Simple March Tests for PSF Detection in RAM

Transcription

1 Smple March Tests for PSF Detecton n RAM Ireneusz Mroze Balysto Techncal Unversty Computer Scence Department Wejsa 45A, 5-35 Balysto POLAND mroze@.pb.balysto.pl Eugena Buslowsa Balysto Techncal Unversty Computer Scence Department Wejsa 45A, 5-35 Balysto POLAND ebus@.pb.balysto.pl Abstract Prevous research has outlned that the only march tests can be n use now to test modern memory chps. Ther transparent versons are very effcent for the smple fault testng and dagnoses. In the case of Pattern Senstve Faults PSF, they are not such effcent. Conventonal memory tests based on only one run march test have constant and low faults coverage for PSF. To ncrease the probablty of the detecton of such type of faults, multple run March test sessons can be used. As shown earler, the ey element of multple run March test algorthms are memory bacgrounds. Only n the case of optmal set of bacgrounds the hgh fault coverage can be acheved. There are many dfferent march tests whch we can use n multplyng test scheme. However accordng to weghted fault coverage measure for march tests, t s not necessary to use complex tests to acheve hgh fault coverage n multbacground tests. The hgh fault coverage espesally for PSF we can acheve usng the smplest tests. Effcency of mulbacground test sessons based on two smplest march tests MATS and MPS3N and optmal selected bacgrounds s the man subject of ths paper. All of the analytcal calculatons are confrmed and valdated by adequate experments. Introducton Faults modeled from the memory defects can be summarzed as follows [, 2]; Stuc-at-Fault SF: Ether a cell or a lne s stuc to logcal 0 or. Transton Fault TF: The 0 or 0 transton s mpossble on a cell or a lne. Couplng Fault CF: When n a cell there s a transton 0 or 0, the content of the other cell s changed. CF s generalzed to a -couplng fault when cells are changed and s classfed nto Inverson or Idempotent couplng faults dependng upon what content changed [3]. Retenton Faults RF: A cell fals to retan ts logc value after some tme. Ths fault s caused by a broen pullup resstor. Neghborhood Pattern Senstve Fault NPSF: a typcal neghborhood pattern senstve faults preventng the base cell from beng transted to a certan value s called statc NPSF, and an NPSF s called dynamc when a transton on the neghborhood cells trggers a transton on the base cell. The neghborhood pattern senstve fault NPSF model s not new, but t s stll wdely dscussed n the lterature of memory testng, and becomng more and more mportant for memory testng. The problems wth testng of semconductor memores are very dfferent from testng logc. The man reason s that the fault behavour of memores s nherently analog, whle the used fault models have a dgtal logcal nature. Tradtonal March algorthms [] have been wdely used n RAM testng because of ther lnear tme complexty, hgh fault coverage, and ease n bult-n self-test BIST mplementaton. It s nown that the tradtonal March algorthms do not generate all neghborhood patterns that are requred for testng the NPSFs, however, they can be modfed to get detecton abltes for NPSFs. Based on tradtonal March algorthms, dfferent approaches have been proposed to detect NPSFs, such as the tlng method [, 4], two-group method [], row-march algorthm [4] and transparent testng [3, 5, 6]. 2 Transparent memory testng March tests are superor n terms of test tme and smplcty of hardware mplementaton and consstng of sequences of March elements. The March element ncludes sequences of read/wrte r/w operatons, whch are all appled to a gven cell, before proceedng to the next cell. The way of movng to the next cell s determned by the address sequence order. Durng the testng, March tests mae use of address sequences called up and down sequences, denoted as and. The notaton means don t care the drecton of address order. It should be mentoned that the address sequences do not necessarly have to be countng

