JP5452270B2 - Dimensional measuring apparatus and semiconductor device manufacturing method using the same - Google Patents

Description

  The present invention relates to a program for analyzing the dimensions of a minute structure measured using a dimension measuring apparatus, and in particular, a dimension analysis that can accurately extract statistics that characterize variations when there are spatial variations in dimensions. The present invention relates to a program and a dimension measuring apparatus equipped with the program. The present invention further relates to a method for efficiently manufacturing a high-performance semiconductor device by controlling the dimensions of elements with high accuracy.

With the miniaturization of metal-insulator-semiconductor (MIS) transistors, the variation in their characteristics increases, and as a result, the probability of hindering circuit operation has increased. For this reason, it is necessary to accurately grasp the variation in the MIS transistor characteristics. The characteristics of the MIS transistor, in particular the threshold voltage, depends on the length of the gate electrode (hereinafter referred to as the gate length) measured in the charge flowing direction in the active region (hereinafter referred to as the channel). It is known that the gate length is distributed in a direction (channel width direction) perpendicular to the direction of charge flow, and this phenomenon is usually called LWR (line width roughness). The MIS transistor characteristics mainly depend on the value L _{g obtained} by averaging the gate length in the channel width direction, but also depend on the gate length variance (or standard deviation), the channel width W _g and the correlation distance ζ of the LWR. . This point is described in detail in, for example, Proceedings of SPII by Leunissen et al., Vol. 5752 (2005), pages 499 to 509.

With regard to the dispersion of L _g and gate length described above, standardization of the measurement method was carried out in cooperation with the related industries, and Semi-P47-0307 “Test Method for Evaluation of Line Edge Roughness and Line Wids”・ Standardized as "Roughness". The standard uses a scanning electron microscope called CD-SEM to measure the width (corresponding to the gate length) of a wiring having a length of a predetermined (2 μm) or more at a predetermined interval (10 nm or less), The distribution of the wiring width is grasped by the standard deviation.

  On the other hand, with respect to the correlation distance ξ, a method has been used in which an autocorrelation function is obtained based on the measurement result of the wiring width and the correlation distance is determined using an exponential function of distance. This is described in detail in, for example, Proceedings of SPII, Constantoudis, Vol. 5375 (2004), pages 967 to 977. There is also a method for obtaining the spatial variation spectrum of the wiring width by comparing it with a power function of the wave number. This method is also described in the above-mentioned literature by Constant Two Dis.

  Furthermore, it goes without saying that it is necessary to form a wiring having a length of 2 μm or more in measuring the 2 μm area required by the above-mentioned semi-standard. Often require CD-SEMs that can be observed under different magnifications. However, it is not always possible to satisfy these conditions at a site where semiconductor devices are actually produced. For this reason, in order to cope with the case where the above conditions cannot be met, a method is proposed in which a long wiring is virtually constructed by connecting a plurality of measurement results, and the average value and standard deviation are obtained from the distribution of the wiring width. Has been. This may be referred to as a patchwork method, and details are described in, for example, Japanese Journal of Applied Physics, Yamaguchi et al., Volume 7B (2005), pages 5575 to 5580. .

Proceedings of SPII, Vol. 5752 (2005), pages 499 to 509 Semi-P47-0307 "Test Method for Evaluation of Line Edge Roughness and Line Widow Roughness" Proceedings of SPII, 5375 (2004), pages 967 to 977 Japanese Journal of Applied Physics, Volume 7B (2005), pages 5575 to 5580

  Problems in obtaining the correlation distance or variance using the conventional method will be described. In both cases, the method using autocorrelation function and the method using spectrum are used for calculation so that the result (autocorrelation function or spectrum) obtained by actual measurement matches the result obtained by calculation. The correlation distance and variance of the measurement object are determined by adjusting the correlation distance and variance. For example, the measurement is usually performed at a predetermined interval in a finite area as described in Semi-P47-0307. For this reason, when calculating the autocorrelation function or spectrum by calculation, it is necessary to assume the same region and interval as in the actual measurement. Of these, the spectrum is calculated by the present inventors in accordance with actual measurement conditions in Journal of Applied Physics, Vol. 106 (2009), pages xxx-1 to xxx-8. Has been reported. However, when the patchwork method is used, there is a problem that the correlation distance cannot be analyzed because the autocorrelation function or spectrum is not theoretically elucidated.

  The conventional method also has the following problems. When obtaining a spectrum, it is ideally necessary to take measurements infinitely and average the results. However, the actual number of measurements is limited. When the number of times is small, the jaggedness called jaggy generated in the spectrum becomes large, which is an obstacle to analysis. In the patchwork method, this problem becomes serious. That is, in the case where n wirings (whose length is L) are combined to form one virtually long wiring (having a length nL), a virtual long wiring that can be formed. Is reduced to 1 / n of the number of original wirings (hereinafter referred to as element wirings), and as a result, there is a problem that jaggy increases remarkably.

In order to solve the problem of the patchwork method, in the present invention, when the element wirings are combined to form a virtual long wiring, the spatial arrangement order of the element wirings is completely disturbed by random numbers and combined. . In this way, when the correlation function of the wiring width is an exponential function of distance, the inventors of the present invention can theoretically express the spectrum _{IAS, τ} of the combined virtual long wiring by the following equation. I found it.

ここで、

here,

であり、τは１からｎＮまでの値をとる。要素配線はｙ方向に延伸するとした。

Τ takes a value from 1 to nN. The element wiring is assumed to extend in the y direction.

  When the autocorrelation function is not an exponential function, if this is φ (y), the spectrum of the virtual long wiring can be obtained by the following equation instead of the equation (1).

なお、上記（１）式および（３）式により表されるＩ_AS,τをｋ_τの関数として見た場合、その関数形は要素配線を結合しない場合の結果と等しい。ただし、要素配線の場合においてはｋ_τがＫ₀≡２π／Ｌ＝ｎｋ₀の整数倍である値のみをとるのに対し、仮想的長配線の場合においてはそれ以外にｋ₀の整数倍の値もとる。この結果のみからは、仮想的長配線のスペクトルが結合しない場合のスペクトルを内挿したものであるかのように推測しがちである。しかし、同推測が常に正しいとは限らないことを後述する。なお、（１）式右辺により仮想的長配線のＩ_AS,τを求めるに際しては、ｎＮをＮに代入するのでなくＮをそのままにして計算することに注意が必要である。

In addition, _{when IAS, τ} represented by the above equations (1) and (3) is viewed as a function of _kτ , the function form is equal to the result when element wiring is not coupled. However, in the case of element wiring, k _τ takes only a value that is an integer multiple of K ₀ ≡2π / L = nk ₀ , whereas in the case of a virtual long wiring, it is an integer multiple of k ₀ other than that. Take value. From this result alone, it tends to be inferred as if the spectrum when the spectrum of the virtual long wiring is not combined is interpolated. However, it will be described later that the assumption is not always correct. Note that when calculating IAS _{, τ} of the virtual long wiring from the right side of the equation (1), care should be taken not to substitute nN for N but to calculate NAS as it is.

  Needless to say, when obtaining a spectrum from the actual measurement result, it is desirable to measure as many wirings as possible under the same conditions in order to reduce spectrum jaggies. Furthermore, when configuring a virtual long wiring by combining element wiring, the present invention allows the same element wiring to be shared between different virtual long wirings. As a result, the number of virtual long wirings that can be formed is almost unlimited, and the number of average operations can be dramatically increased, so that spectrum jaggies can be greatly reduced. The element wiring may be a part of a long wiring virtually cut out. In addition, it is possible to use what is virtually cut out from the wiring formed adjacently, but among the wirings formed in parallel, the one near the end has a dimensional distribution different from the one near the center. Care must be taken as there are cases.

