IEE5501 Solid State Physics
Lecture 3:
Sommerfeld Model
Prof. Ming-Jer Chen
Department of Electronics Engineering
National Chiao-Tung University
03/10/2014
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From Wikipedia, the free encyclopedia
Paul Drude
(1863-1906)
Arnold Sommerfeld
(1868-1951)
Hans Bethe
Lev Landau
(1906-2005)
(1908-1968)
(Nobel Prize in Physics 1967) (Nobel Prize in Physics 1962)
(Sommerfeld was Bethe’s doctoral advisor)
In 1900 Drude developed a powerful model to explain the thermal, electrical, and optical
properties of matter.
In 1933, Arnold Sommerfeld and Hans Bethe modified the Drude model, simply by replacing
the classical gas (follow Maxwell distribution) with a Fermi gas (Quantum Mechanical version
of an ideal gas; follow Fermi-Dirac distribution), leading to the Drude-Sommerfeld model.
In 1957, Lev Landau proved that a gas of interacting particles can be described by a system of
almost non-interacting 'quasiparticles' that, in the case of electrons in a metal, can be well
described by the Drude model.
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(So, the Drude-Sommerfeld model is popular to study advanced devices like graphene FET.)
Given an electric field
Can you derive it, starting from the
velocity distribution f() in a Fermi
spherical gas? (Care must be taken.)
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Still under Independent Electron Approximation
Free Electron Approximation
Relaxation Time Approximation
Different view of electron transport,
Only by Fermi velocity at Fermi surface
So, focus on the fastest (Fermi) electrons only.
How many of energies within the sphere, even
at T = 0K?
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Derive a velocity distribution for a Fermi sphere
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As claimed in the textbook, the resulting mean free path in a
Fermi gas picture appears to be reasonable. But, do you think
if it is right?
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On the Fermi gas
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Energy and Entropy
related quantities
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Calculated quantities are still
insufficient to explain data
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Dimensionality
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