1

a1, x

a2, yΓ

X M

X a2*, ky

a1*, kx

kx = 0, ky = 0

Γ

kx = 0.5 a1*, ky = 0

X

kx = 0, ky = 0.5 a2*

X

kx = 0.5 a1*, ky = 0.5 a2*

M

kx = 0.25 a1*, ky = 0 kx = 0, ky = 0.25 a2* kx = 0.25 a1*, ky = 0.25 a2*

Two-dimensional lattice

2

∑=Ψsr

srsr yxcyx,

,, ),(),( χ

Crystal orbitals

( )aiskairkc yxsr += exp,

3

( ) 2/122/2/2 yx kkk +== ππλ

k = (kx,ky) the wave vector of electronshowing the direction and length of the wave

For square array with N atoms in each direction(kx,ky) = (2π/Na) (p,q), p, q are integers

-π/a = kx, ky < + π/a

E(k) = α + 2β{cos(kxa + cos(kya)}

Two-dimensional lattice

4

5

6

7

Graphite

8

9

10

(a) Molecular orbitals of C60. (b) Band structure of K3C60.

(c) Corresponding density-of –states curves.

11

Total density of states for NbO.The Fermi level corresponds to a d3

electron count.

12diamond (C), silicon (Si), germanium (Ge), Gray tin (Sn)

Band theory diagrams

13

Band Structure of Insulatorsand Semiconductors

> 6eV= 3eV

14

Density of states in (a) metal, (b) semimetal (e.g. graphite).

(a) (b)

Density of state= dn/dE

n = number of states

15

Fermi distribution (a) at T= 0, and (b) at T> 0. The population decays exponentially at energies well above the Fermi level.

Population,1

1/)( +

= − kTEeP µ

Fermi level- the highest occupied orbital at T= 0

(a) (b)

where, µ = chemical potential

When E= µ, P= 1/2

16

Fermi distribution at T> 0 for (a) Intrinsic semiconductor, (b)Fermi distribution and the band gap

(a) (b)population

17

Extrinsic semiconductor: (a) n-type, e.g. P doped Si(b) p-type, e.g. Ga doped Si.

18

19

20

21

Control of the electrical properties of solids by the location and filling of their energy bands. (a)Typical metal with a partially filled bands. (b) Metal generated by the overlap of filled and empty bands. (c) Small gap between filled and empty bands. As the temperature increases, then the upper band may become thermally populated, a semiconductor. (d) Similar to (c) except that population of the upper band arises through photoexcitation. (e) A large gap between the two bands, an insulator. (f) Two bands just touch , a semimetal.

Electrical Properties

22

23

24

25

26

The Photoelectric Effect• Albert Einstein considered electromagnetic energy to be

bundled into little packets called photons.Energy of photon = E = hv

Where, h = Planck constant ( 6.62 x 10-34 J s ) v = frequency (Hz) of the radiation

– Photons of light hit surface electrons and transfer their energy

hv = B.E. + K.E.

– The energized electrons overcome their attraction and escape from the surface

• Photoelectron spectroscopy detects the kinetic energy of the electron escaped from the surface.

hve- (K.E.)

27

28

• X-ray Photoelectron Spectroscopy (XPS) - using soft x-ray (200-2000 eV) radiation to

examine core-levels.

• Ultraviolet Photoelectron Spectroscopy (UPS) - using vacuum UV (10-45 eV) radiation to examine

valence levels.

Photoelectron spectroscopy- a single photon in/ electron out process

29

He(I) UPS spectrum of HCl gas.

1. Loss of a bonding electron decreases the bond order, increasing the bond length in the resulting cation compared to the parent molecule.

2. Loss of a nonbonding electron has no effect on bond order or bond length.

3. Loss of an antibonding electron increases the bond order, decreasing the bond length of the cation compared to the parent molecule.

