6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-1Lecture 9 - MOSFET (I)MOSFET I-V CharacteristicsMarch 6, 2003Contents:1. MOSFET: cross-section, layout, symbols2. Qualitative operation3. I-V characteristicsReading assignment:Howe and Sodini, Ch. 4, §§4.1-4.3Announcements: Quiz #1, March 12, 7:30-9:30 PM,Walker Memorial; covers Lectures #1-9; open book; musthave calculator.6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-2Key questions• How can carrier inversion be exploited to make a tran-sistor?• How does a MOSFET work?• How does one construct a simple first-order model forthe current-voltage characteristics of a MOSFET?6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-31. MOSFET: layout, cross-section, symbolssourcegatedrainbodygate oxideinversion layerchannelpolysilicon gateppnnp+n+n+n+p+n+n+n+n+Key elements:• inversion layer under gate (depending on gate voltage)• heavily-doped regions reach underneath gate ⇒ in-version layer electrically connects source and drain• 4-terminal device: body voltage important6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-42 Circuit symbolsTwo complementary devices:• n-channel device (n-MOSFET) on p-Si substrate(uses electron inversion layer)• p-channel device (p-MOSFET) on n-Si substrate(uses hole inversion layer)n+n+pBulk orBodyDrainSourceGate(a) n-channel MOSFET D−G−IDpBp+p+nBulk orBodyDrainGate(b) p-channel MOSFETSource+_VSGDS−G++_VGSIDnIDnBVSD > 0VDS > 0+_VBS+_VSBDGBSSSBDG−IDp6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-52. Qualitative operationWater analogy of MOSFET:• Source: water reservoir• Drain: water reservoir• Gate: gate between source and drain reservoirssource draingatedepletion regioninversion layern+pn+VGSVGSDGSBVDSVDSIDwaterWant to understand MOSFET operation as a function of:• gate-to-source voltage (gate height over source waterlevel)• drain-to-source voltage (water level difference betweenreservoirs)Initially consider source tied up to body (substrate orback).6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-6Three regimes of operation:2 Cut-off regime:• MOSFET: VGS<VT, VGD<VTwith VDS> 0.• Water analogy: gate closed; no water can flow regardlessof relative height of source and drain reservoirs.depletion regionn+n+DGSpno inversion layeranywhereno water flowVGD<VTVGS<VTID=06.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-72 Linear or Triode regime:• MOSFET: VGS>VT, VGD>VT, with VDS> 0.• Water analogy: gate open but small difference in heightbetween source and drain; water flows.depletion regionn+n+DGSpinversion layereverywhereVGD>VTVGS>VTElectrons drift from source to drain ⇒ electrical current!• VGS↑→ |Qn|↑→ ID↑• VDS↑→ Ey↑→ID↑VDSsmall VDSIDVGS>VT00VGSVTsmall VDSIDVDS06.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-82 Saturation regime:• MOSFET: VGS>VT, VGD<VT(VDS> 0).• Water analogy: gate open; water flows from source todrain, but free-drop on drain side ⇒ total flow indepen-dent of relative reservoir height!depletion regionn+n+DGSpinversion layer"pinched-off" at drain sideVGD<VTVGS>VTIDindependent of VDS: ID= IDsatVDSIDVDSsat=VGS-VTVGDsat=VT00saturationlinear6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-93. I-V characteristicsGeometry of problem:depletion regioninversion layern+pn+VBS=0VGS>VTDGSB0LyVDSID2 General expression of channel currentCurrent can only flow in y-direction:Jy= Qn(y)vy(y)Total channel current:Iy= WQn(y)vy(y)Drain terminal current is equal to minus channel current:ID= −WQn(y)vy(y)6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-10ID= −WQn(y)vy(y)Rewrite in terms of voltage at channel location y, Vc(y):• If electric field is not too big:vy(y) '−µnEy(y)=µndVc(y)dy• For Qn(y) use charge-control relation at location y:Qn(y)=−Cox[VGS− Vc(y) − VT]for VGS− Vc(y) ≥ VT.All together:ID= WµnCox(VGS− Vc(y) − VT)dVc(y)dySimple linear first-order differential equation with one un-known, the channel voltage Vc(y).6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-11Solve by separating variables:IDdy = WµnCox(VGS− Vc− VT)dVcIntegrate along the channel in the linear regime:-for y =0,Vc(0) = 0-for y = L, Vc(L)=VDS(linear regime)Then:IDZL0dy = WµnCoxZVDS0(VGS− Vc− VT)dVcor:ID=WLµnCox(VGS−VDS2− VT)VDS6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-12For small VDS:ID'WLµnCox(VGS− VT)VDSKey dependencies:• VDS↑→ID↑ (higher lateral electric field)• VGS↑→ ID↑ (higher electron concentration)• L ↑→ID↓ (lower lateral electric field)• W ↑→ID↑ (wider conduction channel)VDSsmall VDSIDVGS>VT00VGSVTsmall VDSIDVDS0This is the linear or triode regime.6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-13In general,ID=WLµnCox(VGS−VDS2− VT)VDSEquation valid if VGS− Vc(y) ≥ VTat every y.Worst point is y = L, where Vc(y)=VDS, hence, equa-tion valid if VGS− VDS≥ VT, or:VDS≤ VGS− VTVDSIDVGSVGS=VTVDS=VGS-VT00term responsible for b end over of ID: −VDS26.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-14To understand why IDbends over, must understand firstchannel debiasing:VDS000yLLLyy|Qn||Ey|Vc000VGSVTVDS0LyVGS-Vc(y)Cox(VGS-VT)local gateoverdriveAlong channel from source to drain:y ↑→ Vc(y) ↑→|Qn(y)|↓→|Ey(y)|↑Local ”channel overdrive” reduced closer to drain.6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-15Impact of VDS:00yLLLyy|Qn|Vc0000VDSVDSVDSVDS=0VDS=0VDS=0|Ey|As VDS↑, channel debiasing more prominent⇒ IDrises more slowly with VDS6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-161.5 × 46.5 NMOSFETOutput characteristics ( VGS=0− 3 V, ∆VGS=0.5 V ):Zoom close to origin:6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-17Transfer characteristics (VDS=0.1 V ):6.012 - Microelectronic Devices and Circuits - Spring 2003 Lecture 9-18Key conclusions• The MOSFET is a field-effect transistor:– the amount of charge in the inversion layer is con-trolled by the field-effect action of the gate– the charge in the inversion layer is mobile ⇒ con-duction possible between source and drain• In the linear regime:– VGS↑⇒ ID↑: more electrons in the channel– VDS↑⇒ ID↑: stronger field
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