2 sequences. As an example of the standard memory tests MATS test { w0; r0, w; r, w0} can be consdered, whch ncludes just three phases. The frst phase s memory ntalzaton wrtng all zero bacground, whle the other two phases are sets of read and wrte operatons allow detectng target faults. The MATS test detects all stuc-at faults, address faults, some transton faults and some couplng faults, as well as small porton of NPSF []. The transparent technque s a well nown memory testng approach that retreves the ntal contents of the memory once the test phase has been fnshed. It s therefore sutable for perodc feld testng whle allowng preservng the memory content. A transparent BIST s based on a transparent March test that uses the memory ntal data to derve the test patterns. The wrte data can be ether the read value or ts opposte value. A transparent test algorthm ensures that the last wrte data s always equal to the frst read value n order to satsfy the transparency property. The procedure to derve a transparent test algorthm from a non transparent one see [6] can be summarzed by the followng steps:. Remove the ntal sequence ntalzaton sequence. In most cases, removng such a sequence allows to reduce the test length, wthout affectng the fault coverage. 2. Add read operatons at the begnnng of all sequences startng wth wrte operatons. 3. Add extra sequence to preserve transparency that s, to retreve the ntal content of the cells. 4. Derve the predcton algorthm. Ths s done by deletng all wrte operatons from the test sequences, thereafter the resulted sequences are appended at the begnnng of the test algorthm. The transparent verson of the MATS test has the next notaton { ra, wa; ra, wa} [6], where a {0, } and a s the negaton of the value of a. Transparent tests are partcularly sutable for Bult-In Self-Test. A pure Transparent March memory BIST should mplement the test algorthm ssued from the above procedure. However, step 4 s mandatory only f an n-stu sgnature comparson capablty s requred. In ths case, the sgnature resultng from the predcton sequences and the one resultng form the remanng test sequences are compared aganst each other to produce the test s status. In some cases le Adaptve Sgnature Analyses [7] and Symmetrc Memory Tests [8] ths step should be avoded. For further dscussons, let us focus on two March memory tests, namely MATS:{ ra, wa; ra, wa}, whch allow to avod predcton phases based on Symmetrc memory testng [8], and modfed PS3N test - MPS3N: { ra, wa, ra, wa, ra} [9]. It s qute mportant to emphasze that mplementaton of MPS3N n some cases do not need the value of fault free sgnature, and the MPS3N testng procedure can be nterrupt by the system at any tme due to the preservng the ntal memory contents at any stage of testng. In a case of MATS test ntal contents wll be at the end of test procedure. The man advantage of the transparent memory testng s the test pattern flexblty to ntalze the memory wth the desred bacground to cover specfc fault models not covered by standard March tests. 3 MATS and MPS3N memory tests effcency analyses To nvestgate the memory march tests, let us suppose that NPSF ncludes memory cells wth ncreasng order of addresses α0, α, α2,..., α, such a way that α0 < α < α2 <... < α and base cell has the address α, where 0. Let us focus on the Passve NPSF PNPSF as the most dffcult faults to be detected. Frst of all, t should be emphaszed that due to scramblng nformaton, as well as specfc optmzaton technques, there s a huge amount of such type of faults. Any arbtrary memory cells out of all N memory cells can be nvolved nto the PNPSF. Ths notaton means that arbtrary cells are nvolved nto the PNPSF and one of the cells s a base cell b and the rest cells are the neghbors n. Any arbtrary cell out of cells s the base cell for whch two transtons can be consdered, so