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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“One should not work on semiconductors, that is a filthy mess; who knows whether they really exist.”
Wofgang Pauli 1931
Face-centered cubic (fcc)
in terms of Bloch functions at k = 0:
Schroedinger’s equation for a single electron in a periodic potential V(r):
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 (1) over unit cell: 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 (1) over unit cell:
8-band kp method
(4 bands x 2 spins)