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Semiconductor Laser Physics. “ One should not work on semiconductors, that is a filthy mess; who knows whether they really exist.” Wofgang Pauli 1931. Crystal lattice and energy bands. Cubic diamond lattice. Face-centered cubic (fcc). Zinc blende structure.

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Semiconductor Laser Physics

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Semiconductor laser physics

Semiconductor Laser Physics

“One should not work on semiconductors, that is a filthy mess; who knows whether they really exist.”

Wofgang Pauli 1931

Semiconductor laser physics

Crystal lattice and energy bands

Semiconductor laser physics

Cubic diamond lattice

Face-centered cubic (fcc)

Semiconductor laser physics

Zinc blende structure

Semiconductor laser physics

Semiconductor laser physics

Miller indices

Semiconductor laser physics

Electron states in bulk semiconductors

Semiconductor laser physics

- Bloch functions


in terms of Bloch functions at k = 0:

kp method

Schroedinger’s equation for a single electron in a periodic potential V(r):



Semiconductor laser physics

Obtain after multiplying by and integrating (1) over unit cell:

Note the coupling between bands via kp term and spin-orbit interaction

This is a matrix diagonalization problem; however it is still too complicated because of too many bands

Next step: Lowdin’s perturbation method to reduce the size of the problem

Semiconductor laser physics

The Luttinger-Kohn basis for un0(r) states:

S,X,Y,Z are similar to S-like and P-like atomic states (lowest order spherical harmonics Y00, Y10, Y11 etc.)

Semiconductor laser physics

Note strong non-parabolicity


8-band kp method

(4 bands x 2 spins)

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