Lecture #32fS and W vs. VG (p-type Si)Total Charge Density in Si, QsMOS Capacitance MeasurementMOS C-V Characteristics (p-type Si)Capacitance in Accumulation (p-type Si)Flat-Band CapacitanceCapacitance in Depletion (p-type Si)Capacitance in Inversion (p-type Si)Slide 10Supply of Substrate Charge (p-type Si)Capacitor vs. Transistor C-V (or LF vs. HF C-V)Quasi-Static C-V MeasurementDeep DepletionEE130 Lecture 32, Slide 1Spring 2007Lecture #32OUTLINEThe MOS Capacitor:•Capacitance-voltage (C-V) characteristicsReading: Chapter 16.4EE130 Lecture 32, Slide 2Spring 2007S and W vs. VG (p-type Si))(for 1)(212222TGFBsiAFBGoxoxsiAsVVVqNVVCCqNVFBVTVG2FS:)(for 1)(2122TGFBsiAFBGoxoxSiASSiVVVqNVVCCqNW accumulation depletion inversion0VGaccumulation depletion inversion0AFSiT)(2qN2εWW:VFBVTEE130 Lecture 32, Slide 3Spring 2007invdepaccsQQQQ Total Charge Density in Si, QsVGaccumulation depletion inversion0VFBVTWqNAdepQVGaccumulation depletion inversion0VFBVT)(TGoxVVC invQVGaccumulationdepletion inversion0VFBVT)(FBGoxVVC accQVGaccumulation depletion inversion0VFBVTQinvslope = -CoxEE130 Lecture 32, Slide 4Spring 2007GsGGATEdVdQdVdQC MOS Capacitance MeasurementvaciacC-V MeterSiGATEMOS Capacitor• VG is scanned slowly• Capacitive current due to vac is measureddtdvCiacacEE130 Lecture 32, Slide 5Spring 2007GsdVdQC MOS C-V Characteristics (p-type Si)VGaccumulation depletion inversionVFBVTQinvslope = -CoxVGaccumulation depletion inversionVFBVTCCoxIdeal C-V curve:EE130 Lecture 32, Slide 6Spring 2007oxGaccCdVdQC Capacitance in Accumulation (p-type Si)• As the gate voltage is varied, incremental charge is added/subtracted to/from the gate and substrate.• The incremental charges are separated by the gate oxide.M O SQQQ-QCoxEE130 Lecture 32, Slide 7Spring 2007Flat-Band Capacitance•At the flat-band condition, variations in VG give rise to the addition/subtraction of incremental charge in the substrate, at a depth LD•LD is the “extrinsic Debye Length”–characteristic shielding distance, or the distance where the electric field emanating from a perturbing charge falls off by a factor of 1/e SiDoxFBLCC11ASiDNqkTL2CoxCDebyeEE130 Lecture 32, Slide 8Spring 2007SioxdepoxWCCCC1 111Capacitance in Depletion (p-type Si)• As the gate voltage is varied, the width of the depletion region varies. Incremental charge is effectively added/subtracted at a depth W in the substrate.M O SQQQ-QCoxWCdepSiAFBGoxGdepqNVVCdVdQC)(21 2EE130 Lecture 32, Slide 9Spring 2007Capacitance in Inversion (p-type Si)CASE 1: Inversion-layer charge can be supplied/removed quickly enough to respond to changes in the gate voltage. Incremental charge is effectively added/subtracted at the surface of the substrate.M O SQQCoxWToxGinvCdVdQC Time required to build inversion-layercharge = 2NAo/ni , where o = minority-carrier lifetime at surfaceEE130 Lecture 32, Slide 10Spring 2007Capacitance in Inversion (p-type Si)CASE 2: Inversion-layer charge cannot be supplied/removed quickly enough to respond to changes in the gate voltage. Incremental charge is effectively added/subtracted at a depth WT in the substrate.M O SQQWTmin1)2(21 1 111CqNCWCCCCSiAFoxSiToxdepoxCoxCdepEE130 Lecture 32, Slide 11Spring 2007Cox gatep-type Si-WT AC DCCox gate p-type SiCox gate p-type Si CdepWCox gatep-type SiWTN+DC and ACAccumulation: Depletion:Inversion:Supply of Substrate Charge (p-type Si) Cdep,min++ ++++-- -- - - -- ----Case 1 Case 2EE130 Lecture 32, Slide 12Spring 2007Capacitor vs. Transistor C-V (or LF vs. HF C-V)p-type Si:VGaccumulation depletion inversionVFBVTCMOS transistor at any f,MOS capacitor at low f, orquasi-static C-VMOS capacitor at high fCminCmax=CoxCFBEE130 Lecture 32, Slide 13Spring 2007The quasi-static C-V characteristic is obtained by slowly ramping the gate voltage (< 0.1V/s), while measuring the gate current IG with a very sensitive DC ammeter. C is calculated from IG = C·(dVG/dt)Quasi-Static C-V MeasurementVGaccumulation depletion inversionVFBVTCCmax=Coxp-type Si:CminCFBEE130 Lecture 32, Slide 14Spring 2007Deep Depletion•If VG is scanned quickly, Qinv cannot respond to the change in VG. The increase in substrate charge density Qs must then come from an increase in depletion charge density Qdep depletion depth W increases as VG increases C decreases as VG
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