optical properties of thin film

1

Kurdistan Iraqi Region Ministry of Higher Education Sulaimani University College of Science Physics Department

Optical Properties of Thin Film

Prepared by

Rnjdar Rauff M.

Ali Bakr Ali

Supervised by

Dr. Omed Gh. Abdullah

2005-2006

2

Contents Chapter One: Basic Concepts. 1.1 Introduction. 1.2 The Structure of Solid Material. 1.2.1 Crystalline Materials. 1.2.2 Amorphous Materials. 1.3 Differences between crystalline and amorphous solids 1.4 Classification of Amorphous Materials. 1.5 Thin film. 1.6 Thin film deposition. 1.6.1 Chemical deposition. 1.6.2 Physical deposition. Chapter Two: Band Structure. 2.1 Introduction. 2.2 Band Theory. 2.3 Density of State. 2.4 Band Structure of Crystalline Materials. 2.5 Band Structure of Amorphous Materials. 2.5.1 The Davis-Mott Model. 2.5.2 The Cohen Fritzchc Ovshinsky Model (CFO). 2.5.3 Marshall-Owen Model. Chapter Three: Optical properties. 3.1 Introduction. 3.2 Optical properties of amorphous and crystal materials. 3.3 Optical absorption. 3.4 Processes of absorption in semiconductors. 3.5 Optical properties of thin film. 3.6 Absorption Edge. Chapter four: Calculations. 4.1 Introduction. 4.2 Optical energy for allowed direct transitions. 4.3 Optical energy for forbidden direct transitions. 4.4 Optical energy for allowed indirect transitions. 4.5 Optical energy for forbidden indirect transitions. 4.6 Width of the tail of localized states. References. Appendixes.

3

Chapter One

Basic Concepts

1.1 Introduction:

A crystalline solid exhibits translational invariance so that the atoms arrange

themselves in a regular pattern, with a specific lattice spacing between

neighboring atoms, and the same number of nearest neighbor atoms for each

atom. In the amorphous state the number of neighboring atoms varies, and there

is no regular pattern over long distances, although varying amounts of local order

may be present. The latter description is similar at first glance to a liquid at a

given time, but an amorphous state differs from a liquid in detail. Atoms in the

amorphous state do not move far from their equilibrium sites, whereas in a liquid

such movement is common. If a liquid is cooled instantaneously (quenched), it

will usually go to an amorphous state. In contrast, crystalline states are obtained

by slow cooling, with frequent small heating during the cooling process to

remove fault lines. This process is known as annealing.

1.2 The Structure of Solid material:

Solids can fall into one of two categories; those which possess long-range-

order in the disposition of their atoms, and those which do not. The first type of

material is known as a crystal, while the second is termed an amorphous

material.

That is, in a crystal the sites of atoms are determined simply by repeating

some sub-unit of the crystal at regular intervals to fill all space. Mathematically

we describe a crystal in terms of a regularly arranged set of points whose

distribution throughout space looks identical from any point in the set (the

4

lattice), and a prescription telling us how many atoms of each type to associate

with each point and where they should go in relation to that point (the basis).

For example, the sodium chloride crystal structure is based upon the face

centre cubic lattice in which the lattice points are arranged as if at the corners of

an array of adjoining cubes, but with an additional lattice point at the centre of

each face. The basis then dictates that each lattice site be given two atoms (one

Sodium and one chlorine) separated from each other by a distance equal to half

the cube side length.

Different materials have different underlying lattices and different kinds of

basis. There are an infinite number of possible atomic bases, but symmetry

dictates that there are only 14 possible different types of lattice (in 3D), and that

these can be further categorised into just 7 different types of symmetry. The 14

different lattices are known as Bravais lattices, and the 7 different symmetry

groups are known as the crystal systems.

Crystals are the most widely studied solids from the theoretical point of

view, because we can learn about the behaviour of an entire crystal just by

studying a very small portion (remember, the structure simply repeats itself at

regular intervals). Furthermore, crystals are extremely important in everyday life,

in industry, in science and technology: metals are crystalline, for example. In

recent years, amorphous materials, which are very important in the real world,

have attracted much attention, particularly with regard to their structural,

electrical, optical, and magnetic properties. It is not easy to visualize or illustrate

the geometrical arrangement of atoms in an amorphous solid, so that from the

theoretical point the studies of these materials are much more difficult.

5

1.2.1 Crystalline Materials:

More than 90% of naturally occurring and artificially prepared solids are

crystalline. Minerals, sand, clay, limestone, metals, carbon (diamond and

graphite), salts (NaCl, KCl etc.), all have crystalline structures. A crystal is a

regular, repeating arrangement of atoms or molecules. The majority of solids,

including all metals, adopt a crystalline arrangement because the amount of

stabilization achieved by anchoring interactions between neighboring particles is

at its greatest when the particles adopt regular (rather than random)

arrangements.

In the crystalline arrangement, the particles pack efficiently together to

minimize the total intermolecular energy.

Fig (1-1): Schematic illustration of the difference between

a crystalline and amorphous of SiO2.

6

Crystal structures may be conveniently specified by describing the

arrangement within the solid of a small representative group of atoms or

molecules, called the ‘unit cell.’ By multiplying identical unit cells in three

directions, the location of all the particles in the crystal is determined.

The simplest crystalline unit cell to picture is the cubic, where the atoms are

lined up in a square, 3D grid. The unit cell is simply a box with an atom at each

corner. Simple cubic crystals are relatively rare, mostly because they tend to

easily distort. However, many crystals form body-centered-cubic (bcc) or face-

centered-cubic (fcc) structures, which are cubic with either an extra atom

centered in the cube or centered in each face of the cube. Most metals form bcc,

fcc or Hexagonal Close Packed (hpc) structures; however, the structure can

change depending on temperature.

Crystalline structure is important because it contributes to the properties of

a material. For example, it is easier for planes of atoms to slide by each other if

those planes are closely packed. Therefore, lattice structures with closely packed

planes allow more plastic deformation than those that are not closely packed.

Additionally, cubic lattice structures allow slippage to occur more easily than

non-cubic lattices. This is because their symmetry provides closely packed

planes in several directions. A face-centered cubic crystal structure will exhibit

more ductility (deform more readily under load before breaking) than a body-

centered cubic structure. The bcc lattice, although cubic, is not closely packed

and forms strong metals.

1.2.2 Amorphous Materials:

An amorphous solid is a solid in which there is no long-range order of the

positions of the atoms. (Solids in which there is long-range atomic order are

called crystalline solids.) Most classes of solid materials can be found or

prepared in an amorphous form.

7

A solid substance with its atoms held apart at equilibrium spacing, but with

no long-range periodicity in atom location in its structure is an amorphous solid.

Examples of amorphous solids are glass and some types of plastic. They are

sometimes described as super cooled liquids because their molecules are

arranged in a random manner some what as in the liquid state.

1.3 Differences between crystalline and amorphous solids:

Although the heart of the difference between crystalline and amorphous

solids occurs on the atomic level, there are several physical characteristics which

can often indicate one type or the other. Crystalline substances have regular

shapes, and form flat faces when they are cleaved or broken. When they are

heated, crystalline solids melt at a definite temperature (unless they decompose

before melting). The regularity of crystalline solids is due to the arrangement of

structural units into an orderly array or lattice.

The x-ray diffraction pattern for single crystal is regular arranged pattern.

