LASER: A LAyout Sensitivity ExploreR Report and User's Manual
Contents
1. Research Report ISSN 0167 9708 Coden TEUEDE Faculty of Elec LASER A LAyout Sensitivity ExploreR Report and User s Manual by Jose Pineda de Gyvez EUT Report 89 E 216 ISBN 90 6144 216 8 March 1989 Eindhoven University of Technology Research Reports EINDHOVEN UNIVERSITY OF TECHNOLOGY Faculty of Electrical Engineering Eindhoven The Netherlands ISSN 0167 9708 Coden TEUEDE LASER A LAyout Sensitivity ExploreR Report and User s Manual by Jose Pineda de Gyvez EUT Report 89 E 216 ISBN 90 6144 216 8 Eindhoven March 1989 CIP GEGEVENS KONINKLIJKE BIBLIOTHEEK DEN HAAG Pineda de Gyvez J LASER a layout sensitivity explorer Report and user s manual by J Pineda de Gyvez Eindhoven University of Technology Faculty of Electrical Engineering Fig EUT report ISSN 0167 9708 89 E 216 Met lit opg reg ISBN 90 6144 216 8 SISO 663 42 UDC 621 382 681 3 06 NUGI 832 Trefw elektronische schakelingen computer aided design iii Abstract As the IC pattern resolutions tend to become smaller the layout geometry plays a more important role in IC yield The probability that a chip will fail is directly related to the way that the IC artwork is laid out By examining the possible places where catastrophic defects may occur one can prevent potential faults and thus estimate the reliability of the design Rrealistic yield simulation tools must con2. LASER User s Manual AD H WN CONTENTS USER s MANUAL 1 1 USER INTERFACE MAIN OPTIONS LAYOUT MASK e bm NS NR MEE A SG ARA ANALYSIS DIAGNOSTICS AND TROUBLESHOOTING 7 1 USER DIAGNOSTICS 7 2 SYSTEM DIAGNOSTICS pd 000000 d A TA A w Sie LIST OF FIGURES Figure 1 Main options of the system Figure 2 Selection of layouts Figure 3 Selection of masks 2 Figure 4 View menu Figure 5 Options for analysis zl nA nA P uy 1 USER s MANUAL LASER LAyout Sensitivity ExploreR is a system for IC layout yield prediction due to catastrophic spot defects The system finds interactively the critical regions susceptible to local deformations and computes also the layout sensitivity The user can adjust the defect size distribution according to the manufacturing environments in order to find the probability of failure of the artwork Once that the POF is found the yield of the artwork for a span of defect densisities in number of defects per cm2 can be computed Defect clustering can also be taken into account 1 1 USER INTERFACE LASER assumes that the current directory contains the layouts to be analysed Each mask in the layout is treated independently of the others and defects are modelled as squares MOUSE INTERFACE LASER is a highly interactive system that makes use of mouse based interface systems The l
3. Ferguson Inductive fault analysis of MOS integrated circuits IEEE Des amp Test Comput Vol 2 No 6 Dec 1985 p 13 26 Walker H and S W Director VLASIC A catastrophic fault yield simulator for integrated circuits IEEE Trans Comput Aided Des Integrated Circuits Syst Vol CAD 5 1986 p 541 556 Pineda de Gyvez J and J A G Jess On the definition of critical areas for IC photolithographic spot devices Paper at lst European Test Conf Paris 12 14 April 1989 Organized by Soci t des Electriciens et des Electroniciens 48 rue de la Procession F 75724 Paris Cedex 15 Maly W Modeling of lithography related yield losses for CAD of VLSI circuits IEEE Trans Comput Aided Des Integrated Circuits amp Syst Vol CAD 4 1985 p 166 177 Chen I and A J Strojwas Realistic yield simulation for IC structural failures In Digest of Technical Papers 4th IEEE Int Conf on Computer Aided Design ICCAD 86 Santa Clara Cal 11 13 Nov 1986 New York IEEE 1986 P 220 223 Ferris Prabhu A V Role of defect size distributions in yield modeling IEEE Trans Electron Devices Vol ED 32 1985 p 1727 1736 Bentley J L and T A Ottmann Algorithms for reporting and counting geometric intersections IEEE Trans Comput Vol C 28 1979 p 643 647 11 12 13 14 15 16 17 18 29 Preparata F P and M I Shamos Computational geometry An introducti
4. does We selected three different defect size distributions one for each mask in manufacturing lines the defect size distributions are seldom the same for all the masks see Fig 18 We made on purpose the distribution for the diffusion mask have a 293 long tail for large defect sizes the distribution for the poly mask to peak at defects larger than the minimum resolution of 6 um and finally the one for the metal mask to represent a mature process Prob Density Function 0 2 METAL POLY O 10 20 30 40 50 60 70 80 90 100 Defect Size in um Figure 18 Defect Size Distribution 0 15 0 1 0 05 The layout probability of failure for bridges and cuts is shown in Figs 19 and 20 Metal Mask BRIDGES Something that is worthwhile noticing here is the similitude in the POFs of the PLA and STD It is customary to think that the larger the layout the more likely to fail In fact the curves show the contrary The explanation to this is because the PLA uses long lines in a very uniform patron even when sometimes they are used to connect just one transistor This style increases the risk of catching unnecessary defects along the lines The STD uses the lines also to interconnect however they are not in a regular style and furthermore there are many empty spaces among them The right shift in the curve of the TM with respect to the other two confirms its safeness for smali defects Although for large defects it is q
5. left determine the predecessor edge of predecessor m the polygon edge IF m left gt p right determine the successor edge and Successor m exit the search BREAK if the polygon edge intersects the stored edge IF pinm if the id s of the edges are different make a susceptible site and reinstall the nonintersected f sections of the retrieved edge IF p id m id S amp MAKE SITE MAX p left m left MIN p right m right m top pi bottom sweep Mem mnp make possible susceptible sites at the extremes of the polygon edge IF predecessor S MAKE SITE predecessor right p left predecessor top pi bottom CORNER IF successor S MAKE SITE p right successor left successor top pi bottom CORNER Figure 8 Creation of susceptible sites for bridges The extraction of susceptible sites for breaks is essentially the same except that in the algorithm the END line segments are the ones that are stored in the data structure M and instead of processing line segments of different id s the id s must be the same In some situations the algorithm will apparently find the same critical region for both vertical and horizontal sweeps This is because we assumed that the sender terminals can be either vertical or horizontal Recall from our example of Fig 3 that a simple cond
6. critical area is twice as much to be precise in the form of a cross as shown in Fig 18 The PLA shows again a steep slope due to the regularity in its layout The STD proofs to be the best for large defects due to the empty spaces Diffusion Mask CUTS In the STD approach the use of gates makes the ratio of the transistors bigger in order to compensate delays This results in wider patterns which are less likely to be cut by small defects a fact which is reflected in its sensitivity The PLA s and TM s sensitivities are very similar due to the reasons explained above The sensitivity analysis gives an insight of the way the masks are laid out It reveals the endurance of the masks for different defect sizes However the probability of occurrence of each defect size is not the same Furthermore the probability that a defect of a very large size occurs is almost neglectable and hence the sensitivity analysis cannot reflect what would happen to the layout in a manufacturing 2 Metal Mask Sensitivity CUTS 1 9 8 7 6 3 A 3 2 AG a 0 10 20 30 40 50 60 70 80 90 100 Defect Size in um Poly Mask Sensitivity CUTS Hbb an aneion a 0 10 20 30 40 50 60 70 80 90 100 Defect Size in um Diffusion Mask Sensitivity CUTS OM L BD zl Ev 6 19 20 30 40 50 60 70 80 90 10 Defect Size in um Figure 17 Layout sensitivity to cuts environment whereas the layout probability of failure POF
