Method for implementing a CD-SEM characterisation technique

Abstract

A method for implementing a scanning electron microscopy characterisation technique for the determination of at least one critical dimension of the structure of a sample in the field of dimensional metrology, known as CD-SEM technique, the method including producing an experimental image representative of the structure of the sample and derived from a scanning electron microscope, from a first theoretical model based on parametric mathematical functions, calculating a second theoretical model obtained by algebraic summation of a corrective term, the corrective term being the convolution product between a given convolution kernel and the first theoretical model, the second theoretical model comprising a set of parameters to determine, and determining the set of parameters present in the second theoretical model by means of an adjustment between the second theoretical model and the experimental image.

Claims

1. Method for implementing a scanning electron microscopy characterisation technique for the determination of at least one critical dimension of the structure of a sample in the field of dimensional metrology, known as CD-SEM technique, said method comprising: producing an experimental image representative of the structure of the sample and derived from a scanning electron microscope; from a first theoretical model based on parametric mathematical functions, calculating a second theoretical model obtained by algebraic summation of a corrective term, said corrective term being the convolution product between a given convolution kernel and the first theoretical model, said second theoretical model comprising a set of parameters to be determined, the first and second theoretical models being a mathematical representation of the structure of the sample in the experimental image; determining the set of parameters present in the second theoretical model by means of an adjustment between said second theoretical model and said experimental image, the adjustment corresponding to a minimisation of a difference between said second theoretical model and said experimental image.

2. The method according to claim 1, wherein the second theoretical model is calculated according to the following formula:
Img(x,y)=G(x,y)C.sub..sup.+F(x,y)*[G(x,y)G.sub.o]dxdy in which: (x,y) are the spatial coordinates associated with each point of the image along the two orthogonal directions x and y; G(x,y) is the first theoretical model based on parametric mathematical functions; Img(x,y) is the second theoretical model obtained by the application of the corrective term; F(x,y) is the given convolution kernel; G.sub.o is the background of the intensities present on the experimental image; C is an adjustment constant.

3. The method according to claim 2, wherein the convolution kernel is a symmetrical one-dimensional function and wherein the convolution kernel is a Gaussian taken along the x axis, said Gaussian having a full width at half maximum proportional to sigma according to the following formula: $\mathrm{Img}\left(x,y\right)=G\left(x,y\right)-C{}_{-}^{+}{e}^{-\frac{{\left(x-x^{}\right)}^2}{2{}^2}}*\left[G\left(x^{},y\right)-{\stackrel{\_}{G}}_0\right]{\mathrm{dx}}^{}.$

4. The method according to claim 2, wherein the convolution kernel is a two-dimensional symmetrical function and wherein the convolution kernel is two-dimensional symmetrical in the directions respectively parallel and normal to the scanning direction of the primary electron beam according to the following formula: $\mathrm{Img}\left(x,y\right)=G\left(x,y\right)-C{}_{-}^{+}{e}^{-\frac{{\left(x-x^{}\right)}^2}{2{}_x^2}}{e}^{-\frac{{\left(y-y^{}\right)}^2}{2{}_y^2}}*\left[G\left(x^{},y^{}\right)-{\stackrel{\_}{G}}_0\right]{\mathrm{dx}}^{}{\mathrm{dy}}^{}.$

5. The method according to claim 1, wherein a primary electron beam scans a surface of the sample according to a TV or raster scan method, the scanning direction being the horizontal direction or x axis.

6. The method according to claim 1, wherein the convolution kernel is a symmetrical one-dimensional function.

7. The method according to claim 1, wherein the convolution kernel is a two-dimensional symmetrical function.

8. The method according to claim 1, wherein the convolution kernel has a mono-dimensional profile asymmetric along the scanning direction of the primary electron beam or a two-dimensional profile asymmetric along the scanning direction of the primary electron beam.

