Pitch measurement system, pitch measurement device, pitch measurement method, and pitch measurement program

Abstract

To provide a pitch measurement system, a pitch measurement device, a pitch measurement method and a pitch measurement program, which achieve improvement in accuracy for pitch measurement of a diffraction grating.SOLUTION: A pitch measurement system 100 includes: a diffraction signal acquisition unit 51 that acquires a diffraction signal based on a diffraction X-ray detected by a detection unit 32 in a state of being rotated so that a ratio of a rotation angle of a first rotation stage 33 and a rotation angle of a second rotation stage 35 is 1:2; a pitch calculation unit 52 that calculates a pre-correction pitch dm which is a value before correction of a pitch of a diffraction grating 80 according to a θ / 2θ method on the basis of the diffraction signal; a distribution information acquisition unit 53 that acquires distribution information of the diffraction X-ray in a two-dimensional coordinate system for each order; a correction data acquisition unit 54 that determines correction data used for correction of the pre-correction pitch on the basis of the distribution information; and a pitch correction unit 55 that uses the correction data to correct the pre-correction pitch dm and acquires a post-correction pitch d.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present disclosure relates to a pitch measurement system, a pitch measurement device, a pitch measurement method, and a pitch measurement program that determine the pitch of a diffraction grating by predetermined arithmetic processing. [Background technology]

[0002] Diffraction gratings are optical elements with a periodic uneven structure on their surface, and are widely used as spectroscopic elements that disperse white light, which is a mixture of various wavelengths, into individual wavelengths. Diffraction gratings are also widely used as standard specimens with precisely determined spacing between grooves (lattice constant, hereafter referred to as pitch) for scale and magnification calibration of semiconductor inspection equipment such as electron microscopes. The pitch of a diffraction grating is measured by AFM (Atomic Force Microscope) or optical diffractometer, as well as by GI-SAXS (Glazing Incidence Small Angle X-ray Scattering).

[0003] GI-SAXS is widely used as a method capable of measuring minute pitches, particularly those of 100 nm or less, with high accuracy and high throughput (see, for example, Patent Document 1). The X-ray diffraction device of Patent Document 1 is capable of measuring pitch using the θ / 2θ method, in which the analysis target and the detection unit are rotated at a ratio of 1:2 to obtain a diffraction signal. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2001-96261 A Summary of the Invention [Problem to be solved by the invention]

[0005] As mentioned above, diffraction gratings are often used as standard samples for the scale and magnification calibration of semiconductor inspection equipment, and high reliability is required for the measured pitch. In measuring the pitch of a diffraction grating using GI-SAXS, the pitch is measured using the diffracted X-rays generated by each grating, but interference between the diffracted X-rays from the bottom and top surfaces of the grating causes errors in the measurement of the diffraction angle, which in turn causes errors in the pitch measurement, resulting in a problem of reduced pitch measurement accuracy.

[0006] An object of the present disclosure is to provide a pitch measurement system, a pitch measurement device, a pitch measurement method, and a pitch measurement program that realize improved accuracy in pitch measurement of a diffraction grating. [Means for solving the problem]

[0007] The present disclosure solves the above problems by the following solving means. Note that, for ease of understanding, the following description will be given with reference symbols corresponding to the embodiments of the present disclosure, but the present disclosure is not limited thereto.

[0008] The first disclosure includes a first rotation stage (33) that can rotate with a diffraction grating (80) to be measured attached thereto, an X-ray source (21) that irradiates X-rays onto the diffraction grating (80), a detection unit (32, 32A) that detects at least diffracted X-rays diffracted by the diffraction grating (80), a second rotation stage (35) to which the detection unit (32, 32A) is attached and that can rotate together with the detection unit (32, 32A), a diffraction signal acquisition unit (51) that acquires a diffraction signal based on the diffracted X-rays detected by the detection unit (32, 32A) while the first rotation stage (33) and the second rotation stage (35) are rotated in conjunction with each other so that the ratio of the rotation angle of the first rotation stage (33) to the rotation angle of the second rotation stage (35) is 1:2, and a diffraction signal acquisition unit (51) that acquires a diffraction signal based on the diffracted X-rays detected by the detection unit (32, 32A) based on the diffraction signal acquired by the diffraction signal acquisition unit (51) using a θ / 2θ method. a distribution information acquisition unit (53) that acquires distribution information of the diffracted X-rays in a two-dimensional coordinate system of a first axis and a second axis, where a value of a rotation angle of the diffraction grating (80) is taken as a first axis and a value of a rotation angle of the detection unit (32, 32A) is taken as a second axis, for each order based on a diffraction signal based on the diffracted X-rays detected by the detection unit (32, 32A) while the first rotation stage (33) and the second rotation stage (35) are rotated individually; a correction data acquisition unit (54) that determines correction data to be used for correcting the pre-correction pitch based on the distribution information; and a pitch correction unit (55) that corrects the pre-correction pitch using the correction data to acquire the corrected pitch.

