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.
The band structure ?
First Brillouin zone E vs. k band diagram 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“compound 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
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 applacations Large Area, Full Color Displays LED Traffic Lights
the first principles calculation guess first compare charge convergence new
Empirical tight binding Hv= < |Hv-ESv|= 0
The Hamiltonian in sp3d2
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
Density of states for InN
Band structure of InAs by ETB
Density of states for InAs
Band structure of InSb by ETB
Density of states for InSb