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


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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.

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

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The tightbinding lcao method a realistic treatment of semiconductor materials

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


Tightbinding method realistic treatment for semiconductor materials

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.


The tightbinding lcao method a realistic treatment of semiconductor materials

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


The tightbinding lcao method a realistic treatment of semiconductor materials

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


The tightbinding lcao method a realistic treatment of semiconductor materials

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


The tightbinding lcao method a realistic treatment of semiconductor materials

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)


The tightbinding lcao method a realistic treatment of semiconductor materials

  • 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)


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