[0009] The second disclosure is a pitch measurement system (100, 100A) described in the first disclosure, in which the correction data acquisition unit (54) acquires distribution information of the diffracted X-rays acquired for each order by dividing it into a first function corresponding to a first axis direction that is a direction along the first axis and a second function corresponding to a second axis direction that is a direction along the second axis, and the pitch correction unit (55) calculates the corrected pitch using the first function and the second function.

[0010] A third disclosure is a pitch measurement system (100, 100A) described in the first disclosure, wherein the correction data acquisition unit (54) acquires, for each order of the diffracted X-rays, a first peak width which is the peak width of the diffracted X-rays in a first axis direction which is a direction along the first axis, an actual position which is the position of the maximum point of the diffracted X-rays in the first axis direction, and a second peak width which is the peak width of the diffracted X-rays in a second axis direction which is a direction along the second axis, and the pitch correction unit (55) calculates the corrected pitch using the first peak width, the actual position, and the second peak width.

[0011] A fourth disclosure is a pitch measurement system (100, 100A) according to any one of the first to third disclosures, wherein the pitch correction unit (55) determines the corrected pitch by numerically analyzing, for the corrected pitch, an arithmetic equation including the pre-corrected pitch, a diffraction angle during correction obtained in a process in which the pitch correction unit (55) calculates the corrected pitch, and the pitch during correction obtained in the process of the calculation.

[0012] A fifth disclosure is a pitch measurement system (100, 100A) described in the fourth disclosure, in which the pitch correction unit (55) determines an actual position, which is the position of the maximum point of the diffracted X-ray in a second axis direction, which is a direction along the second axis, from the uncorrected pitch and Bragg's condition equation, and corrects the uncorrected pitch in calculating the corrected pitch.

[0013] A sixth disclosure is a pitch measurement system (100, 100A) according to any one of the first to third disclosures, wherein the detection unit (32, 32A) has an analyzer that narrows the line of the diffracted X-rays generated by the diffraction grating (80).

[0014] The seventh disclosure relates to a first rotation stage (33) that can rotate with a diffraction grating (80) to be measured attached thereto, an X-ray source (21) that irradiates X-rays onto the diffraction grating (80), a detection unit (32, 32A) that detects at least diffracted X-rays diffracted by the diffraction grating (80), a second rotation stage (35) to which the detection unit (32, 32A) is attached and that can rotate together with the detection unit (32, 32A), a diffraction signal acquisition unit (51) that acquires a diffraction signal based on the diffracted X-rays detected by the detection unit (32, 32A) while the first rotation stage (33) and the second rotation stage (35) are rotated in conjunction with each other so that the ratio of the rotation angle of the first rotation stage (33) to the rotation angle of the second rotation stage (35) is 1:2, and a diffraction signal acquisition unit (51) that acquires a diffraction signal based on the diffracted X-rays detected by the detection unit (32, 32A) based on the diffraction signal acquired by the diffraction signal acquisition unit (51). The pitch measurement device (10, 40) includes: a pitch calculation unit (52) that calculates a pre-correction pitch, which is a value of the pitch of the diffraction grating (80) before correction, by a θ method; a distribution information acquisition unit (53) that acquires distribution information of the diffracted X-rays for each order in a two-dimensional coordinate system of a first axis and a second axis, where a value of a rotation angle of the diffraction grating (80) is taken as a first axis and a value of a rotation angle of the detection unit (32, 32A) is taken as a second axis, based on a diffraction signal based on the diffracted X-rays detected by the detection unit (32, 32A) while the first rotation stage (33) and the second rotation stage (35) are rotated individually; a correction data acquisition unit (54) that determines correction data to be used for correcting the pre-correction pitch based on the distribution information; and a pitch correction unit (55) that corrects the pre-correction pitch using the correction data to acquire the corrected pitch.