7. for an NMOS technology of 6um of minimum resolution features Table 1 shows the total area and dimensions of each layout in um units Ee ka F TTER metal poly diffusion Figure 14 a PLA b TM c STD To give the reader a feeling of how the critical regions are displayed we show in Fig 15 the poly layer of the TM and its critical regions for bridges and cuts for defect sizes of 30um and 12um respectively We analysed each layout for defects in the range from 1 to 100um The sensitivities for bridges and cuts of each mask are shown in Figs 16 and 17 respectively TABLE 1 Layout dimensions Layout PLA 767 TM 453 STD 771 Vertical Dim 18 Horizontal Dim 503 390 756 Figure 15 Critical regions are shown in black a Bridges b Cuts Area 385801 176670 582876 19 Metal Mask Sensitivity BRIDGES O 10 20 30 40 50 60 70 80 90 100 Defect Size in um Poly Mask Sensitivity BRIDGES er Ny bk Dn ZA D M 0 10 20 30 40 50 60 70 80 100 Defect Size in um Diffusion Mask Sensitivity BRIDGES e cn H wp E A xo 0 10 20 30 40 50 60 70 80 9 100 Defect Size in um Figure 16 Layout Sensitivity for bridges From the figures we can observe the following Metal Mask BRIDGES The TM is the best compromise for small defects in the range from 6 to more or less 15pm This is mainly because it is the smallest layout and thus the total cr
8. regions A brief example helps to visualize this Assume that we have a pattern of length a and width 2a as shown in Fig 3a If the current is injected at the left side of the pattern and received at the right side then a defect of size x such that a lt x lt 2a will not introduce a fault even if it completely cuts the pattern in the vertical direction The reason why is because there is still continuity between the terminals where the current is injected and where it is expected to arrive In this case only defects of size x gt 2a can introduce a fault and the critical areas would be in the horizontal direction as depictured in Fig 3b Assume now that the current is injected at the top and received at the bottom of the pattern For this situation defects of size x gt a are fatal because the pattern can be broken in two nonequipotential regions if the defect is situated anywhere along the critical area depictured in Fig 3c b Figure 3 Two different critical areas a a single conductor b Critical area if the current is applied at the left or right side of the pattern c Critical area when the current is applied at the top or bottom of the pattern We denote the terminals where the current is applied as senders and the terminals that the current has to reach as receivers These terminals play an important role in our solution to the problem of finding the critical areas as it will be seen later 3 FINDING THE LAYOUT CRITICAL AR
9. size calculate the magnitude that the edges of the susceptible sites have to be shrinked depending upon in which swecp was the susceptible site found take an action shrink the abscissae if they intersect form a critical region c top 5 top displace Cldefect_size lec BREAK VERTICAL c bottom s top displace c top s bottom displace if c bottom lt c top I c left s left displace c right s right displace Cldefect size le BREAK CORNER c left s right displace c right 5 left displace c bottom sS top displace c top s bottom displace if c left lt c right Ac bottom lt c top Cldefect_size c BREAK shrink the ordinates if they intersect form a critical region shrink the abscissae and the ordinates if the abscissae intersect each other and the ordinates also do form a critical region Figure 11 Creation of critical regions scan position is updated everytime that the top of a rectangle is found The scanning stops when the top of the critical mask is reached We denote the bottom of a critical region as V_BEGIN and the top as V END Let C cy Cn be the set of line segments of the critical regions in ascending y order M the order relation of line segments sorted in ascending x order The main loop of the algorithm sweeps a scanl
10. the layout and that in fact the critical regions compose a critical mask specifically for the defect size in turn The algorithm is shown in Fig 11 see page 12 It would have been nice if it were possible to compute the critical area immediately after every critical region was found just by finding the area of the rectangle However this is not possible because the critical areas tend to overlap and it is necessary to compensate the total critical area by subtracting the area of even number of overlaps and by adding the area of odd number of overlaps see Fig 12 This implies book keeping of overlaps and every time search for intersections These kind of problems belong to the area of computational geometry and for a vast number of examples the reader is referred to 11 A simple way to overcome the bookkeping of intersections is to use once more a scanline algorithm Area A B C AnB ANC BnC AnNBne Figure 12 Overlapping regions in the computation of critical areas The algorithm runs a scanline from the bottom to the top of the critical mask and computes the area of all the rectangle s sections that lie between the previous scanline position and the current position The FOREACH defect_size displace defect_size 2 FOREACH sjeS SWITCH s label HORIZONTAL c left s right displace c right s left displace if c left lt c right I c bottom s bottom displace 12 for each defect
11. 4 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 Figure 22 LIST OF FIGURES Pattern sensitive area for shorts Pattern sensitive area for breaks Two different critical areas a a single conductor b Critical area if the current is applied at the left or right side of the pattern c Critical area when the current is applied at the top or bottom of the pattern We lt a Forming the critical areas geometrically by modifying the edges of the patterns a Bridges b Cuts O Hes ces cae Ee The critical areas for both bridges and cuts are found by shrinking the susceptibles sites r Susceptible sites for bridges Susceptible sites for cuts a The sender terminals are on the top and lower right end b The sender terminals are on the bottom and left side Creation of susceptible sites for bridges Creating critical regions for bridges from their susceptible sites a Susceptible sites from the vertical sweep b Susceptible sites from the horizontal sweep c Critical regions formed EE ae ee Creating critical regions for cuts from their susceptible sites a Susceptible sites from the vertical sweep b Susceptible sites from the horizontal sweep c Critical regions formede cal 18 AE eS we ae EE ENEE Overlapping regions in the computation of critical areas Creation of critical regions Computation of the critical areas PLA OJ IM c STD s e ak Sw E n Critical regions ar
12. EAS A great deal of computational efforts can be saved if the critical areas are found geometrically rather than analytically Under the geometrical approach 12 13 the critical areas for bridges are found by expanding each pattern by an amount equal to half of the defect size and then by comparing if the expansions intersect If so then the amount of intersection corresponds to the critical area between the patterns see Fig 4a In the case of critical areas for cuts every pattern is shrinked by half of the defect size and a critical area is established only when the shrinked edges intersect each other see Fig 4b critical area critical aree defect b Figure 4 Forming the critical areas geometrically by modifying the edges of the patterns a Bridges b Cuts The simplest way to extract the critical areas for bridges is to compare a pattern against all the other patterns but this is computationally prohibitive Also the expansion of the patterns implies that a layout extraction has to be executed for each defect size For the areas sensitive to cuts the problem is simpler since no neighbour patterns are necessary Hence the problem is reduced to shrink the patterns and to search for intersections among them like corners or overlaps Our algorithm is based on the geometrical approach explained above However instead of proceeding directly to establish the critical areas we determine first the regions where a defect of an
13. G EXTREMUM CONTROL BASED ON COMPARISON OF MEASURED AND ESTIMATED VALUE EUT Report 88 E 197 1988 ISBN 90 6144 197 8 198 Liu Wen Jiang AN EXTREMUM HUNTING METHOD USING PSEUDO RANDOM BINARY SIGNAL EUT Report 88 E 198 1988 ISBN 90 6144 198 6 199 J wiak L THE FULL DECOMPOSITION OF SEQUENTIAL MACHINES WITH THE OUTPUT BEHAVIOUR REALIZATION EUT Report 88 E 199 1988 ISBN 90 6144 199 4 200 Huis in t Veld R J A FORMALISM TO DESCRIBE CONCURRENT NON DETERMINISTIC SYSTEMS AND AN APPLICATION OF IT BY ANALYSING SYSTEMS FOR DANGER OF DEADLOCK EUT Report 88 E 200 1988 ISBN 90 6144 200 1 201 Woudenberg H van and R van den Born HARDWARE Biwer WITH THE AID OF DYNAMIC PROGRAMMING EUT Report 88 201 1988 ISBN 90 6144 201 X 202 Engelshoven R J van and R van den Born COST CALCULATION FOR INCREMENTAL HARDWARE SYNTHESIS EUT Report 88 E 202 1988 ISBN 90 6144 202 8 203 Delissen J G M THE LINEAR REGRESSION MODEL Model structure selection and biased estimators EUT Report 88 E 203 1988 ISBN 90 6144 203 6 204 Kalasek V K i COMPARISON OF AN ANALYTICAL STUDY AND EMTP IMPLEMENTATION OF COMPLICATED THREE PHASE SCHEMES FOR REACTOR INTERRUPTION EUT Report 88 E 204 1988 ISBN 90 6144 204 4 Eindhoven University of Technolo Research Reports ISSN 0167 9708 Faculty of Electrical Engineering Coden TEUEDE 205 206 207 208 209 210 211 212 213 214 215 Butterweck