While for amorphous several concentric broad and diffuse rings are obtained, as

shown in figure (1-2).

8

1.4 Classification of Amorphous Materials:

Semiconductors are used in a wide variety of applications. Most practically

useful semiconductors are made from crystalline materials. However, some non-

crystalline materials also have useful semiconducting properties. There are two

classes of amorphous semiconductors most commonly investigated: amorphous

germanium, silicon and carbon with tetrahedral coordination and also amorphous

semiconductors containing one or more of the chalcogenide elements, S, Se or

Te. For tetrahedral amorphous materials, the covalent network is macroscopically

extended in three dimensions. In other words, paths of covalent bonds connect

every atoms with every other atom in a macroscopic sample of the material.

However, some solids are representable by disconnected covalent networks: they

are molecular solids. Molecular solids are characterized by the coexistence of

strong (primarily covalent) and weak (intermolecular, primarily ``van der

Waals’’) forces. The chalcogen crystal materials are notable among the molecular

solids. It is very important to notice that molecular solids are naturally classified

into several distinct categories on the basis of the molecular network

dimensionality

1.5 Thin film:

Thin films are material layers of about 1 µm thickness. Electronic

semiconductor devices and optical coatings are the main applications benefiting

from thin film construction. Some work is being done with ferromagnetic thin

films as well for use as computer memory. Ceramic thin films are also in wide

use. The relatively high hardness and inertness of ceramic materials make this

type of thin coating of interest for protection of substrate materials against

corrosion, oxidation and wear. In particular, the use of such coatings on cutting

tools may extend the life of these items by several orders of magnitude.

App

• m

• m

• g

• t

p

• o

• c

• w

Spec

•

•

•

•

•

prop

Typi

•

•

•

plication of

microelec

magnetic

gas sensor

tailored m

properties

optics-ant

corrosion

wear resis

cial Prope

Different

not fully

under str

different

quasi - tw

strongly

This wil

perties.

ical steps

Emission

Transpor

Condens

Fig (1

of thin film

tronics-ele

sensors - s

rs, SAW d

materials-l

s

ti-reflectio

protection

stance

erties of T

t from bul

dense

ress

t defect str

wo dimens

influence

ll change

in making

n of partic

rt of partic

sation of p

1-3): Simp

ms:

ectrical co

sense I, B

devices

layer very

on coating

n

Thin Films

lk materia

ructures fr

sional (ve

d by surfa

electrica

g thin film

cles from s

cles to sub

particles on

ple mode f

9

onductors,

or change

y thin fi

s

s:

als, thin fil

rom bulk

ry thin film

ace and int

al, magnet

ms:

source ( he

bstrate (fre

n substrate

for deposit

, electrical

es in them

lms to d

lms may b

ms)

terface eff

tic, optica

eat, high v

ee vs. direc

e.

tion a thin

l barriers,

m

develop m

be:

fects

al, therma

voltage . .

cted)

n film.

diffusion

materials

al, and m

.)

barriers...

with new

mechanica

.

w

l

10

1.6 Thin film deposition:

Thin film deposition is any technique for depositing a thin film of material

onto a substrate or onto previously deposited layers. "Thin" is a relative term, but

most deposition techniques allow layer thickness to be controlled within a few

tens of nanometers, and some allow one layer of atoms to be deposited at a time.

Deposition techniques fall into two broad categories, based on whether they are

understood in terms of chemistry, or of physics.

1.6.1 Chemical deposition:

Here, a fluid precursor undergoes a chemical change at a solid surface,

leaving a solid layer. An everyday example is the formation of soot on a cool

object when it is placed inside a flame. Since the fluid surrounds the solid object,

deposition happens on every surface, with little regard to direction; thin films

from chemical deposition techniques tend to be conformal, rather than

directional.

Chemical vapor deposition (CVD) is a chemical process for depositing thin

films of various materials. In a typical CVD process the substrate is exposed to

one or more volatile precursors, which react and/or decompose on the substrate

surface to produce the desired deposit. CVD is widely used in the semiconductor

industry, as part of the semiconductor device fabrication process, to deposit

various films including: polycrystalline, amorphous, and epitaxial silicon, SiO2,

silicon germanium, tungsten, silicon nitride, silicon oxynitride, titanium nitride,

and various high-k dielectrics. The CVD process is also used to produce

synthetic diamonds. A number of forms of CVD are in wide use and are

frequently referenced in the literature.

11

• Atmospheric pressure CVD (APCVD) - CVD processes at atmospheric

pressure.

• Atomic layer CVD (ALCVD) - a CVD process in which two

complementary precursors (eg. Al(CH3)3 and H2O) are alternatively

introduced into the reaction chamber. Typically, one of the precursors will

adsorb onto the substrate surface, but cannot completely decompose without

the second precursor. The precursor adsorbs until it saturates the surface and

further growth cannot occur until the second precursor is introduced. Thus

the film thickness is controlled by the number of precursor cycles rather

than the deposition time as is the case for conventional CVD processes. In

theory ALCVD allows for extremely precise control of film thickness and

uniformity.

• Low-pressure CVD (LPCVD)-CVD processes at subatmospheric pressures.

Reduced pressures tend to reduce unwanted gas phase reactions and

improve film uniformity across the wafer. Most modern CVD process are

either LPCVD or UHVCVD.

• Metal-organic CVD (MOCVD) - CVD processes based on metal-organic

precursors, such as Tantalum Ethoxide, Ta(OC2H5)5, to create TaO.

• Plasma-enhanced CVD (PECVD) - CVD processes that utilize a plasma to

enhance chemical reaction rates of the precursors. PECVD processing

allows deposition at lower temperatures, which is often critical in the

manufacture of semiconductors.

• Rapid thermal CVD (RTCVD) - CVD processes that use heating lamps or

other methods to rapidly heat the wafer substrate. Heating only the substrate

rather than the gas or chamber walls helps reduce unwanted gas phase

reactions that can lead to particle formation.

• Remote plasma-enhanced CVD (RPECVD) - Similar to PECVD except

that the wafer substrate is not directly in the plasma discharge region.

12

Removing the wafer from the plasma region allows processing temperatures

down to room temperature.

• Ultra-high vacuum CVD (UHVCVD) - CVD processes at very low

pressures, typically in the range of a few to a hundred millitorrs.

1.6.2 Physical deposition:

Physical deposition uses mechanical or thermodynamic means to produce a

thin film of solid. Since most engineering materials are held together by

relatively high energies, and chemical reactions are not used to store these

energies, commercial physical deposition systems tend to require a low-pressure

vapor environment to function properly; most can be classified as physical vapor

deposition. The material to be deposited is placed in an energetic, entropic

environment, so that particles of material escape its surface. The whole system is

kept in a vacuum deposition chamber, to allow the particles to travel as freely as

possible. Since particles tend to follow a straight path, films deposited by

physical means are commonly directional, rather than conformal.

Some examples of physical deposition are given below:

1- Thermal evaporator:

Uses an electric resistance heater to melt the material and raise its vapor

pressure to a useful range. This is done in a high vacuum, both to allow the vapor

to reach the substrate without reacting with or scattering against other gas-phase

atoms in the chamber, and reduce the incorporation of impurities from the

residual gas in the vacuum chamber. Obviously, only materials with a much

higher vapor pressure than the heating element can be deposited without

contamination of the film. The source of vaporized material is usually one of two

types.

