Analysis device, analysis method and analysis program

Abstract

To provide an analysis device capable of highly accurately measuring only an inclination of two directional components of columnar scatterers periodically aligned in a plate-like sample at high speed, an analysis method and an analysis program.SOLUTION: An analysis device 120 includes: a measurement data storage part 123 for storing data of scattering intensity from a plate-like sample measured by X-ray transmission in one-time ω scan; a coordinate conversion part 125 for converting coordinates of a scattering vector into coordinates of an inclination of the scatterer, regarding a waveform based on the intensity of the two directional components of a specific diffraction point by using the data of the measured scattering intensity; a peak position specification part 126 for specifying a peak position of the intensity waveform relative to the converted coordinates of the inclination; and an inclination calculation part 127 for calculating a difference between the specified peak position and a peak position determined assuming that the scatterer is not inclined from a direction perpendicular to a surface of the plate-like sample, as the inclination of the scatterer in the two direction components.SELECTED DRAWING: Figure 4

Description

[Technical field]

[0001] The present invention relates to an analysis device, an analysis method, and an analysis program for analyzing the microstructure of a plate-shaped sample formed by periodically arranging columnar scatterers that are long in the thickness direction. [Background technology]

[0002] Conventionally, transmission small-angle X-ray scattering (tSAXS) has been used to nondestructively and easily measure the pattern shape of semiconductor devices that are becoming increasingly finer three-dimensionally due to deep trench patterns. As applications of this measurement method, a method is known in which a highly adaptable complex shape model is assumed for columnar scatterers arranged periodically within a plate-like sample, and it takes time to precisely specify the shape through measurement and analysis (see Patent Document 1), and a method is known in which a simple shape model is assumed for low accuracy but is measured in a short time (see Patent Document 2). In addition, a method has been proposed in which the inclination of the scatterer is calculated from the measurement results obtained by scanning in two directions without a shape model (see Patent Document 3). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Patent No. 7100897 [Patent Document 2] Patent No. 7168985 [Patent Document 3] International Publication No. 2020 / 028412 Summary of the Invention [Problem to be solved by the invention]

[0004] In the actual semiconductor inspection process, there is a need not only for the analysis of complex shapes for which the method described in Patent Document 1 is effective. For example, there are situations where it is desired to measure only the inclination of a columnar scatterer relative to the sample surface in a short time while maintaining accuracy. The techniques described in Patent Documents 2 and 3 are characterized by their simplicity and are able to meet this need to some extent. However, it is difficult to measure the inclination of two-directional components of a columnar scatterer with high accuracy and to complete the measurement and analysis in a short time.

[0005] The present invention has been made in consideration of the above circumstances, and aims to provide an analysis device, analysis method, and analysis program that can quickly and accurately measure only the tilt of the two-directional components of columnar scatterers periodically arranged in a plate-shaped sample. [Means for solving the problem]

[0006] (1) In order to achieve the above-mentioned object, the analytical device of the present invention is an analytical device for analyzing the microstructure of a plate-shaped sample formed by a periodic arrangement of columnar scatterers that are long in the thickness direction, and is characterized by comprising a measurement data memory unit that stores data on the scattering intensity from the plate-shaped sample measured by transmitting X-rays in a single omega scan, a coordinate conversion unit that uses the measured scattering intensity data to convert the coordinates of the scattering vector for a waveform based on the intensity of two-directional components of a specific diffraction point into the coordinates of the tilt of the scatterer, a peak position identification unit that identifies the peak position of the intensity waveform for the coordinate-converted tilt coordinate, and a tilt calculation unit that calculates the difference between the identified peak position and a peak position obtained under the assumption that the scatterer is not tilted from the direction perpendicular to the surface of the plate-shaped sample, as the tilt of the scatterer, in the two-directional components.

[0007] (2) In the analysis device described in (1) above, the coordinate conversion unit is characterized in that it performs coordinate conversion into the coordinate of the inclination of at least one of the two directional components of the scattering vector by a single analysis using a diffraction point where one of the coordinates of the two directional components of the scattering vector is 0.

[0008] (3) In the analysis device described in (1) above, the coordinate conversion unit performs coordinate conversion into the coordinates of the inclination of the scatterer of the two directional components by loop analysis using diffraction points where none of the coordinates of the scattering vector of the two directional components is zero.

[0009] (4) In the analytical device according to any one of (1) to (3) above, the two directional components are a direction parallel to a surface of the plate-like sample and a y direction component perpendicular to the x direction and in which a unit cell is oriented.

[0010] (5) Furthermore, in the analytical device described in any one of (1) to (3) above, the two directional components are a direction parallel to the surface of the plate-shaped sample and are a direction a0, which is the scan direction of the ω scan, and a1, which is perpendicular to the a0 direction.

