Lecture 13: Part I: MOS Small-Signal ModelsLecture OutlineTotal Small Signal CurrentRole of the Substrate PotentialBackgate TransconductanceFour-Terminal Small-Signal ModelMOSFET Capacitances in SaturationGate-Source Capacitance CgsGate-Drain Capacitance CgdJunction CapacitancesP-Channel MOSFETSquare-Law PMOS CharacteristicsSmall-Signal PMOS ModelMOSFET SPICE ModelPart II: Currents in PN JunctionsDiode under Thermal EquilibriumReverse BiasForward BiasDiode I-V CurveMinority Carriers at Junction Edges“Law of the Junction”Minority Carrier ConcentrationSteady-State ConcentrationsDiode Current DensitiesFabrication of IC DiodesDiode Small Signal ModelDiode CapacitanceCharge StorageDiode CircuitsDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13Lecture 13: Part I: MOS Small-Signal ModelsProf. NiknejadDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadLecture OutlineMOS Small-Signal Model (4.6)Diode Currents in forward and reverse bias (6.1-6.3)Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadTotal Small Signal Current( )DS DS dsi t I i= +DS DSds gs dsgs dsi ii v vv v� �= +� �1ds m gs dsoi g v vr= +TransconductanceConductanceDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadRole of the Substrate PotentialNeed not be the source potential, but VB < VSEffect: changes threshold voltage, which changes the drain current … substrate acts like a “backgate”QBSDQBSDmbvivigQ = (VGS, VDS, VBS)Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadBackgate TransconductanceResult:2 2Tn mD DmbBS Tn BSBS pQ Q QV gi igv V vVgf�� �= = =� � �- -( )02 2T T SB p pV V Vg f= + - - -Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadFour-Terminal Small-Signal Model1ds m gs mb bs dsoi g v g v vr= + +Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadMOSFET Capacitances in SaturationGate-source capacitance: channel charge is not controlled by drain in saturation.Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadGate-Source Capacitance CgsWedge-shaped charge in saturation effective area is (2/3)WL(see H&S 4.5.4 for details)ovoxgsCWLCC )3/2(Overlap capacitance along source edge of gate oxDovWCLC (Underestimate due to fringing fields)Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadGate-Drain Capacitance CgdNot due to change in inversion charge in channelOverlap capacitance Cov between drain and sourceis CgdDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadJunction CapacitancesDrain and source diffusions have (different) junctioncapacitances since VSB and VDB = VSB + VDS aren’t the sameComplete model (without interconnects)Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadP-Channel MOSFETMeasurement of –IDp versus VSD, with VSG as a parameter:Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadSquare-Law PMOS CharacteristicsDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadSmall-Signal PMOS ModelDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadMOSFET SPICE ModelMany “levels” … we will use the square-law “Level 1” modelSee H&S 4.6 + Spice refs. on reserve for details.Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13Part II: Currents in PN JunctionsDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadDiode under Thermal EquilibriumDiffusion small since few carriers have enough energy to penetrate barrierDrift current is small since minority carriers are few and far between: Only minority carriers generated within a diffusion length can contribute currentImportant Point: Minority drift current independent of barrier!Diffusion current strong (exponential) function of barrierp-type n-type DNAN-------------+++++++++++++0Ebiqf,p diffJ,p driftJ,n diffJ,n driftJ−−++−−ThermalGenerationRecombinationCarrier with energybelow barrier heightMinority Carrier Close to JunctionDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadReverse BiasReverse Bias causes an increases barrier to diffusionDiffusion current is reduced exponentiallyDrift current does not change Net result: Small reverse currentp-type n-type DNAN-------+++++++( )bi Rq Vf ++−Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadForward BiasForward bias causes an exponential increase in the number of carriers with sufficient energy to penetrate barrier Diffusion current increases exponentiallyDrift current does not change Net result: Large forward currentp-type n-type DNAN-------+++++++( )bi Rq Vf ++−Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadDiode I-V CurveDiode IV relation is an exponential functionThis exponential is due to the Boltzmann distribution of carriers versus energyFor reverse bias the current saturations to the drift current due to minority carriers1dqVkTd SI I e� �= -� �� �dqVkTdsII1-( )d d SI V I� - � =-Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. NiknejadMinority Carriers at Junction EdgesMinority carrier concentration at boundaries of depletion region increase as barrier lowers … the function is)()(ppnnxxpxxp(minority) hole conc. on n-side of barrier(majority) hole conc. on p-side of barrierkTEnergyBarriere/)((Boltzmann’s Law)kTVqDBe/)( AnnNxxp )( Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 13 Prof. A. Niknejad“Law of the Junction”Minority carrier concentrations at the edges of thedepletion region are given by:kTVqAnnDBeNxxp/)()(kTVqDppDBeNxxn/)()(Note 1: NA and ND are the majority carrier concentrations on the
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