Patent Application: US-7699905-A

Abstract:
according to the invention , a structure , decomposable into at least one elementary structure or base element , is illuminated and then provides an optical response , at least one geometrical parameter of the base element is determined , and a value is attributed to it , a regression algorithm is implemented which determines modified values of the parameter , in order to make the difference between the theoretical response of the base element and the acquired result at most equal to a threshold , and to obtain an image of the structure , and as long as the separation between the acquired and theoretical responses is not satisfactory , new subdivisions of the base element are performed .

Description:
in scatterometry , particularly in the field of microelectronics , the method most utilised for calculating the spectrum of a theoretical object is the rcwa method , that is , the method of rigorous coupled wave analysis ( se for example document [ 2 ]). other methods exist ( for example the chandezon method , and methods using green &# 39 ; s functions ), but the rcwa method has very rapidly been adopted because of its simplicity , rapidity , and quasi - universal nature . although it may be implemented with other methods , the present method is extremely well adapted to the rcwa ( see document [ 2 ]) and to the differential method ( see document [ 3 ], chapter 4 ), as will be seen in what follows . in the case of the rcwa method , when the profile of a line which it is desired to characterise is not rectangular , this profile is cut into slices parallel to the plane of the substrate on which the line is formed . when the rcwa method is used , the base element is therefore rectangular . but in the case of the differential method , the preferred base element is the trapezium . the shape which it is desired to characterise is therefore cut up into trapezia ( see for example document [ 6 ]). if the slices are sufficiently small , the signature of the cut - up object is identical to that of the perfect , non - cut - up object . ( note that the method of green &# 39 ; s functions or the chandezon method does not make use of cutting up the profile ). cutting - up is therefore a calculation artefact which permits use of the rcwa or differential methods , which deal only with slices . we note that the refractive index does not change with height in each slice for the rcwa method , and that the calculation time is a linear function of the number of slices or layers . fig2 a and 2b schematically show the process of cutting a rounded trapezoidal profile of a line which is formed on a substrate 10 . the uncut profile is referenced 12 . in fig2 a , this profile is cut up into rectangles 14 for processing by the rcwa method . in fig2 b , the profile is cut up into trapezia 16 to be treated by the differential method . in what follows , it is shown in a very generic manner how the quasi - totality of the algorithms are constructed for regression in scatterometry . reference is made to fig3 , which schematically shows an example of a conventional adjustment process . the geometry 18 studied , defined by a few geometrical parameters , is cut up into rectangles 20 in order to be processed by the rcwa method . the signature 32 of the modelled object is calculated , then compared with the experimental signature 24 . from the difference between these signatures , a variation of the geometrical parameters is deduced . the process is then resumed with a new geometry defined by the modified parameters , and so on , until the difference between the theoretical signature and the experimental signature is less than a predefined threshold . it is noted that in the example considered the profile of the object studied , which is formed on a substrate 26 , is a trapezium ; the latter is defined by three parameters : its large base , of initial length w1 , its small base , of initial length w2 , and its height , of initial value h . so , in the prior art , a type of geometry is fixed from the start ( for example , a rectangle or a trapezium ) and the parameters of this geometry are adjusted as a function of the result of comparison between the signature of the ideal object and the experimental signature . when the rcwa method or the differential method is used , it is necessary , as has been seen , to pass through an intermediate phase of cutting - up . this cutting - up phase is obligatory and seems to be more of a disadvantage which has to be accommodated when such numerical methods are used , rather than a useful step . in the present invention , this step of cutting - up is used shrewdly , by considering that the geometrical object which is sought is the cut - up object itself . if it is desired to trace the connection between conventional method and a process according to the invention , it will be said that in this process the starting object is a pile of rectangles , and that the number of parameters is twice the number of rectangles . the initial phase of cutting - up therefore has no place in this process , since the object is already constituted by rectangles which may be directly exploited by the rcwa . this aspect of the invention is schematically illustrated by fig4 . seen there is a process of adjustment by means of an object which is formed on a substrate 28 and whose profile is defined by a family of rectangles 30 . in the example considered , this family comprises four rectangles , each of these being characterised by a height h i and a width w i , i running from 1 to 4 . without doing anything , the geometry defined by the parameters h i , w i changes to a cut - up geometry . then , as has