13

The simpler, older type relies on resistive heating of a thin folded strip

(boat) of tungsten, tantalum, or molybdenum by a high direct current. Small

amounts of the coating material are loaded into the boat. A high current (10-100

A) is passed through the boat, which undergoes resistive heating. The coating

material is then vaporized thermally. Because the chamber is at a greatly reduced

pressure, there is a very long mean free path for the free atoms or molecules, and

the heavy vapor is able to reach the moving substrates at the top of the chamber.

Here it condenses back to the solid state, forming a thin, uniform film.

Several problems are associated with thermal evaporation. Some useful

substances can react with the hot boat, which can cause impurities to be

deposited with the layers, changing optical properties. In addition, many

materials, particularly metal oxides, cannot be vaporized this way, because the

material of the boat (tungsten, tantalum, or molybdenum) melts at a lower

temperature. Instead of a layer of zirconium oxide, a layer of tungsten would be

deposited on the substrate.

2- Electron beam evaporator:

Fires a high-energy beam from an electron gun to boil a small spot of

material; since the heating is not uniform, lower vapor pressure materials can be

deposited.

3- Sputtering:

Sputtering is a physical process whereby atoms in a solid target material are

ejected into the gas phase due to bombardment of the material by energetic ions

as shown in figure (1-4). It is commonly used for thin-film deposition, as well as

analytical techniques.

14

Sputtering is a process used to deposit a very thin film onto a substrate

whilst in a vacuum. A high voltage is passed across low pressure gas to create a

plasma of electrons and ions in a high energy state. The ions hit a target of the

desired coating material and cause atoms from that material to be ejected and

bond with the substrate. Sputtering is largely driven by momentum exchange

between the ions and atoms in the material, due to collisions. The process can be

thought of as atomic billiards, with the ion (cue ball) striking a large cluster of

close-packed atoms (billiard balls). Although the first collision pushes atoms

deeper into the cluster, subsequent collisions between the atoms can result in

some of the atoms near the surface being ejected away from the cluster. The

number of atoms ejected from the surface per incident ion is called the sputter

yield and is an important measure of the efficiency of the sputtering process.

Other things the sputter yield depends on are the energy of the incident ions,

the masses of the ions and target atoms, and the binding energy of atoms in the

solid.

The target can be kept at a relatively low temperature, since the process is

not one of evaporation, making this one of the most flexible deposition

techniques. It is especially useful for compounds or mixtures, where different

components would otherwise tend to evaporate at different rates. The schematic

of sputter deposition are shown in figure (1-5).

15

Fig (1-4): The impact of an atom or ion on a surface produces sputtering from the surface as a result of the momentum transfer from the in-coming particle. Unlike many other vapour phase techniques there is no melting of the material.

Fig (1-5): Sputter deposition process.

4- Pulsed laser deposition:

Pulsed laser deposition is a thin film deposition technique. It uses a pulsed

laser beam to carry out a process of ablation in order to deposit materials as thin

films. Generally, a high vacuum is necessary for their operation. Pulses of

focused laser light transform the target material directly from solid to plasma; the

resulting plume of plasma is thrown perpendicularly away from the surface by

thermal expansion. As expansion cools the plume, it will revert to a gas, but

16

sufficiently high vacuum will allow momentum to carry this gas to the substrate,

where it condenses to a solid state. Pulsed laser deposition systems work by an

ablation process. Pulses of focused laser light to transform the target material

directly from solid to plasma; this plasma usually reverts to a gas before it

reaches the substrate.

Technique Advantages Disadvantages

Sputtering

Dense films

Good uniformity

Wide range of inorganic materials

relatively slow

Thermal Evaporation Fast

Relatively simple

Limited range of materials

Low density films without

ion or plasma assist

e-Beam Evaporation Fast

Wide range of inorganic materials high voltages

CVD Gives good control of coating

chemistry

Difficult to scale

Often uses hazardous liquids

or gases

17

Chapter Two Band Structure

2-1 Introduction:

Thin films science and technology plays an important role in the high-tech

industries. Thin film technology has been developed primarily for the need of the

integrated circuit industry. The demand for development of smaller and smaller

devices with higher speed especially in new generation of integrated circuits

requires advanced materials and new processing techniques suitable for future

giga scale integration (GSI) technology. In this regard, physics and technology of

thin films can play an important role to acheive this goal. The production of thin

films for device purposes has been developed over the past 40 years. Thin films

as a two dimensional system are of great importance to many real-world

problems. Their material costs are very small as compared to the corresponding

bulk material and they perform the same function when it comes to surface

processes. Thus, knowledge and determination of the nature, functions and new

properties of thin films can be used for the development of new technologies for

future applications.

Thin film technology is based on three foundations: fabrication,

characterization and applications. Some of the important applications of thin

films are microelectronics, communication, optical electronics, catalysis, and

coating of all kinds, and energy generation and conservation strategies.

2.2 Band theory:

Band theory is a part of solid state physics that examines the behavior of the

electrons in solids. It postulates the existence of energy bands, continuous ranges

of energy values which electrons may or may not occupy.

18

Band theory is used to explain why different substances have varying

degrees of electrical resistance. The electrons of a single free-standing atom

occupy atomic orbitals, which form a discrete set of energy levels. According to

molecular orbital theory, if several atoms are brought together into a molecule,

their atomic orbitals split, producing a number of molecular orbitals proportional

to the number of atoms. When a large number of atoms (of order 1020 or more)

are brought together to form a solid, the number of orbitals becomes exceedingly

large, and the difference in energy between them becomes very small. However,

some intervals of energy contain no orbitals, no matter how many atoms are

aggregated.

Any solid has a large number of bands. In theory, it can be said to have

infinitely many bands (just as an atom has infinitely many energy levels).

However, all but a few lie at energies so high that any electron that reaches those

energies escapes from the solid. These bands are usually disregarded.

Many models have been constructed to try to explain the origin and

behavior of bands. These include:

1- The nearly-free electron model, a modification of the free electron model.

2- The Kronig-Penney mode.

Bands have different widths, based upon the properties of the atomic

orbitals from which they arise. Also, allowed bands may overlap, producing (for

practical purposes) a single large band. While the density of energy states in a

band is very great, it is not uniform. It approaches zero at the band boundaries,

and is generally greatest near the middle of a band. Not all of these states are

occupied by electrons ("filled") at any time. The likelihood of any particular state

being filled at any temperature is given by the Fermi-Dirac statistics.

The probability is given by the following:

simp

num

Ferm

f

where:

k i

T i

EF

Regardle

ple step fu

At non z

mber of sta

mi level ar

( )Ef+

=

1

is Boltzma

is the temp

F is the Fer

ess of the

unction:

zero temp

ates below

re filled. A

kTEE f

e−

−+

1

ann's cons

perature,

rmi energy

temperatu

peratures,

w the Ferm

As shown

19

stant,

y (or 'Ferm

ure, f(EF)

the step

mi level a

in figure (

mi level').

= 1 / 2.

"smooths

are empty

(2-1).

