6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-1Lecture 2 - Semiconductor Physics (I)September 13, 2005Contents:1. Silicon bond model: electrons and holes2. Generation and recombinatio n3. Thermal equilibrium4. Intrinsic semiconductor5. Doping; extrinsic semiconductorReading assignment:Howe and Sodini, Ch. 2, §§2.1-2.36.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-2Key questions• How do semiconductors conduct electricity?• What is a ”hole”?• How many electrons and holes are there in a semicon-ductor in thermal equilibrium at a certain tempera-ture?• How can one engineer the conductivity of semicon-ductors?6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-31. Silicon bond model: electrons and holesSi is in Column IV of periodic table:IIIAIVAVAVIAIIBBCNOAl SiPSZnGaGeAsSeCdInSnSbTe567813141530 31333448 495051163252Electronic structure of Si atom:• 10 core electrons (tightly bound)• 4 valence electrons (loosely bound, responsible for mostchemical properties)Other semiconductors:• Ge, C (diamond form), SiGe• GaAs, InP, InGaAs, InGaAsP, ZnSe, CdTe(on average, 4 valence electrons per atom)6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-4Silicon crystal structure:5.43 A°A°3sp tetrahedral bond2.35• Silicon is a crystalline material:– long range atomic arrangement• Diamond lattice:– atoms tetrahedrally bonded by sharing valence elec-trons (covalent bonding)• Each atom shares 8 electrons:– low energy and stable situation• Si atomic density: 5 × 1022cm−36.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-5Simple ”flattened” model of Si crystal:two electrons in bond4 valence electrons (–4 q),contributed by each ion silicon ion (+ 4 q)At 0K:• all bonds satisfied → all valence electrons engaged inbonding• no ”free” electrons6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-6At finite temperature:+incomplete bond (mobile hole)–mobile electron• finite thermal energy• some bonds are broken• ”free” electrons (mobile negative charge, −1.6×10−19C)• ”free” holes (mobile positive charge, 1.6 × 10−19C)”Free” electrons and holes are called carriers:• mobile charged particlesBeware: picture is misleading!• electrons and holes in semiconductors are ”fuzzier”:they span many atomic sites.6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-7A few definitions:• in 6.012, ”electron” means freeelectron• not concerned with bonding electrons or core electrons• define:n ≡ (free) electron concentration [cm−3]p ≡ hole concentration [cm−3]6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-82. Generation and RecombinationGeneration = break up of covalent bond to form elec-tron and hole• requires energy from thermal or optical sources (orother external sources)• generation rate: G = Gth+ Gopt+ ... [cm−3· s−1]• in general, atomic density n, p ⇒G 6= f(n, p)– supply of breakable b onds virtually inexhaustibleRecombination = formation of bond by bringing to-gether electron and hole• releases energy in thermal or optical form• recombination rate: R [cm−3· s−1]• a recombination event requires 1 electron + 1 hole ⇒R ∝ n · pGeneration and recombinatio n most likely at surfaces whereperiodic crystalline structure is broken.6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-93. Thermal equilibriumThermal equilibrium =steady state + absence of external energy sourceshυδ<θ>δt=0• Generation rate in thermal equilibrium: Go= f(T )• Recombination rate in thermal equilibrium: Ro∝ no·poIn thermal equilibrium:Go= Ro⇒ nopo= f(T ) ≡ n2i(T )Important consequence:In thermal equilibrium and for a given semiconduc-tor, np product is a constant that depends only ontemperature!6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-10Electron-hole formation can be seen as chemical reaction:bond*)e−+ h+similar to water decomposition reaction:H2O*)H++ OH−Law-of-mass action relates concentration of reactantsand reaction products. For water:K =[H+][OH−][H2O]Since:[H2O] [H+], [OH−]Then:[H2O] ' constantHence:[H+][OH−] ' constant6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-114. Intrinsic semiconductorQuestion: In a perfectly pure semiconductor in thermalequilibrium at finite temperature, how many electronsand holes are there?Since when a bond breaks, an electron and a hole areproduced:no= poAlso:nopo= n2iThen:no= po= nini≡ intrinsic carrier concentration [cm−3]In Si at 300 K (”room temperature”): ni' 1×1010cm−3nivery strong function of temp erature: T ↑→ni↑Note: an intrinsic semiconductor need not be perfectlypure [see next]6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-125. Doping: introduction of foreign atoms to engineersemiconductor electrical propertiesA. Donors: introduce electrons to the semiconductor(but not holes)• For Si, group-V atoms with 5 valence electrons (As,P, Sb)IIIAIVAVAVIAIIBBCNOAl SiPSZnGaGeAsSeCdInSnSbTe567813141530 31333448 4950511632526.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-13• 4 electrons of donor atom participate in bonding• 5th electron easy to release– at room temperature, each donor releases 1 elec-tron that is available for conduction• donor site become positively charged (fixed charge)As+immobile ionized donor–mobile electronDefine:Nd≡ donor concentration [cm−3]• If Nd ni, doping irrelevant(intrinsic semiconductor) → no= po= ni6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-14• If Nd ni, doping controls carrier concentrations(extrinsic semiconductor) →no= Ndpo=n2iNdNote: no po: n-type semiconductorExample:Nd=1017cm−3→ no=1017cm−3, po=103cm−3.In general: Nd∼ 1015− 1020cm−3log Ndlog nolog ponoponiniintrinsicextrinsicelectrons=majority carriersholes=minority carriersChemical reaction analogy:dissolve a bit of KOH into water ⇒ [OH−] ↑, [H+] ↓6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-15B. Acceptors: introduce holes to the semiconductor(but not electrons)• For Si, group-III atoms with 3 valence electrons (B)IIIAIVAVAVIAIIBBCNOAl SiPSZnGaGeAsSeCdInSnSbTe567813141530 31333448 4950511632526.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-16• 3 electrons used in bonding to neighboring
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