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Semiconductor Laser Physics

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“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

http://britneyspears.ac/lasers.htm

Miller indices

Electron states in bulk semiconductors

- Bloch functions

Express

in terms of Bloch functions at k = 0:

kp method

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

(1)

(2)

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

Note the coupling between bands via kp 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

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.)

Note strong non-parabolicity

Ga0.47In0.53As

8-band kp method

(4 bands x 2 spins)