ISCAS
2000
-
IEEE
In e na ional Symposium on Ci cui s and
Sys ems,
May
28-31,
2000,
Gene a, Swi ze land
A
Me hodology o MOS T ansis o Misma ch Pa ame e
Ex ac ion and Misma ch Simula ion
T. Se ano-Go a edona and B. Lina es-Ba anco
Na ional Mic oelec onics Cen e (CNM),
Ed.
CICA, AV. Reina Me cedes s/n,
41012
SPAIN. Phone:
34-5-4239923
Fax:
34-5-4624506, E-mail: bemabe
@
imse.cnm.es
Abs ac
This pape p esen s a me hodology o misma ch pa ame e
ex ac ion and misma ch simula ion using con en ional elec ical
simula o s, like HSpice.
A
measu emen and ex ac ion p ocedu e
has been ca e ully designed o be able o ob ain eliable
measu emen s o he misma ch pa ame e s o a gi en echnology.
The co ec ness o his ex ac ion p ocedu e me hod has been
checked h ough h ee di e en alida ion me hods.
We
also
p esen wo me hods o pe o ming misma ch simula ion wi h
con en ional ci cui simula o s (like HSpice) using he ex ac ed
pa ame e s.
I.
In oduc ion
P ecise analog
CMOS
ci cui design equi es a ailabili y
o con iden ansis o misma ch models du ing he design and
simula ion s ages. Du ing he design phase o an analog
VLSI
ci cui , designe s ace many cons ain s imposed by he design
speci ica ions, such
as
speed, bandwid h, noise, p ecision,
powe consump ion, a ea consump ion, which need o be aded
o o op imum o e all pe o mance. Designe s mus ely on
accu a e simula ion ools in o de
o
achie e
a
well op imized
inal design. Simula ion ools a e eliable as long
as
hey a e
based on good models ob ained h ough con iden
cha ac e iza ion echniques. O en i
is
no possible o simula e
p ope ly he p ecision limi s ha can be achie ed by a ce ain
ci cui opology in
a
gi en ab ica ion p ocess because
VLSI
ci cui manu ac u e s a ely p o ide ansis o misma ch
in o ma ion. T ansis o misma ch a ec s o se ol age o
di e en ial pai s, e o s in cu en mi o s, e o s in a ays o
iden ical cu en sou ces,
...
.
Elsewhe e [1],[2], we ha e p esen ed
a
e y simple and
cheap me hodology o cha ac e ize ansis o misma ch as a
unc ion o ansis o wid h and leng h plus
a
new i e
pa ame e s misma ch model ha achie es be e esul s han
o he misma ch models p e iously epo ed in li e a u e [3],[4].
In his pape , we e i y he co ec ness o his new misma ch
model and he measu emen lex ac ion p ocedu e h ough h ee
di e en alida ion me hods. Also, we p esen wo di e en
me hods o using he expe imen ally ex ac ed misma ch
ansis o pa ame e s in a con en ional elec ical simula o , like
HSpice, o p edic he o se ol age o di e en ial pai s
(o
wha e e ci cui speci ica ion we may be in e es ed a ). The
simula ed o se is compa ed e sus he expe imen ally
measu ed one, showing
a
good ag eemen be ween bo h.
Fo
misma ch cha ac e iza ion o a gi en echnology we
ab ica e a special pu pose chip in he co esponding
echnology[ 13.
Ou
chip consis s o a ma ix o
8
x
8
cells. Each
cell con ains
NMOS
and
PMOS
ansis o s o 30 di e en sizes.
Since, some ansis o s in he pe iphe y p esen la ge sys ema ic
de ia ions wi h espec o hose in he inne cells, only he la e
ansis o s whe e conside ed[5]. T ansis o pa ame e
misma ches a e ob ained by measu ing pai s o iden ical
ansis o s loca ed in adjacen cells. Since in he chip he e a e
6
x
6
e ec i e cells, he e a e
6
ows, each o which p o ides
5
pai s o adjacen cells. This esul s in 30 adjacen ansis o pai s
( o
each ansis o size and ype).