At T=0, t

out", so

y, and som

(2.1)

the distrib

(2.2)

that an ap

me states

bution is a

ppreciable

above the

a

e

e

2-3 D

ener

matt

phys

or a

leve

spac

is th

the e

Density of

Density

rgy interva

ter physic

sical syste

function

els in a sol

ce (k-spac

where V

he number

energy ran

f state:

of state c

al. Density

cs that qu

em. It is of

g(k) of th

lid. In 3-d

e) is

V is the vol

r of allow

nge E to E

can be de

y of state

uantifies h

ften expre

he waveve

dimensions

lume of th

wed energy

E + dE (an

20

efined as

(DOS) is

how close

essed as a

ector k. It

s, for exam

he solid. A

y levels p

nd equivale

the densi

a property

ely packed

function g

is usually

mple, the d

A more pre

er unit vo

ently for k

ity of ene

y in statist

d energy

g(E) of th

y used wit

density of

ecise defin

olume of t

k).

ergy level

tical and c

levels are

he internal

th electron

f states in

(2.3)

nition is a

the materi

s per unit

condensed

e in some

energy E

nic energy

reciproca

s; g(E) dE

ial, within

t

d

e

E,

y

l

E

n

mom

the

appe

To find

mentum fo

In terms

This give

The amo

difference

ears in den

the dens

or a particu

of E and d

es a densit

orphous st

e in length

nsity of sta

sity of en

ular partic

dE. For ex

,

ty of state

tate means

h and ang

ate diagra

21

nergy stat

cle is used

xample for

es at energ

s that the

gles of lat

am as three

tes, the r

d, to expres

r a free ele

gy E per un

chemical

ttice bond

e essential

relation be

ss k and d

ectron:

nit volume

band is b

d, therefor

l regions a

etween en

dk in g(k)d

(2.4)

e,

(2.5)

broken as

re all ene

as in the fi

nergy and

dk

a result in

ergy levels

igure:

d

n

s

22

In figure (2-2b), first region (a) is the extended state which originated from

the crystallization structure of material. The charge carriers in this region is free

to move. The second region (b) is the tall state which originated from the

disordering. The density of localized tail state proportion with the increase in

disordering while the extended state of valence and conduction inversely

proportion with disordering. The last region (c) is the deep state which is

originated from dangling bonds, impurities and defects.

The band energy can be divided to two sub-band, the extended band which

is related to long range order and the charge carrier have a possibility of moving

in a certain path through the material. The charge carrier in this band can move

by hopping only. The space of energy between extended conduction band and

extended valence band called the mobility gap as in fig (2-2a) above.

2.4 Band structure of crystalline material:

We can distinguish the crystalline state from the existence of the long-

range order in three dimensions or from the arrangement of atomic structure, in

crystalline material the atomic structure repeat itself in a periodical way.

The crystal has a band contain a huge number of energy levels equal to the

number of atoms; therefore the band energy appears as a continuous spectrum. If

the atom in crystal becomes close to neighboring atom, each energy level will

split into two level and if the atoms get closer up to distance equal to the atomic

equilibrium distance for lattice, the energy level will split into two well separated

bands, as in the figure (2-3):

23

The distance between the two bands is called the forbidden gap. There are

no energy levels in the forbidden gap or (energy gap). The two splitted bands

called the valence and conduction band. The electrons in valence band have a

possibility of moving to the conduction band if they have a chance to get energy

equal or more than the energy gap.

2.5 Band structure of amorphous material:

The amorphous semiconductor and insulator are known to have to some

extend the short range order, the disordering reflect itself on density of state

diagram. Energy band in amorphous will be divided to two band, the first one

present the extended state range order. The second one present the tail of

localized state witch can be related to disordering.

24

The difference between the energy of the extended state conduction band

and the extended state of valance band called the mobility gap. This gap is

unreal, in other words, the amorphous material has no real energy gap because of

the interference of localized states.

There are several models have been proposed and all use the concept of

localized states and mobility gap ,but vary as the extent of the supposed edges of

distributions of localized states and these models are:

1- Davis and Mott model.

2- The Cohen, Fritzsche and Ovshinsky model(C.F.O model).

3- Marshall-Owen Model.

2-5-1 The Davis-Mott model:

The Davis and Mott model based on the idea of making a strong distinction

between localized states. Some of the localized state originates from the lack of

long-range order and others are due to defects in the structure the lack of long-

range order creates localized states extents only to EA and EB in the mobility gap

as in the figure (2-4).

The defects states from longer tails but of insufficient density to pin the

Fermi level .They further proposed the existence of a band of compensated levels

near the middle of the band gap in order to pin the Fermi level.

The center band may split into a donor-acceptor band, as shown in

figure(2-5).

25

Figure (2-4:) Density of state N(E) as a function of energy (E) in an amorphous

semiconductor according to Davis and Mott.

Figure(2-5): Density of state N(E) as a function of energy (E) In an

amorphous semiconductor with acceptor and donor peaks Due to dangling bonds (modified Davis and mott model).

26

2.5.2 The Cohen, Fritzsche and Ovshinsky model (C.F.O model): The amorphous semiconductors alloys are highly disordered so that the tails

of the conduction band and valance band can overlap as in the figure (2-6):

Figure (2-6): Density of state N(E) in an amorphous semiconductor

(C.F.O model).

Cohen pointed that a localized state is always identitiable either as a

valance band tail state or as a conduction band tail state even when its energy lies

in the overlapping region.

Redistribution in the conduction band tail, and which are negatively

charged, and empty states in the valance band tail which are positively charged.

27

2.5.3 Marshall-Owen Model:

Marshall and Owen suggest that the position of the fermi level is

determined by the well separated bands of donors and acceptors in the upper and

lower halves of the mobility gap as shown in figure(2-7)

Figure (2-7): Marshall and Owen model.

28

Chapter Three

Optical properties

3.1 Introduction:

When light is incident on a semiconductor, the optical phenomena of

absorption, reflection, and transmission are observed. From these optical effects,

we obtain much of the information. From absorption spectrum as a function of

photon energy, a number of processes can be contributed to absorption. At high

energies photons are absorbed by the transitions of electrons from filled valence

band states to empty conduction band states.

For energies just below the lowest forbidden energy gap, radiation is

absorbed due to the formation of excitants, and electron transitions between band

and impurity states. The transitions of free carriers within energy bands produce

an absorption continuum which increases with decreasing photon energy. Also,

the crystalline lattice itself can absorb radiation, with the energy being given off

in optical phonons. Finally, at low energies, or long wavelengths, electronic

transitions can be observed between impurities and there associated bands.

Many of these processes have important technological applications; for

example, intrinsic photo detectors utilize band to band absorption. While

semiconductor Lasers generally operate by means of transitions between

impurity and band states.

3.2 Optical properties of amorphous and crystal materials:

The general theory and many of the experimental results on amorphous

semiconductors have been summarized by Mott and Davis. They show that one

feature of such materials is some sort of energy band structure, but show also

that the normally sharp cutoff in the density of states curves at the band edges is

29

replaced by a tailing into the normally forbidden energy gap .Thus we expect a

difference in the absorption spectra, particularly at the fundamental absorption

edge, between samples of the same basic material but for which one is crystalline

and the other amorphous.

From the stand point of electron motion a mobility or pseudo gap is defined

and is larger for amorphous materials than for crystals having the same chemical

compositions. The equivalent gaps from the optical stand point will depend on

the form of excitation process taking place in the material when photons are

absorbed. Thus a variety of possibilities will arise, depending on whether the

transitions involved are direct or indirect.

The theory of such transitions has been presented by Davis and Mott and

they take account of the localized electronic states in the mobility or pseudo-gap.

