1EE130 Lecture 26, Slide 1Spring 2003Lecture #26ANNOUNCEMENT• The lowest HW grade will be dropped for each studentOUTLINE• Small-signal MOSFET model• MOSFET scaling• Velocity saturation• Short-channel MOSFETsEE130 Lecture 26, Slide 2Spring 2003Small Signal Model• Conductance parameters:)(0TGSoxeeffconstVGDmDsatconstVDDdVVmLCWVIgIVIgDG−=∂∂==∂∂===µλ2EE130 Lecture 26, Slide 3Spring 2003Inclusion of Additional ParasiticsEE130 Lecture 26, Slide 4Spring 2003Cutoff Frequency• fmaxis the frequency where the MOSFET is no longer amplifying the input signal– Obtained by considering the small-signal model with the output terminals short-circuited, and finding the frequency where |iout/ iin| = 1→ Increased MOSFET operating frequencies are achieved by decreasing the channel lengthLVVmLWCgfTGSeffoxem1)(22max∝−==πµπ3EE130 Lecture 26, Slide 5Spring 2003MOSFET Scaling• MOSFETs have scaled in size over time– 1970’s: ~ 10 µm– Today: ~50 nm• Reasons:– Speed–DensityEE130 Lecture 26, Slide 6Spring 2003–IDS↑ as L ↓ (decreased effective “R”)– Gate area ↓ as L ↓ (decreased load “C”)– Therefore, RC ↓ (implies faster switch)Benefit of Transistor Scaling4EE130 Lecture 26, Slide 7Spring 2003CCV1 V2 V3 VddVdd 0V2V1tV32τd.......................delaynpropagatio:dτCircuit Example – CMOS InverterEE130 Lecture 26, Slide 8Spring 2003dsatNdddsatPdddICVdelaydownpullICVdelayuppulldelayuppulldelaydownpull22)(21≈−≈−−+−≡τ)11(4dsatPdsatNdddIICV+=τ)|(|22andddgdsatddonddPNVVIVIVRR===τdis reduced by increasing IDsat5EE130 Lecture 26, Slide 9Spring 2003satv+=1µ• velocity saturation haslarge and deleterious effect on the IDsatof MOSFETS<<sat: v = µ >>sat: v = µsatVelocity SaturationEE130 Lecture 26, Slide 10Spring 2003LVVVmVVCLWIsatDSDSDSTGSeffoxeDS+−−=1)2(µLVIchannel-longIsatDSDSDS/1+=MOSFET I-V with Velocity Saturation6EE130 Lecture 26, Slide 11Spring 2003LVVVVVdVdIsatTGSTGSDsatDSDS/)(211)(2,0Solving for −++−==LVVmVsatTGSDsat11+−=satsatvµ2≡A simpler and more accurate VDsatis:m = 1 + 3Toxe/WdmEE130 Lecture 26, Slide 12Spring 2003Drain Saturation Voltage VDsat• If EsatL >> VGS-VTnthen the MOSFET is considered “long-channel”. This condition can be satisfied when– L is large, or – VGSis close to VTLVVmVsatTnGSDsatE11+−=7EE130 Lecture 26, Slide 13Spring 2003Question: At Vgs= 1.8 V, what is the VDsatof an NFET with Toxe= 3 nm, VT = 0.25 V, and Wdm= 45 nm for (a) L =10 µm, (b) L = 1 um, (c) L = 0.1 µm, and (d) L = 0.05 µmSolution: From VGS , VT, and Toxe, µnis 200 cm2V-1s-1. sat= 2vsat/µ = 8 ×104V/cmm = 1 + 3Toxe/Wdm= 1.211−+−=LVVmVsatTGSDsatEXAMPLE: Drain Saturation VoltageEE130 Lecture 26, Slide 14Spring 2003(a) L = 10 µm, VDsat= (1/1.3V + 1/80V)-1= 1.3 V(b) L = 1 µm, VDsat= (1/1.3V + 1/8V)-1= 1.1 V(c) L = 0.1 µm, VDsat= (1/1.3V + 1/.8V)-1= 0.5 V(d) L = 0.05 µm, VDsat= (1/1.3V + 1/.4V)-1 = 0.3 V11−+−=LVVmVsatTGSDsat8EE130 Lecture 26, Slide 15Spring 2003Substituting VDsatfor VDSin IDSequation gives:LVVIchannel-longLVVVVCmLWIsatTGSDsatsatTGSTGSeffoxeDsat−+=−+−=11)(22µVery short channel case:TGSsatVVL−<<) / m()(2mVVCWvVVCWITGSoxesatTGSsatnoxeDsat−=−=µ• IDsatis proportional to VGS–VTrather than (VGS –VT)2IDsatwith Velocity SaturationEE130 Lecture 26, Slide 16Spring 2003Summary: NMOSFET I-VLVVVmVVCLWIsatDSDSDSTnGSeffoxeDSE+−−=1)2(µ• Linear region:• Saturation region:LVVVVCmLWIIsatTnGSTnGSeffoxeDsatDSE)(1)(22−+−==µ××==holesfor cm/s 106selectronfor cm/s 108/266sateffsatsatvvµE9EE130 Lecture 26, Slide 17Spring 2003Very-Short-Channel MOSFETs•IfEsatL << VGS-VTn:⇒ IDsatis not sensitive to L• To increase IDsat(for faster circuit operation), we must increase Coxe(VGS-VTn), i.e. reduce Toxeand VTnmVVLVTnGSsatDsat)( −<≅ E)( )(2TnGSsatoxeTnGSsateffoxeDsatVVvCmWVVCmWI−=−= EµEE130 Lecture 26, Slide 18Spring 2003Short-channel MOSFET:• IDsatis proportional to VGS-VTnrather than (VGS-VTn)2• VDsatis lower than for long-channel MOSFET• Channel-length modulation is apparent0 1 22.5Vds (V)0.00.10.20.30.4Ids (mA/µm)L = 0.15 µmVgs = 2.5VVgs = 2.0VVgs = 1.5VVgs = 1.0VVt = 0.4 VVds (V)Ids (µA/µm)L = 2.0 µmVgs = 2.5VVgs = 2.0VVgs = 1.5VVgs = 1.0V0.00.010.020.03Vt = 0.7 VShort- vs. Long-Channel MOSFET10EE130 Lecture 26, Slide 19Spring 2003Velocity Overshoot• When L is comparable to or less than the mean free path, some of the electrons travel through the channel without experiencing a single scattering event →projectile-like motion (“ballistic transport”)⇒ The average velocity of carriers exceeds vsate.g. 35% for L = 0.12 µm NMOSFET⇒ Effectively, vsatand Esatincrease when L is very smallEE130 Lecture 26, Slide 20Spring 2003PMOSFET I-V with Velocity SaturationLVVVmVVCLWIsatDSDSDSTpGSeffoxeDSE+−+−=1)2(µ• Linear region:• Saturation
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