1 / 7

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.

rumor
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related