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ALWAYS: A SYSTEM FOR WAFER YIELD ANALYSIS Report and

1. generate the number of good dice randomly random_dice number_dice good_dice bias place the generated good dice random_placement radius number_dice retum TRUE LIG As with the yield vs area simulations the distributions can be given in a file or can be drawn directly on screen After the wafers are created it is possible to examine each one of them and also to perform any of the map analyses on the composite simulated wafer In these simulated maps the only statistics reported are the yield of the function and the mean and standard deviation of dice for the function As a final remark recall that the input data implies site yields Thus the map interpretation depends on the interpretation given to the site lFor instance if the site yield represents a defect of a specific size x then the wafer simulated will show the regional distribution of defects Of course the radial distributions represent the radial yield of defects at radius R and the smaller the die size the more accurate the simulation is since in this case it represents the position of a defect in the wafer 17 7 SUMMARY AND CONCLUSIONS Standard tools of statistical means of control have been available for many years However their use on a routine basis has been somewhat limited This is due mainly to a lack of easy access to the appropiate data the tedious hand plotting of charts or wafer maps and the difficulty of keeping an up to da
2. IEEE J Solid State Circuits Vol SC 7 1972 p 389 395 Calhoun D F and L P McNamee A means of reducing custom LSI interconnection requirements IEEE J Solid State Circuits Vol SC 7 1972 p 395 404 Maly W and F J Ferguson J P Shen Systematic characterization of physical defects for fault analysis of MOS IC cells In Proc 15th Int Test Conf Philadelphia 15 18 Oct 1984 New York IEEE 1984 P 390 399 Campbell D M and Z Ardehali Process control for semiconducting manufacturing Semicond Int Vol 7 No 6 June 1984 p 127 131 Mallory C L and D S Perloff T F Hasan R M Stanley Special yield analysis in integrated circuit manufacturing Solid State Technol Vol 26 No 11 Nov 1983 p 121 127 Burggraaf P CAM software Part 1 Choices and capabilities Semicond Int Vol 10 No 6 June 1987 p 55 61 Myers B A Creating interaction techniques by demonstration IEEE Comput Graphics amp Appi Vol 7 No 9 Sept 1987 p 51 60 Maly W and M E Thomas J D Chinn D M Campbell Double bridge test structure for the evaluation of type size and density of spot defects Pittsburgh Pa SRC CMU Center for Computer Aided Design Department of Electrical and Computer Engineering Carnegie Mellon University 1987 Research Report No CMUCAD 87 2 Chen I and A J Strojwas A methodology for optimal test structure design for statistical process characterization and diagno
3. SITE_YIELD draw_die x y functional_yield functional_yield functional_yield total_number_of_dice In order to be able to find clusters in the wafer it is necessary to define clearly what a cluster means We define a cluster as a number of contiguos dice that have the same site yield Thus clustered elements can be in the horizontal vertical or even diagonal directions with respect to a seed element The seed element is the dic which was taken as a reference for the search of contiguos dice The routine that implements this search uses the principle of the depth search algorithm The main idea behind this algorithm is to take one die that has the cluster yield specified and then look if its neighbours also have the specified yield Since the number of neighbours and their directions is unknown it is necessary to check for the neighbours of the neighbours and then for the neighbours of the neighbours of the neighbours and so on At first glance we see that this routine is suited for recursivity Next to determine whether the dice found form a cluster or not we simply check against the number of elements that make up a cluster This parameter is a user entry thus we can find clusters of one two or more elements The next routine finds the dice that 10 have the same site yield and marks them in the cluster wafer This routine is part of a main one where first the seed element is set and later it is inves
4. SPATIAL DISTRIBUTION OF TRAFFIC IN A CELLULAR MOBILE DATA NETWORK EUT Report 87 E 168 1987 ISBN 90 6144 168 4 Vinck A J and Pineda de Gyvez K A Post IMPLEMENTATION AND EVALUATION OF A COMBINED TEST ERROR CORRECTION PROCEDURE FOR MEMORIES WITH DEFECTS EUT Report 87 E 169 1987 ISBN 90 6144 169 2 Hou Yibin DASM A tool for decomposition and analysis of sequential machines EUT Report 87 E 170 1987 ISBN 90 6144 170 6 Monnee P and M H A J Herben MULTIPLE BEAM GROUNDSTATION REFLECTOR ANTENNA SYSTEM A preliminary study EUT Report 87 E 171 1987 ISBN 90 6144 171 4 Bastiaans M J and A H M Akkermans ERROR REDUCTION IN TWO DIMENSIONAL PULSE AREA MODULATION WITH APPLICATION TO COMPUTER GENERATED TRANSPARENCIES EUT Report 87 E 172 1987 ISBN 90 6144 172 2 Zhu Yu Cai ON A BOUND OF THE MODELLING ERRORS OF BLACK BOX TRANSFER FUNCTION ESTIMATES EUT Report 87 E 173 1987 ISBN 90 6244 173 0 Berkelaar M R C M and J F M Theeuwen TECHNOLOGY MAPPING FROM BOOLEAN EXPRESSIONS TO STANDARD CELLS EUT Report 87 E 174 1987 ISBN 90 6144 174 9 Janssen P H M FURTHER RESULTS ON THE McMILLAN DEGREE AND THE KRONECKER INDICES OF ARMA MODELS EUT Report 87 E 175 1987 ISBN 90 6144 175 7 Janssen P H M and P Stoica T SSderstrdm P Eykhoff MODEL STRUCTURE SELECTION FOR MULTIVARIABLE SYSTEMS BY CROSS VALIDATION METHODS EUT Report 7 E 176 1987 ISBN 90 6144 176 5 Stefanov B and A Veefkind L Zarkova ARCS IN CESIUM S
5. menu to the main menu then by clicking once on the bar ALWAYS positions itself in the edit menu and then by clicking on the bar again the main menu is achieved INPUT FORMAT The input data of ALWAYS consists of the status good or bad of each die in every wafer for all the lots and projects to be analysed The project and the lot are directories and the wafer is the file characterising the information The project directory has to be as follows gt project_name pro the lot directory like jot_name lot and the wafer file as wafer_name waf The data in the wafer file is given as coordinates with the status of the die the format is as follows x y 1 for good dice or x y 0 for bad dice x and y represent the coordinates of a die inside the wafer ERROR REPORT If there were errors in the wafer files ALWAYS generates a file containing information of these errors i e that a die is out of the wafer or out of the mask etc The name of this file is always errors Mistakes comitted during the session are reported in the interface line this kind of errors are for instance an invalid die size or trying to select a lot without having selected a project first etc INVOCATION ALWAYS has also a configure file that presets the size of the wafer of the mask and of the dice The name of this file is config always and its syntax is as follows wN mN xN yN h N vN where N represents the size in all the case
6. versions will provide pop up menus It is not a disadvantage to have static screen menus when the number of nested menus is small although the ever increasing availability of UIMSs 21 promotes an upward to this kind of interfaces Future work involves providing facilities to have dice of different sizes in the same wafer and also facilities to correlate wafers with dice of different sizes and shapes among others 18 We presented a simple yet complete package for wafer yield analysis As in every beginning things are not that easy When there were no layout editors people used to do their designs by hand or by creating isolated programs to easy this enormous task suddenly the first layout editors appeared and became more and more popular up to the point where nowadays it is an indispensable and easy to obtain tool Similarly the idea of the Wafer Yield Editor shows that it is easy to Construct a system to help in the analysis of yield improvernent Sophisticated CAM tools 20 that provide statistical process and quality control and analysis and simulation of yield management are also available However these systems are oriented to automate the wafer processing in silicon foundries and their scope differs from yield analysis ALWAYS is an example of a tool for research of yield analysis which everybody can make at little expense ALWAYS is not only suited for usage in the silicon foundry but also in the layout designers rooms th
7. 1 2N ndu gt o wrt 7 z 0 dice oe ee The statistics that we showed so far are for correlated functions The history map has a set of uncorrelated statistics First the yield here is evaluated as Lys 8 where N is the total number of dice that were good during the analysis and N represents the total number of dice in the analysis The variation between wafers is inspected by evaluating the yield of good dice in each wafer Then the mean yield x and variance s2 for wafers is given by 1 i N FY w p Sha 10 w N 1 fa i where Y is the yield of each wafer and N is the total number of wafers involved in the analysis The uncorrelated mean yield and variance for lots and projects is also evaluated as 1 iN tyy 11 ray Ni 11 sta i N 3 Y 12 Nore 12 where Y represents the yield of good dice in the lot or project and N the total number of lots or projects Finally the mean of the distribution of working chips and its standard deviation is evaluated as x u F x40 13 x N dice 1 XEN wje x o E G t 14 x dice where x represents the site frequency of a dic and f x represents the number of dice that exhibit the site frequency Cluster statistics are considered in a similar way First we find the number of clusters C and their total number of elements G in the composite wafer We also evaluate the mean number of clusters x and the mean number of clustered elem
8. an independent random variable and altogether constitute a random sample for whose mean xp and variance s are given according to 25 by 1 iN YSY 3 Xp Nm i 3 2 Loe 2 4 Sp VY s EM 37 i where Y represents each partial yield and N is the size of the sample These two quantities give an idea of the performance of the function per lot or per project Furthermore a 95 degree of confidence of the mean yield value is evaluated If xp and sp are the values of the mean and standard deviation of the sample of size N then the 1 100 confidence interval for the population mean y is Sere ees E 5 2 VN 2 VN This means that if we had more lots or projects we could assert wiih 1 amp 100 degree of confidence that the true avcrage lot yield is between the two boundaries Since the methodology exploits correlation of wafers we also provide an expected value of dice and its standard deviation This expected value is the mean of the distribution of dice that accomplished a specific function If z is a rardom variable representing the site frequency in other words the number of times that a dic can accomplish the function and f z is the number of dice that exhibit the site frequency in the composite wafer then the mean is given by 2 Newer b E 6 2 1 dice where Ngice is the total number of dice in the wafer and Nwafer is the number of wafers in the analysis The standard deviation is given by
