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 cellse. g., GaAs, a = 5.65 Å (Angstroms) = 0.565 nm.

The band structure ?

First Brillouin zone E vs. k banddiagram 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)

Compound Semiconductors (alloys)

For optoelectronics, most devices are fabricated of“compoundsemiconductors” 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 cellis identical (random III site location), but we treat such alloys ascrystalline to a first approximation

The Human eye response

Lasers and LEDs for displays or lighting must emit in the 430-670 nm wavelength region (bandgaps of 3.0-1.9 eV).

Technologically Available Materials

Some of the applacationsLarge Area, Full Color Displays LED Traffic Lights

the first principles calculation guess first

i

i

new

compare charge convergence

i

Empirical tight binding

|Hv-ESv|= 0

Hv= < v|H|

|| ii a

The Hamiltonian in sp3d2

sa xa ya za d1a d2a sc xc yc zc d1c d2c

sa Esa 0 0 0 0 0 Vss*g0 Vsapc*g1 Vsapc*g2 Vsapc*g3 0 0

xa 0 Epa 0 0 0 0 g1*-Vscpa Vxx*g0 Vxy*g3 Vxy*g2 Vxad1c*g1 yVxad1cg1

ya 0 0 Epa 0 0 0 g2*-Vscpa Vxy*g3 Vxx*g0 Vxy*g1 g2*-Vxad1 yVxad1cg2

za 0 0 0 Epa 0 0 g3*-Vscpa Vxy*g2 Vxy*g1 Vxx*g0 0 kVxad1c*g3

d1a 0 0 0 0 Eda 0 0 Vd1axc*g1 g2*-Vd1axc 0 Vd1d1g0 0

d2a 0 0 0 0 0 Eda 0 yVd1axc*g1yVd1axcg2 kVd1axcg3 0 Vd1d1g0

sc Vss*g0 g1*-Vscpa g2*-Vscpa g3*-Vscpa 0 0 Esc 0 0 0 0 0

xc Vsapc*g1 Vxx*g0 Vxy*g3 Vxy*g2 Vd1axc*g1yVd1axc*g1 0 Epc 0 0 0 0

yc Vsapc*g2 Vxy*g3 Vxx*g0 Vxy*g1 g2*-Vd1axcyVd1axcg2 0 0 Epc 0 0 0

zc Vsapc*g3 Vxy*g2 Vxy*g1 Vxx*g0 0 kVd1axcg3 0 0 0 Epc 0 0

d1c 0 Vxad1c*g1 g2*-Vxad1 0 Vd1d1g0 0 0 0 0 0 Edc 0

d2c 0 yVxad1cg1 yVxad1cg2kVxad1c*g3 0 Vd1d1g0 0 0 0 0 0 Edc

The equation came from ETB

Volume optimization for InN by wien2K

Volume optimization for InAs by wien2K

Volume optimization for InSb by wien2K

Band structure of InN by wien2k

Band structure of InAs by wien2k

Band structure of InSb by wien2k

Band structure of InN by ETB

B a n d stru c tu re o f In N

-15

-10

-5

0

5

10

15

20

1 2 1 4 1 6 1 8 1 1 0 1

W L Γ K v e c to r X K

Density of states for InN

DOS for InN

-16 -12 -8 -4 0 4 8 12 16

energy eV

DO

S (

arb

itra

ry u

nit

s)

Band structure of InAs by ETBb a n d stru c tu re o f In A s

-15

-10

-5

0

5

10

15

1 2 1 4 1 6 1 8 1 1 0 1

W L Γ K v e c to r X K

Density of states for InAsDOS for InAs

-15 -10 -5 0 5 10 15 20

energy eV

DO

S (

arb

itra

ry u

nit

s)

Band structure of InSb by ETBB a n d stru c tu re o f In S b

-10

-8

-6

-4

-2

0

2

4

6

8

10

1 2 1 4 1 6 1 8 1 1 0 1

W L Γ K v e c to r X K

Density of states for InSbDOS for InSb

-10 -8 -6 -4 -2 0 2 4 6 8 10

energy eV

DO

S (

arb

itra

ry u

nit

s)