••• National Research
`
`Council Canada
`
`Ottawa, Canada
`K1AOR6
`
`Consell national
`de recherches Canada
`
`Ottawa, Ontario
`K1AOR6
`
`==~
`
`Registration No. 5435
`
`Port paye a Ottawa
`Coomer de deuxieme c1asse
`Enregistrement no 5435
`
`."'fllll~~y 1t'1
`
`'
`
`Canadian Journal of
`Physics
`Volume67
`
`Number4
`
`April1989
`
`Journal canadien de
`physique
`Volume67
`numero4
`
`avril1989
`
`Proceedings of the Fourth Canadian Semiconductor Technology Conference
`
`Compte rendu de Ia quatrieme conference canadienne sur Ia technologie des semi-conducteurs
`
`James B. Webb and John L. Brebner
`
`173 Organizers Comments/Commentaires des organisateurs
`
`Lynnette D. Madsen and Jacques S. Mercier
`
`174 Rapid densification of borophosphosilicate glass
`
`E. P. Keyes and N. G. Tarr
`
`179 Effect of annealing on polysilicon emitter transistors
`
`M. Parameswaran, Lj. Rjstic, A. C. Dhaded,
`H. P. Baltes, W. Allegretto, and A. M. Robinson
`
`184 Fabrication of micro bridges in standard complementary metal oxide
`semiconductor technology
`
`S. Blain, J. E. Klemberg-Sapieha,
`M. R. Wertheimer, and S. C. Gujrathi
`
`190 Silicon oxynitride from microwave plasma: fabrication and
`characterization
`
`R. D. Audas and D. E. Brodie
`
`195 Fabrication of devices using vacuum deposited a-Si
`
`M. Simard Normandin, I. Emesh, G. D' Asti,
`A. C. de Wilton, and N. Pearce
`
`199 Characterization of silicon oxide films deposited using
`tetraethy lorthosilicate
`
`Lj. Ristic, T. Q. Truong, M. Doan,
`D. Mladenovic, and H. P. Baltes
`
`207
`
`Influence of surface effects on the sensitivity of magnetic-field
`sensors
`
`W. Allegretto, A. Nathan, K. Chao,
`and H. P. Baltes
`
`212 Two-dimensional numerical simulations of electrothermal behav(cid:173)
`iour in very large scale integrated contacts and vias
`
`B. P. C. Tsou, Kan M. Chu, and D. L. Pulfrey
`
`218
`
`Series resistance calculations for polysilicon tunnel junction emit(cid:173)
`ter transistors
`
`Zarrin Ghaemi
`
`221 Application of data screening to the characterization of integrated
`circuits
`
`D. A. Davidson and 0. Berolo
`
`225 GaAs charge-coupled devices
`
`A. J. Howard, T. J. Anderson, S. Larochelle,
`I. C. Bassignana, P. Mandeville,
`and M. N. Svilans
`
`232 Electrically active multilayer n-GaAs-p-AlGaAs quarter wave
`mirrors grown by molecular beam epitaxy
`
`D. J. Day, M. Trudeau, S. P. McAlister,
`and C. M. Hurd
`
`238
`
`Instability and gate voltage noise in GaAs metal-semiconductor
`field-effect transistors
`
`T. Steiner, Yo Zhang, S. Charbonneau,
`A. Villemaire, M. L. W. Thewalt, M. Maciaszek,
`and R. P. Bolt
`
`242 Optical techniques for characterizing SI GaAs
`
`(Continued on inside back cover I Lire la suite ala page 3 de la couverture)
`Printed in Canada by I Imprime au Canada Pl!f The Runge Press Limited
`
`

`

`221
`
`Application of data screening to the characterization of integrated circuits
`
`ZARRIN GHAEMI
`Northern Telecom Electronics Limited, P.O. Box 3511, Station C, Ottawa, Ont., Canada KJY 4H7
`Received August 11, 1988
`
`Large amounts of integrated-circuit test data may be too great to be analysed by (human) visual graph inspection, and must
`be inspected by an automatic method. In this paper, a method called data screening is described. Data screening automatically
`identifies the presence of abnormalities (unexpected clusters and (or) outliers) in sets of test data, and has been implemented
`in a program in a statistical software package called Enhansys. The method has been used on actual test data with good results.