[0011] (6) Furthermore, in the analysis device described in any one of (1) to (5) above, the coordinate conversion unit is characterized in that it uses a waveform accumulated over a plurality of diffraction points as a waveform based on the intensities of the two-directional components of the specific diffraction point.

[0012] (7) Furthermore, the analytical method of the present invention is a method for analyzing the microstructure of a plate-shaped sample formed by a periodic arrangement of long columnar scatterers in the thickness direction, and is characterized by including the steps of: preparing data on scattering intensity from the plate-shaped sample measured by X-ray transmission in a single omega scan; using the measured scattering intensity data, transforming the coordinates of the scattering vector for a waveform based on the intensities of two-directional components of a specific diffraction point into coordinates of the inclination of the scatterer; identifying the peak position of the intensity waveform for the coordinate-transformed inclination coordinate; and calculating the difference between the identified peak position and a peak position obtained under the assumption that the scatterer is not inclined from the direction perpendicular to the surface of the plate-shaped sample, as the inclination of the scatterer, in the two-directional components.

[0013] (8) Furthermore, the analysis program of the present invention is an analysis program for analyzing the microstructure of a plate-shaped sample formed by a periodic arrangement of columnar scatterers that are long in the thickness direction, and is characterized in that it causes a computer to execute the following processes: preparing data on the scattering intensity from the plate-shaped sample measured by X-ray transmission in a single omega scan; using the measured scattering intensity data, transforming the coordinates of the scattering vector for a waveform based on the intensity of two-directional components of a specific diffraction point into the coordinates of the inclination of the scatterer; identifying the peak position of the intensity waveform for the coordinate-transformed inclination coordinate; and calculating the difference between the identified peak position and the peak position obtained under the assumption that the scatterer is not inclined from the direction perpendicular to the surface of the plate-shaped sample, as the inclination of the scatterer, in the two-directional components. [Brief description of the drawings]

[0014] [Figure 1] FIG. 1 is a perspective view showing a transmission type CD-SAXS measurement system. [Diagram 2] 1A and 1B are diagrams showing a unit lattice of a hole pattern and a relationship between a silicon wafer and a lattice vector, respectively. [Diagram 3] 13 is a graph showing the scattering intensity profile of the diffraction point (11) versus Qz. [Figure 4] FIG. 1 is a block diagram showing a measurement system of the present invention. [Diagram 5] FIG. 2 is a plan view showing the configuration of a measuring device. [Figure 6] 1 is a flowchart showing a measurement and analysis procedure of the present invention. [Figure 7] 13A and 13B are flowcharts showing single-time analysis and loop analysis, respectively. [Figure 8] 13 is a graph showing a QZ waveform based on the intensity versus θX of a diffraction spot where QY=0 nm−1. [Figure 9] 1 is a graph showing a QZ waveform based on the intensity versus θY of a diffraction spot where QX=0 nm−1. [Figure 10] 13 is a graph showing a QZ waveform based on the intensity versus θX of a diffraction spot where QX≠0 nm−1. [Figure 11] 1 is a graph showing a QZ waveform based on intensity versus θY of a diffraction spot where QY≠0 nm−1. [Figure 12] 13A and 13B are a graph and a table showing the optimization of the XY components of the tilt, respectively. [Figure 13] (a) and (b) are graphs showing a diffraction image subject to a single analysis of θX and a QZ waveform based on the intensity versus θX of a diffraction point at QY=0 nm−1, respectively. [Figure 14] (a) and (b) are graphs showing a diffraction image subject to a single analysis of θY and a QZ waveform based on the intensity versus θY of a diffraction point at QX=0 nm−1, respectively. [Figure 15] (a) and (b) are graphs showing the diffraction image and the QZ waveform based on the intensity of the diffraction point versus θX, respectively, which are the subject of loop analysis. [Figure 16] (a) and (b) are graphs showing the diffraction image and the QZ waveform based on the intensity of the diffraction point versus θY that are the subject of loop analysis, respectively. [Figure 17] (a) and (b) are graphs showing a diffraction image subject to a single analysis of θX and a QZ waveform based on the intensity versus θX of a diffraction point at QY=0 nm−1, respectively. [Figure 18] This is the diffraction image that is the subject of a single analysis of θY. [Figure 19] (a) and (b) are graphs showing the diffraction image and the QZ waveform based on the intensity of the diffraction point versus θX, respectively, which are the subject of loop analysis. [Figure 20] (a) and (b) are graphs showing the diffraction image and the QZ waveform based on the intensity of the diffraction point versus θY that are the subject of loop analysis, respectively. [Figure 21] This is the diffraction pattern that is the subject of a single analysis. [Figure 22] 1 is a graph showing a diffraction image to be analyzed in a single run and a QZ waveform based on the intensity of a diffraction point relative to a0. [Figure 23] 1 is a graph showing a diffraction image to be analyzed in a single run and a QZ waveform based on the intensity of a diffraction point relative to a1. [Figure 24] 1 is a graph showing a diffraction image subject to loop analysis and a QZ waveform based on the intensity of a diffraction point relative to a0. [Diagram 25] 1 is a graph showing a diffraction image subject to loop analysis and a QZ waveform based on the intensity of a diffraction point relative to a1. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] Next, an embodiment of the present invention will be described with reference to the drawings. In order to facilitate understanding of the description, the same reference numerals are used to refer to the same components in each drawing, and duplicated description will be omitted.

