Method for characterisation by CD-SEM scanning electronic microscopy

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, includes producing an experimental image; from a first theoretical model based on parametric mathematical functions, calculating a second theoretical model U(P.sub.i,t.sub.i) describing the signal measured at the position P.sub.i at the instant t.sub.i, the second model U(P.sub.i,t.sub.i) being obtained by algebraic summation of a corrective term S(P.sub.i,t.sub.i); determining the set of parameters present in the second theoretical model; wherein the corrective term S(P.sub.i,t.sub.i) is calculated by summing the signal coming from the electric charges deposited by the primary electron beam at a plurality of instants t less than or equal to t.sub.i.

Claims

1. A method for implementing a scanning electron microscopy characterisation technique for the determination of at least one critical dimension of a 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 U(P.sub.i,t.sub.i) describing a signal measured at the position P.sub.i at the instant t.sub.i, said second model U(P.sub.i,t.sub.i) being obtained by algebraic summation of a corrective term S(P.sub.i,t.sub.i), said second theoretical model comprising a set of parameters to be determined; 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; wherein said corrective term S(P.sub.i,t.sub.i) is calculated by summing a signal originating from electric charges deposited by a primary electron beam at a plurality of instants t less than or equal to t.sub.i.

2. The method according to claim 1, wherein the second theoretical model is calculated according to the following formula: $U\left(P_i,t_i\right)=\left[\stackrel{i}{\underset{j=1}{.Math.}}{Q}_j{R}_j\left(P_i-P_j\right)\right]-S\left(P_i,t_i\right)$ in which: U(P.sub.i,t.sub.i) is the second theoretical model calculated in correspondence with the position P.sub.i on the surface of the sample at the instant t.sub.i; the index ji scans the sequence of positions P.sub.j of the primary electron beam illuminated at the instants t.sub.j, up to the position P.sub.i illuminated at the instant t.sub.i, the primary electron beam being able to illuminate the same position at different instants; Q.sub.j is the electric charge deposited by the primary electron beam when the beam illuminates the position P.sub.j; R.sub.j is the parametric mathematical function containing the parameters describing the topography of the sample and the charge creation efficiency at the position P.sub.j; (P.sub.iP.sub.j) is a Kronecker delta, which is equal to one when P.sub.i=P.sub.j and zero otherwise; .sub.j=1.sup.iQ.sub.jR.sub.j(P.sub.iP.sub.j) is the first theoretical model of the signal measured at the position P.sub.i at the instant t.sub.i and takes into account the topography of the sample, the deposited electric charge, the charge efficiency and the multiple passages of the primary electron beam during scanning; S(P.sub.i,t.sub.i)=.sub.j=1.sup.i(P.sub.iP.sub.i)[.sub.k=1.sup.iC.sub.kQ.sub.kR.sub.kF.sub.s(P.sub.jP.sub.k)F.sub.t(t.sub.ft.sub.k)] is the corrective term; F.sub.s(P.sub.iP.sub.j) is a spatial dispersion function taking into account the distance between the electric charge at the position P.sub.j and the position P.sub.i; F.sub.t(t.sub.it.sub.j) is a temporal dispersion function taking into account the temporal difference between the deposition of the electric charge at the position P.sub.j at the instant t.sub.j and the measurement of the signal at the position P.sub.i at the instant t.sub.i; C.sub.j is the effective charge accumulation coefficient at the position P.sub.j.

3. The method according to claim 2, wherein the current of primary electrons is constant and equal to Q.sub.0, the primary electron beam illuminates each position P.sub.j a single time and the second theoretical model is calculated according to the following formula: $U\left(P_i,t_i\right)=U_0\left(P_i,t_i\right)-Q_o\underset{j=1}{\overset{i}{.Math.}}{R}_j{C}_j{F}_s\left(P_i-P_j\right).Math.F_t\left(t_i-t_j\right)$ in which u.sub.0(P.sub.i,t.sub.i)=Q.sub.0R.sub.i.