14. H J and J H F Ritzerfeld M J Werter FINITE WORDLENGTH EFFECTS IN DIGITAL FILTERS A review EUT Report 88 E 205 1988 ISBN 90 6144 205 2 Bolten M H J and G A P Jacobs EXTENSIVE TESTING OF AN ALGORTTHM FOR TRAVELLING WAVE BASED DIRECTIONAL DETECTION AND PHASE SELECTION BY USING TWONFIL AND EMTP EUT Report 88 E 206 1988 ISBN 90 6144 206 0 Schuurman W and M P H Weenink STABILITY OF A TAYLOR RELAXED CYLINDRICAL PLASMA SEPARATED FROM THE WALL BY A VACUUM LAYER EUT Report 88 E 207 1988 ISBN 90 6144 207 9 Lucassen F H R and H H van de Ven A NOTATION CONVENTION IN RIGID ROBOT MODELLING EUT Report 88 E 208 1988 ISBN 90 6144 208 7 J zwiak L MINTMAL REALIZATION OF SEQUENTIAL MACHINES The method of maximal adjacencies EUT Report 88 E 209 1988 ISBN 90 6144 209 5 Lucassen F H R and H H van de Ven OPTIMAL BODY FIXED COORDINATE SYSTEMS IN NEWTON EULER MODELLING EUT Report 88 E 210 1988 ISBN 90 6144 210 9 Boom A J J van den Ho CONTROL An exploratory study EUT Report 88 E 211 1988 ISBN 90 6144 211 7 Zhu Yu Cai ON THE ROBUST STABILITY OF MIMO LINEAR FEEDBACK SYSTEMS EUT Report 88 E 212 1988 ISBN 90 6144 212 5 Zhu Yu Cai M H Driessen A A H Damen and P Eykhoff New SCHEME FOR IDENTIFICATION AND CONTROL EUT Report 88 E 213 1988 ISBN 90 6144 213 3 Bolten M H J and G A P Jacobs IMPLEMENTATION OF AN ALGORTTHM FOR TRAVELLING WAVE BASED DIRECTIONAL DETECTION EUT Report 89 E 214 1989 I
15. SBN 90 6144 214 1 Hoeijmakers M J en J M Vleeshouwers EEN MODEL VAN DE SYNCHRONE MACHINE MET GELIJKRICHTER GESCHIKT VOOR REGELDOELE INDEN EUT Report 89 E 215 1989 ISBN 90 6144 215 X
16. assigning unique identification numbers to every polygon For subsequent processing the boundary of the polygons is decomposed in line segments Each line segment inherits the identification number of the polygon We further classify the line segments in two types The vertical horizontal line segments at the bottom left of the polygon are of type BEGIN and the ones at the top right are of type END Each vertical line segment is specified by its x coordinate and the y values of the lower and upper endpoints Each horizontal line segment is similarly specified by its y coordinate and the x values of its left and right endpoints Finally we store the horizontal and vertical line segments in two different data structures We use a scanline algorithm 10 to extract the susceptible sites In each case we perform two opposite layout sweeps A bottom up sweep that covers all the susceptible sites parallel to the scanline and a left right sweep that encompasses all the sites parallel to this scanline The top down sweep or VERTICAL sweep scans the horizontal line segments The left right sweep or HORIZONTAL sweep the vertical ones As the algorithms for finding susceptible sites for bridges and cuts are very similar the explanation to follow is restricted to bridges Later we mention the changes to mend the same algorithm for cuts In each sweep a susceptible site is identified when a BEGIN line segment and an END line segment are parallel and adja
17. ave the critical regions for bridges 7 Cannot allocate space to save the critical regions for cuts 8 Cannot reallocate space to save the critical regions for bridges 9 Cannot reallocate space to save the critical regions for cuts 10 Cannot allocate space to save the critical areas for bridges 11 Cannot allocate space to save the critical areas for cuts 12 Cannot allocate space to save the layout probability of failure POP 13 Cannot allocate space to save the defect size for the layout POF 14 Cannot initialize data structure binary trees 15 Cannot insert member in the binary tree 16 Cannot allocate space to save the sensitivity to bridges 17 Cannot allocate space to save the sensitivity to cuts 18 Cannot allocate space to save the defect size for the defect size distr 19 Cannot allocate space to save the defect size distribution 20 Cannot allocate space to create susceptible sites 21 Cannot allocate space to initialize the colors of the layers 22 Cannot allocate space to display the set of layers on screen 23 Cannot allocate space to save the layers found in the tech file 24 Cannot allocate space to perform the horizontal sweep of the layout 25 Cannot allocate space to perform the vertical sweep of the layout 26 Cannot allocate space to save the defect density 27 Cannot allocate space to save the yield Eindhoven University of Technology Research Reports ISSN 0167 9708 aculty o lectrical Engi
18. cent to each other The susceptible sites have rectangular shape where the width is defined by the intersection of the BEGIN and END line segments and the length by the distance between the two line segments To cover possible bridges at the corners we also find the line segments immediately to the left and immediately to the right of the BEGIN line segment When a susceptible site is formed we label it as VERTICAL or HORIZONTAL depending on the sweep in which it was found An exception to this labeling is when the susceptible site was formed from a corner of the BEGIN line segment In this case we label the susceptible site as CORNER The justification of labeling the susceptible sites is because in step 2 we need to know what coordinates to shrink either the abscissae or the ordinates before we can deduce if a critical area is established Since the critical areas tend to grow as the defect size grows and thus to overlap each other there is no need to look for more neighbour line segments to form the susceptible sites This effect of overlapping of critical areas is known as the proximity effect 2 Let P pj 1 Pi ny be the set of polygon line segments in ascending y order M the order relation of line segments sorted in ascending x order and S a data structure to store the susceptible sites found The main loop of the algorithm sweeps a scanline through the set P We use the data structure M to store the END line segments ordered by t
19. d 1 Evidence exists 2 that there are programs for computing them however they have not been reported in the literature Also due to the complexity of the layouts several authors prefer to derive equivalent layouts to simplify the problem as is the case of the concept of virtual layouts introduced in 7 and the one of equivalent layouts in 8 It is desirable that a layout sensitivity extractor finds the critical areas for several defect sizes at the time Otherwise the system can be impractical from the efficiency point of view since each extraction costs the designer s time not to mention the computational resources involved Moreover one is usually interested in a range of defect sizes and not in solely one Up to now it was possible to find the critical areas for complex layouts using a statistical Monte Carlo simulation and analytical methodologies were restricted only to very regular and simple layouts We present a layout verifier capable of identifying the critical areas in complex layouts Unlikely to Monte Carlo approaches our methodology is based purely on the geometry of the patterns The implementation is based on a scanline algorithm and performs only one layout extraction for any span of defect sizes The extraction of critical areas forms part of a large system for IC layout yield estimation The system has capabilities to display the critical regions onscreen and provides facilities such as the computation of the layo
20. d that the system is constructing the layout If there are more layouts than the ones that are displayed move the cursor to the option and click the left button of the mouse To go back to the previous frame click in the option To go to the main menu click the left button anywhere in the display area Figure 2 Selection of layouts 4 MASK This option selects any of the masks existing in the current layout To pick up one mask move the cursor to its name and click the left button of the mouse If there are more masks than the ones that are displayed move the cursor to the I option and click the left button of the mouse To go back to the previous frame of masks click in the option To go to the main menu click the left button anywhere in the display area Figure 3 Selection of masks 5 VIEW This menu allows to zoom in and zoom out the layout mask Also if it is not necessary to analyse the whole layout it can be bounded in this menu If the layout is not bounded when going back to the main menu the display area will show again the original layout or mask Figure 4 View menu ZOOM IN This option allows to zoom in the layout or mask A cross at the top left corner of the screen appears Move the cross to the layout and click the left button A rubberbox appears Extend the box up to where the zoom operation is desired and then click the left button LASER will show the section of the layout enclosed in
