Compound Semiconductors Lecture Notes PDF

Unit-2: Lecture-2: Compound Semiconductors Dr. Vaibhav S. Kathavate Assistant Professor (Adjunct), Department of Metallurgy and Materials Engineering, COEP Technological University, (Formerly College of Engineering Pune), Shivajinagar, Pune 411 005,...

Unit-2: Lecture-2: Compound Semiconductors Dr. Vaibhav S. Kathavate Assistant Professor (Adjunct), Department of Metallurgy and Materials Engineering, COEP Technological University, (Formerly College of Engineering Pune), Shivajinagar, Pune 411 005, Maharashtra, India.  Compound Semiconductors…. Compound semiconductors are made from two or more elements, typically from groups III-V or II-VI of the periodic table. They have an average of 4 valence electrons per atom, similar to 𝑺𝒊. Examples include 𝑮𝒂𝑨𝒔, 𝑰𝒏𝑷, 𝑺𝒊𝑪, 𝒁𝒏𝑶, etc. Mechanisms Direct Bandgap Indirect Bandgap 𝑮𝒂𝑨𝒔 and 𝑰𝒏𝑷 𝑺𝒊𝑪 Optoelectronics High Power Ele. 2 Compound Semiconductors: Range of Bandgaps…. Source- https://ocw.mit.edu/courses/6-772-compound-semiconductor-devices-spring-2003/ 3 Compound Semiconductors…. Advantages: High electron mobility, direct band gaps, radiation hardness, and high temperature stability/operation. Limitations: High cost, low thermal conductivity, and smaller wafer size. High Frequency and Infrared Detectors and Micro and milli-meter Power Electronics Imagers Wave Devices 𝑮𝒂𝑨𝒔 and 𝑰𝒏𝑷 𝑰𝒏𝑺𝒃 𝑮𝒂𝑨𝒔 and 𝑰𝒏𝑷 Source- Source- Source- https://www.miracle.net.in/ https://www.azosensors.com/article. https://www.keysight.com/us/en/pro aspx?ArticleID=339 ducts/ 4 Compound Semiconductors…. Source- Status of the Compound Semiconductor Industry 2024, Yole Intelligence 2024. 5  Unit-2: Lecture-1: Semiconductors: Intrinsic and Extrinsic, Mechanisms of Conduction, and Hall Effect Dr. Vaibhav S. Kathavate Assistant Professor (Adjunct), Department of Metallurgy and Materials Engineering, COEP Technological University, (Formerly College of Engineering Pune), Shivajinagar, Pune 411 005, Maharashtra, India. At the End of this Session…. Classification of solids based on Band Gap Theory  Intrinsic and Extrinsic Semiconductors  Mechanisms of Conduction in Intrinsic and Extrinsic Semiconductors  Hall Effect 2 Classification of Solids Based on Band Gap Theory…. Insulator Conduction Band Semiconductor 𝑬𝑪 Conduction Conductor Energy, E Band 𝑬𝑮 ≥ 𝟓 𝒆𝑽 𝑬𝑪 Conduction Band 𝑬𝑮 ≈ 𝟏 𝒆𝑽 𝑬𝑽 𝑬𝑽 𝑬𝑮 = 𝟎 Valence Band Valence Band Valence Band Conditions for Conduction: (i) there should be empty states in the valence band and (ii) movement of free electrons in conduction band Insulators: Both these conditions are not possible due to wide band gap. Conductors: Both these conditions are satisfied due to zero band gap (i.e., electrons can move from valence band to conduction band, thus leaving the empty states behind). 3 Intrinsic Semiconductors…. Intrinsic Semiconductor Intrinsic Semiconductors: Pure semiconductors (𝑺𝒊 and 𝑮𝒆) CB Energy, E Electrical conductivity is determined from their inherent conductive 𝑬𝒈 properties. Electron-hole pair generation VB e e e e e e e e + + + + + + e e e e e e e e + + + + + + e e e e e e e e + + + + + + e e e e e e e e 𝑺𝒊, 𝑮𝒆 and many other group 𝐈𝐕𝐀 element: ( 𝒔𝒑𝟑 ) diamond A certain amount of energy is required Each 𝑺𝒊 atom is surrounded cubic structures with highly to excite the electrons thus leaving by 4 valance electrons directional covalent bonds behind positively charged holes 4 Intrinsic Semiconductors: Mechanism of