# VLSI Design I; A. Milenkovic 1

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1 PE/EE 47, PE 57 VLI esign I L6: tatic MO Logic epartment of Electrical and omputer Engineering University of labama in Huntsville leksandar Milenkovic ( www. ece.uah.edu/~milenka ) www. ece.uah.edu/~milenka/cpe57-3f [dapted from Rabaey s igital Integrated ircuits,, J. Rabaey et al. and Mary Jane Irwin ( www. cse. psu.edu/~mji ) ] ourse dministration Instructor: leksandar Milenkovic Office Hrs: MW 7:3-8:3, E7-L T: Fathima Tareen Office Hrs: Friday : : M, E46 URL: Text: igital Integrated ircuits, nd Edition Rabaey et. al., (October) Lab: ue eptember 9, 3 Lab: eptember 5 (posted), ue: October Hw: eptember 5 (posted), ue eptember 9 Project: efault project # posted! 9/5/3 VLI esign I;. Milenkovic The MO urrent-ource Model G I = for V G V T I I = k W/L [(V G V T )V min V min /](+λv ) for V G V T with V min = min(v G V T, V, V T ) and V GT = V G - V T etermined by the voltages at the four terminals and a set of five device parameters NMO PMO V T (V) γ(v.5 ) V T (V).63 - k (/V ) 5 x -6-3 x -6 λ(v - ) /5/3 VLI esign I;. Milenkovic 3 VLI esign I;. Milenkovic

2 R eq (Ohm) x The Transistor Modeled as a witch V G V T R on Modeled as a switch with infinite off resistance and a finite on resistance, R on Resistance inversely proportional to W/L (doubling W halves R on ) (V) (for V G =, V = /) For >>V T +V T /, R on independent of Once approaches V T, R on increases dramatically (V) NMO(kΩ) PMO (kω) /5/3 VLI esign I;. Milenkovic R on (for W/L = ) For larger devices divide R eq by W/L Other (ubmicon) MO Transistor oncerns Velocity saturation ubthreshold conduction Transistor is already partially conducting for voltages below V T Threshold variations In long-channel devices, the threshold is a function of the length (for low V ) In short-channel devices, there is a drain-induced threshold barrier lowering at the upper end of the V range (for low L) Parasitic resistances resistances associated with the source and drain contacts Latch-up R G R 9/5/3 VLI esign I;. Milenkovic 5 MO Inverter: teady tate Response V OL = V OH = V M = f(r n, R p ) R p V out = V out = R n V in = V in = 9/5/3 VLI esign I;. Milenkovic 6 VLI esign I;. Milenkovic

3 Transforming PMO I-V Lines Want common coordinate set V in, V out, and I n I p = -I n V Gn = V in ; V Gp = V in - V n = V out ; V p = V out - I n Vout V in = V in =.5 V in = V in =.5 V Gp = - V Gp = -.5 Mirror around x- axis V in = + V Gp I n = -I p Horiz. shift over V out = + V p 9/5/3 VLI esign I;. Milenkovic 7 PMO.5 V in = V -4 MO Inverter Load Lines NMO V in =.5V I n () V in =.5V.5 V in =.V V in =.V V in =.5V V in =.5V V in = V V in = V V in =.5V.5 V in =.5V V in =.V V in =.V V in =.5V V in =.5V V in = V V out (V).5um, W/L n =.5, W/L p = 4.5, =.5V, V Tn =.4V, V Tp = -.4V 9/5/3 VLI esign I;. Milenkovic 8 MO Inverter VT V out (V) NMO off PMO res.5.5 NMO sat PMO res NMO sat PMO sat.5 NMO res PMO sat NMO res PMO off V in (V) 9/5/3 VLI esign I;. Milenkovic 9 VLI esign I;. Milenkovic 3

4 MO Inverter: witch Model of ynamic ehavior R p V out V out L R n L V in = V in = 9/5/3 VLI esign I;. Milenkovic MO Inverter: witch Model of ynamic ehavior R p V out V out L R n L V in = V in = Gate response time is determined by the time to charge L through R p (discharge L through R n ) 9/5/3 VLI esign I;. Milenkovic Relative Transistor izing When designing static MO circuits, balance the driving strengths of the transistors by making the PMO section wider than the NMO section to maximize the noise margins and obtain symmetrical characteristics 9/5/3 VLI esign I;. Milenkovic VLI esign I;. Milenkovic 4

