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) = 0.565 nm.
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The crystal structure of the III-V semiconductors Diamond and Zincblende Lattices Unit cells for silicon (Si) and gallium arsenide (GaAs) Silicon - diamond.
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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