EE2411UC Berkeley EE241 B. NikolicEE241 - Spring 2002Advanced Digital Integrated CircuitsLecture 2MOS Models, Technology ScalingUC Berkeley EE241 B. NikolicDigital Gate• Basic Properties• Functionality• Robustness• ∆ Swing, Noise margins• Delay• tPLH, t PHL• Power, energy consumption• Power-Delay-Product• Area•DensityEE2412UC Berkeley EE241 B. NikolicBasic CMOS GateProperties• Output levels determined by supply• Large noise margins• Performance loss at low voltagesUC Berkeley EE241 B. NikolicThe MOS Transistorn+n+p-substrateDSGBVGSxLV(x)+–VDSIDMOS transistor and its bias conditionsEE2413UC Berkeley EE241 B. NikolicMOS Currentl Vertical field set by VGSinduces channel chargel Gradual charge assumptionl Fixed charge is completely cancelled at VGS= VThl Charge in the channel isQn= Cox(VGS– VTh- VC(x)) l By Ohm’s law,IDS= WQn(x)v = WCox(VGS– VTh- VC(x)) µEl Also E = dVC(x)/dxl Key assumption is that v = µE, and mobility is constantUC Berkeley EE241 B. NikolicMOS CurrentIDS= WCox(VGS– VTh- VC(x)) µEIDS= WCox(VGS– VTh- VC(x)) µ(VC(x)/dx)l When integrated:DSDSThGSoxDSVVVVCLWI−−µ=2l Transistor saturates when VGD= VTh, the channel pinches off at drain’s side.( )22ThGSoxDSVVCLWI −µ=EE2414UC Berkeley EE241 B. NikolicMOS Currentn+n+SGVGSDVDS > VGS - VTVGS - VT+-Pinch-offUC Berkeley EE241 B. NikolicMOS Transistor ModelsLongchannelShortchannel[Rabaey]EE2415UC Berkeley EE241 B. NikolicVelocity Saturationξ(V/µm)ξc= 1.5υn(m/s)υsat= 105Constant mobility (slope = µ)Constant velocityUC Berkeley EE241 B. NikolicVelocity Saturationl Velocity is not always proportional to fieldl Modeled through variable mobility (mobility degrades at high fields)nneffEEEv/101+µ=NMOS: n = 2PMOS: n = 1l Hard to solve for n =2l Assume n = 1 (close enough)effsatvEµ=20[Sodini84]EE2416UC Berkeley EE241 B. NikolicVelocity Saturationl Piecewise linear approximation><+µ=CsatCCeffEEvEEEEEv,,1effsatCvEµ=2Toh, Ko, Meyer, JSSC 8/88ECis a function of doping and vertical field (controled by VGS)ECis around 5V/µm in 0.25µm technology.UC Berkeley EE241 B. NikolicMOS Currentl Start with the same charge equation and include mobility degradation:()vxWQInDS=( )( )CThGSoxDSEEExVVVWCI/1+µ−−=( )( )()( )CThGSoxDSEdxxdVdxxdVxVVVWCI/1/+µ−−=EE2417UC Berkeley EE241 B. NikolicMOS Currentl Can integrate and solve:DSDSThGSCDSoxDSVVVVLEVCLWI−−+µ=21l The numerator is the same, the denominator (1+ VDS/ECL) corresponds to mobility degradationl This (already approximated) equation represents well the device behavior, but is too complicated to use in hand calculations[Taur, Ning]UC Berkeley EE241 B. NikolicVelocity Saturationl When does a transistor enter velocity saturation?()( )LEVVLEVVVCThGSCThGSDSat+−−=10.90.70.40VDSat[V]2.521.510.5VGS[V]l In 0.25µm technology, ECL is about 1Vl Can calculate VDSat[Taur, Ning]EE2418UC Berkeley EE241 B. NikolicDrain Current0 0.5 1 1.5 2 2.500.511.522.5x 10-4VDS(V)ID(A)SaturationVelocitySaturationUC Berkeley EE241 B. NikolicDrain Current0 0.5 1 1.5 2 2.500.511.522.5x 10-4VDS(V)ID(A)SaturatedLinearVelocity saturatedEE2419UC Berkeley EE241 B. NikolicMOS Equations( )( )( )−>−>>−−′−<−>>−′−>−>>−−′<=THGSDSATTHGSDSTHGSDSATDSATTHGSTHGSDSATTHGSDSTHGSTHGSTHGSDSATTHGSDSTHGSDSDSTHGSTHGSDVVVVVVVVVVVVLWkVVVVVVVVVVLWkVVVVVVVVVVVVLWkVVI , ,,2 , ,,2 , ,,2,0222UC Berkeley EE241 B. NikolicMOS Models[Rabaey]EE24110UC Berkeley EE241 B. Nikolic0.25µm CMOSUC Berkeley EE241 B. NikolicUnified MOS Modell Model presented is compact and suitable for hand analysis.l Still have to keep in mind the main approximation: that VDSatis constant . When is it going to cause largest errors?l When E scales – transistor stacks.l But the model still works fairly well.EE24111UC Berkeley EE241 B. NikolicAlpha Power Law Modell Alternate approach, sometimes useful for hand analysis( )α−µ=ThGSoxDSVVCLWI2l Parameter α is between 1 and 2.l In 0.25µm technology α ~ 1.2.[Sakurai, Newton, JSSC 4/90]UC Berkeley EE241 B. NikolicMOS Transistor as a Switch Discharging a capacitor• Can solve:()DSDDvii=dtdVCiDSD=EE24112UC Berkeley EE241 B. NikolicMOS Transistor as a SwitchTraversed pathUC Berkeley EE241 B. NikolicMOS Transistor as a SwitchSolving the integral:Averaging resistances:EE24113UC Berkeley EE241 B. NikolicEquivalent ResistanceW/L=1, L=0.25UC Berkeley EE241 B. NikolicCMOS PerformancePropagation delay:()LeqnpHLCRt 2ln=()LeqppLHCRt 2ln=Short channel Long channel)(DDeqVfR≠DDeqVR1∝TDDVV>>forEE24114UC Berkeley EE241 B. NikolicMOS CapacitancesCGSO= CGDO= CoxxdW= CoWUC Berkeley EE241 B. NikolicGate CapacitanceEE24115UC Berkeley EE241 B. NikolicChannel CapacitanceUC Berkeley EE241 B. NikolicMOS CapacitancesEE24116UC Berkeley EE241 B. NikolicPower
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