9. The method according to claim 1, said method being implemented for a calibration of the CD-SEM characterisation technique, said calibration comprising: producing an experimental image representative of the structure of a reference sample of which the geometric dimensions are known, said experimental image derived from a scanning electron microscope; wherein said set of parameters of the second theoretical model include both the known parameters which describe the geometric structure of the reference sample and the parameters to be determined which describe an instrumental response; determining the parameters present in the second theoretical model and describing the instrumental response by means of an adjustment between said second theoretical model and said experimental image representative of the structure of the reference sample.

10. Method for implementing a CD-SEM characterisation technique, said method comprising: producing a first experimental image representative of a structure of a sample of interest and derived from a scanning electron microscope; from a first theoretical model based on parametric mathematical functions, calculating a second theoretical model obtained by algebraic summation of a corrective term, said corrective term being the convolution product between a given convolution kernel and the first theoretical model, said second theoretical model comprising a set of parameters, said set of parameters including both parameters to be determined which describe a geometric structure of the sample of interest and parameters determined according to the calibration according to claim 9 which describes the instrumental response; determining the parameters present in the second theoretical model and describing the structure of the sample of interest by means of an adjustment between said second theoretical model and said first experimental image.

Description

LIST OF FIGURES

(1) Other characteristics and advantages of the invention will become clear from the description that is given thereof below, for indicative purposes and in no way limiting, with reference to the appended figures, among which:

(2) FIG. 1 schematically illustrates an intensity profile of secondary electrons as a function of the profile of a pattern obtained via a CD-SEM type instrumentation;

(3) FIGS. 2a and 2b illustrate an example of parametric mathematical modelling of a CS-SEM image;

(4) FIGS. 3a, 3b, 3c and 3d illustrate examples of dark mark type artefacts observed on experimental CD-SEM images;

(5) FIG. 4 represents the different steps of the method according to the invention;

(6) FIG. 5a represents a CS-SEM image;

(7) FIG. 5b represents a parametric theoretical model of the image 5a;

(8) FIG. 5c represents a theoretical model of the image 5a obtained by application of the method according to the invention;

(9) FIG. 6a illustrates the so-called TV scan (raster scan) method;

(10) FIG. 6b illustrates the sawtooth scanning method;

(11) FIG. 6c illustrates the two-directional scanning method;

(12) FIG. 6d illustrates the scanning method adapted to the objects measured;

(13) FIG. 7a represents an experimental CS-SEM image;

(14) FIG. 7b shows an enlargement of a portion of FIG. 7a illustrating a particular local effect in correspondence with a corner in the structure of the sample;

(15) FIG. 8 illustrates an example of symmetrical profile of the convolution kernel;

(16) FIG. 9 illustrates an example of asymmetric profile of the convolution kernel.

DETAILED DESCRIPTION

(17) FIG. 4 schematically illustrates the different steps of the method 100 according to the invention.

(18) The method 100 according to the invention targets the implementation of a scanning electron microscopy characterisation technique for the determination of at least one critical dimension of the structure of a sample in the field of dimensional metrology. One application may be for example the measurement of a critical dimension of a pattern forming a printed circuit in microelectronics. The shape of the pattern may be any shape. The material of the pattern may also be any material. This pattern may for example be an isolated pattern or belong to a network of patterns repeated periodically. It may be a pattern obtained after any step (lithography, etching, etc.) of a manufacturing method.

(19) A step 101 of the method 100 according to the invention consists in producing an image representative of the structure of the sample and derived from a scanning electron microscope.

(20) According to a preferential embodiment of step 101 according to the invention, the primary electron beam scans the sample according to the so-called raster scan method. This scanning mode is represented by FIG. 6a. According to this scanning mode it is possible to identify a rapid scanning direction along the direction x indicated in FIG. 6a and a slow scanning direction along the direction y indicated in FIG. 6a. According to this scanning method, data acquisition takes place only in correspondence with the horizontal lines, indicated (1) in FIG. 6a. Hereafter, the rapid scanning direction, x in FIG. 6a, will refer to the scanning direction of the primary electron beam.

