JP2016217816A - Pattern measurement device, pattern measurement method, and pattern measurement program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a pattern measurement program, method and device in which the influences of noise are small, and with which it is possible to properly measure way up a high-frequency component.SOLUTION: The program includes the steps of: detecting electrons discharged from a sample that is irradiated with charged particle radiation and acquiring the luminance distribution of an image in which a scanned position and the detected quantity of electrons are correlated; integrating the luminance values of the image in the elongation direction of a pattern end and finding an integrated luminance profile; processing the integrated luminance profile with a function by fitting and obtaining an integrated profile optimization function; processing, by fitting, a measured luminance profile using the integrated profile optimization function, the measured luminance profile being the luminance profile of individual pixel rows not integrated using the integrated profile optimization function, and obtaining an individual profile optimization function; and comparing the individual profile optimization function with the measured luminance profile and determining whether or not the fitting process is good.SELECTED DRAWING: Figure 6

Description

  The present invention relates to a photomask pattern used when a semiconductor device is manufactured by a lithography technique, and an apparatus, method, and program for measuring the shape, particularly roughness, of a pattern generated by transferring a pattern formed on the photomask.

Semiconductor integrated circuits are being miniaturized and highly integrated in order to improve performance and productivity, and lithography technology for forming circuit patterns is also a technology for forming finer patterns with high accuracy. Development is underway. Along with this, there is a demand for more accurate techniques for measuring the dimensions and shapes of patterns.
The size of a photomask pattern used for manufacturing a semiconductor device is less than 100 nm. In a semiconductor device manufacturing process using this, it is necessary to stably form a structure of less than 20 nm. When measuring the dimension and shape of such a fine pattern, a scanning electron microscope (hereinafter sometimes abbreviated as CD-SEM or SEM) specially designed for dimension measurement is used.

  With the miniaturization of semiconductor devices, not only the pattern dimensions but also the roughness of the pattern edges have greatly affected the characteristics of the devices, and it is known that this is particularly noticeable in transistor gate electrodes and the like. It has been. Such a line pattern has a line edge roughness (Line Edge Roughness, hereafter may be abbreviated as LER) focusing only on the roughness of one edge of the line pattern, and the edges on both sides, that is, the line width. Roughness (Line Width Roughness, hereinafter also abbreviated as LWR) is a typical index value. The contact hole is evaluated by a value called CER (Contact hole Edge Roughness or Circle Edge Roughness).

  As means for measuring such roughness, as means for evaluating as an average value of a pattern regularly arranged in a wide area, scatterometry or small angle X-ray scattering can be used as scatterometry or small angle X-ray scattering. However, in order to evaluate a specific minute region, it is most effective to analyze from an observation image by CD-SEM.

  In the following, the evaluation of the line pattern will be described for the sake of simplicity, but the described description can also be applied to the hole pattern.

  FIG. 1 shows a general change in the luminance value of the SEM image corresponding to each point of the pattern (FIG. 1A), and a simplified cross-sectional shape of the line pattern (FIG. 1B). )). In the measurement of the line width of the line pattern, the amount of secondary electrons that can escape from position B is reduced compared to the flat portion at position A in FIG. 1, and secondary electrons can escape from the top and side surfaces at position C. The detected amount of secondary electrons is increased. As a result, the luminance distribution of the secondary electron image observed by scanning and entering the primary electrons has a shape as shown in FIG. In general, in a secondary electron observation image, a portion with a large amount of secondary electrons appears white, and a portion that looks like a white line corresponding to the pattern edge is often called a white band. Also uses the term white band.

  In the measurement of the line width, the luminance profile obtained as shown in FIG. 1A is integrated in the longitudinal direction of the line pattern to increase the number of samplings and obtain a smooth curve. However, when measuring the roughness of the pattern edge, if it is integrated in the length direction, the information on the fine roughness will be lost. In addition, if the primary electron irradiation amount is increased to obtain a signal with less noise without integration, drift due to charging or deformation called shrink in the case of a resist pattern occurs, and accurate measurement cannot be performed. There's a problem.

  Further, in roughness measurement, there are cases where it is expressed by a single numerical value, such as root mean square (hereinafter sometimes abbreviated as RMS) that does not consider the spatial frequency of roughness, but in recent years the frequency has been Analysis focusing on components is becoming important. For example, Patent Document 1 mentions the undulation of a line pattern called wiggling having a period of several tens of nanometers to several hundreds of nanometers.

  The spatial frequency characteristic of roughness can be expressed by power spectral density (hereinafter sometimes abbreviated as PSD). The analysis using the power spectrum of roughness has been developed in advance for the purpose of evaluating the roughness of the surface with a three-dimensional shape measuring device as in Patent Document 2, for example. An example of evaluation using a probe microscope is shown in Patent Document 3.

  The roughness analysis by the scanning probe microscope can also be applied to the semiconductor device and the photomask which is the circuit original, but the time required for the measurement is much shorter because the scanning electron microscope is overwhelmingly shorter. It is effective to use a scanning electron microscope to evaluate the measurement points. A method and apparatus for evaluating the LER of a pattern formed on a substrate using a scanning electron microscope is described in Patent Document 4.

