NNSE508_EM-L6-Drude

NNSE508_EM-L6-Drude - NNSE 508 EM Lecture#6 1 Lecture...

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Unformatted text preview: NNSE 508 EM Lecture #6 1 Lecture contents • Metals: Drude model – Conductivity – frequency dependence • Plasma waves • Difficulties of classical free electron model NNSE 508 EM Lecture #6 2 Phenomenology of electron transport: relaxation time • In conductors, valence electrons are treated as free electrons: “free particle swarm” (Drude model) – Electron motion in the field: • Electrons experience collisions similar to gas molecules in the kinetic theory of gasses – Extra average velocity due to electric field: – Equivalent to a friction force on a “free” electron : – Thermal velocity is much higher than drift velocity” – Motion in real space = thermal motion + drift + scattering dv m qE dt d q v E m Relaxation time 1 2 7 3 10 B th d k T cm v v m s d d dv v m qE m dt NNSE 508 EM Lecture #6 3 Phenomenology of electron transport: mobility • Current density is proportional to drift velocity of carriers • Concentration n is taken as a density of valence electrons • In the steady state drift velocity is proportional to the field ( –drift mobility): - with mobility [cm 2 /V-s] introduced in metals and semiconductors • And current density ( s –conductivity) gives Ohm’s law: q m d J qnv d J qnv qn E E s 2 q qn n m s d q v E E m NNSE 508 EM Lecture #6 4 Resistivity of metals Room temperature resistivity of single crystalline metals • Drude theory was successful to describe basic tendencies of metal conductivity: Dependence on • Crystalline quality • Temperature • Alloying • Frequency NNSE 508 EM Lecture #6 5 Frequency dependence of conductivity of metals • Let’s use simple microscopic picture: (relaxation time approximation) and find how the conductivity depends on frequency of EM field Assuming the electric field along x-direction: • We get • The response of the material can be described...
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NNSE508_EM-L6-Drude - NNSE 508 EM Lecture#6 1 Lecture...

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