an Equality with the Proportionality Constant, ρ
  • Units for 
    • ρ → [Ω-m2]/m
    • ρ → Ω-m
electrical conductivity
conductANCE is the inverse of resistANCE

Conductance, G

Matl Prop → “”

Area, A

Length, L

Electrical Conductivity
  • Similarly, conductIVITY is the inverse of resistIVITY
  • Units for 
    •  = 1/ρ → 1/ Ω-m
  • Now Ω−1 is Called a Siemens, S
    • σ → S/m
ohm related issues
Recall Ohm’s Law

L

V

Ohm Related Issues
  • J  Current Density in A/m2
  • E  Electric Field in V/m
    • In the General Case
  • E =J is the NORMALIZED, Resistive, Version of Ohm’s Law
normalized conductive ohm
Recall Ohm’s Law

L

V

Normalized, Conductive Ohm
  • Rearranging
  • G is Conductance
  • Recall also
  • J = σE is the Normalized, Conductive Version of Ohm’s Law
some conductivities in s m

Metals

Conductivity (107 S/m)

Some Conductivities in S/m
  • Metals  107
  • SemiConductors
    • Si (intrinsic)  10-4
    • Ge  100 = 1
    • GaAs  10-6
    • InSb  104
  • Insulators
    • SodaLime Glass  10-11
    • Alumina  10-13
    • Nylon  10-13
    • Polyethylene  10-16
    • PTFE  10-17
conductivity example
Conductivity Example
  • What is the minimum diameter (D) of a 100m wire so that ΔV < 1.5 V while carrying 2.5A?

100m

-

e

I = 2.5A

+

-

Cu wire

DV

  • Recall
  • Also G by σ & Geometry
  • For Cu: σ = 6.07x107 S/m
conductivity example cont
Conductivity Example cont
  • What is the minimum diameter (D) of a 100m wire so that ΔV < 1.5 V while carrying 2.5A?

100m

-

e

I = 2.5A

+

-

Cu wire

DV

  • Solve for D
  • Sub for Values
electronic conduction
As noted In Chp2 Electrons in a FREE atom Can Reside in Quantized Energy Levels

The Energy Levels Tend to be Widely Separated, Requiring significant Outside Energy To move an Electron to the next higher level

Electronic Conduction
  • In The SOLID STATE, Nearby Atoms Distort the Energy LEVELS into Energy BANDS
    • Each Band Contains MANY, CLOSELY Spaced Levels
solid state energy band theory
Consider the 3s Energy Level, or Shell, of an Atom in the SOLID STATE with EQUILIBRIUM SPACING r0Solid State Energy Band Theory

By the Pauli Exclusion Principle Only ONE e− Can occupy a Given Energy Level

band theory cont
The N atoms per m3 with Spacing r0 produces an Allowed-Energy BAND of Width ΔE

Most Solids have N = 1028-1029 at/m3

Thus the ΔE wide Band Splits into 1029/m3 Allowed E-Levels

Band Theory, cont.
  • Leads to a band of energies for each initial atomic energy level
    • e.g., 1s energy band for 1s energy level
energy band calc
Given

ΔE 15 eV

N  5 x 1028 at/cu-m

Then the difference between allowed Energy Levels within the Band, E

Energy Band Calc
  • The Thermal Energy at Rm Temp is 25 meV/at, or about 1026 times E
    • Thus if bands are Not Completely Filled, e- can move easily between allowed levels
electronic conduction metals
In Metals The Electronic Energy Bands Take One of Two Configurations

Partially Filled Bands

e- can Easily move Up to Adjacent Levels, Which Frees Them from the Atomic Core

Overlapping Bands

e- can Easily move into the Adjacent Band, Which also Frees Them from the Atomic Core

Energy

Energy

empty

band

empty

GAP

band

partly

filled

filled

valence

valence

band

band

filled states

filled states

filled

filled

band

band

Electronic Conduction - Metals
metal conduction cont
Atoms at Their Lowest Energy Condition are in the “Ground State”, and are Not Free to Leave the Atom Core

In Metals, the Energy Supplied by Rm Temp Can move the e− to a Higher Level, making them Available for Conduction

V+

E-Field

V-

Net e- Flow

Current Flow

Metal Conduction, Cont.
  • Metallic Conduction Model → Electron-Gas or Electron-Sea
  • Note: e-’s Flowing “UPhill” constitutes Current Flowing DOWNhill
insulators semiconductors

Energy

Energy

empty

ConductionBand

ConductionBand

empty

band

band

?