  Patent Document 4 describes that the position of a pattern end is determined using a threshold method, and the LER between the pattern bottom and the vicinity of the surface is evaluated by using a plurality of thresholds. . When the position of the pattern edge is accurately determined using the threshold method, the random noise needs to be sufficiently small. This is because if the white band portion contains fine noise, there are a plurality of points that cross the threshold, making it difficult to automatically detect the pattern edge. Therefore, in Patent Document 4, an image obtained by scanning a plurality of times of electron beams is subjected to integration processing, and then smoothing processing is performed using a Hamming window. In such a method, when the left and right luminances of the white band are different, if the window width is equal to or greater than the white band width, the intersection with the threshold value of the smoothed luminance profile is shifted due to the luminance difference. There is a problem.

  A wide variety of window functions have been devised. However, the problem that the pattern end position is shifted due to the luminance difference cannot be solved. As another method, a spectrum smoothing method called a Savitzky-Golay method is also available. Non-Patent Document 1 describes that when this method is appropriately used, even if there is a luminance difference between the left and right sides of the white band as described above, the variation in the position that intersects the threshold value is small.

  However, in the above method, depending on the relationship between the noise frequency and the white band width, it is possible to avoid multiple occurrences of crossing the threshold value determined by the maximum value and the minimum value for one white band. May not be possible.

  Therefore, by fitting the brightness profile of the white band with a function and optimizing the parameters included in the function to minimize the sum of squares of the difference from the observed SEM image brightness value, fitting by the so-called least square method (optimum) The method for determining the position of the pattern edge by the above is devised and is described in Non-Patent Document 2.

  In Non-Patent Document 2, a left-right asymmetric Gaussian function is selected on the basis of the luminance peak position as a function expressing the white band. For example, a smooth luminance profile obtained by integrating and averaging luminance values in the longitudinal direction of the line pattern is standardized to optimize the width and background height of the Gaussian function with respect to the left and right sides of the white band. When the function thus obtained is fitted to each pixel in the longitudinal direction of the line pattern and normalized by the peak height, the fitting parameters at that time are the background height and the peak width.

  In Patent Document 5, the amount of electrons to be irradiated is limited in order to reduce shrinkage when measuring a resist pattern, or the deformation of the resist pattern accompanying electron beam irradiation is stored as a function, and the measured value is stored. A method of correcting is described.

JP 2014-135214 A JP-A-7-332920 JP 2000-19094 A JP 2003-37139 A International Publication No. 2003-2186

Yasushi Nishiyama; Hidemitsu Hakii; Isao Yonekura; Keishi Tanaka; Yasutaka Kikuchi, "Influence of the charging effect on the precision of measuring EUV mask features," Proc. SPIE 7971, Metrology, Inspection, and Process Control for Microlithography XXV, 79710C (20 April 2011); Thomas Verduin; Pieter Kruit; Cornelis W. Hagen, "Determination of line edge roughness in low-dose top-down scanning electron microscopy images," J. Micro / Nanolith. MEMS MOEMS. 13 (3), 033009 (August 13, 2014 );

  When the amount of electrons irradiated on the sample is reduced, a random noise component is added to the measured amount of secondary electrons. FIG. 2 shows an example of an approximate function of the luminance profile of an image by a left-right asymmetric Gaussian function as described in Non-Patent Document 2. An example of the result of adding random noise to the approximate function is also shown.

  As shown in FIG. 2, when noise is applied to each pixel, the measured luminance value is finely distributed above and below the approximate function. As a result, the threshold method is directly affected by noise. When evaluating LER, it can be seen that, for example, if the smoothing process is not performed in the longitudinal direction of the line pattern, it leads to measurement variations of the pattern edge. In such a case, as shown in Non-Patent Document 2, a representative approximate function is calculated from the result of integrating the luminance profile in the longitudinal direction of the line pattern, and is calculated by a non-linear least square method. It can be expected that the influence of noise can be suppressed by determining the pattern edge position based on a function optimized by the non-linear least square method using the total offset amount as a fitting parameter.

  By the way, it is a simple means to obtain the result obtained by integrating the above approximate representative functions in the longitudinal direction of the line pattern from the function parameter fitting. However, there are three problems described below.

  As a first problem, since the profile integrated in the longitudinal direction of the line pattern includes a roughness component, it is easily estimated that the width is wider than a profile measured at an ideal line edge without roughness. it can.

  As a second problem, there is a case where a so-called drift phenomenon occurs in which an image is distorted due to a shift of an incident position of primary electrons due to charging of the surface of an object to be measured. When the line pattern is a straight line perpendicular to the scanning direction and should be a straight line perpendicular to the bottom in the measurement image, this drift phenomenon results in a straight line or a curved line on the measurement image. Also in this case, it can be easily estimated that the integrated profile is wider than the case where the drift phenomenon does not occur.