there s 2 dstnct PNPSF dependng on the base cell poston postons. For neghborhood pattern there are 2 dfferent patterns. Then the exact number of all PNPSF wthn the N memory cells s determned accordng to the followng equaton [9]: N N L PNPSF = 2 2 = 2 The number Q M PNPSF of detectable faults durng the one MATS memory test run s: N Q M PNPSF = 2 And the fault coverage FC for MATS s: FC M = Q MPNPSF L PNPSF 00% = 00% 3 2 The exact values of fault coverage for dfferent and for MATS test are presented n Table. In the case of MPS3N test we can do the same nvestgaton n some other way. Any arbtrary memory cells out of all N memory cells can be nvolved nto the PNPSF. It means that any arbtrary cells out of N may be the neghborhood cells and one arbtrary cell out of rest

3 Table. PNPSF fault coverage for MATS test FC M N may be a base cell. Because n base cell two transtons can be consdered, so there s N dstnct PNPSF for chosen neghborhood cells. In neghborhood cells, there are 2 possble patterns. Therefore the number of all PNPSF whch was determned by can be determned by 4 too. N L 2 PNPSF = 2 N 2 = 2 N N 4 It s easy to show that L PNPSF = L 2 PNPSF. Now, the number Q M3N PNPSF of detectable faults durng the one MPS3N memery test run s 5: N Q M3N PNPSF = 2 N 5 And the fault coverage FC for MPS3N s: FC M3N = Q M3NPNPSF 00% = L 2 PNPSF 2 6 The exact values of fault coverage for dfferent and for MPS3N test are presented n Table 2. Table 2. PNPSF fault coverage for MPS3N test FC M3N There are some solutons whch allow to ncrease the values of FC M shown n Table and Table 2. Among those the most promsng s the multple run memory testng. The ey dea behnd ths approach s the dfferent bacground selecton for ncreasng the fault coverage. Let us analyze the effcency of ths approach for dfferent number of bacgrounds. In the case of two bacgrounds the fault coverage wll be twce as hgh as when the second bacground s nverse verson of the frst one. More complcated problems arse for three and four runs of memory test wth the dfferent bacgrounds. 4 Bacground selecton To acheve hgh fault coverage of PNPSF for mult-run memory testng, t s qute mportant to choose approprate bacgrounds. In the case of tests whch allow to generate only one pattern le MATS, MPS3N, the selecton algorthm for optmal bacground selecton can be based on the followng statements [0]. Statement In the case of m runs of the memory test whch allow to generate only one pattern wthn neghborng cells based on bacgrounds a 0, a, a 2,..., a m, an optmal set of such type of bacgrounds should have the maxmal Hammng dstance HDa, a j between any par a, a j,where, j {0,, 2,..., m }. There are not nown effcent algorthms to generate more then four bacgrounds whch satsfed statement. For the case of four runs of memory test, tang nto account Statement, we have to estmate the maxmum mnmal possble Hammng dstance between any pars B, B j, B, B l, B, B r, B j, B l, B j, B r and B l, B r out of four bacgrounds {B, B j, B l, B r } j l r {, 2,..., 2 N }. Mathematcally ths problem can be formulated as []: MMHDB, B j, B l, B r = MAX { =j l =r {,2,...,2 N } MIN[ 7 HDB, B j, HDB, B l, HDB, B r, HDB j, B l, HDB j, B r, HDB l, B r ]}. Let we have got three frst arbtrary bacgrounds B, B j and B l wth optmal value of MMHDB, B j, B l. As shown earler, for large N ths value can be regarded as nteger number, then HDB, B j = HDB, B l = HDB l, B j =. We have to emphasze that n the case of three bacgrounds, t s mpossble to get greater value of MMHDB, B j, B l, that s why n the case of four bacgrounds, MMHDB, B j, B l, B r also can not be greater than. It means that n the case of four bacgrounds, the best soluton wll be obtaned when dstances between the fourth bacground and the frst three bacgrounds are equal: HDB r, B = HDB r, B j = HDB r, B l =. Due to the fact that bacgrounds B and B j have S 0 B, B j S 0 B, B j = dfferent bts, the thrd bacground B l have been generated by the selecton of part of ts bts from bacground B and the another part from B j, as well as nverson of all S 00 B, B j S B, B j = equal bts for B and B j. In the case when we create the next bacgroundb r as the selecton of another parts of S 0 B, B j

