1. The crystal structure of the III-V semiconductors
Diamond and Zincblende Lattices
Unit cells for silicon (Si) and gallium arsenide (GaAs) Silicon - diamond lattice GaAs - zincblende (cubic zinc sulfide) lattice (most other III-V and many II-VI semiconductors have zincblende lattice)Diamond and zincblende lattice based on tetragonal pattern of bonds from each atom to nearest neighbors-two interlocking facecentered- cubic lattices lattice parameter (or constant), a- repeat length of the unit cells
e. g., GaAs, a = 5.65 Å (Angstroms) = nm.

2. The band structure ?

3. First Brillouin zone E vs. k band diagram of zincblende semiconductors
One relevant conduction band is
formed from S- like atomic orbitals
“unit cell” part of wavefunction is
approximately spherically symmetric.
The three upper valence bands are
formed from (three) P- like orbitals
and the spin-orbit interaction splits off
lowest, “split-off” hole (i. e., valence)
band. The remaining two hole bands
have the same energy (“degenerate”)
at zone center, but their curvature is
different, forming a “heavy hole” (hh)
band (broad), and a “light hole” (lh)
band (narrower)

4. Compound Semiconductors (alloys)
For optoelectronics, most devices are fabricated of“compound
semiconductors” particularly III-V materials made from
•Group III (Al, Ga, In) and
•Group V (N, P, As, Sb) elements
•Sometimes Si and Ge (Group IV) are used as photodetectors
•Sometimes II-VI (e.g. ZnSe) and IV-VI materials (e.g., PbTe)
Alloys of compound semiconductors used extensively to adjust the basic materials properties, e.g., lattice constant, bandgap,refractive index, optical emission or detection wavelength
EXAMPLE –
InxGa1- xAs (where x is the mole fraction of indium)
InxGa1- xAs is not strictly crystalline because not every unit cell
is identical (random III site location), but we treat such alloys as
crystalline to a first approximation

5. The Human eye response
Lasers and LEDs for displays or lighting must emit in the nm wavelength region (bandgaps of eV).

6. Technologically Available Materials

7. Some of the applacations
Large Area, Full Color Displays
LED Traffic Lights

8. the first principles calculation guess first
compare charge convergence
new

9. Empirical tight binding
Hv= <
|Hv-ESv|= 0

10. The Hamiltonian in sp3d2

11. The equation came from ETB

12. Volume optimization for InN by wien2K

13. Volume optimization for InAs by wien2K

14. Volume optimization for InSb by wien2K

15. Band structure of InN by wien2k

16. Band structure of InAs by wien2k

17. Band structure of InSb by wien2k

18. Band structure of InN by ETB

19. Density of states for InN

20. Band structure of InAs by ETB

21. Density of states for InAs

22. Band structure of InSb by ETB

23. Density of states for InSb