Fo
each ansis o pai , ou cu es we e measu ed. Two o
hem while ope a ing in he ohmic egion and he o he wo
o
sa u a ion (always in s ong in e sion). These cu es a e
(1)
(2)
Cu el:I,,(V,,)
,V,,
=
OV,V,,=O.l,
VGse
11.5,5.01
Cu e2:/,,(Vs,),V,,
=
3.0V,VD,
=
0.1
V,V,,
E
LO,
2.01
Cu e3:/,S(V,,5),V,,
=
OV,V,,
=4.0V,VG,E
[1.5,5.01
(3)
Cu e4:1,,(VS,),V,,
=
3.0V,V0,
=~.OV,V,,E
[O,
2.01
(4)
The ollowing s ong in e sion la ge signal ansis o model is
assumed [I]-[2],
whe e,
(
s,)
=
Vm
+
Y
I
&%-
h
I
(6)
and
VD,,,,l
is de ined as,
DS,
=
VD.5
o
ohmic
egion
(7)
V,,
-
V,( V,,)
o
sa u a ion
These cu es depend nonlinea ly on he
la ge signal
pa ame e s
o be ex ac ed
(
p,
V,,,
e,,
e,
and
y
)
as well
as
on
he measu ed da a poin s
{
V,,
)
and
{
V,,
).
The e o e, hese
la ge-signal pa ame e s
should be ex ac ed using nonlinea
mul i-pa ame e s cu e i ing echniques. Fo a gi en
ansis o pai , he misma ch in he ex ac ed
la ge-signal
pa ame e s
is
ob ained by i ing he cu en misma ch da a
AIDs/IDs
o i s heo e ical equa ion
[1]-[2],
and ex ac om i he
misma ch pa ame e s
(Ap/p,
AV,,,
AB,,
AB,,
Ay
)
simul aneously o cu es
1
o
4.
This measu emen /ex ac ion p ocedu e
is
epea ed o he
N,
=
30
ansis o pai s.
Fo
each ex ac ed
misma ch
pa ame e
AP
,
i s
s anda d de ia ion
qAP)
is
compu ed,
as
well
as
all co ela ions be ween pai s o
misma ch pa ame e s
‘(AP1.AP2)
‘
11.
Valida ion
o
he Misma ch Model
In his sec ion, we desc ibe a ew es s ha we ha e
pe o med o e i y he co ec ness o ou misma ch model and
measu emen /ex ac ion p ocedu e. The chip we ha e used o
ou measu emen s is ab ica ed in a s anda d
1.0pin
double-me al single-poly
CMOS
echnology.
A.
P ecision
Tes
A
i s es o alida e ou measu emen p ocedu e was o
measu e, epea edly he same ansis o 30 imes and ollow he
same pa ame e ex ac ion and s a is ical cha ac e iza ion
0-7803-5482-6/99/$10.00 02000
IEEE
IV-
109
p ocedu e. We ob ain
a
se o s anda d de ia ions ha gi e us an
indica ion o he e o o ou ins umen s and ma hema ical
algo i hms.
When measu ing he pa ame e
P
misma ch be ween wo
ansis o s he esul ing measu ed
AP
alue has wo
componen s,
AP
=
APR<"I
+
(9)
whe e
AP,,,,
is
he eal misma ch in pa ame e
P
be ween
bo h ansis o s and
AP,,,,,,
is an e o componen in oduced
by he measu emen se -up and pa ame e ex ac ion
p ocedu e. By epea ing many measu emen s we ob ain he
quad a ic de ia ion
because he andom ansis o misma ch and he measu emen
e o s a e supposed
o
be unco ela ed. By epea ing he same
measu emen o e he same ansis o , we measu e
B(~~,,,~,~,)
.
The alues o
(J(,~,,,~~,~
esul ed o be less han
113
o hose
o
a(Ap)
in he wo s case, and we e no mally below
1/10.
I
N,
is
he numbe o measu emen s o
a
no mally
dis ibu ed andom a iable, and hese measu emen s a e used
o compu e
a
s anda d de ia ion
o
his a iable,
a,,,,,p,,,,,~,
hen
he e is
a
con idence in e al o he eal s anda d de ia ion
(JR~~I
161
-L(Nl)
o ui ip , d
ORsol
acoiii,ii!!s /
.
(I
When
N,
=
30
he
95%
con idence in e al is
=
0.8
,
lI
=
1.3
.
