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Download the complete Physics project topic and material (chapter 1-5) titled STUDY OF OPTICAL PROPERTIES OF LEAD SELENIDE (PbSe) USING KRAMERS-KRONIG RELATION here on PROJECTS.ng. See below for the abstract, table of contents, list of figures, list of tables, list of appendices, list of abbreviations and chapter one. Click the DOWNLOAD NOW button to get the complete project work instantly.

 

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  • Name: STUDY OF OPTICAL PROPERTIES OF LEAD SELENIDE (PbSe) USING KRAMERS-KRONIG RELATION
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ABSTRACT

Rapid advances in a semiconductor manufacturing and associated technologies have increased the need for the study of how to make them more efficient which lead to the study of the optical properties of Lead Selenide a group IV-VI semiconductor. The optical properties of Lead selenide in the range of 1.0-6.0eV were obtained using Maxwell’s equation of electromagnetism and Kramers-Kronig relations.

In this energy range the crystal of PbSe is observed to have distinct behavior at energies 1.00, 1.53, 2.05, 2.84, 3.10, 4.42, 4.95 and 5.74eV indicating high absorption, refection and decay of the photon. At higher energy values 5.72-6.00eV the decay and absorption loss rate is reduced.

Thus as a result of these optical properties PbSe can be used for variety of devices.

Thus the result for these optical properties can be used in a wide range of optoelectronic devices, such devices include optical pyrometer and spectrometer

 

 

TABLE OF CONTENTS

Title page                                                                                                                   i

Certification                                                                                                               ii

Dedication                                                                                                                 iii

Acknowledgement                                                                                                     iv

Table of Content                                                                                                       v-viii

Abstract                                                                                                                      ix

List of figures                                                                                                             x

List of tables                                                                                                               xi

CHAPTER ONE – INTRODUCTION

1.1     INTRODUCTION TO SEMICONDUCTOR                                                 1

1.1.2 N-type and P-type semiconductor                                                                      2

1.1.3 Intrinsic and Extrinsic semiconductor                                                                  2

1.1.3.1 Intrinsic semiconductor                                                                                    2

1.3.1.2 Extrinsic semiconductor                                                                                    3

1.2       GROUP IV-VI SEMICONDUCTOR                                                                  4

1.3 LEAD SELENIDE                                                                                                   4

1.3.1 Introduction and Application                                                                              4

1.3.2 Physical and Structure Properties                                                                       5

  • Applications of Lead Selenide. 6

1.3.4 Theory of operation                                                                    7

1.4       Kramers- Kronig Relationship                                                                        7

1.5       Objective of The Study                                                                                  8

CHAPTER TWO – LITERATURE REVIEW                                        

2.1       Introduction to Optical Theorem                                                                    9

2.2       Theory of the Optical Properties                                                                     9

2.2.1    Optical Conductivity                                                                                      10

2.2.2    Relation of the Complex Dielectric Function to Observables                        14

2.3       Derivation of Kramers-Kronig Relations                                                        16

2.4       Physical Interpretation of Kramers Kronig Relation                                      17

CHAPTER THREE – METHODOLOGY

3.1       Index of Parameters                                                                                        20

3.2       Formulas                                                                                                          21

3.3       Calculations                                                                                                    22

 

 

CHAPTER FOUR – RESULTS AND DISCUSSIONS

4.1       RESULTS                                                                                                                   26

4.11     The Reflectance Spectrum of Lead Selenide in the Photon Energy Range 1.00-6.00eV                                                                                                                                                          26

4.1.2        The Reflection Coefficient of Lead Selenide in Photon Energy of Range 1.00-6.00eV                                                                                                                                                                  27

4.1.3         The Refractive Index of Lead Selenide in Photon Energy of Range 1.00-6.00eV                                                                                                                                                              28

4.1.4 The Extinction Coefficient of Lead Selenide in Photon Energy of Range 1.00-6.00eV                                                                                                                                                              29

4.1.5       The Real Part of the Complex Dielectric Constant of Lead Selenide in Photon Energy of Range 1.00-6.00eV                                                                                                                            30