`
`Les ensembles de donnees resultant des tests effectues sur les circuits integres peuvent devenir trop considerables pour etre
`analyses par inspection visuelle (humaine) de graphiques et doivent alors etre examines par des moyens automatiques. Dans
`cet article, une methode appelee «data screening» est decrite. Cette methode identifie, de fac;on automatique, Ia presence
`d'anomalies (groupements ou ecarts inattendus) dans les ensembles de resultats de tests. Elle a ete mise en reuvre sous forme
`d'un programme inclus dans un ensemble de logiciels statistiques denomme «Enhansys». Son application a des ensembles de
`resultats de tests a donne de bons resultats.
`
`[Traduit par Ia revue]
`
`Can. J. Phys. 67, 221 (1989)
`
`1. Introduction
`Typically, assessment of integrated-circuit (device) manu(cid:173)
`facturability is done by characterizing a sample of the devices
`(called the characterization devices) fabricated under typical
`production conditions before they are introduced into manufac(cid:173)
`turing. Assessment is done by applying a large number of tests
`to the characterization devices while varying the input voltage
`and ambient temperature. Specifically, the characterization
`devices are tested at room nominal (RN) and extreme condi(cid:173)
`tions, i.e., low (L) and high (H) voltage and temperature com(cid:173)
`binations: LH, HL, HH, and LL. These five combinations are
`applied to each device in the sample, and its response is
`recorded. These raw test data from each of the devices in the
`sample are then used by a product engineer to characterize the
`entire sample of devices. The analysis starts (see Fig. 8 for
`example), by first plotting this data on a graph showing extreme
`conditions against nominal conditions where each point rep(cid:173)
`resents the test results of one device.
`To ensure an accurate characterization, one should do an
`analysis on data generated under a rea~onably uniform and con(cid:173)
`trolled environment. It is assumed that all the characterization
`devices are tested under the same conditions, and therefore the
`test results are a good representation of device behavior. In
`practice, this assumption is acceptable if the factors causing the
`test results to deviate from the true value are either known or
`have negligible significance. However, in actual device testing
`there may be many unknown conditions or variables (such as
`human errors) that could cause erroneous test results. For exam(cid:173)
`ple, the test machine may malfunction, or the test program may
`not accurately record or measure the performance of the device.
`Of course, it is also possible for the computer to mess up the
`results before they get to the product engineer.
`To recognize',data that are a good representation of device
`behavior from those which are not, one should scan through
`the data and use common sense and engineering judgment. One
`common and simple method used to scan the data is to plot
`them (for example, by histogram or scatter diagram) and then
`visually inspect the result. Most of the data naturally tend to
`group into a cluster (see Fig. 1), but some abnormalities may
`appear. Common abnormalites are clusters (a large group of
`
`Printed in Canada/lmprime au canada
`
`points lying outside the main group, see Fig. 2.) and outliers
`(one or several points lying outside the main group, see Fig. 3).
`Visual inspection is a reasonable approach if there are not
`too many plots to examine. It is, however, subject to human
`error, and it is time consuming if a large number of tests are
`done on a device. Automatic data screening is introduced to
`minimize this problem. The raw test data are run through a
`program written in a statistical software package called Enhan(cid:173)
`sys. This minimizes the time and effort used in detecting abnor(cid:173)
`malities in the data.
`In this paper, we discuss how a data-screening method is
`applied to the raw test data obtained from the testing of inte(cid:173)
`grated circuit devices. Data screening is then followed by a
`statistical procedure to determine guard bands (1, 2).
`
`2. Data screening
`The data-screening method described in this paper uses sta(cid:173)
`tistical coefficients, i.e., the correlation coefficient, the kur(cid:173)
`tosis coefficient, the skewness coefficient, as well as statistical
`variables, i.e., mean and standard deviation, to detect abnor(cid:173)
`malities. Seven data-screening pattern (DSP) types have been
`identified in measured raw test data: normal (Fig. 1), cluster
`out (Fig. 2), multicluster-horizontal outlier (Fig. 3), shotgun
`(or equally spaced, Fig. 4), multicluster-comer outlier (Fig.
