CMOS ANALOG DESIGN USING ALL-REGION MOSFET MODELING

pageCMOS Analog Design 1

MOS-AK/Baltimore, 2009

CMOS ANALOG DESIGN USING ALL-REGION MOSFET MODELING

Márcio Cherem Schneider and Carlos Galup-Montoro

●Compact MOSFET model

● Circuit examples:

MOSFET sizing in amplifiers

Self-biased current reference

Federal University of Santa Catarina, Brazil

page

COMPACT MOSFET MODEL

� For constant VG, it follows that

( )I ox G FB s BQ C V V Qφ′ ′ ′= − − − −

( )I ox s B ox b s ox sdQ C d dQ C C d nC dφ φ φ′ ′ ′ ′ ′ ′= − = + =

( )1 ( )b G

G

ox

C Vn n V

C

′= + =

′

Charge sheet approximation of the inversion charge

Definitions:

oxide capacitance per unit area surface potential

inversion charge per unit area flat-band potential

bulk charge per unit area gate-to-bulk voltage

oxC′

BQ′

sφ

FBV

GV

IQ′



UNIFIED CHARGE CONTROL MODEL (UCCM)-1

n+ n+

p

VSVG VD

1 tC I

ox I

dV dQnC Q

φ ′= −

′ ′

( )

ox b ox

G

C C nC

n n V

′ ′ ′+ =

=

Ii

t

QC

φ

′′ = −

I ox sdQ nC dφ′ ′=

t

kT

qφ =

S C DV V V≤ ≤

s i

C i ox b

d C

dV C C C

φ ′=

′ ′ ′+ +

1

1

I

ox t

Q

nC φ

′− <

′�

�

WI

SI



1 tC I

ox I

dV dQnC Q

φ ′= −

′ ′ Integrating between V

C and VP

yields UCCM

lnIP I IP C t

ox IP

Q Q QV V

nC Qφ

′ ′ ′−− = +

′ ′

UNIFIED CHARGE CONTROL MODEL (UCCM)-2

IP ox t

II

ox t

Q nC

Qq

nC

φ

φ

′ ′= −

′′ =

′−

Thermal charge

Normalized inversion charge density

( 1 ln )P C t I I

V V q qφ ′ ′− = − +Normalized UCCM



CHARGE-SHEET MODEL (CSM)

I ox sdQ nC dφ′ ′=

( )2 2

2

IS IDD t IS ID

ox

Q QWI Q Q

L nC

µφ

′ ′−′ ′= − −

′

s ID I t

d dQI WQ W

dy dy

φµ µ φ

′′= − +

drift diffusion drift diffusion

2

2

tS ox

I C n Sφ

µ ′=Normalization (specific) current

2

2

tSH ox

I C nφ

µ ′=Sheet (or square) normalization

current

WS

L=

D F R S f r SH f rI I I I i i SI i i = − = − = −

page

WEAK, MODERATE, STRONG INVERSION

CMOS Analog Design 6


D F R S f rI I I I i i = − = −

( ) ( ) ( ) ( ) ( )2

2 1 1f r IS D IS D IS D f r

i q q q i′ ′ ′= + ⇒ = + −

WI MI SI

1 100fi< <1fi < 100 fi<

0.4 9Iq′< < 9 Iq′<0.4Iq′ <



Long-channel MOSFET ),(),( DGSGRFD VVIVVIIII −=−=

IF: forward current IR: reverse current

IF=

IR=

FORWARD AND REVERSE CURRENTS

(Forward) Saturation

D F R FI I I I= − ≅

Triode

D F RI I I= −

Triode for VDS→0

; F R D F R FI I I I I I≅ = − <<



Common-source characteristics

( )1 2 ln 1 1P S t f fV V i iφ − = + − + + −

UNIFIED I-V RELATIONSHIP (UICM)

since

D S f r S f

f r

I I i i I i

i i

= − ≅

>>

1,00E-09

1,00E-08

1,00E-07

1,00E-06

1,00E-05

1,00E-04

1,00E-03

0,00E+00 5,00E-01 1,00E+00 1,50E+00 2,00E+00 2,50E+00 3,00E+00 3,50E+00 4,00E+00 4,50E+00

10-3

10-6

10-9

VS = 0 V

3.0

2.5

2.0

1.5

0.5 1.0

0 1 2 3 4 VG (V)

ID (A) VD = VG

WI

MI

SI

VD

ID

VGVS



Pinch-off voltage and slope factor as functions of VG [0.18 µm CMOS technology].