[0016] [First embodiment] [Transmission CD-SAXS] The present invention is suitable for analyzing the microstructure of a plate-shaped sample in which long columnar scatterers are periodically arranged in the thickness direction, and can be applied to calculate the inclination of the scatterers of the sample by transmission CD-SAXS that can be performed at the laboratory level. It is particularly suitable for analyzing the shape of semiconductor devices with deep groove microfabrication patterns, such as three-dimensional NAND and DRAM. The present invention is effective for non-destructive and simple measurement of deep groove micropatterns with very large aspect ratios, and is suitable for analyzing structures buried in a substrate. There is a high demand for measurement of the shape of deep groove patterns even in recent three-dimensional semiconductor devices, and the present invention can greatly contribute to in-line measurement of three-dimensional semiconductor devices.

[0017] FIG. 1 is a perspective view showing a transmission CD-SAXS measurement system. In transmission CD-SAXS, the sample is rotated (ω rotation) based on the direction of incidence of X-rays perpendicular to the sample surface, and the dependence of the integrated intensity of each diffraction line on the sample rotation angle is measured. The sample is rotated to determine the scattering vector Q Z This is to obtain information in the depth direction by changing the

[0018] [Scattering vector and sample structure] Figure 2(a) and (b) show the unit lattice of the hole pattern and the relationship between the silicon wafer and the lattice vector, respectively. When there is a unit lattice with lattice constants a and b and a lattice angle γ, the diffraction condition of the diffraction index (h, k) is the scattering vector Q X , Q Y , Q Z It is given by:

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[0019] For example, in the case of a silicon wafer sample, a mark called a notch is made, and the XY directions of the sample and the scattering vector Q X , Q Y In the following, the XY direction of the sample and the scattering vector Q X , Q Y In the following description, it is assumed that the directions of the arrows are the same.

[0020] In addition, if the a-axis is rotated by φ with respect to the notch, the tilt angle (θ WX ,θ WY ) can be calculated as follows:

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[0021] [Tilt angle and Q Z Waveform] When a cylindrical scatterer has a central axis perpendicular to the surface of the sample, the shape factor of the cylindrical scatterer is expressed as follows:

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[0022] Also, Q X Direction and Q Yθ X and θ Y The shape factor of a cylindrical scatterer tilted by is expressed as follows:

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[0023] Considering the area within the dashed lines in the above equations (2) and (3), Q X Direction and Q Y θ X and θ Y When the angle is inclined only by Q Z The waveform in the direction will be translated by the following amount:

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[0024] θ X and θ Y The following equation can be derived to represent this.

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[0025] In fact, the Q Z The waveform positions are different. Figure 3 is a graph showing the scattering intensity profile of the diffraction point (11) versus Qz. The circle plot shows the Qz distribution caused by a cylindrical scatterer with its central axis perpendicular to the surface of the sample. Z The square plot represents the Q due to a cylindrical scatterer with its central axis tilted from the normal to the sample surface. ZIn the example shown in Figure 3, the Q Z Waveform difference ΔQz is 0.0022 nm -1 It is.

[0026] [Measurement system configuration] Next, the configuration of the measurement system 100 of the present invention will be described. Fig. 4 is a block diagram showing the measurement system 100. The measurement system 100 includes a measurement device 110 and an analysis device 120, and enables transmission CD-SAXS measurement and analysis by irradiating a plate-shaped sample with X-rays and measuring the scattering intensity. The analysis device 120 controls the measurement device 110, and manages the measurement data together with the control data, enabling data analysis. The specific configuration will be described below.

[0027] [Measurement device configuration] 5 is a plan view showing the configuration of the measurement device 110. The measurement device 110 includes an X-ray source 111, a mirror 112, slits S1, S2, GS, a sample stage 115, a vacuum path 116, a beam stopper 118, and a detector 119. The distance L0 from the X-ray source 111 to the sample S0 and the camera length L can be set to, for example, 1000 mm and 3000 mm, respectively.

