Section 2 oms

  • Published on
    20-Jun-2015

  • View
    282

  • Download
    0

Embed Size (px)

DESCRIPTION

OM 2

Transcript

<ul><li> 1. Section II.. InsulatorsCharge Transport Theory, narrow bandsDelocalized (Bloch) Wave FunctionsLocalized Wave FunctionsExcitonsPeirels Distortion (1D systems)</li></ul> <p> 2. Review of Electronic Properties ofSolids Free Electron Fermi Gas 3. Energy Bands, Semiconductors, Doping 4. Hydrogen Molecule 5. Charge Transport TheoryGeneral 6. Figure 9.11. (a) Energy levels in an isolated silicon atom and (b) in asilicon crystal of N atoms, illustrating the formation of energy bands. Thevalence band contains 4N states and can accommodate all 4N valenceelectrons. 7. Figure 7.1. Schematic plot of the single particle energy spectrum in a bulksemiconductor for both the electron and hole states on the left side of the panel with appropriate electron (e) and hole (h) discrete quantum statesshown on the right. The upper parabolic band is the conduction band, thelower the valence. 8. Holes 9. Figure 9.12. A valence electron jumping across the energy gap in puresilicon resulting in the generation of a free electron and hole in the crystal: (a) energy band model, (b) bond model. 10. Figure 9.13. Extrinsic n-type silicon doped with P donor atoms. (a) Energyband diagram and (b) Bond model. 11. Figure 9.14. Extrinsic p-type silicon doped with B acceptor atoms. (a)Energy band diagram and (b) Bond model. 12. Electronic structures of Organic Molecules(1) Core electrons.(2) s electrons, localized between two atoms.(3) n electrons, located at a particular heteroatom, usually have high orbital energy and could be promoted easily.(4) p electrons, delocalized over an array of atoms, usually have high MO energy and could be promoted easily. 13. Linear Combination of AtomicOrbitals LCAO 14. Density Functional Theory 15. Background 1920s: Introduction of the Thomas-Fermi model. 1964: Hohenberg-Kohn paper proving existence of exact DF. 1965: Kohn-Sham scheme introduced. 1970s and early 80s: LDA. DFT becomes useful. 1985: Incorporation of DFT into molecular dynamics (Car-Parrinello) (Now one of PRLs top 10 cited papers). 1988: Becke and LYP functionals. DFT useful for some chemistry. 1998: Nobel prize awarded to Walter Kohn in chemistry for development of DFT. 16. (r1 , s1 ,..., rN , sN ) 17. Lecture 8:Introduction to Density FunctionalTheory Marie Curie Tutorial Series: Modeling BiomoleculesDecember 6-11, 2004Mark TuckermanDept. of Chemistry and Courant Institute of Mathematical Science 100 Washington Square East New York University, New York, NY 10003 18. Amorphous Semiconductors 19. Lets estimate the mean free path, lmax=l. Letvmax=v.The carrier mobility is defined as= e/m*, where is the carrier relaxationtime.Consider for mfree carrier=m*=m.We take l=v .and mv2=3/2 kT, all of which givesl=(3kTm/e2 ) or l=0.7 where l is in angstrom units and is incm2/v sec 20. Transport between isolated molecules 21. Excitons 22. A peculiarity in some One-dimensional systems:Peierls Distortion</p>