6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-1 Lecture 2 - Semiconductor Physics (I) September 13, 2005 Contents: 1. Silicon bond model: electrons and holes 2. Generation and recombination 3. Thermal equilibrium 4. Intrinsic semiconductor 5. Doping; extrinsic semiconductor Reading assignment: Howe and Sodini, Ch. 2, §§2.1-2.36.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-2 Key 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 2-3 1. Silicon bond model: electrons and holes Si is in Column IV of periodic table: IIIA IVA VA VIA 5 6 7 8 B C N O 13 14 15 16 IIB Al Si P S 30 31 32 33 34 Zn Ga Ge As Se 48 49 50 51 52 Cd In Sn Sb Te Electronic structure of Si atom: • 10 core electrons (tightly bound) • 4 valence electrons (loosely bound, responsible for most chemical properties) Other semiconductors: • Ge, C (diamond form), SiGe • GaAs, InP, InGaAs, InGaAsP, ZnSe, CdTe (on average, 4 valence electrons per atom)atomic densit6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-4 Silicon crystal structure: A ° 3sp tetrahedral bond 2.35 ° 5.43 A• 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 y: 5 × 1022 cm− 31022cm− − 3Si atomic density: 55 ×6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-5 Simple ”flattened” model of Si crystal: 4 valence electrons (– 4 q), contributed by each ion silicon ion (+ 4 q) two electrons in bond At 0K: • all bonds satisfied → all valence electrons engaged in bonding • 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.carriers:10−−19−1.66×101C)C6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-7 A few definitions: • in 6.012, ”electron” means free electron • define: • not concerned with bonding electrons or core electrons n ≡ (free) electron concentration [cm−3] p ≡ hole concentration [cm−3]6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-8 2. Generation and Recombination Generation = break up of covalent bond to form elec-tron and hole • requires energy from thermal or optical sources (or other external sources) −1]• generation rate: G = Gth + Gopt + ... [cm−3 · s • in general, atomic density n, p ⇒ G = f (n, p) – supply of breakable bonds virtually inexhaustible Recombination = formation of bond by bringing to-gether electron and hole • releases energy in thermal or optical form −1] • recombination rate: R [cm−3 · s• a recombination event requires 1 electron + 1 hole ⇒ R ∝ n · p Generation and recombination most likely at surfaces where periodic crystalline structure is broken.6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-9 3. Thermal equilibrium Thermal equilibrium = steady state + absence of external energy sources hυ δ<θ> δt =0 In thermal equilibrium: Go = Ro ⇒ Important consequence: • Go = f (T ) • Ro ∝ no ·po nopo = f (T ) ≡ n2 i (T ) Generation rate in thermal equilibrium: Recombination rate in thermal equilibrium: In thermal equilibrium and for a given semiconduc-tor, np product is a constant that depends only on temperature!6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-10 Electron-hole formation can be seen as chemical reaction: bond e − + h+ similar to water decompositi on reaction: H2OH+ + OH− Law-of-mass action relates concentration of reactants and reaction products. For water: [H+][OH−]K = [H2O] Since: [H2O] [H+], [OH−] Then: [H2O] constant Hence: [H+][OH−] constant6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-11 4. Intrinsic semiconductor Question: In a perfectly pure semiconductor in thermal equilibrium at finite temperature, how many electrons and holes are there? Since when a bond breaks, an electron and a hole are produced: no = po Also: 2 nopo = ni Then: no = po = ni ni ≡ intrinsic carrier concentration [cm− 3] In Si at 300 K (”room temperature”): ni 1× 1010 cm− 31010cm− − 3ni11×1 ni very strong function of temperature: T ↑→ ni ↑ Note: an intrinsic semiconductor need not be perfectly pure [see next]6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-12 5. Doping: introduction of foreign atoms to engineer semiconductor electrical properties A. Donors: introduce electrons to the semiconductor (but not holes) • For Si, group-V atoms with 5 valence electrons (As, P, Sb) IIIA IVA VA VIA 5 6 7 8 B C N O 13 14 15 16 IIB Al Si P S 30 31 32 33 34 Zn Ga Ge As Se 48 49 50 51 52 Cd In Sn Sb Te6.012 - 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 electron Define: Nd ≡ donor concentration [cm−3] • If Nd ni, doping irrelevant (intrinsic semiconductor) → no = po = nie semiconductor6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 2-14 • If Nd ni, doping controls carrier concentrations (extrinsic semiconductor) → Note: no poExample: no = Nd po = n2 i Nd : n-typ-type semiconductornn-−3Nd =1017 cm−3 → no =1017 cm−3 , po =103 cm . −3In general: Nd ∼ 1015 − 1020 cmlog no log po po majority carriersholes=minority
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