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© Digital Integrated Circuits2nd Inverter

Digital Integrated Digital Integrated CircuitsCircuitsA Design PerspectiveA Design Perspective

The InverterThe InverterJuly 30, 2002

© Digital Integrated Circuits2nd Inverter

CMOS InverterCMOS Inverter

Polysilicon

In Out

VDD

GND

PMOS 2

Metal 1

NMOS

OutIn

VDD

PMOS

NMOS

Contacts

N Well

© Digital Integrated Circuits2nd Inverter

Two InvertersTwo Inverters

Connect in Metal

Share power and ground

Abut cells

VDD

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CMOS Inverter: Transient ResponseCMOS Inverter: Transient Response

tpHL = f(Ron.CL)

= 0.69 RonCL

VoutVout

Rn

Rp

VDDVDD

Vin 5 VDDVin 5 0

(a) Low-to-high (b) High-to-low

CLCL

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Voltage TransferVoltage TransferCharacteristicCharacteristic

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CMOS Inverter Load CharacteristicsCMOS Inverter Load Characteristics

IDn

Vout

Vin = 2.5

Vin = 2

Vin = 1.5

Vin = 0

Vin = 0.5

Vin = 1

NMOS

Vin = 0

Vin = 0.5

Vin = 1Vin = 1.5

Vin = 2

Vin = 2.5

Vin = 1Vin = 1.5

PMOS

© Digital Integrated Circuits2nd Inverter

CMOS Inverter VTCCMOS Inverter VTC

Vout

Vin0.5 1 1.5 2 2 .5

0.5

11.

52

2.5

NMOS resPMOS off

NMOS satPMOS sat

NMOS offPMOS res

NMOS satPMOS res

NMOS resPMOS sat

© Digital Integrated Circuits2nd Inverter

Switching Threshold as a function Switching Threshold as a function of Transistor Ratioof Transistor Ratio

100

101

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

MV

(V

)

Wp

/Wn

© Digital Integrated Circuits2nd Inverter

Determining VDetermining VIHIH and V and VILIL

VOH

VOL

Vin

Vout

VM

VIL VIH

A simplified approach

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Gain as a function of VDDGain as a function of VDD

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

Vin

(V)

Vou

t(V

)

0 0.5 1 1.5 2 2.5-18

-16

-14

-12

-10

-8

-6

-4

-2

0

Vin

(V)

gain

© Digital Integrated Circuits2nd Inverter

Impact of Process VariationsImpact of Process Variations

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

Vin (V)

Vo

ut(V

)

Good PMOSBad NMOS

Good NMOSBad PMOS

Nominal

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Propagation DelayPropagation Delay

© Digital Integrated Circuits2nd Inverter

CMOS Inverter Propagation DelayCMOS Inverter Propagation DelayVDD

Vout

Vin = VDD

Ron

CL

tpHL = f(Ron.CL)

= 0.69 RonCL

t

Vout

VDD

RonCL

1

0.5

ln(0.5)

0.36

© Digital Integrated Circuits2nd Inverter

0 0.5 1 1.5 2 2.5

x 10-10

-0.5

0

0.5

1

1.5

2

2.5

3

t (sec)

Vou

t(V)

Transient ResponseTransient Response

tp = 0.69 CL (Reqn+Reqp)/2

?

tpLHtpHL

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Design for PerformanceDesign for Performance

Keep capacitances small: Cload, Cgate, Cdiff

Increase transistor sizes: W/L watch out for self-loading!

Increase VDD (????)

