Lecture 17Body Effect ExampleChannel-Length Modulation and LVelocity SaturationImpact of Velocity SaturationShort-Channel MOSFET ID-VDSDrain Induced Barrier Lowering (DIBL)NMOSFET in OFF StateSub-Threshold Leakage CurrentShort-Channel MOSFET ID-VGSVTH Design Trade-OffMOSFET Large-Signal Models (VGS > VTH)MOSFET Transconductance, gmMOSFET Small-Signal Model (Saturation Region of Operation)Derivation of Small-Signal Model (Long-Channel MOSFET, Saturation Region)PMOS TransistorPMOS I-V EquationsCMOS TechnologyComparison of BJT and MOSFETEE105 Spring 2008 Lecture 17, Slide 1Prof. Wu, UC BerkeleyLecture 17OUTLINE• NMOSFET in ON state (cont’d)– Body effect– Channel‐length modulation– Velocity saturation• NMOSFET in OFF state• MOSFET models• PMOSFET• Reading: Finish Chap. 6EE105 Spring 2008 Lecture 17, Slide 2Prof. Wu, UC BerkeleyBody Effect Example()0222where TH TH B SB BASioxVV VqNCγϕϕεγ=+ +−=18 3Example: Typical values ~0.50.48V for 10 cm (substrate doping)A substrate bias of 1V produce a shift of 0.2VBASBTHNVVγϕ−===EE105 Spring 2008 Lecture 17, Slide 3Prof. Wu, UC BerkeleyChannel‐Length Modulation• The pinch‐off point moves toward the source as VDSincreases.Æ The length of the inversion‐layer channel becomes shorter with increasing VDS.Æ IDincreases (slightly) with increasing VDSin the saturation region of operation.()()()()[]2,,2,111112: channel length modulation coefficient1* Note: in Razavi: 12DsatDS DSsatDsat n ox GS TH DS DsatDsat n ox GS TH DSLILLL LLV VWICVV VVLWICVVVLμλλμλΔ⎛⎞∝≅+⎜⎟−Δ⎝⎠Δ∝ −⎡⎤=−+−⎣⎦=−+EE105 Spring 2008 Lecture 17, Slide 4Prof. Wu, UC Berkeleyλand L• The eff ect of channel‐length modulation is less for a long‐channel MOSFET than for a short‐channel MOSFET.1 short channel MOSFET has larger Lλλ∝⇒EE105 Spring 2008 Lecture 17, Slide 5Prof. Wu, UC BerkeleyVelocity Saturation• In state‐of‐the‐art MOSFETs, the channel is very short (<0.1μm); hence the lateral electric field is very high and carrier drift velocities can reach their saturation levels.– The electric field magnitude at which the carrier velocity saturates is Esat.vE6622,,8 10 cm/s for electrons in Si6 10 cm/s for holes in SiNMOS: 250 cm /V-s 30,000 V/cmPMOS: 80 cm /V-s 80,000 V/cmFor 0.1 m0.3 V for NMOS0.8 V for PMsatnsatnsatDsatDsatvEELVVμμμ⎧×=⎨×⎩⎧≈⇒≈⎪⎨≈⇒≈⎪⎩=== OS⎧⎪⎨⎪⎩Drift velocity: Slope = vEμμ=Saturation Velocity: satvEE105 Spring 2008 Lecture 17, Slide 6Prof. Wu, UC BerkeleyImpact of Velocity Saturation• Recall that• If VDS> Esat×L, the carrier velocity will saturate and hence the drain current will saturate:• ID,satis proportional to VGS–VTHrather than (VGS–VTH)2• ID,satis not dependent on L• ID,satis dependent on W)()( yvyWQIinvD=()satTHGSoxsatinvsatDvVVWCvWQI−==,EE105 Spring 2008 Lecture 17, Slide 7Prof. Wu, UC Berkeley• ID,satis proportional to VGS‐VTHrather than (VGS‐VTH)2• VD,satis smaller than VGS‐VTH• Channel‐length modulation is apparent (?)Short‐Channel MOSFET ID‐VDSP. Bai et al. (Intel Corp.), Int’l Electron Devices Meeting, 2004.EE105 Spring 2008 Lecture 17, Slide 8Prof. Wu, UC Berkeley• In a short‐channel MOSFET, the source & drain regions each “support” a significant fraction of the total channel depletion charge Qdep×W×LÆ VTHis lower than for a long‐channel MOSFET• As the drain voltage increases, the reverse bias on the body‐drain PN junction increases, and hence the drain depletion region widens.