Charge Transport…. - + e e e e - e e e e e Charge Carriers: Electrons + + + + - + + + + e - + (negatively charged) and holes e e e e - e e e e + - (positively charged). + + + - + + + + + - + Holes: Towards Negative e e e e e e e e e - + Terminal. + + + - + + + + - + e e e e - e e e e e + Electrons: Towards Positive 𝑬 Terminal. Net Effect: Electrons (negatively charged) will move from left to right (towards positive terminal) and in the direction opposite to the applied electric field, while holes (positively charged) will move from right to left (towards negative terminal) in the direction of the applied electric field. Conduction in Pure 𝑺𝒊 and 𝑮𝒆 (Intrinsic Semiconductor) 5 Intrinsic Semiconductors: Quantitate Relationship for Electrical Conduction…. Current density (𝑱) in intrinsic semiconductor is a contribution of both electrons and holes; 𝑱 = 𝒏𝒆 𝒒𝑽𝒆 + 𝒏𝒉 𝒒𝑽𝒉 (𝒏𝒆 and 𝒏𝒉 are the number of electrons and holes in conduction per unit volume, respectively. 𝑽𝒆 and 𝑽𝒉 are the drift velocities of electrons and holes, respectively) Dividing the entire equation by (𝑬) electric field; 𝑱 𝒏𝒆 𝒒𝑽𝒆 𝒏𝒉 𝒒𝑽𝒉 𝑱 𝑽𝒆 𝑽𝒆 = + (but 𝑬 = 𝝈 (Electrical Conductivity) and 𝑬 = 𝝁𝒆 and 𝑬 = 𝝁𝒉 (Electron 𝑬 𝑬 𝑬 and Hole Mobility) 𝝈 = 𝒏𝒆 𝒒𝝁𝒆 + 𝒏𝒉 𝒒𝝁𝒉 But in pure or intrinsic semiconductor 𝒏𝒆 = 𝒏𝒉 = 𝒏 (Electron-Hole pair generation) 𝝈 = 𝒏𝒒𝝁𝒆 + 𝒏𝒒𝝁𝒉 𝝈 = 𝒏𝒒(𝝁𝒆 +𝝁𝒉 ) 𝝁𝒆 >≫ 𝝁𝒉 (for Intrinsic Semiconductor) 6 Extrinsic Semiconductors…. Extrinsic Semiconductors: Dilute substitutional solid solution. Impurities (mainly solute atoms) are doped with solvent atoms Both solute and solvent atoms has different valance characteristics The concentration of impurities (or solute atoms) varies from 𝟏𝟎𝟎 to 𝟏𝟎𝟎𝟎 𝒑𝒑𝒎 Added imparities can be of donor or acceptor type Extrinsic Semiconductor n-type (Donor doped) p-type (Acceptor doped) Majority Carriers CB CB Energy, E 𝑬𝑪 Energy, E 𝑬𝑫 𝑬𝑨 𝑬𝑽 VB VB Minority Carriers 7 Extrinsic Semiconductors: n-type (Donor)…. n-type (Donor doped) Consider a 𝑺𝒊 lattice surrounded by 4 valance electrons. CB If an impurity atom of 𝑷 is doped then it will disturb the 𝑺𝒊 lattice, as 𝑷 has Energy, E 𝟓 surrounding valance electrons (Group V) (One extra valance electron) 𝑬𝑫 The energy required to remove that extra electron is ~ 𝟎. 𝟎𝟒𝟒 𝒆𝑽 which is 𝟓% of the 𝑬𝒈 ~ 𝟏 𝒆𝑽 required to overcome for the conduction process. VB 𝑬 e e e e e - + - e e e e e + - + Si Si Si Si - Si Si Si Si - + e e e e e - - e e e e e + - + Si Si P e Si - Si Si P+ Si e + - - + e e e e e - e e e e e + 8 Extrinsic Semiconductors: p-type (Acceptor)…. p-type (Acceptor doped) Consider a 𝑺𝒊 lattice surrounded by 4 valance electrons. CB If an impurity atom of 𝑩 is doped then it will disturb the 𝑺𝒊 lattice, as 𝑩 has 𝑬𝑪 Energy, E 𝟑 surrounding valance electrons (Group III) (One hole will be generated) 𝑬𝑨 The binding energy required to remove the electron is ~ 𝟎. 𝟎𝟒𝟓 𝒆𝑽 which is 𝑬𝑽 𝟓% of the 𝑬𝒈 ~ 𝟏 𝒆𝑽 required to overcome for the conduction process. VB 𝑬 e e e e e - + - e e e e e + - + Si Si Si Si - Si Si Si Si - + e e e e e - - e e e e + - + Si Si B Si - Si Si B- Si + - - + e e e e e - e e e e e + 9 Hall Effect…. Hall Effect: Generation of voltage of difference (Hall Voltage) in a perpendicular direction to a magnetic field across a semiconductor. Why Semiconductors? Sir Edwin H. Hall, an Ideal number of charge carriers American Physicist (1879) As 𝑻 charge carriers Hall Effect: Charge accumulation balances 𝒊𝑩 𝑽𝑯 = Lorentz forces 𝑭 = 𝒆[𝑬 + (𝑽 × 𝑩)] 𝒏𝒆𝒅 𝒊𝑩 For