[0028] MoKα can be used for the X-ray source 111. The mirror 112 splits the X-rays emitted from the X-ray source 111 and irradiates the split X-rays toward the sample S0. The slits S1 and S2 are made of a material capable of blocking X-rays and form a slit section that narrows the split X-rays. This configuration enables irradiation of X-rays at multiple rotation angles ω close to the perpendicular direction to the surface of the plate-shaped sample S0. It is preferable to select specific angles in the range of -10° to 10° for the multiple rotation angles ω. The slit GS can limit the spot size of the X-rays on the sample surface to several tens of μm or less. Basically, the beam size is determined by the slits S1 and S2, and the GS is used to remove parasitic scattering occurring in the slits S1 and S2. However, when making a very small spot, the beam can also be made smaller by the GS.

[0029] The sample stage 115 supports the sample S0 on the stage, and can adjust the orientation of the plate-shaped sample S0 by a driving mechanism under the control of the analysis device 120. Y In addition to the ω rotation angle, the χ and φ rotation angles can also be adjusted. By adjusting these angles, the incident angle of the dispersed X-rays on the sample S0 can be changed, and the scattering intensity can be measured according to the diffraction angle.

[0030] The sample S0 is formed in a plate shape, and scatterers are periodically arranged in a direction parallel to the main surface of the sample. An example of the scatterers is holes. That is, a typical sample is a silicon wafer substrate, and in this case, the scatterers are holes formed by etching. The higher the integration level, the more important it is to be able to confirm the formation of hole shapes that meet the specifications.

[0031] The scatterer is not limited to the above-mentioned holes, but may be a pillar. That is, the present invention can be applied to a silicon substrate sample on which cylinders are periodically formed on the surface. Also, the scatterer may be a sample on which a line pattern (space pattern) such as a long molecular array is formed.

[0032] The vacuum path 116 maintains the path of the scattered beam in a vacuum to prevent beam attenuation while increasing the camera length. The beam stopper 118 absorbs the direct beam. The detector 119 is, for example, a semiconductor two-dimensional detector that can move on a circumference from the sample position, and can detect the scattering intensity of X-rays. The measuring device 110 and the analyzing device 120 are connected, and the detected scattering intensity data is sent to the analyzing device 120.

[0033] The measuring device 110 preferably has a laser light source and a detector for reflected light. It is possible to adjust the orientation of the plate-shaped sample by utilizing the reflection of the laser light so that the surface of the plate-shaped sample is perpendicular to the direction of incidence of the X-rays. The orientation thus adjusted can be used as the reference, where ω=χ=0°.

[0034] [Analysis equipment configuration] The analysis device 120 is composed of, for example, a PC having a memory and a processor, and can execute various processes by executing a program. By processing the measurement data obtained from the measurement device 110, it becomes possible to analyze the microstructure of a plate-shaped sample formed by periodically arranging long scatterers in the thickness direction.

[0035] The analysis device 120 includes a computer 121, an input device 128, and an output device 129. The computer 121 also includes a measurement control unit 122, a measurement data storage unit 123, a mathematical formula storage unit 124, a coordinate conversion unit 125, a peak position identification unit 126, and a slope calculation unit 127. The computer 121 may be a PC terminal or a server on the cloud. Each unit can send and receive information via a control bus L.

[0036] The measurement control unit 122 controls the measurement device 110 and manages control data and measurement data. For example, the measurement control unit 122 controls the sample stage 115 by a driving mechanism and adjusts the orientation of the sample S0.

[0037] The measurement data storage unit 123 stores the measured X-ray intensity data. The measured intensity data is measured at an ω rotation angle near the perpendicular direction to the surface of the plate-shaped sample, and is scattered from the plate-shaped sample as the X-rays pass through and detected by the detector. Data measured in one ω scan is sufficient. The formula storage unit 124 stores formulas for fitting the scattering intensity and for coordinate conversion.

[0038] The coordinate conversion unit 125 uses the measured scattering intensity data to convert the coordinates of the scattering vector into the coordinates of the inclination of the scatterer for a waveform based on the intensities of the two-directional components of a specific diffraction point.

[0039] The coordinate conversion unit 125 first calculates the Q Z It is preferable to use a waveform that is integrated over a plurality of diffraction points as a waveform based on the intensities of two-directional components of a specific diffraction point. This allows the peak position to be identified with high accuracy.

[0040] The coordinate conversion unit 125 is Z Depending on the presence or absence of a waveform, a single analysis or a loop analysis is performed. The details of the single analysis and the loop analysis will be described later. The coordinate conversion unit 125 selects the diffraction points to be subjected to the single analysis or the loop analysis by the user or automatically. θ X In a single analysis of Q Y =0nm -1 Select the diffraction point of θ Y In a single analysis of Q X =0nm -1 In the loop analysis, select the diffraction point of Q X ≠0 nm -1 Katsu Q Y ≠0 nm -1 In either case, it is preferable to select a diffraction point with a large intensity. Although the analysis device 120 is capable of both single analysis and loop analysis, it may be an apparatus capable of only one of them.