been seen above , the theoretical signature 32 is calculated , and is compared with the experimental signature 34 . a variation of parameters is deduced from the difference of these signatures . the process is then repeated with a new geometry defined by the modified parameters , and so on , until the difference between the theoretical signature and the experimental signature is below a predefined threshold . at first sight , the use of objects defined by a family of rectangles has no advantages . on the contrary , the problem with three variables in the example of fig3 becomes a problem with eight variables in the example of fig4 . nevertheless , an important advantage results from it : the sets of sequences of additions of variables then become evident , given that an object with n rectangles is more complex than an object with m rectangles if n & gt ; m ( reference is made to the example of the invention , given hereinafter ). the advantage of using sequences of additions of variables falls out immediately : there are fewer problems due to multiple solutions , because of the increased number of parameters of the geometry , and the calculation time is reduced ( reference is also made to the example of the invention given hereinafter ). the invention will now be described in a simple case relating to a lithographic pattern and in which the rcwa method and a rectangular base element are used . no final profile ( for example , trapezium or rounded trapezium ) is fixed . the regression is always performed using sequences , but the number of sequences is not fixed ( it may be very large ), contrary to the research methods for which the final profile is fixed . the regression is ended when the difference between the theoretical spectrum and the measured spectrum is sufficiently small , the limiting difference being fixed by the user . 1 . a rectangular starting object 36 ( see fig5 a ) is close enough to the object having sides h 0 1 ( height ) and f 0 1 ( width ) which is to be found ( and which is for example defined by the manufacturing process ) and , using a regression program , the height and width of the rectangle are adjusted to give best coincidence of the theoretical spectrum and the experimental spectrum . this constitutes the first sequence , which is denoted ( h 1 , f 1 ). this sequence is known in the state of the art . 2 . once the best rectangle has been found ( having height h 1 and width f 1 ), this rectangle is split into several rectangles , for example two rectangles ( fig5 b ). the parameters ( height and width ) of these two rectangles are denoted by h 0 k and f 0 k , where k takes the values 1 and 2 . 3 . the 2 × 1 variables h 0 k and f 0 k , where 1 is the number of slices ( here 1 = 2 ), are adjusted for best coincidence of the theoretical and experimental spectra for each slice . this adjustment leads to the parameters ( h 1 , f 1 ) and ( h 2 , f 2 ) for the slices ( fig5 c ). 4 . the operations of subdivision and adjustment are repeated until theory and experiment are in agreement . a profile is obtained in this way of the kind of profile 38 of fig5 d . in conclusion , the solution found is a set or rectangles which form an image of the profile , and not a set of parameters of a fixed geometrical profile . four particular embodiments of the process according to the invention are described below . two of these embodiments use rectangles as base elements , and the two other embodiments use trapezia . as a method of field calculation , the rcwa method is used in the case of rectangles , and the differential method in the case of trapezia ( but this is not necessary ). these embodiments are described for the characterisation of two important structures , namely lithographed resist profiles and notched grids . the usable regression algorithms are numerous ; only some of them are cited which are already widely used in scatterometry : the simplex method ( see chapter 10 of document [ 4 ]), the levenberg - marquardt method ( see chapter 10 of document [ 4 ]), and the drège method ( see document [ 5 ]). the use of one or other of these does not modify the invention in any way . the use of rectangular base elements and the characterisation of the shape of resist lines are first considered . this type of profile is very frequently encountered during exposure and engraving of resist patterns ( by electron beam or photolithography ). the characterisation of this step is fundamental in microelectronics , because a large part of the remainder of the pattern manufacturing process depends on it . in fact , in general the first step of this process is concerned . the corresponding embodiment has already been described hereinabove with reference to fig5 a - 5d . the primitive object is constituted by a single rectangle . for the subdivision of the different rectangles , there could be chosen , between each sequence , for example : ( 1 ) to cut up all the rectangles indiscriminately , or ( 2 ) to cut up the rectangle having the greatest height , or ( 3 ) to cut up the rectangle whose variation induces the greatest variation in the global signature , or ( 4 ) to cut up the rectangles whose size is greater than a certain value ( it is useless to cut up a rectangle which is already very small ), or ( 5 ) to perform this operation on a sub - family of rectangles . we now consider the characterisation of notched grids , always with the use of rectangular base elements . for a few years , these structures have become of great importance in microelectronics . they are lines constituted by a very fine base ( a few tens of nanometres in width ) on which rests a wider line , the shape of which is more or less rounded . in