Semiconductors 𝑽𝑯 = 𝑹𝑯 −𝒏𝒆 𝝁𝟐𝒆 +𝒏𝒉 𝝁𝟐𝒉 𝒅 There are two charge carriers 𝑹𝑯 = 𝒆(𝒏𝒆 𝝁𝟐𝒆 +𝒏𝒉 𝝁𝟐𝒉 )𝟐 𝟏 𝑹𝑯 = For Large Magnetic Fields in Semiconductors 𝒆(𝒏𝒉 − 𝒏𝒆 ) Ref- resourcefulphysics.org 10 Unit-1: Lecture-4: Electrical and Thermal Conductivity, Wiedemann- Franz Law, Classical, and Quantum Free Electron Theory of Electrical Conduction Dr. Vaibhav S. Kathavate Assistant Professor (Adjunct), Department of Metallurgy and Materials Engineering, COEP Technological University, (Formerly College of Engineering Pune), Shivajinagar, Pune 411 005, Maharashtra, India. Electrical Conductivity and Resistivity: From Previous Pages…. Ohm’s Law: Electric current flow 𝒊 is proportional to the applied voltage 𝑽 and inversely proportional to the resistance 𝑹 of the wire…. 𝝆 = Resistivity (𝜴𝒎) It is always convenient to express the current 𝑽 𝒍 𝒊= 𝑹=𝝆 𝑨 = Area carrying capacity (conductivity) of the materials 𝑹 𝑨 𝒍 = Length rather than the resistance…. 𝑽 𝒊= is the macroscopic form of Ohm’s Law, from microscopic 𝟏 𝟏 𝟏 𝑹 𝝈 = (𝜴 𝒎 ) viewpoint, Ohm’s Law can be expressed as; 𝑱 = 𝑬 or 𝑱 = 𝑬𝝈 𝝆 𝝆 𝑱 = Current Density (𝑨/𝒎𝟐 ) Ref- W. Smith and J. Hashemi, Foundations of Materials Science and Engg., 6th Ed., McGrow Hill, New York (2019). 𝑬 = Electric field (𝑽/𝒎) 2 Why walking on tiles feels cooler than walking on carpet in the same room maintained at the same temperature? The answer is Thermal Conductivity. Generally, thermal conductivity of tiles is higher than the carpet/clothes, and hence, our feet once touch the tiles, Heat Transfer through feels cooler compared to carpet. Conduction….. Thermal Conductivity: How much heat (or rate of energy) is transferred through the object per unit area having a finite temperature gradient. During many instances, conductivity values are expressed in 𝑊/𝑚 𝐾. Many metals are the good conductors of electricity and heat (i.e., they have high conductivity). 3 Thermal Conduction in Metals: Main Mechanism….. Heat Transfer in Metals: Movement of free electrons followed by lattice vibration. The internal structure of a metal molecule contains free electrons that can move freely through the bulk of the material. These free electrons collide rapidly with other particles causing the internal structure of a metal to vibrate faster and heat up quicker. These rapid vibrations promote energy and heat flow throughout the metal. - - - - - - - + + + + + + + - - - - - - - - - + + + + + + + + + - - - - - - - + + + + + + + - - - - - - - + + + + + + + 4 Thermal Conduction in Metals: Main Mechanism….. Thermal conductivity mainly depends on the order of molecules/crystals. Highly Ordered vs. Disordered Thermal Conductivity of Metals: 𝑆𝑖𝑙𝑣𝑒𝑟 > 𝐶𝑜𝑝𝑝𝑒𝑟 > 𝐺𝑜𝑙𝑑 > 𝐴𝑙 > 𝑍𝑛 > 𝑁𝑖 > 𝐵𝑟𝑎𝑠𝑠 > 𝐵𝑟𝑜𝑛𝑧𝑒 > 𝐹𝑒 > 𝑃𝑙𝑎𝑡𝑖𝑛𝑢𝑚 > 𝑆𝑡𝑒𝑒𝑙 > 𝑃𝑏 > 𝑆𝑡𝑎𝑖𝑛𝑙𝑒𝑠𝑠 𝑆𝑡𝑒𝑒𝑙 Applications: Thermal appliances and tools, Electronics and electrical use, Heat dissipation through solar panels, Automobiles, Heat exchangers, Domestic use/purposes. 5 Variation of Thermal Conductivity…. Solids Liquids Gases Temperature Temperature Temperature Thermal Conductivity Thermal Conductivity Thermal Conductivity Predominantly depends on Molecular diffusion effect Molecular collision electronic effect Increase in movement of Increase in temperature Molecular collision free electrons and causes increase in increases with an consequently the lattice randomness of increase in temperature vibration molecules/movement Obstruction in path and hence Hence, decrease in thermal Hence, increase in thermal thermal conductivity decreases conductivity conductivity 6  In Solids and Liquids In Gases Ref- Poirier and Geiger, Transport Phenomena in Materials Processing, Springer, Switzerland (2016). 