21. e shown in black a Bridges b Cuts Layout Sensitivity for bridges Layout sensitivity to cuts Defect Size Distribution Layout Probability of Failure POF for bridges Layout Probability of failure POF for cuts Mask yield Final Layout yield 10 11 11 12 13 17 19 21 22 23 24 25 26 LASER Report 1 INTRODUCTION Traditional layout verification is the task of validating the design rules imposed by the technological process i e verifying the width of patterns the space between them etc Under this approach external sources that can lead to incorrect layouts are in most of the cases not taken into account These external sources manifest themselves in the form of layout contaminants i e undesired dust particles that drastically change the shape of a pattern and as a result the affected region is said to be a defect in the layout Nowadays the significance of these defects is crucial to the successful manufacturing of the chip in spite of a precise control of the line features As the processes tend to mature and to advance to smaller resolution features other forms of layout verfication become imperative One such form of verification is to foresee the artwork endurance in real manufacturing environments and a mean to achieve this is by finding the critical areas where a short or a break can happen in the layout Critical areas have a lot of potential due to the ease of predicting the IC artwork yiel
22. e will help to visualize the creation of critical areas Let us first consider the case of critical areas for bridges Assume that we have two L shaped conductors running parallel to each other with space s between them and that a defect of size s lt x lt L is placed among them The susceptible sites for bridges are identified as A and B Susceptible site A was obtained in the vertical sweep see Fig 9a thus their abscissae are shrinked Susceptible site B was obtained in the horizontal sweep see Fig 9b hence the ordinates are shrinked The resulting critical regions are shown in Fig 9c susceptible sites critical area a b Figure 9 Creating critical regions for bridges from their susceptible sites a Susceptible sites from the vertical sweep b Susceptible sites from the horizontal sweep c Critical regions formed Now let us consider the case of cuts for a conductor with also an L shape Fig 10a shows the susceptible sites A and B which were extracted during the vertical sweep Fig 10b shows the suceptible sites C and D extracted during the horizontal sweep For the former sites the abscissae are shrinked and for the latter sites the ordinates Fig 10c shows the critical areas for a defect of size w lt x lt L Notice that no critical area was established for the susceptible sites A and D The reason is because the shrinked edges for these sites do not overlap for the defect size If the defect size is of such a magnitude tha
23. ectrical meaning i e a via a transistor a wire etc Depending upon the structure the patterns in each mask have a significance other than simple conductores i e a poly pattern over a diffusion pattern form a transistor Therefore we distinguish two kinds of critical areas 6 1 Pattern Sensitive Area is the area where the center of a defect must fall to cause a fault to the pattern such as breaking it or joining it with another pattern 2 Structure Sensitive Area on the other hand is the area where the center of a defect must be situated in order to introduce a fault to a complete electrical structure like a transistor a via etc For layout verification purposes the first kind of sensitive areas are of interest Notice that these critical areas are more concerned with the layout rather than with the electrical circuit The fault models considered are only two namely the bridge undesired joined patterns the cut undesired broken patterns In our approach we find the critical areas per mask thus no interdependance between masks is considered It is difficult to model the shape of defects since in reality they are rough edged splotches Hence modeling defects as squares provides a solution that is sufficiently correct besides that the algorithms become much faster and simpler 2 1 PATTERN SENSITIVE AREA FOR BRIDGES Under the pattern approach all the patterns are considered as interconnectors and a fault appears o
24. eft button of the mouse is used to point at any of the options in the menus If the system is in critical mode it increments the defect size and the critical regions are displayed onscreen In this mode the middle button is used to decrement the defect size The right most button is used to exit the system by clicking it twice INPUT FORMAT The input to LASER consists of files describing the layout masks The layouts are for a Manhattan type of geometry and the layouts have to be flat i e no hierarchy is allowed The format is as follows lt mask_name gt x1 x2 yl y2 where mask name is the name of the mask x1 x2 yl y2 are the coordinates of the mask pattern The file s name must be lt file_name gt crt ERROR REPORT If there were errors in the input file LASER generates a file containing information of these errors i e that x2 was less than x1 etc The name of this file is laser error Mistakes committed during the session are reported in the interface line at the bottom of the screen examples of these mistakes are that a mask was attempted to be selected without first selecting the layout INVOCATION LASER has a configure file that presets the minimum defect size defect size step colors of each one of the masks The name of this file is laser tech and the syntax is as follows min_size CONSTANT step_size CONSTANT masks type I masks type R G B mask name where R G B identify the maximum am
25. erse the susceptible structure in order to obtain the coordinates of the corresponding critical area These coordinates delineate the boundary of the critical area The coordinates of areas sensitive to bridges are obtained by shrinking the related susceptible sites as if we were dealing with a cut except that in this case the coordinates belong in fact to the critical area for a bridge between the patterns see Fig 5 The areas sensitive to cuts are found using the same procedure Store the coordinates in two independent data structures one for bridges and another for cuts each one of them indexed by its defect size Repeat this step until all the range of defect sizes is exhausted For every defect size compute the total critical area enclosed in the set of coordinates found above The total critical area per defect size is the union of the areas of the individual boundaries found in step 2 Notice that the critical areas can overlap hence the total critical area is the union and not the sum of the area of each boundary From the procedure above it can be seen that only one layout extraction is necessary steps 0 1 and also that no matter how large the defect size is the identification of critical areas will always be found in a linear time proportional to the number of susceptible sites which in turn reflect the complexity of the layout step 2 edge shrinkage edge shrinkage i lt _ lt susc site lt susc site gt me cri
26. fect density 2 maximum defect density and 3 defect cluster parameter The densities have to be given in number of defects per cm2 7 DIAGNOSTICS AND TROUBLESHOOTING There are basically two types of diagnostics One is referred as user diagnostics and it concerns all the interface messages between the user and LASER The other types of diagnostics are referred as system diagnostics These messages deal with the internal programming of LASER such as to allocate memory space for layout structures or to search for layout files etc The latter type of diagnostics appears only when there are conflicts between LASER and the operating system 7 1 USER DIAGNOSTICS The following are the error messages displayed by LASER A brief explanation of its meaning is given These messages appear as a result of an incorrect usage of the features of LASER Their interpretation during the session is straightforward Layout file is corrupted check laser errors for errors The input data of the layout file contained errors Select first the mask An attempt to put the system in critical mode was done The system is in critical mode only when the mask is known Layout has not been selected An attempt to pick up a mask without previously selecting the layout Mode has not been selected An attempt to display the critical regions was made Select first the mode BRIDGES or CUTS Nothing to be hardcopied No layout has been selected to be analyzed thus there