(21) According to another embodiment of step 101 according to the invention, the primary electron beam scans the sample according to the so-called sawtooth method. This scanning mode is represented by FIG. 6b. In this figure, the solid line represents the data acquisition phase (thus formation of the image), the dotted line designating the phase of simple displacement of the primary electron beam without data acquisition. The grey arrows represent the scanning direction of the primary electron beam.

(22) According to another embodiment of step 101 according to the invention, the primary electron beam scans the sample according to the so-called bi-directional method. This scanning mode is represented by FIG. 6c. In this figure, the solid line represents the data acquisition phase (thus formation of the image). Unlike FIGS. 6a and 6b, in this case the acquisition of data is made by scanning the surface both in the direction of increasing values of the coordinate x and in the direction of decreasing values of the coordinate x. The grey arrows represent the scanning direction of the primary electron beam.

(23) According to another embodiment of step 101 according to the invention, the primary electron beam scans the sample according to a method adapted to the shape of the objects to characterise. This scanning mode is represented by FIG. 6d.

(24) According to a step 102 of the method 100 according to the invention, from a parametric theoretical model of the surface of the sample a second theoretical model is calculated capable of taking into account dark mark type alterations of intensity, such as those present in the extension of the edges and often having the shape of black trails.

(25) More specifically, step 102 of the method 100 according to the invention comprises the modification of a first theoretical model called G(x, y) to obtain a second theoretical model called Img(x, y). The model G(x, y) is a parametric model of the response of the microscope to the structure of the sample obtained for example by one of the methods described in the articles CD characterization of nanostructures in SEM metrology (C. G. Frase, E. Buhr, and K. Dirscherl, Meas. Sci. Technol., vol. 18, n.sup.o 2, p. 510, Feb. 2007) or Analytical Linescan Model for SEM Metrology (C. A. Mack and B. D. Bunday, Metrology, Inspection and Process Control for Microlitography XXIX, Proc. SPIE Vol. 9424 2015) or AMAT or other. The function G(x, y) thus represents a theoretical image of the structure of the sample without effects linked to the scanning direction. For example, the theoretical image without scanning effect G(x, y) is obtained by the application of the model M((x, y)) where (x, y) is the signed distance to the edges of the imaged object. Like the function M(x), this theoretical model contains a set of parameters to be determined and that represent both information on the geometry of the sample and on the instrumental response without the scanning direction taken into account.

(26) Next the second theoretical model, Img(x, y), is calculated. Said second theoretical model is obtained by algebraic summation of a corrective term to the first theoretical model, said corrective term being a convolution product between a given convolution kernel and the first theoretical model.

(27) According to an embodiment of step 102 of the method 100 according to the invention, the second theoretical model is calculated according to the following formula
Img(x,y)=G(x,y)C.sub..sup.+F(x,y)*[G(x,y)G.sub.0]dxdy

(28) In which: G(x,y) is the first theoretical model based on parametric mathematical functions; (x,y) are the spatial coordinates associated with each point of the image along the two orthogonal directions x and y; Img(x,y) is the second theoretical model obtained by the application of the corrective term; F(x,y) is the given convolution kernel; G.sub.0 is the background of the intensities present on the experimental image; C is an adjustment constant.

(29) An advantage of this embodiment arises in the formula (1) of the convolution product calculated between the kernel F(x, y) and the difference G(x, y)G.sub.0. The subtraction of the background intensity G.sub.0 in fact makes it possible to cancel the convolution product where the response is constant, and thus the corrective term, when G(x, y)=G.sub.0. This condition is verified for the points of the surface of the sample that are far away from the patterns, thus for portions of the image on which the black trails are not present and for which the correction is not necessary.

(30) Generally speaking, the convolution kernel F(x, y) is a function of the spatial coordinates (x,y) or instead spatial coordinates chosen according to any coordinates system.

(31) The present invention may be implemented with any function F(x,y), providing that the result of formula (1) presented above is well defined. As an example, according to the different embodiments of the present invention, symmetrical, asymmetrical or anisotropic convolution kernels may be used.