In the following, the results of studies conducted to verify the effectiveness of the above means of the present invention will be described. First, in order to verify the validity of the above equation (1), calculation is performed using the spectrum of the virtual long wiring formed by using the element wiring formed by simulation using the Monte Carlo method and the equation (1). FIG. 1A shows an example of the result of comparison with the spectrum obtained. FIG. 4B is an enlarged view of a portion surrounded by a rectangle in FIG. In the figure, a spectrum obtained when the width of a virtual long wiring in which 20 element wirings having a length of 2000 nm are connected in random order is measured at an interval of 10 nm is shown, and the white circle indicates the result by the Monte Carlo method. A black circle shows the result calculated by the equation (1). In addition, the result by the Monte Carlo method is a result of forming 4000 virtual long wirings while allowing sharing of 524 created element wirings, and averaging spectra obtained therefrom. Since both agree well, it can be confirmed that not only the expression (1) is valid, but also the calculation using the Monte Carlo method performed by the present inventors is also valid. For reference, in the figure, a spectrum (hereinafter referred to as a continuous spectrum) obtained when measurement is performed at infinitely small intervals in an infinitely wide area is shown by a solid line. By measuring the line width that varies in accordance with the continuous spectrum in finite intervals, it is seen that the spectrum is deformed into axially symmetrical ones a straight line expressed by k = nNk _0/2 as an axis. Here, n and N are assumed to be even numbers (the same applies hereinafter). It is known that such deformation is caused by a phenomenon called aliasing. From the above figure, it can be seen that the spectrum obtained by measuring at a finite interval deviates greatly from the original spectrum for wave numbers near and above the symmetry axis. These are phenomena that also occur in the spectrum of unconnected element wirings. On the other hand, there is a periodic variation that does not exist in the original spectrum, which is a feature that can be seen only in the virtual long wiring. Therefore, in order to appropriately determine the dispersion of dimensional variation and the correlation distance, it is important to calculate the spectrum according to equation (1) in accordance with the measurement conditions and compare it with the spectrum obtained by measurement.

Next, the results of examining the effect of averaging the spectrum will be described. The decrease in jaggies due to spectrum averaging is reported, for example, by Bunday et al. In Proceedings of SPAI, Vol. 5375 (2004), pages 515 to 533. However, the examination of the average effect in the known examples including the report is qualitative, and it has hardly been used as a reference for the examination of the jaggy of the virtual long wiring in which the element wiring is combined. Therefore, first, the average effect of the spectrum of the element wirings that are not coupled was examined. An example of the result is shown in FIG. Here, the spectrum of 5240 wirings created by the calculation using the Monte Carlo method described above is obtained, and the spectrum J _τ obtained by averaging some of these is calculated analytically with n = 1 in the equation (1). The difference ε from the spectrum I _τ is shown as a function of the average number N _PSD . The wiring length is 2000 nm, the LWR correlation distance is 30 nm, and the assumed measurement interval is 10 nm. Ε was calculated by the following formula.

同図から、平均回数とともにモンテカルロ法によるスペクトルが解析的結果に漸近するので、平均操作がスペクトルのジャギー低減に効果を発揮することが理論的かつ定量的に確認できる。また、同図はジャギーを所望の水準に留めるのに必要な平均回数を求める上でも有用である。図３は、要素配線を５個結合して形成した仮想的長配線のスペクトルのジャギーについて、図２と同様モンテカルロ法により検討した結果である。ここで、要素配線の長さは２０００ｎｍ、ＬＷＲの相関距離は３０００ｎｍ、想定した測定間隔は１０ｎｍであり、要素配線の総数Ｎ_fは２０個（中白の丸）および２００個（中黒の丸）とした。仮想的長配線の間で要素配線の重複を許容しない場合においては形成することのできる仮想的長配線の数はそれぞれ４個と４０個であるが、同図においては重複を許容しているので仮想的長配線をほぼ無数に形成することができる。同図から、スペクトルを平均する回数が重複を許容しない場合の上限を超えても誤差がさらに減少するので、重複を許容することがジャギー低減に有効であることが分る。誤差の減少はやがて止まるが、到達した最小値は要素配線の数の多い方が小さい。なお、スペクトルの平均回数が要素配線の数の概ね５倍を超えるとジャギー低減効果が飽和する。図４には、仮想的長配線を構成する要素配線の数が２０個である場合の結果を示す。図３と図４を比較すると、結合する要素配線の数が異なる場合においてもスペクトルの誤差はスペクトルを平均する回数によりほぼ決定されることが分る。この結果は、スペクトルのジャギー低減という観点からは結合する要素配線の数を制限する必要のないことを示している。上記平均効果を実際にスペクトルにより確認するために、上記図３と図４を求める際に計算したスペクトルの例を図５に示す。同図（ａ）と（ｂ）においては、要素配線の総数が２０、その結合数も同じ２０である。（ａ）においては平均回数が１であるので、要素配線の重複を許容しない場合に対応する。これに対して、（ｂ）は重複を許容して２０００回平均した結果である。（ｂ）において形成した２０００個の仮想的長配線においては、これらを構成する要素配線は全て同じであり、要素配線を結合する順序のみが異なる。それにもかかわらず（ｂ）のスペクトルのジャギーが（ａ）のスペクトルのジャギーよりも小さいことが明瞭に見て取れる。また、図５（ｃ）は、（ｂ）における要素配線の総数を２００個へと増加させた場合の結果である。（ｂ）と（ｃ）とでは平均回数が同じであるが、要素配線の総数が大きい（ｃ）の方がスペクトルのジャギーが小さくなっている。なお、上記説明においてスペクトルを平均する際には、通常、配線幅のフーリエ変換の絶対値の二乗を波数毎に平均する。このため、「スペクトルを平均する」ことは「フーリエ変換の絶対値の二乗を平均する」ことと等価であることは言うまでもない。

Since the spectrum by the Monte Carlo method asymptotically approaches the analytical result together with the average number, it can be confirmed theoretically and quantitatively that the average operation is effective in reducing the spectrum jaggies. This figure is also useful for obtaining the average number of times required to keep jaggy at a desired level. FIG. 3 shows the result of examining the spectrum jaggy of a virtual long wiring formed by combining five element wirings by the Monte Carlo method as in FIG. Here, the length of the element wiring is 2000 nm, the LWR correlation distance is 3000 nm, the assumed measurement interval is 10 nm, and the total number N _{f of the} element wiring is 20 (inner white circle) and 200 (inner black circle). ). The number of virtual long wirings that can be formed is 4 and 40, respectively, in the case where the overlapping of element wirings is not allowed between the virtual long wirings. A virtually unlimited number of virtual long wires can be formed. From the figure, it can be seen that the error is further reduced even if the number of times of averaging the spectrum exceeds the upper limit when the overlap is not allowed, so that it is effective to reduce the jaggy. The reduction in error will eventually stop, but the minimum value reached is smaller when the number of element wirings is larger. When the average number of spectrums exceeds approximately five times the number of element wirings, the jaggy reduction effect is saturated. FIG. 4 shows a result when the number of element wirings constituting the virtual long wiring is 20. Comparing FIG. 3 and FIG. 4, it can be seen that the spectrum error is almost determined by the number of times the spectrum is averaged even when the number of coupled element wirings is different. This result indicates that it is not necessary to limit the number of element wirings to be combined from the viewpoint of reducing spectrum jaggy. FIG. 5 shows an example of a spectrum calculated when obtaining FIG. 3 and FIG. 4 in order to actually confirm the average effect by the spectrum. In FIGS. 2A and 2B, the total number of element wirings is 20, and the number of connections is also the same. In (a), since the average number is 1, this corresponds to a case where duplication of element wiring is not allowed. On the other hand, (b) shows the result of averaging 2000 times while allowing overlap. In the 2000 virtual long wirings formed in (b), the element wirings constituting these are all the same, and only the order of coupling the element wirings is different. Nevertheless, it can be clearly seen that the spectrum jaggy of (b) is smaller than the spectrum jaggy of (a). FIG. 5C shows the result when the total number of element wirings in FIG. 5B is increased to 200. In (b) and (c), the average number of times is the same, but in the case of (c) where the total number of element wirings is larger, the spectrum jaggy is smaller. In addition, when averaging a spectrum in the said description, the square of the absolute value of the Fourier transform of wiring width is normally averaged for every wave number. Therefore, it goes without saying that “averaging the spectrum” is equivalent to “averaging the square of the absolute value of the Fourier transform”.

