The crystal structure of the III-V semiconductors

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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
cells e. 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
  ofcompound
• 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

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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 applacations
Large Area, Full Color Displays
LED Traffic Lights
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the first principles calculation guess first
compare charge convergence
new
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Empirical tight binding

H?v lt
H?v-ES?v 0
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The Hamiltonian in sp3d2
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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
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Density of states for InN
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Band structure of InAs by ETB
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Density of states for InAs
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Band structure of InSb by ETB
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Density of states for InSb
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