  As a third problem, there is a case where there is a deviation between the XY coordinates on which the pattern of the object to be measured is formed and the XY coordinates of the CD-SEM. Various factors can be considered for this, but as a result, the measurement image rotates slightly. Therefore, it can be easily estimated that the integration profile becomes wider as described above.

  Therefore, for the above typical reasons, it is necessary to consider that the luminance profile integrated in the longitudinal direction of the line pattern is wider than the ideal average profile. Non-Patent Document 2 describes the first problem and states that this component can be ignored. However, the second and third problems are not described.

In Non-Patent Document 2, the integration profile is expressed by an asymmetric standardized Gaussian function shown in (Equation 1). Here, b _L and b _R are the baseline levels of the left and right of the white band, respectively, σ _L and σ _R correspond to the width of the white band, and from the peak position of the luminance profile, the left side and the right side respectively. This is a value equivalent to the standard deviation defined by the Gaussian function distribution function. μ represents the peak position of the luminance profile.

In Non-Patent Document 2, fitting is performed on a luminance profile composed of the luminance of each pixel column that is not integrated, using b _L and b _R of Mathematical Formula ₁ and σ _L and σ _R as fitting parameters. Looking for.

  Such a method is a very effective means when the measured luminance profile is finely and sparsely distributed above and below the ideal function, as shown in FIG.

  However, depending on the CD-SEM apparatus and its measurement conditions, the ideal state as shown in FIG. FIG. 3 shows a part of the luminance profile integrated in the longitudinal direction of the line from the image integrated by scanning the electron beam 16 times, and is the white band part on the left side of a certain line pattern.

  As shown in Non-Patent Document 2, when a fitting is performed using the left-right asymmetric Gaussian function shown in (Equation 1), a good solution as shown by the solid line in FIG. 3 can be found.

  As a typical method of fitting, several methods collectively called a nonlinear least square method can be applied. Typically, an initial value of a fitting parameter included in a function is given, and repeated calculation is performed so that the sum of squares of the difference between the function and the actual measurement value is minimized to obtain an optimum fitting parameter. In such a method, the calculation result converges faster as the initial value of the fitting parameter is closer to an appropriate solution. On the other hand, when the initial value is not appropriate, there is a characteristic that the residual sum of squares does not converge to a sufficiently small value and a solution cannot often be obtained.

  (A), (b), and (c) of FIG. 4 are examples of luminance profiles that are not integrated in the longitudinal direction of the line pattern, and a part of the luminance values plotted with a single pixel width in the direction orthogonal to the line pattern. Three are selected. In these, the actually measured values are not finely distributed above and below the Gaussian function as shown in FIG. 2, but are somewhat smooth curves. In such a case, when trying to fit with the least squares method expressed by a Gaussian function, there is not a single point where the residual sum of squares becomes a minimum, and multiple minimum points appear and the solution cannot be specified. In such a nonlinear least squares algorithm, the frequency with which an optimal solution cannot be obtained increases.

  3 and 4 show the luminance profile on the left side of the line pattern. Therefore, in consideration of the principle described with reference to FIG. 1, the actual pattern edge is on the left side of the peak of the luminance profile, and the threshold method or the maximum gradient that is typically used in the past is used. Also in the method of calculating points, the portion on the left side of the peak of the luminance profile is used. Therefore, in this case, the information on the left side of the peak of the luminance profile is more important than the right side of the peak.

  On the other hand, when FIG. 3 and FIG. 4 are compared, FIG. 4 shows various behaviors while FIG. 3 gradually decreases from the peak to the right side. As described above, if a portion that is not so important for fitting is included in the range of the fitting process, good fitting cannot be performed. As a result, the resulting pattern edge position varies.

  Whether such a problem occurs or whether a good fitting can be obtained as shown in FIG. 2 is determined by quantitatively judging the noise frequency and amplitude characteristics. If there is a problem, it is necessary to describe it in the processing program so as to determine the pattern edge position by an improved procedure, but until now, an effective method for that purpose has not been generally known.

  The present invention has been made in view of such a problem, and even if the edge roughness of a pattern is measured without performing a smoothing process in the longitudinal direction of the pattern, the influence of noise is small, and even a high-frequency component is appropriate. It is an object of the present invention to provide a measurement program that can be measured, a measurement method using the program, and a measurement apparatus using the measurement program.

  One aspect of the present invention for solving the above-described problem is a pattern measurement program to be executed by a computer of a pattern measurement apparatus, which irradiates a measurement target sample on which a pattern is formed while scanning a charged particle beam, The computer obtains the luminance distribution of the image that detects the electrons emitted from the sample and associates the scanning position with the detected amount of electrons, and the computer calculates the luminance value of the image in the direction in which the pattern edge extends. A step of obtaining an integrated luminance profile by integrating, a step of performing a fitting process for approximating the integrated luminance profile by a function to obtain an integrated profile optimization function, and a computer using the obtained integrated profile optimization function , For the measured luminance profile that is the luminance profile of the individual pixel columns that are not integrated The step of performing the fitting process using the calculation profile optimization function to obtain the individual profile optimization function, and the computer compares the individual profile optimization function with the actually measured brightness profile to perform the fitting process for the integrated brightness profile and the actually measured brightness profile. A pattern measurement program including a step of determining pass / fail.

