Lecture 6: Integrated Circuit ResistorsLecture OutlineResistivity for a Few MaterialsElectronic Properties of SiliconPeriodic Table of ElementsThe Diamond StructureStates of an AtomEnergy Band DiagramModel for Good ConductorBond Model for Silicon (T=0K)Bond Model for Silicon (T>0K)Holes?Yes, Holes!More About HolesThermal Equilibrium (Pure Si)Doping with Group V ElementsDonor AccountingDonor Accounting (cont)Doping with Group III ElementsMass Action LawCompensationCompensation (cont.)Thermal EquilibriumDrift Velocity and MobilityMobility vs. Doping in Silicon at 300 oKDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6Lecture 6: Integrated Circuit ResistorsProf. NiknejadDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadLecture OutlineSemiconductors Si Diamond StructureBond Model Intrinsic Carrier ConcentrationDoping by Ion ImplantationDriftVelocity Saturation IC Process Flow Resistor LayoutDiffusionDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadResistivity for a Few MaterialsPure copper, 273K 1.56×10-6 ohm-cmPure copper, 373 K 2.24×10-6 ohm-cmPure germanium, 273 K 200 ohm-cmPure germanium, 500 K .12 ohm-cmPure water, 291 K 2.5×107 ohm-cmSeawater 25 ohm-cmWhat gives rise to this enormous range?Why are some materials semi-conductive?Why the strong temp dependence?Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadElectronic Properties of SiliconSilicon is in Group IV –Atom electronic structure: 1s22s22p63s23p2–Crystal electronic structure: 1s22s22p63(sp)4–Diamond lattice, with 0.235 nm bond lengthVery poor conductor at room temperature: why?(1s)2(2s)2(2p)6(3sp)4Hybridized StateDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadPeriodic Table of ElementsDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadThe Diamond Structure3sp tetrahedral bondA43.5A35.2Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadStates of an AtomQuantum Mechanics: The allowed energy levels for an atom are discrete (2 electrons can occupy a state since with opposite spin)When atoms are brought into close contact, these energy levels splitIf there are a large number of atoms, the discrete energy levels form a “continuous” bandEnergyE1E2...E3Forbidden Band GapAllowedEnergyLevelsLattice ConstantAtomic SpacingDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadEnergy Band DiagramThe gap between the conduction and valence band determines the conductive properties of the materialMetal–negligible band gap or overlapInsulator –large band gap, ~ 8 eVSemiconductor–medium sized gap, ~ 1 eVValence BandConduction BandValence BandConduction Bande-Electrons can gain energy from lattice (phonon) or photon to become “free”band gape-Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadModel for Good ConductorThe atoms are all ionized and a “sea” of electrons can wander about crystal:The electrons are the “glue” that holds the solid togetherSince they are “free”, they respond to applied fields and give rise to conductions+ + + + + ++ ++ + + + + ++ ++ + + + + ++ +On time scale of electrons, lattice looks stationary…Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadBond Model for Silicon (T=0K)Silicon Ion (+4 q)Four Valence ElectronsContributed by each ion (-4 q)2 electrons in each bondDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadBond Model for Silicon (T>0K)Some bond are broken: free electronLeave behind a positive ion or trap (a hole)+-Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadHoles?Notice that the vacancy (hole) left behind can be filled by a neighboring electronIt looks like there is a positive charge traveling around!Treat holes as legitimate particles.+-Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadYes, Holes!The hole represents the void after a bond is brokenSince it is energetically favorable for nearby electrons to fill this void, the hole is quickly filledBut this leaves a new void since it is more likely that a valence band electron fills the void (much larger density that conduction band electrons)The net motion of many electrons in the valence band can be equivalently represented as the motion of a hole BandFilled StatesEmptyiivbivbvqvqvqJ )()()(StatesEmptyiStatesEmptyivbqvvqJ )(Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadMore About HolesWhen a conduction band electron encounters a hole, the process is called recombinationThe electron and hole annihilate one another thus depleting the supply of carriersIn thermal equilibrium, a generation process counterbalances to produce a steady stream of carriersDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadThermal Equilibrium (Pure Si)Balance between generation and recombination determines no = poStrong function of temperature: T = 300 oKoptthGTGG )()( pnkR RG )()( TGpnkth)(/)(2TnkTGpnithK300atcm10)(310 TniDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadDoping with Group V ElementsP, As (group 5): extra bonding electron … lost to crystal at room temperature+ImmobileChargeLeft BehindDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadDonor AccountingEach ionized donor will contribute an extra “free” electronThe material is charge neutral, so the total charge concentration must sum to zero: By Mass-Action Law:000dqNqpqnFree ElectronsFree HolesIons(Immobile))(2Tnpni0020diqNnnqqn00220 nqNqnqndiDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 6 Prof. A. NiknejadDonor Accounting (cont)Solve
View Full Document
Unlocking...