It will be described below that it is necessary to set the number n of element wirings to be combined to an appropriate value in obtaining the LWR statistics. FIG. 6 shows a result of normalizing a spectrum obtained by measuring var (w) / ξ when a width of a 2000 nm long wiring is measured at intervals of 10 nm. Here, the results when the correlation distances are 1000 nm, 2000 nm, and 3000 nm are shown. When normalized in this way, it can be seen that even if the values of the correlation distances are different, the spectra may almost coincide. At this time, between ξ = 1000 nm, c (1 < c < 3) as a constant, the variance is var (w), the correlation distance is ξ, and the spectrum is the variance is cvar (w) and the correlation distance is cξ. Therefore, the variance and correlation distance cannot be determined. One of the measures for solving such a problem is to set the length L of the length measurement region of the element wiring so that the minimum value of the wave number is smaller than the reciprocal of the correlation distance. That is, it is necessary to satisfy L > 2πξ. Although it is not always possible to satisfy the same condition, even in such a case, if the above wiring is combined as an element wiring, a flat portion in the spectrum in a region having a small wave number as shown in FIG. Appears. The maximum value of the spectrum in this part is I _{AS, 1} (τ = 1), and asymptotically approaches I ₀ together with n. Since values obtained by normalizing I ₀ with different ξ by var (w) / ξ are different from each other, if n is made sufficiently large so that I _{AS, 1} is substantially equal to I ₀ , a region having a large wave number is obtained. By comparing the spectra in the vicinity of τ = 1, it is possible to determine the variance and the correlation distance. For reference in appropriately selecting the value of n, FIG. 7 shows the ratio of I _{AS, 1} and I ₀ as a function of n. The above-mentioned ratio is smaller as ξ / L is larger. However, when n is 10 or more, the ratio becomes almost 1 regardless of the value of ξ / L, and the dispersion and the correlation function can be determined with high accuracy.

  By using the dimension analysis program of the present invention, it becomes possible to accurately extract statistics such as the average value, variance, standard deviation, correlation distance, etc. of the dimensions of the structure based on the captured image of the structure. Further, by using the dimension measuring apparatus of the present invention equipped with the same dimension analysis program, it is possible to consistently quickly and accurately grasp from the photographing of the structure to the extraction of various statistic quantities. Furthermore, if the manufacturing method of the present invention using the same dimension measuring device for process management is used, the dimensional accuracy of the fine structure constituting the semiconductor device is improved, so that the manufacturing yield and quality of the semiconductor device are improved. To do.

The figure which shows the spectrum of LWR of the virtual long wiring which couple | bonded element wiring. The figure which shows the magnitude | size of jaggy in the spectrum which averaged between the some samples. The figure which shows the magnitude | size of jaggy in the spectrum of LWR of the virtual long wiring which connected five element wiring. The figure which shows the magnitude | size of jaggy in the spectrum of LWR of the virtual long wiring which couple | bonded 20 element wiring. The figure which shows the effect of the average operation performed allowing duplication of element wiring. The figure which shows the spectrum of LWR with a long correlation distance. The figure which shows the value of the spectrum with respect to the minimum wave number. The figure which shows the 1st screen displayed on the display apparatus by 1st Example of this invention. The figure which shows the value of the spectrum with respect to a specific wave number. The figure which shows the 2nd screen displayed on the display apparatus by 1st Example of this invention. The figure which shows the 3rd screen displayed on the display apparatus by 1st Example of this invention. The figure which shows the 4th screen displayed on the display apparatus by 1st Example of this invention. The figure which shows the 5th screen displayed on the display apparatus by 1st Example of this invention. The figure which shows an example of the screen displayed on the display apparatus by 2nd Example of this invention. The figure which shows the 1st screen displayed on the display apparatus by the 3rd Example of this invention. The figure which shows the 2nd screen displayed on the display apparatus by the 3rd Example of this invention. The figure which shows the spectrum of the virtual long wiring which couple | bonded the element wiring from which the length of a measurement area | region differs. The figure which shows the 4th Example of this invention. The figure which shows the 5th Example of this invention. The figure which shows the 6th Example of this invention.

First Embodiment FIG. 8 shows an example of a screen displayed on a display device (monitor) while the dimensional analysis program of the present invention is operating. In this example, 452 electronic files (hereinafter simply referred to as files) having even numbers as part of their names beginning with “LWR-PR1-0002” and ending with “LWR-PR1-0904” are “/ root / It is stored in an electronic folder (hereinafter simply referred to as a folder) designated by “mnt / cd-meas / pr1”. The file name is specified by the contents displayed in boxes 1 and 4-6. It will be obvious how the file name is specified from the contents entered in these boxes. The folder name is specified by the contents entered in box 3. Box 3 is a pull-down menu for the convenience of inputting a folder name. Image processing software called Terminal PC (Terminal-PC) sold by Hitachi High-Technologies Co., Ltd., in which the above-mentioned files are obtained by photographing fine lines made of photoresist using a CD-SEM. The result of measuring 200 times at intervals of 10 nm using is recorded. These measurement conditions are entered in boxes 7 and 8, respectively. Note that the contents of these boxes 7 and 8 can be automatically read from the file in which the measurement conditions are recorded.

When the button 23 labeled “Spectra” is clicked, data is sequentially read from the above-described file and analyzed. Among the analyzed results, the average value of the dimensions is displayed in the box 11 and the spectrum is displayed in the graph 21 (white circle). The spectrum indicated by white circles is obtained as follows. First, element wirings having the data recorded in the above file as widths are randomly extracted by the number input in the box 9 and then combined to form a virtual long wiring to obtain a spectrum. At that time, the order of combining the extracted element wirings is also random. In this way, the spectrum of the virtual long wiring obtained by the number inputted in the box 10 and averaged is the spectrum indicated by white circles. In addition, the graph 21 uses the contents inputted in the boxes 12 (variance of dimensions in the first component of the LWR) and 13 (correlation distance of dimensional variations in the first component), and the expressions (1) to (3) are used. Using the contents inputted in the spectrum I _{AS, τ, 1st of} the first component calculated in accordance with ( ₁₎ , boxes 14 (size dispersion in the second component of the LWR) and 15 (correlation distance of size variation in the second component) ( Also, the result (solid line) of the sum of the second component spectrum I _{AS, τ, 2nd} calculated by the formulas (1) to (3) and the constant value (the contents of the box 17) corresponding to the spectrum I _noise caused by the image noise. It is displayed. The reason why the constant value independent of the wave number is added as a component caused by noise is that the noise is generally white (it is constant regardless of the wave number) and is independent as a random variable. The box 18 displays a variance var _noise having a size caused by the _noise . There is a relationship represented by the following equation between I _noise and var _noise .