27. heir left coordinates Initially M is empty Whenever a BEGIN line segment is encountered during the sweep we check for intersections with the horizontal line segments in M We also look in M for the line segment immediately to the left predecessor and to the right successor of the BEGIN line segment The data structure M is updated in such a form that only the intersected sections of the intersected line segment are deleted from M If an intersection was found a new susceptible site is made and stored in the S data structure The algorithm is directly applicable for the vertical sweep For the horizontal sweep the coordinates have to be rotated 90 degrees clockwise That is the lower coordinate of the vertical line segment becomes the left coordinate the top coordinate becomes the right one and the x value becomes the y value Whenever a susceptible site is formed in this sweep the coordinates must be rotated 90 degrees counterclockwise in order to set the correct orientation of the site The algorithm for finding susceptible sites related to bridges is shown in Fig 8 9 MAKE SITE left right bottom top creates a susceptible site with the given coordinates Meg sen predecessor successor FOREACH p EP for every edge of the polygon IF pi type END if the edge type is END insert Me pn the edge in the M data structure ELSE FOREACH m eM for every edge in M IF m right lt p
28. iffusion Mask Yield CUTS amp BRIDGES Defect Density in 1 cm2 Figure 21 Mask yield 26 LAYOUT YIELD 0 1000 2000 3000 4000 5000 Defect Density in 1 cm2 Figure 22 Final Layout yield 27 8 CONCLUSIONS The significance of the critical areas is relevant to the study of layout yield We presented a system capable of finding the critical areas in complex layouts Unlikely to statistical Monte Carlo simulations the implementation is based purely on the geometry of the patterns Two properties that distinguish our approach are that the critical areas for any range of defect sizes can be found by doing just one layout extraction and that the critical areas can be displayed on the screen These features ease the design verification task and allow to highlight the weakest portions of IC artwork An exhaustive analysis of three different layout styles was carried on to compare their endurance in a manufacturing environment 28 REFERENCES 1 Stapper C H 2 3 4 C5 C6 7 8 9 10 Modeling of integrated circuit defect sensitivities IBM J Res amp Dev Vol 27 1983 p 549 557 Stapper C H Modeling of defects in integrated circuit photolithographic patterns IBM J Res amp Dev Vol 28 1984 p 461 475 Ferris Prabhu A V Modeling the critical area in yield forecasts IEEE J Solid State Circuits Vol SC 20 1985 p 874 878 Shen J P and W Maly F J
29. in Xpeak We can express now the average POF as max f D x S x dx where min and max are the minimum and maximum defect sizes respectively The POF shows if given the defect size distribution only one defect per defect size occurs In manufacturing environments this is unreal A density of defects of all the sizes exists Therefore in order to predict the layout yield it is necessary to take into account this defect density The number of faults is directly related to the number of defects that can appear This can be expressed as A 0 defect_density Ajgyou where is the average probability of failure and Ajgyou is the area of the IC The layout yield is the probability of manufacturing the artwork without faults To compute yield it is necessary to consider the spatial distribution of defects Defect densities vary from wafer to wafer 18 from region to region within the wafer and even somtetimes tend to cluster in several wafer sections An accurate model that takes all these factors into account is presented in 14 and is the one we incorporated in our system The yield model is presented as zL Y 1 fA P where B is the defect density clustering parameter 16 7 LAYOUT ANALYSIS We implemented a combinational function in three different layout styles namely a Programmable Logic Array PLA a Transistor Matrix TM 15 and a Standard Cells place and route approach STD 16 see Fig 14 The layouts are
30. ine through the set C We store the V_BEGIN line segments twice in the M data structure The first time ordered by their left coordinate denoted as H_BEGIN and the second time ordered by their right coordinate denoted as H_END Initially M is empty Whenever a V_END line segment is found during the sweep we check if it is above the last scan position If so we proceed to sweep the M data structure We determine the width of the slice of area from every pair of line segments in M The length from the current y value of the V_END line segment and the y value of the first horizontal line segment retrieved or the y value of the last scan position whichever is applicable An auxiliary variable helps to discover if two or more rectangles overlap Everytime that a H_BEGIN H_END line segment comes the variable is incremented decremented Thus when the value of the variable is zero it means that a new nonintersected rectangle comes Every line segment retrieved from M is deleted to update the data structure The algorithm is presented in Fig 13 old top em top oo area 0 FOREACH c C defect_size IF c type BEGIN Mec left Mec right ELSE IF c top gt top top c top nest 0 FOREACH meM IF nest 0 bottom vo length width 0 ELSE width m key last key length top bottom area area length width last_key mt key 13 for every edge of the cri
31. is nothing to be copied Only entire layouts can be bounded An attempt to bound a single mask was done Defect size is undefined An attempt to find the defect size distribution was done Find first the critical Tegions up to the defect size for what you want to compute the defect size ditribution Critical regions have not been formed The system cannot compute the sensitivity without that the user finds the critical regions first Sensitivity undefined Compute first the sensitivity and then find the probability of failure Probability of failure is undefined Compute first the probability of failure before trying to compute the yield 7 2 SYSTEM DIAGNOSTICS The following are the messages that can appear as a consequence of a conflict between LASER and the operating system They appear as SYSXX Message where XX is the number of the message and Message is a short legend of the problem If any of these messages appears 1 check ownership of directories 2 check that the directories are accesible 3 check that the files are readable 4 check that the files are writable 5 check that there is enough memory usage space 6 consult with your system manager for help The diagnostics are 1 Cannot allocate space to plot the defect size 2 Cannot open file laser print 3 Cannot allocate space to plot the defect density 4 Cannot allocate space to create the layout 5 Cannot open the layout file 6 Cannot allocate space to s
32. itical area is 20 less than the other ones However as the defect size increases the sensitivity raises with a steep slope due to the fact that the metal mask is laid out in a very regular manner and because the spacing between lines is small We can see that the PLA follows the same trend but with a less steep slope mainly due to a relaxed spacing between wires and also due to a less number of adjacent lines which reduces the chances of a bridge among them On the other hand the STD is the best compromise for very large defects The layout style is very relaxed the four channels of metal wires are laid out very apart from each other and also notice the right top corner of the layout where there is a big unutilized space Poly Mask BRIDGES Once more the TM is the best for small defects ranging from 6 to 25um We can also see that even for large defects the mask is quite tolerant The reason is because it appears as a non regular mask wires are used mainly to form transistors and are used as interconnectors only when it is necessary The PLA shows a very regular patron and thus the sensitivity raises with a steep slope Notice that its sensitivity is almost twice as much compared to TM The crossing in the curves is because the TM s area is smaller The STD exhibits a quasi regular patron especially in the feed throughs This aspect is worthwhile noticing because one might think that because of the large empty spaces it is more tolerant
