EE4353_Lecture_3 Review_LC_Subthreshold_Regime_SCE

# EE4353_Lecture_3 Review_LC_Subthreshold_Regime_SCE - EE...

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EE 4353 Lecture 3 Long Channel MOSFET Professor H.-H. Tseng Aug 31, 2011

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Transistor Transfer Characteristics Saturation region I d 1/2 vs Vg for a fixed applied V d Linear scale Saturation region Vd > V dsat (= Vg – Vt) I dsat = (1/2) (W/L) m ns C ox (Vg-Vt) 2 = (1/2) (W/L) m ns C ox V d sat 2 Function of mobility Note: For Vg < Vt, I dsat is nonzero Something wrong with the theory!!
The origin of Subthreshold current The Boltzmann distribution of electron energies allows some of the more energetic electrons at the source to enter the channel and flow to the drain, resulting in a subthreshold current that is an exponential function of gate source voltage.

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Or Cox oxide Depletion region interface Vg Define capacitor divider Ratio Cr Cr = [ 1 + (C d +C it )/C ox ] Want to small Cr want to have large C ox If Cox >> (Cd+ Cit ) Cr approaches to minimum 1 Equivalent circuit showing capacitor divider between gate and substrate which determines sub-threshold current
Sub-V t region Linear I dst = m ns (C d + C it )(W/L)(kT/q) 2 [1- exp (-q V d /kT)] exp[(q/kT)(Vg-Vt)/(C r ) ] As Vg=Vt (a boundary condition), I dst = m ns (C d + C it )(W/L)(kT/q) 2 [1- exp (-q V d /kT)] = 100 nA W/L (from Fig) Therefore, I dst = 100 W/L exp[(q/kT)(Vg-Vt)/(C r )] in nA unit Sub-Vt current is linear wrt Vg, the value of slope is important physically Little Vd influence on I dst (for long L) Little Vd influence on V t (for long L)

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I dst = 100 (W/L) exp[(q/kT)(Vg-Vt)/(C r ) ] Where Cr = [ 1 + (C d +C it )/C ox ] S ≡ dVg/d(log I dst ) = ln10 [dVg/d(ln I dst )] = 2.3 (kT/q) [Cr ] S is called Subthreshold Swing, 1/S is the slope of log (I dst ) vs V g shown before I dst ~ 100 (W/L) 10 (Vg–Vt)/ S dst =100 W/L nA I dst ~ 100 (W/L) 10 –Vt/S = I off ( off-state current) for Vg=0, V d =V dd From above equation, for very small Vg (Vg =0), I dst is reduced to I leakage of S/D junctions affects the standby power dissipation Physically, if Vt is too low, sub-threshold Id can not turn off fully at Vg=0 due to Q inv does not drop to 0 abruptly Vt decreases I dsat (the Xtor output) increases, but I off increases Want a small S better efficiency of Vg in modulating I dsat and reduce I off the importance to have a steep slope 1/S What is I off ? What is Subthreshold Swing S?
7 Performance I d,sat = Ion= (W/ L g ) μ C ox ( V dd V t ) 2 P ACTIVE = a.f.C. V dd 2 P STANDBY =( I subth +I GIDL + I g ). V dd a: Active ratio I subth = I off

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## This note was uploaded on 09/22/2011 for the course EE 4353 taught by Professor Tseng during the Spring '11 term at Texas State.

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EE4353_Lecture_3 Review_LC_Subthreshold_Regime_SCE - EE...

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