ラジオボタン１９と２０が選択されているので、画像雑音がないとして計算した結果（破線）および無限の大きさを有する領域を連続的に測定した場合に想定される結果（一点鎖線）もグラフ２１には表示されている。なお、ボタン群２２を適宜クリックすることによりグラフ２１の座標軸の範囲を変更することが可能である。ボックス１２ないし１５、および１７の内容の内の少なくとも一つが変更されるとこれら値を用いて再度計算が行われ、結果が即座に更新されるようになっている。これにより、上記ボックス１２ないし１５および１７の内容を様々に変化させながら計算結果（実線）が実測結果（白丸）と一致する値を探索することにより、画像雑音の影響を受けることなく寸法変動をもたらす第１成分と第２成分の分散と相関距離を高精度に決定することができる。このようにして最適化された実線の結果は白丸の結果と良く一致しており、ホトレジスト細線の寸法変動がいずれも指数関数型の自己相関関数を有する二つの成分によりもたらされていることおよび本発明の（１）式がスペクトル解析に有効であることが確認できる。

Since the radio buttons 19 and 20 are selected, the result calculated when there is no image noise (dashed line) and the result assumed when an area having an infinite size is continuously measured (dashed line) are also shown in the graph 21. Is displayed. Note that the range of the coordinate axes of the graph 21 can be changed by appropriately clicking the button group 22. When at least one of the contents of boxes 12 to 15 and 17 is changed, the calculation is performed again using these values, and the result is immediately updated. As a result, by changing the contents of the boxes 12 to 15 and 17 in various ways and searching for a value where the calculation result (solid line) matches the actual measurement result (white circle), the size variation can be reduced without being affected by image noise. It is possible to determine the dispersion and correlation distance of the first component and the second component to be provided with high accuracy. The results of the solid line optimized in this way are in good agreement with the results of the white circle, and that the dimensional variation of the photoresist fine line is both caused by two components having an exponential autocorrelation function and It can be confirmed that the expression (1) of the present invention is effective for spectrum analysis.

を（１）式により計算する。ここで、ｖａｒ(ｗ₁)は第１成分の分散であるが、

を求める上でその値は必要ない。
（ｃ）第１成分のスペクトルを次式により計算する。

（ｄ）第２成分の相関距離ζ₂の値を適当に仮定し、第２成分のスペクトルＩ_τ,2ndを規格化した

を（ｂ）と同様にして計算する。ここでｖａｒ(ｗ₂)は第２成分の分散であるが、

を計算する上でその値が必要でないのは

の場合と同じである。
（ｅ）第２成分の分散の暫定値ｖａｒ_τ,2ndを次式により計算する。

ここで、Ｉ_meas,τは実測結果から求めたスペクトルである。
（ｆ）τ＜ｎである波数ｋ_τに対して、これら暫定値ｖａｒ_τ,2ndの平均ｖａｒ_AV,2ndを計算する。（ｇ）第２成分のスペクトルを次式により計算する。

（ｈ）和Ｉ_τ,ALL≡Ｉ_τ,1st＋Ｉ_τ,2nd＋Ｉ_noiseを求める。
（ｉ）所定の波数領域においてＩ_τ,ALLとＩ_meas,τとが最も良く一致するように、（ｄ）ないし（ｈ）を反復しξ₂を最適化する。その値をξ_tempor,2とする。ここでも（ａ）と同様、ｋ_mn＝ｍｎｋ₀(ｍ＝０，１，…，Ｎ−１)である波数に対しては両者の比較を行わない。
（ｊ）第１成分の分散の暫定値ｖａｒ_tempor,1stを次式により計算する。

（ｋ）第１成分のスペクトルを次式により計算する。

（ｌ）上記（ｅ）ないし（ｇ）によりＩ_τ,2ndを再度計算する。
（ｍ）第１成分の分散の暫定値が変化しなくなるまで（ｊ）ないし（ｌ）を反復する。
（ｎ）第１成分の分散の暫定値が変化しなくなるまで（ｄ）から（ｍ）を反復する。
（ｏ）上記（ｎ）によりｖａｒ_tempor,1stとξ_tempor,2が一定となるのみならず、ｖａｒ_AV,2ndも一定となる。これら一定値がそれぞれボックス１２，１５および１４に表示される。また、第１成分の相関距離とスペクトルの雑音成分は上記（ａ）により決定された値がそれぞれボックス１３と１７に表示される。 When the button 24 labeled “Fit” is clicked, the above-described operation of optimizing the contents to be input in the boxes 12 to 15 and 17 by trial and error can be automatically performed. Even in this case, it goes without saying that the automatically determined content can be corrected again by the manual method described above. The automatic optimization work is performed as follows.
(A) LWR first component (component of the shorter correlation distance) wavenumber region is dominant in (here, to not 0.01cm ^-1 0.314cm ^-1) in, ignoring the presence of the second component Then, the correlation distance ξ ₁ of the first component and the noise component I _noise of the spectrum are determined so that the spectrum calculated using the equations (1) to (3) matches the actual measurement result. The upper limit of the frequency domain is equal to the coordinate nnK _0/2 axis of symmetry due to aliasing effects. In order to exclude the influence of the system fluctuation described later, the calculation result is not compared with the actual measurement result for the wave number of k _mn = mnk ₀ (m = 0, 1,..., N−1). . Here, the variance var _{init, 1st} of the first component is also obtained at the same time, and this is an initial value in a series of calculations described below from (b).
(B) Substituting ξ ₁ into equation (2) to normalize the spectrum I _{τ, 1st} of the first component

Is calculated by equation (1). Where var (w ₁ ) is the variance of the first component,

The value is not necessary for obtaining.
(C) The spectrum of the first component is calculated by the following equation.

(D) The value of the correlation distance ζ ₂ of the second component is appropriately assumed, and the spectrum I _{τ, 2nd} of the second component is normalized.

Is calculated in the same manner as in (b). Where var (w ₂ ) is the variance of the second component,

The value is not necessary to calculate

Is the same as
(E) The provisional value var _{τ, 2nd} of the variance of the second component is calculated by the following equation.

Here, I _{meas, τ} is a spectrum obtained from an actual measurement result.
(F) The average var _{AV, 2nd} of these provisional values var _{τ , 2nd} is calculated for the wave number k _τ where τ <n. (G) The spectrum of the second component is calculated by the following equation.

(H) the sum _{I τ, ALL ≡I τ, 1st} + I τ, seek _2nd + I _noise.
(I) Repeat (d) to (h) to optimize ξ ₂ so that I _{τ, ALL} and I _{meas, τ} are best matched in a predetermined wave number region. _Let that value be ξ _{tempor, 2} . Again, as in (a), the comparison is not performed for the wave number where k _mn = mnk ₀ (m = 0, 1,..., N−1).
(J) The provisional value var _{tempor, 1st} of the variance of the first component is calculated by the following equation.

(K) The spectrum of the first component is calculated by the following equation.

(L) Calculate _{Iτ, 2nd} again according to the above (e) to (g).
(M) Repeat (j) to (l) until the provisional value of the variance of the first component does not change.
(N) Repeat (d) to (m) until the provisional value of the dispersion of the first component does not change.
(O) According to the above (n), not only var _{tempor, 1st} and ξ _{tempor, 2} are constant, but var _{AV, 2nd} is also constant. These constant values are displayed in boxes 12, 15 and 14, respectively. In addition, the correlation distance of the first component and the noise component of the spectrum are displayed in boxes 13 and 17, respectively, as determined by (a) above.

  In the above iterative calculation, since the value obtained in (a) is used as the initial value of the variance of the first component, the variance value of the first component finally determined by (n) is the initial value. Is almost equal to For this reason, in many cases, sufficient accuracy can be obtained if the iteration in (n) is repeated at most twice. Even if (n) is omitted, there are many cases where there is no practical problem.

