Optical Properties Of Thin Film

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

1

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. 2

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-rangeorder 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

3

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.

4

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.

5

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 facecentered-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 bodycentered 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. 6

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).

7

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 noncrystalline 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.

8

Appplication of thin film ms: •

m microelec tronics-eleectrical coonductors,, electricall barriers, diffusion barriers....

•

m magnetic sensors - sense s I, B or changees in them m

•

g sensorrs, SAW devices gas d

•

t tailored m materials-l layer veryy thin films to develop d m materials with new w p properties s

•

o optics-ant ti-reflectioon coatings

•

c corrosion protectionn

•

w resisstance wear

Speccial Propeerties of Thin T Filmss: Differentt from bullk materiaals, thin fillms may be: b •

not fully dense

•

under strress

•

differentt defect strructures frrom bulk

•

quasi - tw wo dimenssional (very thin film ms)

•

strongly influenced by surfaace and intterface efffects This willl change electricaal, magnettic, opticaal, thermaal, and m mechanical

propperties. Typiical steps in makingg thin film ms: •

Emissionn of particcles from source s ( heeat, high voltage v . . .)

•

Transporrt of particcles to subbstrate (freee vs. direccted)

•

Condenssation of particles p onn substratee.

Fig (11-3): Simpple mode for f deposittion a thinn film. 9

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.

10

•

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. 11

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.

12

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.

13

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).

14

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 15

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

Dense films Sputtering

Good uniformity

relatively slow

Wide range of inorganic materials

Thermal Evaporation

e-Beam Evaporation

CVD

Limited range of materials

Fast

Low density films without

Relatively simple

ion or plasma assist

Fast Wide range of inorganic materials Gives good control of coating chemistry

high voltages Difficult to scale Often uses hazardous liquids or gases

16

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.

17

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:

18

f (E ) =

1 1+ e

−

E−E f

(2.1)

kT

where: k iis Boltzmaann's consstant, T is i the temp perature, EF is the Ferrmi energy y (or 'Ferm mi level'). Regardleess of the temperatu ure, f(EF) = 1 / 2. At T=0, tthe distrib bution is a simp ple step fuunction:

(2.2) At non zero z temp peratures, the step "smooths out", so that an ap ppreciablee num mber of staates below w the Ferm mi level are a empty y, and som me states above thee Ferm mi level arre filled. As A shown in figure ((2-1).

19

2-3 Density D off state: Density of state can c be deefined as the densiity of eneergy levels per unitt enerrgy intervaal. Density y of state (DOS) is a property y in statisttical and condensed c d mattter physiccs that qu uantifies how h closeely packed d energy levels aree in somee physsical systeem. It is offten expreessed as a function g(E) g of thhe internal energy E, E or a function g(k) of th he waveveector k. It is usually y used witth electron nic energy y dimensionss, for exam mple, the density d off states in reciprocal leveels in a sollid. In 3-d spacce (k-space) is (2.3) he solid. A more preecise definnition is as; g(E) dE E where V is the vollume of th is th he numberr of allow wed energy y levels per unit vo olume of tthe materiial, within n the energy e ran nge E to E + dE (an nd equivaleently for k). k

20

To find the denssity of en nergy stattes, the relation r beetween en nergy and d mom mentum foor a particu ular particcle is usedd, to expresss k and ddk in g(k)d dk In terms of E and dE. d For ex xample forr a free eleectron:

,

(2.4)

This givees a densitty of statees at energgy E per un nit volumee,

(2.5) The amoorphous sttate meanss that the chemical band is bbroken as a result in n the differencee in length h and ang gles of latttice bond d, thereforre all eneergy levelss appeears in dennsity of staate diagraam as threee essentiall regions aas in the fiigure:

21

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 longrange 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):

22

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.

23

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 longrange 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).

24

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). 25

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.

26

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.

27

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

28

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:

α (ω ) = A(hω − Eopt )2 hω

(3.1)

where:

A = (4π c )σ ο nο ∆E

(3.2)

And where σ ο is the electrical conductivity at absolute zero, ∆E the width of the tail of localized states in the normally forbidden band gap, nο the refractive index and Eopt the optical energy gap.

