NNSE618-L4-so-bands-kp

NNSE618-L4-so-bands-kp - NNSE 618 Lecture #4 1 Lecture...

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Unformatted text preview: NNSE 618 Lecture #4 1 Lecture contents Spin-orbit coupling Valence band Band structures of semiconductors NNSE 618 Lecture #4 2 Degenerate valence band: Spin-orbit coupling S L r H so ) ( Hamiltonian of spin-orbit interaction includes orbit momentum L and spin S operators SO-coupling is a relativistic effect Responsible for fine structure of atomic levels Interaction significant close to nucleus (smaller than inner Bohr radius) Treated as a perturbation: need to find an average over the unperturbed state Probability to find electron inside the inner shell~ 1/ Z 2 For the state with quantum numbers l and s, the SO coupling will be determined by total angular momentum j dr dV r c m 1 2 1 2 2 ) 1 ( ) 1 ( ) 1 ( 2 2 1 2 2 2 2 s s l l j j S L J S L 2 S p r L 2 2 2 e Zm r r Ze r V 2 ) ( 4 4 2 2 2 me Z c e Fine structure constant NNSE 618 Lecture #4 3 Degenerate valence band: Spin-orbit coupling States with different j will have different energies !...
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NNSE618-L4-so-bands-kp - NNSE 618 Lecture #4 1 Lecture...

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