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Delay as a function of VDelay as a function of VDDDD

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.41

1.5

2

2.5

3

3.5

4

4.5

5

5.5

VDD

(V)

t p(nor

mal

ized

)

© Digital Integrated Circuits2nd Inverter

2 4 6 8 10 12 142

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8x 10

-11

S

t p(sec

)

Device SizingDevice Sizing

(for fixed load)

Self-loading effect:Intrinsic capacitancesdominate

© Digital Integrated Circuits2nd Inverter

1 1.5 2 2.5 3 3.5 4 4.5 53

3.5

4

4.5

5x 10

-11

t p(sec

)

NMOS/PMOS ratioNMOS/PMOS ratio

tpLH tpHL

tp = Wp/Wn

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Inverter SizingInverter Sizing

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Inverter ChainInverter Chain

CL

If CL is given:- How many stages are needed to minimize the delay?- How to size the inverters?

May need some additional constraints.

In Out

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Inverter DelayInverter Delay

• Minimum length devices, L=0.25m• Assume that for WP = 2WN =2W

• same pull-up and pull-down currents• approx. equal resistances RN = RP

• approx. equal rise tpLH and fall tpHL delays• Analyze as an RC network

WNunit

Nunit

unit

PunitP RR

W

WR

W

WRR

11

tpHL = (ln 2) RNCL tpLH = (ln 2) RPCLDelay (D):

2W

W

unitunit

gin CW

WC 3Load for the next stage:

© Digital Integrated Circuits2nd Inverter

Inverter with LoadInverter with Load

Load (CL)

Delay

Assumptions: no load -> zero delay

CL

tp = k RWCL

RW

RW

Wunit = 1

k is a constant, equal to 0.69

© Digital Integrated Circuits2nd Inverter

Inverter with LoadInverter with Load

Load

Delay

Cint CL

Delay = kRW(Cint + CL) = kRWCint + kRWCL = kRW Cint(1+ CL /Cint)= Delay (Internal) + Delay (Load)

CN = Cunit

CP = 2Cunit

2W

W

© Digital Integrated Circuits2nd Inverter

Delay FormulaDelay Formula

/1/1

~

0int ftCCCkRt

CCRDelay

pintLWp

LintW

Cint = Cgin with 1f = CL/Cgin - effective fanoutR = Runit/W ; Cint =WCunit

tp0 = 0.69RunitCunit

© Digital Integrated Circuits2nd Inverter

Apply to Inverter ChainApply to Inverter Chain

CL

In Out

1 2 N

tp = tp1 + tp2 + …+ tpN

jgin

jginunitunitpj C

CCRt

,

1,1~

LNgin

N

i jgin

jginp

N

jjpp CC

C

Cttt

1,

1 ,

1,0

1, ,1

© Digital Integrated Circuits2nd Inverter

Optimal Tapering for Given Optimal Tapering for Given NN

Delay equation has N - 1 unknowns, Cgin,2 – Cgin,N

Minimize the delay, find N - 1 partial derivatives

Result: Cgin,j+1/Cgin,j = Cgin,j/Cgin,j-1

Size of each stage is the geometric mean of two neighbors

- each stage has the same effective fanout (Cout/Cin)- each stage has the same delay

1,1,, jginjginjgin CCC

© Digital Integrated Circuits2nd Inverter

Optimum Delay and Number of Optimum Delay and Number of StagesStages

1,/ ginLN CCFf

When each stage is sized by f and has same eff. fanout f:

N Ff

/10N

pp FNtt

Minimum path delay

Effective fanout of each stage:

© Digital Integrated Circuits2nd Inverter

ExampleExample

CL= 8 C1

In Out

C11 f f2

283 f

CL/C1 has to be evenly distributed across N = 3 stages:

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Optimum Number of StagesOptimum Number of Stages

For a given load, CL and given input capacitance Cin

Find optimal sizing f

ff

fFtFNtt pN

pp lnln

ln1/ 0/1

0

0ln

1lnln2

0

f

ffFt

f

t pp

For = 0, f = e, N = lnF

f

FNCfCFC in

NinL ln

ln with

ff 1exp

© Digital Integrated Circuits2nd Inverter

Optimum Effective Fanout Optimum Effective Fanout ffOptimum f for given process defined by

ff 1exp

fopt = 3.6for =1

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Buffer DesignBuffer Design

1

1

1

1

8

64

64

64

64

4

2.8 8

16

22.6

N f tp

1 64 65

2 8 18

3 4 15

4 2.8 15.3

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Power DissipationPower Dissipation

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Where Does Power Go in CMOS?Where Does Power Go in CMOS?

