Lecture #30Bulk Semiconductor Potential, fFVoltage Drops in the MOS SystemMOS Band Diagrams (n-type Si)Biasing Conditions for p-type SiAccumulation (n+ poly-Si gate, p-type Si)Accumulation Layer Charge DensityDepletion (n+ poly-Si gate, p-type Si)Depletion Width W (p-type Si)Voltage Drops in Depletion (p-type Si)Surface Potential in Depletion (p-type Si)Threshold Condition (VG = VT)MOS Band Diagram at Threshold (p-type Si)Threshold VoltageStrong Inversion (p-type Si)Inversion Layer Charge Density (p-type Si)EE130 Lecture 30, Slide 1Spring 2007Lecture #30OUTLINE The MOS Capacitor•ElectrostaticsReading: Chapter 16.3EE130 Lecture 30, Slide 2Spring 2007Bulk Semiconductor Potential, F•p-type Si:•n-type Si:FiFEbulkEq )(0)/ln( iAFnNqkT0)/ln( iDFnNqkTEcEFEvEiqFEcEFEvEi|qF|EE130 Lecture 30, Slide 3Spring 2007Voltage Drops in the MOS System•In general, where qVFB = MS = M – SVox is the voltage dropped across the oxide(Vox = total amount of band bending in the oxide) sis the voltage dropped in the silicon (total amount of band bending in the silicon) For example: When VG = VFB, Vox = s = 0 i.e. there is no band bendingsoxFBGVVV)()( surfaceEbulkEqiiSEE130 Lecture 30, Slide 4Spring 2007MOS Band Diagrams (n-type Si)•Inversion–VG < VT–Surface becomes p-type•Accumulation–VG > VFB–Electrons accumulate at surface •Depletion–VG < VFB–Electrons repelled from surfaceDecrease VG (toward more negative values) -> move the gate energy-bands up, relative to the Sidecrease VGdecrease VGEE130 Lecture 30, Slide 5Spring 2007Biasing Conditions for p-type SiVG = VFBVG < VFBVT > VG > VFBincrease VGincrease VGEE130 Lecture 30, Slide 6Spring 2007Accumulation (n+ poly-Si gate, p-type Si)EcEFSEv|qS| is small, 0Ec= EFMEvM O S3.1 eV4.8 eVp-type Si+_VGVG < VFB++ ++++---- - -GATE|qVG |oxFBGVVV | qVox |Mobile carriers (holes) accumulate at Si surfaceEE130 Lecture 30, Slide 7Spring 2007FBGoxVVV 0)( FBGoxaccVVCQAccumulation Layer Charge Densityp-type Si+_VGVG < VFB++ ++++---- - -GATEQacc (C/cm2)From Gauss’ Law:oSiOoxoxaccooxoxSiOaccoxxCCQxVQ/ε where/ε/22 (units: F/cm2)xoEE130 Lecture 30, Slide 8Spring 2007Depletion (n+ poly-Si gate, p-type Si)EcEFSEvEc= EFMEv3.1 eV4.8 eVp-type Si+_VGVT > VG > VFB------++++ + +GATEqVGqVox qSM O SWSi surface is depleted of mobile carriers (holes)=> Surface charge is due to ionized dopants (acceptors)EE130 Lecture 30, Slide 9Spring 2007Depletion Width W (p-type Si)•Depletion Approximation:The surface of the Si is depleted of mobile carriers to a depth W.•The charge density within the depletion region is•Poisson’s equation:•Integrate twice, to obtain S:)0( WxqNA)0( εεWxqNρdxdSiASi22WqNSiASASSiqNW2To find s for a given VG, we need to consider the voltage drops in the MOS system…EE130 Lecture 30, Slide 10Spring 2007Voltage Drops in Depletion (p-type Si)oxSsiASFBoxSFBGCqNVVVV2p-type Si+_VG------++++ + +GATEQdep (C/cm2)From Gauss’ Law:oxdepooxoxSiOdepoxCQxVQ/ε/2 Qdep is the integrated charge density in the Si:SSiAAdepqNWqNQ2EE130 Lecture 30, Slide 11Spring 2007Surface Potential in Depletion (p-type Si)•Solving for S, we haveoxSsiASFBGCqNVV2 1)(2122siAFBGoxoxsiASqNVVCCqN2221)(212siAFBGoxoxsiASqNVVCCqNEE130 Lecture 30, Slide 12Spring 2007 AsurfaceFiFiFiiiFSNnEbulkEEsurfaceEEbulkEsurfaceEbulkE)()()(2)()(2Threshold Condition (VG = VT)•When VG is increased to the point where s reaches 2F, the surface is said to be strongly inverted.(The surface is n-type to the same degree as the bulk is p-type.)This is the threshold condition.VG = VTEE130 Lecture 30, Slide 13Spring 2007AFSiTiAFSqNWWnNqkT)2(2ln22MOS Band Diagram at Threshold (p-type Si)EcEFSEvEc= EFMEvqVGqVox qsM O SWTqFqFEE130 Lecture 30, Slide 14Spring 2007oxFSiAFFBTCqNVV)2(22Threshold Voltage•For p-type Si:•For n-type Si: oxSsiASFBoxSFBGCqNVVVV2oxFSiDFFBTCqNVV222 EE130 Lecture 30, Slide 15Spring 2007AFsiTFSqNWW)2(22Strong Inversion (p-type Si)p-type Si+_VG------++++ + +GATESignificant density of mobile electrons at surface(surface is n-type)As VG is increased above VT, the negative charge in the Si is increased by adding mobile electrons (rather than by depleting the Si more deeply), so the depletion width remains ~constant at W= WTxM O SxWTEE130 Lecture 30, Slide 16Spring 2007oxinvToxinvoxFsAFFBoxinvdepFFBoxSFBGCQVCQCqNVCQQVVVV )2(22 )(2 )( TGoxinvVVCQ Inversion Layer Charge Density (p-type
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