the crystal structure of the iii-v semiconductors diamond and zincblende lattices unit cells for...
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![Page 1: The crystal structure of the III-V semiconductors Diamond and Zincblende Lattices Unit cells for silicon (Si) and gallium arsenide (GaAs) Silicon - diamond](https://reader036.vdocuments.site/reader036/viewer/2022081418/56649edb5503460f94bea6b7/html5/thumbnails/1.jpg)
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.
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The band structure ?
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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)
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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
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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).
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Technologically Available Materials
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Some of the applacationsLarge Area, Full Color Displays LED Traffic Lights
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the first principles calculation guess first
i
i
new
compare charge convergence
i
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Empirical tight binding
|Hv-ESv|= 0
Hv= < v|H|
|| ii a
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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
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The equation came from ETB
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Volume optimization for InN by wien2K
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Volume optimization for InAs by wien2K
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Volume optimization for InSb by wien2K
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Band structure of InN by wien2k
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Band structure of InAs by wien2k
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Band structure of InSb by wien2k
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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
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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)
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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
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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)
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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
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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)
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