In amorphous materials the K-conservation rule breaks down and thus K is not

a good quantum number .If we assume that the matrix element for optical

transitions has the same value whether or not the initial and final states are

localized, and also that the densities of states at the band edges are linear

functions of the energy, then we may deduce α. The equation for optical

absorption coefficient α at a given angular frequency w then reduces to the form:

( ) ( ) ωωωα hh2

optEA −= (3.1)

where:

( ) EncA ∆= οοσπ4 (3.2)

And where οσ is the electrical conductivity at absolute zero, E∆ the width

of the tail of localized states in the normally forbidden band gap, οn the

refractive index and optE the optical energy gap.

30

Thus the optical energy gap may be determined from the extrapolation to

( ) 021=ωαh of a plot of ( ) 2

1ωαh v. ( )ωh . Such a theory describes optical

absorption associated with forbidden indirect transitions.

The spectrally transmittances where determined by means of a Perkin-

Elmer spectrophotometer and typical results shown in the figure (3-1):

3.3 Optical absorption:

The energy gap in a semiconductor is responsible for the fundamental

optical absorption edge. The fundamental absorption process is one in which a

photon is absorbed and an electron is excited from an occupied valence band

state to an unoccupied conduction band state. If the photon energy ( )ωh is less

Figure (3-1):

31

than the gap energy, such processes are impossible and the photon will not be

absorbed. That is, the semiconductor is transparent to electromagnetic radiation

for which ( )gapE<ωh . For ( )gapE>ωh on the other hand, such inter band

absorption processes are possible (with a qualification that we will discuss

shortly). In high quality semiconductor crystals at low temperatures, the density

of states rises sharply at the band edge and consequently the absorption rises

very rapidly when the photon energy reaches the gap energy.

Observation of the optical absorption edge is the most common means of

measuring the energy gap in semiconductors.

As an example, consider the semiconductor GaAs commonly used in

electro-optical applications. The band gap energy is ( )eVEgap 4.1= . This

corresponds to a photon frequency ( )Hz14101.2 ×=ω and a wavelength

( )nmm 900109.0 6 ≈×≈ −λ . This wavelength lies just outside the visible range

in the very near infrared. This tells us that GaAs is transparent to infrared light,

but is opaque (strongly absorbing) in the visible.

This is true of many common semiconductors because their energy gaps are

of order 1eV or less. There is a complication to the fundamental absorption

process that limits the usefulness of some semiconductors for optical

applications. These include, unfortunately, silicon, the most ubiquitous material

in semiconductor applications. Recall that when we studied the optical phonon

modes, we found that the intersection of the photon’s dispersion relation and that

of the optical modes occurs very close to k = 0. This is because the photon

wavelength λ photon at the relevant frequency is much longer than a typical

inter atomic spacing a , in the crystal lattice. Thus λπ2=photonk photon is

very small on the scale of the Brillouin zone akBZ π= .

32

Now considering an inter band electronic transition, we see that such

transitions must be essentially vertical on the band diagram. This is required if

the process is to conserve momentum: electronphoton khhk ∆= .

This condition is readily satisfied if the maximum of the VB and the

minimum of the CB occur at the same k-value (often k = 0 as in the diagram

below). If the band structure has this feature, the gap is said to be direct [see

figure (3-2)].

Such semiconductors are very useful for electro-optical applications.

Figure (3-2): Direct optical transition.

What if the VB maximum and CB maximum do not occur at the same k-

value? In this case the gap is said to be an indirect gap. Absorption over the

band gap cannot conserve energy and momentum without the participation of

another particle, usually a phonon. The process then corresponds to photon→

conduction electron plus phonon.

33

Energy conservation requires WEgap hh +=ω where W is the frequency

of the phonon created in the process.

To conserve momentum, the phonon must have a wave vector K phonon =

k(CB max) – k(VB min) since k photon ≈ 0. Indirect absorption processes are

possible (after all they satisfy the necessary conservation conditions), but

because of the participation of a third particle (the phonon), their transition

probabilities are much lower than those of direct processes. This kind of

absorption process is illustrated in the diagram below.

Figure (3-3): Indirect optical transitions.

Despite the inefficiency of electron-hole excitation (interband absorption) in

indirect semiconductors, these materials nevertheless have important

applications. One example is the crystalline silicon solar cell.

34

Figure (3-4): Comparison between direct and indirect transitions.

3.4 Processes of absorption in semiconductors:

Within these energy level systems we can have a variety of mechanisms by

which electrons (and holes) absorb optical energy. Most of these processes can

occur in quantum wells, wires, and dots, as well as in bulk material:

1- Band-to-band: an electron in the valence band absorbs a photon with enough

energy to be excited to the conduction band, leaving a hole behind.

2- Band-to-exciton: an electron in the valence band absorbs almost enough

energy to be excited to the conduction band. The electron and hole it leaves

behind remain electrically "bound" together, much like the electron and

proton of a hydrogen atom.

35

3- Band-to-impurity or impurity to band: an electron absorbs a photon that

excites it from the valence band to an empty impurity atom or from an

occupied impurity atom to the conduction band.

4- Free carrier: an electron in the conduction band, or hole in the valence band,

absorbs a photon and is excited to a higher energy level within the same set

of bands (i.e., conduction or valence). In quantum structures there can be

photon absorption due to carriers being excited between the quantum levels

within the same band (termed "intra-band"), as well as between the various

quantum levels in one band and those in another "(inter-band").

5- Intra-band: these transitions can occur only between even and odd index

levels and are only operative for light polarized parallel to the direction of

quantization. That is, in a quantum well the light must be polarized normal

to the well itself, and in the direction of the composition variation.

6- Inter-band: inter-band transitions can occur between conduction and valence

bands, or between different valence bands (light-hole, heavy-hole, and spin-

off). There are transitions can be active for either polarization of the light,

depending on the symmetries of the respective bands.

3.5 Optical properties of thin film:

Optical measurement constitutes the most important means of determining

the band structures of semiconductors. Photo induced transitions can occur

between different bands, which lead to the determination of the energy band gap,

or within a single band such as the free carrier absorption. Optical measurements

can also be used to study lattice vibrations.

The transmission coefficient T and the reflection coefficient R are the two

important quantities generally measured. For normal incidence they are given by:

( ) ( )( )λπ

λπxRxRT

8exp14exp1

2

2

−−−−

= (3.3)

36

( )( ) 22

22

11

knknT

+++−

= (3.4)

Where, λ is the wave length, n the refractive index, k the absorption

constant, and x the thickness of the sample.

The absorption coefficient per unit length α is given by:

λπα k4

= (3.5)

By analyzing the λ−T or λ−R data at normal incidence, or by making

observations of R or T for different angles of incidence, both n and k can be

obtained and related to transition energy between bands.

Near the absorption edge the absorption coefficient can be expressed as:

( )γωα gE−∝ h (3.6)

Where ( )ωh is the photon energy, ( )gE is the band gap, and γ is a

constant. In the one electron approximation γ equals 21 and

23 for allowed

direct transitions and forbidden direct transitions, respectively maxmin kk = as

transitions (a) and (b) shown in figure (3-5); the constant γ equals 2 for indirect

transitions [transition (c) shown in figure (3-5)], where photons are involved. In

addition, γ equals 3 for allowed indirect transitions to exciton states, where an

exciton is a bound electron-hole pair with energy levels in the band gap and

moves through the crystal lattice as a unit.

