An Automated Technique to Identify Defective CMOS Devices based on Linear Regression Analysis of Transient Signal Data

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Jody Cross
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1 n utomatd Tchniqu to dntify fctiv MO vic bad on Linar Rgrion nalyi of Tranint ignal ata Jam F. luqullic*, onald M. and tvn. Lvitan+ *partmnt of, Univrity of Maryland, altimor of omputr cinc, Univrity of ittburgh +partmnt of lctrical nginring, Univrity of ittburgh btract Tranint ignal nalyi i a digital dvic tting mthod that i bad on th analyi of voltag tranint at multipl tt point and on witching tranint on th upply rail. W how that it i poibl to idntify dfctiv dvic by analyzing th tranint ignal maurd at tt point on path not nitizd from th dfct it. Th mall ignal variation gnratd at th tt point ar analyzd in both th tim and frquncy domain. Linar rgrion analyi i ud to how th abnc of corrlation in th ignal acro th output of bridging and opn drain dfctiv dvic. tatitical mthod and an algorithm for idntifying dfctiv dvic ar prntd that i bad on th tandard dviation of rgrion ridual computd ovr a comprd rprntation of th ignal.. ntroduction Tranint ignal nalyi (T) [] i a paramtric approach to tting digital intgratd circuit. fct dtction i accomplihd in T by analyzing th tranint ignal of a dvic maurd imultanouly at multipl tt point. Th approach offr two ditinct advantag ovr othr logic and paramtric tting mthod. Firt, dvic coupling mchanim prmit th dtction of dfct at tt point that ar not on logic ignal propagation path from th dfct it (off-path nod). onquntly, dirct obrvation of logic fault i not ncary in T. cond, th cro-corrlation of multipl tt point ignal allow ignal variation caud by proc tolranc to b ditinguihd from tho caud by dfct. Thi i tru bcau proc tolranc ffct tnd to b global, cauing ignal chang on all tt point of th dvic. n contrat, ignal variation caud by a dfct tnd to b rgional and mor pronouncd on tt point clot to th dfct it [2]. n thi papr, w focu on th dvlopmnt of a tatitical mthod that can b ud to automat th T tting proc. W introduc ignatur Wavform (W) a a man of capturing ignal variation btwn dfct-fr and dfctiv dvic and formulat a tatitic bad on a compact rprntation of th W calld Trapzoidal Rul ra (TR). W valuat th ffctivn of th TR in capturing th ignal variation obrvabl in th W paratly in th tim and frquncy domain. Th valuation i prformd by analyzing th TR from tt point pairing of dfct-fr and dfctiv dvic uing linar rgrion. Th rgrion lin computd for ach pairing of th TR of dfct-fr dvic track th variation introducd by proc tolranc. Th dviation or ridual of th TR of dfctiv dvic ar computd with rpct to th rgrion lin and ar ummarizd in a tatitic, th tandard dviation. Th tandard dviation computd for dfct-fr and dfctiv dvic ar compard to dtrmin th ffctivn of th TR in capturing th ignal variation introducd by dfct. Th analyi i prformd uing th tim, Fourir magnitud and pha W obtaind from four hardwar xprimnt. On xprimnt i ud a a control xprimnt to valuat rror in th timat of th rgrion lin. Th rult of th thr rmaining xprimnt how that th pha TR ar conitnt with th ignal bhavior obrvd in th W and ar bt abl to captur th variation producd by dfct. ad on th rult, w propo an algorithm that can b ud to automat th dtction of dfct. 2. ackground aramtric dvic tting tratgi [3] ar bad on th analyi of a circuit paramtric proprti, for xampl, propagation dlay, magnitud of quicnt upply currnt or tranint rpon. Many typ of paramtric tt hav bn propod [4] but rcnt rarch intrt ha focud primarily on thr typ; Q [5], [6], and dlay fault tting [7]. Q i bad on th maurmnt of an upply currnt whn all nod hav tabilizd to a quicnt valu. Q ha bn hown to b an ffctiv diagnotic tchniqu for MO bridging dfct, but i not applicabl to all typ of MO dfct [8]. Rcntly, concrn hav bn raid ovr th applicability of Q to dp

