Introduction to Solids and Semiconductors PDF

Introduction to Solids and Semi-conductors Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar  Disclaimer: The content in this presentation should only be used as an aid to learning. This is by no means exhaustive treatment of the topics. Sources us...

Introduction to Solids and Semi-conductors Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar  Disclaimer: The content in this presentation should only be used as an aid to learning. This is by no means exhaustive treatment of the topics. Sources used, if any, have been cited. Most importantly, the content developed here should be used in the same spirit as has been dealt with during classroom teaching. This material is NOT Stand-alone material. Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar  Introduction to Solids and Semiconductors. ▪ Free electron theory of metals and energy bands. ▪ Types of electronic materials: metals, semiconductors, and insulators. ▪ Intrinsic and extrinsic semiconductors, p-n junction (formation and I-V ▪ characteristics) ▪ Dependence of Fermi level on carrier-concentration and temperature (equilibrium carrier statistics) ▪ Carrier generation and recombination, Carrier transport: diffusion and drift. LEARNING OUTCOMES: To distinguish between different types of solids, predict the occupation probability of energy levels in solids and understand carrier transport. Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar Classification Chart of Electrical Engineering Materials Electrical Engineering Materials Conductors Semiconductors Insulators Magnetic Materials Low resistance which Intrinsic High resistance which Ferromag. allows electrical suppresses electrical current flow Extrinsic current flow Paramag. Diamag. Electrical Properties Antiferromag. S/Cs: Can both allow Ferrites. or suppress current Adapted from: http://www.electrical4u.com/classification-of-electrical-engineering-materials/ Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar  Electrical properties Metals Insulators Semiconductors ρ ~ 10-8 to ρ ~ 107 to 1016 Ω-m ρ ~ 10-4 to 106 Ω-m 10-6 Ω-m Ex.: Silver, copper Ex.: Glass, wood Ex.: Germanium, Silicon ❖ Classical theory: Free electron theory: Nucleus (+ve charge) immobile, electrons (-ve charge) move freely. Very less resistance. ❖ Could not explain all results. QUANTUM FREE ELECTRON THEORY Remember that at quantum level contributions of individual entities become important, the properties of INDIVIDUAL entities must be known. Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar Peek into the History Band theory Bloch Sommerfeld, velocity distribution (F-D) Ohm’s Law but conductors? Insulators? Lorentz, velocity distribution (M-B) Drude, free electron theory Ohm’s Law but conductors? Insulators? Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar  What does Quantum theory introduce? ❖ Introduces a set of QUANTUM NUMBERS LABELS. ❖ These numbers distinctly identify the state of an atom. ❖ Principal quantum number ‘n’: Size and energy of electron orbit. n = 1, 2, 3, …. ❖ Orbital quantum number ‘l’: Shape of an electron orbit. l = from 0 to n-1. ❖ Orbital magnetic quantum number ‘ml’: Orientation of orbit. ml : from –l to +l. ❖ Spin quantum number ‘ms’: Direction of spin, ±1/2. So, each electron can be labeled as having a set of four distinct quantum numbers. No two electrons in an atom can have the same set of quantum numbers: Pauli’s exclusion principle. Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar  Quantum Theory Discreteness of energy levels. ∞ distance NO INTERACTION At closer distances, atoms interact. Energy levels get affected. More so for the outermost electrons. Potential Pauli’s exclusion principle must be Energy satisfied. So, creation of new energy levels, closer to previous ones takes place. Physics // E & TC// A&B // Aug’24 Semester Distance Dr. Rupali Nagarin (nm) Splitting of energy levels 3s 2p 2s Will be arranged 1s in periodic manner Energy 2p 2s Distance Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar  Energy bands Valence electrons occupy the Valence band. What is valence band? Highest occupied energy band. Quantum theory tells us that not all energy Copper levels are allowed. Thus, next higher energy Atom band that is allowed is known as Conduction band. CB top of the Eg The gap between the energy bands of valence VB and conduction band is known as band-gap. bottom of the Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar  Lithium Filling of levels: Availability of LEVELS and ELECTRONS Li: Atomic No. = 3; 1s2, 2s1 Let ‘N’ Li atoms be combined. Total electrons = 3N. Remember: Each level splits into (2l+1)N levels, if N atoms are combined. 1s level: Now has N levels, can accommodate: 2N e-s 2s level: Now has N levels, can accommodate: 2N e-s Available electrons: 2s 2N electrons (1s) + N electrons (2s) = 3N Filling electrons up: 1s Out of 3N, 2N can occupy 1s band (lower energy) + N can go to 2s band. Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar  Diamond (Carbon) C: Atomic No. = 6; 1s2, 2s2, 2p2 Let ‘N’ C atoms be combined. Total electrons = 6N. Filling electrons up: 2py,Z 1s level: Now has N levels, can accommodate: 2N e-s Completely Filled 2s level: Now has N levels, 2px can accommodate: 2N e-s Completely Filled 2p level can accommodate 6N electrons. 2s Electrons left = 2N. Thus, remaining 2N electrons can occupy 2px band. 1s Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar  Diamond (Carbon) C: Atomic No. = 6; 1s2, 2s2, 2p2 Let ‘N’ C atoms be combined. Total electrons = 6N. Band separation at lattice constant ~ 5.7 eV Source: https://csclub.uwaterloo.ca/~matedesc/ece209-notes.html Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar  Silicon Si: Atomic No. = 14; 1s2, 2s2, 2p6, 3s2, 3p2 Let ‘N’ Si atoms be combined. Total electrons = 14N. Filling electrons up: 3py 1s level: Now has N levels, can accommodate: 2N e-s Completely Filled 3px 2s level: Now has N levels, can accommodate: 2N e-s Completely Filled 3s 2p level : Now has 6N levels, can accommodate 6N electrons. 3s level: Now has N levels, 2p can accommodate: 2N e-s Completely Filled 2s Electrons left = 2N. 1s Thus, remaining 2N electrons can occupy 3px band. Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar  Silicon Si: Atomic No. = 14; 1s2, 2s2, 2p6, 3s2, 3p2 Let ‘N’ Si atoms be combined. Total electrons = 14N. Band separation at lattice constant ~ 1.12 eV Source: http://www.tutorvista.com/content/physics/physics-iv/semiconductor-devices/energy-bands.php Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar  Classification of solids - Band Theory Metals Insulators Semiconductors Have no VB, Filled VB Filled VB only CB Empty CB Empty or almost empty CB Large Eg(5-10 eV) Small Eg resistivity Thus, large resistivity. Eg Eg Highest occupied energy level at zero kelvin Fermi level. Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar  This is the first part only. Rest will follow. Physics // E & TC// A&B // Aug’24 Semester Dr. Rupali Nagar