Lecture II.
. Insulators
Charge Transport Theory,
narrow bands
Delocalized (Bloch) Wave
Functions
Localized Wave Functions...
Review of Electronic Properties of
Solids
Free Electron Fermi Gas
•Electron in a box: example
 Electrons are sufficiently delocalized in
•conjugated molecules that they can be
•considered...
Energy Bands, Semiconductors,
Doping
Hydrogen Molecule
Charge Transport Theory
General
Figure 9.11. (a) Energy levels in an isolated silicon atom and (b) in a
silicon crystal of N atoms, illustrating the forma...
Figure 7.1. Schematic plot of the single particle energy spectrum in a bulk
semiconductor for both the electron and hole s...
Holes
Figure 9.12. A valence electron jumping across the energy gap in pure
silicon resulting in the generation of a free electr...
Figure 9.13. Extrinsic n-type silicon doped with P donor atoms. (a) Energy
band diagram and (b) Bond model.
Figure 9.14. Extrinsic p-type silicon doped with B acceptor atoms. (a)
Energy band diagram and (b) Bond model.
Electronic structures of Organic Molecules
(1) Core electrons.
(2) s electrons, localized between two atoms.
(3) n electro...
Linear Combination of Atomic
Orbitals
LCAO
Density Functional Theory
Background
• 1920s: Introduction of the Thomas-Fermi model.
• 1964: Hohenberg-Kohn paper proving existence of exact DF.
• ...
1 1( , ,..., , )N Ns s r r
Lecture 8:
Introduction to Density Functional
Theory
Marie Curie Tutorial Series: Modeling Biomolecules
December 6-11, 200...
Amorphous Semiconductors
Let’s estimate the mean free path, lmax=l. Let
vmax=v.
The carrier mobility is defined as
μ= eτ/m*, where τ is the carrier...
Transport between “isolated”
molecules
Excitons
A peculiarity in some One-
dimensional systems:
Peierls Distortion
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Lecture 2 oms

  1. 1. Lecture II. . Insulators Charge Transport Theory, narrow bands Delocalized (Bloch) Wave Functions Localized Wave Functions Excitons Peirels Distortion (1D systems)
  2. 2. Review of Electronic Properties of Solids Free Electron Fermi Gas
  3. 3. •Electron in a box: example  Electrons are sufficiently delocalized in •conjugated molecules that they can be •considered as an electron box  Electronic absorption of β-carotene 0.294nm
  4. 4. Energy Bands, Semiconductors, Doping
  5. 5. Hydrogen Molecule
  6. 6. Charge Transport Theory General
  7. 7. Figure 9.11. (a) Energy levels in an isolated silicon atom and (b) in a silicon crystal of N atoms, illustrating the formation of energy bands. The valence band contains 4N states and can accommodate all 4N valence electrons.
  8. 8. Figure 7.1. Schematic plot of the single particle energy spectrum in a bulk semiconductor for both the electron and hole states on the left side of the panel with appropriate electron (e) and hole (h) discrete quantum states shown on the right. The upper parabolic band is the conduction band, the lower the valence.
  9. 9. Holes
  10. 10. Figure 9.12. A valence electron jumping across the energy gap in pure silicon resulting in the generation of a free electron and hole in the crystal: (a) energy band model, (b) bond model.
  11. 11. Figure 9.13. Extrinsic n-type silicon doped with P donor atoms. (a) Energy band diagram and (b) Bond model.
  12. 12. Figure 9.14. Extrinsic p-type silicon doped with B acceptor atoms. (a) Energy band diagram and (b) Bond model.
  13. 13. 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.
  14. 14. Linear Combination of Atomic Orbitals LCAO
  15. 15. Density Functional Theory
  16. 16. 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 PRL’s 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.
  17. 17. 1 1( , ,..., , )N Ns s r r
  18. 18. Lecture 8: Introduction to Density Functional Theory Marie Curie Tutorial Series: Modeling Biomolecules December 6-11, 2004 Mark Tuckerman Dept. of Chemistry and Courant Institute of Mathematical Science 100 Washington Square East New York University, New York, NY 10003
  19. 19. Amorphous Semiconductors
  20. 20. Let’s estimate the mean free path, lmax=l. Let vmax=v. The carrier mobility is defined as μ= eτ/m*, where τ is the carrier relaxation time. Consider for mfree carrier=m*=m. We take l=v τ . and ½mv2=3/2 kT, all of which gives l=√(3kTm/e2 ) μ or l=0.7 μ where l is in angstrom units and μ is in cm2/v sec
  21. 21. Transport between “isolated” molecules
  22. 22. Excitons
  23. 23. A peculiarity in some One- dimensional systems: Peierls Distortion

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