In ou case
alApl
and
o(~~,,,~
ha e been
ob ained by
N,
=
30
measu emen s.
On
he o he hand, we
can de ine
a
(conse a i e) con idence in e al o
2
7
71
7,
(12)
( 11
)
x
(J&
,,,,,)
=
Inax[qAPR
(,,
))
I
=
H
x
a&)
-
;
x
0;AP
,,,(
",)
.7
,
-7
1,
( L)
X';A/',
,,,,,)
=
ninla~APRen,)l
=
;xa[AP)- ~lXa{AP
,,,,,,
!<)
By
de ining
i
ollows ha
Fig.
1
depic s he alues o and
L
as
a
unc ion o
a
when
N,
=
30.
No e ha e en o alues o
a
as
high
as
0.5
he e
is
s ill
a
easonable con idence in e al o
olAPRm,)
(app oxima ely
+
50%
).
Since, in ou case, he wo s case
a
is
less
han
1/3,
by Fig.
1
we can see ha o his wo s case,
he con idence in e al is no signi ican ly deg aded. This kind
o p ecision es is also called in he li e a u e
epea abili y
s udy
[4].
Howe e , wi h his
epea a6ili y
s udy,
he only
hing we can conclude is ha wha e e has been measu ed, i
has been measu ed wi h accep able p ecision. Bu ha does
no assu e ha he ob ained s a is ical misma ch pa ame e s
a e
a
good measu emen o he physical quan i ies
qAP)
and
hei espec i e co ela ions
(Ap,,Ap,)
.
To e i y his, o he es s
ha e o be pe o med.
B.
P edic ing
a(A,D5,,os~
o
he Measii ed Cu es
he ollowing exp ession
is
ob ained,
I we compu e he s anda d de ia ion o
a(Alns,lD,5)
in eq.(8),
20
15
10
05
00
00
01
02
03
04
05
06
07 08
09
10
a
Fig.
1:
Plo
o
k
and
as
a unc ion o
a
cu e
I.
w=*m
cu e
I.
w=*
C Ne
1.
W.lW
2345
cu e
I
w=*m
2515
08
06
04
2345
C Ne
I
w=z
4m
2
I
Fig.
2:
Simula ed (solid lines) and measu ed alues (ma ked
symbols) o
a(,ln ,,Ds)
o cu e
1
o all ansis o geome ies
Thus, using he ex ac ed misma ch pa ame e s,
o,,~,~,
,
a(,,,
,
aIAy)
,
qA8
),
a(,e
and hei co esponding co ela ion
coe T lcien s, we cin compu e he expec ed cu en misma ch
cu es Fig.
2
shows
o
he
30
geome ies o NMOS
ype ansis o s
a
compa ison be ween he measu ed
a(,, sl,osl
(ma ked wi h symbols) e sus he compu ed ones (solid ines)
o cu e
1.
An excellen ag eemen
is
obse ed o
all
cu es
1
o
4
[2].
This is al eady a e y good indica ion ha we a e ex ac ing
co ec enough misma ch pa ame e s. Al hough we a e
p edic ing he same cu es we ha e used o ex ac he misma ch
pa ame e s, he se o misma ch pa ame e s we a e ex ac ing
is
unique, alid o all
4
cu es.
Howe e ,
a
mo e se e e
es
would be o p edic o he
cu es, ob ained unde di e en bias condi ions. This
is
he es
desc ibed nex .
C.
P edic ing Di e en ial Pai s O se Vol age
In his sec ion, we use he ex ac ed s a is ical misma ch
pa ame e s o p edic he o se ol age o di e en ial pai s. To
ob ain di ec measu emen s
o
di e en ial pai s inpu ol age
o se , o each pai
o
ansis o s in ou misma ch
cha ac e iza ion chip we measu e he ollowing cu e
Ios(Vc5),
V,,
=
c e,V,,
=
~.OV,V,,E [2.99V,3.01VI1
(16)
once o each ansis o o he pai . The measu ed ansis o
a e
placed in adjacen cells loca ed
363pm
apa . Fig.
3
shows he
IV-110
2
990
2
995
3
000
3
oQ5
VP
Fig.
3:
Measu ed
o se
ol ages o
one
ai
o
NMOS
ansis o s
Table
1
measu ed poin s
o
one pai o NMOS ansis o s
o
size
40pmx40pm.
