Unit 1 - 23PHE103 Applied Physics for Electronics Engineering PDF

UNIT I CRYSTAL PHYSICS In this unit the following chapters are covered.  Single crystalline, polycrystalline and amorphous materials  Single crystals  Directions and planes in a crystal  Coordination number and packing factor for SC, BCC...

UNIT I CRYSTAL PHYSICS In this unit the following chapters are covered.  Single crystalline, polycrystalline and amorphous materials  Single crystals  Directions and planes in a crystal  Coordination number and packing factor for SC, BCC, FCC and HCP structures  Crystal Growth techniques 1. INTRODUCTION  The matter is usually existed in solid state or fluid state.  All the materials are composed of atoms and molecules.  A solid is an essentially an ordered array of atoms by electric forces to form a very large molecule.  The properties and behavior of solid materials differ from one to another due to their crystal structures by the way of arrangement of atoms.  Solids are classified as crystalline materials and Non-crystalline (Amorphous) materials. Crystalline Non–Crystalline (Amorphous) 1. Regular Arrangement of atoms. 1. Irregular Arrangement of atoms 2. Internal symmetry of atoms. 2. No internal symmetry of atoms 3. Directional property 3. No directional property. 4. Anisotropic 4. Isotropic 5. Eg: Al, Cu, Steel 5. Eg. Glass, Rubber, Plastic Crystalline Materials: Crystalline Materials are either a single crystal or poly-crystal with regular arrangement of atoms. Single Crystal: The entire material is made up of only one material. Poly-Crystal: It is a collection of many small crystals. Crystalline materials are made up of either metallic crystals or non metallic crystals. 1 Example: Metallic Crystals: Iron, Copper, Silver, Aluminium, Tungsten, Gold, etc. Non-Metallic Crystals: Carbon, Germanium, Silicon, polymers, etc. Non –Crystalline (Amorphous): The materials in which atoms are arranged in irregular form. Eg: Rubber, Glass. Plastics 1.1 CRYSTAL STRUCTURE AND FUNDAMENTAL TERMS OF CRYSTALLOGRAPHY Crystal structure The arrangement of atoms in the crystal is called crystal structure. It is described in terms of its Crystallographic axes and the angles between them. The crystal structure is the basis of understanding the properties of materials. Crystallography The crystals can exist in a wide range of sizes and the size of the crystal depends upon the rate at which it is formed. The study of the geometrical form and other physical properties of crystalline solids are called Crystallography. Fundamental Crystallographic terms Lattice Points It denotes the position of regular and periodic arrangement of atoms. 2 Space lattice An arrangement of atoms of a crystal as lattice points in three dimensions is called space lattice. A three dimensional collection of points is called a space lattice, in which each atom has identical surroundings. Lattice lines or directions The lines joined between the lattice points are called lattice lines or lattice directions. Lattice point Lattice lines Lattice planes Lattice plane The crystal lattice may be considered as an aggregate of a set of parallel equidistant planes passing through the lattice points. These planes are known as lattice planes. (a) (b) (d) (c) Different lattice planes For a particular lattice, these sets of phase may be chosen in different ways, for example (a), (b), (c) (d) etc. 3 Basis It is a unit assembly of atoms or molecules which are identified with respect to the position of lattice points. The basis must be identical in composition, arrangement and orientation. When the basis is repeated with correct periodicity in all directions gives the actual Crystal structure. Therefore a space lattice is combined with a basis to get a Crystal structure. + = (a) Space lattice (b) Basis (c) Basic associated (d) Crystal structure with space lattice Space lattice + Basis = Crystal structure Unit cell It is the smallest unit and fundamental building block of a crystal. Which, when repeated indefinitely in three dimension gives the whole crystal structure. Lattice point Unit cell Lattice Parameters of a unit cell The Lattice Parameters of a unit cell is defined by both intercepts (a, b, c,) and interfacial angles (). In Figure the axis length OA = a, OB = b and OC = c determines the intercepts of the unit cell. The angles between the three intercepts are known as interfacial angle. Y The angle between the axis Y and Z =  B The angle between the axis Z and X =  b The angle between the axis X and Y =    o a A c X  C Z 4 Primitive Cell It is defined as unit cell which contains lattice points at corner only. (Or) It is the simplest type of unit cell contains only one lattice point per unit cell. Example: Simple cubic If there are more than one lattice points in a unit cell it is called a non primitive cell. All primitive cells are unit cells, but, all unit cells are not primitive cells. 1.2 CRYSTAL SYSTEMS The Crystal System Crystals are classified into 7 crystal systems on the basis of lattice parameters. The basic crystal systems are 1. Cubic 2. Tetragonal 3. Orthorhombic 4. Monoclinic 5. Triclinic 6. Rhombohedral 7. Hexagonal Each of the 7 Crystal systems are discussed briefly as follows. Cubic system Y This is a crystal system with three axes of a equal lengths perpendicular to each other. 90° 90° a i.e., a = b = c and X a 90°      = 90° Example: Z Sodium chloride (Na Cl), Calcium Fluoride (CaF2). Tetragonal system Y In this system, there are three axes perpendicular to each other. Two axes are equal in length b and third axis is either longer or shorter. 90° 90° a i.e., a = b  c and c X 90°      = 90° Example: Ordinary white tin, indium Z 5  Y Orthorhombic system In this system, there are three axes perpendicular to each other. b These axes are all of different lengths. 90° i.e., a  b  c and 90° a X c      = 90° 90° Example: Sulphur, Topaz. Z Monoclinic system In this system, there are three axes of different lengths. Two axes are perpendicular to each other and third are obliquely inclined. i.e., a  b  c and    = 90°;   90° Example: Na2 SO3, FeSO4. Triclinic system In this system, there are three axes of unequal lengths, all oblique to each other. i.e., a  b  c and       90° Example: Copper sulphate (CuSO4), Potassium dichromate (K2Cr2O7) Rhombohedral system In this system, there are three axes equal in lengths and are equally inclined to each other at an angle other than 90o. i.e., a = b = c and       90° Example: Calcite 6 Hexagonal system In this system, two axes (say horizontal) are equal 120° in one plane at 120° with each other. The third axis (say vertical) is different (i.e., either longer or shorter c than the other three axes) and perpendicular to this plane. i.e., a = b  c and 90° 90° b a    = 90°; 120°  = 120° Example: Quartz, tourmaline S. Crystal System Axial length Interaxial angles Example No. ( a, b, c ) () 1 Cubic a=b=c  =  =  = 90° NaCl CaF2 2 Tetragonal a=bc  =  =  = 90° Indium SnO2 3 Orthorhombic abc  =  =  = 90° Sulphur, Topaz, BaSO4 BaSO4 4 Monoclinic abc  =  =  90° 90°;  90° NaSO4 Gypsu FeSO4 5 Triclinic abc       90° CuSO4 K2Cr2 O7 6 Rhombohedral a=b=c  =  =   90° Calcite Sb 7 Hexagonal a=bc  =  = 90°; = 120° Zn, Mg 7 1.3 BRAVAIS LATTICES It is found that the point symmetry of crystal lattice can lead to 14 different types of lattices in three dimensional spaces. The 14 Bravais Lattices are illustrated in Figure. a a a c c a a a a a a a a a a P F I P I Cubic Tetragonal c c c c a a a a b b b b P C F I Orthohombic c  a a a a a a R P Rhombohedral (Trigonal) Hexagonal c c   c a a   b b a P C  P Monoclinic Triclinic  These 14 different types of arrangement are called Bravais lattices.  Each type of this arrangement can be represented by a unit cell.  The Bravais Lattices formed by unit cells are marked by the following symbols : 8  Primitive or Simple Lattice – P Body Centered Lattice – I Face Centered Lattice – F Base Centered Lattice – C Fourteen Bravais Lattices S.No. System Symbol types No. of possible 1. Cubic P I F 3 2. Tetragonal P I 2 3. Orthorhombic P C I F 4 4. Monoclinic P C 2 5. Triclinic P 1 6. Rhombohedral P 1 7. Hexagonal P 1 14 Bravais Lattices 1.4 RELATION BETWEEN LATTICE CONSTANT & DENSITY Consider a cubic crystal of lattice constant „a‟. The density of the crystal =  = a3  Mass  Volume of the unit cell  Density    Volume  Mass in each unit cell = a3 ……….