  Another aspect of the present invention is a pattern measurement method that performs the same processing as each step of the above-described pattern measurement program.

  Another aspect of the present invention is a pattern measurement device that performs the same processing as each step of the pattern measurement program described above.

  According to the present invention, even if the edge roughness of a pattern is measured without performing a smoothing process in the longitudinal direction of the pattern, the measurement program is capable of appropriately measuring even a high frequency component with little influence of noise. It is possible to provide a measurement method used and a measurement apparatus using the same.

Explanatory diagram showing the relationship between the cross-sectional shape of the measurement object and the brightness of the SEM image Explanatory diagram of luminance profile approximation function and noise component added to the approximation function The figure which showed the brightness | luminance profile obtained by integrating | accumulating a brightness | luminance value in the line longitudinal direction of the line left part of the line of the SEM image which measured the line pattern, and the result of fitting the right and left of the brightness | luminance profile peak with a separate Gaussian function The figure which showed the luminance profile which is not integrating | accumulating a luminance value in the longitudinal direction of a line about the left side part of the line of the SEM image which measured the line pattern Figure showing the result of fitting the measured individual brightness profile with a symmetric Gaussian function A graph showing the result of fitting the measured area with the asymmetrical Gaussian function on the condition that the left side of the peak is larger than the right side of the fitting area with respect to the individual brightness profile. Illustration of typical shape of power spectral density function of line edge roughness For a single line pattern observation image, the autocovariance function and an example of the power spectral density function obtained from the result of detecting the pattern edge position using the threshold method without performing integration processing in the longitudinal direction of the line. Illustration shown An example of a self-covariance function and an example of a power spectral density function obtained from the result of detecting the pattern end position using the threshold method without performing integration processing in the longitudinal direction of the line for 10 line pattern observation images. Illustration shown The figure which showed the self-covariance function and the power spectral density function obtained from the result of detecting the pattern edge position using the threshold method for an image to which a Gaussian filter with a width of 5 pixels is applied Explanatory drawing which showed the autocovariance function and power spectral density function which were obtained from the result of having detected the pattern edge part position using the method which concerns on one Embodiment of this invention

  Embodiments of the present invention A scanning particle and a detected amount of secondary electrons are related by using a measuring device that irradiates a charged sample beam while scanning the sample to be measured and detects secondary electrons emitted from the sample. A method, apparatus, and program for measuring and evaluating the edge roughness of a pattern formed on a sample from the luminance distribution of the attached secondary electron image.

  Here, as a strict meaning, there may be a case where the backscattered primary electrons incident on the sample together with the secondary electrons are detected at the same time. However, in order to simplify the description, the generic name including both secondary electrons and backscattered electrons emitted from the sample to be measured will be referred to as secondary electrons.

  A program according to an embodiment of the present invention (hereinafter referred to as the present program) is a program for measuring the edge (edge) roughness of a pattern from a secondary electron image obtained by observing the pattern. Then, the integrated luminance profile is obtained by integrating the luminance values in the extending direction of the edge, the integrated luminance profile is approximated by a function, and its parameters are obtained to obtain the integrated profile optimization function. Next, an individual profile optimization function obtained by optimizing the fitting parameters included in the integration profile optimization function is obtained for the actually measured luminance profile that is the luminance profile of the individual pixel columns that are not integrated, and the individual profile optimization function is obtained. The edge position of the pattern is specified from the parameters related to the position of the pattern. The program further includes selecting a processing method by comparing the individual profile optimization function and the actually measured luminance profile.

  In this program, the function used to perform the fitting process on the integrated luminance profile and the integrated profile optimization function include a parameter characterizing the width of the white band. Specifically, it is selected from a Gaussian function, a Lorentz function, a mixed function of a Gaussian function and a Lorentz function (pseudo-voigt function), a forked function, or a combination thereof.

  In this program, the initial value of the fitting parameter when obtaining the individual profile optimization function is orthogonal to the integration direction for generating the integrated luminance profile and the extending direction of the pattern edge recognized by observing the pattern. It may be determined by a process of determining whether or not the angle is deviated. That is, when an angle shift is detected, a process of obtaining an individual profile optimization function using an initial value of a function obtained by correcting the integrated luminance profile optimization function based on the angle shift amount is included. The extending direction of the pattern edge (end) is obtained by partially integrating the luminance values of the image at different positions in the extending direction of the pattern edge to obtain a plurality of partial integration profiles, and from the positional relationship of the obtained partial integration profiles It may be recognized.

  This program is not limited to an optimization algorithm as long as it is calculated so as to optimize with a policy that the residual sum of squares with the measured luminance profile is minimized. Typically, it is possible to use a method for determining convergence when the value of the residual sum of squares becomes sufficiently small during the calculation process or when the degree of improvement in the iterative calculation becomes sufficiently small.