29

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

(αhω ) 12 = 0

of a plot of (αhω )

1

2

v. (hω ) . Such a theory describes optical

absorption associated with forbidden indirect transitions. The spectrally transmittances where determined by means of a PerkinElmer spectrophotometer and typical results shown in the figure (3-1):

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 (hω ) is less

30

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 hω < E gap . For hω > E gap 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

(E = 1.4eV ) . This Hz ) and a wavelength

electro-optical applications. The band gap energy is corresponds to a photon frequency

(λ ≈ 0.9 × 10

−6

(ω = 2.1× 10

14

gap

)

m ≈ 900nm . 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 k photon = 2π λ photon is very small on the scale of the Brillouin zone k BZ = π a .

31

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: hk photon = h∆k electron . 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 kvalue? 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.

32

Energy conservation requires hω = E gap + hW 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

applications. One example is the crystalline silicon solar cell.

33

have

important

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.

34

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 spinoff). 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:

(1 − R )exp(− 4πx λ ) T= 2

(3.3)

1 − R 2 exp(− 8πx λ )

35

2 ( 1− n) + k2 T= (1 + n )2 + k 2

(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:

α=

4πk

(3.5)

λ

By analyzing the T − λ or R − λ 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:

α ∝ (hω − E g )γ

(3.6)

( )

Where (hω ) is the photon energy, E g

is the band gap, and γ is a

1 3 constant. In the one electron approximation γ equals and for allowed 2

2

direct transitions and forbidden direct transitions, respectively k min = k max 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.

36

Near the absorption edge, where the values of

(hω − E ) g

become

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

(

free hole and electron must be into account. For hω ≤ E g

)

the absorption

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

(

)

the exciton. When hω >> E g , higher energy bands participate in the transition processes, and complicated band structures are reflected in the absorption coefficient.

37

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:

⎛ hω ⎞ ⎟ ⎝ ∆E ⎠

α (ω ) = α ο exp⎜

(3.7)

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

ω = 2πν , 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:

α (ω ) = B (hω − Eopt )n hω

(3.8)

38

Where hω is incident photon energy and exponent n can take 0.5 or 1.5 for allowed and forbidden direct transitions respectively, Eopt the optical energy gap, and:

B=

4πσ ο cnο ∆E

(3.9)

Where σ ο is the electrical conductivity at absolute zero, ∆E the width of the tail of localized states in the normally forbidden band gap. nο the refractive index. The following expression is suggested for indirect transitions:

α (ω ) = B (hω − Eopt ± E ph )n hω

(3.10)

Where E ph 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

(αhω )

1

n

as a function of hω

should be linear, when this procedure is used, from the zero absorption extrapolatied value of hω the value of optical gap can be calculated.

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

39

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:

α (ω ) = B (hω − Eopt ) hω 1 2

(4.1)

One can calculate the energy gap for allowed direct transition by plotting figure between (αhω )

2

versus (hω ) , as shown in figure (3.1) to

figure (3.5). It is obvious that the extension of this curve will intersection with (hω ) , which its value is Eopt for this type of transition. The values of

40

Eopt 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. Percentage

Optical energy

Cr2O3:Co3O4

gap (eV)

100 : 0

3.28

75 : 25

2.67

50 : 50

2.08

25 : 75

1.97

0 : 100

1.92

11

16

100% Cr2O3

x 10

14

12

(alfa*hv) 2

10

8

6

4

2

0 2.6

2.8

3

3.2

3.4

3.6

3.8

4

hv

Figure (4-1): Optical energy for allowed direct transitions for 100% Cr2O3 41

11

15

75% Cr2O3 + 25% Co3O4

x 10

(alfa*hv) 2

10

5

0 2.2

2.3

2.4

2.5

2.6

2.7 hv

2.8

2.9

3

3.1

3.2

Figure (4-2): Optical energy for allowed direct transitions for 75% Cr2O3 : 25% C03O4 11

11

50% Cr2O3 + 50% Co3O4

x 10

10

9

8

(alfa*hv) 2

7

6

5

4

3

2

1 1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

hv

Figure (4-3): Optical energy for allowed direct transitions for 50% Cr2O3 : 50% C03O4