VP[V]

PINCH-OFF VOLTAGE AND SLOPE FACTOR

0G TP

V VV

n

−≅

( )0 1 3 2 ln 1 3 1P SV V − = = + − + + − if=3 at pinch-off



( )21 1

f S

ms S IS f

S t

di IWg I Q i

dV Lµ

φ′= − = − = + −

BmbDmdSmsGmgD VgVgVgVgI ∆+∆+∆−∆=∆

Calculation of gms

TRANSCONDUCTANCES

0mg ms md mb

g g g g− + + =

D F R S f rI I I I i i = − = −

( ) ( ) ( )2

2

( 1 ln )

f r IS D IS D

P C t I I

i q q

V V q qφ

′ ′= +

′ ′− = − +



Transconductance

-to-current ratio11

2

)()(

)(

++=

rfRF

tdms

iI

g φ 1≅

( )

2

f ri≅

WI (if <1)

SI (if >>1)

TRANSCONDUCTANCE-TO-CURRENT RATIO

n

ggg mdms

mg

−=

msmg

gg

n=

in saturation:

10-4 10-2 100 102 104if

tox

= 28 nm (IS

= 26 nA)

model

102

101

100

gms/IF

tox

= 5.5 nm (IS

= 111 nA)

1

10

100

1,00E-04 1,00E-03 1,00E-02 1,00E-01 1,00E+00 1,00E+01 1,00E+02 1,00E+03 1,00E+04

Seqüência1

Seqüência2

Seqüência3



for

mo i

L

b

gv v

j Cω

ω ω

≅ −

>>

COMMON-SOURCE STAGE

GBW



EXAMPLE: GBW = 10 MHz, CL = 10 pF

= 80·10-6 A/V2, n = 1.35

W/L IDsi (µµµµA)1 ID (µµµµA)2

∞∞∞∞ 0 22

500 6.6 28.6

100 33.2 55.2

50 66.4 88.4

10 332 354

oxCµ ′

2 628 A/Vm L

g GBW Cπ µ= ⋅ ⋅ =

1 Strong inversion model

2 Accurate all-region MOSFET model



ALL-REGION MOSFET MODEL

6 31.35 628 10 .26 10 22 µWI m tI ng Aφ − −= = ⋅ ⋅ ⋅ =

( )1

2 /

mD WI Dsi m t

ox t

gI I I ng

C W Lφ

µ φ

= + = +

′

( )( )

/1

/

thD WI

W LI I

W L

= +

( ) ( )/ 2m ox tth

g W L Cµ φ′=

D WI DsiI I I= +



ASPECT RATIO VS. CURRENT EXCESS

( )( )

/1

/

thD WI

W LI I

W L

= +



SELF-CASCODE MOSFET (SCM)

Sat.

Triode

I2=NIx

2

1 2 2

1

11 1f f f

Si i i

S Nα

= + + =

2

2 2

2

1 11 1 ln

1 1

fXf f

t f

iVi i

i

αα

φ

+ − = + − + + + −

2 2

1 1 2( ) ( 1)

S f x

S f f x

I i NI

I i i N I

=

− = +

Applying UICM to both M1 & M2



V-I CHARACTERISTICS OF SCM

2

2 2

2

1 11 1 ln

1 1

ln

fXf f

t f

X t

iVi i

i

V

αα

φ

φ α

+ − = + − + + + −

=In WI:

Sat.

Triode

2

1

11 1

S

S Nα

= + +

I2=NIx



VOLTAGE FOLLOWING (NMOS)

CURRENT MIRROR (PMOS)1

9ln( )

ref S tV V JKφ= +

1 B. Gilbert, AICSP vol. 38, pp. 83-101, Feb. 2004

In WI:



SELF-BIASED CURRENT SOURCE

(SBCS)

VFCM



VFCM

DESIGN OF A SBCS

2

1

11 1 1 1 1 3

S

S Nα

= + + = + + =

1 30 11 30 1 10 ln 2.93

1 10 1

X

t

V

φ

+ −= + − + + = + −

M1 &M2 in MI: if2 = 10 S2= S1, N = 1

2

2 2

2

1 11 1 ln

1 1

fXf f

t f

iVi i

i

αα

φ

+ − = + − + + + −

Let us choose

M3 &M4 in WI: if3(4) <<1

2.93ln 18.7X

t

Veα α

φ≅ ⇒ = ≅

4 4

3 3

118.7 1 1 8.85

1

S S

S S

= + + ⇒ =

Output current: Iref=10 nA

ISHn-channel≅100 nA, I

SHp-channel≅40 nA

=1

=10 nA

2 2 2 2 110 nA 1 nA 0.01

S f SI i I S S= → = → = =

Let us choose if3=0.187 →→→→ [ ]4 3 4 3/ 1 2 / 0.01

f fi i S S= + = 4 4 4 4

10 nA 1 A 10S f S

I i I Sµ= → = → =

4

3 1.138.85

SS = =



DESIGN OF A SBCS - Summary

S if ir

M1 0.01 30 10

M2 0.01 10 0

M3 1.13 0.187 0.01

M4 10 0.01 0

M8, M8(a) 1 0. 1 0

M9, M9(a) 1 0. 1 0

MP (all) 2.5 0.1 0

410S =

VFCM

=1

=10 nA

21 0.0S =

2.93X t

V φ= 2.93X t

V φ=

31.13S =1

1 0.0S =



SBCS: IOUT vs. VDD AT CONSTANT TEMPERATURE1

1E. M. Camacho-Galeano et al. pp 2230-2233, ISCAS 2008



REFERENCE

CMOS ANALOG DESIGN USING ALL-REGION MOSFET MODELING

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