2 56 66 // ridging dfct tatic hazard pul in dfct-fr circuit ub-micron tchnologi [9]. vral dynamic upply currnt -bad approach hav inc bn propod to ovrcom th limitation caud by th tatic natur of th Q tt [][][2]. n gnral, th -bad mthod ar not hamprd by th low tt application rat and ar not a nitiv to dign tyl a Q, howvr, howvr, thy do not provid a man of accounting for proc tolranc and ar thrfor ubjct to aliaing problm. ltrnativly, dlay fault tting tak advantag of th fact that many MO dfct cau a chang in th propagation dlay of ignal along nitizd path. ifficulti with dlay fault tting includ th complxity of tt gnration and path lction [3]. Franco and Mcluky [4] and othr [5][6] hav propod xtnion to dlay fault tting that addr om of th difficulti. 3. xprimnt ummary n thi ction, w prnt a ummary of th xprimnt tup and how th typ and location of th dfct that w introducd into a t of tt dvic. W conductd hardwar xprimnt on thr vrion of th 85 c432 bnchmark circuit: a vrion with intntionally inrtd bridging dfct, a vrion with intntionally inrtd opn drain dfct and a dfct-fr vrion. Four dvic of ach vrion wr fabricatd. Th four dfct-fr dvic and on t of ithr th opn drain or bridging dfctiv dvic wr ud in ach xprimnt. Four xprimnt wr conductd, two bridging xprimnt labld ntrnodal-ridging and Fdback-ridging, and two opn drain xprimnt labld Opn-rain and ontrol. Th ignal maurmnt wr takn on cor logic tt tt pad placd on th output nod of th gat driving th vn primary output, labld 223, , 42, 43, 43, and 432. wa alo maurd on V a an ighth output ignal. Figur how portion of th chmatic diagram from // // O 37 O 223 O 329 O 42 // O 43 // tatic hazard pul in dfct-fr circuit O 43 O // ridging dfct O 43 ntrnodal ridging xprimnt Fdback ridging xprimnt Figur. ortion of th c432 howing th nitizd path from th ridging xprimnt. O 223 O 329 O 37 O 42 O 43 th c432 for th bridging xprimnt. Th dottd lin in th figur rprnt th bridging dfct which wa cratd in th layout by inrting a firt-lvl to cond-lvl mtal contact btwn th output lin of a 4-input gat and an invrtr. n th dfct-fr dvic, a tatic hazard cau a pul to propagat to O 42 and 43 along path hown hadd in th figur. inc th output of th invrtr drivn by 56 i low, th bridg liminat th pul in th bridging dfctiv dvic. Th lft id of Figur how th nitizd path for th Fdback ridging xprimnt. lthough th dfct i on a nitizd path driving O 432, th circuit oprat logically corrctly undr thi tt qunc. Th bridging dfct i hown in th figur a a dottd lin but i phyically rprntd a an xtra pic of cond-lvl mtal btwn th output of two 4-input gat. Figur 2 how th nitizd path through th dfctiv gat for th Opn rain (top) and ontrol xprimnt (bottom). Th lft id of Figur 2 how an opn drain dfct in th tranitor-lvl chmatic diagram of a 4-input gat. thr micron wid pic of firt-lvl mtal ha bn rmovd btwn th p-tranitor drain pair. oth of th opn drain xprimnt tt thi typ of dfct in two diffrnt gat in th circuit. Th tt qunc for th Opn-rain xprimnt gnrat a numbr of