42

11

11

25% Cr2O3 + 75% Co3O4

x 10

10

9

8

(alfa*hv) 2

7

6

5

4

3

2

1 1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

hv

Figure (4-4): Optical energy for allowed direct transitions for 25% Cr2O3 : 75% C03O4 11

11

100% Co3O4

x 10

10

9

8

(alfa*hv) 2

7

6

5

4

3

2

1 1.5

1.6

1.7

1.8

1.9 hv

2

2.1

2.2

2.3

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

43

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:

α (ω ) = B (hω − Eopt ) hω 3 2

(4.2)

One can calculate the energy gap of forbidden direct transition by plotting figure between (αhω ) 3 versus (hω ) , as shown in figure (3.6) to 2

figure (3.10). It is obvious that the extension of this curve will intersection with (hω ) , which its value is Eopt for this type of transition. The values of

Eopt 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

Optical energy

Cr2O3:Co3O4

gap (eV)

100 : 0

2.86

75 : 25

2.47

50 : 50

1.99

25 : 75

1.79

0 : 100

1.73

44

100% Cr2O3 12000

11000

10000

9000

(alfa*hv) 2/3

8000

7000

6000

5000

4000

3000

2000 2.6

2.8

3

3.2

3.4

3.6

3.8

4

hv

Figure (4-6): Optical energy for forbidden direct transitions for 100% Cr2O3 75% Cr2O3 + 25% Co3O4 12000

11000

10000

(alfa*hv) 2/3

9000

8000

7000

6000

5000

4000 2.2

2.3

2.4

2.5

2.6

2.7 hv

2.8

2.9

3

3.1

3.2

Figure (4-7): Optical energy for forbidden direct transitions for 75% Cr2O3 : 25% C03O4

45

50% Cr2O3 + 50% Co3O4 11000

10000

(alfa*hv) 2/3

9000

8000

7000

6000

5000 1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

hv

Figure (4-8): Optical energy for forbidden direct transitions for 50% Cr2O3 : 50% C03O4 25% Cr2O3 + 75% Co3O4 11000

10000

(alfa*hv) 2/3

9000

8000

7000

6000

5000 1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

hv

Figure (4-9): Optical energy for forbidden direct transitions for 25% Cr2O3 : 75% C03O4

46

100% Co3O4 10500

10000

9500

9000

(alfa*hv) 2/3

8500

8000

7500

7000

6500

6000

5500 1.5

1.6

1.7

1.8

1.9 hv

2

2.1

2.2

2.3

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:

α (ω ) = B (hω − Eopt ± E ph )2 hω

(4.3)

The energy gap for allowed indirect transition can be calculated simply by plotting figure between (αhω ) 2 versus (hω ) , as shown in figure (3.11) 1

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

(hω ) ,

which its value is will be

47

(E

opt

+ E ph ) or

(E

opt

− E ph ) for this type of transition; and from these two values Eopt can

be calculated. The values of Eopt 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

Optical energy

Cr2O3:Co3O4

gap (eV)

100 : 0

2.835

75 : 25

2.450

50 : 50

1.973

25 : 75

1.795

0 : 100

1.785

48

100% Cr2O3 1200

1100

1000

(alfa*hv) 1/2

900

800

700

600

500

400 2.6

2.8

3

3.2

3.4

3.6

3.8

4

hv

Figure (4-11): Optical energy for allowed indirect transitions for 100% Cr2O3 75% Cr2O3 + 25% Co3O4 1200

1100

(alfa*hv) 1/2

1000

900

800

700

600

500 2.2

2.3

2.4

2.5

2.6

2.7 hv

2.8

2.9

3

3.1

3.2

Figure (4-12): Optical energy for allowed indirect transitions for 75% Cr2O3 : 25% C03O4

49

50% Cr2O3 + 50% Co3O4 1050

1000

950

(alfa*hv) 1/2

900

850

800

750

700

650

600 1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

hv

Figure (4-13): Optical energy for allowed indirect transitions for 50% Cr2O3 : 50% C03O4 25% Cr2O3 + 75% Co3O4 1050