[0041] When a single analysis is being performed, the coordinate conversion unit 125 performs coordinate conversion to the coordinate of the tilt of at least one of the two directional components of the scatterer using a diffraction point where one of the coordinates of the scattering vector of the two directional components is 0. This allows for single coordinate conversion. The two directional components are two directional components parallel to the surface of the plate-like sample. The two directional components are preferably the x direction in which the unit lattice is oriented and the y direction perpendicular to the x direction, which are parallel to the surface of the plate-like sample. This allows for easy calculation of the tilt angles of the two components for a sample whose unit lattice orientation is known.

[0042] When loop analysis is being performed, the coordinate conversion unit 125 performs coordinate conversion into the coordinates of the tilt of the scatterer in two directions by loop analysis using diffraction points where none of the coordinates of the scattering vector in two directions is 0. This makes it possible to calculate the tilt angle with high accuracy using many diffraction points.

[0043] The peak position identifying unit 126 calculates Q Z Peak locations are identified for the waveform.

[0044] The peak position identifying unit 126 obtains a formula for fitting from the formula storage unit 124 and calculates Q Z The peak position of the waveform is calculated. The peak position identifying unit 126 checks whether the fitting is optimal or not, and changes the parameters until it is optimal. X and θ Y The convergence of these two parameters is the X component of the inclination of the scatterer, T X and Y component T Y It is.

[0045] The tilt calculation unit 127 calculates the difference between the identified peak position and the peak position obtained under the assumption that the scatterer is not tilted from the direction perpendicular to the surface of the plate-like sample, as the tilt of the scatterer in two directions. This makes it possible to shorten the measurement and analysis time and calculate the tilt angle of the two direction components with high analytical accuracy.

[0046] The input device 128 is, for example, a keyboard or a mouse, and accepts input to the computer 121. A user can select the type of analysis and the diffraction points via the input device 128. The output device 129 is, for example, a display, and outputs a selection screen and analysis results.

[0047] [Measurement and analysis methods] (Overall flow) Next, a method of measurement and analysis using the above-mentioned system configuration will be described. Fig. 6 is a flow chart showing the procedure of measurement and analysis. As shown in Fig. 6, first, a plate-shaped sample is placed and its position is adjusted (step S101). Then, the scattering intensity is measured by one ω scan (step S102). This is the end of the measurement.

[0048] In the analysis, first, the Q of each diffraction point is calculated based on the measurement data. Z The waveform is acquired (step S103). Then, the user's selection is accepted, and Q X and Q YIt is determined whether or not a single-time analysis for independently analyzing and is selected (step S104). If a single-time analysis is not selected (= a loop analysis is selected), a loop analysis is executed (step S105), and the process proceeds to step S108.

[0049] If a single analysis is selected, Q X =0nm -1 and Q Y =0nm -1 Q in both Z It is determined whether or not a waveform exists. If not, the process proceeds to step S105. If present, a single analysis is executed (step S107). Then, the analysis result is output (step S108), and the series of procedures is terminated.

[0050] 7(a) and (b) are flowcharts showing the single-step analysis and the loop analysis, respectively. As shown in FIG. 7(a), in the single-step analysis, Q Y =0nm -1 Using the diffraction point at which the tilt angle is x-component, θ X The peak position of Q is determined (step S201). X =0nm -1 Using the diffraction point at which the tilt angle is Y component, θ Y The peak position is then determined (step S202), and the single analysis is completed.

[0051] In addition, as shown in Figure 7(b), the loop analysis shows that Q X ≠0 nm -1 A diffraction point with a reasonable θ Y Using θ X The peak position of θ is determined (step S301). X , θ Y It is determined whether or not θ has converged (step S302). X , θ Y The loop analysis can be performed by checking whether the difference or change in is equal to or less than a threshold value. If convergence has occurred, the loop analysis is terminated. If convergence has not occurred, the process proceeds to step S303.

[0052] Next, QY ≠0 nm -1 The diffraction point was determined to be θ X Using θ Y The peak position of θ is determined (step S303). X , θ Y It is determined whether or not θ has converged (step S304). If it has converged, the loop analysis is terminated. If it has not converged, the process proceeds to step S301. X , θ Y are the X and Y components of the tilt angle. Note that in the above analysis, X , θ Y Although there is a specific order to the analysis, the order may be reversed. Also, each process in the above analysis can be performed by executing a program.

