Band to Band Transitions
– Wide band gap semiconductors
HgS (Vermillion)
CdS (Cadmium Yellow)
As2S3 (Realgar)
In these complexes the color comes from absorption of light
that leads to excitation of an electron from a filled valence
band to an empty conduction band.
Energy Bands in Extended Solids
Molecules:
Discrete Molecular
Orbitals
Extended Solids:
Continuous Bands
of MO’s
1
1 Na
atom
2 Na
atoms
4 Na
atoms
Most
Antibonding
Band of MO’s
Filled MO’s
Energy
Empty MO’s
1D Chain of Sodium Atoms
Most
Bonding
Large # Na
atoms
Metals and Semiconductors
Semiconductors
Energy
Band gap separates the filled
and empty states
Electrons have to be excited
across the band gap (or doping
has to occur) in order to
conduct electricity.
Band Gap (Eg)
Metals
Partially filled band
Electrons can easily move
between filled and empty MO’s.
This leads to high electrical and
thermal conductivity.
2
Tetrahedral Semiconductors (C, Si, Ge, Sn)
Conduction Band
(Empty)
Antibonding MO’s
E(σ
E(σ*)*)-E(σ
E(σ)
Band Gap
(Eg)
sp3 hybrid orbitals
Valence Band
(Filled)
Bonding MO’s
sp3 hybrid orbitals
Band Width, W
Absorbance
Band Gap Energy, Eg = E(σ*) – E(σ) – W
Conduction
Band
Eg
400 nm
Energy
Only visible light
with energy less
than Eg is reflected,
the remaining visible
light is absorbed
Wavelength
Energy
700 nm
Eg
UV
Valence
Band
IR
Band Gap (eV
(eV)) Color
> 3.0
White
3.0-2.4
Yellow
2.3-2.4
Orange
1.8-2.3
Red
< 1.8
Black
Example
ZnO
CdS
GaP
HgS
CdSe
3
Semiconductor Band Gap & Color
7
CdS
6
ZnS
ZnSe
Reflectance
5
CdSe
4
CdSe
Eg = 1.7 eV
3
2
1
0
200
300
400
500
600
700
800
900
Wavelength (nm)
ZnS
Eg = 3.6 eV
CdS
Eg = 2.4 eV
ZnSe
Eg = 2.6 eV
Band Gaps of the Group 14 Elements
Element
Lattice
Parameter
(Å)
Bond
Distance
(Å)
Band Gap,
eV (nm)
C
3.57
1.55
5.5 eV
(230 nm)
Si
5.43
2.35
1.1 eV
(1100 nm)
Ge
5.66
2.45
0.66 eV
(1900 nm)
α-Sn
6.49
2.81
< 0.1 eV
(12,000 nm)
Why does the band gap get smaller as we
move down the periodic table?
4
Spatial Overlap and Band Gap (Eg)
Conduction Band
Empty
Antibonding
Eg
Eg
Valence Band
Filled
Bonding
When we decrease the bond distance it increases the orbital overlap.
(We can estimate the overlap as proportional to d-2.5, where d is the
bond distance.) This has the following effect on the band gap:
•Primary Effect:
Effect: Increases bondingbonding-antibonding separation, E(σ
E(σ∗)-E(σ
E(σ) ↑
•Secondary Effect:
Effect: Increases the bandwidth, W ↑
•Net Effect:
Effect: Increases the Band gap, Eg ↑
Band Gaps of the Group 14 Elements
Compound
Lattice
Parameter
(Å)
Bond
Distance
(Å)
Δχ
Band Gap,
eV (nm)
Ge
5.66
2.45
0.0
0.66 eV
(1900 nm)
GaAs
5.65
2.45
0.4
1.42 eV
(890 nm)
ZnSe
5.67
2.46
0.8
2.70 eV
(460 nm)
CuBr
5.69
2.46
0.9
2.91 eV
(430 nm)
The band gap gets larger as the
electronegativity difference, Δχ,
between cation and anion increases.
5
Ionicity and Band Gap (Eg)
Conduction Band
(Antibonding)
Antibonding)
Eg
Eg
Valence Band
(Bonding)
What are the effects of increasing the electronegativity difference?