9. from the process of interest The data gathered for the analysis can be collected from electrical sort systems or by optically decoding the ink dot pattem placed on the wafers during the sort procedure This allows automatic printout of the maps in an easy form for further manipulation of data Input data to the yield editor consists of all the die positions and their status good or bad of each wafer in each lot for each project We define a set of wafers as a lot and a set of lots as a project This classification allows us to hierarchise the information Hence the database description follows a tree structure where the parent is the product itself the children represent each one of the lots of the product and the grandchildren represent the individual wafers for each lot see Fig 1 Since the information flows from grandparent to grandchildren a double linked structure is unnecessary and thus we only have single connected lists this saves some memory space in defining extra pointers and simplifies the code since only one link has to be updated for deleting or inserting elements in the list project 1M DRAM LOTESA LOT 3B W3A 1 W3A 2 H3A 3 W3B 4 K3B 2 W3B 3 Figure 1 a The information is hierarchised in a tree structure b An example Intemally we place the dice in a square matrix that we call the mask The mask represents the photolithographic mask of the technological process Once that the projects lots and wafers for the anal
10. good luck 2 USIERS MANUAL ALWAYS is a system used for spatial yield estimation and prediction of wafers It is able to quantify yield variations between lots of wafers and between the wafers themselves by doing wafer map and distribution analyses Its features are explained in detail through the rest of this manual 2 1 USER INTERFACE ALWAYS assumes that the current directory contains all the projects to be analysed The taxonomy of ALWAYS is shown in Fig 3 In it are shown in detail the options of the system and the nesting levels of the menus ALWAYS Figure 3 Taxonomy of ALWAYS The following are the interfaces required to work with ALWAYS MOUSE INTERFACE ALWAYS is a highly interactive system that makes use of mouse based interface systems The left button of the mouse is used to point at any of the options of the menus The button in the middle is in effect when the overlap or alternate options are enabled or at the moment of capturing information in the simulation menu The button to the right is used to exit ALWAYS at any moment by doubleclicking it DONE EXIT BAR In the lower left comer of the screen a red bar called the done exit bar is constantly displayed This bar has two effects one is to confirm any operation realised in the menu such as to capture data curves in the simulation menu and its other use is to go one menu backwards For instance if it is desired to go back from the adjust
11. in the field to the nght of the screen The map will display all the dice that have a site yield equal or bigger than the one specified The dice that have a bigger site yield are displayed in yellow and the ones that have the specified site yield in magenta ALWAYS rounds the specified yield to the lower nearest yield since the Site yield depends on the number of wafers available for the analysis Consider the case where there is only one wafer active and an up range of 67 was specified Obviously for this case there are only two site yiclds O and 100 For this example ALWAYS will round the site yield to 0 and will display the bad dice in magenta and the good dice in yellow LOW RANGE MAP With this option it is necessary to specify the maximum site yield to be displayed This is done by entering the yield value in the field to the right of the screen The map will display all the dice that have a site yield equal or lower than the one specified The dice that have a lower site yield are displayed in yellow and the ones with the specified yield in magenta ALWAYS rounds the specified yield to the lower nearest yield since the site 14 yield depends on the number of wafers available for the analysis Consider the case where there is only one wafer active and a low range of 67 was specified Obviously for this case there are only two site yields 0 and 100 For this example ALWAYS will round the site yield to 0 and only the bad dice are sho
12. key wafer size mask size adjust dead dice xiy Figure 5 Edit Menu WAFER SIZE By clicking in this option ALWAYS asks to enter the new size of the wafer This inquiry is present in the form of a field at the right side of the screen MASK SIZE This option allows to modify the size of the mask The new size is also entered in a field at the righ side of the screen ADJUST This option allows to displace the wafer from the center of the mask For more details refer to the wafer displacement section DEAD DICE This option allows to select the dead dice The dead dice are dice that are not considered for the analysis In this form one can selectively activate or disactivate regions in the wafer When one clicks in this option a new select cancel menu appears If the select option is clicked then ALWAYS is ready to create dead dice in the wafer To create any dead die just click in its position in the wafer To cancel dead dice first click in the cancel option and then in any of the existing dead dice The current dead dice are lost if there is a modification made to the wafer size mask size or die size X Y This option allows to visualise the numerical coordinates of a die To see the coordinates of a die click in its position in the wafer The numerical coordinates appear to the right of the screen and the die selected is highlighted 1li 2 3 1 WAFER DISPLACEMENT This me
13. one of the existing projects for the analysis the same with a file iots The file wafers contains the functional yield of each one of the wafers involved in the analysis The partial wafer maps of each project and of each lot are named as project_name pro project_name_lot_name lots 1 Cannot open the file projects in the Amp directory 2 Cannot open the file lot in the imp directory 3 Cannot open the file always errors 4 Cannot open the file wafers in the Amp directory 5 Cannot write in the wafers file 6 Cannot open the partial composite wafer map for each lot 7 Cannot write the partial composite map of each lot 8 Cannot open the file to store the composite wafer of each project 9 Cannot write the partial composite map of each project 10 Cannot open the analysis file 11 Cannot write in the analysis file 12 Cannot open the simulation file 13 Cannot write in the simulation file 14 Cannot open always print 15 Cannot open wafers for reading 16 Cannot read wafers 17 Cannot open projects or lots for reading 18 Cannot read lots or wafers 19 Cannot read lots or wafers 20 Cannot open cluster file 21 Cannot read file for clusters 22 Cannot read composite wafer for cluster analysis 23 Cannot link an active project 24 Cannot create header of project list 25 Cannot store the project name 26 Cannot create header of lot list 27 Cannot link an active
14. then the graph shows the absolute radial yield of the composite wafer If lt CR gt is typed alone it is interpreted as zero ANGULAR DISTRIBUTION This option also asks for the site yield which is going to be looked for angularly This data is entered in the field to the right of the screen The graph shows the angular yield of dice that have a site yield equal or above the user s yield If zero is 15 specified then the graph shows the absolute angular yield of the composite wafer If lt CR gt is typed alone it is interpreted as zero CUMULATIVE DISTRIBUTION This option shows the cumulative distribution of site frequencies FREQUENCY DISTRIBUTION This option shows the frequency of occurrence of the different site yields for all the dice in the composite wafer The information is displayed in a histogram fashion YIELD vs AREA This option evaluates the yield vs area of the composite wafer The user is also asked to give the site yield which is going to be searched The graph displays the yield of the dice that have a site yield equal or bigger than the user s for several area sizes If zero is specified then the absolute yield vs area of the composite wafer is shown lt CR gt alone is also interpreted as zero 16 2 6 SIMULATIONS ALWAYS provides two kinds of simulations one is a yield vs area simulation and the other is the creation of wafer maps When using the draw option to capture distri
15. will be asked to enter the horizontal and vertical dimensions of the new dic Now change the size of the wafer to 76mm by clicking in the wafer size option and entering this new valuc So far we already have the correct wafer and dice dimensions but the configuration is still different The filter program that we mentioned assumes that the rightmost die and closest to the flat side of the wafer has coordinates 8 0 We can investigate which are the coordinates of this die or any other by clicking in the X Y option and then clicking in the dic itself The mask size is 73mm thus we need to displace the wafer 1 6mm to the right and 1 6mm down from the center of the mask Adjust first the mask size by clicking in the mask size option and enter the new dimension and later switch to the adjustment menu by clicking in the adjustment option Set here the step size to 0 4mm and then move the wafer four times to the right and four times down Of course you are free to give any other step size of your choice Now we are able to proceed with the analysis The red bar down to teft of the screen is the done exit bar Clicking once in this bar we will retum to the cdit menu and clicking again it will position us back in the main menu Let us select now the data for the analysis Click in the set option We are facing now the set menu which allows us to set projects lots and wafers for our analysis Let us pick up first the enhancement data Click
16. yield prediction and estimation are very important issues for the IC design and process development It is well known that the local yield varies from wafer to wafer and that by examining batches of wafers it is possible to correlate non functional circuits and their contributions to yield loss Sometimes it is desirible not only to analyse data but also to simulate the effect of density variations in a wafer and between wafers or to excercise new yield models and compare their results to real data i For these and more reasons the creation of a user friendly interactive environment is imperative This research is concerned with the development of the Wafer Yield Editor ALWAYS AnaLiser of WAfer YieldS ALWAYS is a menu oriented system designed to analyse spatial distributions of wafers Graphical representations in the form of wafer maps curves and charts are used extensively for user interface Flexibility to create wafer masks wafers and chips of different dimensions as well as several miscellaneous tools such as hardcopy overlapping of extracted wafer maps etc are provided Simulation of wafer maps and yield vs area predictions are also available And finally data is read and stored in a very simple database structure All the algorithms through this report are shown in a C like syntax 2 INPUT DATA AND DATABASE DESCRIPTION The starting data is a set of wafer maps of working and nonworking circuits of individual wafers produced
