Chapter 1 1

OutlineReading: Livingston, Chapter 1.1-1.6

Ohms Law Macroscopic Microscopic

Drudes Model Hydrodynamic Fluid Model Hall Effect

Definition and description Free charge carrier density vs. mobility

Temperature Alloying

Applications

Chapter 1 2

Ohms Law: MacroscopicOhms Law

Conventions:

Chapter 1 33

Ohms Law: Microscopic

Chapter 1 4

Drudes Model: Free Electron Theory of Metals (1)

Paul Drude(1863-1906)Credited with the free electron theory of 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

Chapter 1 5

Drude Model: Free Electron Theory of Metals (2)E

e-

e-e-

e-

x

A net e- motion = current

Chapter 1 6

Hydrodynamic Fluid Model: Resistance as Viscosity

XedtdmmaF =

+== DD vv

XedtdmmaF === Dv

Xem =Dv

X1vD m

e= X

me

=Dv

1=No drag:

With drag:

If viscosity is so large, terminal velocity is reached and dvD/dt = 0

then

compare to

andincreasing viscosity (decreasing collision time)

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

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.

~ 5x10-3 m2/V-s

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):

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

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

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

Chapter 1 12

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

Chapter 1 13

Chapter #1: Review Questions

1. What is Ohms 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?

Chapter 1 14

Important Equations

RIIVP 2==

IRV =

LV

=X

AIJ =

ALR =

X=J

1= X=Dv

eNe=

DeeNJ v=

me =

2/13

=

mkTvth

BDH v=X

eNR

eH

1=

BRHH J=X

Important ConstantsSpeed of light in vacuum: c = 3.0 x 108 m/sMass of an electron: m = 9.11 x 10-31 kgBoltzmann constant: kB = 1.38 x 10-23 J/KAvogadros Number: NA = 6.022 x 1023 /mole