MOS TransistorMOS CapacitorMOS Terminal Voltages and Modes of OperationModes of OperationModes of OperationModes of OperationMOS I-V CharacteristicsMOS I-V Characteristics (Linear)MOS I-V Characteristics (Linear)MOS I-V Characteristics (Saturation, linear, cutoff)Shockley 1st order transistor modelsMOS I-V CharacteristicsMOS I-V CharacteristicsThreshold VoltageThreshold VoltageThreshold VoltageThreshold VoltageBody EffectNon-Ideal I-V effectsVelocity Saturation and Mobility DegradationVelocity Saturation and Mobility DegradationChannel Length ModulationSubthreshold ConductionJunction LeakageTunnelingTemperature and Geometry Dependence1Principles of VLSI Design CMPE 413MOS Transistor DetailsMOS TransistorSo far, we have treated MOS transistors as ideal switches.An ON transistor passes a finite amount of currentDepends on terminal voltagesNeed to derive current-voltage (I-V) characteristics.Transistor gate, source and drain all have capacitanceWe will also look at what a degraded level really means.Positive/negative voltage applied to the gate (with respect to substrate) enhances the num-ber of electrons/holes in the channel and increases conductivity between source and drain.Vt defines the voltage at which a MOS transistor begins to conduct. For voltages less than Vt (threshold voltage), the channel is cut off.ICV∆ t∆⁄()=t∆ CI⁄()V∆⋅=2Principles of VLSI Design CMPE 413MOS Transistor DetailsMOS CapacitorGate and body form a MOS capacitorOperating Modes:Accumulation Vg < 0Depletion 0< Vg < VtInversion Vg > Vtpolysilicon gate(a)silicon dioxide insulatorp-type body+-Vg < 0(b)+-0 < Vg < Vtdepletion region(c)+-Vg > Vtdepletion regioninversion region3Principles of VLSI Design CMPE 413MOS Transistor DetailsMOS Terminal Voltages and Modes of Operation Mode of operation depends on the terminal voltages. Vg, Vs, Vd  Vgs = Vg -Vs Vgd = Vg -Vd Vds = Vd - Vs = Vgs - Vgd Source and Drain are symmetric diffusion terminals By convention, source is terminal at lower voltage Hence Vds > 0 NMOS body is grounded. First assume that source is 0 too. Three modes of operation Cutoff Linear Saturation4Principles of VLSI Design CMPE 413MOS Transistor DetailsModes of OperationNMOS CutoffNo channelIds is 0+-Vgs = 0n+ n++-Vgdp-type bodybgsd5Principles of VLSI Design CMPE 413MOS Transistor DetailsModes of OperationNMOS Linear (resistive or non-saturated region)Channel is formed and extends from the source to the drainCurrent flow from drain to source (electrons)Ids increases with VdsSimilar to a linear resistor+-Vgs > Vtn+ n++-Vgd = Vgs+-Vgs > Vtn+ n++-Vgs > Vgd > VtVds = 00 < Vds < Vgs-Vtp-type bodyp-type bodybgsdbgsdIds6Principles of VLSI Design CMPE 413MOS Transistor DetailsModes of OperationNMOS SaturationChannel is pinched off near the drainIds independant of Vds. Ids is a function of Vgs onlyWe refer to it as current saturatesSimilar to a current source+-Vgs > Vtn+ n++-Vgd < VtVds > Vgs-Vtp-type bodybgsdIds7Principles of VLSI Design CMPE 413MOS Transistor DetailsMOS I-V CharacteristicsMOS transistors can be modeled as a voltage controlled switch. Ids is an important parame-ter that determines the behavior, e.g., the speed of the switch. What are the parameters that effect the magnitude of Ids? (Assume Vgs and Vds are fixed). The distance between source and drain (channel length). The channel width. The threshold voltage. The thickness of the gate oxide layer. The dielectric constant of the gate insulator. The carrier (electron or hole) mobility.Summary of normal conduction characteristics: Cut-off: accumulation, Ids is essentially zero. Nonsaturated: weak inversion, Ids dependent on both Vgs and Vds. Saturated: strong inversion, Ids is ideally independent of Vds.8Principles of VLSI Design CMPE 413MOS Transistor DetailsMOS I-V Characteristics (Linear)In Linear Region, Ids depends onHow much charge is in the channel?How fast is the charging moving?Channel ChargeMOS structure looks like parallel plate capacitor while operating in inversion (Gate-Oxide-channel)n+ n+p-type bodyWLtoxSiO2 gate oxide(good insulator, εox = 3.9)polysilicongaten+ n+p-type body+Vgdgate++source-Vgs-drainVdschannel-VgVsVdCgQchannelCV=CCgεoxWLtox---------⎝⎠⎛⎞CoxWL()== =Coxεoxtox---------=VVgcVt−VgsVds2---------−⎝⎠⎛⎞Vt−==9Principles of VLSI Design CMPE 413MOS Transistor DetailsMOS I-V Characteristics (Linear)Carrier VelocityCharge is carried by an electronCarrier velocity v is proportional to lateral E-field between source and drainNow we knowHow much charge Qchannel is in the channelHow much time t each carrier takes to cross from source to drainv µE=µcalled mobilityEVdsL⁄=t−LV⁄=Time of carrier to cross channel:IdsQchannelt⁄=µCoxWL-----VgsVt−()Vds2---------−⎝⎠⎛⎞Vds=β VgsVt−()Vds2---------−⎝⎠⎛⎞Vds=βµCoxWL-----=10Principles of VLSI Design CMPE 413MOS Transistor DetailsMOS I-V Characteristics (Saturation, linear, cutoff)MOS I-V characteristics (saturation)If Vgd < Vt channel pinches off near the drainWhen Vds > Vdsat = Vgs - VtNow drain voltage no longer increases currentShockley 1st order transistor modelsIdsβ VgsVt−()Vdsat2---------------−⎝⎠⎛⎞Vdsatβ2---VgsVt−()2==Ids=0β2---VgsVt−()2VdsVdsat<β VgsVt−()Vds2---------−⎝⎠⎛⎞VdsVdsVdsat>VgsVt<CutoffLinearSaturation11Principles of VLSI Design CMPE 413MOS Transistor DetailsMOS I-V CharacteristicsFollowing are the parameters on the previous slideVoltage-Current Characteristics for NMOSβµCoxWL-----=Coxεoxtox---------=Process dependent parametersµand Geometry dependent factors (designer controlled)WL-----Vds (V)Ids (mA)VGS = 1VVGS = 2VVds =Vdsat= Vgs - VtVGS = 3VVGS = 4VVGS = 5V1.0 2.0 3.0 4.0 5.01212Principles of VLSI Design CMPE 413MOS Transistor DetailsMOS I-V CharacteristicsAll dopings and voltages reversed for PMOS. Mobility µp is determined by holes Typically it is 2-3 times lower than that of electronsTypical values for AMI 0.6 µm technology that we use in the labβ for NMOS and PMOSNMOS gain approximately 2-3 times higher than PMOS. Thus W/L for PMOS needs to be higher to provide same amount of current (same rise and fall times).µn350cm2V-sec⁄=ε 3.9ε03.9 8.8514−×10 F/cm (permittivity of silicon dioxide)×==tox10nm=µp120cm2V-sec⁄=βn350 3.9 8.8514−×10××0.1 105−×--------------------------------------------------------------WL-----120.8WL-----µAV2⁄==βp120 3.9 8.8514−×10××0.1