17. 186 2 Kaiser F and L Stok R van den Born DESIGN AND IMPLEMENTATION OF A MODULE LIBRARY TO SUPPORT THE STRUCTURAL SYNTHESIS EUT Report 87 E 187 1997 ISBN 90 6144 187 0 J zwiak L THE FULL DECOMPOSITION OF SEQUENTIAL MACHINES WITH THE STATE AND OUTPUT SEHAVIOUR REALIZATION EUT Report 88 E 188 1988 ISBN 90 6144 188 9
18. 338 Stapper C H Yield model for fault clusters within integrated circuits IBM J Res amp Dev Vol 28 1984 p 636 640 Gupta A and W A Porter J W Lathrop Defect analysis and yield degradation of integrated circuits IEEE J Solid State Circuits Vol SC 9 1974 p 96 103 Yanagawa T Yield degradation of integrated circuits due to spot defects IEEE Trans Electron Devices Vol ED 19 1972 p 190 197 Stapper C H Defect density distribution for LSI yield calculations IEEE Trans Electron Devices Vol ED 20 1973 p 655 657 Stapper C H LSI yield modeling and process monitoring IBM J Res amp Dev Vol 20 1976 p 228 234 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 Stapper C H and F Armstrong K Saji Integrated circuit yield statistics Proc IEEE Vol 71 1983 p 453 470 Walker H and S W Director VLASIC A catastrophic fault yield simulator for integrated circuits IEEE Trans Comput Aided Des Integrated Circuits amp Syst Vol CAD 5 1986 p 541 556 14 15 16 17 18 19 20 21 22 23 24 EE Walker D M H Yield simulation for integrated circuits Ph D Thesis Pittsburgh Pa Carnegie Mellon University 1986 Gupta A and J W Lathrop Yield analysis of large integrated circuit chips
19. EEDED NOBLE GASES RESULTING FROM A MAGNETICALLY INDUCED ELECTRIC FIELD EUT Report 87 E 177 1987 ISBN 90 6144 177 3 Janssen P H M and P Stoica ON THE EXPECTATION OF THE PRODUCT OF FOUR MATRIX VALUED GAUSSIAN RANDOM VARIABLES EUT Report 87 E 178 1947 ISBN 90 6144 178 1 Lieshout G J P van and L P P P van Ginneken GM A gate matrix layout generator EUT Report 87 E 179 1987 ISBN 90 6144 179 x Ginneken L P P P van GRIDLESS ROUTING FOR GENERALIZED CELL ASSEMBLIES Report and user manual EUT Report 87 E 180 1987 ISBN 90 6144 180 3 Bollen M H J and P T M Vaessen FREQUENCY SPECTRA FOR ADMITTANCE AND VOLTAGE TRANSFERS MEASURED ON A THREE PHASE POWER TRANSFORMER EUT Report amp 7 E 181 1987 ISBN 90 6144 181 1 Zhu Yu Cai BLACK BOX IDENTIFICATION OF MIMO TRANSFER FUNCTIONS Asymptotic properties of prediction error models EUT Report 87 E 182 1987 ISBN 90 6144 182 xX Zhu Yu Cai ON THE BOUNDS OF THE MODELLING ERRORS OF BLACK BOX MIMO TRANSFER FUNCTION ESTIMATES EUT Report 87 E 183 1987 ISBN 90 6244 183 8 Kadete H ENHANCEMENT OF HEAT TRANSFER BY CORONA WIND EUT Report 87 E 184 1987 ISBN 90 6144 184 6 Hermans P A M and A M J Kwaks I V Bruza J Dijk THE IMPACT OF TELECOMMUNICATION ON RURAL AREAS IN DEVELOPING COUNTRIES EUT Report 9 7 E 185 1987 ISBN 90 6144 165 4 Fu Yanhong THE INFLUENCE OF CONTACT SURFACE MICROSTRUCTURE ON VACUUM ARC STABILITY AND ARC VOLTAGE EUT Report 87 E 186 1987 ISBN 90 6144
20. a comment to the plot This text is entered in the interface line If no text is given the hardcopy is aborted The file can be spooled for printing RETRIEVE This option allows to retrieve an analysis from the database A list of analysis is displayed to the right of the screen An analysis is selected by clicking on its name Inmediately after an analysis has been retrieved its characteristics are displayed on screen i e if it is a functional map its yield the size of the wafer used etc STORE This option allows to store the last analysis performed in the database The name of the file is asked in the interface line If no name is given and only lt CR gt is typed the function is aborted 20 SHELL This option is used to stop ALWAYS temporarly and to go back to the system s shell To retum to ALWAYS type lt CTRL D gt 21 3 DIAGNOSTICS AND TROUBLESHOOTING There are basically two types of diagnostics One is refered as user diagnostics and it concems all the interface messages between the user and ALWAYS The other type of diagnostics are refered as system diagnostics These messages deal with the internal programming of ALWAYS such as to allocate memory space for wafer maps or to search for wafer files etc The latter type of diagnostics appear only when there are conflicts between ALWAYS and the operating system 3 1 USER DIAGNOSTICS The following are the error messages displayed by ALWAYS A brief expl
21. ace_y 0 displace_y lt die_size_y displace_y delta_y for i 0 i lt number_dice_in_x i for j 0 j lt number_dice_in_y j if die_in_wafer i j dice if dice gt max max dice max_x displace_x max_y displace_y j dice 0 H Dg Figure 5 Wafer displacement from the center of the mask The final configuration of the wafer i e the size the dice s size etc is considered as the prototype wafer and will be used in the analyses and simulations 4 THE MAP AND DISTRIBUTION ANALYSES The analysis is based on cumulative results by doing the Boolean And on a set of wafers The result is a composite wafer map which contains the cumulative yield by site location as shown in Fig 6 This methodology and its benefits were already reported for a specific application in 16 and for a spatial analysis in 19 We extend it by considering not only the individual wafer variations but also by taking in account the lot and project variations of the product Figure The Boolean And of wafers In Fig 7 we can see the typical flow of an analysis This kind of wafer convolution allows also to consider the mean and standard deviations between lots and between projects a well known problem 11 Furthermore the methodology exploits the fact that wafers have statistically dependent yield patterns for certain processing steps and also that wafer yields are usually correlated when proc
22. anation of its meaning is given These messages appear as a result of an incorrect usage of the features of ALWAYS Their interpretation during the session is straightforward Analysis can be corrupted check always errors for errors It was found during the loading of the wafer data that some dice are illegal Inspect the file always errors for specific details on these dice Invalid wafer size The size of the wafer is zero Invalid mask size The size of the mask is zero Invalid die size The size of the die is zero Impossible to draw wafer check sizes This occurs when an attempt to draw the wafer is made but any of the wafer size the mask size and the die size is incorrect Dead site position out of wafer If the wafer is displaced from the mask ALWAYS verifies that the dead dice remain within the wafer Non existent dead site An attempt to cancel a non existent dead die was made Wafer size is not available The wafer size was zero at the moment of finding the maximum number of dice in the wafer Mask size is not available The mask size was zero at the moment of finding the maximum number of dice in the wafer Die size is not available The die size was zero at the moment of finding the maximum number of dice in the wafer Errors in configure file Syntax errors were detected in the file always config Project was not previously allocated An attempt to cancel a non active project was made Lot was not previously allocate
23. as analysis type 58 Cannot create space for angular distribution 59 Cannot create header of displayed files list 60 Cannot link file in displayed files list 61 Cannot store the name of the displayed file 62 Cannot store the name of the simulation file to be displayed 63 Cannot store the name of the distribution file to be displayed 64 Cannot store the name of the analysis file to be displayed 65 Cannot store the name of the project path 66 Cannot store the name of the lot path 67 Cannot create space for statistical analysis 68 Cannot create alternate map for alternate or overlap options 69 Cannot create space to retrieve a distribution 70 Cannot create space for alternate map simulation 71 Cannot create space for the simulated wafer map 72 Cannot create space for radial map in simulation phase 73 Cannot create space for radial number of dice during simulation 74 Cannot create space for alternate yield vs area distribution 75 Cannot create spacel to retrieve distribution file 76 Cannot allocate space to show the current distribution 77 Cannot allocate space to retrieve the distribution Eindhoven University of Technology Research Reports ISSN 0167 9708 Faculty of Electrical Engineering Coden TEUEDE 168 169 170 172 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 Linnartz J P M G
24. ays achieve the maximum number of dice in the wafer or simply it does not look like the real life wafer However the availability of a mask with all the dice allows to move the wafer frame in order to obtain the real life dice configuration Thus the wafer can be shifted up down left or right through the mask at user s will The amount of shifting is specified in displace_x and displace_y in the previous routine In addition to the normal dice it is also possible to specify dead dice The locations of these dice are considered dead and are not taken in account for analyses or simulations In production wafers they represent the test sites for instance It is also possible to obtain the maximum number of dice in the wafer according to 15 see Fig 5 In our case the parameters G and H are made to be less or equal to the size of the die in the horizontal and vertical directions respectively The following routine finds the displacement of the wafer with respect to the mask center in order to obtain the maximum number of dice Notice that this is a very expensive routine since it has to iterate die_size_x die_size_y i j times before it can output correct results The accuracy of the routine depends on the delta values the smaller they are the more accurate results we obtain maximum dice max max_x max_y 0 displace_x displace_y 0 for displace_x 0 displace_x lt die_size_x displace_x delta_x for displ
25. butions for simulations ALWAYS assumes that the last y coordinate remains constant if the distribution was not drawn up to the maximum value of the domain of the function For instance if the maximum value of the domain is let us say 35 and the last coordinates drawn were 23 0 8 ALWAYS assumes that from the domain 23 to 35 the function has a constant value of 0 8 2 6 1 YIELD vs AREA SIMULATION This simulation is based on the negative binomial formula of yield ALWAYS offers several alternatives to feed the input data to the yield formula It is possible to give the mean and standard deviations of the distribution or to draw on line the distribution and to store it for future use or to retrieve any distributions existing in the database The mean and standard deviations of any distribution are shown in the fields in the mean distribution and standard deviation options The distribution represents the number of defects per die The menu is shown in Fig 10 mean distribution standard deviation Figure 10 Yield Area Simulation Menu MEAN DISTRIBUTION This is the mean of the population of the hypothetical sample The value is entered in a field to the right of the screen STANDARD DEVIATION This is the standard deviation of the population of the hypothetical sample The value is entered in the field to the right of the screen DRAW If this option is chosen ALWAYS is able to interpret the distribution drawn on