33. nd a good response for online tasks The layout sensitivity is defined as the ratio of the area where a defect must be situated to introduce a fault to the total layout area Acritical SO Atayout A sensitivity analysis reveals the endurance of the mask for different defect sizes and it shows in fact the cummulative probability that a mask will fail due to defect sizes less or equal to a predefined size However the probability of occurrence of each defect size is different Furthermore the probability of occurrence of very large defects is almost neglectable Therefore the sensitivity analysis cannot reflect what would happen to the layout in a real manufacturing environment whereas a layout probability of failure analysis does This layout probability of failure results from the probability that the layout will fail due to a defect of a certain size and the probability that the defect will in fact occur in the manufacturing conditions For this reason it is necessary to characterize a defect size distribution Several analytical defect size distributions 1 7 9 that can do this have appear in the literature We adopted the one presented in 7 due to its flexibility of being adapted to real manufacturing conditions The distribution is expressed as Kx D x Dy ren O lt x lt S Xpeak X peak Kx D x D p 1 SE Xpeak SX SX max D x 0 Xmax lt x pore oDe gat apa 2 X max EA C iaa S See pi I x 1 q 1
34. neering Coden TEUEDE 188 J zwiak J THE FULL DECOMPOSITION OF SEQUENTIAL MACHINES WITH THE STATE AND OUTPUT BEHAVIOUR REALIZATION EUT Report 88 E 188 1988 ISBN 90 6144 188 9 189 Pineda de Gyvez J ALWAYS system for wafer yield analysis EUT Report 88 E 189 1988 ISBN 90 6144 189 7 190 Siuzdak J OPTICAL COUPLERS FOR COHERENT OPTICAL PHASE DIVERSITY SYSTEMS EUT Report 88 E 190 1988 ISBN 90 6144 190 0 191 Bastiaans M J LOCAL FREQUENCY DESCRIPTION OF OPTICAL SIGNALS AND SYSTEMS EUT Report 88 E 191 1988 ISBN 90 6144 191 9 192 Worm S C J MULTI FREQUENCY ANTENNA SYSTEM FOR PROPAGATION EXPERIMENTS WITH THE OLYMPUS SATELLITE EUT Report 88 192 1988 ISBN 90 6144 192 7 193 Kersten W F J and G A P Jacobs ANALOG AND DIGITAL SIMULATION OF LINE ENERGIZING OVERVOLTAGES AND COMPAR SON WITH MEASUREMENTS IN A 400 kV NETWORK EUT Report 88 E 193 1988 ISBN 90 6144 193 5 194 Hosselet L M L F MARTINUS VAN MARUM A Dutch scientist in a revolutionary time EUT Report 88 E 194 1988 ISBN 90 6144 194 3 195 Bondarev V N ON SYSTEM IDENTIFICATION USING PULSE FREQUENCY MODULATED SIGNALS EUT Report 88 E 195 1988 ISBN 90 6144 195 1 196 Liu Wen Jiang Zhu Yu Cai and Cai Da Wei MODEL BUILDING FOR AN INGOT HEATING PROCESS Physical modelling approach and identification approach EUT Report 88 E 196 1988 ISBN 90 6144 196 X 197 Liu Wen Jiang and Ye Dau Hua A NEW METHOD FOR DYNAMIC HUNTIN
35. nly when nonequipotential regions are joined together Fig 1 shows the case of two single conductive lines each of width w length L and space s between them with L gt s Assume that an extra spot of material occurs between the two conductors if the size of this defect is such that x gt s the critical area can be expressed as Aps WpsLps 1 where Wps x 5 Lps L x Wps and Lps represent the critical width and length of the critical area respectively The end effects of the defect are also accounted in the length of the critical area ho x 2 5 Wes s h hy Los L 2 x 2 Figure 1 Pattern sensitive area for shorts 2 2 PATTERN SENSITIVE AREA FOR CUTS A cut appears when an equipotential region is fragmented into two or more nonequipotential patterns Fig 2 represents a single conductor of widht w and length L with L gt w Assume that a defect in the form of missing material occurs If the size is such that x gt w the critical area can be modelled as Apr WpgLpp 2 where Wo i M Lpp L x Wpy and Lpg represent the width and length of the critical area respectively The end effects are also consider in the length of the critical area hy x 2 ha x 2 Won nr hy hy PB PB L 2 x 2 L Figure 2 Pattern sensitive area for breaks The problem of dealing with lose patterns is that the flow of the current must be known in order to decide if the pattern is fragmented in nonequipotential
36. on Berlin Springer 1985 Texts and monographs in computer science Maly W and J Deszczka Yield estimation model for VLSI artwork evaluation Electron Lett Vol 19 1983 p 226 227 Maly W Realistic fault modeling for VLSI testing In Proc 24th IEEE ACM Design Automation Conf Miami Beach Fla 28 June 1 July 1987 New York IEEE 1987 P 173 180 Stapper Jr C H On a composite model to the IC yield problem IEEE J Solid State Circuits Vol SC 10 1975 p 537 539 Ginneken L P P P van and J T J van Eijndhoven J A H C M Brouwers Doubly foulded transistor matrix layout In Digest of Technical Papers 6th IEEE Int Conf on Computer Aided Design ICCAD 88 Santa Clara Cal 7 10 Nov 1988 New York IEEE 1988 P 134 137 Theeuwen J F M and M R C M Berkelaar Logic optimisation with technology and delay in mind Paper 3 3 in Proc Int Workshop on Logic Synthesis Research Triangle Park N C 12 15 May 1987 Available from Microelectronics Center of North Carolina P O Box 12889 Research Triangle Park NC 27709 U S A Maly W and A J Strojwas S W Director VLSI yield prediction and estimation A unified framework IEEE Trans Comput Aided Des Integrated Circuits amp Syst Vol CAD 5 1986 p 114 130 Stapper C H The effects of wafer to wafer defect density variations on integrated circuit defect and fault distributions IBM J Res amp Dev Vol 29 1985 p 87 97
37. ount of red R green G blue B This file has to exist prior to invoking LASER LASER assumes that the technology file is in the current directory if it is not specified in the invocation To start LASER type critical technology file lt CR gt SCREEN ORGANIZATION The menu area to the left is used to select any of the menu s options The interface line at the bottom is used by LASER to display messages and to capture input data for the analysis The display area is the section where the layout is displayed and also where the results of any of the analysis performed are projected 2 MAIN OPTIONS This is the main menu of the system From here it is possible to select a layout and the mask to be analysed to carry on an analysis to put the system in critical mode to make viewing operations like zoom and to hardcopy the display area LASER works in two modes passive mode which allows to view the layout and critical mode that allows to find the catastrophic regions due to different defect sizes LAYOUT SENSITIVITY EXPLORER Perast lu EINDHDYEN UNIVE SITY OF IECHNOLCCF TT hardcopy Figure 1 Main options of the system LAYOUT This option allows to select any new layout for analysis Every time that a new layout is selected the system is reset to passive mode and any analysis previously computed is lost MASK This option allows to select any of the masks of the previously selected layo
38. s menu move the cursor to the option area and then click the left button To go back to the previous menu click the left button rede in the display area When LASER asks for data only the numbers CR Backspace and the sign a are enabled To indicate to LASER that the data is See type lt CR gt GE gt GE 83 OZR 154 tee 725 256 701 324 IST poet lan gt F 2 d y FE Oe GE CD e tatu ere Sue Figure 5 Options for analysis SIZE DISTRIBUTION This option allows to set the defect size distribution according to three parameters 1 the defect peak size 2 p the monotonously incrementing part of the distribution and 3 q the EAEN Y decrementing part of the distribution For details of this been refer to the technical section 6 of the report LASER asks one parameter at the time in the interface line The data is also captured in this line The distribution shown is the pdf of defects SENSITIVITY LASER computes the sensitivity of which either mode BRIDGE or CUT was active FAILURE PROBABILITY Once that the defect size distribution and the sensitivity are computed the probability of failure can be found If any of the sensitivity or defect size distribution is not previously computed LASER will report so YIELD In order to calculate the yield the sensitivity defect size distribution and probability of failure have to be computed The yield is calculated according to three parameters 1 minimum de