4. The method according to claim 3, wherein the response of the sample in the absence of topography is R.sub.0 and the background intensity U.sub.b(P.sub.i,t.sub.i) due to the excess of charge is subtracted from the second theoretical model to eliminate the emission from non-structured regions of the sample, the background intensity being calculated according to the following formula $U\left(P_i,t_i\right)-U_b\left(P_i,t_i\right)\left(R_i-R_0-\underset{j=1}{\overset{i}{.Math.}}\left(R_j{C}_j-R_0{C}_0\right)F_s\left(P_i-P_j\right).Math.F_t\left(t_i-t_j\right)\right)$ $\mathrm{In}\mathrm{which}{U}_b\left(P_i,t_i\right)=Q_0{R}_0\left[1-\underset{j=1}{\overset{i}{.Math.}}{C}_j{F}_S\left(P_i-P_j\right)F_T\left(t_i-t_j\right)\right].$

5. The method according to claim 2, wherein the temporal dispersion function is an exponential function with time constant : $F_t\left(t\right)=e^{-\frac{t}{}}$

6. The method according to claim 2, wherein the temporal dispersion function is a Cauchy type distribution function: $F_t\left(t\right)=\frac{1}{1+{\left(\frac{t}{}\right)}^2}$

7. The method according to claim 2, wherein the spatial dispersion function is of the form: $F_s\left(r\right)=e^{-\frac{{.Math.r.Math.}^2}{2{}^2}}$

8. The method according to claim 1, wherein the primary electron beam scans the surface of the sample according to the TV or raster scan method, the scanning direction being the horizontal direction or x axis, the scanning speed v.sub.x being constant.

9. The method according to claim 8, wherein the second theoretical model is calculated according to the following formula: $U\left(x\right)-U_b\left(x\right)\left[R\left(x\right)-R_0-{}_0^x\left(C\left(x^{}\right)R\left(x^{}\right)-C_0{R}_0\right){}_{x}F\left(x-x^{}\right){\mathrm{dx}}^{}\right]$ in which: x is the spatial coordinate in the scanning direction of the primary electron beam; U.sub.b (x) is the background intensity at the position x; Q.sub.0(x) is the charge deposited by the primary electron beam in correspondence with the position x; $F\left(x-x^{}\right)=F_S\left(x-x^{}\right)F_t\left(\frac{x-x^{}}{v_x}\right)$ contains the spatial dispersion function and the temporal dispersion function expressed as a function of the coordinate x, the scanning speed v.sub.x being constant.

10. 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 a structure of a reference sample of which the geometric dimensions are known, said image being 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 second theoretical model comprising a set of parameters, said set of parameters including 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.

11. The method for implementing a CD-SEM characterisation technique according to claim 1, wherein 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 second theoretical model comprising a set of parameters, said set of parameters including both the parameters to be determined which describe the geometric structure of the sample of interest and the parameters determined according to a calibration which describe an 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 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 shows several CD-SEM images acquired on the same sample but with a different scanning angle;

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

(7) FIG. 6 illustrates the so-called TV or raster scan method.

DETAILED DESCRIPTION

(8) FIG. 4 shows a series of CD-SEM images taken on a same sample. Each image has been acquired by scanning the surface of the sample according to a different angle. It is obvious that by varying the scanning angle, the images obtained change. This clearly shows that the path of the beam has an influence on the image formation process: the signal measured at a given position on the sample changes according to the path followed by the primary electron beam.

(9) These observations may be explained by evoking the charging effects described above, including temporal effects.

(10) It appears necessary to model the signal measured at a given position on the surface of the sample while taking into account the positions scanned by the primary electron beam before arriving at the given position.

(11) When the incident beam of primary electrons is advancing at the point r on the sample, secondary electrons are generated with an efficiency (r). This efficiency is linked to the nature of the materials present at the point r but also in its vicinity and the geometry of the structure considered.

(12) In addition, the primary electron beam is not punctiform but has a spatial distribution of incident current density. The actual efficiency when the beam is centred on the point P is:
R(P)=(r)f(rP)dr

(13) Where f(r) is the normalised spatial distribution of electrons. This distribution function follows a decreasing law, for example composed of Gaussian functions. Hereafter it is considered that the contribution to the point P is the spatially integrated contribution of the response on the spatial extension of the beam.

(14) The instantaneous response at the point P is thus a result of several complex factors. When backscattered and secondary electrons are generated, they create a distribution of charges leading to the generation of an electrostatic field that is going to modify the signal detected during the displacement of the incident beam. These generated fields generally decrease if discharging processes exist (external electrostatic fields, dissipation of charges by the sample, etc.). However, this discharging time is often longer than the characteristic time between two measurement points of the microscope, which perturbs the formation of the image.

(15) The present invention models the effect of these charges using a corrective term S.