26. d An attempt to canccl a non active lot was made Wafer was not previously allocated An attempt to cancel a non active wafer was made Non analysis has been performed An attempt lo store or to hardcopy a non existent analysis was made Out of boundary While drawing a distribution an attempt to draw out of the grid was made 22 Function definition violated More than one value for the same domain value was tried to be drawn Non existent simulations An attempt to retrieve inexistent simulations was made Non existent distributions An attempt to retrieve inexistent distributions was made Non existent analysis An attempt to retrieve inexistent analysis was made Non existent projects An attempt to retrieve inexistent projects was made No project is active An attempt to select a lot without having selected a project was made Non existent lots An attempt to retrieve inexistent lots was made No lot is active An attempt to select a wafer without having selected a lot was made Non existent wafers An attempt to retricve inexistent wafers was made Invalid number of wafers The number of wafers was zero when trying to run the wafer map simulation Upper distribution is undefined The upper boundary radial distribution was undfined when trying to run the wafer map simulation Lower distribution is undefined The lower boundary radial distribution was undfined when trying to run the wafer map Simulation Syntax errors in file Reading aborted Sy
27. d the relative upper and lower radial distributions of lt lt eese dice The menu is shown in Fig 11 uppe T distribution lower distribution Figure t1 Wafer Map Simulation Menu WAFERS Enter the number of wafers of the ot in the field to the right of the screen UPPER DISTRIBUTION This option allows to specify the upper radial distribution For details refer to the section radial distributions LOWER DISTRIBUTION This option allows to specify the lower radial distribution For details refer to the section radial distributions RUN This option executes the simulation The simulation process for each wafer is shown on screen Dice in green are good and dice in red are bad VIEW This option allows to view the simulated wafers individually The wafers are displayed to the right of the screen To make one active click on its name The dice shown in green are good and the dice in red are bad These wafers are mantained only temporarly if a new simulation is executed they are lost and the new set of wafers is made active To store permanently any of the wafers view it and then go to the tools menu and store it as an R lt analysis When ALWAYS is exited the wafers are deleted SHOW MAP This option allows to carry on several map analyses on the composite simulated wafer For details refer to the map analyses 2 6 2 1 RADIAL DISTRIBUTIONS This menu is the same for the upper and lowe
28. during the present analysis and to make a hardcopy of the analysis or simulations The tools menu is shown in Fig 13 _ alternate overlap hardcopy store retrieve shell Figure 13 Tools Menu ALTERNATE When an analysis is retrieved from the database this option allows to alternate it with any other analysis in the analysis menu This option is enabled here and it has effect only in the analysis menu By clicking the middle button in that menu whatever is displayed is swapped with the currently retrieved analysis If the middle button is clicked again then the original analysis is restored Thus the function acts as a toggle The dice of the retrieved analysis are shown in orange OVERLAP When an analysis is retrieved from the database this option allows to overlap it over any other analysis in the analysis menu This option is enabled here and it has effect only in the analysis menu By clicking the middle button in that menu whatever is displayed is overlapped by the currently retrieved analysis If the middle button is clicked again then the original analysis is restored Thus the function acts as a toggle The dice of the retrieved wafer are in orange and any die collapsing with the current analysis is shown in gray HARDCOPY This option creates a plotfile of the last analysis or simulation performed The plotfile is in postscript format and it is called always print ALWAYS asks for text which is used as
29. e locations which were good all the time in the whole set of wafers selected for the analysis Additionally the correlated mean and standard deviations between lots and projects is also evaluated for good dice From the practical point of view this map is useful in determining which are the most correlated dice in a wafer in order to assure a minimum wafer yield for evaluating product costs for instance Zero Map The zero map shows all the die locations which were bad all the time in the whole set of wafers selected for the analysis As with the functional map the mean and standard deviations 2re evaluated but this time is for bad locations This map shows immediately which are the dice detractors and maior contributors to yield loss one can also observe from this map the least correlated regions in a wafer Up range Map This map shows ail the die locations which showed a specific yield or above it for the whole set of wafers The correlated statistics are also evaluated for lots and projects i e the specified yield is also Icoked up in every lot and in every project The specific yield is a user entry We can use this map for instance to investigate the gencral correlation of a specific process step along the entire lot Let s say that the input data were process parameters like the Vt of depletion transistors then by asking to show the 50 site yield or more we can infere about the uriiformity of the ion implantation process step f
30. e theoretical yield modelers office etc The most significant features of ALWAYS are summarised as follows 1 A simple database structure allows to examine lots and individual wafers 2 Full flexibility to edit the characteristics of the prototype wafer 3 The analysis techinique allows to estimate the contributions of both correlated and uncorrelated detractors to the total yield Such information can be used to study the effect of process changes on product yield 4 Simple simulation tools to estimate the wafer yield It is our believe that a simple package like ALWAYS provides a positive impact on yield improvement 19 REFERENCES 1 2 3 4 5 6 7 C8 C9 10 11 12 13 Ham W E Yield area analysis Part 1 A diagnostic tool for fundamental integrated circuit process problems RCA Rev Vol 39 1978 p 231 249 Warner Jr R M Applying a composite model to the IC yield problem IEEE J Solid State Circuits Vol SC 9 1974 p 86 95 Stapper Jr CH On a composite model to the IC yield problem IEEE J Solid State Circuits Vol SC 10 1975 p 537 539 Ferris Prabhu A V and L D Smith H A Bonges J K Paulsen Radial yield variations in semiconductor wafers IEEE Circuits amp Devices Mag Vol 3 No 2 March 1987 p 42 47 Stapper C H On yield fault distributions and clustering of particles IBM J Res amp Dev Vol 30 1986 p 326
31. eat these steps for each one of the wafers As a word of comment all the wafers were not processed identically some variations as the concentration of dopants were changed Hence in the following discussion we avoid making any statistical inferences of the results We simply use them to show some of the features of ALWAYS The real life configuration of the dice in the wafers to be analysed is shown in Fig 1 Figure 1 Dice configuration in the EFFIC wafers Eindhovense Fabricage Faciliteit voor geIntegreerde Circuits Eindhoven Fabrication Facility for Integrated Circuits 1 1 GETTING STARTED Start ALWAYS by typing always lt CR gt As we already mentioned ALWAYS stands for AnaLyser of WAfer YicldS the current version is 1 0 we hope to make more improvements Now try clicking the Icft button of the mouse This button is used to point at any of the menu sclections the button in the center is used to show analyses previously stored and the button to the right is used to exit the program this can be done by doubleclicking it You are now facing the main menu oplions of ALWAYS At the top are displayed the characteristics of the protoype wafer and as we can sce they differ very much from our real life wafer Move the cursor to the edit option and click the left button This menu allows to edit the characteristics of the prototype wafer First we know that our dice are biggcr thus click in the die size option you
32. ences scsso Ware TEE A BMA WEY MeO Dew Aa 19 Appendix User s Manual ALWAYS Report 1 INTRODUCTION The ever growing complexity of very large scale integrated circuit chips demands tools to analyse the spatial yield distribution of wafers and to relate this information to the particular layout for fault prediction 13 14 17 24 26 and design yield estimation Increasing the levels of semiconductor integration to larger chips with more and more transistors addresses topics such as the yield associated with individual process steps like etching metallisation etc or the spatial distribution of random and systematic sources of yield loss 27 28 29 The actual production wafers are an excellent source of information available at minimum effort and low cost that reliably reflect the limiting factors existing in the technology process Interaction with these factors can be aided by analysing the wafer maps where functional nonfunctional and partially functional regions can easily be observed Better circuit designs and yield improvements can be achieved by understanding the properties of complete wafers and by redirecting these results exactly to the process and design stages where they belong It is then necessary a tool to manage the enormous amount of data coming from the manufacturing lines and to condense it in useful information for the process engineer the layout designer the quality engineer etc or for whom
33. ents xg with their respective variances s s per lot and per project This is done as follows 1 i N ree LCi 15 2 1 So x 16 Sc N I p gt iT Xe 1 i N XG WL 17 2 ae 2 s YG xo 18 14 where C represents the number of clusters G the number of clustered elements and N the size of the sample i e the number of lots or projects A 95 confidence interval for the mean number of clusters and of clustered elements is also evaluated This minimum set of statistics allows us to inspect the variations between wafers lots and projects 15 6 SIMULATIONS ALWAYS provides two kinds of simulations One is the evaluation of the yield vs area and the other is the creation of wafer maps The yield vs area is evaluated using a distribution of the number of defects per chip and its formula is given according to 12 as by 2 on Y AD 1 19 where A is the area of the die in the prototype wafer D is the average defect density and the coefficient of the defect density variation In this simulation the user is able to give the mean and the standard deviations as input data or to create a file containing the description of the distribution to be used or can draw the distribution online The wafer map simulation is for one lot The number of wafers in the lot is a user entry and the characteristics of the wafer correspond to the prototype wafer The input data to simulate wafer maps consists
