EE105 - Spring 2007 Microelectronic Devices and CircuitsPeriodic Table of ElementsElectronic Properties of SiliconThe Diamond StructureStates of an AtomSiliconElectron-Hole Pair InteractionFree Electron Density as a Function of TemperatureN Type DopingP Type DopingSummary of Charge CarriersThermal Equilibrium (Pure Si)Mass Action LawCompensated DopingFirst Charge Transportation Mechanism: DriftMobility vs. Doping in Silicon at 300KCurrent Flow: General CaseCurrent Flow: DriftVelocity SaturationSecond Charge Transportation Mechanism: DiffusionCurrent Flow: DiffusionExample: Linear vs. Nonlinear Charge Density ProfileEinstein's RelationResistivity of Uniformly Doped SiSheet Resistance (Rs)Using Sheet Resistance (Rs)IdealizationsEE105 - Spring 2007Microelectronic Devices and CircuitsLecture 2Semiconductor Basics2Periodic Table of Elements3Electronic Properties of SiliconSilicon is in Group IV (atomic number 14)–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 State4The Diamond Structure3sp Tetrahedral BondA43.5A35.25States of an AtomQuantum Mechanics: The allowed energy levels for an atom are discrete (2 electrons with opposite spin can occupy a state)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 Spacing6SiliconSi has four valence electrons. Therefore, it can form covalent bonds with four of its neighbors. When temperature goes up, electrons in the covalent bond can become free.7Electron-Hole Pair InteractionWith free electrons breaking off covalent bonds, holes are generated.Holes can be filled by absorbing other free electrons, so effectively there is a flow of charge carriers.8Free Electron Density as a Function of Temperature Eg, or bandgap energy, determines how much effort is needed to break off an electron from its covalent bond.There exists an exponential relationship between the free-electron density and bandgap energy.15 3/ 2 320 10 30 15 35.2 10 /( 300 ) 1.08 10 /( 600 ) 1.54 10 / gEkTiiin T e electrons cmn T K electrons cmn T K electrons cm-= �= = �= = �9N Type DopingIf Si is doped with group-V elements such as phosphorous (P) or arsenic (As), then it has more electrons and becomes N type (electron). Group-V impurities are called Donors10P Type DopingIf Si is doped with group-III elements such as boron (B), then it has more holes and becomes P type. Group-III impurities are called Acceptors11Summary of Charge Carriers12Thermal Equilibrium (Pure Si)Balance between generation and recombination determines no = poStrong function of temperature: T = 300 K210( )( )( ) ( )( ) / ( )( ) 10-3 cm at 300Kth optthth iiG G T GR k n pG Rk n p G Tn p G T k n Tn T= += �=� =� = =@13Majority Carrier Conc.= Doping Conc.Minority Carrier Conc.(Mass Action Law)N-TypeP-TypeMass Action LawThe product of electron and hole densities is ALWAYS equal to the square of intrinsic electron density, regardless of doping levels2 10 3( 300 , 10 ) K cmo o i ip n n T n-� = = =ddNNn 0aaNNp 020idnpN@20iannN@14Compensated DopingSi is doped with both donor and acceptor atoms:–More donors than acceptors: Nd > Na N type–More acceptors than donors: Na > Nd P type22 iio d a od ao a d oa dnn N N pN Nnp N N nN N= - =-= - =-15First Charge Transportation Mechanism: DriftThe process in which charge particles move because of an electric field is called drift. Charge particles will move at a velocity that is proportional to the electric field.EvEvnephMobility16Mobility vs. Doping in Silicon at 300KTypical values135045022 V-sec / cm V-sec / cmnpmm==17Current Flow: General CaseElectric current is calculated as the amount of charge in v meters that passes thru a cross-section if the charge travel with a velocity of v m/s. I v W h n qIJ v n qWh=- � ���= =- ��18( )n np ptot n pn pJ E n qJ E p qJ E n q E p qq n p Emmm mm m= ��= ��= ��+ ��= +Current Flow: DriftSince velocity is equal to E, drift characteristic is obtained by substituting v with E in the general current equation.The total current density consists of both electrons and holes.19Velocity SaturationA topic treated in more advanced courses is velocity saturation.In reality, velocity does not increase linearly with electric field. It will eventually saturate to a critical value.000011satsatbEvbv EEvmmmmm=+==+20Second Charge Transportation Mechanism: DiffusionCharge particles move from a region of high concentration to a region of low concentration.21Current Flow: DiffusionDiffusion current is proportional to the gradient of charge (dn/dx) along the direction of current flow. Total diffusion current density consists of both electrons and holes.( )n np ptot n pdnJ qDdxdpJ qDdxdn dpJ q D Ddx dx==-= -Diffusion Coefficient22Example: Linear vs. Nonlinear Charge Density ProfileLinear charge density profile means constant diffusion current, whereas nonlinear charge density profile means varying diffusion current. LNqDdxdnqDJnnnddnnLxLNqDdxdnqDJ exp23Einstein's RelationWhile the underlying physics behind drift and diffusion currents are totally different, Einstein’s relation provides a link between the two.pqkTD24Resistivity of Uniformly Doped Si1 1n nnnJ E n q Enqnqm ss mrs m= ��= �== =1 Ohm's LawV R IV E LI J tWI V EL LJ E EA RtW RtW RtWL LRtW tWsrs= �= �= �� �= = = = =� �� �= =25Sheet Resistance (Rs)IC resistors have a specified thickness – not under the control of the circuit designerEliminate thickness, t, by absorbing it into a new parameter: the sheet resistance (Rs)SL L LR RWt t W Wrr� �� � � �= = =� �� � � �� �� � � �“Number of Squares”26Using Sheet Resistance (Rs)Ion-implanted (or “diffused”) IC resistor27IdealizationsWhy does current density Jn “turn”?What is the thickness of the resistor?What is the effect of the contact
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