GAP

GAP

filled

filled

Valence

valence

band

band

filled states

filled states

filled

filled

band

band

7

Insulators & Semiconductors
  • Insulators:
    • Higher energy states not accessible due to lg gap
      • Eg > ~3.5 eV
  • Semiconductors:
    • Higher energy states separated by smaller gap
      • Eg < ~3.5 eV
metals vs t vs impurities
The Two Basic Components of Solid-St Electronic Conduction

The Number of FREE Electrons, n

The Ease with Which the Free e-’s move Thru the Solid

i.e. the electron Mobility, µe

6

Cu + 3.32 at%Ni

5

-m)

Cu + 2.16 at%Ni

4

Resistivity, 

deformed Cu + 1.12 at%Ni

3

-8

Cu + 1.12 at%Ni

(10

2

“Pure” Cu

1

0

-200

-100

0

T (°C)

Metals -  vs T,  vs Impurities
  • Consider The ρ Characteristics for Cu Metals
metals vs t impurities cont
Since “Double Ionization” of Atom Cores is difficult

n(Hi-T)  n(Lo-T)

Thus T, Impurities and Defects must Cause Reduced µe

These are all e- Scattering Sites

Vacancies

Grain Boundaries

6

Cu + 3.32 at%Ni

5

-m)

Cu + 2.16 at%Ni

4

Resistivity, 

deformed Cu + 1.12 at%Ni

3

-8

Cu + 1.12 at%Ni

(10

2

“Pure” Cu

1

0

-200

-100

0

T (°C)

Metals -  vs T, Impurities cont
  • Impurities; e.g., Ni above
  • Dislocations; e.g., deformed
metal mathiessen s rule
The Data Shows The Factors that Reduce σ

Temperature

Impurities

Defects

These Affects are PARALLEL Processes

i.e., They Act Largely independently of each other

Metal  - Mathiessen’s Rule
  • The Cumulative Effect of ||-Processes is Calculated by Mathiessen’s Rule of Reciprocal Addition
resistivity relations for metals
Temperature Affects may be approximated with a Linear ExpressionResistivity Relations for Metals
  • For A Single Impurity That Forms a Solid-Solution
  • Where
    • A is an Alloy-Specific Constant, Ω-m/at-frac
    • ci is the impurity Concentration in in the atomic-fraction Format
      • At-frac = at%x(1/100%)
  • Where
    • 0 is the Resisitivity at the Baseline Temperature, Ω-m
    • a is the Slope of ρvs T Curve, Ω-m/K
relations for metals cont
In alloys where the impurity results, not in Solid-Solution, but in the Formation of a 2nd Xtal Structure, or Phase, Use a Rule-of-Mixtures Relation for ρi

Use Vol-Fractions as the Weighting Factor

ρRelations for Metals cont
    • Where
      • ρk is the Resistivity of phase-k
      • Vk is the Volume-Fraction of phase-k
  • Plastic Deformation
    • There is no Simple Relation for This
      • Consult individual metal or alloy data
example estimate
Est. σfor a Cu-Ni alloy with yield strength of 125 MPa

From Fig 7.19 Find Composition for Sy = 125 MPa

180

160

140

strength (MPa)

120

10

0

21 wt%Ni

8

0

Yield

60

0

10

2

0

3

0

4

0

5

0

wt. %Ni, (Concentration C)

r

5

0

Ohm-m)

40

3

0

Resistivity,

-8

2

0

(10

1

0

0

0

10

2

0

3

0

4

0

5

0

wt. %Ni, (Concentration C)

Example  Estimate σ
  • So need 21 wt% Ni
    • Find ρfrom Fig 18.9
  •   30x10-8Ω-m
    • And σ= 1/ρ
  •  σ= 3.3x106 S/m
all done for today
All Done for Today

UsingBandGaps

To Make

LEDs

slide27

Chabot Engineering

Appendix

Bruce Mayer, PE

Licensed Electrical & Mechanical [email protected]

slide28

http://www.chemistry.wustl.edu/~edudev/LabTutorials/PeriodicProperties/MetalBonding/MetalBonding.htmlhttp://www.chemistry.wustl.edu/~edudev/LabTutorials/PeriodicProperties/MetalBonding/MetalBonding.html

whiteboard work
WhiteBoard Work
  • Derive Relation for e- Drift Velocity, vd
  • Calculate the Drift Velocity in a 20 foot Gold Wire Connected to a 9Vdc Batt
    • Assume Au Atoms in the Solid Are Singly Ionized, contributing 1 conduction-e- per atom (monovalent)
  • Compare (random) THERMAL Velocity
ad