(1) The number of atoms per unit cell = n The atomic weight of the material = M Avogadro‟s number = N (i.e., Number of molecules per kg mole of the substance) Mass of each molecule =M N Where M is atomic weight M Mass in each unit cell = n …………….. (2) (for n atoms) N 9 From equations (1) and (2), we have nM a 3  N nM  Na 3   Number of atoms per unit cell   Atomic weight   Avogadros number    Lattice cons tan t  3 From the above equation, the value of lattice constant „a‟ can be calculated. 1.5 MILLER INDICES  Miller indices are certain numbers which are used to represent crystal planes.  The miller indices are also defined as the reciprocals of the intercepts made by the plane on the crystallographic axes when reduced to smallest numbers.  They are always whole number.  A set of parallel planes are represented by the same Miller indices.  The common notations used to represent a plane in the Miller indices are h,k,l.  They are commonly written as (h k l). The following procedure is used to find the Miller Indices of a plane or face. 1. Determine the coefficient of the intercepts of the plane. 2. Take reciprocals for the coefficients. 3. Convert it to the smallest integers by taking LCM 4. Enclose these integers in brackets (h k l) to get Miller indices.  5. Use a bar in Miller indices if the intercept is on the negative side Eg. h k l 10  Z  F c C B E H A Y b D G a X Various planes cutting crystallographic axes Plane Intercept Reciprocals Smallest Miller Indices of Multiples Coefficient Integers having of the same ratio Intercepts ABC 1a 2b 1c 1 1 1 2 1 2 (2 1 2) 1 2 1 1 1 1 DEF 2a 3b 4c 6 4 3 (6 4 3) 2 3 4 1 1 1 GH 3a 4b  c 3 4  4 3 0 (4 3 0) Important features of the Miller indices i) All equally spaced parallel planes have the same index numbers ( h k l ) ii) A plane parallel to one of the co-ordinate axes has an intercept of infinity. iii) If the miller indices of two planes have the same ratio (i.e., 422 or 211), then the Planes are parallel to each other. iv) If a normal is drawn to a plane ( h k l ), it is the direction of the plane indicated as [ h k l ]. 11 Summary of Miller Indices:  A set of three integers to indicate the crystal plane  The reciprocal of the intercepts  Written by ( h k l) Procedure for calculating Miller Indices: 1. Determine the coefficient of the intercepts 2. Take reciprocals for the coefficients. 3. Convert it to the smallest integers by taking LCM 4. Enclose these integers in brackets (h k l) 5. Use a bar the intercept is on the negative side, Eg. h k l Example: Step I : 2a 3b 3c 2 3 3 1 1 1 Step II : 2 3 3 6 6 6 Step III : 2 3 3 Step IV : ( 3 2 2 ). Miller Indices are (3 2 2) 1.6 INTERPLANAR SPACING FOR (h k l) PLANES OF A CUBIC STRUCTURE Consider a plane ABC,  P is a point on the plane.  Let OP be normal to the plane from the origin.  h, k, l are the miller indices of the plane.  The intercepts, OA = a h , OB = a k , OC= a l  OP = d is the perpendicular distance from the origin.   , , are the angles, Cos () = dh a Cos () = dk a Cos () = dl a 12  But Cos2  + Cos2  + Cos2  = 1 ( By the law of Cosine’s property) d 2 h2 d 2 k 2 d 2l 2  2  2 1 a2 a a d2 2 2  h  k2  l2 1  a a2 a d2  , d  h2  k 2  l 2  h  k 2  l2 2 1.7 SIMPLE CUBIC (SC) STRUCTURE 1 Number of atoms per unit cell: 8 x =1 8 Co-ordination Number =6 a Atomic radius: r = 2 Atomic Packing Factor v (APF) = V 4 3 1 x πr = 3 a3  4 a 2 3 3a 3  APF   0.52  52% 6 In SC, only 52% is filled with atoms and 48 % is empty. It is loosely packed structure. Eg: Polonium 1.8 BODY CENTERED CUBIC (BCC) STRUCTURE 1 Number of atoms per unit cell: 8 x +1=2 8 Co-ordination Number =8 13 Atomic radius: (DF) 2  (DG) 2  (FG) 2 (4r) 2  (DC) 2  (CG) 2  a 2 16r 2  a 2  a 2  a 2 3a2 r2  16 3a r 4 Atomic Packing Factor v (APF) = V 4 3 2 x πr 3 = a3 3   8 3 a  4   3  3a 8  3 3 3 a3  64 x 3 a 3  3 APF   0.68  68% 8 In BCC, 68% is filled with atoms and 32 % is empty. It is tightly packed structure. Eg: Chromium. 1.9 FACE CENTRED CUBIC ( FCC) STRUCTURE  1  1 Number of atoms per unit cell: 8 x    6 x   4  8  2 Co-ordination Number = 12 Atomic radius: (DB) 2  (DC) 2  (CB) 2 (4r) 2  a 2  a 2 16r 2  2 a 2 2a2 r2  16 a2 r2  8 a a r  8 2 2 14  4 3 4 x πr v 3 Atomic Packing Factor: APF = = V a3 3 16  a     2 2  3 3a 16  a 3  3 x 16 2 x a 3  APF   0.74  74% 3 2 In FCC, 74% is filled with atoms and 26 % is empty, It is tightly packed structure. Eg: Nickel 1.10 HEXAGONAL CLOSE PACKED (HCP) STRUCTURE No. of atoms/unit cell = (top layer)+ (Bottom layer) + (Centre) = = 1 + 1 + 1+ 3 = 6 atoms Co-ordination Number: Coordination Number is 12 Atomic Radius: Nearest distance between two atoms is 2r = a a r = 2 15 Calculation of c/a ratio (or) Axial ratio: Let „C‟ is the height of the unit cell & „a ‟ be the distance between two atoms. Consider triangle ABO, In triangle ABY, AY Cos 30o = , AB AY = AB Cos 30o 3 AY = AB , 2 3 AY = a --------- (1) 2 In triangle AXZ, (AZ)2 = (AX)2 + (XZ)2 --------- (2) C  2 a2 = (AX)2 +   --------- (3)  4  2 But AX = AY (from the figure) 3 2 3 AX = a 3 2 a AX = ---------- (4) 3 Substitute equation (4) in equation (3) 2  a   C2  a2 =   +    3   4 , a2  C2  a2 = +   3  4  C2 a 2 3a 2  a 2 2a 2 a 2   4 3 3 3 2 C 8 2  a 3 C 8   1.633 a 3 Atomic Packing Factor: (APF) 4 6  π r3 v 3 APF   V 6  Triangle ABO  height 24  r 3 APF  1 3  6  (BO)(AY)  C 2 16  Put ra 2 3 a 24    APF  2  3 3  3  (a) a C   2  24  a 3 APF   3 8  3  3  (a) a C   2  24  a 3 APF   3  24 x 3 a  a xC  2  2 a APF  3 3 C C 8 a 3 But  and  , a 3 C 8 2 3 APF  3 3 8 2 2 APF   3 8 3x2 2  APF   0.74  74% 3 2 In HCP, 74% is filled with atoms and 26 % is empty. It is tightly packed structure. Eg: Zinc Comparison of SC, BCC, FCC, and HCP structures Charateristics SC BCC FCC HCP No. of Atoms per Unit 1 2 4 6 Cell Co-ordination No. 6 8 12 12 a a 3 a a Atomic Radius 2 4 2 2 2   3  2  Atomic Packing factor =0.52 =0.68 =0.74 =0.74 6 8 6 3 2 Packing Density 52 % 68 % 74% 74% Example Polonium Cr, Fe Pb, Ni Mg, Co 17 1.11 CRYSTAL GROWTH TECHNIQUES The crystal growth techniques are classified into Five types. They are,  Solution growth technique  Melt growth technique  Hydrothermal growth technique  Gel growth technique  Vapour growth technique 1.11.1. Melt Growth Technique  It is a method for making large single crystals.  In this method, the materials melted uniformly and grown as single crystal.  Elemental semiconductors (Ge and Si), can be prepared.  In this method, high homogeneity crystals are produced  It involved the method of Crystal pulling.  There are two techniques of crystal pulling 1. Bridgeman Technique and 2. Czochralski Technique 1. Bridgeman Technique Principle: Moving the melt from the hot zone to the cold zone of the furnace.  At first the material is melted in the crucible at the hot zone.  A seed crystal is melted with the melt.  The crucible is then moved slowly into the cooler zone.  Then the melt converts to a solid single-crystal.  Two kinds of Bridgeman technique with the same concept Horizontal Bridgeman Technique  In this method, a silica crucible containing molten material is pulled horizontally through a furnace.  The shape of the resulting crystal is determined by the crucible 18 Vertical Bridgeman Technique  In this technique the crystal is pulled vertically.  No interactions between the boat and the crystal  Crystals can be grown without seed crystal.  Here melt composition can be controlled during the growth.  It gives cylindrical shape crystal  But in horizontal Bridgman technique the D-shaped crystals are grown. Advantages  Less defects.  Low cost. Disadvantages  No desired shape  Wastage of single crystal 2.Czochralski Technique  It is invented in 1916. It is used to obtain single crystals of semiconductors Principle  The crystal pulling method is involved.  