  In this case, it may be determined that the optimization cannot be performed as a process when the value of the residual sum of squares is not sufficiently small or the calculation cannot be continued. In that case, the optimization function is stored as an undetermined state for the individual profile optimization function at that position.

  In this program, the process of comparing the individual profile optimization function and the measured luminance profile is performed by calculating the intersection of the individual profile optimization function and the measured luminance profile within the range determined based on the parameter characterizing the width of the white band. Including counting.

  In the comparison between the individual profile optimization function and the actually measured luminance profile, the count value at the intersection of the individual profile optimization function and the actually measured luminance profile is compared with a set threshold value.

  In this program, when the count value of the intersection between the individual profile optimization function and the actually measured luminance profile is smaller than the set threshold value, and when the individual profile optimization function is stored as undecided state Based on the luminance peak position of the white band, the data on the lower side (concave side) of the data on the higher side (convex side) of the end of the corresponding measured pattern end It includes re-optimization processing under conditions where the weight increases. In order to increase the weight of the luminance value on the lower side, the number of data points in the region on the lower side of the pattern with respect to the peak position of the luminance value may be increased.

  For example, in the case of a line-like repetitive pattern called a line and space, a high side means a line part and a low side means a space part.

  As one of the means for assigning the weight, one of the number of data from the luminance peak position of the white band is made larger than the other.

  As a specific amount of weighting, the larger weight is from the peak position to the minimum value of the set range, and the smaller weight is from the peak position until the inflection point is detected.

  Further, as another means for assigning the weight, the residual square is calculated by multiplying the square of the residual by different counts on the left and right of the luminance peak position of the white band.

  The individual edge position determined based on the individual profile optimization function is the peak position of the function or the inflection point on the lower side of the measured pattern end.

  The pattern measurement method according to the embodiment of the present invention determines an individual edge position, calculates an approximate function, obtains the edge position and the difference between the approximate functions for each pixel column, and squares the square of the sum of the squares thereof. The edge roughness is measured by measuring a power spectral density obtained by a method of measuring a mean square root (also referred to as a root mean square or rms) roughness or a Fourier transform of an autocovariance function.

  A pattern measurement apparatus according to an embodiment of the present invention is a pattern measurement apparatus that can measure pattern edge roughness by the pattern measurement method.

  Embodiments of the present invention will be described below in detail with reference to the drawings.

  As shown in FIG. 1, when a line pattern is measured with a CD-SEM having a detector on the top of the object to be measured, a white band that typically has a high luminance at the end of the pattern and appears white. Appears. This is because at the position of point B in FIG. 1, the secondary electron emission probability decreases and the corresponding pixel becomes dark, and at point C in FIG. 1, the secondary electron emission probability increases and the corresponding pixel becomes bright. .

  The luminance profile in which the luminance values are plotted in the direction across the line is ideally a smooth curve as shown in FIG. However, when a large amount of electrons are irradiated to reduce the noise level, the sample is charged, contaminants mainly composed of carbon are deposited on the surface, and the resist pattern shrinks and the dimensions change. To do. Therefore, in practice, measurement is generally performed with as little electron irradiation dose as possible.

  The area where the pattern edge roughness is calculated from the line pattern observation image may be set manually. Furthermore, by detecting a peak from the luminance distribution integrated in the longitudinal direction of the line and inputting in advance as a parameter a width corresponding to the observation condition, it is possible to automatically extract a region including the peak.

  Further, when a plurality of lines and spaces are in one image, the signal intensity is lowered at the position B as shown in FIG. 1, and luminance information of the line portion and the space portion is registered in advance. As a result, it is also possible to automatically determine whether the space between the plurality of white bands is a line or a space.

  The square and rhombus points in FIG. 3 are a part of the luminance profile integrated and averaged in the longitudinal direction of the line pattern, and are the white band part on the left side of the line pattern. If fitting is performed individually with a Gaussian function on the left and right sides, that is, the points of the square and the rhombus, with this peak as a boundary, a good fit is obtained as shown by the solid line in FIG.

  The left and right differences in the height, width, and height offset values of the two Gaussian functions obtained in this way are recorded, and the next step is the fitting of the measured luminance profile, which is the luminance profile that has not been integrated. It can be an initial value.

  As described above, the integrated luminance profile obtained by simple integration in the vertical or horizontal direction of the image includes not only the edge roughness but also a rotation component caused by charging drift or sample stage deviation. There is a possibility, and it is thought that the range is wider than ideal measurement conditions.

  In order to distinguish between drift and rotation, it is possible to judge from the behavior when the electron irradiation conditions when acquiring an image, for example, the current value, the scanning speed, the scanning direction, the number of integrations, the order of integration, and the like are changed.

  As for the rotation component, the noise is accumulated in a plurality of areas rather than the entire image so that the noise is sufficiently small to create a plurality of accumulated luminance profiles, and the approximate function is obtained by the peak position or the above fitting process. It can be extracted from the shift amount of the peak position.

