LCAO Method - Solid State Physics - Lecture Slides, Slides of Solid State Physics

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The

Tightbinding(LCAO) Method^ A Realistic Treatment ofSemiconductor 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.

-^ 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 Schrödinger

Equation

That is, it would require us to do some

CHEMISTRY!!

-^ What follows is a quick, mostly qualitative review of elementary molecular physics.

Wavefunctions

Ψ^ & energy levels

ε^ for molecular

orbitals in a

Diatomic Molecule AB An^ s-electron

on atom

A^ bonding with an

s-electron

on atom

B.

Result:^

A^ ^ bonding orbital

(occupied; symmetric on exchange of

A^ &^ B)

Ψ^ = ( ψ

+^ ψ sA sB

A^ ^ antibonding orbital

(unoccupied; antisymmetric on exchange of

A^ &^ B)

Ψ^ = ( ψ

-^ ψ sA sB

ψ sA^

ψ sB

Ψ^ for^ σ Ψ^ for^ σ^ bonding orbital antibonding orbital ε^ for^ σ^ antibonding orbital^ ε^ for^ σ^ bonding orbital

ε^ for atomic

 For a s electrons homopolar molecule^ (A = B)

Wavefunctions

Ψ^ & energy levels

ε^ for molecular

orbitals in a

Diatomic Molecule AB An^ s-electron

on atom

A^ bonding with an

s-electron

on atom

B.

For a^ heteropolar molecule

(A^ ^ B) ε^ for atomic

 s^ electrons onatoms^ A

&^ B

Ψ^ for^ σ^ antibonding orbital Ψ^ for^ σ^ bonding orbital ε^ for^ σ^ antibonding orbital ε^ for^ σ^ bonding orbital

Result:^

A^ ^ bonding orbital

(occupied; symmetric on exchange of

A^ &^ B)

Ψ^ = ( ψ

+^ ψ sA sB

A^ ^ antibonding orbital

(unoccupied; antisymmetric on exchange of

A^ &^ B)

Ψ^ = ( ψ

-^ ψ sA sB

-^ Combine 2 atomic p

orbitalsx

& get

π^ bonding

&

π^ antibonding

molecular orbitals: π^ bonding:

Ψ^ = (

ψ +xA

ψ )/(2)xB^

½

(occupied; symmetric on exchange of

A^ &^ B)

π^ antibonding:

Ψ^ = (

ψ -^ xA

ψ )/(2)xB^

½

(unoccupied; antisymmetric on exchange of

A^ &^ B) docsity.com