7 Wiedemann-Franz Law.…. Proposed by German Scientists; Gustav Wiedemann and Rudolph Franz Connects the thermal conductivity and electrical conductivity of the metals. Wiedemann-Franz Law: The ratio of electronic contributions of thermal conductivity (𝒌) and electrical conductivity (𝝈) is constant and equivalent to temperature (𝑻). 𝒌 𝑳 here represents the Lorentz = 𝑳𝑻 Heat and electrical 𝝈 number with unit (𝑾𝜴 ). 𝑲𝟐 transport both involve free The value of “𝑳” is not same for all the electron movement inside metals the metal. 𝒌 and 𝝈 both changes with change in 𝑻 Ref- W. Smith and J. Hashemi, Foundations of Materials Science and Engg., 6th Ed., McGrow Hill, New York (2019). 8 Classical Theory of Electrical Conduction…. - - - - Cu Cu Cu Cu Drude Model - - - - Metal is a 3D array of atoms with freely moving electrons Cu Cu Cu Cu (Classical Free Electron Theory) - - - - For Ex.: In 𝑪𝒖, there is one free electron per 𝑪𝒖 atom Cu Cu Cu Cu + + + + + +  In the absence of electric field (𝑬) , + movement of electron is random. 𝑬 𝑬 + + + + + +  Upon the application of (𝑬), all the electrons move in a same direction, opposite to the + + + + + + direction of (𝑬) Classical Free Electron Theory and Concept of Drift Velocity…. 9 Classical Theory of Electrical Conduction: Applications…. Electrical Conductivity Thermal Conductivity Amount of electric charge conducted per unit Amount of heat conducted per unit time, per unit time, per unit area, per unit electric field. cross sectional area, per unit temperature gradient. 𝑸 𝑸 = 𝒌𝑨 𝒅𝑻⁄ (𝑸 is the heat transferred) 𝝈= (𝑸 is the electric charge conducted) 𝒅𝒙 𝒕𝑨𝑬 𝝈= 𝑰 𝑸 (since = 𝑰) 𝑸 𝑨𝑬 𝒕 𝒌= 𝑨 𝒅𝑻 𝒅𝒙 𝑱 𝑰 𝝈= (since = 𝑱) 𝑬 𝑨 𝑱 = 𝝈𝑬 Wiedemann-Franz Law  Macroscopic Ohm’s Law  Can’t explain Compton, Photoelectric, and Ferromagnetic Effect 10 Unit-1: Lecture-3: Band Gap Theory Dr. Vaibhav S. Kathavate Assistant Professor (Adjunct), Department of Metallurgy and Materials Engineering, COEP Technological University, (Formerly College of Engineering Pune), Shivajinagar, Pune 411 005, Maharashtra, India. At the End of this Session…. Energy Levels in Atoms Band Gap How Band Gap forms? (Illustration) Classification of Solids based on Band Gap Theory Direct and Indirect Band Gap Significance of Band Gap Theory 2 Structure and Contributing Length Scales: Brush up…. Z What Next ?... What is there X inside atom?.... Y Devices/Parts Microstructure Crystals Unit cell/Atoms meso micro nano Å 32 18 Positively charged nucleus - - - - Revolving electrons (negatively charged) in different Different shells: - + - shells 𝑲, 𝑳, 𝑴, 𝑵 Different energy - - - No. of electrons in each shell: 𝟐 × (𝒏𝟐 ) levels of electrons - Each shell is further divided into subshells 𝒔, 𝒑, 𝒅, 𝒇 3 Energy Levels of Electrons in an atom…. 32 14 𝟒𝒇 18 - N 10 𝟒𝒅 - - - 32 𝑬𝟒 6 𝟒𝒑 - + - - 2 𝟒𝒔 - - - No. of electrons = no. 10 𝟑𝒅 M of energy levels to 𝑬𝟑 18 6 𝟑𝒑 Electron from each shell has different accommodate each 2 𝟑𝒔 electrons in orbitals energy levels For ex., 𝟐 electrons in 𝑲 shell are L 6 𝟐𝒑 characterized by energy level 𝑬𝟏. 𝑬𝟐 8 2 𝟐𝒔 In the same vein, 𝟏𝟖 electrons in 𝑴 K shell are identified by energy level 𝑬𝟑. 𝑬𝟏 2 2 𝟏𝒔 4 How Energy Bands Are Formed ?