(16) The charge creation efficiency is proportional to R(r) and is a function of the illuminated material and its geometry (and thus of the position). The immediate effect in r at time t on the signal is called T(r,t)=I(t)R(r)C(r). With C(r) reflecting an effective charge coefficient, where I(t) is the current when the incident beam is in r.

(17) The effect of the charges is dispersed spatially with a distribution function F.sub.s(r). This distribution is maximum in r=0 and decreases with the distance r.

(18) The effect of the charges decreases over time since it may be assumed that charge dissipation processes exist that have a characteristic time constant . F.sub.t(t) will be taken.

(19) It is generally considered that the incident beam follows a sequence of positions r.sub.p as a function of time t.sub.p, where p is a position index.

(20) The model takes into account the fact that several times may exist such that P(t)=P(t) with tt. The scanning may thus comprise redundant points, which happens notably when the images are accumulated over several passages (frames).

(21) FIG. 5 illustrates the different steps of the method 100 according to the invention.

(22) The first step IMAGE of the method 100 according to the invention includes the acquisition of an experimental image representative of the surface of the sample and derived from a scanning electron microscope.

(23) This step includes for example the scanning of the portion of sample of interest with the primary electron beam and the formation of an image obtained by measuring the emitted secondary electrons.

(24) The second step MODEL of the method 100 according to the invention includes the modelling of the measured signal using a second theoretical model U(P.sub.i,t.sub.i) obtained from a first parametric model by summation of a corrective term S(P.sub.i, t.sub.i). The model U(P.sub.i,t.sub.i) gives the intensity of the signal of secondary electrons at the position P.sub.i at the instant t.sub.i.

(25) The first theoretical model is constructed from parametric mathematical functions and contains a set of parameters describing the structure of the sample as well as the instrumental response. It may be considered that the first theoretical model takes into account the topography of the sample, the deposited electric charge, the charge efficiency and the multiple passages of the primary electron beam during scanning.

(26) The corrective term takes into account the excess charges deposited by the primary electron beam during scanning. This corrective term is constructed by summing the contributions coming from the charges deposited at each position during scanning of the primary electron beam. The corrective term includes a spatial dispersion function to take into account the topography of the sample. The corrective term also includes a temporal dispersion function to take into account charge dissipation phenomena. The corrective term takes into account potential multiple passages of the primary electron beam.

(27) The third step FIT of the method 100 according to the invention includes the adjustment of the model U(P.sub.i,t.sub.i) on the experimental image acquired at the first step. The adjustment step makes it possible to find the values of the parameters describing the geometry of the sample after having taken into account artefacts linked for example to charging effects.

(28) The corrective term may be written at point P.sub.i at the instant t.sub.i as:

(29) $S\left(P_i,t_i\right)=\underset{j=1}{\overset{i}{.Math.}}\left(P_i-P_j\right)\left[\underset{k=1}{\overset{j}{.Math.}}{C}_k{Q}_k{R}_k{F}_S\left(P_j-P_k\right)F_t\left(t_j-t_k\right)\right]$

(30) The index ji scans the sequence of positions P.sub.j of the primary electron beam illuminated at the instants t.sub.j, up to the position P.sub.i illuminated at the instant t.sub.i, the primary electron beam being able to illuminate the same position at different instants.

(31) The summation on the index j relative to the Kronecker delta function takes into account the possibility of several passages of the primary electron beam at the point P.sub.i illuminated at the instant t.sub.i.

(32) The summation on the index k makes it possible to calculate the corrective term for each passage of the primary electron beam at the position P.sub.j. This summation takes into account the points P.sub.k scanned by the primary electron beam at the instants t.sub.k preceding the instant t.sub.j.

(33) Q.sub.k is the charge deposited when the beam is at the position P.sub.k. This charge is a function of the current but also of the time during which it may be considered that the beam is at the position P.sub.k, that is to say the scanning speed. The quantity R.sub.k also appears in the first theoretical model of the surface of the sample and contains the parameters describing the geometry of the sample as well as the parameters describing the instrumental response and the charge creation efficiency.

(34) The parameter C.sub.k is an effective charge coefficient.

(35) The function F.sub.s(rP.sub.k) is a spatial dispersion function and the function F.sub.t(tt.sub.k) is a temporal dispersion function.