4 S 0 B, Bj = dfferent bts from bacgrounds B and B j and nverson of all S 00 B, B j S B, B j = bts, ths bacground can be regarded as the thrd bacground compared wth B and B j. It follows from the concluson that the bacground B r has the same dstances HDB r, B = HDB r, B j = as the bacground B l HDB l, B = HDB l, B j =. From the procedure of generaton of B l and B r, we can conclude that n the S 0 B, B j S 0 B, B j = postons wth the dfferent bts for B and B j bacgrounds, B l and B r have nverse value of bts. Then HDB l, B r =. To summerze t s easy to show that HDB, B j = HDB, B l = HDB j, B l = HDB, B r = HDB j, B r = HDB l, B r =. For the prevous example, n the case of two bacgrounds B = 000, B j = 000 the thrd bacground B l = b l b l2 b l3 b l4 b l5 b l6 = 0 have been generated to satsfy the equalty HDB, B j = HDB, B l = HDB j, B l =. To generate new fourth bacground B r, ts frst and second bts have to be nverse value compared wth B and B j, namely b r =, due to b = b j = 0 and b r2 = 0, because b 2 = b j2 =. Then another part compared wth the case of the B l generaton of the bts two bts wth opposte value n B and B j should tae the value from one bacground, let t be B j for example, b r3 = b r4 = 0 and the second part the values from bacground B for example, b r5 = b r6 = 0. The fnal result s B r = b r b r2 b r3 b r4 b r5 b r6 = whch s satsfy to the next statement: Statement 2 In the case of four runs of the memory test whch allows to generate only one pattern wthn neghborng cells based on four bacgrounds B,B j,b l and B r j l r {, 2,..., 2 N } when N s one bt-wde memory sze, an optmal set of such type of bacgrounds should satsfy the followng equalty : HDB, B j = HDB, B l = HDB j, B l = = HDB, B r = HDB j, B r = = HDB l, B r 8 Accordng to algorthm presented n [], we can generate the set of four optmal bacgrounds. As an example of such type of optmal bacgrounds for the case of transparent four runs of memory testng the followng set of bacgrounds can be chosen for N = 9 and all bts of frst bacground are zero: B = b b 2 b 3 b 4 b 5 b 6 b 7 b 8 b 9 = B 2 = b 2 b 22 b 23 b 24 b 25 b 26 b 27 b 28 b 29 = 000 B 3 = b 3 b 32 b 33 b 34 b 35 b 36 b 37 b 38 b 39 = 000 B 4 = b 4 b 42 b 43 b 44 b 45 b 46 b 47 b 48 b 49 = 000 Ths set of bacgrounds wll be used n the next secton to calculate four runs of MATS and MPS3N test effcency especally n terms of PSF. 5 Four runs of MATS and MPS3N memory test effcency analyses Let assume that N s dvsble by 3. Let s start our nvestgaton wth MATS test. For the frst bacground B Q M B = Q M PNPSF. Bacground B 2 generates Q M B 2 = new patterns and bacground B 3 due to ts structure allows to generate the addtonal porton of patterns calculated as: Q M B 3 =. Full amount of the patterns generated after three runs of the MATS test based on B, B 2, B 3 patterns equals to: N Q M B 2 3 = 2. Bacground B 4 due to ts structure allows to generate the addtonal porton of patterns calculated as Q M B 4 =

5 Full amount of the patterns generated after four runs of the MATS test based on the set of B, B 2, B 3, B 4 patterns equals to: N Q M B = 3 2 Tang nto account that for real applcatons, N s a bg nteger number, << N and N >> N last equaton n the case of even N can be smplfed to Q M B N! 2 3! 2 3!! 