34. essed in the same lot or under similar conditions projects Figure 7 The convolution of wafers in a typical analysis The within wafer yield variations are inspected by using the concept of site yield A site yield shows how many times in the complete set of wafers involved in the analysis a particular die accomplished a function For instance if our analysis consists of a lot of ten wafers and one die in the composite wafer was only five times good then its functional site yield is of 50 Thus we can write the site yield as y Eru site Na 1 where Fse is the site frequency in other words the number of times that the die was projected and N is the number of wafers involved in the analysis It is obvious that by using this approach we can account for wafer to wafer and lot to lot variations as weil as regional variations in wafers ALWAYS can execute two kinds of analysis on data One is called the map analysis and the other the distribution analysis The map analysis displays the composite wafer map with the projected dice that accomplished the function and its purpose is mainly intended to see the correlated spatial behaviour of the input data The distribution analysis on the other hand quantifies the behaviour of the input data by showing the curves of different types of distributions of the final composite wafer map The map analysis that ALWAYS can carry on are Functional Map The functional map shows all the di
35. g is completed we can face then the analysis menu Remember that we selected only one wafer thus some options will be meaningless although you are free to try them We will find first all the good dice in the wafer so click in the functional map option The dice displayed in green are the good dice the rest are blank To the right are some statistics Mainly they are the yield of good dice the number of projects lots and wafers involved in the analysis the average lot yield the variations in the lot yield the project average and variation yield and finally the expected number of dice that accomplish the function Since we have only one wafer one project and one lot the project and lot variation values are the same Now find the bad dice thus click in the zero map The dice in red are the bad dice To the right are also displayed statistics corresponding to this map The yield shown is now for bad dice Click now in the distribution option to check the radial and angular distributions of this wafer Click first in the radial option you will be asked to give the site yield type 100 to mean that we want to find the radial distribution of good dice Now let us see the angular distribution click in the angular distribution option and answer also with 100 for the site yield If you try a number other than 100 or 0 ALWAYS will try to adjust it with respect to the number of existing wafers in the analysis for instance if you type 75 the
36. ighlighted furthermore if one clicks at one of the lots of the project all the wafers that belong to that specific lot will be highlighted It is possible to scroll in each of the windows by clicking in the arrows OOBARC g g im O E m Bi a Figure 4 Main menu SET This option allows to select or to cancel projects lots and wafers for the analysis ANALYSE This option allows to carry on several types of analyses on the wafers selected for this purpose SIMULATE This option allows to simulate the yield vs area or to simulate wafers maps based upon the characteristics of the prototype wafer EDIT This option allows to edit the characteristics of the prototype wafer TOOLS This option is used to save or retrieve data in the database and to use other tools 23 WAFER EDITING This menu allows to change the characteristics of the prototype wafer The changes are the size of the wafer the size of the mask the size of the dice and the displacement of the wafer with respect to the mask It is also possible to select here the dead dice and to visualise the coordinates of each of the dice in the wafer The edit menu is shown in Fig 5 When ALWAYS asks to enter any numerical information the only keys which are enabled are 1 2 3 4 5 6 7 8 9 0 BACKSPACE CR ALWAYS interprets the data when the lt CR gt key is pressed if an undesired number is keyed it can be erased with the lt BACKSPACE gt
37. in the project option To the right of the screen are displayed all the projects that are present in the current directory In our case there are only two The depletion and the enhan projects Since we said that we are going to analyse first the enhancement data click in the select option and then in the enhan project The name of the project should have been highlighted otherwise try again Now click in the done exit bar to indicate that we want that project this last action is interpreted as done with the menu and exit it SO we are positioned again in the set rnenu Now let us choose the lots Click in the lots option In a similar fashion to the projects the lots are displayed to the right of the screen These lots are the lots that belong 10 the project previously chosen that is project enhan Select the lot 5600 We have now the project and the lot for our analysis Try to select wafer 5600e 1 by doing similar operations to the project or lot sciection Click in the done exit bar until we get back to the main menu again Now you will sce in the three small windows to the right the project lots and wafers involved for the analysis We have now the correct prototype wafer and we already chose the data for the analysis so let us analyse this data Click in the analysis option at the bottom you will see displayed a message informing that ALWAYS is loading the data corresponding to the wafer 5600e1 After the loadin
38. ion file in advance by typing it and the last altemative is to draw it directly on screen We shall try this last option Click in the draw option ALWAYS paints a grid whose ordinate is the wafer radius and the absice is the radial yield Try to draw the distribution shown in Fig 2 First click in the grid at coordinates 0 0 6 they are also displayed at the right side of the screen this is the initial point a rubberband for line drawing will appear direct the rubberband to the next point and click there the rubberband should have been fixed up to the new point and a ncw rubberband starting at the last point appears Continuc to do so until you finish drawing the distribution If you commit a mistake click the middle button of the mousc to undo the last linc To finish drawing click in the done exit bar Relative Radial Dice Yield t gt are a ahs TO o ro a 7 n GOP aeaaee a Sa oj ei eae 5 1 j j i 38 76 11 4 15 2 180 226 266 304 342 38 0 Distance Irom Wafer Centar Figure 2 Lower relative radial yield for the example Now let us run the simulation so click in the run option The simulation phase starts automatically and every wafer is displayed After the simulation is finished the wafers can be viewed through the view option and also they can be analysed through the show map option These analyses are the same that we investigated before From now on you are on your own have an enjoyable time with ALWAYS and
39. ion of the type of input data in question For our previous example of Vts this map shows the scanning uniformity of the ion beam of the ion implanter if there were doubts about the equipment or the effectiveness of the mask employed for this process step For our example of defect sizes this maps shows the distribution of defects of a specific size along the wafer and through the entire lot Cluster map In this analysis the user is asked to specify the number of elements that define a cluster and the site yield for the dice The resulting map shows the clusters according to the previous specifications Statistics such as the numbers of clusters and the number of clustered dice are reported Lets investigate now into a bit more of detail the generation of the map analyses The next piece of code shows how do we find the functional map however this routine can easily be extended to find the other map analyses We make use of the fact that the information is stored in a matrix thus we first check whether the element in tum of the matrix in other words the die lays inside of the wafer and if it does whether it accomplished a hundred per cent yield If both conditions are satisfied we can proceed to project the die by drawing it and also to update the computation of the functional yield functional_map for x 0 x lt total_dice_in_x x for y 0 y lt total_dice_in_y y if die_in_wafer x y if composite_wafer x y
40. ividual wafer and the info map of all the wafers allows to see ihe contribution to yield improvement or detraction of the single wafer The overlap and alternate functions act as toggles so to get the initial info map click again the middie button of the mouse and see how does the retrieved map disappear The last feature that we arc going to review is the wafer map simulation Go to the main menu and click in the simulate option and then click in the wafer map option In order to simulate wafer maps we must provide the number of wafers to be simulated the upper radial yicld and finally the lower radial yield If any of this conditions is missing the simulation will not run Now ict us say that we want to simulate a lot of 10 wafers Click in the wafers option and then type 10 in the field to the night of the screen Click in the upper distribution in order to set the upper radial yicid A new menu will appear click in the retrieve option This option retrieves all the distributions cxisting in the database In this case there is only one the upper Click on its name and wait until it is drawn on screen at that moment ALWAYS knows already which is the upper yield distribution We are missing only the lower yicld Click in the done exit bar to go backwards and then click in the lower distribution option ALWAYS provides several mechanisms to capture a distribution we already tried one the retrievement another onc is to create the ditribut
41. llaneous Tools 3 0 Diagnostics and Troubleshooting 3 1 User Diagnostics 3 2 System Diagnostics 1 A TUTORIAL This section is not intended to give an exhaustive explanation of ALWAYS it is rather aimed to demonstrate the essential features of ALWAYS in a normal session but without getting down into formal rules For more details refer to the report or to the user s manual This tutorial assumes that the user is seated behind a terminal with ALWAYS running The tutorial example is located in the directory PATH always tutonal The wafers to be analysed consist of a sequence of tests to evaluate the threshold voltage adjustment at EFFIC Four lots are derived two are for depletion transistors and the others for enhancement transistors Thus we created two projects one is called depletion and the other enhan EFFIC uses wafers of 3 inches of diameter and the size of the dice in question is 5 8mm by side The results of the measurements are stored in a directory named PATH measurements We created a filter to interpret these results for ALWAYS first we evaluate the average and standard deviations of the threshold voltages in each wafer then knowing these values we make a process window of acceptance of the voltage value We say that the threshold voltage is good if its value lays within 30 and 30 of the average value Next we simply pass from the coordinate system of the ATE to ours for more convenience and simplicity Finally we rep