A rotating seed crystal is dipped into the melt and slow pulling of the seed gives the crystal in cylindrical shape. 19 Construction:  It consists of silica crucible in which raw materials are kept and melted by a heating furnace.  A seed crystal is fixed at the bottom of the nickel seed holder.  The seed holder has small tube for passing cool air or water to reduce the thermal conductivity of the seed crystal.  A rotating shaft is fixed with the seed holder to pull and rotate the crystal.  The rotation of shaft also helps for uniform mixing of the melt and dopant.  A small tube is given for adding impurities to obtain n-type or p-type semiconductor.  The entire set up is kept inside a high vacuum chamber to avoid contamination and oxidation. Working  The raw materials kept in silica crucible are melted with the help of furnace.  Then the seed crystal is slowly allowed to touch the top of the melt.  Now the temperature is reduced below the melting, the melt is freezing and changed into solid on the seed crystal.  Now the seed crystal is pulled out very slowly and the crystal also grows in size. Factors to be controlled  The pulling rate of the crystal  Temperature of the melt and  Temperature gradient of the crystal  Heat balance equation to control the growth, VρL = K ( dT/dX) Advantages  Large diameter of crystals can be obtained  No contact with the walls of the crucible.  Desired shape of crystal can be obtained  Computer and Sensors are used  It is simple, reliable, low cost and high efficiency. Disadvantages  More defects are created. 20 1.12 SILICON CHIP PRODUCTION PROCESS The silicon chip production process is a complex and multi-step process that involves the following major steps: 1. Wafer manufacturing: A cylindrical ingot of pure silicon is sliced into thin wafers. The wafers are then polished to a high degree of smoothness. 2. Oxidation: A thin layer of silicon dioxide is grown on the surface of the wafer. This layer will act as an insulator between the different layers of the chip. 3. Photolithography: A pattern of the desired circuit is transferred to the silicon dioxide layer using a photolithography process. This process uses light to expose a light-sensitive polymer called photoresist. 4. Etching: The exposed areas of the photoresist are then etched away, leaving the desired circuit pattern on the silicon dioxide layer. 5. Ion implantation: Dopant atoms are implanted into the silicon wafer to create the desired electronic properties. Dopants are atoms that have either one more or one fewer electron than silicon. 6. Deposition: Thin layers of other materials, such as metal, are deposited on the wafer to form the conductive paths and contacts of the chip. 7. Testing: The finished chips are then tested to ensure that they meet the desired specifications. The silicon chip production process is a highly automated process that is performed in clean rooms to prevent contamination. The process is also very expensive, and it can take several months to produce a working chip. Here are some of the challenges in the silicon chip production process:  The need for increasingly pure and defect-free silicon wafers.  The need for smaller and more complex circuit patterns.  The need for more precise and accurate lithography processes.  The need to control contamination in the clean room environment. The silicon chip production process is constantly evolving as new technologies are developed. The goal is to produce chips that are smaller, faster, and more energy- efficient. 21  Part A Questions 1. Which of the following is a type of crystal structure? (a) Simple cubic (b) Body-centered cubic (c) Face-centered cubic (d) All of the above 2. The coordination number of a simple cubic structure is: (a) 6 (b) 8 (c) 12 (d) None of the above 3. The atomic packing factor of a face-centered cubic structure is: (a) 0.74 (b) 0.68 (c) 0.52 (d) None of the above 4. Which of the following materials has a body-centered cubic structure? (a) Iron (b) Copper (c) Sodium chloride (d) Diamond 5. Which of the following materials has a face-centered cubic structure? (a) Iron (b) Copper (c) Sodium chloride (d) Diamond 6. The Miller indices of a plane that intersects the x-, y-, and z-axes at a/4, 2a/3, and a/2, respectively, are: (a) (121) (b) (312) (c) (213) (d) None of the above 22 7. The Bragg equation is: (a) 2d sin θ = nλ (b) 2d cos θ = nλ (c) 2d tan θ = nλ (d) None of the above 8. Which of the following is a type of defect in crystals? (a) Point defect (b) Line defect (c) Surface defect (d) All of the above 9. Which of the following is a type of point defect? (a) Vacancy (b) Interstitial (c) Substitutional impurity (d) All of the above 10. Which of the following is a type of line defect? (a) Edge dislocation (b) Screw dislocation (c) Both (a) and (b) (d) None of the above 11. Which of the following is a type of surface defect? (a) Step (b) Kink (c) Terrace (d) All of the above 12. Which of the following properties of crystals is affected by defects? (a) Electrical conductivity (b) Mechanical strength (c) Optical properties (d) All of the above 13. which of the following is a technique used to study the crystal structure of materials? (a) X-ray diffraction (b) Neutron diffraction (c) Electron microscopy (d) All of the above 23 14. Which of the following is a type of X-ray diffraction? (a) Single-crystal X-ray diffraction (b) Powder X-ray diffraction (c) Both (a) and (b) (d) None of the above 15. Which of the following is a type of neutron diffraction? (a) Elastic neutron diffraction (b) Inelastic neutron diffraction (c) Both (a) and (b) (d) None of the above Part B Questions 1. What is Bravais Lattice? 2. State the values of coordination number for HCP structure and diamond structure. 3. Define Unit Cell. 4. What are miller indices? 5. An element has a HCP structure. If the radius of the atom is 1.605ºA,find the height of unit cell. 6. Name the seven crystal systems. 7. A unit cell has the dimensions a = b= c = 4.74Ao and α = β = γ = 60o. What is its crystal structure? 8. A crystal plane cuts at 3a, 4b and 2c distances along the crystallographic axes. Find the Miller indices of the plane. 9. Define atomic packing fraction. 10. What is primitive cell? Give an example. 11. Name few techniques of crystal growth from melt. 12. Distinguish between crystalline material and amorphous material. 13. What is the coordination number of diamond unit cell? 14. Calculate the d-spacing of (321) planes of a simple cubic cell of lattice constant 0.41 nm. 15. What is the coordination number of diamond unit cell? 16. How carbon atoms are arranged in diamond and graphite structures? 17. Write down the relation between atomic radius and lattice parameter of HCP. 18. Why is diamond called as loosely packed system? 19. Define Space Lattice. 24 20. What are the Lattice parameters of an Unit Cell? 21. Bismuth has a = b = c = 4.74AU and angles α = β = γ = 60°. What is its crystal structure? 22. State the conditions imposed on the cell parameters for crystal systems having the largest number of Bravais lattices and the least number of nearest neighbours. 23. Which crystal structure is having least co- ordination number? Give example. 24. What are the co-ordination numbers for SC, BCC, FCC structures? 25. State the expression for interplanar spacing for a cubic system interms of lattice constantand Miller indices. 26. Define Atomic radius (r). 27. Define Co-ordination Number. 28. What is the principle of Bridgeman Technique? 29. What is Horizontal Bridgeman Technique? 30. What are the advantages and disadvantages Horizontal Bridgeman Technique? 31. What is Vertical Bridgeman Technique? 32. What is the principle of Czochralski crystal growth Technique 33. Give the Comparison between Bridgman technique and Czochralski Technique. 34. What are the advantages and disadvantages Czochralski crystal growth Technique? 35. Name the crystal structures of the following : (a) Gold (b) Germanium (c) Barium (d) Zinc. Part C Questions 1. What is packing factor? Prove that the packing factor of HCP crystal structure is 0.74. 