(36) When charging phenomena are neglected, the signal measured during the sequence is:

(37) $U\left(P_i,t_i\right)=\underset{j=1}{\overset{i}{.Math.}}{Q}_j{R}_j\left(P_i-P_j\right)$

(38) The signal measured is a summation of all the positions scanned by the primary electron beam. The Kronecker delta (P.sub.iP.sub.j) is equal to one when P.sub.i=P.sub.j and zero otherwise. Indeed, when the beam illuminates the position P.sub.i, the signal is recorded in the pixel P.sub.i of the detector. If the beam passes again on the same point, the signal will be integrated (added to the preceding signal). The detector thus has a memory.

(39) According to an embodiment, the second theoretical model is obtained according to the following formula:

(40) $U\left(P_i,t_i\right)=\left[\underset{j=1}{\overset{i}{.Math.}}{Q}_j{R}_j\left(P_i-P_j\right)\right]-S\left(P_i,t_i\right)$

(41) The minus sign in front of the corrective term S arises from the fact that the charging often results in darker zones on the CD-SEM images, i.e. an attenuation of the signal without charging. In some cases however, the impact of charging may on the contrary be positive, according to the sign of the effective charge coefficient.

(42) An benefit of this embodiment is to take into account the effects of both spatial and temporal charging. In addition, this embodiment takes into account the fact that the primary electron beam can pass several times by the same position.

(43) The second theoretical model may thus take the following form:

(44) $U\left(P_i,t_i\right)=\underset{j=1}{\overset{i}{.Math.}}\left(P_i-P_j\right)\left[Q_j{R}_j-\underset{k=1}{\overset{j}{.Math.}}{Q}_k{R}_k{C}_k{F}_s\left(P_j-P_k\right).Math.F_t\left(t_j-t_k\right)\right]$

(45) The dispersion function F.sub.t(t.sub.jt.sub.k) takes into account the charge dissipation phenomena which cause a decrease in the excess charges deposited during the passage of the primary electron beam.

(46) According to an embodiment, the temporal dispersion function takes the form:

(47) $F_t\left(t\right)=e^{-\frac{t}{}}$
where is the characteristic charge dissipation time.

(48) According to another embodiment, slower decreases may be taken into account using a Cauchy type distribution function:

(49) $F_t\left(t\right)=\frac{1}{1+{\left(\frac{t}{}\right)}^2}$

(50) The spatial dispersion function makes it possible to take into account the distance between the position P.sub.i at which the second theoretical model is calculated and the charge Q.sub.j at the position P.sub.j.

(51) According to an embodiment, the spatial dispersion function may have a Gaussian type bell shape:

(52) $F_s\left(r\right)=e^{-\frac{{.Math.r.Math.}^2}{2{}^2}}$

(53) Other spatial distribution functions may be used, according to the surface scanning mode chosen, for example. Asymmetric spatial distribution functions may also be chosen.

(54) In most CD-SEM images two simplifying hypotheses may be applied. The first hypothesis is that the current of primary electrons is constant during scanning and equal to Q.sub.0. The second hypothesis is that the surface of the sample is scanned once, without multiple passages of the primary electron beam. The second hypothesis corresponds to the absence of redundant points: the condition P(t)=P(t) with tt is never verified.

(55) The second theoretical model may then be calculated according to the following formula:

(56) $U\left(P_i,t_i\right)=U_0\left(P_i,t_i\right)-Q_o\underset{j=1}{\overset{i}{.Math.}}{R}_j{C}_j{F}_s\left(P_i-P_j\right).Math.F_t\left(t_i-t_j\right)$
in which U.sub.0(P.sub.i, t.sub.i)=Q.sub.0R.sub.i is the signal obtained at the position P.sub.i at the instant t.sub.i without taking into account charging effects.

(57) One benefit of this embodiment is to obtain a formula that is simpler to implement in the course of step FIT of the method according to the invention.