[0053] (Single analysis) The details of single analysis are explained with examples. Single analysis is X =0nm -1 and Q Y =0nm -1 Q in both Z This is an analysis method that can specify the tilt angle by using a formula in a single step when a waveform exists. In this case, θ X and θ Y can be calculated independently.

[0054] In a single analysis, first, Q Y =0nm -1 Using only the diffraction points of Q Z The horizontal axis of the waveform is θ X Figure 8 shows the coordinate transformation of Q Y =0nm -1 θ of the diffraction point X Q based on strength against Z 1 is a graph showing a waveform.

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[0055] On the other hand, Q Z For the waveform, Q X =0nm -1 Using only the diffraction points of Q Z The horizontal axis of the waveform is θ Y Figure 9 shows the coordinate transformation of Q X =0nm -1 θ of the diffraction point Y 1 is a graph showing a waveform based on intensity for a given frequency.

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[0056] In such a single analysis, Q X and Q Y θ X , θ Y On the other hand, the diffraction points used for the analysis are Q X =0nm -1 , Q Y =0nm -1 It is necessary to prepare diffraction points of

[0057] (Loop analysis) Loop analysis is X =0nm -1 and Q Y =0nm -1 Q Z When no waveform is present, θ X , θ Y This is an analysis method that can specify the tilt angle by repeatedly calculating and converging the numerical value. An example of the loop analysis will be explained below.

[0058] First, θ Y Give a reasonable initial value to θY It is preferable to assume that Q = 0. X ≠0 nm -1 Using the diffraction points at Q Z The horizontal axis of the waveform is expressed as θ X Figure 10 shows the Q X ≠0 nm -1 θ of the diffraction point X Q based on strength against Z 10 is a graph showing waveforms. X The intensity is integrated on the top, and the θ value is calculated by peak search on the waveform representing the integration on the top of Figure 10. X Determine the peak position.

[0059] Next, θ X is given as the determined peak position. Furthermore, Q Y ≠0 nm -1 Using the diffraction points at Q Z The horizontal axis of the waveform is expressed as θ Y Figure 11 shows the Q Y ≠0 nm -1 Diffraction point θ Y Q based on strength against Z 12 is a graph showing waveforms. For the multiple waveforms shown in the lower part of FIG. Y The intensity is integrated on the top, and the θ value is calculated by peak search on the waveform representing the integration on the top of Figure 11. Y Determine the peak position of θ X , θ Y The above θ X , θ Y The determination of the peak position is repeated.

[0060] Rotation axis is Q X or Q Y If the measurements are made under conditions consistent with the Y =0nm -1 or Q X =0nm -1 Q ZThere are cases where the waveform does not exist. In such cases, the X and Y components of the tilt angle cannot be determined independently, but by using loop analysis, the X and Y components of the tilt angle can be determined. Loop analysis is X =0nm -1 or Q Y =0nm -1 It is possible to use even diffraction points with a large number of diffraction points.

[0061] 12(a) and 12(b) are a graph and a table showing the optimization of the XY components of the inclination, respectively. X and θ Y The peak positions of each are T X and T Y In the example shown in Figure 12(a) and (b), the numerical values ​​converge in about four cycles of the loop analysis.

[0062] [Example 1] The following is an example of the embodiment. X =0nm -1 and Q Y =0nm -1 Q in both Z As an example of application when a waveform exists, a silicon wafer sample was rotated 45° around an axis perpendicular to the wafer surface with respect to the notch, and the sample was rotated ω around an axis in the diagonal 45° direction of XY to perform measurements. The tilt angle was calculated based on the obtained measurement data.

[0063] Fig. 13(a) and (b) show the θ X The diffraction pattern and Q Y =0nm -1 θ of the diffraction point X Q based on strength against Z 14(a) and 14(b) are graphs showing waveforms of the Y The diffraction pattern and Q X =0nm -1 θ of the diffraction point Y Q based on strength against Z 1 is a graph showing a waveform.

[0064] Figure 15(a) and (b) show the diffraction image and the θ of the diffraction point, which are the subject of loop analysis, respectively. X Q based on strength against Z 16(a) and 16(b) are graphs showing the waveforms of the diffraction images and the θ Y Q based on strength against Z 1 is a graph showing a waveform.

[0065] The loop analysis converged in 4 cycles. Figure 15(b) and Figure 16(b) show the Q values ​​at the 3.5th and 4th cycles, respectively. Z These are the waveforms of the Q Z In a single analysis, the X component of the tilt angle T X and the Y component of the tilt angle T Y The results are -0.865deg and 1.082deg, respectively. In the loop analysis, the X component of the tilt angle T X and the Y component of the tilt angle T Y The results were -0.864deg and 1.080deg, respectively. Thus, the results of each analysis agreed with a high degree of accuracy.

