E
s*
sb
E
Looking
only
at
this
region
in 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.
P
Mn
Mn
P
Polymeric unit
An actual example, calculated using an M.O.theory
%Mn in orbital (state)
%P in orbital (state)
P
Mn
Mn
P
Polymeric unit
Using Band Diagrams: Conductivity
Conductivity - in two flavors
1. 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
Metallic Conductor
Semi Conductor
Insulator
Empty
bands
conduction band
valence band
filled
bands
no
band
gap
small
band
gap
Large
Band
Gap
More typically simplified to show only “frontier” bands:
Metallic Conductor
Semi Conductor
Insulator
conduction band
Fermi level
ef
no
band
gap
valence band
DE < 10 kJ/mol
ef
small
band
gap
DE ~ 10 -100 kJ/mol
ef
Large
Band
Gap
DE > 400 kJ/mol
How Defects Improve Semi-Conduction
Pure Germanium
Gallium-Doped Ge
Ga more
Electropositive:
Pure Ge
Band
Gap
small
band
gap
Adds “Orbitals”
At Higher
Energy
With Fewer
Electrons
Gallium-Doping creates positive holes,
as an acceptor band:
DE ~ 0.66 eV
A p-type semi-conductor
How Defects Improve Semi-Conduction
Pure Germanium
Arsenic-Doped Ge
As is more
small Electronegative:
Pure Ge
Band
Gap
band
gap Adds “Orbitals”
At Lower
Energy
Partially Filled
with Electrons
Arsenic-Doping creates negative holes,
as a donor band
DE = 0.66 eV
An n-type semi-conductor
How Defects Lead to Devices
PN Junctions = Diodes
n-type
p-type
Fermi level in n-type
semi-conductor is at
higher energy than
for the p-type:
ef
ef
small
band
gap
Spontaneous flow of electrons
in one direction only.
Directional Flow of electrons -->
current goes in one direction only
In a pn junction,
current spontaneously
flows 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)
Se
- uses photoconductivity of Selenium
paper w/ image
Se
Ink (toner)
Se
How Defects Lead to Devices: Thermochromic
Materials
- example based on HgM2I4 materials
Prototype
Cubic ZnS (zinc blende),
two adjacent cells
Replace S with I,
Zn (at vertices) with Hg,
Zn (in middle) with Cu
Replace S with I,
Zn (at vertices) with Hg
Zn (in middle) with Ag
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