2. Derive an expression for the interplanar spacing in a cubic structure. 3. What are Miller indices? Mention the steps involved to determine the Miller indices with example. 4. Explain the terms: atomic radius, coordination number and packing factor and Show that the packing factor for Face Centered Cubic and Hexagonal Close Packed structures are equal. 5. Define atomic packing factor. Calculate the number of atoms, atomic radius, coordination number and atomic packing fraction for BCC and FCC structures. 6. Describe Bridgman method of crystal growth. 7. Explain the construction and working of Czocholski technique for growing crystals with its advantages. 8. Explain Silicon Chip Production Process. 25  Problems 1. The lattice constant of a metal with a cubic lattice is 2.88 Å. The density of metal is 7200 kg/m3. Calculate the number of unit cell present in 1kg of the metal. 2. The lattice constant for a FCC structure is 4.938 Å. Calculate the inter planar spacing of (220) planes. 3. The material zinc has HCP structure. If the radius of the atom is 1/4th of the diagonal of hexagon, calculate the height of the unit cell in terms of atomic radius. 4. Calculate the interplanar spacing for (101) plane in a simple cubic crystal whose lattice constant is 0.42 nm. 5. An element has a HCP structure. If the radius of the atom is 1.605ºA, find the height of unit cell. 6. The distance between successive planes of Miller indices (111) is 2.078ºA for a metal having FCC structure. Find the atomic radius and volume of its unit cell. 7. The material zinc has HCP structure. If the radius of the atom is 1/4th of the diagonal of hexagon, calculate the height of the unit cell in terms of atomic radius. 8. Iron has BCC structure with atomic radius 0.123Ao. Find the lattice constant of the unit cell. 9. Copper has FCC structure and its atomic radius is 1.273 A. Find Lattice parameter and Density of copper. Given Atomic weight of copper =63.5, Avogadro number = 6.026x1026 mol-1. 10. The lattice constant of a cubic crystal is 2.5 Å. Find the lattice spacing for (310) and (213) planes in the lattice. 11. Show that in an ideal hexagonal closed packed structure the c/a ratio is 1.663 and its atomic packing factor equals to that of the face-centered cubic structure. 12. Calculate the d-spacing of (321) planes of a simple cubic cell of lattice constant 0.41 nm. 26  UNIT II PHOTONICS In this unit the following chapters are covered.  Population of energy levels  Einstein‟s A and B coefficients- derivation  He-Ne laser, Semiconductor lasers: homojunction and heterojunction  Applications of Lasers in Science, Engineering and Medicine  Digital Laser Material Processing technology 2. INTRODUCTION  Laser is an acronym for “Light Amplification by Stimulated Emission of Radiation”  The first Laser is Ruby Laser invented by T. Maiman in 1960.  The operating frequency of Laser is 1014 Hz to 1015 Hz in the visible region. Characteristics of laser 1. High Coherence 2. High Monochromaticity 3. High Directionality 4. High Intensity Difference between Ordinary Light and Laser Light S.No Ordinary light Laser light 1 Angular spread is more Angular spread is less 2 No directionality Highly directional 3. Less intensity High intensity 4. Not a coherent beam Coherent beam 5. Polychromatic monochromatic Ex: Sunlight, Hg vapour 6 Ex : He- Ne Laser, Co2 laser, etc., lamp,etc., 27 2.1. SPONTANEOUS EMISSION AND STIMULATED EMISSION Spontaneous emission and stimulated emission are two processes by which atoms or molecules emit photons. Spontaneous emission occurs when an electron in an excited state decays to a lower energy state and emits a photon. The photon's energy is equal to the difference in energy between the two states. The direction and polarization of the emitted photon are random. Stimulated emission occurs when an electron in an excited state is exposed to a photon of energy equal to the difference in energy between the two states. The photon interacts with the electron, and the electron decays to the lower energy state, emitting a photon in the same direction and with the same polarization as the incoming photon. The main difference between spontaneous emission and stimulated emission is that spontaneous emission occurs randomly, while stimulated emission is triggered by the presence of a photon. This makes stimulated emission much more efficient than spontaneous emission. Stimulated emission is the key process that allows lasers to work. In a laser, the atoms or molecules are first excited to a high energy state. Then, a photon is emitted, which stimulates other atoms or molecules to emit photons. This process is repeated, resulting in a beam of coherent light. Differences between spontaneous emission and stimulated emission Characteristic Spontaneous Emission Stimulated Emission Triggered by the presence of Occurs randomly a photon Direction of emitted Same as the direction of the Random photon incoming photon Polarization of emitted Same as the polarization of the Random photon incoming photon Efficiency Low High Used in Fluorescent lamps, LEDs Lasers 28 2.2. POPULATION INVERSION  It is defined as the state in which number of atoms in higher energy state is greater than that in the lower energy state.  At thermal equilibrium, the number of atoms N2 at higher energy states is much less than the number of atoms at lower energy state N1. ( N1>N2) E2 N2 E1 N1 Normal State  The process of obtaining more number of atoms in higher energy state than that of lower energy state (N2>N1) is known as population inversion. N2 E2 E1 N1 Population Inversion  Consider a three level system in which three energy levels E 1, E2, and E3 are present and population in those energy level are N1, N2, and N3 respectively. In normal conditions E1 < E2 < E3 and N1 > N2 > N3. E3 N3 E2 N2 E E1 N1 N  E1 is the ground state and its life time is unlimited.  E3 is the highest energy state and it is the unstable state due to its less life time. 29   E2 is the excited state and it is metastable state with more life time.  When suitable form of energy is supplied to the system then the atoms are excited from ground state (E1) to excited state (E2 and E3).  Due to instability, excited atoms will come back to ground state after the life time of the energy states E2 and E3.  If this process is continued then atoms will excite continuously to E 2 and E3.  Since E3 is the most unstable state atoms will fall into E2 immediately. At a stage the population in E2 will become more than the population in ground state. This condition is called population inversion and it is as shown in figure.  From Boltzmann statistics, N1  E  E1    exp   2  ---------- (1) N2  KT   We know that the energy of excited state (E2) is always greater than the energy of ground state (or lower energy state). So, we can write E2 > E1.  E  E1    So, exp   2  is always less than 1. So, N1 is greater than N2. i.e., N1 >> N2.  KT   But for laser production we must have N2 > N1, which is called population inversion. For population inversion, N = N2 - N1 must be positive.  To achieve population inversion, i.e., N2 > N1, various pumping processes are used for laser action. Conditions for population inversion 1. The population inversion is to be achieved. 2. Stimulated emission should be predominant over spontaneous emission 2.3. EINSTEIN’S QUANTUM THEORY OF LASER RADIATION Consider two energy levels E1 and E2, N1 - number of atoms in the ground state (E1), N2 - number of atoms in the excited state (E2) When the atoms are incident with photons, there are three processes can occur. 1. Stimulated Absorption. 2. Spontaneous Emission. 3. Stimulated Emission. 30 Stimulated Absorption  When the atoms in the ground state are incident with photons of energy (h),then the atoms are excited to higher energy state.  It is called stimulated absorption. Number of upward transitions per unit volume per sec N12 = A12 Q N1 Where A12 the probability of absorption per unit time Q the energy of incident radiation SPONTANEOUS EMISSION:  The atom from the excited state returns to the ground state by emitting a photon (in coherent) of energy (E2-E1 = h) without any applied energy (Q = 0).  