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Band structure of cubic semiconductors (GaAs) near the center of the Brillouin zone

Band structure of cubic semiconductors (GaAs) near the center of the Brillouin zone. E. el. el. s 1 -Ga. 4-fold. hh. p 3 -As. 6-fold. hh. lh. lh. 2-fold. so. With spin-orbit coupling included. Atom. Non-relativistic solid. Basics of k.p-theory for bulk.

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Band structure of cubic semiconductors (GaAs) near the center of the Brillouin zone

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  1. Band structure of cubic semiconductors (GaAs) near the center of the Brillouin zone E el el s1-Ga 4-fold hh p3-As 6-fold hh lh lh 2-fold so With spin-orbit coupling included Atom Non-relativistic solid

  2. Basics of k.p-theory for bulk Problem: Band structure at k = 0 is known. How to determine for k-vectors neark = 0? Perturbation theory: V(r) periodic

  3. Can be generalized for all bands near the energy gap: Very few parameters that can be calculated ab-initio or taken from experminent describe relevant electronic structure of bulk semiconductors k.p theory for bulk (cont'd) Advantage: main contribution from top val. bands Only 2 parameters determine mass:

  4. k.p theory for bulk (cont'd) Advantage: main contribution from top val. bands

  5. Envelope Function Theory: method of choice for electronic structure of mesoscopic devices Problem: How to solve efficiently... Periodic potential of crystal: rapidly varying on atomic scale Non-periodic external potential: slowly varying on atomic scale Ansatz: Product wave function ... Envelope Function F Periodic Bloch Function u x Result: Envelope equation (1-band) builds on k.p-theory...

  6. + + + + + + + Example for U(r): Doped Heterostructures Ec (z) + EF EF + + neutral donors Ec Unstable Charge transfer Thermal equilibrium Resulting electrostatic potential follows from ... Fermi distribution function Self-consistent “Schrödinger-Poisson” problem

  7. Quantization in heterostructures cb Band edge discontinuities in heterostructures lead to quantized states Material A B A vb cb electron Schrödinger eq. (1-band): hole vb

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