…. - - - Pauli’s Exclusion Principle 𝑬𝒙 + + + 𝑬𝒚 No two electron in an interacting system have 𝑬𝒛 same quantum state and so is the energy - 𝑬𝒙 - - - - - -𝒙 𝑬 + + + + + + + - - - - - - - + + + + + + + - - - - - - - “N” atoms means “N” energy levels + + + + + + + - - - - - - - Energy Band + + + + + + +  When “N” no. of atoms brought together (or closer) to form a system (or solid), single energy level get split into discrete energy levels which are very close to each other (precisely satisfying Pauli’s Exclusion Principle).  This further leads to the formation of energy bands. 5 How Energy Bands Are Formed ?…. Pauli’s Exclusion Principle No two electron in an interacting system have same quantum state and so is the energy “N” atoms means “N” energy levels Energy Band All the atoms are characterized by same energy levels when they are far away from each other (i.e., increase in interatomic distance). Therefore, the graph will yield a straight line. With a decrease in interatomic distance, energy levels of atoms will no longer remain same and they will be discretized in energy bands. See the left portion of graph, lines in blue color represents the discretized energy bands. 6  Formation of Band Gap: Illustration…. Conduction Band Distribution of electrons in Carbon atom: 6 States 6 electrons 1𝑠 2𝑠 2𝑝 2 Electrons 4 States 𝟐𝒑 There will be “2” 1𝑠 states, “2” 2𝑠 states and 0 Electrons Energy Gap 8S “6” 2𝑝 states required to accommodate the 4E 𝟐𝒔 energy levels. Energy 4S 2 States As the difference between the 𝟐𝒔 and 𝟐𝒑 4E 2 Electrons energy levels is smaller, they will merge in Valence Band to a single band with a decrease in “𝒂”. 2 States With further decrease in “𝒂”, filled energy 𝟏𝒔 2 Electrons levels (valence band) get separated from empty energy levels (conduction band). Interatomic Distance (a) Upper most filled band- Valence Band Lower most empty band- Conduction Band 7  Formation of Band Gap: Illustration…. Conduction Band Upper most filled band- Valence Band 6 States Lower most empty band- Conduction Band 2 Electrons 4 States 𝟐𝒑 0 Electrons  Only lower most conduction band and top Energy Gap 8S most valence bands take part in conduction 4E 𝟐𝒔 Energy 4S process. 2 States 4E 2 Electrons Valence Band 2 States 𝟏𝒔 2 Electrons Interatomic Distance (a) HW: Construct an Energy Band Gap diagram for semiconductor materials 𝑺𝒊 and 𝑮𝒆. 8 Classification of Solids Based on Band Gap Theory…. Insulator Conduction Band Semiconductor 𝑬𝑪 Conduction Conductor Energy, E Band 𝑬𝑮 ≥ 𝟓 𝒆𝑽 𝑬𝑪 Conduction Band 𝑬𝑮 ≈ 𝟏 𝒆𝑽 𝑬𝑽 𝑬𝑽 𝑬𝑮 = 𝟎 Valence Band Valence Band Valence Band Conditions for Conduction: (i) there should be empty states in the valence band and (ii) movement of free electrons in conduction band Insulators: Both these conditions are not possible due to wide band gap. Conductors: Both these conditions are satisfied due to zero band gap (i.e., electrons can move from valence band to conduction band, thus leaving the empty states behind). 9 Direct and Indirect Band Gap…. Band Gap: Minimum energy difference between conduction and valence band 𝑬𝑪 − 𝑬𝑽. From quantum mechanics view point, electron is represented in the form of wave having wavelength 𝝀 and 𝒑𝟐 𝒉𝟐 𝒌𝟐 its energy 𝑬 = = (𝒑- momentum, 𝒉- Planck’s constant, 𝒎- mass of 𝒆 and 𝒌- propagation const.) 