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MOSFET I Vs Operation of a transistorn type operationSource Channel DrainPositive gate bias attracts electrons into channel.Channel now becomes more conductive Some important equations inthe inversion regime Depthdirection VT ms 2 B ox Insulator.Source Channel Drain ox Qs CoxQs qNAWdm SubstrateWdm 2 S 2 B qNA VT ms 2 B 4 S BqNA Cox.Qinv Cox VG VT MOSFET Geometry How to include y dependentpotential without doing the wholeproblem over . Assume potential V y varies slowlyalong channel so the x dependent andy dependent electrostats areindependent GRADUAL CHANNEL APPROXIMATION .Ignore Ex yPotential is separable in How to include y dependent potentials VG S 2 S SqNA Cox S 2 B V y .Need VG V y VT toinvert channel at y Vincreases threshold Since V y largest at drain end end reverts from inversion to.depletion first Pinch off So current j qninvv Qinv tinv vI jA jZtinv ZQinvvQinv Cox VG VT V y .v effdV y dy So current I eff ZCox VG VT V y dV y dyContinuity implies Idy ILI eff ZCox VG VT VD VD2 2 L. But this current behaves like a parabola I eff ZCox VG VT VD VD2 2 LWe have assumed inversion in our model ie always above pinch So we just extend the maximum current into saturation Easy to check that above current is maximum for VDsat VG .Substituting IDsat Cox effZ 2L VG VT 2 What s Pinch off V0G V0G VG VGNow add in the drain voltage to drive a current Initially youget an increasing current with increasing drain bias.When you reach VDsat VG VT inversion is disabled at thedrain end pinch off but the source end is still invertedThe charges still flow just that you can t draw more currentwith higher drain bias and the current saturates W Square law theory of MOSFETs.I eff ZCox VG VT VD VD2 2 L VD VG VTI eff ZCox VG VT 2 2L VD VG VTn Cox VG VT v effVD L Ideal Characteristics of n channel.enhancement mode MOSFET Drain current for REALLY small VDZ 1 2 I D nCi VG VT VD VD L 2 .Z Linear operationI D nCi VG VT VD VD VG VT Channel Conductance gD nCi VG VT .Transconductance gm nCiVD In Saturation Channel Conductance gD 0. Transconductance I D sat nCi VG VT gm nCi VG VT Equivalent Circuit Low Frequency AC Gate looks like open circuit. S D output stage looks like current source with channelconductance I D I D I D VD VGi g D v d g mv g. Equivalent Circuit Higher Frequency AC Input stage looks like capacitances gate to source gate and gate to drain overlap Output capacitances ignored drain to sourcecapacitance small. Equivalent Circuit Higher Frequency AC Input circuit i in j Cgs Cgd v g j 2 fCgatev g Input capacitance is mainly gate capacitance Output circuit i out g mv g.i in 2 fC gategm nCiVD Maximum Frequency not in saturation Ci is capacitance per unit area and Cgate is totalcapacitance of the gate.C gate Ci ZL F fmax when gain 1 iout iin 1 fmax 2 Ci ZL 2 L2NE Maximum Frequency not in saturation . max Inverse transit time v VD L Switching Speed Power Dissipationton CoxZLVD ION.Trade off If Cox too small Cs and Cd take over and you losecontrol of the channel potential e g saturation DRAIN INDUCED BARRIER LOWERING DIBL If Cox increases you want to make sure you don t controlimmobile charges parasitics which do not contribute to. Switching Speed Power DissipationPdyn CoxZLVD2fPst IoffVD inverter Vin 1 Vout 0 inverter .Positive gate turns nMOS onVin 0 Vout 1 inverter Negative gate turns pMOS on So what If we can create a NOT gate.we can create other gates e g NAND EXOR So what Ring Oscillator So what . More importantly since one is open and one is shut at steadystate no current except during turn on turn off Low power dissipation Getting the inverter outputgD 0.gm nCi VG VT What s the gain here Signal