(32) According to an embodiment of step 102 of the method 100 according to the invention, the electron beam scans the surface of the sample according to the so-called raster scan method illustrated by FIG. 6a.

(33) According to an embodiment of step 102, the convolution kernel is a mono-dimensional symmetrical function along one direction of space. FIG. 8 shows an example of symmetrical kernel 300 in the sense of the invention.

(34) According to an embodiment of step 102, the convolution kernel is a Gaussian taken along the x axis, said x axis corresponding to the scanning direction of the primary electron beam, said Gaussian having a full width at half maximum proportional to sigma, according to the following formula:

(35) $\mathrm{Img}\left(x,y\right)=G\left(x,y\right)-C{}_{-}^{+}{e}^{-\frac{{\left(x-x^{}\right)}^2}{2{}^2}}*\left[G\left(x^{},y\right)-{\stackrel{\_}{G}}_0\right]{\mathrm{dx}}^{}$

(36) It may be remarked in this case that the convolution kernel F(x,y) is a constant function along the vertical direction y, which explains why the variable y does not appear in the convolution product.

(37) An advantage of this embodiment is to be particularly suited to taking into account drops in intensity in the extension of the edges in the horizontal direction in the case of scanning in raster scan mode.

(38) According to an embodiment of step 102 of the method 100 according to the invention, the convolution kernel is a symmetrical two-dimensional function.

(39) According to an embodiment of step 102 of the method 100 according to the invention, the convolution kernel is symmetrical in the directions respectively parallel and normal to the scanning direction of the primary electron beam according to the following formula:

(40) $\mathrm{Img}\left(x,y\right)=G\left(x,y\right)-C{}_{-}^{+}{e}^{-\frac{{\left(x-x^{}\right)}^2}{2{}_x^2}}{e}^{-\frac{{\left(y-y^{}\right)}^2}{2{}_y^2}}*\left[G\left(x^{},y^{}\right)-{\stackrel{\_}{G}}_0\right]{\mathrm{dx}}^{}{\mathrm{dy}}^{}$

(41) An advantage of this embodiment is to be able to choose a convolution kernel capable of taking into account particular local effects, for example those in correspondence with the corners of the patterns forming the structure of the sample. FIGS. 7a and 7b illustrate an example of these effects. FIG. 7a is a CS-SEM image of a square shaped structure. FIG. 7b represents an enlargement of the framed portion 10 of FIG. 7a. This figure illustrates a particular example of dark mark indicated by the dashed line 20. More specifically, a dependency in y, which is added to the dependency in x, may be recognised. These observations motivate the necessity of a two-dimensional and potentially anisotropic convolution kernel along the two orthogonal directions x and y. Anisotropic convolution kernel is taken to mean a two-dimensional function having a profile in x different from the profile in y (for example a two-dimensional Gaussian with width .sub.x different from the width .sub.y).

(42) Another advantage of this embodiment is to be able to be adapted to a different scanning method from the raster scan mode.

(43) According to an embodiment of step 102 of the method 100 according to the invention, the convolution kernel has an asymmetric profile along at least one of the directions x or y. An example is illustrated by FIG. 9 which illustrates an example of asymmetric convolution kernel 200 along the x axis. In this case there is, for example, a profile that is in part Gaussian 201 and in part decreasing according to a non-Gaussian dependency in x 202.

(44) An advantage of this embodiment is to be able to adapt the convolution kernel to the scanning mode employed and to the type of patterns present on the sample.

(45) According to a step 103 of the method 100 according to the invention, the adjustment between the formula (1) and the experimental image is carried out. This adjustment makes it possible to find the set of parameters present in (1) that minimises the differences between the theoretical model and the experimental image, for example by using one of the known algorithms that apply the least squares method. Like the model G(x,y), the model Img(x,y) contains several parameters, including the parameters describing the geometry of the sample and used to deliver the critical dimension of interest.