pul which ar cratd by a tatic hazard in th dfct-fr dvic but liminatd by th dfct in th opn drain dvic. Th ontrol xprimnt wa dignd to tt th chang in loading capacitanc introducd by th dfct on O 329 and 37. Howvr, th tt qunc for th ontrol xprimnt do not produc maurabl chang in paramtric bhavior of th Opn-rain dvic. inc th Opn-rain dvic bhav lik dfct-fr dvic undr th condition, w u thi xprimnt a a control xprimnt to valuat th rror in th rgrion lin timat. W latr how that th am Opn-rain dvic can b idntifid a dfctiv whn ttd uing an input timulu that cau a fault (Opn-rain xprimnt). Morovr, inc th O 432

3 Opn rain Vdd 4 input gat mphai of th xprimnt i on th mauring th coupld variation introducd by th paramtric fault at th tt point, w analyz only th tranint ignal of tt point that ar not dirctly affctd by paramtric or logic fault. Out Logic not hown not hown ar hld low not hown ar hld low // // // // // tatic // hazard Opn rain xprimnt ontrol xprimnt 4. Tting Mthod W u ignatur Wavform or W to captur ignal variation btwn dvic a hown in Figur 3. Th plot labld Raw Wavform dpict th tranint wavform of two dvic. Th wavform hown along th top of th plot wr maurd on tt point that wr drivn by a nitizd path. Th wavform hown along th bottom wr maurd on non-nitizd tt point. W crat Tim omain ignatur Wavform from th pair of tranint wavform by ubtracting th tt dvic wavform from th tandard dvic wavform. Th diffrnc wavform, hown in th right plot of Figur 3, ar hadd along a zro balin in ordr to mphaiz th ignal variation. W alo analyz th frquncy domain rprntation of th tranint ignal by crating frquncy domain ignatur Wavform. Th magnitud and pha componnt producd by a icrt Fourir Tranform of th raw tim domain wavform ar ud to gnrat Magnitud and ha W by ubtracting th tt dvic magnitud and pha valu from th corrponding valu of th tandard dvic. n ordr to implify wavform pot-procing, w compr th multi-point W into a ingl floating point valu by computing th ara undr thir curv uing a Trapzoidal Rul intgration mthod. W call th ara valu rult a TR. Figur 4 how th Fourir ha W from two non-nitizd tt point, 329 and 432, of an hardwar xprimnt involving on tandard and vn tt dvic. Th top-mot wavform i th output trac of a dfct-fr dvic that i ud a th tandard. Th W of thr additional dfct-fr dvic ar labld F#x whil th W of four Ridging dfctiv dvic ar labld R#x. Th TR hown to th right of ach plot ar computd ovr th portion of th frquncy rang btwn to 25 MHz Th tatitic that w u to dtct dfct ar bad on tandardizd ridual. tandardizd ridual ar drivd from two dimnional cattr plot of TR. For xampl, th TR hown in Figur 4 dfin a cattr plot of 7 data O 223 O 329 O 42 O 43 tatic hazard ignal O 432 O 37 O 43 O 223 O 42 O 43 O 329 // O 43 O 432 Figur 2. ortion of th c432 howing th nitizd path from th Opn rain and ontrol xprimnt. 5V V.5 Raw wavform tandard dvic wavform Tt dvic wavform T Z O nano c 5V Figur 3. Tim omain ignatur Wavform. ignatur wavform nitizd W on-nitizd W T Z O O 37

