BSTJ 50: 4. April 1971: Statistical Circuit Design: Characterization and Modeling for Statistical Design. (Logan, John)

17.6 MB·English

Statistical Circuit Design:

Characterization and Modeling for
Statistical Design

By JOHN LOGAN

Avelysi ofthe vorntan inthe eletriead performance of dutagrated
cient atnaturesrequavn a kate uf the daeibutions ond inter
{elationshipe of ievice parameter values. This arile presente newt
Techniques for more actuate tounsator madeting and describes the
ttistiol characteriention provera develeped to dese the inte~
rated esreuit mnnafacloriny yroceee ae Jor as the measurable sler~
{sod paramere ave concerned,

Tn matistical davign work tuvolving, crete passive: elewens,
nomial parameter values and peodueion eitribuboas gxe on a=
‘quate deseripton, The situation iv mie nay eated for active deviews
in wie he mivalent einen weed to deseribe Use eviews eequires
paramactere hich ne inertelstd

With inveprated iret, conditions wre further compounded by the
fact Uwe tie jusuanetons of diferent devices on an TC rip gre inter
Alpendeat, Faperinentally, fngrover, 2 bse been found isk the
Integrated cieuis care ann he convensetly seeauple o & manngentle
flgree 0: eurglesiy ov whew conpenatine ete are conse

Tn Lae fullosing stone, the phileophy undoing both our

svodeling appzorab ene he wenercorant teohnieues i ont ined. Thi
je Tllowod ya slesriptien af the trrsstor wel faxoned for ete-
tistical analysis work, highlieting sore populer mikeoneaptions

fising Grom inadequate past meseuremen'a. The impllestion: er
devine mnling in an integrin rem nnvironment are thes eon:
ere, ollowel by a deseription of (he pevolieal methods whieh have
fren succesfully une bo poe: the variably io eet performance
Asin from variations in the manutactusing prowes
MO} ame my overne recamous sores, APR tnt

23 Modatng Phiorophy
"Toe modeling approach found to be most eetive is to cary
levine physi ae fer at possible, then wesi'y or modify the resulta
ly prtical experience. Tbe rly eeu, selene to Be eo
sdrod simultaneously from three fronts, ia thu: the model eset:

(9 Give un sequote qualitative daveription of the electri! be-
havior of the device,
(as) Have ofcent? prenmetors which ave readily meoeursble (or
‘ealeable) and sere ta soso dieription
Gig) Be eompoible with wumerien! iret ndalyaie toh,

Ta the erature met attention has been given to items (@)* an
i) Tae, the greatest impediment to meaning satiaiea) de
ia work ie he Tace of atteion to item (8. Tn consequsnee, thie
isi well dell om the Had Dts of wha as oh ae in mee
tice when real dita ie requir get manninatl cel,

“Tare are wt least two schools of tomeat ano eubjost ot eevice
raglan: moeling to set an amicrinnsng 0! the dewiee plyeion
tnd snodelicg for the purpose of cireuit analyeic. AlDhooch ici desi
able ra have ane model sor bore exzation, i feqhersiy em
to snake sispsfectios inthe eaca of einuis analysis, In a staieeal
Assign, rweeaarly one involving intagrated ereuite, the genera
proper of the aystem have to be ceprevented, With teunssory, the
anportaws pointe sr:

(2 The ntehing of characerstion ash a ain or fuetion voltages,

(G9) The teueking of parstatera within w deviee and from deviee
to device an tn intagrated cree chip

(i) The tempenntune chaenoteristien, willy importent in Rell
Bystam werk, both from Une standonint of Ue variation of
system performance seth tompernsure end alo for aay aging
Meta whieh my be lerperatre dependent.

A genmral deserton of the above pronertins i therefore maui in
lulisioul design eaiher than wa elaburaie prison motel high may
reatly exgord The agnuraey of evalable data

Compara! of generic ode! pe, whieh apne to ineate
‘8 suulhenmtinal eauivalence, srylees some very important tues
‘yliele ta Lranisae nade in run ae. These bats elite to

SEER mete ae soe gm ey sly ete cae a
cnumucrennattes 4D MopsLIxe 1107

the choise of the ileyonont veriabes in Uke model and he sigait-
Seance of tise disvassed i Serio TIL,