39. sider the specific layout It is therefore ideal a CAE tool that automatically explores and predicts the layout reliability for real environmental conditions prevailing in the manufacturing line We present a system capable of interactively finding the critical areas for shorts and breaks the sensitivity and the yield of the IC artwork for any range of defect sizes The implementation is based on a simple scanline algorithm and performs only one layout extraction for any span of defect sizes Pineda de Gyvez J LASER A LAyout Sensitivity ExploreR Report and User s manual Faculty of Electrical Engineering Eindhoven University of Technology 1989 EUT Report 89 E 216 Author s address Automatic System Design Group Faculty of Electrical Engineering Eindhoven University of Technology P O Box 513 5600 MB Eindhoven The Netherlands O ON DH bk Lo iv CONTENTS INTRODUCTION SENSITIVE AREAS 2 1 PATTERN SENSITIVE AREA FOR BRIDGES 2 2 PATTERN SENSITIVE AREA FOR CUTS FINDING THE LAYOUT CRITICAL AREAS EXTRACTION OF SUSCEPTIBLE SITES CREATION AND COMPUTATION OF CRITICAL AREAS SENSITIVITY PROBABILITY OF FAILURE AND YIELD LAYOUT ANALYSIS CONCLUSIONS REFERENCES APPENDIX User s Manual SJ an WN 14 16 27 28 Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 12 Figure 11 Figure 13 Figure 1
40. t it joints or cuts more patterns than the ones related in the susceptible sites the critical regions will still be found correctly because the shrinked edges overlap also This situation was previously mentioned as the proximity effect From this example it is seen that the critical regions are found straightforwardly from the susceptible sites for any defect size Thus no matter how large the defect size is the critical regions are extracted in 11 critical area c Figure 10 Creating critical regions for cuts from their susceptible sites a Susceptible sites from the vertical sweep b Susceptible sites from the horizontal sweep c Critical regions formed a time proportional to the number of susceptible sites The algorithm developed to find the critical regions is the same for bridges and for cuts However the data structures used to store the critical regions must be independent one for each type of fault Let S 51 Sa be the set of the susceptible sites in ascending y order The main loop of the algorithm traverses the set S Foreach susceptible site we check its label and then see if the critical region for a given defect size is established by shrinking the appropriate edges If a critical region is formed we saved it in the data structure C indexed by the defect size This procedure is repeated until the range of defect sizes is exhausted Worthnoticing is that each defect size has its unique critical regions in
41. t step in the analysis is to find the expected layout yield for a ke Metal Mask POF BRIDGES 0 50 100 Defect Size in um Poly Mask POF BRIDGES Defect Size in um Diffusion Mask POF BRIDGES 003 002 001 0 0 50 100 Defect Size in um Figure 19 Layout Probability of Failure POF for bridges defect density We averaged the probability of failure for defect sizes of lum to 100um and simulated the yield for defect densities varying from 1 to 10000 defects per square centimeter with B equal to 1 11 The results obtained are shown in Fig 21 and the curves speak for themselves 24 Metal Mask POF CUTS 005 004 003 002 0 50 100 Defect Size in um Poly Mask POF CUTS 01 005 0 50 100 Defect Size in um Diffusion Mask POF CUTS PLA Defect Size in um Figure 20 Layout Probability of failure POF for cuts The total layout yield is presented in Fig 22 One remarkable conclusion is that the largest layout is not always the most likely to fail as it is depictured in the figure On the other hand regular layouts like the PLA are not always very reliable This aspect should be taken into account since PLAs are frequently used in controllers and these modules play an important role in many designs 25 Metal Mask Yicid CUTS amp BRIDGES Defect Density in 1 cm2 Poly Mask Yield CUTS amp BRIDGES Defect Density in 1 cm2 D
42. the rubberbox in its entire display area ZOOM OUT This option allows to zoom out the layout or mask A cross at the top left corner of the screen appears Move the cross to the layout and click the left button A rubberbox appears LASER calculates a demagnifying factor equal to the extensions of the layout boundaries divided by the extension of the rubberbox The display area shows the layout demagnified SHIFT This option allows to move the layout from its original position in the display area A cross appears at the top left corner of the screen The shifting is calculated by how much is the cross displaced from the center of the layout If the cross is placed to the right of the layout the layout is moved to the right The same applied for left up and down RESET If any zoom or shift operations were performed by clicking in this option the layout or mask that was initially active before entering this menu is redisplayed BOUND This option allows to bound the layout to any section previously zoomed in Only layouts can be bounded masks not A message Bounding layout appears to indicate that the operation is carried on 6 ANALYSIS This menu allows to analyse the sensitivity probability of failure and the yield of the layout Any analysis will be performed up to the current defect size obtained by clicking the left or right mouse buttons when the system was in critical mode To select any of the options of thi
43. tical area critical area BRIDGES CUTS Figure 5 The critical areas for both bridges and cuts are found by shrinking the susceptibles sites 4 EXTRACTION OF SUSCEPTIBLE SITES The susceptible sites for bridges contain all the necessary information to find the related critical areas That is their boundaries represent in fact the edges of the associated patterns which can be joined by a defect Thus it is no longer necessary to compare patterns in order to establish the critical area and neither is necessary to extract the layout for every distinct defect size Fig 6 shows an example of these sites susceptible sites defects Figure 6 Susceptible sites for bridges The susceptible sites for cuts provide the correct magnitude of the pattern from which the critical area can be found straightforwardly For instance a polygon with an L shape contains four different susceptible sites If the sender terminals are on the top and lower right end of the L the susceptible sites are as depictured in Fig 7a If on the other hand the sender terminals are situated on the bottom and left side then the susceptible sites are the ones shown in Fig 7b Figure 7 Susceptible sites for cuts a The sender terminals are on the top and lower right end b The sender terminals are on the bottom and left side Before extracting the susceptible sites we perform a layout preprocessing It consists of converting rectangles to polygons and of
44. tical rectangles if the edge type is BEGIN insert it twice in the M data structure if the current edge is above the scan position update the scan position f for every horizontal edge if it is not intersected by other horizontal edge P reset the width and length calculate the new width and length update the total area safe the last horizontal position bottom MIN m bottom bottom update the bottom and IF bottom lt old top bottom old top IF m type BEGIN gt nest nest 1 ELSE nest nest I old_top top M M mi clip it if necessary if the horizontal edge is BEGIN increment the nesting flevel else decrement it update the last scan position delete the horizontal edge Figure 13 Computation of the critical areas 14 6 SENSITIVITY PROBABILITY OF FAILURE AND YIELD In order to predict the layout yield it is necessary to study the impact that the manufacturing conditions will have on the layout These analyses can be carried on analytically since the critical areas of the layout can be extracted for a span of defect sizes as we showed in previous sections and thus they are known The task of layout endurance analysis can be very fast and furthermore there is no need to recur to Monte Carlo statistical simulations to obtain the yield This results in computational effort savings a
