trends in cmos digital design

Jan. 28, 2015 NIT-Patna: Foundation Day 2015 1

CMOS Digital Circuit DesignHow to Make Both Ends Meet?

Susanta SenInstitute of Radio Physics and Electronics

University of Calcutta


Review of

MOS Transistor


The MOS Transistor


MOS Transistor

Zero Bias


MOS Transistor (contd.)

VDS

ID

Channel Pinches off → Current Saturates

VG

Saturation Current increases with VG

Vt

Threshold Voltage Vt → Device Turns ON

MOS can be used as SWITCH


MOS as SWITCHDesigning Logic Circuits

Logic ‘0’ = 0V : Logic ‘1’ = VDD

n-MOS : VG ≤ Vt → OFF : VG = VDD → ON

p-MOS: Negative VGS required

Connect Source to VDD

Gate Voltage → Negative w.r.t. Channel

VG ≥ VDD– |Vt| → OFF : VG = 0 → ON

S

VDD

VG0 to VDD D

G


n-MOS SWITCHTransferring Logic ‘1’ (VDD):

VDD

Vin = VDD VtVDD

Vo

t

Transistor OFF

Source Impedance High

Weak ‘1’

Transistor ON

Source Impedance Low

Strong ‘0’VDD

Vin = 0 VVo

t

VDD

Transferring Logic ‘0’ (0 V):


p – MOS Switch

Transferring Logic ‘1’ (VDD):

VDD

Vo

t

0V

VDD Strong ‘1’

Transferring Logic ‘0’ (0 V):

0V

0 V

t

Vo

VDD

Vt

Weak ‘0’


CMOS Logic• Use n-MOS to produce Logic ‘0’ → Pull DOWN• Use p-MOS to produce Logic ‘1’ → Pull UP

The CMOS Inverter

Equivalent Circuit

Logic ‘1’ Output



Switching Theory

Revisited

MOS Circuit Design

Digital Logic


Review of Switching Theory

C

A B

F = C iff (A and B)

Switches in Series

A

B

C F = C iff (A or B)

Switches in Parallel


Using n-MOS Switch

Constraint : C = ‘0’

A B

Series Connection

C = ‘0’ F = ‘0’ when (A . B) is TRUE

⇒ A nand B

A

B

C = ‘0’ F = ‘0’ when (A or B) is TRUE

⇒ A nor B

Parallel Connection


Using p-MOS SwitchConstraint : C = ‘1’

A B

C = ‘1’ F = ‘1’ when ( A . B) is TRUE

⇒ A + B

Series Connection

C = ‘1’

A

B

F = ‘1’ when ( A + B) is TRUE

⇒ A . B

Parallel Connection


CMOS Logic Design

• Pull UP Network– Build using p-MOS– Turns ON when Function is TRUE

• Pull DOWN Network– Build using n-MOS– Turns ON when Function is FALSE

• Operationally Complement

• Topologically Dual


CMOS Logic (contd.)

A

A

B

BA

A

B

B

FF

NAND GateNOR Gate


CMOS Design ExampleConsider the Function

f = A . (B + C)

Design the Pull Down Network first

A

B C

Pu

ll U

p

F

B

A

C

f = [A . (B + C)] is true

The Pull Down Network connects

‘f ’ to ground when

Connect Ground


Assignments

1. F = A.B + C

2. F = (A + B).(C + D)

3. F = A + B.C

4. F = A + B.C

5. F = A.C + B.C

6. F = A ⊕ B

Steady State Input-Output Characteristics


VDD

VO

Vi

(=VG)

MOS Amplifier

VDS

ID

VDD

VG

Vi

VO

Load Line

RL

ID

VO = VDD – ID.RL

VDD


Non Linear Load

VDSVDD

ID

VDD

VO

Vi

LOAD LINEVO= VDD – Vdiode

VO

Vi

VDD


Non Linear Load (contd.)

Vi

VO

VB

VDD

VDD

VDS

ID

VDD

VO

Vi


The CMOS InverterAmplifier or Inverter ?

Vi VO

VO

Vi

Gate Bias of PMOS changes with Input Voltage

VDD

VDDVDS

ID

VDD


A Closer Look

In presence of Noise

VOn = f (Vi + vn)

= f (Vi) + vn(∂VO/∂Vi) + vn2(∂2VO/∂Vi

2)+…VO

Vi

noisy_output = noiseless_output +noise x gain + higher order terms

VO= f (Vi) → Gain = ∂VO/∂Vi

ViHViL

VOL

VOH

Digital → Noise immunity Analog → High Gain


Noise Margins

VO

Vi

ViHViL

VOL

VOH

Digital → Noise immunity

NML = VIL – VOL

NMH = VOH – VIH

VOH

ViH

1 {

VOL

ViL

0 {Undefined

Region


Vi VO

VO

Vi

VDD

VDDVDS

ID

VDD

Tuning the Characteristics

• Make the n-MOS wider• It conducts more current

ID = ½ µCox[VGS – Vt]2 (W/L)

• Best Noise Margin • When Vi = Voat VDD/2

• Wp = 3.Wn


When the Signal Changes!