4.1.6       The Imaginary Part of the Complex Dielectric Constant of Lead Selenide in Photon Energy of Range 1.00-6.00eV                                                                                                    31

4.1.7 The Transmittance of Lead Selenide in Photon Energy of Range 1.00-6.00eV                                                                                                                                                                          32

4.1.8 The Absorption Coefficient of Lead Selenide in Photon Energy of Range 1.00-6.00eV                                                                                                                                                            33

4.1.9 The Real Part of the Optical Conductivity Of Lead Selenide in Photon Energy Of Range 1.00-6.00eV                                                                                                                                     34

4.1.10 The Imaginary Part Of The Optical Conductivity Of Lead Selenide in Photon Energy Of Range 1.00-6.00eV                                                                                                                                    35

4.2 INTERPRETATION AND DISCUSSION

4.2.1 The Reflectance Spectrum of Lead Selenide in the Photon

Energy Range 1.00-6.00eV                                                                                        36

4.2.2 The Reflection Coefficient of Lead Selenide in Photon

Energy Range 1.00-6.00eV                                                                                          36

4.2.3 The Refractive Index of Lead Selenide in Photon

Energy Range 1.00-6.00eV                                                                                          36

4.2.4 The Extinction Coefficient of Lead Selenide in Photon

Energy Range 1.00-6.00eV                                                                                          36

4.2.5 The Real Part of the Complex Dielectric Constant Of Lead

Selenide in Photon Energy Range 1.00-6.00eV                                                           36

4.2.6     The Imaginary Part of The Complex Dielectric Constant of Lead selenide In Photon Energy of Range 1.00-6.00eV                                                                                                    37

4.2.6       The Imaginary Part of the Complex Dielectric Constant of Lead Selenide In Photon Energy Of Range 1.00-6.00eV                                                                                         38

4.2.8 The Absorption Coefficient of Lead Selenide in Photon Energy Range 1.00-6.00eV                                                                                                                                                             39

4.2.9   The Real Part of the Optical Conductivity of Lead Selenide in Photon Energy of Range 1.00-6.00eV                                                                                                                                                40

4.2.10 The Imaginary Part of The Optical Conductivity of Lead Selenide in Photon Energy Range 1.00-6.00eV                                                                                                                                    41

CHAPTER FIVE – SUMMARY AND CONCLUSION

REFERENCES

APPENDIX

 

CHAPTER ONE

1.1     INTRODUCTION TO SEMICONDUCTOR

A semiconductor is a solid material that has an electrical conductivity that is intermediate between those of conductors and of an insulator. Semiconductors are important materials, because of their unique electronic properties, they are the materials of choice for modern electronic devices. The tremendous importance of semiconductor in the present-day electronics stems in part of from the fact that their electrical properties are sensitive to small concentration of impurities. Besides their unique properties for electronics applications, semiconductors also have many other important properties that are very useful for photonic device applications. Many semiconductors are also used for acousto-optic devices and nonlinear optical devices. In such applications, which are based solely on the dielectric properties of semiconductors, semiconductors are nothing but another group of dielectric optical materials.

In metals highly mobile electrons roam freely within the structure, in a semiconductor the electrons are trapped by the covalent forces between the atoms that form the lattice. The conductivity of semiconductors is therefore dependent on the amount of charge carriers that participate in the conduction. Conduction in semiconductors occurs via charge carriers known as “electrons and holes”. The electrons are negative charge carriers while the holes are positively charged.

 

 

1.1.2 N-type and P-type semiconductor

Depending on the type of impurity added there are two types of semiconductors N-type and P-type, in N-type semiconductor the majority carriers are electrons and minority carriers are holes, while in the P-type semiconductor majority carriers are holes and the minority carriers are electrons. The properties of a pure semiconductor can be changed very significantly by adding very small amount of impurities of materials having five electrons in their outer most shell and the process is called “doping”.

