The crystal structure of the III-V semiconductors
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Transcript of The crystal structure of the III-V semiconductors
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
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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
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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
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arb
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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
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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
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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
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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 (
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s)