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.
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