•Primary Effect:
Effect: Increases the separation of the valence and
conduction bands (the bonds become more ionic)
•Net Effect:
Effect: Increases the Band gap → Eg ↑
CdS
Structure: Wurtzite
Band Gap: 2.4 eV
Color: Yellow
Cd-S Dist: 2.53 Å
Δχ : 0.8
HgS
Increasing Bond Distance
Decreasing Δχ
Decreasing Eg
ZnS
Structure: Zinc Blende
Band Gap: 3.6 eV
Color: White
Zn-S Dist: 2.33 Å
Δχ : 0.9
Structure: Zinc Blende
Band Gap: 2.0 eV
Color: Red
Hg-S Dist: 2.53 Å
Δχ : 0.6
6
ZnS
ZnSe
Structure: Zinc Blende
Band Gap: 3.6 eV
Color: White
Zn-S Dist: 2.34 Å
Δχ : 0.9
Structure: Zinc Blende
Band Gap: 2.6 eV
Color: Yellow
Zn-Se Dist: 2.43 Å
Δχ : 0.8
CdS
CdSe
Structure: Wurtzite
Band Gap: 2.4 eV
Color: Yellow
Cd-S Dist.: 2.53 Å
Δχ : 0.8
Structure: Wurtzite
Band Gap: 1.7 eV
Color: Yellow
Cd-Se Dist: 2.63 Å
Δχ : 0.7
CdS-CdSe Solid Solutions
Solid Solution = Homogeneous Mixture
The S2- and Se2- ions are randomly distributed
on the anion sites. This differs from a
physical mixture of CdS and CdSe.
7
Cation Oxidation State & Color
PbO
Pb3O4
Pb2+
PbO2
Pb4+
[Xe]4f145d10
Battery Cathode
(Pb2+)2Pb4+O4
[Xe]4f145d106s2
Pigment (red lead)
SnS – Gray
SnI2 – Red-orange
SnS2 – Golden yellow
SnI4 – Brown-yellow
PbS – Black
PbI2 – Yellow
PbS2 – Does not exist
PbI4 – Does not exist
[CrO4]2-
t2 orbitals
(antibonding)
e orbitals
(antibonding)
CT
Energy
Metal (Cr) d-orbitals
Nonbonding
Oxygen 2p MO’s
e orbitals
(bonding)
t2 orbitals
(bonding)
PbCrO4
12 Oxygen 2p orbitals
(4 oxygens x 3 p orbitals)
CT ~ 3.3 eV (~375 nm)
Absorption = Violet
Color = Yellow
8
7
0.7
SrCrO4
SrMoO4
6
0.6
Reflectance
0.5
CrO4(2-)
4
0.4
3
0.3
2
0.2
1
0.1
0
Absorbance (CrO4)
PbMoO4
2-
PbCrO4
5
0
250
350
450
550
Wavelength (nm)
650
LMCT = Ligand to Metal Charge Transfer
ELMCT (CrO4)2- < ELMCT (MoO4)2ELMCT (CrO4)2- > ELMCT (SrCrO4) > ELMCT (PbCrO4)
Antibonding (e)
Mo dx2-y2, dz2
CT
Nonbonding O 2p
[MoO4]2Mo 4d orbitals are
larger than Cr 3d
orbitals
antibonding
interaction increases
Antibonding (e)
Cr dx2-y2, dz2
CT
Antibonding (e)
Mn dx2-y2, dz2
CT
Nonbonding O 2p
Nonbonding O 2p
[CrO4]2-
[MnO4]Cation oxidation
state increases
Cr(VI) → Mn(VII)
d-orbitals become
more electronegative
9
2nd & 3rd Row Transition Metals
eg (σ*)
2nd and 3rd row
transition metals
•d-orbitals are larger
•Metal-ligand antibonding
interactions are stronger
•eg (s*) orbitals are more
antibonding
•Low spin configurations
are always observed
[Co(H2O)6]3+
Δ = 2.25 eV
[Rh(H2O)6]3+
Δ = 4.23 eV
Tuning Charge Transfer Color
SrCrO4
Yellow
SrMoO4
White
SrSO4
White
PbCrO4
Yellow-Orange
PbMoO4
White
PbSO4
White
Ag2CrO4
Brown-Red
Ag2MoO4
Yellow
Ag2SO4
White
CuCrO4
Red-Brown
CuMoO4
Green
CuSO4
Blue
10