5 witching Threshold V M where V in = V out (both PMO and NMO in saturation since V = V G ) V M r /( + r) where r = k p V Tp /k n V Tn witching threshold set by the ratio r, which compares the relative driving strengths of the PMO and NMO transistors Want V M = / (to have comparable high and low noise margins), so want r (W/L) p k n V Tn (V M -V Tn -V Tn /) = (W/L) n k p V Tp ( -V M +V Tp +V Tp /) 9/5/3 VLI esign I;. Milenkovic 3 witch Threshold Example In our generic.5 micron MO process, using the process parameters from slide L3.5, a =.5V, and a minimum size NMO device ((W/L) n of.5) NMO PMO V T (V) γ(v.5 ) V T (V).63 - k (/V ) 5 x -6-3 x -6 λ(v - ).6 -. (W/L) p (W/L) n = 9/5/3 VLI esign I;. Milenkovic 4 witch Threshold Example In our generic.5 micron MO process, using the process parameters, a =.5V, and a minimum size NMO device ((W/L) n of.5) NMO PMO V T (V) γ(v.5 ) V T (V).63 - k (/V ) 5 x -6-3 x -6 λ(v - ).6 -. (W/L) p 5 x ( /) = x x (W/L) n -3 x -6 = (.5.4./) (W/L) p = 3.5 x.5 = 5.5 for a V M of.5v 9/5/3 VLI esign I;. Milenkovic 5 VLI esign I;. Milenkovic 5

6 imulated Inverter V M V M (V) ~3.4 (W/L) p /(W/L) n Note: x-axis is semilog V M is relatively insensitive to variations in device ratio setting the ratio to 3,.5 and gives V M s of.v,.8v, and.3v Increasing the width of the PMO moves V M towards Increasing the width of the NMO moves V M toward 9/5/3 VLI esign I;. Milenkovic 6 Noise Margins etermining V IH and V IL 3 y definition, V IH and V IL are where dv out /dv in = - (= gain) V OH = V out V OL = VIL V M V in piece-wise linear approximation of VT VIH NM H = - V IH NM L = V IL - pproximating: V IH = V M - V M /g V IL = V M + ( - V M )/g o high gain in the transition region is very desirable 9/5/3 VLI esign I;. Milenkovic 7 V out (V) MO Inverter VT from imulation V in (V).5um, (W/L) p /(W/L) n = 3.4 (W/L) n =.5 (min size) =.5V V M.5V, g = -7.5 V IL =.V, V IH =.3V NM L = NM H =. (actual values are V IL =.3V, V IH =.45V NM L =.3V & NM H =.5V) Output resistance low-output =.4kΩ high-output = 3.3kΩ 9/5/3 VLI esign I;. Milenkovic 8 VLI esign I;. Milenkovic 6

7 Gain eterminates gain V in.5.5 Gain is a strong function of the slopes of the currents in the saturation region, for V in = V M (+r) g (V M -V Tn -V Tn /)(λ n - λ p ) etermined by technology parameters, especially channel length modulation (λ). Only designer influence through supply voltage and V M (transistor sizing). 9/5/3 VLI esign I;. Milenkovic 9 Impact of Process Variation on VT urve V out (V) ad PMO Good NMO V in (V) Good PMO ad NMO Nominal process variations (mostly) cause a shift in the switching threshold 9/5/3 VLI esign I;. Milenkovic caling the upply Voltage.5..5 V out (V).5.5 V out (V) V in (V) evice threshold voltages are kept (virtually) constant Gain= /5/3 VLI esign I;. Milenkovic..5 V in (V) evice threshold voltages are kept (virtually) constant VLI esign I;. Milenkovic 7

8 tatic MO Logic MO ircuit tyles tatic complementary MO - except during switching, output connected to either V or via a lowresistance path high noise margins full rail to rail swing VOH and VOL are at V and, respectively low output impedance, high input impedance no steady state path between V and (no static power consumption) delay a function of load capacitance and transistor resistance comparable rise and fall times (under the appropriate transistor sizing conditions) ynamic MO - relies on temporary storage of signal values on the capacitance of high-impedance circuit nodes simpler, faster gates increased sensitivity to noise 9/5/3 VLI esign I;. Milenkovic 3 tatic omplementary MO Pull-up network (PUN) and pull-down network (PN) In In In N In In In N PUN PN PMO transistors only pull-up: make a connection from to F when F(In,In, In N ) = F(In,In, In N ) pull-down: make a connection from F to when F(In,In, In N ) = NMO transistors only PUN and PN are dual logic networks 9/5/3 VLI esign I;. Milenkovic 4 VLI esign I;. Milenkovic 8