(46) According to an embodiment of step 103 of the method according to the invention, a calibration step is carried out to determine the parameters present in the model and linked to the instrumental response. These parameters form part of the set of parameters already present in the first theoretical model and they take into account, for example, the fact that the primary electron beam has a non-zero size. Often the shape of the primary electron beam is described as a Gaussian profile. This Gaussian function taking into account the characteristics of the primary electron beam is called point spread function or PSF. The parameters describing the instrumental response, for example the parameters of the PSF function, may advantageously be determined during a preliminary calibration step. The calibration is obtained by carrying out an adjustment between the formula (1) and the experimental image of a sample of which the structure is known. This makes it possible to fix the geometric parameters during the calibration step and to obtain in a more reliable manner the parameters describing the instrumental response. The values of the parameters describing the instrumental response will next be fixed during the implementation of the CD-SEM technique for the characterisation of an experimental image of interest.

(47) An advantage of carrying out the calibration step is to be able to determine in a more precise and reliable manner the parameters describing the instrumental response. Next these parameters describing the instrumental response will be fixed during the implementation of the CD-SEM technique for the characterisation of an experimental image of interest, which makes it possible to attain a more precise and reliable determination of the parameters describing the structure of the sample and thus the critical dimensions of interest

(48) FIGS. 5a to 5c illustrate the effects obtained thanks to the method according to the invention. FIG. 5a is a CD-SEM image of a sample that it is wished to be characterised. In this example the case of a scanning in raster scan mode is considered. According to this scanning mode, illustrated in FIG. 6a, the primary electron beam rapidly scans the surface of the sample along the direction x and more slowly along the direction y. In this case, the direction x is simply designated as the scanning direction of the primary electron beam. The mark Ta indicates the black trails in the extension of the horizontal edges, along the scanning direction. These artefacts are very frequent on CD-SEM images obtained with this scanning method. FIG. 5b represents the theoretical model of the CS-SEM image based on parametric functions, which have been designated G(x, y) above. The mark Tb indicates the dark marks that are predicted by this type of model. It may be seen in this figure how the intensity of these dark marks is uniquely dependent on the distance to the edges. In addition, no black trail of the type indicated by the arrows Ta is present. FIG. 5c represents the theoretical model of the CS-SEM image calculated by means of the method according to the invention, using the following formula:

(49) $\mathrm{Img}\left(x,y\right)=G\left(x,y\right)-C{}_{-}^{+}{e}^{-\frac{{\left(x-x^{}\right)}^2}{2{}^2}}*\left[G\left(x^{},y\right)-{\stackrel{\_}{G}}_0\right]{\mathrm{dx}}^{}$

(50) The convolution kernel chosen in this case is a one-dimensional Gaussian taken along the x axis. The image 5c derived from the method according to the invention reproduces the characteristics of the experimental image 5a in a more precise manner with respect to the theoretical model derived from the parametric functions (image 5b). More specifically, in image 5c may be seen black trails, indicated by the arrows Tc, which reproduce the black trails observed on the CS-SEM image 5a. These images show how the method according to the invention reproduces precisely the dark mark type artefacts or black trails in the extension of the edges along the scanning direction of the primary electron beam.

(51) The implementation of the method according to the invention shown in FIGS. 5a, 5b and 5c may also be accompanied by a calibration step making it possible to obtain in a precise manner the parameters describing the instrumental response of the scanning electron microscope. To do so, it is necessary to acquire beforehand an experimental CD-SEM image of a reference sample of which the geometric dimensions are known. This image is the reference image for the calibration step. An adjustment between the second theoretical model and the reference image is next carried out, by fixing the geometric parameters, which are known in the case of the reference sample. This adjustment makes it possible to obtain the values of the parameters describing the instrumental response, for example the parameters of the PSF, or the amplitude of the signals. The fact of having fixed the geometric parameters during this calibration step makes it possible to obtain in a more reliable and precise manner the parameters describing the instrumental response. The values of said parameters describing the instrumental response will next be fixed during the implementation of the method according to the invention on a sample of interest.