[0015] The eighth disclosure relates to a pitch measurement method in a pitch measurement system (100, 100A) or a pitch measurement device (10, 40) including a first rotation stage (33) that can rotate with a diffraction grating (80) to be measured attached thereto, an X-ray source (21) that irradiates X-rays onto the diffraction grating (80), a detection unit (32, 32A) that detects at least diffracted X-rays diffracted by the diffraction grating (80), and a second rotation stage (35) to which the detection unit (32, 32A) is attached and that can rotate together with the detection unit (32, 32A), in which a diffraction signal acquisition unit (51) acquires a diffraction signal based on the diffracted X-rays detected by the detection unit (32, 32A) while rotating the first rotation stage (33) and the second rotation stage (35) in conjunction with each other so that the ratio of the rotation angle of the first rotation stage (33) to the rotation angle of the second rotation stage (35) is 1:2. a pitch calculation unit (52) calculating a pre-correction pitch, which is a value of the pitch of the diffraction grating (80) before correction, by a θ / 2θ method; a distribution information acquisition unit (53) acquiring distribution information of the diffracted X-rays in a two-dimensional coordinate system of a first axis and a second axis, where a rotation angle of the diffraction grating (80) is a first axis and a rotation angle of the detection unit (32, 32A) is a second axis, for each order based on a diffraction signal based on the diffracted X-rays detected by the detection unit (32, 32A) while the first rotation stage (33) and the second rotation stage (35) are rotated individually; a correction data acquisition unit (54) determining correction data to be used for correcting the pre-correction pitch based on the distribution information; and a pitch correction unit (55) correcting the pre-correction pitch using the correction data to acquire the corrected pitch.

[0016] The ninth disclosure relates to a pitch measurement program used in a pitch measurement system (100, 100A) or pitch measurement device (10, 40) including a first rotation stage (33) that can rotate with a diffraction grating (80) to be measured attached thereto, an X-ray source (21) that irradiates X-rays onto the diffraction grating (80), a detection unit (32, 32A) that detects at least diffracted X-rays diffracted by the diffraction grating (80), and a second rotation stage (35) to which the detection unit (32, 32A) is attached and that can rotate together with the detection unit (32, 32A), in which a diffraction signal acquisition unit (51) in a computer acquires a diffraction signal based on the diffracted X-rays detected by the detection unit (32, 32A) while rotating the first rotation stage (33) and the second rotation stage (35) in conjunction with each other so that the ratio of the rotation angle of the first rotation stage (33) to the rotation angle of the second rotation stage (35) is 1:2. a pitch calculation unit (52) calculating a pre-correction pitch, which is a value before the pitch of the diffraction grating (80) is corrected, by a θ / 2θ method; a distribution information acquisition unit (53) acquiring distribution information of the diffracted X-rays in a two-dimensional coordinate system of a first axis and a second axis, where a rotation angle of the diffraction grating (80) is a first axis and a rotation angle of the detection unit (32, 32A) is a second axis, for each order based on a diffraction signal based on the diffracted X-rays detected by the detection unit (32, 32A) in a state in which the first rotation stage (33) and the second rotation stage (35) are rotated individually; a correction data acquisition unit (54) determining correction data to be used for correcting the pre-correction pitch based on the distribution information; and a pitch correction unit (55) correcting the pre-correction pitch using the correction data to acquire the corrected pitch. Effect of the Invention

[0017] According to the present disclosure, a correction process is performed on the pre-correction pitch, which is the measured pitch value using the θ / 2θ method, using correction data obtained from the diffraction signals input over time while rotating the diffraction grating and the diffraction signals input over time while rotating the detection unit.This makes it possible to obtain a corrected pitch in which the effects of interference occurring on the surface of the diffraction grating are mitigated, thereby achieving improved accuracy in diffraction grating pitch measurements. [Brief description of the drawings]

