1 / 8

Band gap

E (eV). Band gap. Empty lattice bands. Density of states Wave vector. Band structure: Semiconductor. [111] [100] [110]. Inverse photoemission. Photoemission. “Empty lattice solution” vs. Experimental bands.

higginsl
Download Presentation

Band gap

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. E (eV) Band gap Empty lattice bands Density of states Wave vector Band structure: Semiconductor [111] [100] [110]

  2. Inverse photoemission Photoemission “Empty lattice solution” vs. Experimental bands E(k) = ħ2/2me (k+Ghkl)2 + V0 Experiment + full theory (lines) E (2eV) E (5eV) Ge (200) (111) Vacuum level EV EV =0 (-111) CBM VBM (-200) (1-1-1) Ghkl = (-1-1-1)  (2/a) (000) V0 V0  k L =(000) k L=(½½½)

  3. 1 2 d-bands 4 3 1 1 s,p-band (like a free electron) d-bands (like atomic energy levels) Band structure: Noble metal Cu    [111] [110]

  4. Ni Fermi level s,p-band (like a free electron) d-bands (like atomic energy levels) Band structure: Transition metal Ni Cu Rigid band model (one less e in Ni)

  5. Delocalized s-electrons vs. localized d-electrons Wave functions of the outer electrons versus distance (in Å = 0.1 nm) for nickel, a transition metal. The 4s electrons are truly metallic, extending well beyond the nearest neighbor atoms (at r1, r2, r3 ). The 3d electrons are concentrated at the centralatomandbehavealmostlikeatomicstates.TheycarrythemagnetisminNi. (r) r (Å)

  6. Two-dimensional -bands of graphene E[eV]  Empty EFermi Occupied K =0 M K Empty * kx,y M K Occupied  In two dimensions one has the quantum numbers E,kx,y. This plot of the energy bands shows E vertically and kx ,ky in the horizontal plane.

  7. “Dirac cones” in graphene A special feature of the graphene -bands is their linear E(k)dispersion near the six corners K of the Brillouin zone (instead of the parabolicrelationfor free electron bands). In a plot of E versus kx,ky one obtains cone-shaped energy bands attheFermi level.

  8. Topological Insulators A spin-polarized version of a “Dirac cone” occurs in “topological insulators”. These are insulators in the bulk and metals at the surface, because two surface bands bridge the bulk band gap. It is impossible topologically to remove the surface bands from the gap, because they are tied to the valence band on one side and to the conduction band on the other. The metallic surface state bands have been measured by angle- and spin-resolved photoemission.

More Related