A Methodology for MOS Transistor Mismatch Parameter Extraction and Mismatch Simulation

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