`5), shotgun-multicluster (Fig. 6), or two cluster- comer out(cid:173)
`lier (Fig. 7). The pattern type is important because it suggests
`the cause of the abnormality.
`By assuming that the raw test data has a normal (Gaussian)
`distribution, we find that a set of raw test data can be classified
`using the function
`[1] DSP = f(sw,b' sn, mw,b• mn, Cc, C8 , Ck)
`where mw,b and sw,b are the mean and standard deviation of the
`worst (w) or best (b) cases of the tests at extreme conditions,
`mn and sn are the mean and standard deviation of the tests at
`nominal conditions, Cc is the correlation coefficient, c. is the
`skewness coefficient, and Ck is the kurtosis coefficient. The
`means mw,b and mn are used only if sw,b = sn = 0. These coef(cid:173)
`ficients Cc, c., and Ck embed test, manufacturing process,
`device, and design variation. For each data set, the statistics
`
`I ..
`
`

`

`222
`
`CAN. J. PHYS. VOL. 67, 1989
`
`c
`R 9
`0
`9 X
`n
`s
`t
`r d
`u
`I
`9
`t m
`e
`
`i
`o
`n
`
`a
`t
`
`.,.
`
`)(
`
`)(
`xX : x
`xx ~ xx
`~)()()(~
`,_x>l'C
`
`)(
`
`)(
`
`)(
`
`)(
`
`)(
`
`- x>l'C
`
`Flo. l.A normal pattern.
`
`Resuh at nominal
`conditions
`
`EC
`X 0
`t n
`r d
`e i
`mt
`e i
`0
`n
`s
`
`X
`Xxxx
`)( )(
`
`)(
`)( )(
`)(
`X X
`)( )(
`
`)(
`
`Nominal
`Conditions
`FIG. 2. A cluster out pattern.
`
`E
`X 0
`t n
`r d
`e i
`mt
`e i
`0
`n
`s
`
`EC
`X 0
`t n
`r d
`e i
`mt
`e
`
`0
`n
`
`X
`
`X
`
`X
`
`X
`
`X
`
`X
`
`X
`
`X
`
`X
`
`X
`
`X
`
`)(
`
`)(
`
`)( X
`
`X
`
`Nominal
`Conditions
`
`)(
`X
`
`)(
`)(
`
`)(
`
`X
`
`X
`
`X
`
`X
`xxXx
`XX X
`X
`)(
`
`)(
`
`EC
`X 0
`t n
`r d
`e i
`mt
`e i
`0
`n
`s
`
`)(
`
`)(
`)(
`
`)(
`)(
`X
`
`)(
`
`Nominal
`Conditions
`FIG. 3. A multicluster- horizontal outlier pattern.
`
`sw,b' sn, mw,b• mn, Cc, C 8 , and Ck are easily computed, and from
`these a decision as to the DSP type can be made.
`Although the DSP function may not properly classify pat(cid:173)
`terns that are marginal or mixed, this has not been a problem
`because the primary goal of the function is to detect abnor(cid:173)
`mality. Once this is done, the pattern types can be identified
`and then the raw test data can be grouped according to the pat(cid:173)
`tern they form so that they may be easily identified.
`The following figures show some of the DSP types that can
`be detected by applying this method. The horizontal (X) axis
`is the nominal condition and the vertical ( Y) axis is the best or
`worst (extreme) condition. This decision is made by testing if
`the above statistical variables are within certain limits. The
`given limits provide good results, but they can be improved
`with further tuning. Note that the standard deviations sn and
`sw,b cannot be zero, because all data in this case would be the
`same. In this case, the distribution would not be normal (Gaus(cid:173)
`sian). Hence, for all the patterns below,
`
`s'------------
`
`Nominal
`Conditions
`FIG. 4. A shotgun or equally spaced pattern.
