Lecture 14Finding ID = f (VGS, VDS)Inversion ChargeDrift Velocity and Drain CurrentSquare-Law CharacteristicsThe Saturation RegionSquare-Law Current in SaturationLinear MOSFET ModelLinear MOSFET in SaturationR. T. HoweEECS 105 Fall 2001 Lecture 14Dept. of EECSUniversity of California at BerkeleyLecture 14• Last time:– MOS field effect transistor (MOSFET) current-voltage characteristics• Today :– Square-law MOSFET model– Linear MOSFET modelR. T. HoweEECS 105 Fall 2001 Lecture 14Dept. of EECSUniversity of California at BerkeleyFinding ID= f (VGS, VDS)• Approximate inversion charge QN(y): drain is higher than the source Æ less charge at drain end of channelR. T. HoweEECS 105 Fall 2001 Lecture 14Dept. of EECSUniversity of California at BerkeleyInversion Charge)()0()( LyQyQyQNNN=+=≈)()0(TnGSoxNVVCyQ−−====)(LyQN)(TnGDoxVVC−−Average inversion charge:DSGSGDVVV−=R. T. HoweEECS 105 Fall 2001 Lecture 14Dept. of EECSUniversity of California at BerkeleyDrift Velocity and Drain Current“Long-channel” assumption: use mobility to find vLVyVyEyvDSnnn/)/()()(µµµ=∆∆−−≈−=Substituting:≈−=NDWvQIR. T. HoweEECS 105 Fall 2001 Lecture 14Dept. of EECSUniversity of California at BerkeleySquare-Law CharacteristicsBoundary: what is ID,SAT?R. T. HoweEECS 105 Fall 2001 Lecture 14Dept. of EECSUniversity of California at BerkeleyThe Saturation RegionWhen VDS> VGS–VTn, there isn’t any inversioncharge at the drain … according to our simplistic modelWhy do curvesflatten out?R. T. HoweEECS 105 Fall 2001 Lecture 14Dept. of EECSUniversity of California at BerkeleySquare-Law Current in SaturationCurrent stays at maximum (where VDS= VGS– VTn= VDS,SAT)ID =Measurement: IDincreases slightly with increasing VDSmodel with linear “fudge factor”ID,SAT =R. T. HoweEECS 105 Fall 2001 Lecture 14Dept. of EECSUniversity of California at BerkeleyLinear MOSFET ModelChannel (inversion) charge: neglect reduction at drainVelocity saturation defines VDS,SAT =EsatL = constant-vsat/ µnDrain current:)],()[(, TnGSoxsatNSATDVVCvWWvQI−−−=−=|Esat| = 104V/cm, L = 0.12 µm Æ VDS,SAT= 0.12 V!R. T. HoweEECS 105 Fall 2001 Lecture 14Dept. of EECSUniversity of California at BerkeleyLinear MOSFET in Saturation)1)((, DSnTnGSoxsatSATDVVVWCvIλ+−=Implication of weaker dependence on
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