“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
Cubic diamond lattice
Face-centered cubic (fcc)
Zinc blende structure
http://britneyspears.ac/lasers.htm
Miller indices
Electron states in bulk semiconductors
kp method
Schroedinger’s equation for a single electron in a periodic potential V(r):
(1)
  eikr unk (r ) - Bloch functions
p̂  i
p 2 [unk (r )eikr ]  [( p  k ) 2 unk (r )]eikr
(2)
Express unk (r ) in terms of Bloch functions at k = 0:
 p2

 V (r )un 0 (r )  En 0 (r )un 0 (r )

 2m0

Obtain after multiplying by u n*0 ( r ) and integrating (1) over unit cell:
p nm 
*
u
n
 0 (r)pum0 (r)dr
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
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
2
1.1
Ga0.47In0.53As
E (eV)
0.2
-0.7
-1.6
-2.5
0
4
8
12
k z (10 6cm -1 )
16
8-band kp method
(4 bands x 2 spins)
20