It is known as spontaneous Emission. Number of downward transitions per unit volume per sec, N21 = B21 N2 Where, B21 Probability of emission per unit time STIMULATED EMISSION:  The atom from the excited state returns to the ground state by emitting a photon (coherent) with the help of external energy (Q).  It is called stimulated emission. Number of downward transitions per unit volume per sec, N21 = A21 Q N2 Where, A21  probability of emission per unit time At steady state, Number of upward Transition = Number of downward Transitions. A12 Q N1 = B21 N2 + A21 Q N2 A12 Q N1 - A21 Q N2 = B21 N2 Q (A12 N1- A21 N2) = B21 N2 B21 N 2 Q =  A12 N1  A21 N 2  Divided by (A21 N2) on both Numerator and denominator, 31  B21 N 2 A21 N 2 Q = A12 N 1  A21 N 2 A21 N 2 B21 A21 Q =. A12 N1 1 A21 N2 but A12 = A21 B21 1 Q =  A21 N1 1 N2 N1  h  According to Boltzmann‟s law,  exp   N2  KT  B21 1 Q =  ----(1) A21  h  exp   1  KT  But we know that the Planck‟s radiation formula is 8h 3 1 Q=  ----(2) C3  h  exp   1  KT  Comparing equations (1) and (2), we get B21 8 h 3  A21 C3 Thus Einstein coefficients (B21 and A21) are determined. 2.4. PRINCIPLE AND WORKING OF LASER The principle of a laser is Light Amplification by Stimulated Emission of Radiation. It works by creating a population inversion, which is a situation where there are more atoms in an excited state than in the ground state. This is done by pumping energy into the laser medium, such as with an electrical current or a light source. 32 Once the population inversion is created, a photon of light can stimulate the emission of another photon from an excited atom. This process is repeated, resulting in a beam of coherent light. The four basic principles of a laser are:  Spontaneous emission: This is the process by which an atom in an excited state decays to a lower energy state and emits a photon.  Stimulated emission: This is the process by which an atom in an excited state is exposed to a photon of energy equal to the difference in energy between the two states. The photon interacts with the atom, and the atom decays to the lower energy state, emitting a photon in the same direction and with the same polarization as the incoming photon.  Population inversion: This is a situation where there are more atoms in an excited state than in the ground state. This is necessary for stimulated emission to occur.  Feedback: This is the process by which the emitted photons are reflected back into the laser medium, stimulating more emission. The laser medium is typically a solid, liquid, or gas. The type of laser medium used depends on the wavelength of light that is desired. For example, a ruby laser uses a solid ruby crystal, while a helium-neon laser uses a gas mixture of helium and neon. The laser cavity is the region in which the laser light is amplified. It is typically made up of two mirrors, one of which is partially reflective and the other of which is totally reflective. The partially reflective mirror allows some of the laser light to escape, while the totally reflective mirror reflects the light back into the cavity. The laser is operated by pumping energy into the laser medium. This can be done with an electrical current, a light source, or another type of energy source. The pumping energy causes the atoms in the laser medium to become excited. Once the population inversion is created, a photon of light can stimulate the emission of another photon from an excited atom. This process is repeated, resulting in a beam of coherent light. The coherent light is emitted from the laser cavity through the partially reflective mirror. 33  The properties of a laser beam are determined by the laser medium, the laser cavity, and the pumping method. The laser beam can be focused to a very small point, making it ideal for applications such as surgery and cutting. It can also be used to generate high-power pulses of light, which are used in applications such as welding and material processing. Lasers are used in a wide variety of applications  Communication: Lasers are used in fiber optic communication systems to transmit data over long distances.  Manufacturing: Lasers are used to cut, weld, and mark materials.  Medical: Lasers are used in surgery, dentistry, and dermatology.  Scientific research: Lasers are used in research in fields such as physics, chemistry, and biology.  Entertainment: Lasers are used in light shows, laser pointers, and barcode scanners. 2.5. SEMICONDUCTOR DIODE LASER There are two types of semiconductors 1. Direct band gap semiconductor : The recombination of electron from conduction band combines directly with a hole in valence band and produces energy in the form of light. Eg: GaAs, GaP, InP 2. Indirect band gap semiconductor : The recombination of electron from conduction band combines with a hole in valence band through traps and produces energy in the form of heat. Eg: Ge, Si  Laser action is possible only in direct band gap semiconductor.  An LED can be converted into a LASER diode by increasing the current density and by polishing the contact surfaces of the P and N junctions of the diode. There are two types of Laser diodes. 1. Homo Junction Laser: The Junctions are made by single crystal Eg: GaAs laser, GaP laser 2. Hetero junction Laser: The junctions are made by different materials. GaAs/GaAlAs laser 34 1. Homojunction Laser: Principle  When the PN junction is forward biased, the electrons from N-region and holes from P-region cross the PN junction and recombine each other.  The electron in conduction band combines with a hole in valence band and hence the recombination of electron and hole produces energy in the form of light.  This photon may induce another electron in the conduction band from valence band and thereby stimulate the emission of another photon. Construction  The active medium is a (GaAs) PN junction. In which the P-region is doped with Ge and N-region is doped with Tellurium (Te).  The PN junction is well polished and acts as optical resonator.  There are two electrodes fixed at each side for forward biasing. 35 Working  When the semiconductor diode is forward biased, electrons from N-region are injected into P-region and holes are injected from P-region to N-region.  Recombination of majority carriers due to injection occurs in the depletion region. The recombination energy is converted into light radiation in the form of photons.  The photons produced during the recombination process again induce the recombination further, and producing more number of photons.  The wavelength of the emitted radiation depends on the band gap and the concentration of donor and acceptor atoms in GaAs. Calculation of wavelength Band gap of GaAs, Eg = 1.44 eV E g  h C but   hC Eg   hC  Eg 6.625 10 34  3 108  1.44 1.6 10 19   8626A 0 The wavelength is near IR region. 36 Advantages  It is used to manufacture the diode  The cost is low Disadvantages  It produces low power output  The output wave is pulsed and will be continuous only for sometime  The laser beam has large divergence.  It has high threshold current density. 2. Hetero junction Laser  Hetero junction is formed when the material on one side of the junction is differed from the other side of the junction.  In GaAs diode laser a hetero junction is formed between GaAs and GaAlAs. Principle: When the PN junction diode is applied with forward biased voltage, recombination of electron – hole takes place and it produces light energy. Finally this light is amplified to produce a laser beam. Construction... Laser  This hetero junction diode laser consists of five layers as shown in figure. The third layer GaAs [N–type] has narrow band gap and acts as active region.  This layer is sand witched between the layers of GaAlAs [P- type] and GaAlAs [N- type].  It also has a top layer made up of GaAs [P–type] and a bottom layer made up of GaAs [N–type]. Both these two layers are heavily doped and used as positive and negative electrodes. 