[0018] [Figure 1] 1 is a diagram showing an entire pitch measurement system 100 according to a first embodiment. [Diagram 2] 1 is a side view illustrating a state in which X-rays are incident on a one-dimensional diffraction grating as an analysis target of the pitch measurement system 100. FIG. [Diagram 3] 1 is a plan view illustrating a state in which X-rays are incident on a one-dimensional diffraction grating as an analysis target of the pitch measurement system 100. FIG. [Figure 4] 10 is an explanatory diagram illustrating a schematic example of an intensity distribution when a diffraction signal is acquired by independently driving a first rotation mechanism and a second rotation mechanism. FIG. [Diagram 5] 1 is an explanatory diagram illustrating an example of how incident X-rays are scattered at an upper surface and a bottom surface of a diffraction grating and then emitted. [Figure 6] 1A and 1B are explanatory diagrams illustrating the movement of a diffraction spot when a diffraction grating on which X-rays are incident is rotated in a positive direction. [Figure 7] 1A and 1B are explanatory diagrams illustrating the movement of a diffraction spot when a diffraction grating on which X-rays are incident is rotated in the negative direction. [Figure 8] 11 is an explanatory diagram illustrating an example of vertical movement of the diffraction spots S of each order as viewed from the diffraction grating 80 side, accompanying rotation of the diffraction grating 80. FIG. [Figure 9] 9 is a graph illustrating various conditions (diffraction spot position, θD, θS) when the diffraction spot shown in FIG. 8 is detected by a detector 32b. [Figure 10] FIG. 10 is a diagram showing an example in which the information in FIG. 9 is converted into information on the θD-θS plane. [Figure 11] 11 is a diagram showing an example of an intensity distribution according to the relationship between the rotation angle (θD) of the detector 32b and the intensity of the diffraction signal, based on the information in FIG. [Figure 12] FIG. 12 is a diagram showing data illustrating the positions of maximum points of each order extracted by applying Gaussian approximation to the intensity distribution of FIG. 11. [Figure 13] This is a diagram in which the intensity distribution of the diffraction signal affected by interference is converted into information on the θD-θS plane. [Figure 14] FIG. 14 is a partially enlarged view of the intensity distribution in FIG. 13. [Figure 15] FIG. 14 is a diagram showing an example of the intensity distribution according to the relationship between the rotation angle (θD) of the detector 32b and the intensity of the diffraction signal, based on the intensity distribution of FIG. [Figure 16] 16 is a graph illustrating the positions of maximum points of each order extracted by applying Gaussian approximation to the intensity distribution of FIG. 15. [Figure 17] 2 is a block diagram illustrating an example of the functional configuration of a pitch calculation device 40. FIG. [Figure 18] 15 is a diagram specifically showing the shifts in the positions where the maximum points appear shown in FIG. 14 are expressed by (θD, θS) coordinate values. [Figure 19] 13 is a graph showing an example of the calculation results. [Figure 20] 13 is a flowchart showing an example of operation when different functions are assumed in the θ D axis direction and the θ S axis direction. [Figure 21] 13 is a flowchart showing an example of operation when the same function is assumed in the θD axis direction and the θS axis direction. [Figure 22] FIG. 13 is a diagram showing an entire pitch measurement system 100A according to a second embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0019] Hereinafter, the best mode for carrying out the present disclosure will be described with reference to the drawings.

[0020] (First embodiment) FIG. 1 is a diagram showing an entire pitch measurement system 100 according to the first embodiment. First, an example of the overall configuration of a pitch measurement system 100 according to an embodiment of the present disclosure will be described with reference to Fig. 1. As shown in Fig. 1, the pitch measurement system 100 includes an X-ray diffraction device 10 and a pitch calculation device 40. In this embodiment, the X-ray diffraction device 10 and the pitch calculation device 40 are combined to configure a pitch measurement device. The X-ray diffraction device 10 includes an optical mechanism section 20 and a support mechanism section 30.

[0021] The optical mechanism section 20 has an X-ray source 21, a collecting mirror 22, and a monochromator 23. The X-ray source 21 includes a vacuum tube that generates X-rays, and irradiates the X-rays to a diffraction grating 80. The collecting mirror 22 collects the X-rays emitted from the X-ray source 21 onto the surface of an analysis target placed on a sample stage 31. The monochromator 23 is used to extract only characteristic X-rays from the X-rays emitted from the X-ray source 21 and convert them into monochromatic light.