37

Near the absorption edge, where the values of ( )gE−ωh become

comparable with the binding of an exciton, the coulomb interaction between the

free hole and electron must be into account. For ( )gE≤ωh the absorption

merges continuously into the absorption caused by the higher excited states of

the exciton. When ( )gE>>ωh , higher energy bands participate in the transition

processes, and complicated band structures are reflected in the absorption

coefficient.

38

3.6 Absorption edge:

The study of optical absorption and particularly the absorption edge is a

useful method for the investigation of optically induced transitions and for the

provision of information about the band structure and energy gap in both

crystalline semiconductors and non-crystalline materials. The principle of this

technique is that a photon with energies greater than the band gap energy will be

absorbed. The absorption edge in many disordered materials follows the Urbach

rule given by:

( ) ⎟⎠⎞

⎜⎝⎛∆

=Eωαωα οhexp (3.7)

Where ( )ωα is the absorption coefficient at an angular frequency of

πνω 2= , and E∆ is the width of the tail of localized states in the band gap.

There are two kinds of optical transition at the fundamental edge of

crystalline and non-crystalline semiconductors, direct transitions and indirect

transition, both of which involve the interaction of an electro-magnetic wave

with an electron in the valance band, which is then raised across the fundamental

gap to the conduction band. For the direct optical transition from the valence

band to the conduction band it is essential that the wave vector for the electron

be unchanged. In the case of indirect transition the interactions with lattice

vibrations (phonons) take place; thus the wave vector of the electron can change

in the optical transition and the momentum change will be taken or given up by

phonons. In other words, if the minimum of the conduction band lies in a

different part of k-space from the maximum of the valence band, a direct optical

transition from the top of the valence band to the bottom of the conduction band

is forbidden.

Mott and Davis suggested the following expression for direct transitions:

( ) ( ) ωωωα hhn

optEB −= (3.8)

39

Where ωh is incident photon energy and exponent n can take 0.5 or 1.5

for allowed and forbidden direct transitions respectively, optE the optical energy

gap, and:

EcnB

∆=

ο

οπσ4 (3.9)

Where οσ is the electrical conductivity at absolute zero, E∆ the width of

the tail of localized states in the normally forbidden band gap. οn the refractive

index.

The following expression is suggested for indirect transitions:

( ) ( ) ωωωα hhn

phopt EEB ±−= (3.10)

Where phE is the photon energy and the value of exponent n take the

values 2 and 3 for allowed and forbidden indirect transitions, see figure (3-6).

Thus, this model suggests that a plot of ( ) n1

ωαh as a function of ωh

should be linear, when this procedure is used, from the zero absorption

extrapolatied value of ωh the value of optical gap can be calculated.

Figure (3-6): Allowed and forbidden indirect transformation.

40

Chapter four

Calculations

4.1 Introduction:

For the sake of more understanding and practice our knowledge, the

analyzed was done on the data of absorption coefficient versus photon energy for

thin films of Chromium Oxide (Cr2O3), Cobalt Oxide (Co3O4), and a mixture of

both compounds in different ratio, reported in reference [8]. All the thin films are

prepared by the method of chemical spry pyrolysis deposition on cover glass

substrates at (673 K), with thickness between (225-275 nm).

The spectra were analyzed and the optical energy gap for both, allowed and

forbidden, direct and indirect transition were evaluated for all data. Also the

width of the localized states inside the forbidden gap is investigated in this

chapter, in the calculation the MATLAB software was used as shown in

Appendix.

4.2 Optical energy for allowed direct transitions:

In the allowed direct transitions the conduction electron transfer from

the top of valence bands to the bottom of conduction bands, with

conservation of momentum. In this case the following relation was

suggested:

( ) ( ) ωωωα hh 21

optEB −= (4.1)

One can calculate the energy gap for allowed direct transition by

plotting figure between ( )2ωαh versus ( )ωh , as shown in figure (3.1) to

figure (3.5). It is obvious that the extension of this curve will intersection

with ( )ωh , which its value is optE for this type of transition. The values of

41

optE for allowed direct transition for all composition are tabulated in

Table(3.1).

Table(3.1): Optical energy gape for allowed direct transitions for all component.

Figure (4-1): Optical energy for allowed direct transitions for 100% Cr2O3

Percentage

Cr2O3:Co3O4

Optical energy

gap (eV)

100 : 0 3.28

75 : 25 2.67

50 : 50 2.08

25 : 75 1.97

0 : 100 1.92

2.6 2.8 3 3.2 3.4 3.6 3.8 40

2

4

6

8

10

12

14

16x 1011

hv

(alfa

*hv)

2

100% Cr2O3

42

Figure (4-2): Optical energy for allowed direct transitions for 75% Cr2O3 :

25% C03O4


50% C03O4

2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.20

5

10

15x 1011

hv

(alfa

*hv)

2

75% Cr2O3 + 25% Co3O4

1.8 1.9 2 2.1 2.2 2.3 2.4 2.51

2

3

4

5

6

7

8

9

10

11x 1011

hv

(alfa

*hv)

2

50% Cr2O3 + 50% Co3O4

43


75% C03O4

Figure (4-5): Optical energy for allowed direct transitions for 100% C03O4

1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.51

2

3

4

5

6

7

8

9

10

11x 1011

hv

(alfa

*hv)

2

25% Cr2O3 + 75% Co3O4

1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.31

2

3

4

5

6

7

8

9

10

11x 1011

hv

(alfa

*hv)

2

100% Co3O4

44

4.3 Optical energy for forbidden direct transitions:

In the forbidden direct transitions the conduction electron transfer from

valence bands to conduction bands vertically, with conservation of

momentum. In this case the following relation was suggested:

( ) ( ) ωωωα hh 23

optEB −= (4.2)

One can calculate the energy gap of forbidden direct transition by

plotting figure between ( )32

ωαh versus ( )ωh , as shown in figure (3.6) to

figure (3.10). It is obvious that the extension of this curve will intersection

with ( )ωh , which its value is optE for this type of transition. The values of

optE for forbidden direct transition for all composition are tabulated in

Table (3.2).

Table(3.2): Optical energy gape for forbidden direct transitions for all component.

Percentage

Cr2O3:Co3O4

Optical energy

gap (eV)

100 : 0 2.86

75 : 25 2.47

50 : 50 1.99

25 : 75 1.79

0 : 100 1.73

45

Figure (4-6): Optical energy for forbidden direct transitions for 100% Cr2O3


: 25% C03O4

2.6 2.8 3 3.2 3.4 3.6 3.8 42000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

hv

(alfa

*hv)

2/3

100% Cr2O3

2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.24000

5000

6000

7000

8000

9000

10000

11000

12000

hv

(alfa

*hv)

2/3

75% Cr2O3 + 25% Co3O4

46


: 50% C03O4


: 75% C03O4

1.8 1.9 2 2.1 2.2 2.3 2.4 2.55000

6000

7000

8000

9000

10000

11000

hv

(alfa

*hv)

2/3

50% Cr2O3 + 50% Co3O4

1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.55000

6000

7000

8000

9000

10000

11000

hv

(alfa

*hv)

2/3

25% Cr2O3 + 75% Co3O4

47

Figure (4-10): Optical energy for forbidden direct transitions for 100%

C03O4

4.4 Optical energy for allowed indirect transitions:

In the allowed indirect transitions the conduction electron transfer from

the top of valence bands to the conduction bands not vertically, that is to say

absorption over the band gap cannot conserve energy and momentum

without the participation of another particle, usually a phonon. In this case

the following relation was suggested:

( ) ( ) ωωωα hh2


The energy gap for allowed indirect transition can be calculated simply

by plotting figure between ( )21

ωαh versus ( )ωh , as shown in figure (3.11)

to figure (3.15). It is obvious that the extension of this curve will

intersection with ( )ωh , which its value is will be ( )phopt EE + or

1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.35500

6000

6500

7000

7500

8000

8500

9000

9500

10000

10500

hv

(alfa

*hv)

2/3

100% Co3O4

48

( )phopt EE − for this type of transition; and from these two values optE can

be calculated. The values of optE for allowed direct transition for all

composition are tabulated in Table (3.3).