1000

950

(alfa*hv) 1/2

900

850

800

750

700

650

600 1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

hv

Figure (4-14): Optical energy for allowed indirect transitions for 25% Cr2O3 : 75% C03O4

50

100% Co3O4 1050

1000

950

(alfa*hv) 1/2

900

850

800

750

700

650 1.5

1.6

1.7

1.8

1.9 hv

2

2.1

2.2

2.3

Figure (4-15): Optical energy for allowed indirect transitions for 100% 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:

α (ω ) = B (hω − Eopt ± E ph )3 hω

(4.4)

The energy gap for forbidden indirect transition can be calculated simply by plotting figure between (αhω )3 versus (hω ) , as shown in figure 1

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

(E

opt

(hω ) ,

which its value is will be

(E

opt

+ E ph ) or

− E ph ) for this type of transition; and from these two values Eopt can

51

be calculated. The values of Eopt 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

Optical energy

Cr2O3:Co3O4

gap (eV)

100 : 0

2.770

75 : 25

2.440

50 : 50

1.950

25 : 75

1.775

0 : 100

1.765

100% Cr2O3 110

100

(alfa*hv) 1/3

90

80

70

60

50 2.6

2.8

3

3.2

3.4

3.6

3.8

4

hv

Figure (4-16): Optical energy for forbidden indirect transitions for 100% Cr2O3 52

75% Cr2O3 + 25% Co3O4 110

105

100

(alfa*hv) 1/3

95

90

85

80

75

70

65 2.2

2.3

2.4

2.5

2.6

2.7 hv

2.8

2.9

3

3.1

3.2

Figure (4-17): Optical energy for forbidden indirect transitions for 75% Cr2O3 : 25% C03O4 50% Cr2O3 + 50% Co3O4 105

100

(alfa*hv) 1/3

95

90

85

80

75

70 1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

hv

Figure (4-18): Optical energy for forbidden indirect transitions for 50% Cr2O3 : 50% C03O4

53

25% Cr2O3 + 75% Co3O4 105

100

(alfa*hv) 1/3

95

90

85

80

75

70 1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

hv

Figure (4-19): Optical energy for forbidden indirect transitions for 25% Cr2O3 : 75% C03O4 100% Co3O4 105

100

(alfa*hv) 1/3

95

90

85

80

75 1.5

1.6

1.7

1.8

1.9 hv

2

2.1

2.2

2.3

Figure (4-20): Optical energy for forbidden indirect transitions for 100% C03O4

54

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:

⎛ hω ⎞ ⎟ ⎝ ∆E ⎠

α (ω ) = α ο exp⎜

(4.5)

⎛ hω ⎞ ln α (ω ) = ln α ο + ⎜ ⎟ ⎝ ∆E ⎠

(4.6)

It is obvious when (Inα ) is plot against (hω ) , 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

Tail width ∆E

Cr2O3:Co3O4

(eV)

100 : 0

0.628

75 : 25

0.848

50 : 50

0.566

25 : 75

0.926

0 : 100

0.757

55

100% Cr2O3 13

12.8

12.6

12.4

ln (alfa)

12.2

12

11.8

11.6

11.4

11.2

11 2.6

2.8

3

3.2

3.4

3.6

3.8

4

hv

Figure (4-21): width of the tail of localized states for 100% Cr2O3 75% Cr2O3 + 25% Co3O4 13

12.8

12.6

ln (alfa)

12.4

12.2

12

11.8

11.6 2.2

2.3

2.4

2.5

2.6

2.7 hv

2.8

2.9

3

3.1

3.2

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

56

50% Cr2O3 + 50% Co3O4 13.1

13

12.9

12.8

ln (alfa)

12.7

12.6

12.5

12.4

12.3

12.2

12.1 1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

hv

Figure (4-23): width of the tail of localized states for 50% Cr2O3 : 50% C03O4

25% Cr2O3 + 75% Co3O4 13

12.9

12.8

ln (alfa)

12.7

12.6

12.5

12.4

12.3 1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

hv

Figure (4-24): width of the tail of localized states for 25% Cr2O3 : 75% C03O4

57

100% Co3O4 13.1

13

12.9

ln (alfa)

12.8

12.7

12.6

12.5

12.4 1.5

1.6

1.7

1.8

1.9 hv

2

2.1

2.2

2.3

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

58

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). 59

[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 glasses0.1 and 0.5 mol% concentrations”, Bull. Mater. Sci., 24, 5, 539-545, (2001).

