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

http://britneyspears.ac/lasers.htm

Miller indices

Electron states in bulk semiconductors

kp method

- Bloch functions)(rkkr

ni ue

(1)

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

ip̂ krk

krk k i

ni

n ruprup e)]()[(]e)([ 22

Express )(rknu in terms of Bloch functions at k = 0:

(2)

rrprp duu m

cellunit

nnm )()( 0*

0 Note the coupling between bands via kp term and spin-orbit interaction

Obtain after multiplying by and integrating (1) over unit cell: )(*0 run

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

)()()()(2 000

0

2

rurErurVm

pnnn

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.)

0 4 8 12 16 20

2

1.1

0.2

-0.7

-1.6

-2.5

k z (10 6cm -1)

E (

eV

)

8-band kp method(4 bands x 2 spins)

Ga0.47In0.53As

Note strong non-parabolicity