[0022] The support mechanism 30 has a sample stage 31, a detector 32, a first rotating stage 33, an arm 34, and a second rotating stage 35. The sample stage 31 is used to place a diffraction grating 80 or the like as an analysis target. The following description will be given on the assumption that the analysis target of the pitch measurement system 100 is the diffraction grating 80.

[0023] The detection unit 32 is for detecting the diffracted X-rays generated by the diffraction grating 80, and has a slit 32a and a detector 32b. The slit 32a narrows the diffracted X-rays generated by the diffraction grating 80. More specifically, the slit 32a is used to extract specific spatial information from the diffracted X-rays generated by the diffraction grating 80. The detector 32b is, for example, a scintillation detector, and detects the intensity of the diffracted X-rays that have passed through the slit 32a, and transmits a diffraction signal that is the detection result to the pitch calculation device 40. That is, the detector 32b inputs the diffracted X-rays that have passed through the slit 32a, detects the intensity of the diffracted X-rays, and transmits a diffraction signal that is information on the detection result to the pitch calculation device 40.

[0024] The first rotation stage 33 has a first rotation mechanism (not shown) that rotates the sample stage 31 around a rotation axis U. The first rotation stage 33 can rotate with the diffraction grating 80 mounted on the sample stage 31 attached, under the control of the first rotation mechanism by the pitch calculation device 40. Here, the rotation angle of the sample stage 31, i.e., the rotation angle of the diffraction grating 80, is defined as a first rotation angle θ S The first rotation stage 33 is directly fixed to the floor surface and rotates independently of the second rotation stage 35.

[0025] The arm unit 34 is an arm-shaped member on which the detection unit 32 is mounted. The arm unit 34 is configured to be rotationally driven in conjunction with the operation of the second rotation stage 35. The arm unit 34 is not in contact with the first rotation stage 33, and rotates independently of the first rotation stage 33. The second rotation stage 35 has a second rotation mechanism (not shown) that rotates the arm section 34 around the rotation axis U. Therefore, the detection section 32 is attached to the second rotation stage 35 via the arm section 34, and the second rotation stage 35 can rotate together with the detection section. The second rotation stage 35 rotates the detector 32b and the slit 32a mounted on the arm section 34 under the control of the second rotation mechanism by the pitch calculation device 40. Here, the rotation angle of the arm section 34, i.e., the rotation angle of the detector 32b and the slit 32a, is defined as a second rotation angle θD The second rotation stage 35 rotates the arm portion 34 and rotates independently of the first rotation stage 33.

[0026] The pitch calculation device 40 manages the state of the analysis target by controlling the operation of the X-ray diffraction device 10. The pitch calculation device 40 is configured by installing a computer program in a computer. More specifically, the pitch calculation device 40 of this embodiment is a computer used for controlling the pitch measurement system 100 and calculating the pitch, and an application program for the measurement system of the present disclosure (for example, a pitch measurement program 43p described later) is installed in the computer. The computer used for controlling the pitch measurement system 100 and calculating the pitch may be a general-purpose smartphone or tablet terminal, a desktop personal computer, a notebook personal computer, or the like, or may be a dedicated computer specialized for controlling the pitch measurement system 100 and calculating the pitch. The computer in this disclosure refers to an information processing device equipped with a control unit, a storage device, and the like.

[0027] In the present embodiment, the pitch calculation device 40 is disposed near the X-ray diffraction device 10, but is not limited thereto. For example, the pitch calculation device 40 may be provided in a server or the like that is installed at a position away from the X-ray diffraction device 10.

[0028] [Effect of interference of diffracted X-rays generated on the surface of a diffraction grating] FIG. 2 is a side view illustrating how X-rays are incident on a one-dimensional diffraction grating as an analysis target of the pitch measurement system 100. As shown in FIG. The optical mechanism 20 reflects the X-rays emitted from the X-ray source 21 by the collecting mirror 22, extracts only the characteristic X-rays by the monochromator 23, and makes the extracted characteristic X-rays obliquely incident on the surface of the diffraction grating 80 near the critical angle as shown in Fig. 2. Hereinafter, the X-rays emitted from the X-ray source 21 and incident on the diffraction grating 80 to be analyzed via the collecting mirror 22 and the monochromator 23 are also referred to as incident X-rays. Note that the incidence angle of the incident X-rays illustrated in Fig. 2 is merely an example.

