EECS130 Integrated Circuit DevicesAnnouncementsQuantitative ID-VDS Relationships – 1st attempt “Square Law”P-MOSFET N-MOSFET IV CharacteristicsAccumulation vs. depletion mode MOSFETQuestionQuestionEffective MobilityInterface roughness and mobilityEffective MobilityEffective MobilityProblem with the “Square Law” ApproachMOSFET I-V – Bulk Charge TheoryThreshold and SubthresholdSubthreshold CurrentSlide Number 16Subthreshold Leakage CurrentSubthreshold Leakage CurrentSubthreshold Swing (S)Slide Number 20EECS130 Integrated Circuit DevicesProfessor Ali Javey10/25/2007MOSFETs– Lecture 3Reading: Chapter 17Announcements•The next HW set is due on Thursday of next week.Quantitative ID -VDS Relationships – 1st attempt “Square Law”()⎥⎥⎦⎤⎢⎢⎣⎡−−μ=22DSDSTGoxnDVVVVCLZIsatDS,DS0 VV<<TGVV >;ID will increase as VDS is increased, but when VG – VDS = VT , pinch- off occurs, and current saturates when VDS is increased further. This value of VDS is called VDS,sat . i.e., VDS,sat = VG – VT and the current when VDS = VDS,sat is called IDS,sat . ()2TGoxsatD,2VVLCZI −μ=satDS,DVV >TGVV >;Here, Cox is the oxide capacitance per unit area, Cox = εox / xoxP-MOSFET N-MOSFET IV CharacteristicsThe PMOS IV is qualitatively similar to the NMOS IV, but the current is about half as large. Why?Accumulation vs. depletion mode MOSFETIdsVgIdsVgN-MOSFETP-MOSFETEnhancement Mode: Transistor is OFF at Vg = 0Depletion Mode: Transistor is ON at Vg = 0Question: How can you control Vt ?QuestionPlot the ID vs. VDS characteristics for an NMOS with the followingparameters:Substrate doping: 1016 cm–3. Oxide thickness = 100 nmGate width = 15 μm; Gate length = 1 μm. Assume μn = 500 cm2/(Vs)1. Find Cox :Cox = εox / xox = 33.3 nF/cm23. Find ID -VDS for different values of VG and plot the graphV15.2222FSiAoxSioxFT=φεεε+φ=NqxV2. Find VT :QuestionPlot the ID vs. VDS characteristics for an NMOS with the followingparameters:Substrate doping: 1016 cm–3. Oxide thickness = 100 nmGate width = 15 μm; Gate length = 1 μm. Assume μn = 500 cm2/(Vs)1. Find Cox :Cox = εox / xox = 33.3 nF/cm23. Find ID -VDS for different values of VG and plot the graphV15.2222FSiAoxSioxFT=φεεε+φ=NqxV2. Find VT :Effective MobilitySurface scattering reduces the mobility of the carriers in a MOSFET device as compared to a bulk Si. This is in part due to the gate induced field acceleration of the carriers toward the “rough” Si/SiO2 interface.Interface roughness and mobilityCharge carriers are scattered near the surface due to this interface roughnessEffective Mobility• phonon scattering• coulombic scattering• surface roughness scattering(Vg +Vt +0.2 V)/6Toxe can be shown to be the average vertical electric field in the inversion layer.Empirically, we often see:()TGnVV −+=θμμ10Effective MobilityEffective MobilityThe variation in mobility as a function of VG -VT has profound effect on the I-V characteristicsProblem with the “Square Law” Approach• Assumes that gate charge is purely balanced by inversion charge• Ignores variation in depletion width with lengthMOSFET I-V – Bulk Charge Theory• Accounting for the depletion width, we have:• So, we finally find (again in the linear region):[]()()FASiTFASiTATGoxinvqNWqNyWWyWqNVVCyQφεεφφεεφ2222)()()()(00=+=−+−−−=()⎥⎥⎦⎤⎢⎢⎣⎡⎥⎥⎦⎤⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛+−⎟⎟⎠⎞⎜⎜⎝⎛+−−−−=FDFDFWDDTGoxnDVVVVVVVCLZIφφφμ43121342232Threshold and SubthresholdSubthreshold CurrentIds(μA/μm)Vgs• The leakage current that flows at Vg <Vt is called the subthreshold current. Previously we had assumed that current is zero, but in reality that’s not the case.90nm technology. Gate length: 45nm for NMOS, 50nm for PMOS• The current at Vgs =0 and Vds =Vdd is called Ioff.Intel, T. Ghani et al., IEDM 2003ηϕ1=+=depoxeoxegsCCCdVdCdepψSCoxVg• Subthreshold current ∝ ns (surface inversion carrier concentration)• ns ∝ eqϕs/kT• ϕs (surface potential) varies with Vg through a capacitor networkIn subthreshold, ϕs = constant +Vg /ηϕSEfVgSubthreshold Leakage Current() / kTVqkTqsgsseendsIηϕ/constant/kTqVgseη/∝∝∝∝+CdepϕsCoxVGdepoxeCCη = 1 +• Subthreshold current changes 10x for η·60mV change in Vg. Reminder: 60mV is (ln10)·kT/q•Subthreshold swing, S : the change in Vgs corresponding to 10x change in subthreshold current. S = η·60mV, typically 80-100mVkTqVgseη/∝dsISubthreshold Leakage Currentis determined only by Vt and subthreshold swing.• Practical definition of Vt : the Vgs at which Ids = 100nA×W/L=>( )kTVVqldsubthreshotgeLWnAI/100)(−( )SVVtgLW/10100−××=××≈ηVgsLog (Ids )Vt100×W/L(nA)IoffWSVtL/10100−××Ioff (nA) =Vds =VddSubthreshold Swing (S)• Smaller S is desirable (lower Ioff for a given Vt ). Minimum possible value of S is 60mV/dec.• What are 3 ways to lower swing?• Limitations⎟⎟⎠⎞⎜⎜⎝⎛+⋅=oxedepCCmVS 160Velocity Saturationsatsv+=1μ• velocity saturation haslarge and deleterious effect on the Ion of MOSFETS<< sat : v = μs>> sat : v = μs
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