polymer compositeband theory-2

aTypical metal with a partially filled bands.. b Metal generated by the overlap of filled and empty bands.. As the temperature increases, then the upper band may become thermally populat

=

Ψ

s r

s r s

c y

Crystal orbitals

( irk a isk a )

cr,s = exp x + y

( 2 2)1 / 2

/ 2 /

λ

k = (kx,ky) the wave vector of electron

showing 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 = k x , k y < + π/a

Two-dimensional lattice

Graphite

(a) Molecular orbitals of C 60 (b) Band structure of K 3 C 60 (c) Corresponding density-of –states curves.

Total density of states for

NbO.The Fermi level

corresponds to a d3

electron count.

Band theory diagrams

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

Density of state

= dn/dE

n = number of states

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/ )

Fermi distribution at T> 0 for (a) Intrinsic semiconductor, (b)

Fermi distribution and the band gap

(a) population (b)

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

(b) p-type, e.g Ga doped Si.

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

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

27

• 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

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.

• Peak shift- charging effect

• Broadening- molecular solid bonding and relaxation

effects.

E

Eg

Decrease in overlapping

of the d-orbitals Metal oxides

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

metallicsemiconductor

Metal sulfides

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

Physics, 2005, vol 1

35

FIG 8: Band structure diagrams of (a) cubic

WO3 and (b) NaWO3

FIG 7: Calculated density of states for cubic tungsten

bronzes, 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.

Figure 1: The color of Na x WO 3 with different x values (degree of reduction of W).

Electrochromic material - color change by applying electric field

semiconducting ⇒ metallic

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

Diffuse reflectance spectra of nanocomposite materials: (a) TiO 2 , (b) K 2 Ti 4 O 9 , (c)

(C 3 H 7 NH 3 ) 2 Ti 4 O 9 , (d) C 6 H 12 (NH 3 ) 2 Ti 4 O 9 and (e) (Fe 3 (CH 3 COO) 7 OH)Ti 4 O 9 .

Absorption edges and band gap energies of nanocomposites and precursors

• high refractive index (n > 2.5, comparing to

Photocatalysis over a Semiconductor

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

Band gap of TiO2

~ 3.2 eV

J AM CHEM SOC 2004, 126, 5851-5858

Electronic Band Structure of Titania Semiconductor

Nanosheets Revealed by Electrochemical and

Photoelectrochemical Studies

p- n junction Excess

electron

excesshole

No current flows

(reverse bias)

Current flows

(forward bias)

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

Photovoltaic Cell

Simple PV Systems PV with Battery Storage

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)

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

Large Area Pulsed Solar SimulatorVisible

Solar Spectrum

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

A newly established indium gallium nitride system of alloys

(In 1-x Ga x N) covers the full solar spectrum