While many of the spectrums (white circles) of the actual measurement results shown in the graph 21 agree well with the above calculation results (solid line), the wave number k _mn = mnk ₀ (m = 0, 1,..., N−1) The value of the actual measurement result is greatly deviated from the calculation result. The results of the study by the present inventors regarding the cause will be described below. Assume that the wiring width of the element wiring constituting the virtual long wiring is w _{s, α} (s = 0, 1,..., N−1). Here, s indicates a measurement position in the element wiring, and α is a number for identifying the element wiring. When s is fixed and w _{s, α} is infinitely averaged between the element wirings is W _s , and the spectrum is I _{SYS, m} (m = 0, 1,..., N−1), the wave number k described above. spectrum value for _mn is found that the (1) formula to (3) the value I _aS to be calculated from the _equation, nI to _{mn SYS, m} is plus _{I aS, mn + nI SYS,} m. Since W _s is not a random variable unlike w _{s, α} , hereinafter, the variable is referred to as a system variable, and the variation in the wiring width represented by the variable is referred to as a system variation. According to the above results, the amount added to the spectrum due to system fluctuation is proportional to n. In order to verify this, the value of the spectrum obtained from the measurement results with m fixed is shown as a function of n in FIG. In the figure, the results for m = 1, 2, 7, 8 are shown. As expected from the above theoretical analysis results, it can be confirmed that the spectrum value for the wave number _kmn is a linear function of n. Note that the coefficient of n in the same-order function is equal to I _{SYS, m} .

When the button 25 labeled “System” in FIG. 8 is clicked, a screen for analyzing the system variable is displayed as shown in FIG. The white circles in the graph 28 on the same screen indicate the results of averaging measured w _{s, α} with s fixed in order to approximate the value of the system variable. The solid line is a result obtained by approximating the result indicated by the white circle with a polynomial whose degree is the number input in the box 30. In addition, the white circle in the graph 29 indicates the following equation based on the actual measurement result.

により求めたシステム変動のスペクトルＩ_SYS-MEAS,mであり、実線は上記多項式近似の結果のスペクトルである。ボックス３０に入力した値を変更すると、直ちに新しい値の下で多項式近似を再度実行しその結果をグラフ２８および２９に表示するようになっている。グラフ２９の白丸と実線とがほぼ一致するところから、図８のグラフ２１において波数ｋ_mn＝ｍｎｋ₀に対するスペクトルの値が実測結果と計算結果とで大きく異なっている原因がシステム変動にあることが分る。なお、図１０のボタン３１をクリックすると図８の画面にもどる。

Is the spectrum I _{SYS-MEAS, m} of the system variation obtained by the above equation, and the solid line is the spectrum resulting from the above polynomial approximation. When the value entered in the box 30 is changed, the polynomial approximation is immediately performed again under the new value, and the result is displayed in the graphs 28 and 29. Since the white circle and the solid line in the graph 29 almost coincide with each other, in the graph 21 in FIG. 8, there is a system variation that causes the spectrum value for the wave number k _mn = mnk ₀ to greatly differ between the actual measurement result and the calculation result. I understand. When the button 31 in FIG. 10 is clicked, the screen in FIG. 8 is restored.

The distribution due to the system fluctuation is displayed in the box 16 in FIG. 8, and the value is calculated as follows. The average value of the wiring width in the virtual long wiring formed by combining the element wirings is (w) _α and the variance is var (w) _α.

により配線幅の分散ｖａｒ(ｗ)_measを求める。ここでｖａｒ((ｗ)_α)_ASと（ｖａｒ(ｗ)_α)_ASは、スペクトルを求めるためにボックス１０に入力された数だけ形成した一連の仮想的長配線を標本とする母集団における(ｗ)_αの分散およびｖａｒ(ｗ)_αの平均値である。上記ｖａｒ(ｗ)_measからボックス１２，１４および１８に表示された値を引き算したものがボックス１６に表示してある。他方、システム変動のスペクトルを上記（６）式を用いて計算し、次式

To obtain the distribution var (w) _meas of the wiring width. Here, var ((w) _α ) _AS and (var (w) _α ) _AS in the population using a series of virtual long wires formed as many as the number input in the box 10 for _obtaining the spectrum as samples. w) is the average value of the variance and var (w) _alpha of _alpha. A value obtained by subtracting the value displayed in the boxes 12, 14 and 18 from the var (w) _meas is displayed in the box 16. On the other hand, the spectrum of system fluctuation is calculated using the above equation (6).

により求めた分散は０.１５ｎｍ²となり、ボックス１６に表示された値と一致する。なお、（８）式におけるｋ₀は（２）式により計算される。さらに、多項式近似の結果から求めた分散も０.１７ｎｍ²となり上記値とほぼ一致する。

The dispersion obtained by (1) is 0.15 nm ² , which matches the value displayed in the box 16. Note that k _{0 in} equation (8) is calculated by equation (2). Further, the dispersion obtained from the result of the polynomial approximation is also 0.17 nm ² , which substantially coincides with the above value.

FIG. 11 is an example of a screen displayed when the button 26 in FIG. 8 is clicked. The three types of straight lines in the graphs 32 and 33 represent an infinite value (w) _α of the wiring width in the virtual long wiring in which the element wirings having the LWR whose statistics are the values displayed in the boxes 12 to 15 are combined. The standard deviation σ ((w) _α ) in the collected population is

により計算した結果を仮想的長配線の長さｎＬおよび結合した要素配線の数ｎの関数としてそれぞれ示したものである。ここで、Ｉ_AS,0,1stとＩ_AS,0,2ndは仮想的長配線のＬＷＲのスペクトルを構成する二つの成分のτ＝０における値を図８のグラフ２１における実線と同様にして計算した結果である。なお、ｋ₀は（３）式により計算されるので

The results calculated by the above are respectively shown as a function of the length nL of the virtual long wiring and the number n of the combined element wirings. Here, I _{AS, 0,1st} and I _{AS, 0,2nd} are calculated in the same manner as the solid line in the graph 21 of FIG. 8 by calculating the values at τ = 0 of the two components constituting the LWR spectrum of the virtual long wiring. It is the result. Since k ₀ is calculated by equation (3),

である。上記３種の直線においては要素配線の長さＬが異なり、それぞれ５０ｎｍ，２００ｎｍ，２０００ｎｍである。これらＬの値は、ボックス３４により指定される。また、グラフ３２における曲線（一点鎖線）は、長さがｎＬである単一の要素配線における結果を同様にして計算した結果を示す。このようにして求めたσ((ｗ)_α)は、１本の仮想的長配線において求めた(ｗ)_αが真の値(ｗ)にどれほど近いかを示す指標となる。すなわち、モンテカルロ法を用いた計算によると(ｗ)_αは正規確率分布をしており、この場合、(ｗ)は９９.７％の確率で(ｗ)_α−３σ((ｗ)_α)ないし(ｗ)_α＋３σ((ｗ)_α)の範囲に、９５％の確率で(ｗ)_α−２σ((ｗ)_α)ないし(ｗ)_α＋２σ((ｗ)_α)の範囲に、６８％の確率で(ｗ)_α−σ((ｗ)_α)ないし(ｗ)_α＋σ((ｗ)_α)の範囲に存在することになる。上記グラフ３２によると、仮想的長配線の長さをそろえた比較においては、要素配線の短い方がσ((ｗ)_α)が小さく(ｗ)_αが(ｗ)に近いことが分る。他方グラフ３３によると、ｎをそろえた比較においては要素配線の長い方がσ((ｗ)_α)の小さいことが分る。したがって、これらグラフを参照することにより実際の状況に応じて配線幅の平均値を高精度に測定するための条件を適切に設定することが可能となる。