(58) On account of charging effects, a CD-SEM image acquired on a sample without topography and with a single material is not flat but will have an intensity U.sub.b(P.sub.i,t.sub.i) given by the following formula:

(59) 0$U_b\left(P_i,t_i\right)=Q_0{R}_0{\left[1-\underset{j=1}{\overset{i}{.Math.}}{C}_j{F}_s\left(P_i-P_j\right).Math.F_t\left(t_i-t_j\right)\right]}_o$
Where R.sub.0 is the response of the substrate. If this term is subtracted from the image calculated according to the second theoretical model, this gives:

(60) $U\left(P_i,t_i\right)-U_b\left(P_i,t_i\right)\left(R_i-R_0-\underset{j=1}{\overset{i}{.Math.}}\left(R_j{C}_j-R_0{C}_0\right)F_s\left(P_i-P_j\right).Math.F_t\left(t_i-t_j\right)\right)$

(61) If the charging phenomena are homogenous at the surface of the sample, it is possible to consider that the effective charge parameter has the same value at any point of the surface of the sample c.sub.ic.sub.0 and this gives:

(62) $U\left(P_i,t_i\right)-U_b\left(P_i,t_i\right){}_i-C_0\underset{j=1}{\overset{i}{.Math.}}{}_i{F}_s\left(P_i-P_j\right).Math.F_t\left(t_i-t_j\right)$
Where .sub.i=R.sub.iR.sub.0.

(63) A benefit of this embodiment is to obtain a modelling in which the background has a zero response and that only the contrasted parts, that is to say giving rise to R.sub.pR.sub.00, induce the charging phenomenon.

(64) A benefit of this embodiment is that the background may be subtracted by image processing and the calculation of the charging is only performed on the structured parts of the sample.

(65) The scanning of the surface of the sample for the acquisition of a CD-SEM image may be carried out according to several methods. An often used technique is the so-called raster scan technique, also called TV scan technique, illustrated in FIG. 6. According to this scanning mode, it is possible to identify a rapid scanning direction along the direction x indicated in FIG. 6 and a slow scanning direction along the direction y indicated in FIG. 6. According to this scanning method, data acquisition takes place only in correspondence with the horizontal lines, indicated (1) in FIG. 6. Hereafter, the rapid scanning direction, x in FIG. 6, will refer to the scanning direction of the primary electron beam.

(66) When this scanning method is used, each line of the image is scanned at constant speed and this gives:

(67) $t_i-t_j=\frac{x_i-x_j}{v_x}$

(68) This comes down to writing the second theoretical model according to the following formula:

(69) $U\left(x_i,t_i\right)=Q_i{R}_i-\underset{j=1}{\overset{i}{.Math.}}{Q}_j{R}_j.Math.C_j{F}_s\left(x_i-x_j\right).Math.F_t\left(\frac{x_i-x_j}{v_x}\right)$

(70) If the multiple passages of the primary electron beam are excluded, the calculation of the second theoretical model comes down to:

(71) $U\left(x_i,t_i\right)=Q_i{R}_i-\underset{j=1}{\overset{i}{.Math.}}{Q}_j{R}_j.Math.C_{j}F\left(x_i-x_j\right)$

(72) Where

(73) $F\left(x\right)=F_s\left(x\right).Math.F_t\left(\frac{x}{v_x}\right).$
This formula corresponds to a corrective term of truncated convolution product type with the instantaneous response T.

(74) In other words, the corrective term is a convolution product between the first parametric model and a given convolution kernel. The convolution product is calculated on the positions scanned by the primary electron beam before arriving at the position P.sub.i at the instant t.sub.i and makes it possible to take into account the charges deposited by the beam.

(75) The second theoretical model may also be calculated in continuous variables using the following formula:

(76) $U\left(x\right)-U_0\left(x\right)R\left(x\right)-R_0-{}_0^x{v}_x{\mathrm{dx}}^{}\left[C\left(x^{}\right)R\left(x^{}\right)-C_0{R}_0\right]F\left(x-x^{}\right)$

(77) A benefit of this embodiment is the simplification of the calculation steps, the integration being performed exclusively on a single spatial variable.

(78) The invention also relates to the implementation of a calibration step of a CD-SEM technique. This calibration step is carried out in order 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, may advantageously be determined during a preliminary calibration step. The calibration is obtained by carrying out an adjustment between the second theoretical model 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.

(79) 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.

(80) The invention also relates to a method for implementing a CD-SEM characterisation technique comprising the following steps: 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 second theoretical model comprising a set of parameters, said set of parameters including both the parameters to determine which describe the geometric structure of the sample of interest and the parameters determined according to the above calibration which describe 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 experimental image.

(81) Beneficially, this method for implementing a CD-SEM characterisation technique is particularly efficient. Thanks to this method, it is possible to produce a CS-SEM image of a sample of interest and to measure at least one critical dimension of said sample while taking into account the instrumental response and charging effects.