22 Measurement Philosophy

From she mussterestandpoing che ms: inporleal coasiderstion
i that of efferively detouping cho me) prramsters. Thi is done
fuck chet enh meastement,o7 sot of mencurenenis, uniquely defines
specific parameter, The ubity co do the depends very meh on the
‘ouplity of We model structure and may be dealt to wrhiove in
those detailed physial medal”

Satisieal data ie expensive; ie 38 noeeetary, then, Lo depend an
the minnie eet of dts pointe and to maximiee thee ue, Tn addi-
tion, i is expoiont to identify parameters whic nce consistently
the tame in = given family of devices. This is cone farther in
Sevtion ILL whith to some estent ietatee tke form of mode! desired
Further, to mnie mearunement fort, it > eoerlil to ise the
some statinteal data for both nontinea® and small signa! mole! The
Alevelopren. of a siteble sna sigval model for this puspese is oo0-
Sdezed in Seton TV,

"Two approrls exist Gor determining the 0

(9 Oban dhe phyeieal properties uf the devon such aa geometry
tnd doping protic, wel esirulale ihe teortica) pacamcter
values for tho model

(Gi) Derive the parwnelers from electrical measurements at the

‘levies terainoe,

In statistical work, ita (8) miore aterutive aw Ue process
variaiiey may not be wel krown. Lo addition, eamplex intersotions
tiny be compeneated for in Wie dizeet measurement techniqie. Por
tlovioe sige poste fabriswin, nbvinasy a combination of) he
{id hasta be ueed, ecu o7 meted date tan provos sree
Aesioe,

{a Modis So Comma Uae

AL the present tis, two forme of nonlinear transistor models
appear fo be in vogue im generel purpose nelwork snal¥ie programs
‘The nj diferee between the ten anprontes esi the mefenenee
Curr used fnthe representation of ths sep len. pararesee. "The
{ra mnvifesistions eve een identiid as

(08 The ineeion amode, bored on the dds currents ineated wt
the juntions
OS muck seth exezase vecusenu Jousiuy sem IO

(69) The transport model, bowl on the aurrnts traversing th bare
reggon

In the past it has been said” that sine the tr anode appear to be
sathama‘ially aquivaln:, Ue it simple transfo~mstion between
the paramere ant it makos lite difertee which one ie used. Tp
Tae, thie ignore the sjprosimslione ieee ithe mae derivation,
Tt burns out thet th fonetinnel dependeacice of tho model parameters
in case (8) ero oro realists from a phseeal viewpoige and at the
same tine simplify the meseurement procedures required for param-
‘er determination,

2 Buolatin of he Poplar tose
‘To stress tho signifennce of tke elim forthe teeasport mode, the
lowing argunnen i presnted to show the simple® mewsoremeet
requirements ard the wore aecurate dynunie characterisation of thie
rede

as Dt Motel

Figure 1 shows the equivalent circuits ofthe intense transistor for
the tio models under eonserion; the elemcete making up the twa
oquivslene eirecia are ilentiea, consisting of cre eemivonduetar
diodes vo provide for minor's earror injection and two current
ourece ta neennt for minority carrion anspor wero the base
region. The coefciente er, eu, Ry are curent dependent and are
fosonted Gp either functions! og tebulay depesdence te eurvente
iy Tn, te 0 dy eapetively. The importa dierenees between the
tivo madets are the reference cureats used as rentioned in Seetion 3.1

‘The dufning equations are

(4) Lenton Sats (©) Prannpont Baad
Enittor junction inetion: ‘Transport tm emir to
calletor
By = Tarloep (VesnD) ~ 1 Ty = Teen Vel = Te)
Colletaejucotion njesions Transport trom eoleeae

center
Yq = Toslenp (Fox/n tT) = Mh Ty = Teloep (Vie) = 1h)
‘Tae equations for tho termi’ cutrente representing the transistor

Ths ei of parley nt or the Lepr el ayia wih
se CHiCOR envllons be econ mel peee pan ae tle 0
Svea smb Tbe remodeled Table
cotanseraninanios 40 wopELENG 1109

0 Ines mal, 0)

nba Gi en

nowlnesitiee ene

tea bhaate »
bad-ans dna, Loe ®

The emitter Sumetion is forwant Wssed with Pry =O eu that
(nnd J; = 0, thon

[p= -Ien te VI In )
vanes

(dont {word tient

fomponens}eunponent)——_eamponent)

Equation (6) stuns the foncaaentsl diferenee between the own
models by virtue of the makeup of the reerener eueente fy and Ty
Ty rveeente an idee eorypuneat of curzent inthe rene that the col-
Jeeor curvent al enatier as voltage are cole by. the “ideal

