1Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05Electrical Characteristics of MOS Devices• The MOS Capacitor– Voltage components– Accumulation, Depletion, Inversion Modes– Effect of channel bias and substrate bias– Effect of gate oxide charges– Threshold-voltage adjustment by implantation– Capacitance vs. voltage characteristics• MOS Field-Effect Transistor– I-V characteristics– Parameter extraction2Professor N Cheung, U.C. BerkeleyLecture 22EE143 F052) Visit the Device Visualization Websitehttp://jas.eng.buffalo.edu/and run the visualization experiments of1) Charge carriers and Fermi level, 2) pn junctions 3) MOS capacitors4) MOSFETs1) Revisit EE143 Week#2 Reading Assignment- Introduction to IC Devices, www.icknowledge.com- Streetman, Chap 3 Energy Band and Chargecarriers in Semiconductors.3Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05Negligible electron concentration underneath Gate region; Source-Drain is electrically openHigh electron concentration underneath Gate region; Source-Drain is electrically connectedVG < VthresholdVG > VthresholdMetal -Oxide-Semiconductor Transistor [ n-channel]4Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05Work Function of MaterialsEoEVECq ΦSEMICONDUCTOREfEoEfMETALWork function= qΦVacuum energy levelqΦMis determined by the metal materialqΦSis determined by the semiconductor material,the dopant type, and doping concentration5Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05Work Function (qΦM) of MOS Gate MaterialsEo= vacuum energy level Ef= Fermi levelEC = bottom of conduction band EV = top of conduction bandEfAl = 4.1 eVTiSi2= 4.6 eVEfEoqΦMEoqΦMEiECEV0.56eVqχ = 4.15eV0.56eVqχ = 4.15eV (electron affinity)EoEiECEV0.56eVqχ = 4.15eV0.56eVEfn+ poly-Sip+ poly-SiqΦM6Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05Work Function of doped Si substrateqχ = 4.15eV EfEoqΦsEiECEV|qΦF|0.56eV0.56eV* Depends on substrate concentration NBEfEoqΦsEiECEV|qΦF|0.56eV0.56eVqχ = 4.15eV n-type Sip-type SiΦs (volts) = 4.15 +0.56 - |ΦF|Φs (volts) = 4.15 +0.56 + |ΦF|=ΦiBFnNqkTln7Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05The MOS Capacitor SioxFBGVVVV++=oxoxoxxCε=[F/cm2]“metal”oxidesemiconductorVG++_VFBVoxVSi+_+_xoxOxide capacitance/unit area8Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05Flat Band Voltage• VFBis the “built-in” voltage of the MOS:• Gate work function ΦM:Al: 4.1 V; n+ poly-Si: 4.15 V; p+ poly-Si: 5.27 V• Semiconductor work function ΦS :• Vox= voltage drop across oxide (depends on VG)• VSi= voltage drop in the silicon (depends on VG)SMFBVΦ−Φ≡Φs (volts) = 4.15 +0.56 - |ΦF| for n-SiΦs (volts) = 4.15 +0.56 + |ΦF| for p-Si9Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05A) Accumulation: VG< VFBfor p-type substrateVSi≈ 0, so Vox= VG- VFBQSi’ = charge/unit area in Si=Cox(VG- VFB )MOS Operation ModesMOSi (p-Si)Thickness of accumulation layer ~0holes10Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05MOS Operation Modes• B) Flatband: VG= VFBNo charge in Si (and hence no charge in metal gate)•VSi= Vox= 0MOS (p-Si)11Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05C) Depletion: VG> VFB MOS Operation Modes (cont.)MOS (p-Si)qNBxds2dBoxdBFBG2xqNCxqNVVε++=(can solve for xd)BSiSidqNV2xε=VoxVSiDepletion layer12Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05xx=0Q'Metalρ(x)Oxidex=xox−ρxdx=0Q'Metal Semiconductorρ(x)Oxidex=xox=xo+Q'-x−ρxdx=0Q'Metal Semiconductorρ(x)Oxidex=xox=xo+SemiconductorDepletion Mode :Charge and Electric Field Distributionsby Superposition Principle of Electrostaticsxxdx=0Metal SemiconductorE(x)Oxidex=xox=xo+xxdx=0Metal SemiconductorE(x)Oxidex=xox=xo+xxdx=0Metal SemiconductorE(x)Oxidex=xox=xo+=+13Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05D) Threshold of Inversion: VG= VTnsurface= NB(for p-type substrate)=> VSi= 2|ΦF|MOS Operation Modes (cont.)M O S (p-Si)qNBxdmaxFoxBFsFBTGCqNVVV Φ+Φ+== 222 )(εQ’nThis is a definitionfor onset of strong inversion14Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05E) Strong Inversion: VG> VTMOS Operation Modes (cont.)MOS (p-Si)qNaxdmax)(maxTGoxnoxndBoxVVCQCQxqNV−−≈′′+=BFSidqNxΦ=ε4maxQ’nelectronsxdmaxis approximately unchanged when VG> VT15Professor N Cheung, U.C. BerkeleyLecture 22EE143 F0516Professor N Cheung, U.C. BerkeleyLecture 22EE143 F0517Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05p-Si18Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05Most derivations for MOS shown in lecture notes are done with p-type substrate (NMOS) as example.Repeat the derivations yourself for n-type substrate(PMOS) to test your understanding of MOS.Suggested Exercise19Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05VG(more positive)VFBVTAccumulation(holes)depletionstrong inversion(electrons)p-Si substrate (NMOS)n-Si substrate (PMOS)VG(more negative)VFBVTAccumulation(electrons)depletionStrong inversion(holes)20Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05AccumulationDepletionInversionVox= Qa/CoxVSi~ 0Vox=qNaxd/CoxVSi= qNaxd2/(2εs)Vox= [qNaxdmax+Qn]/CoxVSi= qNaxdmax2/(2εs)= 2|ΦF|Voltage drop = area under E-field curve* For simplicity, dielectric constants assumed to be same for oxide and Si in E-field sketches21Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05Appendix-Electron Energy Band- Fermi Level-Electrostatics of device charges22Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05Electron Potential EnergyIsolated atomsAtoms ina solidAvailable statesat discreet energy levelsAvailable statesas continuous energy levelsinside energy bands Conduction Band and Valence Band23Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05The Simplified Electron Energy Band Diagram24Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05xElectron EnergyE-field+-ECEV21xElectron EnergyE-field+-ECEV21Electric potential φ(2) < φ(1)Electric potential φ(2) > φ(1)Energy Band Diagram with E-fieldElectron concentration n kT/)]1()2([qkT/)1(qkT/)2(qeee)1(n)2(nφ−φφφ==25Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05Probability of available states at energy E being occupied f(E) = 1/ [ 1+ exp (E- Ef) / kT] where Ef is the Fermi energy and k = Boltzmann constant=8.617 ∗ 10-5eV/KThe Fermi-Dirac Distribution (Fermi Function)T=0K0.5E -Eff(E)26Professor N Cheung, U.C. BerkeleyLecture 22EE143 F05(2) Probability of available states at energy E NOT being occupied 1- f(E) = 1/ [ 1+ exp (Ef-E) /
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