• Dynamic Power Consumption

• Short Circuit Currents

• Leakage

Charging and Discharging Capacitors

Short Circuit Path between Supply Rails during Switching

Leaking diodes and transistors

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Dynamic Power DissipationDynamic Power Dissipation

Energy/transition = CL * Vdd2

Power = Energy/transition * f = CL * Vdd2 * f

Need to reduce CL, Vdd, and f to reduce power.

Vin Vout

CL

Vdd

Not a function of transistor sizes!

© Digital Integrated Circuits2nd Inverter

Node Transition Activity and PowerNode Transition Activity and PowerConsider switching a CMOS gate for N clock cycles

EN CL Vdd 2 n N =

n(N): the number of 0->1 transition in N clock cycles

EN : the energy consumed for N clock cycles

Pavg N lim

ENN

-------- fclk= n N

N------------

N lim

C

LVdd

2fclk

=

0 1

n N N

------------N

lim=

Pavg = 0 1 C

LVdd

2 fclk

© Digital Integrated Circuits2nd Inverter

Short Circuit CurrentsShort Circuit Currents

Vin Vout

CL

Vdd

I VD

D (m

A)

0.15

0.10

0.05

Vin (V)5.04.03.02.01.00.0

© Digital Integrated Circuits2nd Inverter

How to keep Short-Circuit Currents Low?How to keep Short-Circuit Currents Low?

Short circuit current goes to zero if tfall >> trise,but can’t do this for cascade logic, so ...

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Minimizing Short-Circuit PowerMinimizing Short-Circuit Power

0 1 2 3 4 50

1

2

3

4

5

6

7

8

tsin

/tsout

Pno

rm

Vdd =1.5

Vdd =2.5

Vdd =3.3

© Digital Integrated Circuits2nd Inverter

Static Power ConsumptionStatic Power Consumption

Vin=5V

Vout

CL

Vdd

Istat

Pstat = P(In=1).Vdd . Istat

• Dominates over dynamic consumption

• Not a function of switching frequency

Wasted energy …Should be avoided in almost all cases,but could help reducing energy in others (e.g. sense amps)

© Digital Integrated Circuits2nd Inverter

Leakage CurrentsLeakage Currents

Vout

Vdd

Sub-ThresholdCurrent

Drain JunctionLeakage

Sub-Threshold Current Dominant FactorSub-threshold current one of most compelling issuesin low-energy circuit design!

© Digital Integrated Circuits2nd Inverter

Reverse-Biased Diode LeakageReverse-Biased Diode Leakage

Np+ p+

Reverse Leakage Current

+

-Vdd

GATE

IDL = JS A

JS = 1-5pA/m2 for a 1.2m CMOS technology

Js double with every 9oC increase in temperature

JS = 10-100 pA/m2 at 25 deg C for 0.25m CMOSJS doubles for every 9 deg C!

© Digital Integrated Circuits2nd Inverter

Total Power ConsumptionTotal Power Consumption

Ptot = Pdyn + Pdp + Pstat

= (CLVDD + VDD Ipeak ts)f0-1 + VDD Ileak

Ipeak = Maximum short circuit currentTs = 0-100% transition time of IpeakIleak = The current that flows between the supply rails in

the absence of switching activity.