37  A battery is connected between these two electrodes. This battery is used to pump the charge carriers to achieve the population inversion and produce the laser beam by direct conversion. Working  The working of the hetero junction diode laser is similar to homo junction laser.  The diode is initially forward biased and the charge carriers are injected into the active region from the GaAlAs [P-type] and GaAlAs [N-type] layers.  The charge carriers are injected continuously until the population inversion is achieved. Now, the electrons and the holes in the active region recombines and emits photon spontaneously.  These spontaneously emitted photons induce further the recombination and emit more photons. These photons are reflected back and forth at the junction and finally emit the laser beam.  The wavelength of the laser beam depends on the band gap of the material. If Band gap Eg = 1.55 eV E g  h C but   hC Eg   hC  Eg 6.625  10 34  3  10 8  1.55  1.6  10 19   8014A 0 38 Advantages  It produces continuous wave or pulsed type wave output.  The output power is high.  The laser beam is highly directional and coherent. Disadvantages  Growth of different layers is practically difficult.  It is costlier than homojunction laser. Applications  Mostly used in fibre optic communications.  It is used to read and write CDs and DVDs.  It is used in laser printer. 2.6. HELIUM-NEON LASER A helium-neon laser (He-Ne laser) is a type of gas laser that uses a mixture of helium and neon gas as the gain medium. It is the most widely used gas laser. HeNe lasers are typically used in scientific research, industrial applications, and medical procedures. The He-Ne laser works by creating a population inversion in a mixture of helium and neon gas. This is done by passing an electric current through the gas, which excites the electrons in the helium atoms. The excited helium atoms then collide with the neon atoms, transferring their energy to the neon atoms. This causes the neon atoms to also become excited. 39  When an excited neon atom decays to a lower energy state, it emits a photon of light. This photon can then stimulate other neon atoms to emit photons, creating a chain reaction. This chain reaction results in a beam of coherent light. The wavelength of light emitted by a HeNe laser depends on the energy difference between the two energy levels of the neon atoms. The most common HeNe laser emits light at a wavelength of 632.8 nanometers, which is in the red part of the visible spectrum. Some additional details  The gas mixture in a He-Ne laser typically consists of 9 parts helium to 1 part neon.  The pressure of the gas mixture is typically about 1 torr.  The laser cavity in a He-Ne laser is typically made up of two mirrors, one of which is partially reflective and the other of which is totally reflective.  The output power of a He-Ne laser is typically in the range of 0.5 to 50 milliwatts.  The beam quality of a He-Ne laser is typically very good, with a beam divergence of less than 1 milliradian. Advantages  They are relatively inexpensive to operate.  They are reliable and durable.  They produce a beam of coherent light.  They can be focused to a very small point. Applications  Scientific research: He-Ne lasers are used in research in fields such as physics, chemistry, and biology.  Industrial applications: He-Ne lasers are used to measure distances, align optical components, and etch materials.  Medical procedures: He-Ne lasers are used in surgery, dentistry, and dermatology.  Entertainment: He-Ne lasers are used in light shows and laser pointers. 40 2.7. APPLICATIONS OF LASERS IN SCIENCE, ENGINEERING AND MEDICINE Science: Lasers are used in scientific research in fields such as physics, chemistry, biology, and medicine. They are used to study the structure of molecules, the dynamics of chemical reactions, and the behavior of cells and tissues. Lasers are also used in astronomical observations and in the development of new technologies.  Lasers are used to study the structure of DNA and proteins.  Lasers are used to measure the speed of light.  Lasers are used to study the dynamics of chemical reactions.  Lasers are used to create artificial atoms and molecules.  Lasers are used to study the behavior of cells and tissues. Engineering: Lasers are used in engineering applications such as manufacturing, construction, and surveying. They are used to cut, weld, and mark materials, to measure distances, and to align optical components. Lasers are also used in robotics and in the development of new materials.  Lasers are used to cut metal and plastic.  Lasers are used to weld materials.  Lasers are used to mark materials.  Lasers are used to measure distances.  Lasers are used to align optical components.  Lasers are used in robotics.  Lasers are used in the development of new materials. Medicine: Lasers are used in medical applications such as surgery, dentistry, and dermatology. They are used to cut tissue, to remove tumors, and to correct vision problems. Lasers are also used in the treatment of skin diseases and in the management of pain.  Lasers are used in surgery to cut tissue, to remove tumors, and to correct vision problems.  Lasers are used in dentistry to remove decayed teeth and to prepare teeth for fillings.  Lasers are used in dermatology to remove skin blemishes and to treat skin diseases.  Lasers are used in the treatment of pain.  Lasers are used in the management of cancer. 41 2.8. WORKING PRINCIPLE OF LASER PRINTER A laser printer is a type of printer that uses a laser beam to create an image on a drum. The image is then transferred to paper using toner, which is a powder that is attracted to the charged areas of the drum. The toner is then fused to the paper using heat and pressure. The working principle of a laser printer can be divided into the following steps:  Processing: The image to be printed is first converted into a digital signal by the printer's computer. This signal is then sent to the laser printer's controller.  Charging: The drum is then charged by the controller. The drum is coated with a thin layer of a photosensitive material that can be electrically charged. The controller uses a wire to scan the drum, charging the areas that are to be printed.  Exposing: The laser beam is then scanned across the drum, discharging the areas that are not to be printed. This creates an electrostatic image of the desired image on the drum.  Developing: Toner is then applied to the drum. The toner is attracted to the charged areas of the drum, creating a visible image.  Transferring: The paper is then fed into the printer. The toner is transferred from the drum to the paper using a roller.  Fusing: The toner is then fused to the paper using heat and pressure. This ensures that the toner is permanently attached to the paper.  Cleaning: The drum is then cleaned to remove any remaining toner. The laser printer is a high-speed, high-quality printer that is commonly used in offices and businesses. It is also a popular choice for home use, as it can produce high-quality prints at a relatively low cost. 42 2.9. DIGITAL LASER MATERIAL PROCESSING (DLMP) Digital Laser Material Processing (DLMP) technology is a type of laser processing that uses a digital beam delivery system to control the laser beam with high precision. This allows for very accurate and precise laser cutting, engraving, and marking on a wide variety of materials. DLMP systems typically use a combination of a galvanometer scanning mirror and a spatial light modulator (SLM) to control the laser beam. The galvanometer mirror deflects the laser beam in the X-Y plane, while the SLM modulates the laser beam in the Z plane. This allows for very precise control of the laser beam's position and intensity. Applications  Laser cutting: DLMP systems can be used to cut a wide variety of materials, including metals, plastics, composites, and textiles.  Laser engraving: DLMP systems can be used to engrave text, images, and other designs on a variety of materials.  