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

Miller indices

Electron states in bulk semiconductors

k  p method - Bloch functions (1) Schroedinger’s equation for a single electron in a periodic potential V(r): Expressin terms of Bloch functions at k = 0: (2)

Note the coupling between bands via k  p term and spin-orbit interaction Obtain after multiplying by and integrating (1) over unit cell: 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 u n0 (r) states: S,X,Y,Z are similar to S-like and P-like atomic states (lowest order spherical harmonics Y 00, Y 10, Y 11 etc.)

8-band k  p method (4 bands x 2 spins) Ga 0.47 In 0.53 As Note strong non-parabolicity