30

•Peak shift- charging effect•Broadening- molecular solid bonding and relaxation effects.E

31

Eg

Decrease in overlapping of the d-orbitals

Metal oxides

32

Overlapping of d-orbitals of early transition metal elements in the Oxide structures

Energy level diagram of early transition metal elements in the Oxide structures

33

metallic

semiconductor

Metal sulfides

34

Density-functional studies of tungsten trioxide, tungsten bronzes, and related systems

Physics, 2005, vol. 1

35

36

FIG. 8: Band structure diagrams of (a) cubic WO3 and (b) NaWO3.

37

FIG. 7: Calculated density of states for cubic tungstenbronzes, MWO3, near the Fermi level: (a) WO3, (b) HWO3,(c) LiWO3, (d) NaWO3, (e) KWO3, (f) RbWO3, (g) CsWO3.The Fermi level is indicated in each case.

38

39

Figure 1: The color of Na xWO3 with different x values (degree of reduction of W).

Electrochromic material - color change by applying electric field

semiconducting ⇒ metallic

40

The measurement of absorption edge and band gap properties of novel nanocomposite materials

T. Nguyena, A. R. Hind, Varian Australia

• crystalline phases of TiO2

- anatase, rutile, brookite

• layered titanates- K2Ti3O7, K2Ti4O9

41

Diffuse reflectance spectra of nanocompositematerials: (a) TiO2, (b) K2Ti4O9, (c) (C3H7NH3)2Ti4O9, (d) C6H12(NH3)2Ti4O9 and (e) (Fe3(CH3COO)7OH)Ti4O9.

Absorption edges and band gap energies of nanocomposites and precursors.

42

43

44

• high refractive index (n > 2.5, comparing to 1.45 of SiO2)

- pigments- photonic crystals

• n-type semiconductor (Eg ~ 3.2 eV)- photocatalysts

• reducible center- catalysts or catalyst supports

Titanium(IV) OxideTitanium(IV) Oxide-- propertiesproperties

45

Photocatalysis over a Semiconductor Oxide such as TiO2

Amy Linsebigler et al., Chem. Rev., 95, 735, 1995.

Band gap of TiO2~ 3.2 eV

46

TiO2hν h + e

O2 (ads)O2

+ - -. H+

OOH

.

.

.-O2

OOH. - + O2

+HH2O2hνOH

H2O

Scheme II Possible pathways for formation of hydroxy radical.

47J. AM. CHEM. SOC. 2004, 126, 5851-5858

Electronic Band Structure of Titania SemiconductorNanosheets Revealed by Electrochemical and Photoelectrochemical Studies

48

49

p- n junction Excesselectron

excesshole

No current flows (reverse bias)

Current flows (forward bias)

50

51

Photovoltaic Cell

• A photovoltaic cell, or solar cell, is a semiconductor device that converts light to electricity.

• The cell consists of a thin layer of p-type semiconductor, such as Si doped with Al, in contact with an n-type semiconductor, such as Si doped with P.

• The p-type semiconductor in the solar cell must be very thin - about 1 x 10-4 cm (1 µm).

• This is to reduce the tendency for conduction electrons produced by sunlight to be captured by positive holes and immobilized in covalent bonds.

52

Photovoltaic Cell

53

Simple PV Systems PV with Battery Storage

54

PV Connected to Utilities

This electric vehicle recharging station in southern Florida is powered by a grid-connected PV array mounted on the roof. When no vehicles need charging, power from the modules is transferred to the utility line. (Photo: University of South Florida)

55

Applications and Uses

PV cells and modules are very reliable in space and on the earth. The Hubble space telescope (pictured here) and virtually all communications satellites are powered by photovoltaic technology.

56

Large Area Pulsed Solar Simulator

Visible

Solar Spectrum

57

Light emitting diodes (LED) made of indium gallium nitride (Eg = 0.7 ~ 3.4 eV) held clues to the potential new solar cell material by W. Walukiewicz at Berkerly

In search of better efficient Semiconductors

58

A newly established indium gallium nitride system of alloys (In1-xGaxN) covers the full solar spectrum