Laser marking: DLMP systems can be used to mark barcodes, serial numbers, and other identification information on a variety of materials. DLMP technology offers a number of advantages over traditional laser processing methods  High precision: DLMP systems can achieve very high precision in laser cutting, engraving, and marking.  Fast processing speeds: DLMP systems can process materials very quickly.  Wide range of materials: DLMP systems can be used to process a wide range of materials.  Flexibility: DLMP systems can be used to create a variety of complex shapes and designs. DLMP technology is a rapidly developing field, and new applications are being discovered all the time. DLMP systems are becoming increasingly popular in a variety of industries, including manufacturing, aerospace, medical devices, and consumer products. Specific examples of DLMP technology is being used today 43  Manufacturing: DLMP systems are being used to manufacture a wide variety of products, including medical devices, electronics, and automotive parts.  Aerospace: DLMP systems are being used to manufacture aircraft components, such as wings, fuselages, and engines.  Medical devices: DLMP systems are being used to manufacture medical devices, such as surgical instruments and implants.  Consumer products: DLMP systems are being used to manufacture consumer products, such as eyewear, jewelry, and home décor items. 44  Part A Questions 1. Which of the following is not a property of light? a. Wavelength b. Frequency c. Amplitude d. Mass 2. The term "photonics" refers to the: a. Study of light b. Creation, manipulation, and detection of light c. Application of light in practical devices d. All of the above 3. The wavelength of visible light ranges from: a. 400 to 700 nm b. 700 to 1000 nm c. 1000 to 1500 nm d. 1500 to 2000 nm 4. Which of the following is a type of laser? a. Helium-neon laser b. Ruby laser c. Diode laser d. All of the above 5. The term "photonics" is derived from the Greek words "phos" meaning "light" and "techne" meaning "art" or "craft". a. True b. False 6. The field of photonics is a rapidly growing field with many potential applications. a. True b. False 7. The active region of a diode laser is made of a: a. P-type semiconductor b. N-type semiconductor c. P-N junction d. Both P-type and N-type semiconductors 8. The mode of operation of a diode laser is determined by the: a. Resonant cavity of the laser b. Pumping mechanism of the laser c. Active region of the laser d. All of the above 45 9. The advantages of diode lasers over other types of lasers include: a. Small size and weight b. Low cost c. High efficiency d. All of the above 10. Digital laser material processing (DLM) is a type of laser processing that uses: a. A laser beam to scan a material b. A computer to control the scanning c. A digital data file to define the scan pattern d. All of the above 11. The laser beam used in DLM is typically: a. Continuous wave (CW) b. Pulsed c. Either CW or pulsed d. Depends on the application 12. The scan speed in DLM is typically: a. Low b. Medium c. High d. Very high 13. The spot size of the laser beam in DLM is typically: a. Small b. Medium c. Large d. Very large 14. The future of DLM is expected to be driven by: a. The development of new laser materials b. The development of new scanning methods c. The development of new software d. All of the above 15. The depth of penetration of the laser beam in DLM is typically: a. Small b. Medium c. Large d. Very large 46  Part B Questions 1. Give the principle of semiconductor diode Laser. 2. Mention any four applications of laser in medicine. 3. Define population inversion and metastable state. 4. What are the advantages of heterojunction semiconductor laser over homojunction semiconductor laser? 5. What are the conditions needed for laser action? 6. What are different methods of achieving population inversion? 7. Distinguish between homojunction and heterojunction semiconductor lasers. 8. Name the properties of laser, which are making it suitable for industrial applications 9. Why is population inversion necessary to achieve lasing? 10. How is electrons and holes confinement made in the active region of heterojunction laser? 11. What is meant by population inversion? 12. Can a two level system be used for the production of laser? Why? 13. What do you mean by population inversion? 14. Why He-Ne laser is more efficient than a Ruby laser? 15. Distinguish between ordinary light and laser light. 16. Define metastable state. 17. What are the components of a Laser? 18. Define Active medium. 19. What is the Principle of laser action? 20. What are the three process can occur during laser action ? Define them. 21. Distinguish between Spontaneous emission and Stimulated Emission. 22. What are the Types of Laser? 23. Define Laser Material Processing. Part C Questions 1. Distinguish between spontaneous emission and stimulated emission of radiation. 2. Derive an expression of Einstein‟s A and B coefficient? 3. In detail explain the principle, construction and working of a four level solid state laser. (He-Ne) 4. Explain the principle, construction and working of a Homojunction semiconductor laser. 5. Explain the principle, construction and working of a Hetero junction semiconductor laser. 6. Define laser printing and laser material processing. 7. In details explain the application of laser in science, engineering and medicine. 47  UNIT III FIBRE OPTICS In this unit the following chapters are covered.  Propagation light in Optical Fibres  Numerical Aperture and Acceptance angle  Fibre Optic Communication System  Classification of Optical Fibre, Ray Optics, losses in Optical Fibre  Types of optical sensors, Applications 3.0. INTRODUCTION Principle of Light Propagation in Optical Fibres Optical fibres work on the principle of total internal reflection. Total internal reflection is a phenomenon that occurs when light travels from a denser medium to a less dense medium at an angle greater than the critical angle. The critical angle is the angle of incidence at which the refracted angle is 90 degrees. At this angle, the light ray is totally reflected back into the denser medium. Optical fibres have a core made of a material with a higher refractive index than the cladding that surrounds it. This means that when light enters the core of the fibre at an angle less than the critical angle, it will be totally internally reflected and will travel down the length of the fibre. Propagation of Light in Optical Fibres Light propagation in optical fibres can be described in terms of modes. A mode is a pattern in which light travels through the fibre. The number of modes that can propagate in a fibre depends on the diameter of the core and the difference in refractive index between the core and the cladding. Single-mode fibres have a core diameter that is only slightly larger than the wavelength of light. This means that only one mode can propagate in the fibre. Single- mode fibres are typically used for long-distance communication because they have lower attenuation (loss of signal) than multimode fibres. Multimode fibres have a core diameter that is much larger than the wavelength of light. This means that multiple modes can propagate in the fibre. Multimode fibres are typically used for short-distance communication because they are less expensive than single-mode fibres. 48 3.1. TOTAL INTERNAL REFLECTION It is the basic principle of transmission of signals through the optical fibre. When the light travels from a denser to a rarer medium, when the angle of incidence is greater than the critical angle, the incident ray is totally internally reflected. Condition for Total Internal Reflection 1. Light should travel from denser medium to rarer Medium (n1 > n2). 