`
`)( X
`)( xx
`X X
`)(
`
`EC
`X 0
`n
`r d
`e i
`mt
`e i
`0
`n
`s '----------------------------
`Nominal
`Conditions
`Flo. 5. A multicluster- comer outlier pattern.
`
`X
`
`EC
`X 0
`t n
`r d
`e i
`mt
`e
`
`X
`
`)(
`
`X
`
`0
`n
`
`)(
`
`)(
`
`)(
`
`)(
`)(
`
`X
`
`)(
`
`X
`
`)(
`
`X
`
`X
`
`)(
`
`)(
`X
`
`X
`
`s'-----------------------
`
`Nominal
`Conditions
`FIG. 6. A shotgun - multicluster pattern.
`
`A normal pattern (Fig. 1) indicates that the data does not
`contain any outlier(s) or any noticeable cluster(s). The follow-
`
`b
`
`

`

`223
`
`..
`
`GHAEMI ET AL.
`
`1.7
`
`(/) 1.6
`c
`0
`~ c
`
`0
`(.)
`Q) 1.5
`E
`
`~ x w
`
`1.4
`
`1-
`
`1.3
`
`I
`1.15
`
`I
`1.20
`
`I
`I
`1.35
`1.30
`1.25
`Nominal condition
`Fro. 10. Same as Fig. 8 but shotgun - multicluster pattern.
`
`I
`1.40
`
`I
`
`1.45
`
`EC
`X 0
`n
`r d
`e i
`mt
`i
`e
`0
`
`)(
`
`)(
`)(
`
`)(
`
`)(
`
`)(
`
`)(
`
`)(
`X
`
`)(
`
`)(
`)(
`
`n s'---------------
`
`Nominal
`Conditions
`Fro. 7. A two cluster- corner outlier pattern.
`
`0.11 f-
`
`0.10 -
`
`0.09 f--
`
`0.08 f--
`
`(/) c
`~
`1:l c
`0
`(.)
`Q)
`
`E
`~ x w
`
`. . .
`
`..
`
`....
`
`4.34 f--
`
`4.32 f--
`
`(/) c
`0
`~ 4.30
`c
`0
`(.)
`Q) 4.28
`E
`
`~ w 4.26 c-
`
`4.24
`
`4.22
`
`4.62
`
`I
`4.63
`
`I
`4.64
`4.65
`Nominal condition
`Fro. 11. Same as Fig. 8 but shotgun - multicluster pattern.
`
`I
`4.66
`
`I
`
`4.67
`
`0.07
`
`0.05
`
`0.06
`
`I
`0,07
`Nominal condition
`Fro. 8. Actual raw test data with the DSP pattern type identified by
`the program. Two cluster - corner outlier pattern.
`
`I
`0.08
`
`I
`
`I
`0.09
`
`5.8
`
`5.6
`
`(/) 5.4 f--
`c
`0
`~ 5.2 f--
`c
`0
`(.)
`Q)
`
`E 5.0
`
`~ x w
`
`4.8
`
`4.6
`
`4.41-
`
`3.2
`
`:
`
`...
`..
`
`I
`
`I
`3.4
`
`4.0
`3.8
`3.6
`Nominal condition
`Fro. 9. Same as Fig. 8 but normal pattern.
`
`4.2
`
`0.005 1-
`
`0.004
`
`(/) c
`~
`1:l
`§
`~ 0.003 -
`E
`~
`;B
`
`0.002
`
`I
`
`4.4
`
`ing conditions must be true to get this pattern:
`cs < 0.9,
`0.9 < cc < 1,
`
`or
`
`cs < 0.9,
`2.2 < ck < 4
`0.9 < cc < 1,
`A cluster out pattern (Fig. 2) indicates the existence of mul(cid:173)
`tiple clusters. Here,
`0.5 > cs > 0.9,
`cc < 0.8,
`
`0.00 1 f--L-'--I __ J_I_j_I_.J._
`I_.J._I_j_I_J_I_.!,._._.!...-1_-l
`0.003
`0.000
`0.001
`0.002
`Nominal condition
`Fro. 12. Same as Fig. 9 but cluster out pattern.
