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NNSE618-L12-phonon-scattering

# NNSE618-L12-phonon-scattering - 1 Lecture contents Acoustic...

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NNSE 618 Lecture #12 1 Lecture contents Acoustic phonon scattering Deformation potential Hot carriers

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NNSE 618 Lecture #12 2 Lattice scattering rate calculation 3 3 ' ' 0 2 ' ' , 1 , ' 1 k d k k W f f k k W f f f f t f k k k k coll Goal: calculation of the scattering integral or relaxation time: Step 1. Determine scattering potential Step 2. Calculate matrix elements from k’ to k Step 3. Calculate transition rate from k’ to k using “golden Fermi rule” Step 4. Calculate state relaxation time Step 5. Average relaxation time t i iqr e H r d H H k V k k k 3 * ' ' ) ' ( ) ( 2 ) , ' ( 2 ' k E k E H k k W k k ) ' , ( 1 ) , ' ( 1 ) ( ' ' 0 k k W f f k k W f f k f f t f k k k k coll ) ( k
NNSE 618 Lecture #12 3 Electron-phonon interaction: Acoustic deformation potential Displacement of acoustic wave with a wavevector q : In a long wavelength limit the difference in displacement (strain) : Step 1: Perturbation Hamiltonian is proportional to the strain (D deformation potential) and is slow compared to electrons (we’ll consider it time -independent) In general any electron-phonon interaction will be an oscillating function in space: Optical phonons (non-polar) is proportional to the displacement Optical phonons (polar) is proportional to the displacement and effective electric charge (ionicity of bonds) t i iqr Ae u a q 1  ) ( ) ( ) ( ) ( r iqu u a r u a r u

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NNSE618-L12-phonon-scattering - 1 Lecture contents Acoustic...

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