It is. In the above three types of straight lines, the length L of the element wiring is different and is 50 nm, 200 nm, and 2000 nm, respectively. These L values are specified by box 34. Further, the curve (dashed line) in the graph 32 shows the result of the same calculation for the result of a single element wiring having a length of nL. Σ ((w) _α ) obtained in this way is an index indicating how close (w) _α obtained in one virtual long wiring is to the true value (w). That is, according to the calculation using the Monte Carlo method, (w) _α has a normal probability distribution. In this case, (w) has a probability of 99.7% (w) _α -3σ ((w) _α ) or (w) _α + 3σ ((w) _α ) in the range of 95% probability (w) _α -2σ ((w) _α ) to (w) _α + 2σ ((w) _α ) in the range of 68% (W) _α− σ ((w) _α ) to (w) _α + σ ((w) _α ) with a probability of. According to the graph 32, in the comparison in which the lengths of the virtual long wirings are aligned, it can be understood that σ ((w) _α ) is smaller and (w) _α is closer to (w) when the element wiring is shorter. On the other hand, according to the graph 33, it can be seen that the longer element wiring has smaller σ ((w) _α ) in the comparison with n. Therefore, by referring to these graphs, it is possible to appropriately set conditions for measuring the average value of the wiring width with high accuracy according to the actual situation.

If the graph 33 is used, it is possible to estimate the accuracy of the average value when managing the production process of the semiconductor device using a value obtained by averaging a plurality of measurement results relating to the element dimensions. That is, also in production process management, a value U obtained by averaging the results of measuring the width u of a predetermined pattern a plurality of times at predetermined intervals is taken as one measurement result of the dimension. A value V obtained by averaging n _AV pieces of these measurement results is equal to an average value of the widths of virtual long wirings in which n _AV pieces are combined using the pattern as an element wiring. Therefore, when the measurement conditions of u are the same as the contents of boxes 7 and 8, and the statistic characterizing the fluctuation of u is equal to the value displayed in boxes 12 to 15, the standard deviation σ of the variation occurring in V (V) can be read from the graph 33 as n = n _AV . In addition, according to equation (10), the standard deviation of U variation is σ (U) and the following equation:

によりσ(Ｖ)を求めることもできる。これにより、測定したＶの精度を上記した(ｗ)_αの場合と同様にして把握することができる。なお、Ｖの分散を求めるには（１１）式の両辺を平方すればよい。

Σ (V) can also be obtained by Thereby, the accuracy of the measured V can be grasped in the same manner as in the case of (w) _α described above. In addition, what is necessary is just to square both sides of (11) Formula in order to obtain | require dispersion | distribution of V.

FIG. 12 shows an example of a screen displayed when the button 35 in FIG. 11 is clicked. In the same screen, a graph 36 is a population in which an infinite number of average values L _g in the elements of the same channel length are collected assuming that the channel length of the MIS transistor has an LWR whose value is the value displayed in the boxes 12 to 15. As a function of the channel width W _g , the dispersion σ (L _g ) in

により計算し、ボックス３７に表示された係数ｃを用いてｃσ(Ｌ_g)と−ｃσ(Ｌ_g)を実線により表示したものである。ここで、ｖａｒ(ｗ₁)とｖａｒ(ｗ₂)は、ＬＷＲの第１成分の分散と第２成分の分散であり、その値がボックス１２と１４にそれぞれ表示されている。図１２に示された例においてはｃ＝３であり、この場合ＭＩＳトランジスタの９９.７％においてＬ_gの平均値からの偏差ΔＬ_gがグラフ３６に示された二つの実線の間に分布する。なお、同グラフにおける破線は第１のＬＷＲ成分のみを考慮した場合の結果である。実線と破線を比較すると、１００ｎｍ以上のＷ_gを有するＭＩＳトランジスタのＬ_gの分布に対して第２のＬＷＲ成分が少なからず影響して値が大きくなっており、この点を回路設計上考慮する必要のあることが分る。なお、上記（１２）式および（１３）式は長さＷ_gの配線を無限小の間隔で測定する場合の結果である。この結果は、（１）式および（９）式においてＬをＷ_gで置き換え、Ｗ_g＝ＮΔｙを一定に保ちながらＮ→∞，Δｙ→０とした極限として得られる。

And cσ (L _g ) and −cσ (L _g ) are displayed by solid lines using the coefficient c displayed in the box 37. Here, var (w ₁ ) and var (w ₂ ) are the variance of the first component and the variance of the second component of the LWR, and the values are displayed in boxes 12 and 14, respectively. In the example shown in FIG. 12, c = 3. In this case, the deviation ΔL _g from the average value of L _g is distributed between the two solid lines shown in the graph 36 in 99.7% of the MIS transistors. . In addition, the broken line in the graph is a result when only the first LWR component is considered. Comparing the solid and broken lines, the value affects not a little second LWR components relative distribution of L _g of MIS transistors having 100nm or more W _g are increased, consider the circuit design of this point I know that I need it. The above equations (12) and (13) are the results when the wiring of length W _g is measured at infinitely small intervals. This result is obtained as the limit of N → ∞ and Δy → 0 while replacing L in the expressions (1) and (9) with W _g and keeping W _g = NΔy constant.

  FIG. 13 shows an example of a screen displayed when the button 27 labeled “Analysis” in FIG. 8 is clicked. The variance of the first component (black circle) and the variance of the second component (black triangle) determined by fitting after obtaining the spectrum of the virtual long wiring in the same manner as in FIG. Is displayed on the graph 39, and the correlation distance of the second component is displayed on the graph 40, respectively. The number n of bonds to be analyzed is described in the file having the name displayed in the box 41. According to these graphs, in the sample of this example, when n is 10 or more, the dispersion and correlation distance values determined by fitting are almost constant regardless of n. Therefore, it can be seen that n should be 10 or more in order to evaluate the LWR of the sample prepared under the same conditions as the above sample. This result is consistent with the result of FIG.

  As described above, if the dimension analysis program of the present invention is used, not only the distribution of the wiring width but also the correlation distance can be obtained accurately. In particular, since accurate analysis is possible even when the correlation distance is longer than the measurement region, it is possible to deal with various sites where semiconductor devices are produced, and the dimensional variation of various elements constituting the semiconductor devices can be reduced. It can be estimated with high accuracy. Furthermore, since the variance of components due to image noise can also be obtained quantitatively, it is possible to judge whether the conditions for taking an image and the conditions for measuring dimensions using terminal PC, etc. are good or bad. There are also advantages.

  Although the present embodiment has various functions as shown in FIGS. 8 to 13, at least a part of the object of the present invention can be achieved even when only a part thereof is mounted as required. Needless to say, you can.

Second Embodiment FIG. 14 is an example of a screen displayed on a monitor while another dimensional analysis program according to the present invention is operating. In this program, unlike the program of the first embodiment, it is possible to directly analyze dimensions from an image obtained by photographing a thin line using a CD-SEM. Here, 452 electronic files having an even number as a part of the name beginning with “PR1-0002” and ending with “PR1-0904” are designated by “/ root / mnt / cd-image / pr1”. An example in the case of being stored in a folder is shown. These are images from which the wiring width shown in the first embodiment is measured. The file name is designated by the contents entered in boxes 51 and 4-6. The method of specifying the file name from the contents input in these boxes will be obvious as in the first embodiment. The folder name is specified by the contents entered in the box 53, and the box 52 is a pull-down menu for convenience when inputting the folder name, as in the case of the first embodiment. . The program reads the dimensions from the image with a function similar to that of the terminal PC described above. A file describing conditions for this and a folder for storing the file are designated by boxes 54 and 56. A pull-down menu 55 is provided to assist input to the box 56. It should be noted that the corresponding portions of the contents described in the file specified in the box 54 are automatically input in the boxes 7 and 8.