60

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

61

%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 alfasqwar2(i)=(alfa2(i)*hv2(i))^2; alfa322(i)=(alfa2(i)*hv2(i))^(2/3); alfahvroot2(i)=sqrt(alfa2(i)*hv2(i)); alfahv32(i)=(alfa2(i)*hv2(i))^(1/3); lnalfa2(i)=log(alfa2(i)); 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'); 62

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 alfasqwar3(i)=(alfa3(i)*hv3(i))^2; alfa323(i)=(alfa3(i)*hv3(i))^(2/3); alfahvroot3(i)=sqrt(alfa3(i)*hv3(i)); alfahv33(i)=(alfa3(i)*hv3(i))^(1/3); lnalfa3(i)=log(alfa3(i)); end subplot(1,1,1); plot (hv3,alfa3),xlabel('hv'),ylabel('alfa'),title('50% Cr2O3 + 50% Co3O4'); pause %subplot(2,2,1); plot (hv3,alfasqwar3),xlabel('hv'),ylabel('(alfa*hv) 2'),title('50% Cr2O3 + 50% Co3O4'); pause %subplot(2,2,2); 63

plot (hv3,alfa323),xlabel('hv'),ylabel('(alfa*hv) 2/3'),title('50% Cr2O3 + 50% Co3O4'); pause %subplot(2,2,3); plot (hv3,alfahvroot3),xlabel('hv'),ylabel('(alfa*hv) 1/2'),title('50% Cr2O3 + 50% Co3O4'); pause %subplot(2,2,4); plot (hv3,alfahv33),xlabel('hv'),ylabel('(alfa*hv) 1/3'),title('50% Cr2O3 + 50% Co3O4'); pause subplot(1,1,1); plot (hv3,lnalfa3,'rd'),xlabel('hv'),ylabel('ln (alfa)'),title('50% Cr2O3 + 50% Co3O4'); 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 alfasqwar4(i)=(alfa4(i)*hv4(i))^2; alfa324(i)=(alfa4(i)*hv4(i))^(2/3); alfahvroot4(i)=sqrt(alfa4(i)*hv4(i)); alfahv34(i)=(alfa4(i)*hv4(i))^(1/3); lnalfa4(i)=log(alfa4(i)); end subplot(1,1,1); plot (hv4,alfa4),xlabel('hv'),ylabel('alfa'),title('25% Cr2O3 + 75% Co3O4'); pause %subplot(2,2,1); plot (hv4,alfasqwar4),xlabel('hv'),ylabel('(alfa*hv) 2'),title('25% Cr2O3 + 75% Co3O4'); pause 64

%subplot(2,2,2); plot (hv4,alfa324),xlabel('hv'),ylabel('(alfa*hv) 2/3'),title('25% Cr2O3 + 75% Co3O4'); pause %subplot(2,2,3); plot (hv4,alfahvroot4),xlabel('hv'),ylabel('(alfa*hv) 1/2'),title('25% Cr2O3 + 75% Co3O4'); pause %subplot(2,2,4); plot (hv4,alfahv34),xlabel('hv'),ylabel('(alfa*hv) 1/3'),title('25% Cr2O3 + 75% Co3O4'); pause subplot(1,1,1); plot (hv4,lnalfa4,'rd'),xlabel('hv'),ylabel('ln (alfa)'),title('25% Cr2O3 + 75% Co3O4'); 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 alfasqwar5(i)=(alfa5(i)*hv5(i))^2; alfa325(i)=(alfa5(i)*hv5(i))^(2/3); alfahvroot5(i)=sqrt(alfa5(i)*hv5(i)); alfahv35(i)=(alfa5(i)*hv5(i))^(1/3); lnalfa5(i)=log(alfa5(i)); 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'); 65

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

66