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 CONTENT
CONTENT Page Number
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
LIST OF FIGURES
FIGURE PAGE
- The energy band structure of insulator, semiconductor and a conductor 4
- Crystal structure of lead selenide 5
4.1 Reflectance Spectrum of Lead Selenide 26
4.2 Reflection Coefficient of Lead Selenide 27
4.3 Refractive Index of Lead Selenide 28
4.4 Extinction Coefficient of Lead Selenide 29
4.5 Real part of the Complex Dielectric Constant of Lead Selenide 30
4.6 Imaginary part of the Complex Dielectric Constant of Lead Selenide 31
4.7 Transmittance of Lead Selenide 32
4.8 Absorption Coefficient of Lead Selenide 33
4.9 Real Part of the Optical Conductivity of Lead Selenide 34
4.10 Imaginary Part of the Optical Conductivity of Lead Selenide 35
LIST OF TABLES
TABLE PAGE
3.1 Value of wavelength λ, refractive index n. and the extinction coefficient for PbSe 22
3.2 Values for the optical Properties of Lead Selenide in the photon Energy of 1.00-6.00eV 25
CHAPTER 1
INTRODUCTION
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 semiconductorsis 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.
Figure 1.1 the energy band of insulator, semiconductor and a conductor (www.classle.net, 2015)
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 singleNano-rods and polycrystallinenanotubes 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 mineralclausthalite is a naturally occurring lead selenide.It may be formed by direct reaction between its constituent elements (lead and selenium)
1.3.2 PHYSICAL AND STRUCTURAL PROPERTIES
Figure 1.2 crystal structure of lead selenide (www.webelements.com,2015)
Lead selenide has the following properties
- Formula: PbSe
- Geometry of lead: 6 coordinate: octahedral
- Prototypical structure: NaCl (rock salt)
- Formula weight: 16g/mol
- Band gap: 0.26ev
- Crystal structure: cubic
- Colour: grey
- Appearance: crystalline solid
- Melting point: 1078°C
- Lattice constant: 6.1243Å
- Density: 8100 kg m-3
- Applications of Lead Selenide.
- Infrared detectors for thermal imaging
- Gas analysis
- Hotspot detection
- Industrial process and quality control
- Defense application
Lead Selenide is one of the first materials sensitive to the infrared radiation used for military applications. Early research works on the material as infrared detector were carried out during the 1930s andLead Selenide has been commonly used as an infrared photodetector in multiple applications, from spectrometers for gas and flame detection to infrared fuzes for artillery ammunition.
As a sensitive material to the infrared radiation, Lead Selenide has unique and outstanding characteristics: it can detect IR radiation of wavelengths from 1.5 to 5.2 µm, it has a high detectivity at room temperature (uncooled performance), and due to its quantum nature, it also presents a very fast response, which makes this material an excellent candidate as detector of low cost high speed infrared imagers.
1.3.4 Theory of operation
Lead Selenide is a photoconductor material. Its detection mechanism is based on a change of conductivity of a polycrystalline thin-film of the active material when photons are incident. These photons are absorbed inside the Lead Selenide micro-crystals causing then the promotion of electrons from the valence band to the conduction band. Even though it has been extensively studied, today the mechanisms responsible for its high detectivity at room temperature are not well understood. What is widely accepted is that the material and the polycrystalline nature of the active thin film play a key role in both the reduction of the Auger mechanism and the reduction of the dark current associated with the presence of multiple intergrain depletion regions and potential barriers inside the polycrystalline thin films.
1.4 KRAMERS- KONONIG RELATIONSHIP
The Kramer-kronig relations are a set of mathematical equations connecting the real and the imaginary parts of any complex function which is analytic in the upperhalf plane. These relations are often used to relate the real and the imaginary parts of response functions in physical system because causality implies the analytic condition is satisfied, and conversely analytic implies causality of the corresponding physical system.
For complex function
The Kramers-kronig relation is given by
Where p is the Cauchy principal value
1.5 OBJECTIVE OF THE STUDY
The need for more efficient semiconductor in electronics applications lead to the study of the optical properties of lead selenide.In the study of the optical properties the parameters that are obtained are the reflectance, reflection coefficient, the refractive index, the extinction coefficient, real and imaginary parts of complex dielectric constant, transmittance, absorption coefficient, and the real and optical parts of the optical conductivity. The optical properties will help to understand how lead selenide can be used to fabricate state of the art semiconductor devices and it also serves as the fundamental basis in understanding the behavior in different conditions such as pressure, temperature, doping concentration etc.
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