9 Threshold rops PUN L L PN L L 9/5/3 VLI esign I;. Milenkovic 5 Threshold rops PUN V G - V Tn L L PN V Tp L V G L 9/5/3 VLI esign I;. Milenkovic 6 onstruction of PN NMO devices in series implement a NN function NMO devices in parallel implement a NOR function + 9/5/3 VLI esign I;. Milenkovic 7 VLI esign I;. Milenkovic 9

10 ual PUN and PN PUN and PN are dual networks emorgan s theorems + = [!( + ) =!! or!( ) =! &!] = + [!( ) =! +! or!( & ) =!!] a parallel connection of transistors in the PUN corresponds to a series connection of the PN omplementary gate is naturally inverting (NN, NOR, OI, OI) Number of transistors for an N-input logic gate is N 9/5/3 VLI esign I;. Milenkovic 8 MO NN F 9/5/3 VLI esign I;. Milenkovic 9 MO NN NN F = NN(,) F = F= = F= = F= = F= = = = = 9/5/3 VLI esign I;. Milenkovic 3 VLI esign I;. Milenkovic

11 MO NOR + F 9/5/3 VLI esign I;. Milenkovic 3 MO NOR NOR F = NOR(,) F = = = = = = = = F= F= F= F= 9/5/3 VLI esign I;. Milenkovic 3 omplex MO Gate OUT =!( + ( + )) 9/5/3 VLI esign I;. Milenkovic 33 VLI esign I;. Milenkovic

12 omplex MO Gate OUT =!( + ( + )) 9/5/3 VLI esign I;. Milenkovic 34 tandard ell Layout Methodology Routing channel signals What logic function is this? 9/5/3 VLI esign I;. Milenkovic 35 OI Logic Graph j PUN =!( ( + )) i i j PN 9/5/3 VLI esign I;. Milenkovic 36 VLI esign I;. Milenkovic

13 Two tick Layouts of!( ( + )) uninterrupted diffusion strip 9/5/3 VLI esign I;. Milenkovic 37 onsistent Euler Path n uninterrupted diffusion strip is possible only if there exists a Euler path in the logic graph Euler path: a path through all nodes in the graph such that each edge is visited once and only once. i j For a single poly strip for every input signal, the Euler paths in the PUN and PN must be consistent (the same) 9/5/3 VLI esign I;. Milenkovic 38 onsistent Euler Path n uninterrupted diffusion strip is possible only if there exists a Euler path in the logic graph Euler path: a path through all nodes in the graph such that each edge is visited once and only once. i j For a single poly strip for every input signal, the Euler paths in the PUN and PN must be consistent (the same) 9/5/3 VLI esign I;. Milenkovic 39 VLI esign I;. Milenkovic 3

14 OI Logic Graph PUN =!((+) (+)) PN 9/5/3 VLI esign I;. Milenkovic 4 OI Layout ome functions have no consistent Euler path like x =!(a + bc + de) (but x =!(bc + a + de) does!) 9/5/3 VLI esign I;. Milenkovic 4 NOR NOR/OR Implementation OR How many transistors in each? an you create the stick transistor layout for the lower left circuit? 9/5/3 VLI esign I;. Milenkovic 4 VLI esign I;. Milenkovic 4

15 VT is ata-ependent M 3 M 4 3.5µ/.5 µ NMO.75 µ /.5 µ PMO,: -> F= =, : -> weaker =, :-> M PUN V G = V V int M V G = V The threshold voltage of M is higher than M due to the body effect (γ) V Tn = V Tn V Tn = V Tn + γ( ( φ F + V int ) - φ F ) since V of M is not zero (when V = ) due to the presence of int 9/5/3 VLI esign I;. Milenkovic 43 tatic MO Full dder ircuit in in! out in!um in in 9/5/3 VLI esign I;. Milenkovic 44! out =! in & (!!) (! &!) tatic MO Full dder ircuit!um= out & (!!! in ) (! &! &! in ) in in! out in!um in in out = in & ( ) ( & ) um=! out & ( in ) ( & & in ) 9/5/3 VLI esign I;. Milenkovic 45 VLI esign I;. Milenkovic 5

### VLSI Design I; A. Milenkovic 1

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