2. The angle of incidence should be greater than the critical angle θc of the medium. (θi> θc). Critical Angle It is the angle for which the angle of refraction is 90o and the ray is called Critical ray. Explanation for Total Internal Reflection Consider an optical fibre through which the light ray is entered from denser medium ( n 1) to rarer medium (n2). Let us take three ways of light paths A, B and C. Case I: When θi < θc The light ray A strikes the interface at an angle of incidence θ i , and the ray is refracted at an angle θr into the rarer medium as A1.. Case II: When θi = θc The light ray B strikes the interface at an angle of incidence θ i = θc , and the ray is refracted at an angle 90o and travel along the interface as B1. i.e., θr = 90o. 49 Case III: When θi > θc The light ray C strikes the interface at an angle of incidence θ i > θc , and the ray is totally internally reflected into the same denser medium as C1. This is the condition required for optical fiber communication. Expression for Critical Angle (θc) According to Snell‟s law, n1 sin i  n 2 sin  r For total internal reflection, θi = θc and θr = 90o n 1 sin  C  n 2 sin 90 o n2 sin  C  sin 90 o n1 But sin 90 o  1 n2 sin  C  n1 n  C  Sin 1  2   n1  Expression for Numerical Aperture and Acceptance angle : Acceptance Angle It is the maximum angle at which light is entered into the optical fibre, so that light will totally internally reflect inside the fibre. The light ray OA and enters into the core at angle o and the light ray AB is refracted at an angle r. The angle of incidence i = ( 90o - r ) at B. When i > c, the light is totally internally reflected. 50 Apply Snell‟s law at A, noSino = n1Sin r ---------- (1) Apply Snell‟s law at B. n1 Sin i = n2 Sin 90o ---------- (2) but i = 90o - r and Sin90o = 1 n1 Sin 90o -  = n2 (1) n2 Cos r = ---------- (3) n1 from eq (1), n1 Sin o = Sin  no Sin   1  cos 2  n1 Sin o = 1  cos 2  r no Substitute eq. (3) 2 n1 n2 Sin o = 1 2 no n1  n2 2 2 n1 n1 = 2 no n1 n1  n 2 2 2 n1 Sin o = no n1 n1  n2 2 2 Sin o = n0  n1  n 2  2 2  Acceptance angle o = sin-1  no    but n0 = 1 for air   1 o = Sin-1 n1  n2 2 2 2 This is the expression for Acceptance angle of optical fiber. 51 Numerical Aperture: (N.A)  Sine of acceptance angle is called Numerical Aperture  It measures the light collecting ability of the fibre. N.A = Sino  n1  n 2  2 2  NA =  no    but n0 = 1   1 NA = n1  n2 2 2 2 3.2. FIBRE-OPTIC COMMUNICATION SYSTEM Principle  Initially, the input electrical signals are converted into optical signals.  Then they are transmitted through optical fibres without any loss of energy.  At the end of the fiber, again the light signals are converted into electrical signals by the receiver. The major components of the optical fiber communication system are 1. Transmitter 2. Optical fibre 3. Receiver Transmitter  The electrical signal is applied to the transmitter.  The transmitter consists of an optical modulator and Laser light source. 52   The electrical input signal is modulated by optical modulator by using light source (Laser) and changes into optical pulses. Optical Fibre  It acts as a waveguide to transmit the optical pulses towards the receiver by means of total internal reflection. Receiver  It consists of a photo detector, demodulator and a signal processor.  The photo detector receives the optical pulses and converts into electrical pulses by a demodulator.  The signal processor amplifies the signal and filters the undesired frequencies during transmission.  In this way information is transmitted from transmitting end to receiving end. 3.3. CLASSIFICATION OF OPTICAL FIBRE Categories Types 1. Glass fibre 1. Material 2. Plastic fibre 3. Single mode fibre 2. Number of modes 4. Multimode fibre 5. Step index fibre 3. Refractive index profile 6. Graded index fibre 1. Glass fibre: It is made up of mixture of metal oxides and Silica glasses. Core: SiO2 : Cladding: P2 O5 – Si O2 Core: P2O5 – SiO2 : Cladding: SiO2 Core: GeO2 – SiO2 : Cladding: SiO2 2. Plastic fibre:  Plastic fibres are low cost  It exhibits greater signal attenuation than glass fibres.  More strength and durability.  High numerical aperture [ 0.58 ]  High angle of acceptance up to 70o Core : Polymethyl Methacrylate ( PMMC) Cladding : Co-polymer 53  Core : Polystyrene Cladding : Methyl Methacrylate (MMC) 3. Single Mode Fibre:  In single mode fibre, only one mode ( Light ray path) is transmitted through optical fibre,  Its core diameter is small ( 5-10 µm)  The difference in refractive index of core and cladding is small.  No dispersion  Low energy loss  Used for long distance communication.  Sending the light and connecting two fibres are difficult.  It is very costly due to difficult in fabrication. 4. Multimode Fiber:  In a multimode fibre, many numbers of modes are propagated through optical fibre.  d  NA  2  The total number of modes propagated , N = 4.9  where d - diameter of    the core  Large core diameter  The difference in refractive index of core and cladding is large.  More dispersion  It is used only for short distance communication (LAN)  Sending the light and connecting two fibres are easy  The cost is less and the fabrication is also easy. 54 5. Step index Fibre The refractive index of air, cladding, and core varies step by step, it is called step index fibre. There are two types of step index fibre 1. Step index single mode fibre 2. Step index multimode fibre Step index single mode fibre  It has core refractive index of 5 to 10 µm  It has cladding refractive index of 50 to 125 µm.  Only one light ray path is allowed  Its numerical aperture is very small.  No signal loss due to dispersion.  High data transmission capacity due to higher bandwidth. Step index multimode fibre  It has core refractive index of 50 to 200 µm  It has cladding refractive index of 125 to 300 µm.  Many modes of light ray paths are allowed.  Its numerical aperture is large.  There is signal loss due to dispersion.  Less data transmission capacity due to lower bandwidth. 7. Graded Index Fibre 55   In a graded index fibre, the refractive index of the core varies radially from the axis of the fibre.  It is also called GRIN Fibre.  The refractive index of the core is maximum along the axis and it gradually decreases.  Here the refractive index is minimum at the core cladding interface.  The graded index fibre is in multimode system.  The multimode graded index fibre has very less intermodal dispersion. 3.4. RAY OPTICS Ray optics, also known as geometrical optics, is a model of optics that describes light propagation in terms of rays. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances. The simplifying assumptions of geometrical optics include that light rays:  Propagate in straight-line paths as they travel in a homogeneous medium.  Bend, and in particular circumstances may split in two, at the interface between two dissimilar media.  Follow curved paths in a medium in which the refractive index changes.  May be absorbed or reflected. Ray optics is useful for describing the behavior of light in a variety of optical devices, such as mirrors, lenses, and prisms. It can also be used to explain phenomena such as reflection, refraction, and diffraction. Some of the basic principles of ray optics include:  The law of reflection: The angle of reflection is equal to the angle of incidence.  The law of refraction: Snell's law describes the relationship between the angles of incidence and refraction at the interface of two media with different refractive indices.  The principle of total internal reflection: When light travels from a denser medium to a less dense medium at an angle greater than the critical angle, it will be totally reflected back into the denser medium. 56 Ray optics is a powerful tool for understanding the behavior of light. It is used in a wide range of applications, including:  Optical design: Ray optics is used to design optical devices such as lenses, mirrors, and prisms.  Optical instrumentation: Ray optics is used to develop and design optical instruments such as telescopes, microscopes, and cameras.  Fiber optics: Ray optics is used to understand and design fiber optic systems.  Computer graphics: Ray optics is used to render realistic images in computer graphics. 3.5. LOSSES IN OPTICAL FIBRE When a light is transmitted through the optical fiber, there are three losses will be produced , They are, Attenuation , Distortion and Dis