𝟐𝒎 𝟐𝒎 However, the value of 𝒑 for the top of valence band and bottom of conduction band is not same always. Direct Band Gap Indirect Band Gap 𝑬 ∝ 𝒑𝟐 : Equation of parabola CB Direct Band Gap: Maximum of VB and CB minimum of CB occurs at same "𝒑“. Energy, E Energy, E LEDs and Laser Diode (Compound Band Gap Band Gap semiconductors: GaAs) Indirect Band Gap: Maximum of VB and VB VB minimum of CB occurs at different "𝒑“. All elemental semicond.: Si and Ge Momentum, 𝒑 Momentum, 𝒑 10 Significance of Band Gap Theory…. Semiconductors: The materials which possess the conductivity between conductors and insulators. Applications in Electronics, optical devices, micro-chips, diodes, transistors and many more…. Types of semiconductors based on band gap theory…. Electron-hole pair generation Intrinsic Semiconductor Extrinsic Semiconductor n-type (Donor doped) p-type (Acceptor doped) CB Majority Carriers CB CB Energy, E Energy, E 𝑬𝑪 Energy, E 𝑬𝑪 𝑬𝑫 𝑬𝑨 𝑬𝑽 𝑬𝑽 VB VB VB Minority Carriers 11 Summary and Key Learnings…. Band Gaps: Electron energy levels in an individual atom leads to the creation of energy bands in crystals. Two important bands take part in conduction process; Upper most valence band (VB) (completely filled) Lower most conduction band (CB) (empty) Band Gaps are further classified in two types; Direct Band Gap (where maximum energy level VB and minimum energy level of CB are at same momentum) Indirect Band Gap (where maximum energy level VB and minimum energy level of CB are at different momentum) Band Gap Theory highlights the difference between Conductors, Insulators and Semiconductors. 12 Unit-1: Lecture-2: Classical Free Electron Theory and Concept of Drift Velocity Dr. Vaibhav S. Kathavate Assistant Professor (Adjunct), Department of Metallurgy and Materials Engineering, COEP Technological University, (Formerly College of Engineering Pune), Shivajinagar, Pune 411 005, Maharashtra, India. Classical Free Electron Theory…. Many metals, in general, comprises of metallic bonds. These metallic bonds make the free movement of valence electron possible as they are shared by many adjacent atoms and not bound to any particular atoms BCC FCC (Case I). The valance electrons are sometimes not associated with any type of atoms (i.e., they appear to be individual electrons) (Case II) The outer valence electrons are assumed to be completely free to move between the positive-ion cores (atoms without valence electrons) in the metal lattice Ref- W. Smith and J. Hashemi, Foundations of Materials Science and Engg., 6th Ed., McGrow Hill, New York (2019). 2 Classical Free Electron Theory…. At room temperature, the positive-ion cores have kinetic energy and + + + vibrate about their lattice positions. With increasing temperature, these ions vibrate with increasing + + + amplitudes, and there is a continuous interchange of energy between + + + the ion cores and their valence electrons. In the absence of an electric potential, the motion of the valence electrons is random and restricted, so there is no net electron flow in any direction and thus no current flow. + In the presence of an applied electric potential, the electrons attain a directed drift velocity that is proportional to the applied field but in the Positive Ion Vibration about opposite direction. their own lattice positions Ref- W. Smith and J. Hashemi, Foundations of Materials Science and Engg., 6th Ed., McGrow Hill, New York (2019). 3 Concept of Drift Velocity…. + + + + + + 𝑬 𝑽𝒅 - Drift Velocity 𝑚/𝑠 𝑬 + + + + + + 𝑽𝒅 = 𝝁𝑬 𝝁- Electron Mobility 𝑬- Electric field 𝑉/𝑚 + + + + + + + Positive Ion Vibration about their own lattice positions Ref- W. Smith and J. Hashemi, Foundations of Materials Science and Engg., 6th Ed., McGrow Hill, New York (2019). 