Prof. Ming-Jer Chen Department of Electronics Engineering National Chiao-Tung University

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Prof. Ming-Jer ChenProf. Ming-Jer Chen

Department of Electronics EngineeringDepartment of Electronics Engineering

National Chiao-Tung UniversityNational Chiao-Tung University

03/10/201403/10/2014

IEE5501 IEE5501 Solid State PhysicsSolid State Physics

Lecture 3:

Sommerfeld Model

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From Wikipedia, the free encyclopedia

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.

(So, the Drude-Sommerfeld model is popular to study advanced devices like graphene FET.)

(1863-1906) (1868-1951)

Arnold Sommerfeld Hans Bethe

(1906-2005)

(Sommerfeld was Bethe’s doctoral advisor)

Paul Drude Lev Landau

(1908-1968)(Nobel Prize in Physics 1967) (Nobel Prize in Physics 1962)

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Given an electric field

Can you derive it, starting from thevelocity distribution f() in a Fermispherical gas? (Care must be taken.)

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How many of energies within the sphere, evenat T = 0K?

Different view of electron transport, Only by Fermi velocity at Fermi surface

Still under Independent Electron Approximation Free Electron Approximation Relaxation Time Approximation

So, focus on the fastest (Fermi) electrons only.

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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 thinkif it is right?

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On the Fermi gas

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Energy and Entropyrelated quantities

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Calculated quantities are still insufficient to explain data

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Dimensionality