‘inde f2 Zp on the oer hal, is mace > of #Ro etmpanenle oF
‘otras mich Zp i ove eureu ie onnen
"Thiv gives te flea season for preferring the tramp model in

that it innatively sore satisfying to works wih he components
snpwesimating Uxucelcal belvien, Other experienlal reasons no
{aioe

iy teeseuring Ze nud To (atin et Vie it 8 posible to lo the
voltage deeslence of J) as Zy ae e208 on thr atzslegerichasie
Plots in Bi. 2
1110 ram pons rem TRORNTOAL JOURNAL, APRN 171

“Tamu 1 Cousvietrnns Cano 1N Comvanisy Noxtixnan Moons

er Seu: bw cue af woul cl
Se Semae coe a mem
ie Eee nero curot for ns no

Tn the inverted mode of trmsiataraponaton ifthe eallotorjunetion
Js forward biased wih Vay = 0, then fy ~ O uzd fy = O ging

Sly tee o
Xx 7

(eonideal deat
omaponent) component)

on J, reprceuts an iea!comporent of currert and fa ie
snace up of ideal and nonides! terms, Measurement of fy abd Je tor
lhe inverted Urausstor giver ne vuage dependence of Zp aml Zp
shown in Fig. 2.

"The velaalaney in the injeeion model ie hosen By he fet Uhl
the shor atd inlerwape ae dierent for Ze ae Ty in the Linear pore
tion nf the enrvos whee Toskage 2nd high-leve!effents ase not signi
leant, The Urarapor meal sts ential sige este
sll ofthe wun depen on the base ere” Thue

4

Tee 8

sad

noun ®

“This ne hrm fn to Be He oe experimen wt he ae
rey ofthe meee ad fll thomson noel
{ckeaton in tery es thay ner of fnee=
Sp, towere, our pny mia tan Uo ave rane In Te
foe! ted ia eres catia Tor pose vaso
very gienay Wewstrs Tein fo tte la te
felony i he njeation motel averted aa euen dependent
emancrmaraunes Agi MOoELME a

paramere By Eyl aad Bi
Ue ve eneent fa aqueson

sed i ty (capone mee! to define

‘222 Dynamic Behmior
Tr transite, cree stooge can be divi into two tyne:

9 Fixed charge in the sepletion regions (voltage dependent)
(39) Mobile eng i tant furrest depontent)
‘To aceouns for the shagging sure lich Dow uaser dynamie
ceomdiiona, two cxpaeianees age inv ners eark jonetion as
fhown in Fig. 4 Ca, and Cy ave the voltage dependent capacitances
epreetiing Ue emitter and ealleeoe ception regions.
CCapecitanees Cy, aral Ce ate ourren: dependent and veprosent the
iiwsiiy eaniee cheep atared on aceount 0: the curr. Mw
‘Kenrding to thargs ratio theenp the ekacgre aor ivee’y peo
twetional ta the reference eatrete such fat the eapaetareee, whiek
fee the incremental ehanges of eae wich jmetion voltage, then
Tweome

(4) Lsgecion Mbt () Pransport Motel
fon +

Co = UR Te Ted ePealTe + Ish 00
eg +

Cu = EEE ty Fol: Oally = Toe ON)

= Rel

Tig. 2Transes cuit brs, a) Setar ete (bY Tenor mode
112m sens sremme teomeeas soeesst, ara. sor

Ts tea.
wee OS ee lie
Ppt A HOHE
ete we 2
Vy ose | ow | i oon a

Tn pracsee the puramaiere® Tapitel, Pee(Ta), Pev(tel, Teri) Inve
40 aswount fore mtu of eles, for exten high-level injootion
lets al aoeage ine ellen ano fear Ui hae, To repent
Use elects the paruneter are taade functions uf earent we shown

‘The parameters Tap (Ty) und Pony) depend ox earn: terms which
cowsist of ideal and ropideal componente. More importantly these
tharacterite firee dseribe aot ‘zaaittinte and recombination cine
sitet, This hath bad and unneereary

ede bad tine the recembinucion phenosiens are not nearly a8 wel
uodersod (mainly because of surfsee ects} us tans mee; hense,
lange variations from unit to unit ean be expeste snd infact are fn
in practice,

