EE40 Lecture 31 Prof Chang Hasnain 11 19 07 Reading Supplementary Reader EE40 Fall 2007 Slide 1 Prof Chang Hasnain Week 13 OUTLINE Basic Semiconductor Materials n and p doping Bandgap Gauss s Law Poisson Equation Depletion approximation Diode I V characteristics Lasers and LEDs Solar Cells Reading Supplementary Notes Chap 3 EE40 Fall 2007 Slide 2 Prof Chang Hasnain 1 Conductors Insulators and Semiconductors Solids with free electrons that is electrons not directly involved in the inter atomic bonding are the familiar metals Cu Al Fe Au etc Solids with no free electrons are the familiar insulators glass quartz crystals ceramics etc Silicon is an insulator but at higher temperatures some of the bonding electrons can get free and make it a little conducting hence the term semiconductor Pure silicon is a poor conductor and a poor insulator It has 4 valence electrons all of which are needed to bond with nearest neighbors No free electrons EE40 Fall 2007 Slide 3 Prof Chang Hasnain The Periodic Table III IV V EE40 Fall 2007 Slide 4 Prof Chang Hasnain 2 Unit Cell of Crystalline Silicon Si 1s2 2s2 2p6 3s2 3p2 1 1 Atoms 8 8 6 2 4 8 5 00 1022 cm 3 3 Volume a0 5 43 10 8 cm 3 EE40 Fall 2007 Slide 5 Prof Chang Hasnain Electronic Bonds in Silicon 2 D picture of perfect crystal of pure silicon double line is a Si Si bond with each line representing an electron Si ion charge 4 q Two electrons in each bond Actual structure is 3 dimensional tetrahedral just like carbon bonding in organic and inorganic materials Essentially no free electrons and no conduction insulator EE40 Fall 2007 Slide 6 Prof Chang Hasnain 3 Bandgap Electrons are mobile in the conduction band while holes are mobile in the lower energy valence band The excited electrons move from the valence band into the conduction band leaving holes in the valence band when the crystal is illuminated with photons whose energy is larger than the bandgap energy or when the crystal is sufficiently heated Conduction Band E Ef Band gap E e EE40 Fall 2007 g Valence Band Slide 7 Prof Chang Hasnain Bandgap for Insulator and Metal Insulators have a large band gap usually 3 5 electron E volts eV or greater preventing substantial amounts of charge carriers from flowing Metals are good conductors with E electrons filling up into the conduction band EE40 Fall 2007 Conduction Band Large bandgap Eg E f Valence Band E Conduction Band f Slide 8 Electrons fill into conduction band Small band gap E g Valence Band Prof Chang Hasnain 4 Shockley s Parking Garage Analogy for Conduction in Si Two story parking garage on a hill If the lower floor is full and top one is empty no traffic is possible Analog of an insulator All electrons are locked up EE40 Fall 2007 Slide 9 Prof Chang Hasnain Shockley s Parking Garage Analogy for Conduction in Si Two story parking garage on a hill If one car is moved upstairs it can move AND THE HOLE ON THE LOWER FLOOR CAN MOVE Conduction is possible Analog to warmed up semiconductor Some electrons get free and leave holes behind EE40 Fall 2007 Slide 10 Prof Chang Hasnain 5 Shockley s Parking Garage Analogy for Conduction in Si Two story parking garage on a hill If an extra car is donated to the upper floor it can move Conduction is possible Analog to N type semiconductor An electron donor is added to the crystal creating free electrons EE40 Fall 2007 Slide 11 Prof Chang Hasnain Shockley s Parking Garage Analogy for Conduction in Si Two story parking garage on a hill If a car is removed from the lower floor it leaves a HOLE which can move Conduction is possible Analog to P type semiconductor Acceptors are added to the crystal consuming bonding electrons creating free holes EE40 Fall 2007 Slide 12 Prof Chang Hasnain 6 Fermi Dirac Distribution Fermi Dirac function provides the probability that an energy level is occupied by a fermion which is under thermal equilibrium Electrons as well as holes are Fermions and hence obey Fermi Dirac statistics Fig 5 Fermi function plots at absolute zero mid range and high temperature EE40 Fall 2007 Slide 13 Prof Chang Hasnain Electron and Hole Densities n Nc 1 E E Nce f c Ec Ef kT kT 1 e 1 E E p N v 1 Nve v f E Ef kT 1 e v np N c e E f i Ec kT Nve Ev E f i kT N c N v e Ev Ec kT N c N v e ni pi ni N c N v e Eg kT For instrinsic i e undoped Si ni pi ni 2 EE40 Fall 2007 kT Eg kT Slide 14 Prof Chang Hasnain 7 How to get conduction in Si We must either 1 Chemically modify the Si to produce free carriers permanent or 2 Electrically induce them by the field effect switchable For the first approach controlled impurities dopants are added to Si Add group V elements 5 bonding electrons vs four for Si such as phosphorus or arsenic Extra electrons produce free electrons for conduction or Add group III elements 3 bonding electrons such as boron Deficiency of electrons results in free holes EE40 Fall 2007 Slide 15 Prof Chang Hasnain Doping Silicon with Donors n type Donors donate mobile electrons and thus n type silicon Example add arsenic As to the silicon crystal Mobile electron donated by As ion As Immobile stuck positively charged arsenic ion after 5th electron left The extra electron with As breaks free and becomes a free electron for conduction EE40 Fall 2007 Slide 16 Prof Chang Hasnain 8 Doping with Acceptors p type Group III element boron typically is added to the crystal Immobile stuck negative boron ion after accepting electron from neighboring bond Mobile hole contributed by B ion and later path B The hole which is a missing bonding electron breaks free from the B acceptor and becomes a roaming positive charge free to carry current in the semiconductor It is positively charged EE40 Fall 2007 Slide 17 Prof Chang Hasnain Doping Typical doping densities 1016 1019 cm 3 Atomic density for Si 5 x 1022 atoms cm3 1018 cm 3 is 1 in 50 000 two persons in entire Berkeley wearing a green hat P n junction effect is like EE40 Fall 2007 Slide 18 Prof Chang Hasnain 9 EE40 Lecture 32 Prof Chang Hasnain 11 21 07 Reading Supplementary Reader EE40 Fall 2007 Slide 19 Prof Chang Hasnain Electron and Hole Densities in Doped Si Instrinsic undoped Si n p ni np ni 2 N doped Si Assume each dopant contribute to one electron n Nd Nce E f Ec kT p ni 2 N d p doped Si Assume each dopant contribute to one hole p Na Nve Ev E f kT p ni 2 N a EE40 Fall 2007 Slide 20 Prof Chang Hasnain 10 Summary of n and p type silicon Pure silicon is an insulator At high temperatures it conducts weakly …
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