The CMOS Inverter


VDD

Vo

t Logic ‘0’ Output

Vo

t

VDD

Energy dissipated in Pull Up Network

Energy dissipated in Pull Down Network


A Second Look at Changing Signals!

The CMOS Inverter


VDD

Vo

t Logic ‘0’ Output

Vo

t

VDD

Takes Time to change → Propagation Delay


Attention to Speed

• p-MOS slower than n-MOS– Hole mobility < Electron mobility– Pull-UP → Higher Resistance– Rise time longer

• Make p-MOS wider– Resistance α W/L Ratio– Wp = n. Wn → n = √µn /µp ≅ 2

• Widen transistors connected in Series– Increases Input Capacitance

• Avoid Series connection of p-MOS– Prefer NAND over NOR


∀ µn / µp → 2.7

• p-MOS wider than n-MOS– Wp/Wn = 3 → symmetric characteristics

• Best Noise Margin

• Increased Capacitive Load– Reduced speed

• Wp/Wn = 2 → Best speed

• Design is a trade-off – Speed & Robustness

CMOS Logic Design


LHSO

E

k

HH

LH

SO2 fold degenerate valence band

E

kHH

• Light hole (LH) band moves upward

→ higher probability of occupancy• Low effective mass → higher mobility• Tunable mobility

Promise of Strained Si


a Si=

5.4

3 A aGe= 5.64 Å

Si Substrate

Ge epitaxial layer

Tensile strain

%2.40

0 =−=a

aaε

Si – Ge hetero-structures

aSi= 5.43 Å

Compressive strain


• Si1-xGex has a bulk relaxed lattice constant smaller than Ge.

• Strain decreases

Strain Engineering: Si1-xGex alloySiGe epitaxial layer

Si Substrate Tensile strain

Compressive strain


Virtual substrate for strained-Si

• Strained layers grow up to a critical thickness• Beyond Critical thickness → misfit dislocations appear• As more layers grow → strain relaxes and defects reduce

Strain relaxed Si-Ge Virtual Substrate

Tensile Strained Si epitaxial layer

HRTEM image of Strained Si on Virtual Substrate

Strained-Si

SiGe (X % Ge) buffer cap, 0.9 µm

X % Ge

0.0%Ge

Step graded SiGe buffer, 2.1 µm

Si buffer, 0.5 µm

n-Si (100) substrate

HRTEM


Ref: S. Takagi et al., ISSCC (2003) p. 376

Mobility enhancement with strain


Strained Si Layer Structure

• Strained-Si PMOS layer structure

• Type-II Band Alignment– before charge sharing

– after charge sharing at Zero bias

– Biased to inversion

Si 1

-xG

e x

Rel

axed

Str

ain

ed-S

i

SiO

2

(a)

EC

EV

(b)

EC

EV(d)

EC

EV(c)

Po

ly-S

i


The Device Capacitance Model

EC

EV

EC

EV

Si 1

-xG

e x

Rel

axed

SiO

2

(a)

Po

ly-S

i

Str

ain

ed-S

i

C1

C2

C3

ST

I

Channel

Strained-Si

Si 1-

xG

e x

C4Source / Drain


Design Optimization• NMOS → Min. size : WN = 3λ• PMOS → WP varied from 3λ to 9λ• Calculate

–Propagation delay–Shift from symmetry |(VDD/2 – Logic threshold)|

• Repeat for different strains (%Ge in VS)• Converge (for same WP)

–Min. propagation delay &–Min. shift from symmetry


Parameter Values (250 nm technology)

Parameter ValueDielectric Constant (Si1 x‑ Gex) 11.9 + 4x

Grading Coefficient (m)Bottom → 0.48

Side Wall → 0.32

µ Cox (Bulk)Electron → 150 X 10-6 AV-2

Hole → 30 X 10-6 AV-2

VDD 2.5 V

|VT|n-MOS → 0.43 V

p-MOS → 0.40 V

Channel Length Modulation Parameter

n-MOS → 0.06 V-1

p-MOS → 0.10 V-1


30% Ge

13.0

13.5

14.0

14.5

15.0

15.5

3 5 7 9P-transistor width (lamda)

Pro

pa

ga

tio

n d

ela

y

(nS

)

0

50

100

150

200

250

300

350

400

Sh

ift

fro

m s

ym

me

try

(m

V)

30% Ge composition


35% Ge

12.012.212.412.612.813.013.213.413.613.814.0


Pro

pa

ga

tio

n d

ela

y

(nS

)

0

50

100

150

200

250

300

350

Sh

ift

fro

m s

ym

me

try

(m

V)

35% Ge composition


40% Ge

10.8

11.0

11.2

11.4

11.6

11.8

12.0

12.2

12.4


Pro

pa

ga

tio

n d

ela

y

(nS

)

0

50

100

150

200

250

300

Sh

ift

fro

m s

ym

me

try

(m

V)

40% Ge composition

Min. shift from symmetryMin. Propagation delay

Summary

40% Ge in VS is most optimum

Conclusion

4

5

6

7

8

0.25 0.35 0.45Ge composition (x)

P-T

ran

sis

tor

Wid

th

(lam

bd

a)

S. Sen, S. Chattopadhyay, B. Mukhopadhyay; CODEC-2012

trends in cmos digital design

Engineering

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