Transcript Lecture5

Microscopic Theory of
Conduction
From Classical to Wave
Mechanical Models
The Classical “Electron Gas”
Model - How well did it work?
• Ohm’s Law:
– can correctly predict the form of Ohm’s Law
• Resistivity:
– leads to predictions an order of magnitude
greater than what is observed
– wrong temperature dependence
Using the classical model...
• Compare drift velocity with thermal
velocity of electrons:
3kT
vrms 
me
• Estimate time between collisions:
  Lv
rms
• Calculate the resistivity of copper:
3kTme

ne 2 L
Other problems with the classical
model...
• The “electron gas” should produce a much
higher heat capacity than is observed
• Classical Model has no way to explain
phenomena such as Contact Potentials or
Superconductivity
Classical Gas to Fermi Gas...
• Electrons in the gas
must obey the rules of
quantum mechanics!
• Pauli Exclusion
Principle
• Quantization of
Energy:
– particle in a box
The Fermi Energy
• Electrons in a metal have much greater
energy than the classical particle model
predicts. We can define the Fermi Energy
for electrons as:
2
h 3N 2 / 3
E F
( )
8me V
Electrons travel at much higher velocities
than the “gas model” predicts.
The Quantum Theory of
Conduction...
• Can explain contact potentials and Heat
Capacities
• Invokes electron scattering to explain the
motion of electrons in the conductor
• Develops the idea of bands and the band
theory of conduction; explains conductors,
insulators and semiconductors.