  If the rotation component can be extracted, an integrated luminance profile from which the rotation component has been removed can be generated by performing a reverse convolution process on the entire integrated luminance profile.

  The drift component can be corrected by approximating the shift amount of the plurality of luminance profiles with a curve, but there is a possibility that a long-period LER having a length equivalent to the size of one observation image may be canceled. is there. In such a case, the drift component and the long-period roughness can be discriminated by acquiring a plurality of images and comparing them by overlapping.

  Next, fitting processing is performed on the actually measured luminance profile that is a luminance profile that is not integrated in the longitudinal direction of the line pattern. In this case, an integrated luminance profile fitting result may be used as an initial value, or an integrated luminance profile from which the rotational component is removed may be used.

  FIG. 4 shows an example of the result of outputting the luminance profile for the left end of the line in the SEM image in which the line pattern is observed. These are selected from three that are not smoothed with a width of one pixel in the longitudinal direction of the line.

  When fitting such a profile with a Gaussian function, to reduce the residual sum of squares as much as possible, if the base line of the luminance profile is defined and subtracted, fluctuations in the peak part are emphasized with respect to the overall signal strength. Therefore, it is effective for optimizing the peak portion. In the graph of FIG. 4, since the subtraction process is uniformly performed, the value is smaller than the integrated luminance profile of FIG.

  FIG. 5 shows the result of fitting the luminance profile shown in FIG. 4A by dividing it into left and right with reference to the peak portion and using two Gaussian functions. Although it seems that the fitting is generally possible, when focusing on the left side of the white band used in the conventional threshold method, it cannot be said that the fitting is sufficient considering that the noise of the actual measurement value is small and relatively smooth.

  Therefore, even if the peak position of the fitting function or the left inflection point is used, a deviation from the optimum value estimated from the measurement result occurs, and even if such processing is applied to a large number of individual profiles, it is random. There is a concern that many components are contained. As a means for automatically determining that such a phenomenon has occurred, the number of intersections between the fitting function and the actually measured luminance profile is indicated by an arrow in the graph in FIG. The present inventor has found that there is a characteristic that it is remarkably small as shown. Therefore, it is possible to set a flag for determining whether the fitting process is good or bad using the relationship between the number of processed pixels and the number of intersections between the fitting function and the actually measured luminance profile.

  The relationship between the number of processed pixels and the intersection point may be determined using an empirical formula, or may be determined by preparing a data table and referring to it.

  As another fitting condition, in this program, a fitting process weighted outside the line pattern, that is, on the left side of FIG. 5 is performed. Weighting can be performed by multiplying the square of the difference between the actual measurement value and the fitting function value by a different value on the left and right of the peak, or by changing the number of data points to be processed based on the peak.

  FIG. 6 shows the result of performing the same fitting process on the actually measured luminance profile shown in FIG. 5 by increasing the number of points on the left side of the peak to the number of points on the right side of the peak. The profile on the left side of the peak of interest has greatly improved fitting accuracy compared to FIG. In Non-Patent Document 2, since the left and right offsets and the peak width are used as fitting parameters based on the integration profile, the left and right fitting functions match at the peak position, but in this program, it is not always necessary to match.

From the optimum parameters obtained by fitting in this way, for example, the peak position of the Gaussian function or the inflection point on the left side of the peak can be determined as the pattern edge position. These values can be calculated from μ or (μ−σ _L ) in (Expression 1). When processing is performed for the white band on the right side of the line pattern, the inflection point on the right side of the peak is obtained from (μ + σ _R ) contrary to the above. In this case, it is assumed that the value representing the position increases toward the right. When the direction of the position coordinates is opposite to the above, (μ + σ _L ) and (μ−σ _R ) are obtained.

  By repeating the above processing for the region where the line edge roughness is evaluated, the line edge position can be determined at the sampling frequency of the pixel size of the SEM observation image in the longitudinal direction of the line.

  A known method can be used as the procedure for obtaining the root mean square roughness from the line edge position obtained by the above procedure. A regression line is obtained from each edge position by the method of least squares, an average position of the edge is obtained, the square of the difference from this line is taken, and the square root of the average may be calculated.

Furthermore, in order to evaluate the frequency characteristics of the line edge roughness, the power spectral density can be calculated and evaluated using a known method. The power spectral density can be obtained by Fourier transforming the autocovariance function G (| r ₁ −r ₂ |) of the edge position. Here, r ₁ and r ₂ represent the positions in the longitudinal direction of the line, and the differences h (r ₁ ) and h (r) from the regression line at positions where the distance in the image is | r ₁ −r ₂ | ₂ ), i.e., h (r ₁ ) h (r ₂ ) is calculated and averaged over the combination between all pixels. Mathematically, when the power spectral density is integrated over the entire frequency range, the root mean square roughness representing the roughness of all frequencies is obtained.