[0066] [Example 2] Next, Q X =0nm -1 or Q Y =0nm -1 Q Z As an example of application when no waveform exists, the Y axis (Q Y The measurement was performed by rotating the sample around ω (parallel to the axis), and the tilt angle was calculated based on the obtained measurement data.

[0067] Fig. 17(a) and (b) show the θ X The diffraction pattern and Q Y =0nm -1 θ of the diffraction point X Q based on strength against Z FIG. 18 is a graph showing the waveform of θ Y The diffraction pattern is the target of a single analysis of the rotation axis and QY Since the directions are the same, Q X =0nm -1 Q of diffraction points Z The dependence could not be obtained. Therefore, θ Y A single analysis of

[0068] Figure 19(a) and (b) show the diffraction image and the θ of the diffraction point that are the subject of loop analysis, respectively. X Q based on strength against Z 20(a) and (b) are graphs showing waveforms of the diffraction image and the θ Y Q based on strength against Z 1 is a graph showing a waveform.

[0069] The loop analysis converged in 4 cycles. Figures 19(b) and 20(b) show the Q values ​​at the 3.5th and 4th cycles, respectively. Z These are the waveforms of the Q Z In a single analysis, the X component of the tilt angle T X The result of the loop analysis was -0.864 deg. The X component of the tilt angle T X and the Y component of the tilt angle T Y The X component of the tilt angle T X was matched with high accuracy.

[0070] [Second embodiment] The two directional components do not necessarily have to be the X and Y components. The two directional components can also be the a0 direction, which is the scanning direction of the ω scan, and the a1 direction, which is perpendicular to the a0 direction, which are parallel to the surface of the plate-shaped sample. In this case, even if the orientation of the sample is unknown, the tilt angles of the two components can be calculated based on the scanning direction.

[0071] (Single analysis) In this embodiment, a single analysis is possible. hk The diffraction point in the scan direction (θ hk =0, θhk =π) is used to determine a0 independently using the following equation (10). Note that ω0 is Q Z =0nm -1 is the sample rotation angle corresponding to θ hk is the deviation angle of the diffraction spot with index (hk).

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[0072] Next, a1 is determined using equation (11).

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[0073] Here, the diffraction point in the scan direction (θ hk =0, θ hk =π) and the diffraction points perpendicular to the scan (θ hk = ±π / 2) is selected, hk diverges to 0 or infinity. Therefore, diffraction points excluding those in the scanning direction and those in the direction perpendicular to the scanning direction are selected. Then, using the selected diffraction points, a1 is determined using a0 determined above. In this way, a0 and a1 can be determined in a single iteration as the components of the inclination of the scatterer in the scanning direction and in the perpendicular direction, without looping.

[0074] Then, using the following equation (12), the peak positions of the converged a0 and a1 are converted into the a0 and a1 direction components of the tilt angle into a direction β determined by the notch of the silicon wafer sample.

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[0075] (Loop analysis) The following loop analysis is also possible. Using all diffraction points except for those in the direction perpendicular to the scanning direction (θhk = ±π / 2), give an appropriate value (for example, 0) to a1 as the initial value, and convert the coordinates of Q ZThe peak position of a0 is determined from the waveform using all diffraction points.

[0076] In addition, Q after coordinate transformation in equation (11) Z Based on the waveform, the diffraction points in the scanning direction (θ hk =0, θ hk =π) and the diffraction points perpendicular to the scan (θ hk Use all diffraction points except for a0 (=±π / 2) and determine the peak position of a1 using the a0 determined above.

[0077] The calculation to determine the peak positions of a0 and a1 is repeated until the peak positions of a0 and a1 converge. Once the values ​​converge, use equation (12) to convert the converged peak positions of a0 and a1 into the a0 and a1 direction components of the tilt angle to the direction β determined by the notch of the silicon wafer sample.

[0078] [Example 3] Using the sample used in Example 1, a single analysis was performed based on the a0 and a1 directions. Figure 21 shows a diffraction image that is the subject of a single analysis. Figure 22 shows the Q value based on the intensity of the diffraction image and the diffraction point relative to a0 that is the subject of a single analysis. Z FIG. 23 is a graph showing the waveform of the diffraction image and the Q based on the intensity of the diffraction point a1 to be analyzed in a single analysis. Z 1 is a graph showing a waveform. 0p , a 1p represent the peak positions of a0 and a1, respectively.

[0079] As a result of the analysis, the X component of the tilt angle T X and the Y component of the tilt angle T Y The results obtained were −0.864 deg and 1.082 deg, respectively. The results obtained are in high agreement with the results of Examples 1 and 2.