42. lot in the list 28 Cannot store the name of the active lot 29 Cannot create header of the wafer list 30 Cannot link wafer in the wafer list 31 Cannot store the wafer name 32 Cannot create the header for continuos lot selection 33 Cannot link lot in continuos lot selection 24 34 Cannot store the name of the lot in the continuos lot selection 35 Cannot create the header of the wafer list in continuos selection 36 Cannot link a wafer in continuos selection 37 Cannot open lot directory 38 Cannot open lot directory 39 Cannot create header for coordinate list 40 Cannot link coordinates in the list 41 Cannot allocate partial project map 42 Cannot alloacte partial lot map 43 Cannot allocate composite map 44 Cannot allocate map for storage as analysis type 45 Cannot allocate cluster map 46 Insufficient space for frequency distribution analysis 47 Insufficient space for cumulative distribution analysis 48 Insufficient space for analsysi storage as analysis type 49 Cannot create space for cluster statistics 50 Cannot allocate cluster map for cluster statistics 51 Cannot allocate header of dead dice list 52 Cannot link dead die in the list 53 Cannot create space for simulation map 54 Cannot creatc space for storage of radial distribution as analysis type 55 Cannot create space for radial distribution 56 Cannot create space for radial map 57 Cannot create space for storage of angular distribution
43. nd also all the lots and all the wafers belonging to each lot are made active as well The existent projects are displayed to the right of the screen Each project that is selected or canceled is highlighted in red The arrows in the lower right comer are used to scroll through projects if their number exceeds the size of the window 13 2 5 YIELD ANALYSIS This option offers the ability to carry on several wafer map and distribution analyses All the analyses make use of the wafers selected in the SET option All the user s yield value inputs are assumed to be in per centage 2 5 1 WAFER MAP ANALYSIS The menu option for wafer map analysis is shown in Fig 8 Each analysis is accompanied of a set of statistics that reflect the variations between wafers lots and projects For more details on the analysis options and on the statistics refer to the system description in the first section of this EUT report history ma map Figure 8 Analysis Menu FUNCTIONAL MAP This map shows all the dice that were good all the time in the whole set of wafers involved in the analysis The dice that are good are displayed in green ZERO MAP This map shows all the dice that were bad all the time in the whole set of wafers involved in the analysis The dice that are bad are displayed in red UP RANGE MAP With this option it is necessary to specify the minimum site yield to be displayed This is done by entering the yield value
44. nner radius and r2 is the outer radius of the ring the area is kept constant by taking rz as A m r3 rf A 2 r ma r n Instcad of incrementing the angle in one degree we maximise the angle by obtaining the arc sine of the hypotenuse of the dic and the radius of the wafer This will give us the minimum incremental angle for a full coverage of dice along the scanning line We do the same for the radial increment in this case we take the minimum value between the size of the die in the vertical and horizontal dircctions Since we deal with dic sites it is necessary to find the coordinates of any die for any given x and y vector components of the changing radius This is carried on in the find_dic_at_radiusQ function where the vector components are converted to the corresponding dic coordinates Finally to avoid counting a die which was already considered within the previous angle and or radius we simply mark it and skip it if necessary The next routine applics these concepts radial_distribution area PI wafer_radius wafer_radius 10 0 rl 0 r2 sqrt arca PI squared_x dic_size_in_x die_sizc_in_x squared_y dic_size_in_y die_size_in_y dic_size sqrt squarcd_x squared_y delta_theta asin dic_size wafer_radius delta_radius MIN dic_size_in_x dic_size_in_y do radial_yicld clements_found 0 for theta 0 theta lt 2 PI theta delta_theta for radius rl radius l
45. ns option and then click in the frequency option this last option will display a histogram of the frequency of occurrence of each site yield Before we continue it would be good that you investigate the several options for the analysis by yourself Take your time We shall see now the different tools that we have in ALWAYS so place yourself in the main menu and click in the tools option Click now in the retrieve option this option will display and allow you to select analyses previously stored in the database you will see only one called 5601e which is the one that we created for the purposes of this tutorial Click in the name of the analysis to retrieve it On screen you will see the characteristics of the analysis It is a functional map of one of the wafers Now click in the overlap option This action enables as its name says the overlap function That is whenever we are dealing with any analysis and we want to do an ovcrlap of wafers between the reirieved from the database and the one created from the analysis we use this function and if we want to swap wafers we use the alternate option Now click in the done exit bar to go back to the main menu and then click in the analysis option Choose now the info map so click in there and after the analysis is finished click the middie button of the mousc This action will overlap the wafer that we have just retrieved over the info analysis The combination of an ind
46. ntax error in the distribution file were found No function has been drawn An attempt to show or to store a distribution was made No analysis has been retrieved Either the overlap or altemate options were selected without having retrieved an analysis from the database Function aborted lt CR gt was typed immediately after asking for the name of the file to be stored or after asking for text in the hardcopy option Either the mean or the standard dev is zero Simulation skipped If either of these values is zero the alpha factor is undefined Beta is zero Simulation aborted The beta factor was found to be zero 3 2 SYSTEM DIAGNOSTICS The following are the messages that can appear as a consequence of a conflict between ALWAYS 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 23 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 7 report them to Jose Pineda de Gyvez Eindhoven University of Tech Design Automation Group Room 7 16 The Netherlands Tel 040 473373 ALWAYS uses the tmp directory to write information of the partial maps It creates a file named projects which contains the names of each
47. nu offers the ability to displace the wafer from the center of the mask to recenter the wafer and the mask and to find the maximum number of dice that can be acommodated in the wafer The adjust menu is shown in Fig 6 Figure 6 Wafer Displacement Menu MAXIMUM This option configures the dice in the wafer in such a form that the wafer contains the maximum possible number of dice CENTER This options aligns the center of the wafer with the center of the mask STEP This is the incremental step used to displace the wafer from the mask Its value is displayed immediately below the title UP This options moves up the wafer from the mask DOWN This option moves down the wafer from the mask LEFT This option moves the wafer to the left of the mask RIGHT This option moves the wafer to the right of the mask 12 2 4 INPUT DATA SELECTION This menu allows to select the projects lots and wafers that will be used for analysis The selection of data is hierarchical In order to select any wafer its lot and its project should have been selected previously This menu is shown in Fig 7 gl Figure 7 Data selection Menu WAFER This option selects individual wafers from the lot and project currently active A second menu with the options of select and cancel appears By clicking the select option the names of the existent wafers appear to the right of the screen in order t make them acti
48. of the relative radial distribution of site yields expressed as follows Yp t 20 R Np where N is the number of good dice at radius R and Np is the total number of dice at radius R It is clear that the within wafer variations are considered with a radial distribution Now in order to consider the variations between wafers one has to bear in mind that some wafers exhibit a higher radial yield and some a lower Therefore the input data consists in fact of two radial distributions one for the upper bound and the other for the lower bound Thus the regional variation of the simulated wafers lays between these two limits as Yr YR 21 where Ypg is the upper radial yield and Ypg is the lower radial yield both at radius R Hence the simulation is left to the task of generating a random number of good dice for whose relative radial yield at wafer radius R lays between these two boundaries The next routine applies the former idea The input parameters to the routine are the partial radius and the number of dice at that radius This routine forms part of a main loop in which the the partial radius is incremented from zero to the wafer radius and that for each partial radius the correponding number of dice is found simulate_radial_dice radius number_dice if upper_yield radius lt lower_yield radius errorQ retum FALSE good_dice upper_yield radius number_dice bias good_dice lower_yield radius number_dice
49. or instance Low range map This analysis shows the locations with a specific site yield or less In certain form this map is the complement of the previous one An example of its use is when the input data are defect sizes i e a die is good if the defect size measured for that location is of a predefined value otherwise it is bad We can organise the data in such a way that one project contains information of defects of size x and another project of defects of size y and so on Thus if we select only one project and we ask for the locations where the specific site yield is 50 or less we mean that we want to know the correlation of defects along the whole set of wafers involved in the project The result could be interpreted as an index of how many times defects of the same size showed to be clustered in the same place in half or less of the total wafers involved in the analysis History map This analysis shows numerically the yield of each die location for the whole set of wafers The uncorretated analysis showing the mean and standard deviations between wafers lots and projects is displayed here This numerical information is useful to quantify each site yield of the composite wafer Informative map This is a contour informative map it shows the average and the above and below average site yield of the dice Zero yield locations are distinguished from the rest of the dice This analysis allows to visualise the uniform distribut