Table(3.3): Optical energy gape for allowed indirect transitions for all component.

Percentage

Cr2O3:Co3O4

Optical energy

gap (eV)

100 : 0 2.835

75 : 25 2.450

50 : 50 1.973

25 : 75 1.795

0 : 100 1.785

49

Figure (4-11): Optical energy for allowed indirect transitions for 100% Cr2O3

Figure (4-12): Optical energy for allowed indirect transitions for 75%

Cr2O3 : 25% C03O4

2.6 2.8 3 3.2 3.4 3.6 3.8 4400

500

600

700

800

900

1000

1100

1200

hv

(alfa

*hv)

1/2

100% Cr2O3

2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2500

600

700

800

900

1000

1100

1200

hv

(alfa

*hv)

1/2

75% Cr2O3 + 25% Co3O4

50


Cr2O3 : 50% C03O4


Cr2O3 : 75% C03O4

1.8 1.9 2 2.1 2.2 2.3 2.4 2.5600

650

700

750

800

850

900

950

1000

1050

hv

(alfa

*hv)

1/2

50% Cr2O3 + 50% Co3O4

1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5600

650

700

750

800

850

900

950

1000

1050

hv

(alfa

*hv)

1/2

25% Cr2O3 + 75% Co3O4

51


C03O4

4.5 Optical energy for forbidden indirect transitions:

In the forbidden indirect transitions the conduction electron transfer

from the valence bands to the conduction bands not vertically, that is to say

absorption over the band gap cannot conserve energy and momentum

without the participation of another particle, usually a phonon. In this case

the following relation was suggested:

( ) ( ) ωωωα hh3


The energy gap for forbidden indirect transition can be calculated

simply by plotting figure between ( )31

ωαh versus ( )ωh , as shown in figure

(3.16) to figure (3.20). It is obvious that the extension of this curve will

intersection with ( )ωh , which its value is will be ( )phopt EE + or

( )phopt EE − for this type of transition; and from these two values optE can

1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3650

700

750

800

850

900

950

1000

1050

hv

(alfa

*hv)

1/2

100% Co3O4

52

be calculated. The values of optE for allowed direct transition for all

composition are tabulated in Table (3.4).

Table(3.4): Optical energy gape for forbidden indirect transitions for all component.

Percentage

Cr2O3:Co3O4

Optical energy

gap (eV)

100 : 0 2.770

75 : 25 2.440

50 : 50 1.950

25 : 75 1.775

0 : 100 1.765

Figure (4-16): Optical energy for forbidden indirect transitions for 100% Cr2O3

2.6 2.8 3 3.2 3.4 3.6 3.8 450

60

70

80

90

100

110

hv

(alfa

*hv)

1/3

100% Cr2O3

53

Figure (4-17): Optical energy for forbidden indirect transitions for 75%

Cr2O3 : 25% C03O4


Cr2O3 : 50% C03O4

2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.265

70

75

80

85

90

95

100

105

110

hv

(alfa

*hv)

1/3

75% Cr2O3 + 25% Co3O4

1.8 1.9 2 2.1 2.2 2.3 2.4 2.570

75

80

85

90

95

100

105

hv

(alfa

*hv)

1/3

50% Cr2O3 + 50% Co3O4

54


Cr2O3 : 75% C03O4


C03O4

1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.570

75

80

85

90

95

100

105

hv

(alfa

*hv)

1/3

25% Cr2O3 + 75% Co3O4

1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.375

80

85

90

95

100

105

hv

(alfa

*hv)

1/3

100% Co3O4

55

4.5 width of the tail of localized states:

Width of the tail of localized states (Urbach energy) inside the

forbidden bands, for all compounds can be found in the exponential region

by using the following relation:

( ) ⎟⎠⎞

⎜⎝⎛∆

=Eωαωα οhexp (4.5)

( ) ⎟⎠⎞

⎜⎝⎛∆

+=Eωαωα οhlnln (4.6)

It is obvious when ( )αIn is plot against ( )ωh , the inverse of slop will

be the value of tail localized state, as shown in figure (3.21) to figure (3.25).

The values of Urbach energy E∆ for all composition are tabulated in

Table(3.5).

Table(3.5): width of the tail of localized states for all component.

Percentage

Cr2O3:Co3O4

Tail width E∆

(eV)

100 : 0 0.628

75 : 25 0.848

50 : 50 0.566

25 : 75 0.926

0 : 100 0.757

56

Figure (4-21): width of the tail of localized states for 100% Cr2O3

Figure (4-22): width of the tail of localized states for 75% Cr2O3 : 25% C03O4

2.6 2.8 3 3.2 3.4 3.6 3.8 411

11.2

11.4

11.6

11.8

12

12.2

12.4

12.6

12.8

13

hv

ln (a

lfa)

100% Cr2O3

2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2

11.6

11.8

12

12.2

12.4

12.6

12.8

13

hv

ln (a

lfa)

75% Cr2O3 + 25% Co3O4

57



1.8 1.9 2 2.1 2.2 2.3 2.4 2.512.1

12.2

12.3

12.4

12.5

12.6

12.7

12.8

12.9

13

13.1

hv

ln (a

lfa)

50% Cr2O3 + 50% Co3O4

1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.512.3

12.4

12.5

12.6

12.7

12.8

12.9

13

hv

ln (a

lfa)

25% Cr2O3 + 75% Co3O4

58

Figure (4-25): width of the tail of localized states for 100% C03O4

1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.312.4

12.5

12.6

12.7

12.8

12.9

13

13.1

hv

ln (a

lfa)

100% Co3O4

59

References

[1] M. N. Said, "Studies some of the physical properties of thin films of Barium

Tituate by using Co-Evaporation technique at low pressure", PhD thesis,

Baghdad University, (1996).

[2] David Adler, Brian B. Schwartz, and Martin C. Steele, "Physical properties of

amorphous material", (1988).

[3] M. H. Brodsky, "Amorphous semiconductors", Topics in Applied Physics,

Vol. 36, "Optical properties of amorphous semiconductors", by G. A. N.

Connell, (1979).

[4] C. A. Hogarth, A. A. Hosseini, "Optical absorption near the fundamental

absorption edge in some vanadate glasses", Journal of Materials science 18,

2697-2705, (1983).

[5] C. A. Hogarth and M. N. Khan, "A study of optical absorpition in some

sodium titanium silicate glasses", Journal of Non-Crystalline Solids, 24,

277-282, (1977).

[6] Charles Kittel, “ Introduction to Solid State Physics”, six edition, John Wiley

and Sons, Inc., (1986).