Tes unnecessary ines the informetionvlating the Seu time and
reworainstion Lines ery ronnie ie eventing once gia
ters Bs ed By forey ard ag). Thus, ie elle of basing the charac

i ts om le injelion curvy 36 to fora the insraduedon of
redundant neniealies ia the dymisuie parumnctrs, Thief ouch mene
Sgnifieant for Top(Zs) than for Pep

23 Experimental Boidence

Tnigaion “al dhe injetion svoel was in tab wane bot fox
setua! eonige tie suscsuremerts on Kigh-foecueney cevices, hese
Showed that Tey) wow © trong funtion of Jy eould no! be
_D. Kouher bs defined a oonsistnt oe of charset ue parameters which
ove ie luc [opts pommter ele fa he nice me
Farce Td Pf th iope aoye r CHECERS
penta eealy peli for weatiinc then oad Ye et Pon,
Zodiai,'ifen belie Sistas ncPigicie whe of ane puncte wed
ference te ene * “
cmumscrennaries 4D MopaLise irr)

secounted for in the model snd, i fl, twas imposible lo assign
resoningfil vile 10 Po

"The perameier Telly in the trp, wel on the other hand,
‘wot found ve 6 eseenisiy strlen of Jy. Mere ipportart,

doviees hn cet, Ty wus eazaLant re a wice ronge 02 Zr and.

in fas aomed Ute v's Tom dove co doves. In wiltion twas
found that ceviees ofthe sate Carally which hd difeen.go'd spiking
featientguve apptoximatly the sane valve of Pr, Difering anounis
Gf oli coping conirol the recombinution elie whieh i aleeady se
ound for By the de parameter If

a4 Tniportant Popes for Plecaace Analyse

Consistency of Pe, for fae of device types ie vitally ixportemt
in taleraeo analysis wank singe i roquiros fewer measurement, and
tie ba piven a snl staal deseripion, ys ell yee goodanawers
The explanation for his euperi performance of tho transport model
parameters iy that ry snd Tey are effective transit tines which,
{2 mentional ents, re much Deller behaved then roeombinution
fines ‘Thur for the dynamic ror ae well se the de situation, the
transport quae ceerition eliminates the redusdaney of the injostion
ode

2 Prune Made Most Suite tu Statatoat Design

‘Phe coacluson drasra from these experimental raul i thatthe
transport nis a8 outlined above i tn be prefered for th following
(i) Nonideal components of eurreut da not oon in the equstions
relating input valtage aad outs eure
(ip Teter Ponveate and slog “acto ae Oblsined from one st
fof meamaretenss itt 0 ho,
(iy Panametene exe deoonpled in tage the de non
unin only in the paraeersHy(Zy} end
(i) Chemneteratic time porsmetors daseribing. dynamic behavior
fre ponstant over @ wider ye af enerents and vary Y= from
levies to devine, thersby simplfying the measurement. pro
cedure.
(6) Dynan bebavior ie nure spamately modeled and the wt
sf pees. veziation je decoupled. rom Poy and eontnined
Dredoninanly in B,0

“Thus from eansdortions wf oth accurtey and. measurement con-
enone, the trensport moel is efeeabo and Ins, in fal, been
tied with onsiderable ewes in network analysis programs.”
1106 arm ams, sve ennimceat,socmsst, APR 267

28 Tronsistr Output Charaterisice

2 Defects o the Sodst

"To account for the eects af lk material iw the base, coeetor
fond eiitiee, resistances Ry» Re oad Ry are wld co the intrinsic
rode of Fig. 6) at shown in Tig

“Two effete nos aooounted fori this model wt stand are

( Collstor output resistance

(6) valine mutiieton,

Citra avalanche rulliglicabon i ualiy onto for by male
tiplving the pararnter fog by a fatorof the foram 1/11. — (FV)
‘ere and aze constant, Sines the cvaleaahe oda enol ofcon-
eam in vst cite analyse euntaced chi dliresio, will not
‘be consierod further

is very sigifeant, parLnalarly for device in high-rxistanee
sivas, wa some staple men bad toe found t0 rein we out
pat zesianee, Tho approgch ured is deseibed in Section 83.2 und the
‘equivalent oulpet ree tuner iv eaoulsted fe Appendix

“Mousuroments of By st 4 funetion of Vex for constant bese current
‘are shown in Fg. $ where to important fects shoud be noted
6) Testing fleets dve to increased power distgution grey
Imereane the chunge in By

cay al

a

oFByty

is. Noalcer tutor model