practice , two items of information are of interest , namely the respective sizes of the upper and lower portions and the shape of the upper portion . a big problem for the final users is finding a good geometric model for the shape of the upper portion . fig6 shows an example of notched grid geometry 40 , formed on a substrate 42 . for such a geometry , the sequences of a process according to the invention are easy to determine . fig7 a - 7f are referred to , which schematically show a set of such sequences , permitting the characterisation of a notched grid . the geometry of the dashed grid 44 is only there for facilitating comprehension of fig7 a - 7f . in no case does it enter into the sequences . the first sequence comprises an initialisation phase ( fig7 a ) followed by an adjustment phase ( fig7 b ); the second sequence comprises a subdivision phase ( fig7 c ) followed by an adjustment phase ( fig7 d ); the third sequence comprises a new subdivision phase fig7 e ) followed by a new adjustment phase ( fig7 f ); and so on . at the end of a few sequences , a family of rectangles is obtained which tends to be adjusted to the desired geometric shape . the base 46 is never cut up ; in fact , the optical signatures are often little affected by the base of the geometry ( particularly if this base is of small size ); and during the second sequence , the upper rectangle is cut up into three rectangles , because geometries of circular type are much better decomposed into unit cells with three than with two rectangles ; it has thus been possible to skip the sequence with two rectangles . in fact , the same type of structure as before could be studied , following the same principle but with a different type of elementary pattern , for example the trapezium . an object is represented more finely with trapezoidal elements than with rectangles ( with a constant number of elements ). however , this leads to longer calculation times , since the differential method is then used , which is more complex . this why the rcwa method is the most used . however , it should be noted that the principles stated above may be implemented with a trapezoidal base element , the only difference being that in this case , the base element is described by three parameters , for example the height h , the width w b of the large base , and the width w t of the small base of the trapezium . reference is made to fig8 a - 8f which schematically show another set of sequences of a process according to the invention , enabling the characterisation of a notched grid . the geometry of the dashed grid 48 is only there to facilitate comprehension of fig8 a - 8f . in no case does it enter into the sequences . the first sequence comprises an initialisation phase ( fig8 a ) followed by an adjustment phase ( fig8 b ); the second sequence comprises a subdivision phase ( fig8 c ) followed by an adjustment phase ( fig8 d ); the third sequence comprises a new subdivision phase fig8 e ) followed by a new adjustment phase ( fig8 f ); and so on . at the end of a few sequences , a family of trapezia is obtained which tends to be adjusted to the sought geometric shape . there are two notable differences between the present invention and the prior art . on the one hand , the concept of scatterometry by adjustment ( whether regressions or a search in a library is concerned ) is completely different : the set is no longer sought of parameters of fixed form , parameters which enable adjustment of spectra , but the geometrical model itself which is defined by a set of base elements . this is very important from the user &# 39 ; s viewpoint , since , specifically , he does not always know what the form of the object to be characterized will be . if the chosen model is too simple , the results will be very approximate the shape of the object will be which he desires to characterise ; and if the chosen model is too complex , the results may be false . with the present invention , the model is adapted as the convergence takes place . on the other hand , from the viewpoint of the rcwa resolution method , the cutting into slices is always considered to be a disadvantage in the prior art , since the cutting - up algorithms are complex and since it is always questioned whether the cutting - up fixed by the user is sufficient . in the present invention , this disadvantage is transformed into an advantage , because it is from the cutting - up itself that the information results . the rcwa method is therefore well adapted to this method of “ shape measurement ”. the geometric model is not fixed , which is very practical for the final user ; at the end of the process , the user does not obtain a list of parameters of a predefined geometrical model , but an image of the profile ; the model becomes refined continuously , and the number of slices is , by construction , always optimum : this is not the case for the conventional methods , in which the starting models may be very complex and the number of slices may therefore be very large , hence a longer calculation time ; the problem of local minima which occurs when the number of parameters is large is avoided — to a certain degree — because this number increases continuously ; the resolution of the final geometry is theoretically unlimited , because the number of rectangles which describe the geometry may be increased at will ; and if the method of calculating the signatures is the rcwa method , the profile is then cut up beforehand and consequently is optimum . the series of sequences which is illustrated in fig7 a - 7f is not the most general : nothing prevents commencing with more rectangles if the information on the profile is already