4 Unit-1: Lecture-1: Electrical Conductivity and Resistivity, Resistivity Range, and Free Electron Theory Dr. Vaibhav S. Kathavate Assistant Professor (Adjunct), Department of Metallurgy and Materials Engineering, COEP Technological University, (Formerly College of Engineering Pune), Shivajinagar, Pune 411 005, Maharashtra, India. Man Made Materials Exceeds Total Biomass on the Earth…. Materials Century Fundamental difference Chemical and Physical Prop. Are the differences arise from Metals the structures? What happens at different Non metals/ length scales? Insulators Human Life = Materials Atoms, Molecules, Why Metals are conductors ? Semi Energy, Interatomic conductors Why insulators are not conductors? distance and Various Why semiconductor exhibits prop. Theories between conductors & insulators? 2  What else if we keep the copper wire open/unwounded/non-insulated?  Can you operate PVC wire alone to conduct the electric current?  Copper Wire PVC Wire Wire Conductors/conductivity Copper Wire Insulators Electric Current Wounded/Insula ted in PVC Wire  Copper/Matel PVC/Non metal Why copper conducts electricity and PVC does not? Materials Ability to Conduct What differentiates from copper to PVC? Electric Current…. Electric Conductivity (𝝈) (𝜴 𝟏 𝒎 𝟏 )…. Ref- https://amigoenergy.com/blog/electric-shock-causes-treatment-and-effects/ 3 Electrical Conductivity and Resistivity…. Ohm’s Law: Electric current flow 𝒊 is proportional to the applied voltage 𝑽 and inversely proportional to the resistance 𝑹 of the wire…. 𝝆 = Resistivity (𝜴𝒎) It is always convenient to express the current 𝑽 𝒍 𝒊= 𝑹=𝝆 𝑨 = Area carrying capacity (conductivity) of the materials 𝑹 𝑨 𝒍 = Length rather than the resistance…. 𝑽 𝒊= is the macroscopic form of Ohm’s Law, from microscopic 𝟏 𝟏 𝟏 𝑹 𝝈 = (𝜴 𝒎 ) viewpoint, Ohm’s Law can be expressed as; 𝑱 = 𝑬 or 𝑱 = 𝑬𝝈 𝝆 𝝆 𝑱 = Current Density (𝑨/𝒎𝟐 ) Ref- W. Smith and J. Hashemi, Foundations of Materials Science and Engg., 6th Ed., McGrow Hill, New York (2019). 𝑬 = Electric field (𝑽/𝒎) 4 Resistivity Range…. 𝜴𝒎 Quartz 7.5 × 10 Empirical way to classify the materials into conductors, 10 semi-conductors, and insulators. Insulators 10 All the metals in general are good conductors (free 10 Glass 1 × 10 electrons inside the atoms) Conductors Semi-conductors 10 There is no well defined boundary between semi- 10 conductors and insulators. Silicon 6 × 10 10 1 High Germenium 4.5 × 10 What differentiates the 10 Resistivity conduction mechanisms in 10 Carbon 3.2 × 10 10 metal and non Gold 2.2 × 10 Low 10 Silver 1.5 × 10 Conductivity metals/insulators ???.... Ref- W. Smith and J. Hashemi, Foundations of Materials Science and Engg., 6th Ed., McGrow Hill, New York (2019). 5 Classical Free Electron Theory…. Many metals, in general, comprises of metallic bonds. These metallic bonds make the free movement of valence electron possible as they are shared by many adjacent atoms and not bound to any particular atoms FCC BCC (Case I). The valance electrons are sometimes not associated with any type of atoms (i.e., they appear to be individual electrons) (Case II) The outer valence electrons are assumed to be completely free to move between the positive-ion cores (atoms without valence electrons) in the metal lattice Ref- W. Smith and J. Hashemi, Foundations of Materials Science and Engg., 6th Ed., McGrow Hill, New York (2019). 6