Also shown in Fig.
3
a e he co esponding
in e pola ed lines o he measu emen s
(17)
IDSI(VGS)
=
mlVGs+nl
VGs)
=
m2
VGs
+
n2
Consequen ly, he
o se
ol age o his di e en ial pai
is
gi en by
Fo each pai o ansis o s he cu es o eq.(
16)
we e measu ed
o wo di e en alues o
V,,
.
Fi s o
V,,
=
OV
(no
subs a e e ec ), and second o
Vs,
=
1
V
(wi h subs a e
e ec :
AY
is a ec ing he o se ol age). The s anda d
de ia ion
o
hese o se ol ages was compu ed o each
ansis o size and ype. Table
1,
unde he columns named
“MEASURED’, indica es he measu ed alues o
o(,~~llI)
as
a
unc ion o ansis o size and ype.
In o de o p edic he s anda d de ia ion o his o se
ol age using ou ex ac ed misma chda a, no e ha
(see
Fig.
3)
whe e
qA1
can be compu ed by e alua ing eq.(15) in
sa u a ion,
”%
lD,/s,,,
can be ca@ulaid !sing he mean
ex ac ed la ge signal pa ame e s
(p
,
V,,
,
e,
and
y
).
The
alues o
q
compu ed his way a e
also
shown in Table
1
unde he c8hmns named “COMPUTED’. No e ha he
compu ed alues s ay wi hin he con idence in e als o he
measu ed alues.
111.
Misma ch
Simula ions
The ex ac ed misma ch pa ame e s can be used in
a
con en ional elec ical ci cui simula o , like HSpice, o p edic
ci cui speci ica ions such
as
o se ol ages, e o in he ou pu
cu en o
a
cu en mi o , e c. This can be
a
e y aluable ool
o
design high pe o mance ci cui s. HSpice simula ions ha e been
pe o med in o de
o
p edic he measu ed di e en ial pai s inpu
o se
ol ages o Table
1.
We
desc ibe wo simula ion me hods,
bo h based on Mon e Ca lo simula ions.
A.Me hod
1:
In his me hod he idea is o use he ansis o model
p o ided by he manu ac u e and in oduce in o i andom
a ia ions o some o he mos misma ch sensi i e pa ame e s. In
ou case, he manu ac u e model
is
a
Le el
6
Hspice model.
Ob iously he physical meaning o he la ge signal pa ame e s
(such as
p
,
V,,
,
0
and
y
)
is di e en han o he simple model
we
assumeddu ing ou misma ch cha ac e iza ions (eqs. (5)-(6)).
Besides his, and in ou pa icula case, he manu ac u e model
does
no
include explici ly he mobili y deg ada ion pa ame e
“8”.
Consequen ly, we will use only
o(,glB,
,
qAV,,,)
and
qAY)
and
igno e
all
co ela ions. The way
o
use his misma ch model in
(H)Spice is as ollows.
Each ansis o in he ne lis is subs i u ed by
a
subci cui
call which includes
a
MOS
ansis o o he speci ied size and
whose
p
,
V,,
,
and
y
a e
ecompu ed by adding noise o hem. I
o(,~,~,
,
IS(^^,,)
,
and
qA
a e he ex ac ed misma ch pa ame e s
hen he ecompu ed alues o
p
,
V,,
,
and
y
a e,
whe e
CAW(.)
is
a
no mally dis ibu ed andom numbe
gene a ion ou ine whose
“mean”
and
‘‘sigma”
alues ha e o
be
p o ided. No e ha each de ia ion is di ided by
“h
”.
This
is because he ansis o de ined by eq.
(20)
is de ia ed wi h
espec o
a
nominal one. The HSpice inpu
ile
sec ion ha
pe o ms wha desc ibes eq.