50. projected Through this analysis we can quantify the die correlation of wafers and have a defined idea of correlated site yields A natural consequence of the previous analysis is a cumulative frequency distribution analysis 9 which tells us about the overall behaviour of the whole set of wafers for instance we can see immediately the probability of occurrence of each of the different site yiclds Finally an analysis which could not be omitted is the yield vs area 3 12 In the radial and angular analysis the user is asked to specify the site yield which is going to be looked for This adds flexibility to the analysis since in this form we can obtain a set of different curves for different site yields One example that makes use of this idea is when we want to analyse the frequency of ocurrence of defects in different regions of the wafer So we can obtain radial or angular distributions for 0 1 2 or N defects and each analysis independent of the other ll In the yield vs arca analysis the user is also asked to specify the site yicld The kind of benelits that we can obtain from this feature are i c the number of defects per arca in order to classify clusters 5 6 or simply the traditional yield vs arca curve A routine of interest is the generation of the radial distribution The radial plots are made using concentric rings of constant arca to determine the site yield at a distance r from the center of the water If r is the i
51. r distributions The distribution can either be retrieved from the database or be drawn on screen The menu is illustrated in Fig 12 store retrieve Figure 12 Radial distribution Menu DRAW If this option is chosen ALWAYS is able to interpret the distribution drawn on screen ALWAYS draws a grid with the ordinate size equal to the radius of the prototype wafer and the abscissa size equal to one To draw something point at a location in the grid and then click the first button a rubberband line should appear if one clicks the first button again the line is fixed and the coordinates shown at the right side are saved by ALWAYS if one commits a mistake then click the middle button to undo the last line To stop drawing select any of the options in the select region SHOW This options shows the current distribution used in the simulation STORE This option stores in the database the last distribution drawn The user is asked to give the name of the file in the interface line The file will be characterised by dst in the database RETRIEVE This option retrieves all the distributions from the database They are shown to the right of the screen To make one active click on its name and wait until it is displayed on screen 2 7 MISCELLANEOUS TOOLS The several tools that ALWAYS offers are to store and retrieve analyses in the database to allow to overlap and to alternate retrieved wafers with wafers generated
52. re is obviously no 75 yield there is only O or 100 since we have only one wafer Thus ALWAYS will respond with the analysis for 0 Remeber that our interpretation of site yield implies the number of projected dice from all the wafers that accomplish a function At this point we assume that you are already more or less familiar with the selection of data so let us add more data to the analysis Click twice in the done exit bar to go back to the main menu Now go to the set menu and select all the wafers of the lot 5600 So click in the wafers option then click in select option and then click through each one of the wafers after you have selected ali the wafers click in the done exit bar to indicated that we want all those wafers done and that we want to go back exit Now select also all the wafers of lot 5500 Click in the lots option and then in the select option then click twice in the 5500 This last action will select all the wafers of lot 5500 because ALWAYS allocates when two projects or two lots are selected inmediately one after each other all the elements of the second to last selected item Now go again to the analysis menu so click in the done exit bar and then in the analysis option Let us investigate one of the variable maps click in the up range map and answer with 50 this means that we want to see the dice that were good through half or more of the wafers in the analysis Now click in the distributio
53. redict wafer yields via simple simulation tools The analysis technique investigates the effect of correlated and uncorrelated sources of yield loss Such information can be used to study the changes in the technological process Graphical displays in the form of wafer maps are uscd lo represent the spatial distribution of dice in the wafer Facilities such as radial and angular distribution analyses among others are provided to examine data and hypothetical wafer maps are created to visualise and predict simulated wafer yiclds Pineda de Gyvez J ALWAYS A system for wafer yield analysis Report and user s manual Faculty of Electrical Engineering Eindhoven University of Technology 1988 EUT Report 88 E 189 Author s address Automatic System Design Group Faculty of Electrical Engineering Eindhoven University of Technology P O Box 513 5600 MB EINDHOVEN The Netherlands 0 This research was supported by the Department of Economic Affairs under the OPC program project IC EEL46018 iv CONTENTS Report Te UREROMUET TON stew iecak cos tesiwiines EERE sp amea we ad dees ie 2 Input Data and Database Description ccc eee e cece eee 2 3 Wafer Size and Die Assignments ccceeeceececeeees 4 4 The Map and Distribution Analyses cece cece eee eee 7 SB The Statistitssce ste tieee stata seta gene teenies B55 5 bees 12 7 Summary and ConclusioOnS s sesessresssossosecscesceasne 17 Refer
54. s For simplicity the flat side of the wafer is approximated to 0 04R 15 where R is the wafer radius The final routine looks as follows die_in_wafer i j x die_size_x i y die_size_y j out of the mask 7 if x die_size_x gt mask_size Il y die_size_y gt mask_size return OUTSIDE flat 0 04 wafer_radius left_bottom_x mask_center x displace_x left_bottom_y mask_center y displace_y left_top_x left_bottom_x left_top_y left_bottom_y die_size_y right_bottom_x left_bottom_x die_size_x right_bottom_y left_bottom_y right_top_x right_bottom_x Tight_top_y left_top_y radius Ib sqrt left_bottom_x left_bottom_x left_bottom_y left_bottom_y radius_lt sqrt left_top_x left_top_x lcft_top_y lefi_top_y radius_rb sqrt right_bottom_x right_bottom_x right_bottom_y right_bottom_y radius_t sqrt right_top_x right_top_x right_top_y right_top_y below the flat if left_bottom_y gt 0 amp amp left_bottom_y gt wafer_radius flat retum OUTSIDE in the wafer if radius_lb lt wafer_radius amp amp radius_lt lt wafer_radius if radius_rb lt wafer_radius amp amp radius_rt lt wafer_radius retum INSIDE retum OUTSIDE Some variables are redundant but they were left for a matter of clarity Fixing the wafer s center with the center of the mask does not alw
55. s and w wafer size m mask size x die size in x direction y die size in y direction h wafer shiftment with respect to the mask in x direction v wafer shiftment with respect to the mask in y direction These options can also be given interactively at the moment of starting ALWAYS as always wN mN xN yN hN vN i The i option is to tell ALWAYS to ignore the configure file if it exists DATABASE FILES Every analysis stored by ALWAYS with the store option in the tools menu is characterised by analysis_name ana and in the simulation section by distribution_name dst The analysis file is anon ASCII file and thus is not readable The format of the distribution file is x f x where x domain of the function f x the function Both files are stored in the current directory 2 2 MAIN OPTIONS This is the main menu of the system From here it is possible to edit a wafer to select the data for the analysis to carry on an analysis to make simulations and to use the miscellaneous tools The main menu screen is shown in Fig 4 At the top are displayed the characteristics of the prototype wafer These characteristics are the size of the wafer the size of the mask and the size of the dice At the right are three small windows named PROJECT LOT and WAFER respectively These windows contain the information of the data involved for the analysis If the name of a project is clicked all its lots and all its wafers are h
56. screen First it is necessary to specify the maximum value for the domain of the function in the field to the right of the screen and then the maximum value of the function in the same field Next ALWAYS draws a grid with the dimensions specified by the user To draw something point at a location in the grid and then click the first button a rubberband linc should appear by clicking the first button again the line is fixed and the coordinates shown at the right side are saved by ALWAYS if a mistake is commited then click the middle button to undo the last line To stop drawing select any of the options in the select region or the done exit bar 17 SHOW This options shows the current distribution used in the simulation STORE This option stores in the database the last distribution drawn The user is asked to give the name of the file in the interface line The file will be characterised by dst in the database RETRIEVE This option retrieves all the distributions from the database They are shown to the right of the screen To make one active click on its name and wait until it is displayed on screen RUN This option executes the simulation The result appears as a graph with the yield versus the number of times of the die area 2 6 2 WAFER SIMULATIONS In this menu it is possible to simulate the individual wafers of a lot In order to carry on a simulation it is necessary to specify the number of wafers an
57. sis IEEE Trans Comput Aided Des Integrated Circuits amp Syst Vol CAD 6 1987 p 592 600 Chen I and A J Strojwas Realistic yield simulation for IC structural failures In Digest of Tech 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 25 26 27 28 29 21 Freund J E and R E Walpole Mathematical statistics 3rd ed Englewood Cliffs N J Prentice Hall 1980 Prentice Hall mathematics series Chen I and A J Strojwas Realistic yield simulation for VLSIC structural failures IEEE Trans Comput Aided Des Integrated Circuits amp Syst Vol CAD 6 1987 p 965 980 i Fantini F and C Morandi Failure modes and mechanisms for VLSI ICs A review IEE Proc G Vol 132 1985 p 74 81 Edwards D G Testing for MOS IC failure modes IEEE Trans Reliab Vol R 31 1982 p 9 18 Taylor R G and E Stephens Microcircuit failure analysis Br Telecommun Eng Vol 4 1985 p 39 46 ALWAYS User s Manual CONTENTS 1 0 A Tutorial 1 1 Getting Started 2 0 User s Manual 2 1 User Interface 2 2 Main Options 2 3 Wafer Editing 2 3 1 Wafer Displacement i 2 4 Input Data Selection 2 5 Yield Analysis 2 5 1 Wafer Map Analysis 2 5 2 Distribution Analysis 2 6 Simulations 2 6 1 Yield vs Area Simulation 2 6 2 Wafer Simulations 2 6 2 1 Radial Distributions 2 7 Misce
58. t r2 radius delta_radius x radius cos theta y radius sin theta find_dic_at_radius amp x amp y if radial_mark x y FALSE radial_mark x y TRUE clements_found if composite_wafer x y SITE_YIELD radial_yicld plot r2 radial_yield clements_found rl 12 r2 sqrt area PI ri rl while r2 lt wafer_radius 12 5 THE STATISTICS The wafer maps standing alone are a good means to display the regional distribution of the input data on wafers Although they are a good tool they are usually not cnough One is generally interested in quantifying the results in order to make conclusions of the analysis i c to know the yield of good dice the variations of good dice between wafers cte It is thus necessary to count with a minimum set of statistical information as 10 make inferences about the wafer or set of wafers in analysis The first information is the yicld of the function i e the yicld of good dice the yicld of bad dice etc This yield is evaluated as Yr 2 where Ny is the number of dice that accomplished the function and N is the total number of dice of the composite wafer excluding the dead dice It is also of interest to find how did the function performed in each lot and in each project Thus for each function we give information about the mean yield per lot and per project with their corresponding variances Each partial yicid is