3 2 3!! Then the fault coverage FC MATS B, B 2, B 3, B 4, for the four runs of the MATS test wth nvestgated bacgrounds can be estmated as [2]: FC MATS B, B 2, B 3, B 4, % 9 In the case of MPS3N for the frst all zero bt bacground B Q M3N B = Q M3N PNPSF. Now let n means the number of neghbourhood cells n =. Then the bacground B 2 generates: Q M3N B 2 = 2N n n n n 0 new patterns and bacgroundb 3 due to ther structure allow to generate the addtonal porton of patterns calculated as: Q M3N B 3 =2N n n n n n n Full amount of the patterns generated after three runs of the MPS3N test equals to: N Q M3N B 2 3 =2N n n n n 2 n n n n 2 Bacground B 4 due to ts structure allows to generate the addtonal porton of patterns calculated as: Q M3N B 4 =2N n n n n n 3 Full amount of the patterns generated after four runs of the MPS3N test based on the set of B, B 2, B 3, B 4 bacgrounds equals to N Q M3N B =2N n n n n 3 n 2 n n n 4

6 Accordng to the same assumptons for and N defned earler: Q M3N B n! 2n 3 n n! 2 n 3 n n!! 3 n 3 n 2 n n!! 5 Then the fault coverage FC MPS3N B, B 2, B 3, B 4, for the four runs of MPS3N test wth the nvestgated bacgrounds can be estmated as: FC MPS3N B, B 2, B 3, B 4, 2 n 3 n 2 n 3 n n 2 n 3 n 2 n n 6 Expermental results 6 In ths secton, we want to confrm the analytcal results by adequate experments. In Table 3 the fault coverage of 4rMATS and 4rMPS3N are presented. These results have been calculated accordng to 9 and 6. Table 3. Analytcal results: 4rMATS and 4rMPS3N fault coverage for PNPSF Test/ MATS 47.23% 24.54% 2.42% 3.2% MPS3N 83.33% 47.23% 24.54% 6.24% To valdate analytcal results from Table 3, many experments have been done. The experments was done for PNPSF3 and PNPSF5 faults, dfferent szes of memory and selected optmal bacgrounds from secton 4. In each cases, all PNPSF3 and then PNPSF5 faults were generated. It allowed to obtan exact number of actvated by 4rMATS and 4rMPS3N test sesson faults. So, each tme we could calculate exact value of fault coverage of ths test sessons. All expermental results are presented n Tables 4. As presented n the Table 4 fault coverage confrmed the analytcal results obtaned accordng to 9 and 6. It should be notced that n such type of memory testng, the fault coverage mnmally depends on N. The especally hgh nfluence on the fault coverage can be observed for very small N what n real applcatons has no matter. Table 4. Expermental results: 4rMATS and 4rMPS3N fault coverage for PNPSF3 and PNPSF5 Fault/N MATS PNPSF3 49.% 47.73% 47.48% 47.29% PNPSF5 2.50% 2.46% 2.44% 2.43% MPS3N PNPSF % 84.38% 83.85% 83.38% PNPSF % 24.70% 24.65% 24.58% 7 Conclusons In ths paper, the fault coverage of the test sessons based on smple march algorthms MATS and MPS3N was presented. In one test sesson, the same test had been runnng four tmes on dfferent bacground each tme. The bacground was selected accordng to algorthm whch allows to generate optmal for MATS and MPS3N tests set of bacgrounds. The man attenton n ths paper was focused on the effcency of PSF detecton. We can see that both of the smple tests can be successfully used n multbacgrounds test scheme. If we compare the effcency of the MATS and MPS3N test sessons, we can say that from pont of vew of PSF detecton, MPS3N gves us better results than MATS. For MPS3N test and optmal set of bacgrounds, we have receved very hgh fault coverage for 4rMPS3N and PNPSF3 the fault coverage equal to 83.38%. Moreover, n transparent verson of MPS3N, testng procedure can be nterrupted by the system at any tme due to the preservng the ntal memory contents at any stage of testng. In the case of MATS test, the ntal contents wll be at the end of test procedure. However the bg drawbac of MPS3N test s that t doesn t allow to detect address decoder faults whch are detectable by MATS test. The smple soluton of ths problem s to add to the test sesson, whch s based on MPS3N test, one teraton of MATS test or another very short test whch can detect address decoder faults. Acnowledgement Ths wor was supported by the Rector of Balysto Unversty of Technology and the Dean of Faculty of Computer Scence at Balysto Unversty of Technology grant number: S/WI/6/08.

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