ÆVTHdecreases with increasing drain bias.(The barrier to carrier diffusion from the source into the channel is reduced.)Æ IDincreases with increasing drain bias.Drain Induced Barrier Lowering (DIBL)SourceDrain Drain-qVDSInjectionBarrierDIBLShort-ChannelLong-ChannelEE105 Spring 2008 Lecture 17, Slide 9Prof. Wu, UC BerkeleyNMOSFET in OFF State• We had previously assumed that there is no channel current when VGS< VTH. This is incorrect!• As VGSis reduced below VTH(towards 0 V), the potential barrier to carrier diffusion from the source into the channel is increased. IDbecomes limited by carrier diffusion into the channel, rather than by carrier drift through the channel.(This is similar to the case of a PN junction diode!)ÆIDvaries exponentially with the potential barrier height at the source, which varies directly with the channel potential.EE105 Spring 2008 Lecture 17, Slide 10 Prof. Wu, UC BerkeleySub‐Threshold Leakage Current• Recall that, in the depletion (sub‐threshold) region of operation, the channel potential is capacitively coupled to the gate potential. A change in gate voltage (ΔVGS) results in a change in channel voltage (ΔVCS):• Therefore, the sub‐threshold current (ID,subth) decreases exponentially with linearly decreasing VGS/m/ ; 1 1depoxCS GS GSox dep oxCCVV VmmCC C⎛⎞Δ=Δ× ≡Δ =+ >⎜⎟⎜⎟+⎝⎠log (ID)VGSIDVGS110(log )Sub-tln(10) 60mV/dehreschold swing:DSGSTdISdVSmV−⎛⎞≡⎜⎟⎝⎠=>VTHVTHEE105 Spring 2008 Lecture 17, Slide 11 Prof. Wu, UC BerkeleyShort‐Channel MOSFET ID‐VGSP. Bai et al. (Intel Corp.), Int’l Electron Devices Meeting, 2004.EE105 Spring 2008 Lecture 17, Slide 12 Prof. Wu, UC BerkeleyVTHDesign Trade‐Off• Low VTHis desirable for high ON‐state current:ID,sat∝ (VDD‐ VTH)η1 < η< 2• But high VTHis needed for low OFF‐state current:ÆVTHcannot be reduced aggressively.Low VTHHigh VTHIOFF,high VTHIOFF,low VTHVGSlog ID0EE105 Spring 2008 Lecture 17, Slide 13 Prof. Wu, UC BerkeleyMOSFET Large‐Signal Models (VGS> VTH)• Depending on the value of VDS, the MOSFET can be represented with different large‐signal models. ()()[]()[]satDDSTHGSoxsatsatDsatDDSTHGSoxnsatDVVVVWCvIorVVVVLWCI,,,2,1)(121−+−=−+−=λλμVDS<< 2(VGS-VTH))(1THGSoxnONVVLWCR−=μVDS< VD,satDSDSTHGSoxntriDVVVVLWCI⎥⎦⎤⎢⎣⎡−−=2)(,μVDS> VD,satTriode Region Saturation RegionEE105 Spring 2008 Lecture 17, Slide 14 Prof. Wu, UC BerkeleyMOSFET Transconductance, gm• Transconductance (gm) is a measure of how much the drain current changes when the gate voltage changes.• For amplifier applications, the MOSFET is usually operating in the saturation region.– For a long‐channel MOSFET:– For a short‐channel MOSFET:()(){},21Dm n ox GS TH DS D satGS THIWgCVV VVLVVμλ=−+−=−GSDmVIg∂∂≡(){},1Dm sat ox DS D satGS THIgvWC VVVVλ=+−=−EE105 Spring 2008 Lecture 17, Slide 15 Prof.
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