45. to small defects Diffusion Mask BRIDGES The STD layout is in a column style Almost all the patterns are joined together and the space between columns is big This is why the sensitivity is extremely low On the other hand the style for the PLA is very regular but with a large distance between lines The TM is not regular however the compactness of the layout puts the lines closer It is interesting to notice these two aspects since the two effects seem to be equivalent from the sensitivity point of view The PLA appears to have a higher sensitivity because of the input and output buffers which are not included in the TM The slope is very slanted because even when the lines exhibit regularity they are very interconnected i e many U shapes hence catastrophic bridges are less likely to happen Metal Mask CUTS In this case the PLA is the best compromise because its lines are wider than in the other two layouts Notice the crossing in the curves of the PLA and the STD This is because the channel s lines in the STD are very separated which reduces the chances of a defect cutting more than one Hine at the same time whereas in the PLA even when the lines are wider they are closer to each other The TM simply cannot tolerate large defects Poly Mask CUTS The TM is the best compromise due to the scarce appearence of the lines The abrupt jump for defects in the range of 12 to 15um is a reflection of many square patterns in which the
46. uctor has two different critical regions and only one is in effect depending upon where the sender terminals are situated Since we are dealing with independent masks there is no way to know the signal flow left to right top to bottom That is why the both critical regions are created 10 5 CREATION AND COMPUTATION OF CRITICAL AREAS The task concerning the computation of critical areas is divided in two phases Namely creating the boundary of the critical area for each defect size and then computing the area enclosed in the boundary To simplify the terminology in the context of this paper we name the boundary of the critical area as critical region and the area enclosed in the boundary as critical area As we mentioned before the susceptible sites are the potential places where a defect of any size can cause a fault The critical regions related to bridges are found by traversing the correponding susceptible data structure The edges of each susceptible site are shrinked by half of the defect size to test if the critical region is established When the site is labeled as 1 VERTICAL the abscissae are shrinked 2 HORIZONTAL the ordinates are shrinked and 3ICORNER both the ordinates and abscissae are shrinked In any case if the shrinked edges overlap then the critical region is established The areas sensitive to cuts are found exactly in the same manner except that the data structure traversed is the one related to cuts An exampl
47. uite unreliable Poly Mask BRIDGES A remarkable aspect is that the occurrence of defects in the size range from 15 to 304m seems not to affect drastically the TM despite that the defect size distribution peaks at 10m Once more the regularity in the PLA is its major drawback The STD with its empty spaces is more reliable to large defect sizes Metal Mask CUTS Since the probability of having large defects is very small the PLA proofs to be the safest design with its wide lines The STD and the TM are very similar due to the fact that their lines are narrow 61m The TM shows a higher POF because the lines are laid out uniformly and because of the compactness of the layout Poly Mask CUTS The scarcity in the lines of the TM and the quasi regular lines of the STD results in two layout styles which have more or less the same probability of failure although for small defect sizes the TM is better The PLA has once again the highest POF Diffusion Mask BRIDGES amp CUTS We can see here the dramatic differences in layout style reliabilities when they are not correctly tuned for a defect environment in a manufacturing line Notice that eventhough the probability of occurence of large defects is big the STD style remains atonishing low whereas for the PLA and the TM is very high The layout probability of failure shows what would happen if given a defect size distribution only one defect for each defect size occurs The nex
48. ut Every time that a new mask is selected the system is reset to passive mode VIEW This allows to do zoomming operations on the layout HARDCOPY This option is used to make a hardcopy of the display area LASER creates a postscript file called laser print that the user can spool to the printer ANALYSIS This option allows to analyse the mask and its local deformations such as sensitivity probability of failure and yield BRIDGE or CUT These items put the system in critical mode Before changing the system s mode the layout mask has to be selected When the mask is selected for the first time a message Processing susceptible sites appears to indicate that LASER is collecting all the places where faults can occur When the system is ready the critical regions can be displayed on screen by clicking the left button The critical regions are displayed in white and any intersections with the original mask are shown in cyan Every critical region displayed corresponds to the defect size in turn The defect size can be incremented by clicking the left button of the mouse and decremented by clicking the middle button The defect size increment is equal to the step size indicated in the technology file 3 LAYOUT This option selects any of the layouts existing in the current directory To pick up one layout move the cursor to its name and click the left button of the mouse A message Reading layout appears to indicate
49. ut sensitivity a flexible defect size distribution that can easily be fit to real manufacturing conditions the computation of the layout probability of failure for a given defect size distribution and the prediction of the artwork yield for any span of defect sizes 2 SENSITIVE AREAS It is convenient to examine briefly the nature of defects and their impact in the ICs An IC layer is a piece of solid state surface in the wafer usually shaped by one or more masks Each pattern in the layer has a set of properties such as the mask layer shape matching the integrity of the pattern its thickness in the layer etc Non desirable physical agents introduce changes in the structure of a group of patterns and as a result the properties of these patterns are different from the initial ones These changes are known as defects For our purposes a defect is any deviation in the shape of the IC layer from its corresponding layout mask For instance the absence of a piece of mask can represent the absence or presence of a Certain spot of material in a specific layer Defects can introduce faults A fault is any deviation from the expected behaviour of the IC Some faults are fatal such as stuck at outputs or dc path changes in the topology of the circuit other forms are just performance failures like undesirable delays In our study we concentrate on spot defects that cause catastrophic faults 17 The layout is the union of geometrical structures with an el
50. y size can cause a fault Namely these regions are the empty spaces between patterns for the case of bridges and the patterns themselves for the case of cuts This results in a single layout extraction for any defect size Furthermore for bridges it is no longer necessary to compare the patterns among each other since the places where defects can cause faults are the empty spaces Therefore the problem is reduced to determine the extent of the critical area from these regions according to the defect size For terminology purposes we denote the former regions as susceptible sites for bridges and the latter ones as susceptible sites for cuts We outline now the steps involved in the extraction of critical areas and later we describe them into more detail These steps are mainly a layout extraction to obtain the susceptible sites the creation of critical regions from the susceptible sites and the computation of the critical areas themselves Step 0 Select the layout mask to be analysed Convert the rectangles to polygons Assign unique identification numbers to the polygons Decompose the polygons to line segments Save these line segments for further processing Step I Extract all the susceptible sites for bridges and cuts from the pre processed mask and store them in two different data structures one for bridges and one for cuts We denote these data structures as susceptible structures Step 2 Step 3 For every defect size trav
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