(20)
is:
.subck mod- yp D ain Ga e Sou ce
Bulk
wid h=w
m-mod
D ain Ga e sou ce Bulk
nmos
w=w
1=1
.MODEL
NMOS
NMOS
UPDATE
=
xxx
+
LEVEL
=
6.0
WDEL
=
xxx
LATD
=
xxx
+
XL
=
xxx
+
VTO
=
o-n
TOX
=
xxx BETA
=
be ag
+
GAMMA
=
gannn=-n
VBO
=
xxx LGAMMA=
xxx
+WE
=
xxx
NWM
=
xxx
SCM
=
xxx
+xxx
leng h=l
.pa am be a-n_global- yp=xxxx
.pa am o-n-global- yp=xxxx
.pa am ga”a-n-globalL yp=xxxx
.pa am del a-be a
=
agauss(0,sigma-be a.1)
IV-Ill
I
“1,
S
Fig.
4:
Subci cui o misma ch simula ion using
Me hod
2
.pa am del a- o
=
agauss(O,sigma_ o,l)
.pa am del a-gama
=
agauss(0,sigma-gamma.1)
.pa am be a-n
=
‘be a-n-global- yp*(l+del a-be a)’
.pa am o-n
=
~ oq-global- yp+del a- o‘
.pa am gama-n
=
sgama-n-global- yp+del a-ganuna’
. ends
Using his p ocedu e he di e en ial pai s inpu o se ol ages
desc ibed in he p e ious sec ion we e simula ed o
all
ansis o sizes, wi h and wi hou subs a e e ec . The esul s
a e gi en in Table
1
unde he columns named “SIMULATED
(me hodl)”.
B.
Me hod
2:
The p e ious me hod has wo p oblems:
-
The MOS ansis o model p o ided by he manu ac u e
migh no include some o he la ge signal pa ame e s we
ha e used, like
p,
V,,
,
e
o
y
.
The physical meaning o pa ame e s
p
,
V,,
,
8
o
y
in he
MOS model p o ided by he manu ac u e (i hey a e
p esen ) is p obably di e en o he one in he model we
ha e assumed (eqs.
(5)-(6)).
The e o e,
Me hod
1
is
only
an app oxima e p ocedu e o p edic ing ansis o
misma ch, and he success o his me hod depends on how
much he ansis o model p o ided by he manu ac u e
di e s om he one we ha e assumed.
A
possible al e na i e o
o e come
hese p oblems would
be
o
subs i u e each ansis o in he ne lis by he subci cui
depic ed in Fig.
4.
The subci cui includes
3
MOS ansis o s
and a se o con olled sou ces. T ansis o
MY,,,
is
a nominal
ansis o (wi hou de ia ions) using he model p o ided by he
manu ac u e . T ansis o s
m,,,,,,
and
m,,,,,
a e modeled using
he ansis o model we ha e assumed (eqs.
(5)-(6)).
T ansis o
m,,,,,,
is
a
nominal ansis o and ansis o
in,,,,
is such ha i s
p
,
,VTo,
e
and
y
alues a e modi ied by adding andom
de ia ions. The ol age con olled ol age sou ces ha bias
ansis o s
m,,,,,,
and
md ,,
do he unc ion o copying he
e minal ol ages p esen a ansis o The cu en s
lowing h ough each ansis o a e sensed:
I,,
o
M,wA,N,
I,
o
m,
,”,,,
,
and
l2
o
md ,,
.
T ansis o
M,,,,,,
has
a
cu en
sou ce in pa allel
AI,,
whose alue a each ins an is gi en by
No e ha now we can use ou i e
misma ch pa ame e
(Ap/p,
AV,,,
,
AO,,
,
AB,,
Ay
]
model[l] o de ine he
la ge
signal pa ame e s
o
.
The goal
is
o be able
o
gene a e
o each
m I ,,
hese
5
misma ch pa ame e s
by knowing hei
s anda d de ia ions and espec i e co ela ion coe icien s.
This can be done in (H)Spice
as
ollows. Suppose ha o each
m,,*,.
ansis o we know i s
s a is ical misma ch pa ame e s.
Suppose
also,
ha o each
m,,,,
we can gene a e
5
andom
numbe s
{
xI
,
x?,
s3,
xq,
x8
]
which a e unco ela ed, ha e
ze o mean, and hei s anda d de ia ion
is
o(s,)
=
1l.h.
Using hese i e unco ela ed andom numbe s we can ob ain
i e co ela ed misma ch pa ame e s o
~n,,~,
as
ollows,
Whe e coe icien s
cij
can be ob ained by compu ing he
s anda d de ia ions o he igh and le hand side o eq.
