1 / 7

The Tightbinding (LCAO) Method A Realistic Treatment of Semiconductor Materials!

The Tightbinding (LCAO) Method A Realistic Treatment of Semiconductor Materials!. Tightbinding Method Realistic Treatment for Semiconductor Materials!. For most of the materials of interest , in the isolated atom, the valence electrons are in s & p orbitals.

marvin
Download Presentation

The Tightbinding (LCAO) Method A Realistic Treatment of Semiconductor Materials!

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. The Tightbinding (LCAO) MethodA Realistic Treatment of Semiconductor Materials!

  2. Tightbinding MethodRealistic Treatment for Semiconductor Materials! • For most of the materials of interest, in the isolated atom, the valence electrons are in s & p orbitals. • Before at the bands in the solid, lets first briefly & QUALITATIVELY look at the molecular orbitals for the bonding & antibonding states. • A Quantitative treatment would require us to solve the Molecular SchrödingerEquation That is, it would require us to do some CHEMISTRY!! • What follows is a quick, mostly qualitative review of elementary molecular physics.

  3. s orbitalsarespherically symmetric! Shapes of charge (& probability) densities |ψ|2 for atomic s & p orbitals: p orbitalshavedirectional lobes! The pylobeis along they-axis The pxlobeis along thex-axis The pzlobeis along thez-axis

  4. Ψ forσ antibonding orbital Wavefunctions Ψ & energy levels εfor molecular orbitals in aDiatomic Molecule AB ψsA ψsB An s-electron on atom A bonding with an s-electron on atom B. Ψ forσbonding orbital For ahomopolar molecule (A = B) ε forσ antibonding orbital ε for atomic  s electrons ε for σbonding orbital Result: A  bonding orbital (occupied; symmetric on exchange of A & B) Ψ= (ψsA+ ψsB)/(2)½ A  antibonding orbital(unoccupied; antisymmetric on exchange of A & B) Ψ= (ψsA - ψsB)/(2)½

  5. Wavefunctions Ψ & energy levels εfor molecular orbitals in aDiatomic Molecule AB Ψ forσ antibonding orbital An s-electron on atom A bonding with an s-electron on atom B. Ψ forσbonding orbital For aheteropolar molecule (A  B) ε forσ antibonding orbital ε for atomic s electrons on atoms A & B ε for σbonding orbital Result: A  bonding orbital (occupied; symmetric on exchange of A & B) Ψ= (ψsA+ ψsB)/(2)½ A  antibonding orbital(unoccupied; antisymmetric on exchange of A & B) Ψ= (ψsA - ψsB)/(2)½

  6. Charge (probability) densities |Ψ|2 for molecular orbitals in a Diatomic Molecule AB An s-electron on atom A bonding with an s-electron on atom B to get  bonding(+) &  antibonding(-) molecular orbitals.  bonding orbital: Ψ= (ψsA+ ψsB)/(2)½ (occupied; symmetric on exchange of A & B)  antibonding orbital Ψ= (ψsA - ψsB)/(2)½ (unoccupied; antisymmetric on exchange of A & B)

  7. Combine 2 atomic px orbitals & get π bonding & π antibonding molecular orbitals: π bonding:Ψ = (ψxA+ ψxB)/(2)½ (occupied; symmetric on exchange of A & B) π antibonding:Ψ = (ψxA- ψxB)/(2)½ (unoccupied; antisymmetric on exchange of A & B)

More Related