1Slide 1EE40 Fall 2007 Prof. Chang-HasnainEE40Lecture 31Prof. Chang-Hasnain11/19/07Reading: Supplementary ReaderSlide 2EE40 Fall 2007 Prof. Chang-HasnainWeek 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 32Slide 3EE40 Fall 2007 Prof. Chang-HasnainConductors, Insulators and Semiconductors• Solids with “free electrons” – that is electrons notdirectly involved in the inter-atomic bonding- arethe familiar metals (Cu, Al, Fe, Au, etc).• Solids with no free electrons are the familiarinsulators (glass, quartz crystals, ceramics, etc.)• Silicon is an insulator, but at highertemperatures some of the bonding electrons canget free and make it a little conducting – hencethe term “semiconductor”• Pure silicon is a poor conductor (and a poorinsulator). It has 4 valence electrons, all ofwhich are needed to bond with nearestneighbors. No free electrons.Slide 4EE40 Fall 2007 Prof. Chang-HasnainThe Periodic TableIII IV V3Slide 5EE40 Fall 2007 Prof. Chang-HasnainUnit Cell of Crystalline Silicon• Si (1s2 2s2 2p6 3s23p2 )22 33 8 301 18 6 4# 88 25.00 10(5.43 10 )AtomscmVolume a cm!!" + " += = = ""Slide 6EE40 Fall 2007 Prof. Chang-HasnainElectronic Bonds in Silicon2-D picture of perfect crystal of pure silicon; double line is a Si-Sibond with each line representing an electronTwo electrons in each bondSi ion(charge+4 q)Actual structure is 3-dimensional tetrahedral- just like carbonbonding in organic and inorganic materials.Essentially no free electrons, and no conduction - insulator4Slide 7EE40 Fall 2007 Prof. Chang-HasnainBandgap• Electrons are mobile in the conduction band, while holesare mobile in the lower energy valence band.• The excited electrons move from the valence band intothe conduction band, leaving holes in the valence band– when the crystal is illuminated with photons whose energy islarger than the bandgap energy– or when the crystal is sufficiently heated. Valence Band E Conduction Band Band gap, Eg e- Ef Slide 8EE40 Fall 2007 Prof. Chang-HasnainBandgap for Insulator and Metal• Insulators have alarge band gap,usually 3.5 electron-volts (eV) or greater,preventing substantialamounts of chargecarriers from flowing.• Metals are goodconductors, withelectrons filling upinto the conductionband. Conduction Band E Small band gap, Eg Ef Valence Band Electrons fill into conduction band Large bandgap, Eg Valence Band E Conduction Band Ef5Slide 9EE40 Fall 2007 Prof. Chang-HasnainIf the lower floor is full and top one is empty, no traffic ispossible. Analog of an insulator. All electrons arelocked up.Shockley’s Parking Garage Analogy for Conduction in SiTwo-story parking garage on a hill:Slide 10EE40 Fall 2007 Prof. Chang-HasnainIf one car is moved upstairs, it can move AND THE HOLEON THE LOWER FLOOR CAN MOVE. Conduction ispossible. Analog to warmed-up semiconductor. Someelectrons get free (and leave “holes” behind).Shockley’s Parking Garage Analogy for Conduction in SiTwo-story parking garage on a hill:6Slide 11EE40 Fall 2007 Prof. Chang-HasnainIf 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 freeelectrons).Shockley’s Parking Garage Analogy for Conduction in SiTwo-story parking garage on a hill:Slide 12EE40 Fall 2007 Prof. Chang-HasnainIf a car is removed from the lower floor, it leaves a HOLEwhich can move. Conduction is possible. Analog to P-typesemiconductor. (Acceptors are added to the crystal,“consuming” bonding electrons,creating free holes).Shockley’s Parking Garage Analogy for Conduction in SiTwo-story parking garage on a hill:7Slide 13EE40 Fall 2007 Prof. Chang-HasnainFermi-Dirac Distribution• Fermi-Dirac function provides the probability that anenergy level is occupied by a fermion which is underthermal equilibrium. Electrons as well as holes areFermions and hence obey Fermi-Dirac statistics.Fig. 5. Fermi function plots at absolute zero, mid-range, and high temperature.Slide 14EE40 Fall 2007 Prof. Chang-HasnainElectron and Hole Densities, ,( )( )( ) ( )( )1( )/111( )/1f cv ff i c v f i gv cE E kTc cfcE E kTv vfvE E kT E E kT E kTE E kTc v c v c vn N N eE E kTep N N eE E kTenp N e N e N N e N N e!!! ! !!=!+" #= !$ %!$ %+& '= = =!!2gi ii i iE kTi c vn pn p nn N N e!===For instrinsic (i.e.undoped Si),8Slide 15EE40 Fall 2007 Prof. Chang-HasnainHow to get conduction in Si?For the first approach controlled impurities, “dopants”, are added toSi:orWe must either:1) Chemically modify the Si to produce free carriers (permanent) or2) Electrically “induce” them by the field effect (switchable)(Extra electrons produce “free electrons” for conduction.)Add group V elements (5 bonding electrons vs four for Si),such as phosphorus or arsenicDeficiency of electrons results in “free holes”Add group III elements (3 bonding electrons), such as boronSlide 16EE40 Fall 2007 Prof. Chang-HasnainDoping Silicon with Donors (n-type)Donors donate mobile electrons (and thus “n-type” silicon)Example: add arsenic (As) to the silicon crystal:Immobile (stuck) positively charged arsenic ion after 5th electron leftAsMobile electrondonated by As ionThe extra electron with As, “breaks free” and becomes a freeelectron for conduction9Slide 17EE40 Fall 2007 Prof. Chang-Hasnain Doping with Acceptors (p-type) BMobile hole con-tributed by B ionand later pathImmobile (stuck) negative boron ion after accepting electron from neighboring bondGroup III element (boron, typically) is added to the crystalThe “hole” which is a missing bonding electron, breaks free fromthe B acceptor and becomes a roaming positive charge, free tocarry current in the semiconductor. It is positively charged.Slide 18EE40 Fall 2007 Prof. Chang-HasnainDoping• Typical doping densities:1016~1019 cm-3• Atomic density for Si: 5 x1022 atoms/cm3• 1018 cm-3 is 1 in 50,000– two persons in entireBerkeley wearing a greenhat• P-n junction effect is like10Slide 19EE40 Fall 2007 Prof. Chang-HasnainEE40Lecture 32Prof. Chang-Hasnain11/21/07Reading: Supplementary ReaderSlide 20EE40 Fall 2007 Prof. Chang-HasnainElectron and Hole Densities in Doped Si( )2v fE E kTa vi ap N N ep n N!= ==• Instrinsic (undoped) Si• N-doped Si– Assume each
View Full Document
Unlocking...