of 7
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Chapter 1 2
Ohm’s Law: Macroscopic
Ohm’s Law
Conventions:
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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