N-type doping changes a semiconductor into a material with a surplus of electrons compared to the amount of holes, in that case the semiconductors is called an N-type semiconductor. If the density of electrons is n, density of holes is p. then in an n-type semiconductor, n will be greater than p, the doping atoms are therefore called donors in this case.

P-type doping changes a semiconductor into a material with a surplus of holes compare to the amount of electrons. The semiconductor is called the P-type semiconductor. Similarly in a P-type semiconductor p is greater than n, in this case doping atoms are called acceptors. The process of doping has reduced the number of electrons and increased the number of holes.

1.1.3 Intrinsic and Extrinsic semiconductor

1.1.3.1 Intrinsic semiconductor: Semiconductor in its pure, un-doped form is called intrinsic semiconductor, in intrinsic semiconductor the number of electrons equals the number of holes and thus conductivity is very low as valence electrons are covalently bonded also the free carriers are generated by thermal energy and thus while an electron is created  a hole occurs simultaneously. It is called electron-holes pair.

1.3.1.2 Extrinsic semiconductor: These are semiconductors that are doped are said to have higher and better conductivity. Impurities, donors and acceptors are introduced in the pure intrinsic semiconductor, thermal energy frees electrons from donor atoms and holes from acceptor atoms. Donor doping creates an n-type material by donating an extra electrons. On the other hand the acceptor doping creates a p-type material. The density of dopants is normally higher than free carriers in a semiconductor. Thus as a consequence of doping the conductivity of a semiconductor can be changed. Conductivity is directly related to the amount of free carriers in a semiconductor. Therefore decreasing the amount of free carriers will lead to an increase in conductivity.

Semiconductors are defined by their electric conductive behavior. Metal are good conductors because at their Fermi level, there is a large density of energetically available states that each electron can occupy, metal conductivity decreases with temperature increase because thermal vibrations disrupt the free motion of electrons. Insulators by contrast are very poor conductor of electricity because there is a large difference in energies between the conduction and the valence band. The valence band is occupied by electrons which are free from their parent atoms. Semiconductors on the other hand have intermediate level of electrical conductivity when compared to metals and insulators. Their band gap is small enough that a small increase in temperature promotes sufficient number of electrons from the lowest energy level to the conduction band.

1.2       GROUP IV-VI SEMICONDUCTOR

When any member of the group IV elements, is bounded to the group VI element an IV-VI semiconductor is formed, IV-VI semiconductors are used primarily in optoelectronic devices designed for detection and emission of mid-infrared electromagnetic radiation. Technologically important IV-VI semiconductors include binary PbS, PbSe, PbTe and pseudobinary, tenary and quaternary alloys such as PbSnSe, PbSnTe, PbEuTe, and PbSnSeTe. Depending on the alloy composition and temperature their band gaps range from 0 to over 500 meV. they are direct gap materials with conduction and valence band minima at the L-point in k-space . Such properties make IV-VI semiconductor useful for the fabrication of optoelectronic devices covering the 3µm to 30µm spectral range.

1.3 LEAD SELENIDE

1.3.1 INTRODUCTION AND APPLICATION

Lead selenide (PbSe), is a semiconductor material. It forms cubic crystals of the NaCl structure; it has a direct band gap of 0.27 eV at room temperature. It is a grey crystalline solid material. It is used for manufacturing of infrared detectors for thermal imaging, operating at wavelengths between 1.5–5.2 µm. It does not require cooling, but performs better at lower temperatures. The peak sensitivity depends on temperature and varies between 3.7–4.7 µm single Nano-rods and polycrystalline nanotubes of lead selenide have been synthesized via controlled organism membranes. The diameter of the Nano-rods were approximately 45 nm and their length was up to 1100 nm, for nanotubes the diameter was 50 nm and the length up to 2000 nm. Lead selenide Nano crystals embedded into various materials can be used as quantum dots, for example in Nano crystal solar cells.

Lead selenide is a thermoelectric material. The mineral clausthalite is a naturally occurring lead selenide. It may be formed by direct reaction between its constituent elements (lead and selenium)

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