59. tc then the design engineering stage will benefit itself doing analysis through the yield editor 3 WAFER SIZE AND DIE ASSIGNMENTS The wafer size and die shape are user entries which can be modified at any time Dice are placed on an imaginary square which represents the photolitographic mask of the fabrication process The shape of the dice can take the form of a rectangle of any size and the center of the mask is used as a reference point to center the wafer frame see Fig 2 Figure 3 Wafer position with respect to the mask The placement of dice in the mask goes from left to right and from bottom to top as shown in Fig 4 This is important since dice are clipped to the wafer and partial dice are discarded The size of the mask is also adjustable to any value Figure 4 Die arrangement in the mask Eximining whether a die is in or out of the wafer is a tedious algorithm because it is necessary to check if the four corners of the die lay insicle of the wafer The procedure that we employ calculates the distance from each comer to the center of the mask remember that the wafer is centered with respect to the center of the mask and then evaluates if all these distances are less or equal than the wafer radius The input parameters to this routine are the coordinates of the die with respect to the left comer of the mask To transform the coordinates to distances we simply multiply them by the size of the die in the x and y direction
60. te on line system Hence it is essential that this capabilities be accessible in an easy form 18 ALWAYS provides interactive graphics displays online screen reports hardacopy plots and facilities to store in the database the analysis or simulation just performed as well as to retrieve previous ones These analyses can be overlapped over the current composite wafer to do comparisons or simply be placed instead of the current map As a part of the user friendly interface a set of color graphics to repon wafer maps and distribution charts was included see Fig 8 Also any distributions for the simulations can be drawn online This feature eases the continuos execution of quick simulations for new user s data 4 6 12 6 20 24 2 32 16 aa a 0 6 as a4 03 02 Ot i SRR RE ees Dee Oo eB ed Ee De ee Distance from wafer s center COREE C LJ im C mi B a Relative Frequency of Ocurrence Figure 8 a Example of wafer maps b Example of distributions To facilitate access to the results of every map analysis the statistics are reported immediately to their right They include the yield of the composite wafer the number of projects lots wafers and dice involved in the analysis and the yield variation between lots and between projects ALWAYS is a program wirtten in C and implemented on an Apollo Domain 3000 Workstation System running Unix BSD4 2 The current version supports static menu screens but later
61. tigated if the marked dice form a cluster by comparing the number of cluster elements with the minimum number wor elements find_clusters x y int x y These are the cardinal points i e NW is north west NO north etc NW NO NE WE EA SW SO SE SEED int xoff 9 1 0 1 1 1 1 0 1 0 int yoff 9 1 1 1 0 0 1 1 1 O cluster_map x y mark cluster_elements for next 0 next lt 8 next neighbour_x x xoff next neighbour_y y yoff next if neighbour_x lt 0 neighbour_x 0 else if neighbour_x gt total_dice_in_x neighbour_x total_dice_in_x if neighbour_y lt 0 neighbour_y 0 else if neighbour_y gt total_dice_in_y neighbour_y total_dice_in_y if die_in_wafer neighbour_x neighbour_y if composite_wafer neighbour_x neighbour_y CLUSTER_YIELD if cluster_map neighbour_x neighbour_y mark find_clusters neighbour_x neighbour_y In order to account for the different density variations in the wafer and to quantify the yield loss we provide a radial distribution inspection 1 4 8 of the composite wafer Furthermore the combination of the radial analysis with an angular analysis 7 will facilitate us to observe the behaviour of clustering Another important source of information is a site yield frequency distribution 2 that tell us how many times in the whole set of wafers involved for the analysis a particular die site was
62. tiple spot defects If one wants more accuracy or simply wants to reflect the number of defects it is possible to subdivide the test chip in four where each subdivision represents a defect The data could be now the coordinates of each one of the new subdice and its Status let us say good for a defect present and bad for a defect not present see Fig 2 Figure 2 Dice configuration in the wafer Then when a radial distribution analysis is executed it will mean the radial defect density instead of the original monitor density and furthermore accurate data as the number of defects will also be obtained The flexibility in the database structure as well as in the input data permits the user to cope with almost any situation in spatial yield analysis The only limits thus are restricted to the user itself and to the type of information available for the analysis A well known method of obtaining significant information is by using test structures 22 23 for process monitoring 10 This implies that different types of information are used by different kind of users When the parameters supplied to the editor are i e linewidths resistivity oxide thickness etc then the production stage can have impact on yield through a correct analysis procedure and an appropiate corrective action On the other hand if the parameters are defect distributions distribution of opens and shorts in different layers distribution of good and bad chips e
63. tu I7 Eindhoven esearch Report D University of Technology all Netherlands Faculty of Electric al Eng nen es Always A System for Wafer Yield Analysis Report and User s Manual by J Pineda de Gyvez EUT Report 88 E 189 ISBN 90 6144 189 7 February 1988 Eindhoven University of Technology Research Reports EINDHOVEN UNIVERSITY OF TECHNOLOGY Faculty of Electrical Engineering Eindhoven The Netherlands ISSN 0167 9708 Coden TEUEDE ALWAYS A SYSTEM FOR WAFER YIELD ANALYSIS Report and User s Manual by J Pineda de Gyvez EUT Report 88 E 189 ISBN 90 6144 189 7 Eindhoven February 1988 CIP GEGEVENS KONINKLIJKE BIBLIOTHEEK DEN HAAG Pineda de Gyvez J ALWAYS a system for wafer yield analysis Report and user s manual by J Pineda de Gyvez Eindhoven University of Technology Faculty of Electrical Engineering Fig EUT report ISSN 0167 9708 88 E 189 Met lit opg reg ISBN 90 6144 189 7 SISO 663 42 UDC 621 382 681 3 06 NUGI 832 Trefw elektronische schakelingen computer aided design iii ABSTRACT An interactive environment for the analysis of yicld information necded on modern integrated circuit manufacturing lines is presented The system is able to quantify wafer yiclds yield variations between wafers and within the wafers themselves yields of wafer batches yield variations between batches to identify clusters in wafers and or in lots and is also able to p
64. ve click on their names The name just picked up is highlighted in red To deactivate wafers click in the cancel option and then click in each of the activated wafers The arrows in the lower right comer are used to scroll through wafers if their number exceeds the size of the window LOT This option selects the lots of the project currently active A second menu with the options of select and cancel appears To activate any lots click in the select option To deactivate any lots click in the cancel option If during the activation process the name of a lot is clicked twice or two lots are selected consecutively for the first time then the second to last lot will be made active and also all the wafers belonging to it are made active as well The existent lots are displayed to the right of the screen Each lot that is selected or canceled is highlighted in red The arrows in the lower right comer are used to scroll through lots if their number exceeds the size of the window PROJECT This option selects the projects available in the current directory A second menu with the options of select and cancel appears To activate any projects click in the select option To deactivate any projects click in the cancel option If during the activation process the name of a project is clicked twice or two projects are selected consecutively for the first time then the second to last project will become active a
65. wn HISTORY MAP This map displays the site frequency of each die numerically INFO MAP This is mainly a contour map It shows the dice that have the average site yicld of the analysis and those dice that have a site yield above or below the average The dice that have the average site frequency are displayed in blue the dice that have a site frequency above the average are displayed in magenta the dice that have a site frequency below the average in cyan and finally the dice with zero site yield in red CLUSTER MAP This option finds clusters in the composite wafer The specific site yicld and the minimum number of elements to make a cluster are asked as data The map will display all the dice which accomplished these conditions The clustered dice are shown in purple The statistics show the number of groups of clusters and the number of clustered elements DISTRIBUTIONS These option is to carry on distribution analyses 2 5 2 DISTRIBUTION ANALYSIS The distribution menu is shown in Fig 9 radial distribution angular distribution cumulalive distribution frequency distribution yield area Figure 9 Distribution Menu RADIAL DISTRIBUTION This options asks for the site yield which is going to be looked for radially This data is entered in the field to the right of the screen The graph shows the radial yield of dice that have a site yield equal or above the user s yield If zero is specified
66. ysis are selected it is easy to generate a general matrix which contains the history of all the wafers implied Since the mask can be of arbitrary size bigger or smaller than the wafer it is then necessary to prevent writing wrong information this is done by checking if the die lays inside of the wafer The following routine shows how the tree structure is traversed in order to obtain information from each wafer generate_working_waferQ while project_pointer NULL while lot_pointer NULL while wafer_pointer NULL for x 0 x lt total_dice_in_x x for y 0 y lt total_dice_in_y y if die_in_wafer x y if wafer_pointer gt status x y GOOD composite_wafer x fy 1 wafer_pointer wafer_pointer gt next lot_pointer lot_pointer gt next project_ptr project_ptr gt next It is possible to make analysis between wafers of the same or different lots between lots of the same or different projects and between different projects Notice that the concept of project is very flexible it can mean i e a memory chip a test structure or simply the same memory chip processed with a new equipment or new chemicals in which it was desirable to make a difference between the new and the old process Input data does not necessary have to represent the absolute die coordinates in the wafer Assume for a moment that a test chip contains a monitor to detect up to four mul

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