  FIG. 7 shows a typical shape when the power spectrum of the line edge roughness is plotted on a logarithmic scale. The point A shown in the graph of FIG. 7 is called a correlation distance, which is one index value representing the frequency characteristic of roughness, and the slope of the portion that linearly decreases from the point A to the point B It can be used as a value that characterizes the frequency characteristics of roughness.

  Such a shape of the power spectrum function is typically seen when the roughness is self-affine. In the Fourier transform of the continuous function, an inflection point such as point B is ideally not found and decreases linearly. On the other hand, in the discrete Fourier transform in which sampling is performed for each pixel, it is known that an inflection point appears as a point B at a slightly lower frequency side than the Nyquist frequency at which aliasing starts to occur. .

  Further, when random noise is included when the edge position is measured, the inflection point B appears on the left side of the graph, that is, on the lower frequency side than in the ideal case. Further, due to random noise having no frequency dependence, the roughness component having a higher frequency has a characteristic that the power spectral density becomes flat and the high frequency component becomes invisible.

  Therefore, according to the present invention, it is possible to reduce the noise component of the autocovariance function and more accurately extract the high frequency component in the power spectral density function.

  The case where the embodiment of the present invention is applied to the measurement of the edge roughness of the pattern of the photomask will be described below.

  First, a commercially available photomask blank in which a thin film mainly composed of molybdenum and silicon was formed on a 6-inch square synthetic quartz glass substrate and a negative resist for chemically amplified electron beam was applied thereon was prepared.

  Next, an electron beam irradiating apparatus is used to irradiate an electron beam so that a line pattern is formed on the photomask blank, and a chemical amplification reaction in the resist is advanced by a baking process. Development processing was performed with a developer as a component to form a linear resist pattern.

  Next, the thin film on the glass substrate was etched by plasma using a compound gas containing fluorine using an inductively coupled plasma etching apparatus. Thereafter, the resist remaining on the thin film was removed and washed to produce a photomask on which a line-shaped pattern was formed.

  A digital image obtained by observing a pattern with a designed line width of 200 nm formed on the photomask using a CD-SEM was obtained. The energy of the electron beam during observation was 1000 V, the current value was 5 pA, and the number of integrations was 16. The size of one pixel of the observation image is approximately 1.5 nm.

(Comparative Example 1)
FIG. 8A shows the result of calculating the self-covariance function with a threshold value of 50% for one line pattern. As shown in FIG. 4C, when there is a bend on the white band threshold value side and a plurality of points crossing the threshold value are detected, it is predicted from the pre-calculated integration profile. The point closest to the position is adopted. As a result, a result including a long distance swell of 1000 pixels or more was obtained together with very fine noise.

  FIG. 8B is a power spectral density function obtained by Fourier transforming the data of FIG. The high frequency side is not included up to the limit where aliasing occurs, but is included only halfway. The result is noisy over the entire frequency range in the graph.

(Comparative Example 2)
FIG. 9A shows the result of confirming the effect when the number of data points is increased by performing the same processing as FIG. 8 for 10 line patterns. The long-distance correlation seen in FIG. 8 has disappeared, and can be regarded as specific to the position where the data of FIG. 8 was acquired.

  Since the number of data in FIG. 9 is 10 times that in FIG. 8, if it is caused by the original line edge roughness, statistically noise of about one third from the square root of 10 It can be expected to become an amplitude. FIG. 9B shows the power spectral density obtained from FIG. 9A, and it can be seen that the noise is reduced as compared with FIG. 8B. However, by increasing the data acquisition area, the local phenomenon seen at the position where FIG. 8 is observed cannot be evaluated. Further, since the amplitude of the high-frequency noise in FIG. 9A, which is an autocovariance function, is almost the same as that in FIG. 8A, the sampling noise based on the threshold method is considerably included. I can judge.

(Comparative Example 3)
10 (a) and 10 (b) show a self-covariance function and power spectral density in the same manner as in FIG. 9, after removing noise by applying a two-dimensional Gaussian filter of 5 pixels to the measured image in FIG. It is the result of calculating. The noise level of the autocovariance function is greatly reduced, and this contributes to the smoothing effect in the longitudinal direction of the line out of the two directions of the two-dimensional filter.

  Since smoothing in the longitudinal direction of the line pattern may cause an underestimation of the high frequency roughness component, such a process is not suitable for evaluating the roughness of the high frequency component.

(Example)
FIGS. 11A and 11B are an autocovariance function and a power spectral density function obtained by performing calculation processing with a program using the method according to the present invention for one white band in the observation region similar to FIG. . Compared with the case where the Gaussian filter is applied, the amplitude of the high frequency noise is small compared to FIG. 8A, and the characteristic shape is not lost as shown in FIG. 9A. . Further, since the smoothing process is not performed in the longitudinal direction of the line pattern, underestimation of roughness on the high frequency side can be prevented.