  The read dimensions are recorded in a file having the same number as the corresponding image file starting with the character string specified in box 1 and stored in the folder specified in box 3. In this embodiment, the names of the files in which the dimensions are recorded are “LWR-PR1-0002” to “LWR-PR1-0904”. The results of analyzing these files in the same manner as in Example 1 are displayed in the graph 21. In this way, by using this dimensional analysis program, it is possible to consistently obtain the spectrum from the thin line image and accurately obtain the dimensional dispersion and the correlation distance.

Third Embodiment FIG. 15 is an example of a screen displayed on a monitor while the third dimensional analysis program according to the present invention is operating. In this program, unlike the program of the first embodiment described above, the component having the smaller correlation distance is analyzed based on the spectrum obtained without combining the element wirings. The component with the larger correlation distance is analyzed in the same manner as in the first embodiment. That is, when “ξ1” is selected in the pull-down menu 43 and the button 23 is clicked, data is sequentially obtained from the file designated by the contents displayed in the boxes 1 and 4 to 6 in the same manner as in the first embodiment. Is read. The average value of all these data is displayed in box 11. Next, a spectrum is obtained using the values displayed in the boxes 7 and 8 based on the respective data, and the result of obtaining the average value for each wave number is displayed as a white circle in the graph 42. The number of the same average operations performed for each wave number is equal to the number of the files (452 in this case). Note that the data recorded in the above file was obtained by measuring the sample created under the same conditions as in the first embodiment using an image taken by CD-SEM at different intervals, and the number of measurements was also measured. Different. The results calculated by the equations (1) and (2) using the values displayed in the boxes 12, 13 and 17 are displayed by solid lines. When the button 24 is clicked, the work of optimizing the contents of the boxes 12, 13 and 17 is automatically performed so that the results calculated using the equations (1) and (2) agree with the actual measurement results. Is called.

  Next, when “All ξ” is selected in the pull-down menu 43, FIG. 16 is displayed. When the button 23 is clicked, the spectrum of the virtual long wiring obtained by combining the element wirings is displayed as a white circle on the graph 44 as in the first embodiment. The result calculated by the formulas (1) to (3) is also displayed by a solid line as in the first embodiment. Further, when the button 24 is clicked, the contents of the boxes 12, 14 and 15 are automatically optimized by (b) to (o) in the first embodiment. Note that the value determined in FIG. 15 is used as the value that needs to be determined in (a).

  Needless to say, the operation of optimizing the contents of the box in at least one of FIGS. 15 and 16 may be performed manually.

  In this embodiment, since the length of the region for measuring the element wiring is 500 nm, a CD-SEM having a special function of changing the magnification in the vertical direction and the horizontal direction is not required. For this reason, it can be implemented in many production sites of semiconductor devices.

Further, the advantages of analyzing the first component without combining the element wirings in this embodiment will be described below. FIG. 17 shows the result of calculating the LWR spectrum of the virtual long wiring according to the equations (1) to (3) while changing the length L of the measurement region of the element wiring while maintaining the measurement interval at 5 nm, which is the same as the present embodiment. Indicates. The correlation distance was 3000 nm. As is clear from the figure, when L decreases, the value of the spectrum increases locally but. The present inventors have confirmed that these maximum values are approximately equal to the spectrum value having the L value as the correlation distance. On the other hand, if the correlation distance is small, even if L decreases, the spectrum value hardly changes as long as the wave number is the same (not shown). For this reason, when L is small, the influence of the second component cannot be ignored even in the region where the wave number is large as described in (a) of the first embodiment, and the analysis of the first component is hindered. On the other hand, in the spectrum obtained without coupling the element wirings as in the present embodiment, the first component value is increased because the first component value and the second component value hardly change even if L changes. It can be analyzed with accuracy. However, in this case as well, if L is too small, the accuracy of analysis deteriorates for a reason similar to the case shown in FIG. 6, so it is desirable that L > 2πξ.

Fourth Embodiment FIG. 18 is a schematic view showing an example of a dimension measuring apparatus according to the present invention. This dimension measuring apparatus uses a scanning electron microscope 101 having a function equivalent to that of a normal CD-SEM, a storage device 111 for storing a file recording an image photographed by the microscope, and the dimension analysis program of the second embodiment. The computer 121 is configured to analyze a file stored in the storage device 111. These are electrically connected to each other by communication lines 131 and 132. As a result, not only the average value of the dimensions but also the variance and the correlation distance can be obtained at the same time or within a short time after the image is captured while capturing the thin line image. Furthermore, the result analyzed by the computer 121 is displayed on the monitor 102 built in the scanning electron microscope 101 as necessary, and it is possible to grasp various statistics of dimensions at the measurement site.

  As a result, the measurement result can be quickly reflected on the production site. Further, for example, when it is difficult to ensure the accuracy of dispersion or correlation distance due to excessive image noise, the accuracy of the average value, variance, or correlation length can be quickly increased by changing the image capturing conditions of the scanning electron microscope 101. There is also an advantage that it can be improved.

  Note that the scanning electron microscope 101, the storage device 111, and the computer 121, which are the three components of the dimension measuring device, are not necessarily connected directly to each other, and each of them is connected to a local area network (LAN). ) May be connected indirectly. Further, it goes without saying that the object of the present invention can be achieved even if connected to each other not only via the LAN but also by a wide area network (WAN). Further, the storage device 111 may not be provided, and the scanning electron microscope 101 and the computer 121 may be connected directly or via a LAN or WAN. In this case, a storage device (not shown) built in the scanning electron microscope 101 or the computer 121 serves as the storage device 111.

Fifth Embodiment FIG. 19 is a schematic view showing a second example of the dimension measuring apparatus according to the present invention. In this embodiment, the storage device 111 and the computer 121 in the fourth embodiment are integrated with the scanning electron microscope 101 and incorporated in the housing 151. It goes without saying that the object of the present invention can be achieved even if the storage device 111 and the computer 121 are externally attached unlike the present embodiment. Further, the storage device 111 may not be provided, and the function may be replaced by a storage device built in the scanning electron microscope 101 or the computer 121. Furthermore, the computer 121 may be omitted, and the dimensional analysis program of the second embodiment may be installed in a computer that was originally built in the scanning electron microscope 101.

  In the above figure, the observation result and the dimension measurement result by the CD-SEM function are displayed on the monitor 154. Further, analysis results such as dimension dispersion and correlation distance by the dimension analysis program are displayed on the monitor 155. Reference numeral 156 denotes a keyboard for controlling the CD-SEM function and the dimension analysis program, and 152 and 153 are inlets for taking the measurement wafer into and out of the measurement chamber.

  According to the present embodiment, the statistic statistics can be analyzed quickly at the measurement site, so that the measurement results can be managed and improved to maintain and improve the measurement accuracy and the measurement results can be transferred to the production site. It is possible to execute the reflection more quickly.