4 8 8 d8 g8 r O 329 tandard F# F#2 F#3 R# R#2 R#3 R#4 R - W MHz σ d8 g8 r O 432 tandard Figur 4. xampl Fourir ha W and TR from tt point 329 and 432. F# F#2 F#3 R# R#2 R#3 R#4 R - W MHz xprimnt vic/xprimnt ontrol Opn-rain ntrnodal-ridg Fdback-ridg O/R# O/R# O/R# O/R# F Max Tabl : ummary of ha σ tatitic. point in which th x valu ar dfind by O 329 and th y valu by O 432. cattr plot of othr combination of th tt point ar dfind in a imilar way. W comput a lat quar timat of th rgrion lin through th thr dfct-fr data point of ach cattr plot. ata point ridual ar computd a th ditanc along th y axi btwn th data point and th rgrion lin and ar tandardizd by dividing by th man quar rror of th 3 dfct-fr data point. n [][2], w how that a high dgr of linar corrlation xit among th data point of dfct-fr dvic in th cattr plot. Thi i conitnt with our obrvation that variation in W rulting from proc tolranc ffct occur in all tt point ignal. Thrfor, th rgrion lin track proc tolranc ffct and, in th abnc of unmodld random variabl uch a maurmnt noi and intra-dvic proc tolranc, th data point of dfct-fr dvic would b co-linar. ntad, th data point of dfct-fr dvic ar ditributd around th rgrion lin and dfin a rgion that w call th proc tolranc zon. t i in thi rgion that w xpct to find th data point of dfct-fr dvic. n contrat, w hav obrvd that dfct introduc additional variation in th W of dfctiv dvic that vari dpnding on th tat and poition of th tt point with rpct to th dfct it. Thi cau th data point of dfctiv dvic to fall outid of th proc tolranc zon. Thrfor, th tandardizd ridual of dfctiv dvic captur uncorrlatd variation that rult from dfct in addition to th variation common to all data point, namly, that du to maurmnt noi, intra-dvic proc tolranc and rror in th rgrion lin timat Our dfct dtction critria i bad on th tandard dviation, σ, of th t of tandardizd ridual obtaind for ach dvic ovr all poibl pairing of th tt point ignal. For xampl, if th tranint ignal from ix tt point ar ud in th analyi, thn fiftn cattr plot ar drivd. n our xprimnt, ach cattr plot contain 7 data point, 3 from dfct-fr dvic and 4 from dfctiv dvic. Th tandard dviation of th fiftn tandardizd ridual blonging to ach dvic ar computd with rpct to thir rgrion lin. σ maur th diprion of th data point around th rgrion lin. 5. Rgrion nalyi u to pac limitation, w how only th Fourir pha σ tatitic, which ar uprior to both th tim and Fourir magnitud rult. Tabl how th tandard dviation computd in th four hardwar xprimnt. Th lft-mot column idntifi th dvic with, O indicating Opn-rain and R indicating Ridging. Th σ tatitic of ach of th four xprimnt ar hown in column two through fiv. Th hadd valu in column two i th maximum among th dfctiv dvic valu whil th hadd valu in column thr, four and fiv ar th minimum valu. Th bottom row dpict th maximum fct-fr σ tatitic for ach xprimnt.

5 vral charactritic ar notabl in th rult. Firt, th mallt minimum σ tatitic, givn in column fiv a 4.8, i narly a factor of tn largr than th rgrion lin rror timat of 4.2 givn in column two. Thrfor, th σ tatitic i abl to captur th ignal variation caud by th dfct to a ignificant dgr. cond, thr i conitncy btwn th magnitud of th valu and th amount of variation introducd by th dfct. For xampl, w can rank ach of th xprimnt by counting th numbr of nitizd path diruptd by th dfct. Th tt qunc ud in th Opn-rain xprimnt cau fault on thr nitizd path. Th tt qunc of th ntrnodal-ridging xprimnt cau fault on two nitizd path whil th tt qunc ud in th Fdback-ridging xprimnt cau a fault on a ingl nitizd path. xcpt of a ingl intanc, th rank of th σ tatitic corrpond to thi ordring a hown from lft to right along ach row of column thr through fiv. Thi corrpondnc i not unxpctd inc ach of th faultd path contribut to off-path ignal variation. Th σ tatitic provid th bai on which a dfct dtction algorithm can b dvid. W rcogniz that any typ of