  The present invention can be provided in an embodiment of a pattern measurement program to be executed by a computer, but is provided in an embodiment of a pattern measurement method including a pattern measurement method and a means for performing similar processing. You can also. As described above, according to the present invention, it is possible to evaluate pattern edge roughness with little measurement noise while suppressing information loss of high frequency components due to smoothing. According to the present invention, even if the edge roughness of a pattern is measured without performing a smoothing process in the longitudinal direction of the pattern, the measurement program is capable of appropriately measuring even a high frequency component with little influence of noise. It is possible to provide a measurement method used and a measurement apparatus using the same.

  The present invention can be suitably used for observing the shape of a semiconductor device, a photomask used for manufacturing the semiconductor device, and other microfabricated products and evaluating the roughness characteristics thereof.

Claims (9)

A pattern measurement program to be executed by a computer of a pattern measurement device,
Irradiating the sample to be measured with the pattern formed while scanning the charged particle beam, detecting the electrons emitted from the sample to be measured, and calculating the luminance distribution of the image relating the scanning position and the detected amount of electrons, Obtaining by the computer;
The computer integrating the luminance values of the image in a direction in which the pattern edge extends to obtain an integrated luminance profile;
The computer performs a fitting process to approximate the integrated luminance profile with a function to obtain an integrated profile optimization function;
The computer uses the obtained integration profile optimization function to perform fitting processing using the integration profile optimization function on the actually measured luminance profile that is the luminance profile of individual pixel columns that are not integrated, and optimizes the individual profile. Obtaining an optimization function;
A pattern measurement program comprising: the computer comparing the individual profile optimization function with the measured luminance profile to determine whether the integrated luminance profile and the fitting process for the measured luminance profile are acceptable.   The pattern measurement program according to claim 1, wherein the function used for the fitting process with respect to the integrated luminance profile and the actually measured luminance profile includes a parameter that characterizes a width of a region where the luminance value increases at the pattern end.   The pattern measurement program according to claim 1, wherein a function used for fitting processing for the integrated luminance profile and the actually measured luminance profile is a Gaussian function, a Lorentz function, a pseudo-Forked function, a Forked function, or a combination of these functions. The computer acquires a plurality of partial integration profiles by integrating the luminance values of the images at different positions in the extending direction of the pattern ends; and
The computer calculates a direction in which the pattern end extends in accordance with the plurality of partial integration profiles, and detects an angular deviation between the extension direction and the integration direction of the integrated luminance profile;
The computer corrects a parameter that characterizes the width of the region where the brightness value is high at the edge of the pattern based on the angle shift, and uses the initial parameter for fitting processing in the step of obtaining the individual profile optimization function The pattern measurement program according to claim 2, further comprising:   5. The step of determining whether the fitting process is good or bad is performed by counting the number of intersections between the individual profile optimization function and the actually measured luminance profile, and performing a determination by an arithmetic process based on the counted number. The pattern measurement program according to any one of the above.   For an observation image in which the brightness value is high at the end of the uneven pattern formed on the measurement sample, the weight of the brightness value on the concave side of the pattern is set higher than the peak position of the brightness value. The pattern measurement program according to claim 1, wherein the actual luminance profile fitting process is performed.   7. In order to increase the weight of the luminance value on the concave portion side, the number of data points used for fitting processing is increased in the region on the concave side from the convex portion side of the pattern with respect to the peak position of the luminance value. Pattern measurement program described in 1. A pattern measuring method to be executed by a computer of a pattern measuring device,
Irradiating the sample to be measured with the pattern formed while scanning the charged particle beam, detecting the electrons emitted from the sample to be measured, and calculating the luminance distribution of the image relating the scanning position and the detected amount of electrons, Obtaining by the computer;
The computer integrating the luminance values of the image in a direction in which the pattern edge extends to obtain an integrated luminance profile;
The computer performs a fitting process to approximate the integrated luminance profile with a function to obtain an integrated profile optimization function;
The computer uses the obtained integration profile optimization function to perform fitting processing using the integration profile optimization function on the actually measured luminance profile that is the luminance profile of individual pixel columns that are not integrated, and optimizes the individual profile. Obtaining an optimization function;
And a step of comparing the individual profile optimization function and the actually measured brightness profile to determine whether the integrated brightness profile and the fitting process for the actually measured brightness profile are acceptable. Irradiate the sample to be measured with a pattern while scanning with a charged particle beam, detect the electrons emitted from the sample to be measured, and obtain the luminance distribution of the image that correlates the scanning position with the detected amount of electrons. Means to
Means for accumulating luminance values of the image in the extending direction of the pattern edge to obtain an integrated luminance profile;
Means for performing a fitting process for approximating the integrated luminance profile with a function to obtain an integrated profile optimization function;
Using the obtained integration profile optimization function, the individual profile optimization function is obtained by performing fitting processing using the integration profile optimization function on the actually measured luminance profile that is the luminance profile of the individual pixel columns that are not integrated. Means,
A pattern measuring apparatus comprising: means for comparing the individual profile optimization function and the measured luminance profile to determine whether the integrated luminance profile and the fitting process for the measured luminance profile are acceptable.

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