`
`0.004
`
`A multicluster- horizontal outlier pattern (Fig. 3) indicates
`the existence of a cluster(s) or horizontal outlier(s). Here,
`cs > 1.5,
`cc < 0.5,
`A shotgun or equally spaced pattern (Fig. 4) indicates no
`correlation, outliers, or clusters. Here,
`
`

`

`CAN. J. PHYS. VOL. 67, 1989
`
`224
`
`0.0015
`
`f--
`
`Ul c::
`~ 0.0010
`"C c::
`8
`
`Q) J 0.0005
`
`cs < 1.5,
`cc < 0.5,
`A multicluster - comer outlier pattern (Fig. 5) indicates the
`existence of a cluster(s) or comer outliers. Here,
`cs > 0.8,
`0.6 < cc < 1.0,
`A shotgun-multicluster pattern (Fig. 6) indicates the exist(cid:173)
`ence of a parallel cluster or the existence of the shotgun pattern.
`Here,
`cs < 0.9,
`0.5 < cc < 0.8,
`A two cluster - comer outlier pattern (Fig. 7) indicates the
`existence of two clusters forming a normal (Gaussian) distri(cid:173)
`bution or comer outliers, where
`cs < 0.9,
`0.9 < cc < 1.0,
`
`2 < ck < 2.2
`
`3. Application of the data-screening pattern using
`measured raw test data
`This method has been implemented in a computer program
`written for a statistical package (called Enhansys). Actual raw
`test data are shown in Figs. 8-15, with DSP pattern types auto(cid:173)
`matically identified by the program. This is implemented by
`supplying the data to the program and then applying the DSP
`function [1].
`
`4. Conclusions
`An automatic data-screening method has been presented that
`detects abnormalities (clusters and outliers) in data. The method
`uses statistical coefficients (correlation coefficient, kurtosis
`coefficient, and skewness coefficient) and variables (mean and
`standard deviation) to identify these abnormalities. The method
`has been implemented in a computer program written in a sta(cid:173)
`tistical software package called Enhansys. It has been shown
`to work on real (measured) raw test data by properly identifying
`certain types of patterns in the data. This method provides an
`essential engineering tool by significantly reducing the time and
`effort required to identify abnormalities in raw test data, when
`dealing with a large amount of data. This is useful when dealing
`with the characterization of devices in a manufacturing
`environment.
`
`Acknowledgments
`I would like to thank William Bird, Edward Jones, Tomy
`Issa, John Noguera, Martine Simard-Normandin, and Atique
`Siddiqui for all their valuable comments and assistance in the
`implementation of this method and in the preparation of this
`paper.
`
`1. J. G. NoGUERA AND D. T. AMM. Proceedings of the IEEE Custom
`Intergrated Circuits Conference, Rochester, NY. May 12-15,
`1986.
`2. WILLIAM D. HEAVLIN. Proceedings of the Sernicon West Confer(cid:173)
`ence, San Mateo, CA. May 19-21, 1987.
`
`d
`
`0.0000 ~-__L _
`0.000
`
`__L _
`0.001
`
`___i _
`
`___i _
`
`___ll _ __[ _
`___l _
`0.003
`0.002
`Nominal condition
`Fro. 13. Same as Fig. 8 but cluster out pattern.
`
`__[l __ _j
`0.004
`
`20 f--
`
`Ul c::
`0
`:E 15
`"C c::
`0 u
`Q)
`E
`~
`;B 10
`
`5 - I
`
`I
`
`I
`
`1.2
`
`1.3
`
`1.4
`Nominal condition
`Fro. 14. Same as Fig. 8 but multicluster- horizontal outlier pattern.
`
`1.5
`
`1.6
`
`-3.30 1-
`
`1-
`
`Ul c::
`,g -3 35 f-(cid:173)
`'8
`.
`c::
`0 u
`Q)
`E
`Q)
`~ w -3.40 f--
`
`f--
`
`i
`- 3·45 f--1
`I
`I
`I
`I
`I
`LL---L--~--~--~--L_-~_j
`-3.30
`-3.40
`-3.35
`-3.45
`Nominal condition
`Flo. 15. Same as Fig. 8 but equally spaced pattern.
`
`