Sixth Embodiment FIG. 20 is a schematic view showing an example of a method of manufacturing a semiconductor device according to the present invention. In this embodiment, the scanning electron microscope 101, the storage device 111, and the computer 121 in the fourth embodiment are connected to the communication line 141 to 143, and the exposure apparatus 201, the coating and developing bake device 211 and the etching apparatus 221 are connected to the communication line 146. Or 148 to the LAN 161. In addition to these, a semiconductor manufacturing apparatus is connected to the LAN 161, but is not shown here. Thus, the computer 122 is connected to the LAN 161 via the communication line 145 in order to monitor the operation status of the manufacturing apparatus connected to the LAN 161 and to control its operation. In addition, a storage device 112 is connected to the LAN 161 via the communication line 144 to assist the operation of the computer 122. In this manufacturing method, a photoresist film is applied on a semiconductor substrate on which a thin film to be processed is formed by a coating / developing baking apparatus 211, exposed using an exposure apparatus 201 using a predetermined mask, and then again applied by a developing / developing baking apparatus. Development and baking are performed in 211 to form a photoresist in a desired shape. Next, an image obtained by photographing the shape of the photoresist using the scanning electron microscope 101 is stored in the storage device 111 as an electronic file, and the average value, variance, and size of the dimensions are calculated using the computer 121 in the same manner as in the seventh embodiment. Find the correlation distance. The results are stored in the storage device 112 and analyzed using the computer 122, and then the exposure device 201 or the exposure device 201 or the like as necessary so that various statistics of the dimensions of the photoresist formed on the subsequent semiconductor substrate become desired values. An instruction to change processing conditions is issued from the computer 122 to the coating / developing baking apparatus 211 or both. In addition, if necessary, an instruction to change the processing conditions is given in advance to the etching apparatus 221 that performs processing in the next process so that various statistics of the dimensions of the thin film formed on the semiconductor substrate after processing become a desired value. It may be issued. Thereafter, the thin film is processed using the etching apparatus 221 using the photoresist as a mask. After removing the photoresist mask, the processed thin film is photographed again using the scanning electron microscope 101 and analyzed for statistic statistics in the same manner as described above, and then the thin film on the subsequent semiconductor substrate is analyzed. An instruction to change the processing conditions is issued to the etching apparatus 221 as necessary so that the dimension after processing becomes a desired value.

  In addition, it has been conventionally performed to reflect the measurement result of the CD-SEM in the previous process and the next process so that the average value of dimensions becomes a desired value. Thus, in the case of managing only the average value of dimensions, there are few advantages of the present invention. On the other hand, when trying to manage the dimensional dispersion (or standard deviation), if the conventional method is used, the error caused by the noise included in the image taken with the CD-SEM is large. It is difficult to instruct. For this reason, by reflecting the measurement result by CD-SEM in manufacturing conditions, there are cases where the number of cases outside the management range is increased. On the other hand, if the present invention is used, dispersion can be obtained accurately even when image noise is present and its intensity changes, so that dispersion of dimensions after processing can be managed and controlled with high accuracy. . Furthermore, it is possible for the first time in practice to manage the correlation distance of the dimensional variation by using the present invention.

1, 3-18, 30, 34, 37, 41, 51, 53, 54, 56 Box 2, 43, 52, 55 Pull-down menu 19, 20 Radio buttons 21, 28, 29, 32, 33, 36, 39, 40, 42, 44 Graph 22-27, 31, 35, 38 Button 101 Scanning electron microscope 102, 154, 155 Monitor 111, 112 Storage device 121, 122 Computer 131, 132, 141148 Communication line 151 Case 152, 153 Unloading Entrance 156 Keyboard 161 Local area network 201 Exposure device 211 Coating and developing bake device 221 Etching device

Claims (19)

The dimensions of the measurement structure formed on a semiconductor device which is the subject, was measured at different positions a predetermined direction, a set of results from multiple obtained by the measurement at each position, is virtually constructed based on the binding measurement results obtained by, wavenumber on the horizontal axis, the spectrum of the vertical axis and the signal intensity was calculated and the spectrum was based on multiple identity calculations conditions, by averaging the plurality of spectra size analysis program characterized by having a function of calculating an average spectrum. The dimension analysis program according to claim 1 , wherein element measurement results that are the same set of results are included in a plurality of combined measurement results. Claim 1 or Claim 2 characterized in that the order of combining the element measurement results which are the set of results constituting the set in at least one combined measurement result differs from the actual order in at least a part thereof. The dimension analysis program according to item 2. The at least one combined measurement result is obtained by measuring a plurality of structures in which the element measurement results, which are the set of results constituting the set, are not connected. The dimensional analysis program according to any one of Items 1 to 3. In at least one combined measurement result, at least a part of the element measurement result which is the set of the results constituting the set is obtained by measuring a structure existing in a direction different from the measurement direction. The dimensional analysis program according to any one of claims 1 to 4, wherein: 6. The number of combined spectra obtained based on the combined measurement result used for the average operation is equal to or greater than the number of element measurement results as the set of results . The dimension analysis program according to any one of the above. An average spectrum obtained by the method according to any one of claims 1 to 6 and an integer of K0 where L, K ₀ ≡ 2π / L are the lengths of the regions where the dimensions of the structure are measured By comparing the result calculated using the coupled theoretical formula, which is a theoretical formula with a value in at least a part of the wave number that is twice the value of the theoretical formula for the spectrum of the element measurement result as the set of results A function of determining at least one of a set of constants that characterize a dimensional variation or at least one of a set of constants that characterize a component caused by noise. size analysis program, characterized in that to have a. It has a function of determining at least one value constituting each of a plurality of dimensional variation constants by comparing the average spectrum with the result calculated using the coupling theory formula by changing the wave number region. A dimensional analysis program according to claim 7 . When the interval for measuring the dimensions is set to y ₀ and the wave number region in which the spectrum is examined is reset to a range of ₀ to kmax≡π / y ₀ so as to be equivalent to this , the dimension with the smaller correlation distance The minimum value of the wave number region to be compared to determine at least one value constituting the variation constant determines at least one value constituting this in at least one of the dimension variation constants having a larger correlation distance. 9. The dimensional analysis program according to claim 8, wherein the dimensional analysis program is larger than a minimum value of a wave number region to be compared . Determining at least one value constituting a noise constant when performing a comparison to determine at least one value constituting a dimension variation constant having a non-maximum correlation distance, and determining at least one of the determined values. 10. A dimensional analysis program according to claim 8 , wherein said dimensional analysis program has a function of determining at least one value constituting at least one of other dimensional variation constants by using the dimensional analysis constant. . A spectrum obtained without combining element measurement results as a result of the set in place of an average spectrum when performing comparison to determine at least one value constituting a dimension variation constant whose correlation distance is not maximum is obtained. size analysis program according to any one of paragraph 8 claims to paragraph 10, which comprises using. 8. The method according to claim 7, further comprising a function of analyzing non-stochastic variations in dimensions based on a result obtained by averaging the element measurement results as a set of results for each measurement point. 12. A dimensional analysis program according to any one of items 11. 13. The method according to claim 7, further comprising a function of performing analysis on non-stochastic variation in dimensions based on an average spectrum value for at least a part of a wave number that is an integral multiple of k0. The dimension analysis program in any one of. claims, characterized in that performing the analysis of the distribution of the dimensions based on the value of the average spectrum for at least a portion of the remaining wave number excluding at least part of the wave number is an integer multiple of k0 paragraph 7, second 14. The dimension analysis program according to any one of items 13. The device has a function of estimating a distribution of element dimensions using at least one value constituting a dimensional variation constant determined by comparing an average spectrum with a result calculated using a coupling theory . The dimensional analysis program according to any one of items 7 to 14 of the range. A standard deviation or variance of the average element average value is defined as an average element average value obtained by averaging nA average element values that are average values in the element measurement results as the set of results. 16. The method according to any one of claims 7 to 15, which has a function of estimating using a value obtained by dividing n by the square root of nA or a value obtained by dividing the variance of the element average value by nA. Dimension analysis program. Claims 1 to 16 having a function of displaying an average spectrum obtained by using at least one of the methods described in claims 1 to 6 . The dimension analysis program according to any one of the items. Claims dimension analysis program according to any one of the first term claims to paragraph 17, characterized in that it has a range function of displaying paragraph 7 results calculated using the binding theoretical formula described in. The dimensional analysis program according to any one of claims 1 to 18, which has a function of displaying an estimation result according to claim 14 .

Images