drude model presentation
DESCRIPTION
Drude Model PresentationTRANSCRIPT
Drude Model Overview
• Motivation• Basic Assumptions of the Model• Collision and Relaxation Time• DC, AC Electrical Conductivity• Hall Effect and Magnetoresistance• Why are metals shiny?
Motivation
• Metals are excellent conductors of heat and electricity, are ductile and malleable
• Physicists have tried to construct simple models of the metallic state that account the characteristic metallic properties
• Theory of Paul Drude in 1900 came only a few years after J.J. Thompson discovered the electrons
Metals – Valence Assumption
• Number of protons is Za
• Number of valence electrons is Z• Each metallic atom has:
– A nucleus of charge +Zae– Z valence/conduction electrons free to leave the atom to form electron gas– Za-Z core electrons of charge –(Za-Z)e tightly bound to the nucleus
Classical Thoery: Drude ModelDrude proposed valence electrons constantly bounce between heavier, stationary crystal ions
Drude Model Assumptions• Ions are arranged in fixed positions and cannot move• Collisions between e’s and ions are instantaneous, uncorrelated
events• Ignore all other interactions
– Independent electron approximation– Free electron approximation
• Electron experiences a collision with a probability per unit time 1/– is the mean time between collisions– independent on the electron position or momentum
Equations of MotionElectrons collisions
No collisions
EoM averaged over electrons
Taking a derivative
Average momentum
DC Electric Field
In uniform DC electric field
For steady state Drift velocity
vdtNumber of electrons passing an Area A in time dt
Total charge passing through A in time dt
Current density
DC Electrical Conductivity
With
Ohm’s Law
and
Resistivity
Conductivity
Current is caused by an electric fieldCurrent depends linearly on the strength of the electric fieldCurrent density depends on the conductivity of the material
or
Hall Effect (1879)
Positive Charge Carriers Negative Charge Carriers
Charge carriers deflected toward the top surfaceExcess surface charges creates an electric field Steady state reached
Drude Model: Magnetoresistance
Force acting on each electron
Momentum per electron
In steady state where
In Drude model, ρ(H) is independent of magnetic field.
Magnetoresistance
with
AC Conductivity and the Shiny
Oscillating electric field
Ohm’s Law where
Maxwell’s equations with no net charge
Wave equation where
At high frequencies where
AC Conductivity and the Shiny
ε real and negative, no wave propagationmetal is reflective
ε real and positive, propagating wavesmetal is transparent
For metals the plasma frequency is in the ultraviolet.
Wave equation