[7] J. S. Blakemore, "Solid state physics", Second Edition, by W. B. Saunders

Company, (1974).

[8] Enas S. Al-Mizban, “A Study of Optical and Electrical Properties of Cr2O3

and Co3O4 Thin Films and Their Mixture”, M.Sc. thesis, Baghdad

University, (1997).

[9] Saz Kamal, Shillan Ali, "Comparing between different types of thin films

preparation methods", fourth class report, University of Sulaimani, (2004).

[10] M. Ashraf Chaudhry, M. Shakeel Bilal, A. R. Kausar and M. Altaf, “Optical

band gap of cadmium phosphate glass containing lanthanum oxide”, Il

Nuovo Cimento, 19, 1, 17-21, (1997).

60

[11] M. Thamilselvan, K. Premnazeer, D. Mangalaraj, Sa. K. Narayandass, and

Junsin Yi, “Influence of density of states on optical properties of GaSe thin

film”, Cryst. Res. Technol. 39, 2, 137-142 (2004).

[12] Y. C. Ratnakaram and A. Viswanadha Reddy, “Correlation of radiative

properties of rare earth ions (Pr3+ and Nd3+) in chlorophosphate glasses-

0.1 and 0.5 mol% concentrations”, Bull. Mater. Sci., 24, 5, 539-545, (2001).

61

Appendix

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%% Optical Propertes of Thin Film Co2O3-C03O4 %%%%%

%%%%% with deffrent consentration %%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%% 100% Cr2O3 %%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

hv1=[2.7,2.8,2.9,3.0,3.1,3.2,3.3,3.4,3.5,3.6,3.7,3.8];

alfa1=[0.6,0.7,0.8,1.0,1.3,1.6,1.9,2.2,2.4,2.8,3.1,3.3];

alfa1=alfa1*10^5;

for i=1:12

alfasqwar1(i)=(alfa1(i)*hv1(i))^2;

alfa321(i)=(alfa1(i)*hv1(i))^(2/3);

alfahvroot1(i)=sqrt(alfa1(i)*hv1(i));

alfahv31(i)=(alfa1(i)*hv1(i))^(1/3);

lnalfa1(i)=log(alfa1(i));

end

plot (hv1,alfa1),xlabel('hv'),ylabel('alfa'),title('100% Cr2O3');

pause

%subplot(2,2,1);

plot (hv1,alfasqwar1),xlabel('hv'),ylabel('(alfa*hv) 2'),title('100% Cr2O3');

pause

%subplot(2,2,2);

plot (hv1,alfa321),xlabel('hv'),ylabel('(alfa*hv) 2/3'),title('100% Cr2O3');

pause

62

%subplot(2,2,3);

plot (hv1,alfahvroot1),xlabel('hv'),ylabel('(alfa*hv) 1/2'),title('100% Cr2O3');

pause

%subplot(2,2,4);

plot (hv1,alfahv31),xlabel('hv'),ylabel('(alfa*hv) 1/3'),title('100% Cr2O3');

pause

subplot(1,1,1);

plot (hv1,lnalfa1,'rd'),xlabel('hv'),ylabel('ln (alfa)'),title('100% Cr2O3');

pause

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%% 75% Cr2O3 + 25% Co3O4 %%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

hv2=[2.2,2.3,2.4,2.5,2.7,2.8,3.0,3.1,3.2];

alfa2=[1.3,1.4,1.6,1.7,1.9,2.3,3.1,3.4,3.8];

alfa2=alfa2*10^5;

for i=1:9


alfa322(i)=(alfa2(i)*hv2(i))^(2/3);




end

subplot(1,1,1);

plot (hv2,alfa2),xlabel('hv'),ylabel('alfa'),title('75% Cr2O3 + 25% Co3O4');

pause

%subplot(2,2,1);

plot (hv2,alfasqwar2),xlabel('hv'),ylabel('(alfa*hv) 2'),title('75% Cr2O3 + 25% Co3O4');

pause

%subplot(2,2,2);

plot (hv2,alfa322),xlabel('hv'),ylabel('(alfa*hv) 2/3'),title('75% Cr2O3 + 25% Co3O4');

63

pause

%subplot(2,2,3);

plot (hv2,alfahvroot2),xlabel('hv'),ylabel('(alfa*hv) 1/2'),title('75% Cr2O3 + 25% Co3O4');

pause

%subplot(2,2,4);

plot (hv2,alfahv32),xlabel('hv'),ylabel('(alfa*hv) 1/3'),title('75% Cr2O3 + 25% Co3O4');

pause

subplot(1,1,1);

plot (hv2,lnalfa2,'rd'),xlabel('hv'),ylabel('ln (alfa)'),title('75% Cr2O3 + 25% Co3O4');

pause

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%% 50% Cr2O3 + 50% Co3O4 %%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

hv3=[1.9,2.0,2.1,2.2,2.3,2.4,2.5];

alfa3=[1.9,2.1,2.7,3.0,3.6,3.9,4.1];

alfa3=alfa3*10^5;

for i=1:7


alfa323(i)=(alfa3(i)*hv3(i))^(2/3);




end

subplot(1,1,1);


pause

%subplot(2,2,1);


pause

%subplot(2,2,2);

64


pause

%subplot(2,2,3);


pause

%subplot(2,2,4);


pause

subplot(1,1,1);


pause

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%% 25% Cr2O3 + 75% Co3O4 %%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

hv4=[1.6,1.7,1.95,2.05,2.12,2.2,2.3,2.4];

alfa4=[2.4,2.25,2.6,3.0,3.25,3.5,3.9,4.2];

alfa4=alfa4*10^5;

for i=1:8


alfa324(i)=(alfa4(i)*hv4(i))^(2/3);




end

subplot(1,1,1);


pause

%subplot(2,2,1);


pause

65

%subplot(2,2,2);


pause

%subplot(2,2,3);


pause

%subplot(2,2,4);


pause

subplot(1,1,1);


pause

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%% 100% Co3O4 %%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

hv5=[1.51,1.55,1.61,1.7,1.75,1.85,1.92,2.0,2.1,2.17];

alfa5=[2.85,2.8,2.65,2.5,2.6,3.0,3.35,3.75,4.15,4.65];

alfa5=alfa5*10^5;

for i=1:10


alfa325(i)=(alfa5(i)*hv5(i))^(2/3);




end

subplot(1,1,1);

plot (hv5,alfa5),xlabel('hv'),ylabel('alfa'),title('100% Co3O4');

pause

%subplot(2,2,1);

plot (hv5,alfasqwar5),xlabel('hv'),ylabel('(alfa*hv) 2'),title('100% Co3O4');

66

pause

%subplot(2,2,2);

plot (hv5,alfa325),xlabel('hv'),ylabel('(alfa*hv) 2/3'),title('100% Co3O4');

pause

%subplot(2,2,3);

plot (hv5,alfahvroot5),xlabel('hv'),ylabel('(alfa*hv) 1/2'),title ('100% Co3O4');

pause

%subplot(2,2,4);

plot (hv5,alfahv35),xlabel('hv'),ylabel('(alfa*hv) 1/3'),title('100% Co3O4');

pause

subplot(1,1,1);

plot (hv5,lnalfa5,'rd'),xlabel('hv'),ylabel('ln (alfa)'),title ('100% Co3O4');

pause

end

optical properties of thin film

Documents