NNSE618-L11-lattice_vibrations

NNSE618-L11-lattice_vibrations - 1 Lecture contents Coupled...

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NNSE 618 Lecture #11 1 Lecture contents Coupled oscillators Dispersion relationship Acoustical and optical lattice vibrations Acoustical and optical phonons Phonon statistics Acoustical phonon scattering
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NNSE 618 Lecture #11 2 Few concepts from Solid State Physics 1. Adiabatic approximation ) ( ) ( R E R H L L ) , ( ) , ( r R E r R H Mass of ions >1000 (for most semiconductors >10 2 times greater than mass of electrons Ion velocities >100 times slower Electrons adjust ‘instantaneously” to the positions of atoms When valence and core ectrons are separated, general Schrödinger equation for a condensed medium without spin 0 ( , ) ( , ) ( ) R r r R R Separate ion and electron motion (accuracy ~m/M) = H L + H e ) , ( ) , ( R r E R r H e e
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Lecture #11 3 Few concepts from Solid State Physics 2. Phonons     anhar m l m l m l m l m l l l l L U u u C R R U M p H , 2 , , 0 0 0 2 2 1 2 1 exp 1 ) ( kT n t i ikr k e u u 0 , Hamiltonian for lattice motion (harmonic oscillations) : Displacements show up as plane waves with weak interaction via anharmonicity: Phonon dispersion relation in GaAs     k n k E Energy in a mode: Equilibrium distribution (Bose Einstein):
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NNSE618-L11-lattice_vibrations - 1 Lecture contents Coupled...

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