E

b

*

E

Looking onlyat thisregionin the Rectangle:

We generated a Band Diagram

If we include the relative number of orbitals, we make a Density of States DOS Diagram

We generated a Band Diagram

If we include the relative number of orbitals, we make a Density of States DOS Diagram

We do the same thing again, starting with isolated atoms,Then turn on the bonding, then increase the number of interactions.

Mn MnP

Polymeric unitP

An actual example, calculated using an M.O.theory

Mn MnP

P

Polymeric unit

%Mn in orbital (state)

%P in orbital (state)

Using Band Diagrams: Conductivity

Conductivity - in two flavors1. Electronic conduction - electrons move

• typical of metals; • example: Cu and Al very good• conductivity “predicted” by band diagrams

2. Ionic conduction - ions move• requires “ionic” material• requires defects: vacancy and interstitial

(Schottky and Frenkel types)• example: AgI2 and HgM2I4

MOT analogies with Band Diagram- HOMO / LUMO and type of reactivity- Valence Band / Conduction band and - DE and Band Gap

Emptybands

filledbands

conduction band

valence band

Metallic Conductor InsulatorSemi Conductor

LargeBand Gap

smallband gap

noband gap

conduction band

valence band

Metallic Conductor InsulatorSemi Conductor

LargeBand Gap

smallband gap

noband gap

More typically simplified to show only “frontier” bands:

E < 10 kJ/molE ~ 10 -100 kJ/mol E > 400 kJ/mol

Fermi level f

f

f

Pure Germanium

How Defects Improve Semi-Conduction

E ~ 0.66 eV

Gallium-Doped Ge

smallband gap

Ga moreElectropositive:

Adds “Orbitals” At HigherEnergyWith FewerElectrons

Pure GeBand Gap

Gallium-Doping creates positive holes, as an acceptor band:

A p-type semi-conductor

Pure Germanium

How Defects Improve Semi-Conduction

E = 0.66 eV

Arsenic-Doped Ge

smallband gap

As is moreElectronegative:

Adds “Orbitals” At Lower EnergyPartially Filledwith Electrons

Pure GeBand Gap

Arsenic-Doping creates negative holes, as a donor band

An n-type semi-conductor

How Defects Lead to DevicesPN Junctions = Diodes

Fermi level in n-type semi-conductor is at higher energy thanfor the p-type:

Spontaneous flow of electrons in one direction only.

Directional Flow of electrons --> current goes in one direction only

smallband gap

f

f

n-type p-type

In a pn junction,current spontaneouslyflows in one direction

How Defects Lead to Devices

Band Gap threshold can be exceeded by:

energy as light - photoconductivity

devices: - photocells, photovoltaic cells (GaAs) - solar cells (Si) - pn-junctions with suitable ef

make Light Emitting Diodes (LED)

energy as heat – thermoconductivity

devices: - thermistors

How Defects Lead to Devices: Photocopy (Xerox) Process(photolithography)

- uses photoconductivity of Selenium

Se

Se

Se

paper w/ image

Ink (toner)

How Defects Lead to Devices: Thermochromic Materials

- example based on HgM2I4 materials

Replace S with I,Zn (at vertices) with Hg,Zn (in middle) with Cu

Replace S with I,Zn (at vertices) with HgZn (in middle) with Ag

PrototypeCubic ZnS (zinc blende),two adjacent cells

How Defects Lead to Devices: Thermochromic Materials

- example based on HgM2I4 materials

- adding energy as heat creates defects Cu(+) vacancies (Schottky defects) and interstital sites (Frenkel defects)

- defects change band gap, change color, change conductivity