Restoration BJT vs MOSFET RTL logic vs CMOS logic. DC Input impedance of MOSFET at gate end is infiniteThus current output can drive many inputs FANOUT CMOS static dissipation is low IOFFVDD Normally BJTs have higher transconductance current faster IC qni2Dn WBND exp qVBE kT ID CoxW VG VT 2 L.gm IC VBE IC kT q gm ID VG ID VG VT 2 Today s MOSFET ID IC due to near ballistic operation What if it isn t ideal If work function differences and oxide charges arepresent threshold voltage is shifted just like for MOS.capacitor 2 s qN A 2 B VT VFB 2 B Qf 2 s qN A 2 B ms 2 B . Ci Ci If the substrate is biased wrt the Source VBS thethreshold voltage is also shifted2 s qN A 2 B VBS VT VFB 2 B . Threshold Voltage Control Substrate Bias 2 s qN A 2 B VBS VT VFB 2 B VT VT VBS VT VBS 0 .2 s qN A VT 2 B VBS 2 B Threshold Voltage Control substrate It also affects the I VThe threshold voltage is increased due to the depletion region.that grows at the drain end because the inversion layer shrinksthere and can t screen it any more Wd Wdm Qinv Cox VG VT y I effZQinvdV y dyVT y 2 sqNA Cox 2 B V y ECE 663. It also affects the I VIL effZCox VG 2 B V 2 sqNA 2 B V Cox dVI Z effCox L VG 2 B VD VD2 2 2 2 sqNA 2 B VD 3 2 2 B 3 2 3... We can approximately include.Include an additional charge term from thedepletion layer capacitance controlling V y Q Cox VG VT Cox Cd V y where Cd s WdmQ Cox VG VT MV y M 1 Cd Cox.ID Z effCox L VG VT MVD 2 VD ECE 663 Comparison between differentSquare Law TheoryBulk Charge TheoryBody Coefficient.Still not good below threshold or above saturationECE 663 Mobility Drain current model assumed constant mobility in Mobility of channel less than bulk surface scattering Mobility depends on gate voltage carriers in inversion.channel are attracted to gate increased surfacescattering reduced mobility Mobility dependence on gate voltage1 VG VT Sub Threshold Behavior. For gate voltage less than the threshold weak Diffusion is dominant current mechanism not drift n n o n L I D J D A qADn qADnq s B kT.n 0 ni eq s B VD kTn L ni e Sub threshold B kT. 1 e qVD kT e q s kTWe can approximate s with VG VT below threshold since allvoltage drops across depletion regionqADn ni e B. 1 e qVD kT e q VG VT kT Sub threshold current is exponential function of applied gate voltage Sub threshold current gets larger for smaller gates L Subthreshold Characteristic.Subthreshold Swing log ID VG Much of new research depends onreducing S Ghosh Rakshit Datta.Tunneling transistor Nanoletters 2004 Band filter like operation Sconf min 2 3 kBT e etox m Hodgkin and Huxley J Physiol 116 449 1952a Subthreshold slope 60 Z mV decadeJ Appenzeller et al PRL 04. Much of new research depends onreducing S Increase q by collective motion e g Ghosh Rakshit Datta NL 03 Effectively reduce N through interactions.Salahuddin Datta Negative capacitanceSalahuddin Datta Non thermionic switching T independent Appenzeller et al PRL. Nonequilibrium switchingLi Ghosh Stan Impact Ionization More complete model sub thresholdto saturation. Must include diffusion and drift currents Still use gradual channel approximation Yields sub threshold and saturation behavior for longchannel MOSFETS Exact Charge Model numerical integration. VZ s n VD sID L LD 0 np0 F V . p0 Exact Charge Model Pao Sah Long Channel MOSFEThttp www nsti org Nanotech2006... .MOSFET I-Vs ECE 663 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ECE 663 Threshold Voltage Control Substrate Bias: ECE 663 Threshold Voltage Control-substrate bias ECE 663 It also affects the I-V VG The threshold voltage is increased due to the depletion region that grows at the drain end because the inversion layer shrinks there and canâ€™t screen it any more.