2

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Principles for Power ReductionPrinciples for Power Reduction

Prime choice: Reduce voltage! Recent years have seen an acceleration in

supply voltage reduction Design at very low voltages still open question

(0.6 … 0.9 V by 2010!) Reduce switching activity Reduce physical capacitance

Device Sizing: for F=20– fopt(energy)=3.53, fopt(performance)=4.47

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Impact ofImpact ofTechnology Technology ScalingScaling

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Goals of Technology ScalingGoals of Technology Scaling

Make things cheaper: Want to sell more functions (transistors)

per chip for the same money Build same products cheaper, sell the

same part for less money Price of a transistor has to be reduced

But also want to be faster, smaller, lower power

© Digital Integrated Circuits2nd Inverter

Technology ScalingTechnology Scaling

Goals of scaling the dimensions by 30%: Reduce gate delay by 30% (increase operating

frequency by 43%) Double transistor density Reduce energy per transition by 65% (50% power

savings @ 43% increase in frequency

Die size used to increase by 14% per generation

Technology generation spans 2-3 years

© Digital Integrated Circuits2nd Inverter

Technology Evolution (2000 data)Technology Evolution (2000 data)

International Technology Roadmap for Semiconductors

18617717116013010690Max P power [W]

1.4

1.2

6-7

1.5-1.8

180

1999

1.7

1.6-1.4

6-7

1.5-1.8

2000

14.9-3.6

11-37.1-2.53.5-22.1-1.6Max frequency

[GHz],Local-Global

2.52.32.12.42.0Bat. power [W]

109-10987Wiring levels

0.3-0.60.5-0.60.6-0.90.9-1.21.2-1.5Supply [V]

30406090130Technology node

[nm]

20142011200820042001Year of

Introduction

Node years: 2007/65nm, 2010/45nm, 2013/33nm, 2016/23nm

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ITRS Technology RoadmapITRS Technology Roadmap

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TerminologyTerminology

ITRS: International Technology Roadmap for Semiconductors. It is devised and intended for technology assessment only and is without regard to any commercial considerations pertaining to individual products or equipment

DRAM Half-pitch: The common measure of the technology generation of a chip. It is half the distance between cells in a dynamic RAM memory chip. For example, in 2002, the DRAM half pitch has been reduced to 130 nm (.13 micron).

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Half PitchHalf Pitch

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Technology Scaling (1)Technology Scaling (1)

Minimum Feature SizeMinimum Feature Size

1960 1970 1980 1990 2000 201010

-2

10-1

100

101

102

Year

Min

imum

Fea

ture

Siz

e (m

icro

n)

Propagation DelayPropagation Delay

tp decreases by 13%/year 50% every 5 years!

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Technology Scaling (2) Technology Scaling (2)

Number of components per chipNumber of components per chip

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Technology Scaling Models Technology Scaling Models

• Full Scaling (Constant Electrical Field)

• Fixed Voltage Scaling

• General Scaling

ideal model — dimensions and voltage scaletogether by the same factor S

most common model until recently —only dimensions scale, voltages remain constant

most realistic for todays situation —voltages and dimensions scale with different factors

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Scaling Relationships for Long Channel DevicesScaling Relationships for Long Channel Devices

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Transistor ScalingTransistor Scaling(velocity-saturated devices)(velocity-saturated devices)

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Processor ScalingProcessor Scaling

P.Gelsinger: Processors for the New Millenium, ISSCC 2001

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Processor PowerProcessor Power

P.Gelsinger: Processors for the New Millenium, ISSCC 2001

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Processor PerformanceProcessor Performance

P.Gelsinger: Processors for the New Millenium, ISSCC 2001

© Digital Integrated Circuits2nd Inverter

2010 Outlook2010 Outlook

Performance 2X/16 months 1 TIP (terra instructions/s) 30 GHz clock

Size No of transistors: 2 Billion Die: 40*40 mm

Power 10kW!! Leakage: 1/3 active Power

P.Gelsinger: Processors for the New Millenium, ISSCC 2001

© Digital Integrated Circuits2nd Inverter

Some interesting questionsSome interesting questions

What will cause this model to break? When will it break? Will the model gradually slow down?

Power and power density Leakage Process Variation

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