dvic tting mthod rquir a tt vctor gnration tratgy and w ar currntly invtigating thi iu. Givn a t of uitabl tt vctor pair and a t of known dfct-fr dvic, dvic tting can b carrid out a follow. Th rgrion lin of pairing btwn lctd tt point ignal ar drivd and th σ tatitic computd undr ach of th tt qunc. cond t of known dfct-fr dvic ar ud to valuat th rror in th rgrion lin timat and th proc i rpatd until th rror i accptably mall. Th proc tolranc zon bad on - α confidnc limit ar drivd undr ach tt qunc. Th σ tatitic of ach tt dvic i thn computd and compard againt th proc tolranc zon limit. f a σ tatitic fall outid of th proc tolranc zon undr any of th tt qunc, th dvic i markd a dfctiv. 6. oncluion W prntd a tatitical tchniqu to idntify dfct in digital intgratd circuit that i bad on linar rgrion analyi of tranint ignal data. inc th numbr of tt dvic in our xprimnt wa mall, w timatd th rror in th rgrion lin uing a control xprimnt and found th rgrion lin to b raonably timatd. W compard th σ tatitic of thi xprimnt with tho obtaind from thr dfctiv dvic xprimnt and dtrmind that th Fourir pha analyi yildd valu that wr conitntly largr than th tim domain and Fourir magnitud analyi with rpct to th rgrion lin timation rror. Thrfor, th Fourir pha TR provid th hight dgr of confidnc that a poitiv dfct dtction dciion i corrct. ad on th rult, w propod an algorithm to automat th dtction of dfct in T. Rfrnc [] J. F. luqullic. igital ntgratd ircuit Tting Uing Tranint ignal nalyi, h.. irtation, partmnt of omputr cinc, Univrity of ittburgh, ugut, 997. [2] J. F. luqullic,. M. hiarulli, and.. Lvitan. dntification of fctiv MO vic uing orrlation and Rgrion nalyi of Frquncy omain Tranint ignal ata, ntrnational Tt onfrnc, p. 4-49, ovmbr 997. [3] J. M. odn and. F. Hawkin. lctrical proprti and dtction mthod for MO dfct. n rocding of th uropan Tt onfrnc, p , 989. [4].. ory,. K. Jon,. M.. Richardon, and Y. Z. Xu. Rapid Rliability mnt of VL. lnum r, 99. [5] T. M. tory and W. Maly. MO bridging fault dtction. n ntrnational Tt onfrnc, p , 99. [6] J. F. Frnzl and.. Marino. owr upply currnt ignatur () analyi: nw approach to ytm tting. n ntrnational Tt onfrnc, p , 987. [7].. Hih, R.. Ramun, L. J. Viduna, and W. T. avi. lay tt gnration. n rocding of th 4th ign utomation onfrnc, p , 977. [8].. ingh, H. Rahd, and W. W. Wbr. Q tting of MO opn: n xprimntal tudy. n ntrnational Tt onfrnc, p , 995. [9]. Mcluky(Modrator), K. akr(organizr), W. Maly, W. dham, M. achdv(anlit), Will Q Tting Lak way in p ub-micron Tchnology?, ntrnational Tt onfrnc, anl 7, 996. []. Vinnakota. Monitoring owr iipation for Fault tction. 4th VL Tt ympoium, p , 996 [] J.. aly, H. Ramamurthy, J. Ramirz-ngulo, and M. Yong. pul rpon tting of analog and digital MO circuit. n ntrnational Tt onfrnc, p , 993. [2] R. Z. Makki,. u, and T. agl. Tranint powr upply currnt tting of digital MO circuit. n ntrnational Tt onfrnc, p , 995. [3]. K. ramanick and. M. Rddy. On th dtction of dlay fault. n ntrnational Tt onfrnc, p , 988. [4] F. Franco and. J. Mcluky. lay tting of digital circuit by output wavform analyi. n ntrnational Tt onfrnc, p , 99. [5]. hattrj, R. Jayabharathi,. ant and J.. braham. on-robut Tt for tuck-fault tction Uing ignal Wavform nalyi: Faibility and dvantag. n VL Tt ympoium, p , 996. [6]. Thibault. tction and location of fault and dfct uing digital ignal procing. n VL Tt ympoium, p , 995.

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