available . for example , for the notched lines for which the profile base is very small , the algorithm may be commenced with two or three rectangles . furthermore , according to particular embodiments of the process according to the invention , which are very advantageous for scatterometry , ( a ) the rcwa method is used , which is more rapid and simple than the differential method ( but requires more base elements ); ( b ) the drège regression method is used ; and ( c ) the electromagnetic properties of the rectangles are stored . indeed , the rcwa method uses the rectangles as base objects . it is therefore well suited for the implementation of an algorithm according to the invention . in the drège regression method ( see document [ 5 ]), the evaluation of the difference ( point to point ) between the experimental and theoretical signatures , combined with the evaluation of the derivative of the signatures when one of the parameters changes , leads to a very rapid convergence in a majority of cases . it is however suitable to note that this method requires a complex electromagnetic calculation each time it is desired to calculate a derivative , which takes time except in the case of rectangles ; as will be seen later , the derivative of the diffraction matrix of a rectangle with respect to its height or with respect to its width may be calculated in a very reduced time . the storage of the electromagnetic properties of the rectangles enables the calculation to be notably accelerated . this storage rests on the fact that certain electromagnetic properties of rectangles , namely the eigenvalues and the eigenvectors of the electromagnetic field are independent of the height of the rectangles . it is therefore advantageous to calculate and to store in a library the eigenvalues and the eigenvectors of a rectangle . when the eigenvalues and the eigenvectors of a rectangle are needed , it is then sufficient to seek them in the library in which they are stored . fig9 shows the flow chart of a process according to the invention in the form of blocks . block i schematically shows the acquisition of data by means of an appropriate optical device . a structure 50 which it is desired to characterise is formed on a substrate 52 . a light source 54 enables illuminating the structure 50 . the light reflected by the latter is detected by a reflectometer 56 and by an ellipsometer 58 . the signals provided by these are transmitted to a spectrometer 60 . block ii symbolises the measurements ψ thus obtained and the conditions of measurement θ ( angle of incidence of the light on the structure ) and λ ( wavelength of this light ), which are stored . in block iii , the sub - block 62 represents the choice of a base element from a library 64 of elements . in block iv , the sub - block 66 symbolises the attribution of values to variables , starting from assumed information 68 on the object to be characterised . block v symbolises the variables and elements considered and the values attributed to the variables . block vi shows a sub - block 70 for adjustment of variables , starting from the information of blocks ii and v , and a sub - block 72 of elements of variables and of new values of variables resulting from adjustment . this block vi is a regression block which is not detailed because it uses standard regression procedures already mentioned above . block vii symbolises a test ( comparison of the difference between the theoretical and experimental optical responses at a predefined threshold ) which enables knowing whether the adjustment is satisfactory ( difference lower than threshold ). if this is the case , go to block viii ; the image of the object is considered to be the set of elements obtained by regression and this image 74 is displayed by means of a video monitor 76 which is connected to a computer 78 enabling all the calculations and data processing for characterisation . in the opposite case , go to block ix whose sub - block 80 symbolises the cutting - up of the elements into new elements and sub - block 82 symbolises the new elements , the new variables and the indeterminate values resulting from this cutting - up . starting from these new elements , new variables , and indeterminate values ( sub - block 82 ), the process is recommenced starting from sub - block 66 of block iv . it is stated that in fig9 there is also seen an example of the device according to the invention . comprising the light source 54 , the reflectometer 56 , the ellipsometer 58 , the spectrometer 60 , the computer 78 provided with a video monitor 76 , the computer 78 having in memory the library 64 and processing data provided by the spectrometer 60 by implementing the process according to the invention which has been described with reference to blocks i - ix . in the examples of the invention given above , the reflected image of a structure to be characterised is used as the optical response , this image resulting from the reflection of light by this structure . however , the invention may also be implemented by using , as the optical response , the diffracted image of a structure , resulting from the diffraction of light by this structure . moreover , examples of the invention have been given using rectangles and trapezia as base elements . however , the invention may also be implemented using a square as base element and the length of side of this square as the geometrical parameter . a triangle may also be used as the base element and , as geometrical parameters , the base , an angle adjacent to this base , and the height of the triangle , or the base and two angles adjacent to the latter . 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