(22)
[2].
The ad an age o his me hod is ha he e
is
comple e
independence be ween he simula o model pa ame e s ha
de ine he cu en h ough ansis o
M,w,,,
and ou model
pa ame e s (appea ing in equa ions
(5)-(6)
and ha we ex ac
expe imen ally o each echnology) ha de ine he cu en s
h ough ansis o s
in,,,,,,
and
md ,
.
The e ec o he addi ional
ansis o s
m,,,,,,
and
yie,,
is jus
o
add
a
de ia ion
AIDs
in he
cu en passing h ough he basic ansis o
M,w,4,,
ha
depends on he ope a ing poin and he ansis o geome y.
Using his se -up, and pe o ming Mon e Ca lo simula ions
o
p edic he di e en ial pai inpu o se ol ages o each
ansis o size, wi h and wi hou subs a e e ec , esul s in he
alues shown in Table
1
unde he columns named
“SIMULATED (me hod2)”. No e ha hese alues a e mo e
simila o hose shown in Table
I
unde columns. named
“COMPUTED” han he ones ob ained wi h he i s me hod
o simula ion. Howe e , he alues unde “SIMULATED
(me hod2)” and “COMPUTED” a e no iden ical. The eason
is
ha he coe icien
Io,/g,,,
o eq.
(19)
is
compu ed by he
simula o using he manu ac u e ansis o model ( h ough
ansis o
M,,,,
),
ins ead o he one we ha e assumed (i.e.,
eqs.
(5146)).
IV.
Conclusions
We ha e designed
a
new i e pa ame e s misma ch model
and
a
me hod o ex ac and s a is ically cha ac e ize he
misma ch pa ame e s o
a
gi en echnology. We ha e de eloped
h ee di e en es s in o de o alida e ou misma ch model and
measu emen lex ac ion p ocedu e. The i s es , p e iously
epo ed in li e a u e, assu es ha he measu emen and
ma hema ical compu a ions
ha e
been
done
wi h good
p ecision. The wo o he designed es s e i y he co ec ness o
he misma ch model i sel . In hese es s, we ha e achie ed an
ag eemen wi h he expe imen al esul s ha can no be ob ained
wi h he o he misma ch models p e iously epo ed in
li e a u e. Finally, we ha e p oposed wo di e en me hods o
use ou misma ch model
as
a
design
ool
in
a
con en ional
elec ical simula o . We ha e simula ed he o se ol age o
a
di e en ial pai wi h ou wo me hods and compa ed i e sus
he expe imen ally measu ed one. A e y good ag eemen
be ween simula ions and measu emen s ha e been ob ained.
V.
Re e ences
T. Semno-Go a edona and B. Lina es-Ba anco. “Sys ema ic
Wid h-and-Leng h Dependen
CMOS
T ansis o Misma ch
Cha ac e iza ion and Simula ion,”
Jou nal
o
Analog In eg a ed
Ci cui s and Signal P ocessing,
Decembe 1999.
T. Se ano-Go a edona and B. Lina es-Ba anco, “A New
Fi e-Pa ame e MOS T ansis o Misma ch Model,”
IEEE
Elec on De ice Le e s,
pp 37-39, ol. 21, Janua y 2000.
M.
J.
M.
Pelg om,
A.
C.
J.
Duinmaije ,
and
A. P. G. Welbe s,
“Ma ching P ope ies
o
MOS T ansis o ,”
IEEE Jou nd
o
Solid-S a e Ci cui s,
ol 24, Oc obe 1989, pp. 1433-1440
J.
Bas os,
Clia ac e izu ion
o
MOS
T ansis o Misina ch
. o
Analog Design,
Ph.D. Disse a ion, Ka holieke Uni e is ei
Leu en, Ap il 1998.
A. Pa aso ic,
A.
G.
And eou, and C. R. Wes ga e,
“Cha ac e iza ion
o
Sub h eshold
MOS
Misma ch T ansis o s
o
VLSI
Sys ems,‘’
Analog hi eg u ed Ci cui s
and
Signal
P ocessing,
ol.
8,
pp. 75-85, 1994.
Lenna Rade and Be il Wes e g en,
BETA Ma heina ics
Handbook.
CRC P ess, 1990.
IV-112