ee138 chapter 1_slides - annotated 10-10

8/9/2019 EE138 Chapter 1_Slides - Annotated 10-10

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Chapter 1 2

Ohm’s Law: Macroscopic

Ohm’s Law

Conventions:


3/14


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Chapter 1 4

Drude’s Model: Free Electron Theory of Metals (1)

Paul Drude

(1863-1906)

Credited with

the free

electron theoryof metals

Kinetic Energy Charged Particle

e-

• fixed lattice and “free”

electron gas

• electrons are particles

• collisions with other e-,surfaces, lattice

• random collisions

http://www.youtube.com/watch?v=dyX5I_io7bg


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Chapter 1 5

Drude Model: Free Electron Theory of Metals (2)

E

e-

e-e-

e-

∆x

A net e- motion = current


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Chapter 1 6

Hydrodynamic Fluid Model: Resistance as Viscosity

edt

d mma F −=

+==

D

Dv

vξ

edt

d mma F −=== D

v

em −=D

vξ

ξ

1v

D

m

e−=

τ m

e−=

Dv

τ ξ

1=No drag:

With drag:

If viscosity is so large, terminal velocity

is reached and dvD/dt = 0

then…

compare to

and…increasing viscosity (decreasing collision time)

http://www.youtube.com/watch?v=49Kor-zHQM0


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Chapter 1 7

Compare Thermal Velocity (vth) to Drift Velocity (vD)

Calculate vth at room temperature. Calculate vD for a typical metal in an

electric field of 1 V/m.

µ ~ 5x10-3 m2/V-s


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Chapter 1 8

Hall Effect: Definition & Description (1)

Edwin Hall

(1855-1938)

Credited with

discovering the

Hall Effect v o l t m e t e r

x

z

y

e-e-

Lorentz Force (FL):

Hall Field Force (FH):

(for negative charge carriers)

Define Hall Coefficient (RH):


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Chapter 1 9

Hall Effect: Definition and Description (2)

Link to applet showing the Hall Effect on negatively charged particles:

Link to applet showing the motion of negatively and positively

charged particles in a magnetic field:

http://dev.physicslab.org/asp/applets/javaphysmath/java/partmagn/default.asp

http://jakobvogel.net/go/physics/magnetism/halleffect


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Chapter 1 10

Hall Effect: Mobility and Carrier Density (3)

10

Why do semiconductors & insulators have higher resistivity than metals?

Metals SemiconductorsRH independent of T, alloying, defects RH decreases with increasing T and doping


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Chapter 1 11

Hall Effect: Applications (4)

Hall Probe: Measuring Magnetic Field

Hall Effect Sensors: Sensing Magnetic Field

http://www.youtube.com/watch?v=8lPKIaa7Q50


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Chapter 1 12

Example: A metal has a collision time of 10-14 s. Find the mean free path at room temperature.


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Chapter 1 13

Chapter #1: Review Questions

1. What is Ohm’s Law in macroscopic and microscopic

terms?

2. What are the units of conductivity?

3. Does the kinetic energy of an electron increase or

decrease with temperature?

4. Describe the motion of an electron in a metal under an

applied electric field? What is the mean free path?What is the collision time?

5. What are the units of mobility?

6. What is the Hall Effect?7. What are some applications of the Hall Effect?


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Chapter 1 14

Important Equations

R I IV P 2==

IRV =

L

V =X

A

I J =

A

L R

ρ =

X σ = J

σ ρ

1= X −=

Dv

µ σ e N e

=

Dee N J v−=

m

eτ µ =

2/1

3

=

m

kT vth

B D H

v−=X

e N R

e

H

1−=

B R H H

J−=X

Important Constants

Speed of light in vacuum: c = 3.0 x 108 m/s

Mass of an electron: m = 9.11 x 10-31 kg

Boltzmann constant: kB = 1.38 x 10-23 J/K Avogadro’s Number: N A = 6.022 x 10

23 /mole

ee138 chapter 1_slides - annotated 10-10

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