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Unformatted text preview: Band Diagrams Lecture 13 MTE 208 Learning Objectives Be able to Draw and label parts of band diagrams for metals, semiconductors and insulators Classify materials according to band diagram Be able to utilize the FermiDirac Distribution function to calculate probability that an electron will have a given energy Draw the Fermi Dirac distribution function at different temperatures New Model: Energy Bands Discrete atomic energy levels for separate atoms Become: Energy bands for atoms bonded together in a solid Energy bonding molecular orbital anti bonding molecular orbital atomic orbital atomic orbital Energy 4 atomic orbitals + + + 4 molecular orbitals Energy n atomic orbitals + + + n molecular orbitals + + + + + + + + + + + + + + + + + + + + + = 4 Simple Energy Band Diagrams eV E g 5 . 2 eV E g 5 . 2 > Metals or Partially filled Valence band (VB) Increasing nergy Filled VB Overlaps Empty Conduction Band (CB) Filled VB Filled VB Empty CB Empty CB Semiconductors Insulators E g E g Band Diagrams Tell us Is a material a metal, semiconductor or insulator? Where are the electrons? Are they able to conduct?  How many electrons can conduct Is a semiconductor pure or doped? Is a semiconductor ntype or ptype? Will a material be transparent? Band diagrams and number of free charge carriers Conduction can happen in partially filled bands, not in completely filled or completely empty bands An electron in a filled band requires energy to move into an empty higher energy band where it can exist as a free charge carrier Interaction of Energy and Electrons Electrons can get energy from Collisions with other electrons and atoms (Heat, Thermal Energy) Light (Electromagnetic Radiation) hc=1239.67 eVnm 1234567 hc h E photon = = Example 1 Calculate what wavelengths of light are transmitted through Si and what wavelengths of light are absorbed/ reflected by Si. Si has a band gap of 1.1 eV Light is absorbed if it corresponds to an electron energy transition. Example 2 Calculate what wavelengths of light are transmitted through silica glass and what wavelengths of light are absorbed/ reflected by glass. SiO 2 has a band gap of 9.0 eV 400 to 320 nm = UVA 320 to 290 nm = UVB 290 to 200 nm = UVC What is the probability that the available thermal energy is enough to promote an electron to a higher energy band? Similar to questions we know the answer to: What is the probability that the available thermal energy is enough to Create a vacancy Move an atom Get something over an activation energy barrier Arrheniustype equations and a MaxwellBoltzmann Energy Distribution Electrons are special No two electrons in a material share the same 4 quantum numbers: each has to be different In one energy level, if one electron is spin up, the other is spin down There is no room for a 3 rd electron it has to go to a higher energy level Contrast to marbles filling a cup Because Electrons Dont Share......
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This note was uploaded on 11/28/2010 for the course MTE 209 taught by Professor Tanyafalten during the Fall '09 term at Cal Poly Pomona.
 Fall '09
 TanyaFalten

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