[0080] [Example 4] Using the sample used in Example 1, loop analysis was performed based on the a0 and a1 directions. The diffraction image subjected to loop analysis is the same as the diffraction image subjected to single analysis. Figure 24 shows the Q Z FIG. 25 is a graph showing the waveform of the diffraction image and the Q based on the intensity of the diffraction point with respect to a1, which are the subject of the loop analysis. Z 1 is a graph showing a waveform.

[0081] The loop analysis converged in 4 cycles. Figures 24 and 25 show the Q values ​​at the 3.5th and 4th cycles, respectively. Z These are the waveforms of the Q Z The analysis results show that the X component of the tilt angle T X and the Y component of the tilt angle T Y The results obtained were −0.864 deg and 1.082 deg, respectively. The results obtained are in high agreement with the results of Examples 1 and 2. [Explanation of symbols]

[0082] 100 Measurement System 110 Measuring Equipment 111 X-ray source 112 Mirror 115 Sample stage 116 Vacuum Path 118 Beam Stopper 119 Detector 120 Analysis equipment 121 Computer 122 Measurement control section 123 Measurement data storage unit 124 Formula Memory 125 Coordinate conversion section 126 Peak position identification unit 127 Tilt Calculation Unit 128 Input Devices 129 Output Device GS Slit Q X , Q Y , Q Z Scattering Vector S0 sample S1, S2 slits T X X component of the tilt angle T Y Y component of the tilt angle

Claims

1. An analysis apparatus for analyzing a microstructure of a plate-shaped sample in which columnar scatterers long in a thickness direction are periodically arranged, comprising: a measurement data storage unit for storing data on the scattering intensity from the plate-shaped sample measured by transmitting an X-ray in one ω scan; a coordinate conversion unit that converts the coordinates of a scattering vector into the coordinates of a tilt of a scatterer for a waveform based on the intensities of two directional components of a specific diffraction point using the measured scattering intensity data; a peak position identifying unit that identifies a peak position of the intensity waveform with respect to the coordinate of the tilt that has been converted; and a tilt calculation unit that calculates the difference between the identified peak position and a peak position obtained under the assumption that the scatterer is not tilted from a direction perpendicular to the surface of the plate-shaped sample, as the tilt of the scatterer in the two directional components.

2. 2. The analysis device according to claim 1, wherein the coordinate conversion unit performs coordinate conversion into the coordinate of the inclination of at least one of the two directional components of the scattering vector by a single analysis using a diffraction point where one of the coordinates of the two directional components of the scattering vector is 0.

3. 2. The analysis device according to claim 1, wherein the coordinate conversion unit performs coordinate conversion into the coordinates of the inclination of the scatterer of the two directional components by loop analysis using diffraction points where none of the coordinates of the scattering vector of the two directional components is zero.

4. 4. The analytical device according to claim 1, wherein the two-directional components are a component in an X direction parallel to a surface of the plate-like sample and in a Y direction perpendicular to the X direction of a unit cell.

5. The two-directional components are parallel to the surface of the plate-shaped sample and are the scanning direction of the ω scan. ０ Direction and the a ０ A perpendicular to the direction １ 4. The analysis device according to claim 1, wherein the component is a direction component.

6. 4. The analysis device according to claim 1, wherein the coordinate conversion unit uses a waveform integrated over a plurality of diffraction points as the waveform based on the intensities of the two-directional components of the specific diffraction point.

7. 1. A method for analyzing a microstructure of a plate-shaped sample in which columnar scatterers long in a thickness direction are periodically arranged, comprising the steps of: preparing data on scattering intensity from a plate-shaped sample measured by transmitting an X-ray in one ω scan; A step of converting the coordinates of the scattering vector into the coordinates of the inclination of the scatterer for a waveform based on the intensities of the two directional components of a specific diffraction point using the measured scattering intensity data; determining a peak position of the intensity waveform relative to the coordinates of the transformed slope; and calculating the difference between the identified peak position and a peak position obtained under the assumption that the scatterer is not tilted from a direction perpendicular to the surface of the plate-shaped sample, as the tilt of the scatterer in the two directional components.

8. An analysis program for analyzing a microstructure of a plate-shaped sample in which columnar scatterers long in a thickness direction are periodically arranged, comprising: A process of preparing data of scattering intensity from a plate-shaped sample measured by transmitting an X-ray in one ω scan; A process of converting the coordinates of the scattering vector into the coordinates of the inclination of the scatterer for a waveform based on the intensities of the two directional components of a specific diffraction point using the measured scattering intensity data; identifying a peak position of the intensity waveform relative to the coordinates of the transformed slope; and calculating the difference between the identified peak position and a peak position obtained under the assumption that the scatterer is not tilted from a direction perpendicular to the surface of the plate-shaped sample, as the tilt of the scatterer in the two directional components.

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