[0029] FIG. 3 is a plan view illustrating a state in which X-rays are incident on a one-dimensional diffraction grating as an analysis target of the pitch measurement system 100. As shown in FIG. 3 is a view of FIG. 2 from a different angle, corresponding to a top view of the diffraction grating 80. The X-rays incident on the surface of the diffraction grating 80 are split into reflected X-rays that travel straight without any deviation to the left or right, and diffracted X-rays from the diffraction grating 80. These diffracted X-rays include the effects of the interference of the diffracted X-rays from the bottom and top surfaces of the gratings, in addition to the diffraction caused by the lateral periodic structure of each grating. The diffracted X-rays generated on the surface of the diffraction grating 80 pass through the slit 32a and are detected by the detector 32b as a diffraction signal.

[0030] FIG. 4 is an explanatory diagram that illustrates a schematic example of the intensity distribution when the first rotation mechanism and the second rotation mechanism are independently driven to acquire the diffraction signal. In FIG. 4, the first rotation mechanism of the first rotation stage 33 and the second rotation mechanism of the second rotation stage 35 are driven independently to rotate at a first rotation angle θ S and the second rotation angle θ D The intensity distribution when the diffraction signal is acquired by changing θ D -θ S The figure is shown diagrammatically on a plane. Here, θ D -θ S The plane is a plane that is parallel to the first rotation angle θ S The value of is taken on the first axis, and the second rotation angle θ DIn each drawing of this embodiment, the first axis corresponds to the vertical axis and the second axis corresponds to the horizontal axis, but a coordinate plane in which the first axis corresponds to the horizontal axis and the second axis corresponds to the vertical axis may be used. As shown in FIG. S =θ D θ is the point where the diffraction signal is maximized on a one-dimensional line (line T) of / 2. D Coordinates are virtual position θ′ D0 Then, θ D -θ S The point θ where the diffraction signal is maximum on the two-dimensional plane D Coordinates are the actual position θ D0 Let us assume that.

[0031] θ in Fig. 4 D -θ S In the plane, the first rotation angle θ by the θ / 2θ method S and the second rotation angle θ D In principle, the locus of the diffraction pattern can be drawn with a straight line (straight line T) with a slope of 1 / 2, and the information on the intensity distribution on the straight line is the diffraction signal obtained by the θ / 2θ method. S and the second rotation angle θ D The trajectory when scanning is θ D -θ S When drawn on a plane, it becomes a straight line T with a slope of 1 / 2, as shown in Figure 4. The θ / 2θ method is a method for measuring the magnitude of the diffraction signal along the straight line T, and it is known that when measurement is performed under ideal conditions, the maximum point (the point where the signal is maximum) of the two-dimensional intensity distribution in the diffraction signal exists on the straight line T. Hereinafter, the maximum point of the two-dimensional intensity distribution in the diffraction signal is also referred to as the "maximum point of the diffraction signal".

[0032] FIG. 5 is an explanatory diagram illustrating a state in which incident X-rays are scattered at the upper and bottom surfaces of a diffraction grating and then emitted. 5, the incident X-rays are diffracted from the upper surface (grating top surface) and the bottom surface (grating bottom surface) of the unevenness of the diffraction grating 80, so that the X-rays diffracted from the grating top surface and the grating bottom surface interfere with each other. Due to the effect of this interference, the position of the maximum point of the diffraction signal is shifted by θ S A positional deviation occurs in the axial direction. Therefore, the actual position θD0 and a virtual position θ′, which is the position of the maximum point of the diffraction signal obtained by the θ / 2θ method. D0 In addition, X-rays scattered many times between the bottom and top surfaces of the grating may be diffracted, and interference occurs between the diffracted X-rays generated by the periodic structure in the horizontal direction of the grating, as well as between the top and bottom surfaces of the grating. This interference also affects the actual position θ D0 and virtual position θ′ D0 There is a difference between the actual position θ D0 The position shift of the actual position θ D0 and virtual position θ′ D0 The difference between these (see FIG. 4) causes an error in measuring the pitch of diffraction grating 80. Hereinafter, the interference of X-rays scattered at the top and bottom surfaces of diffraction grating 80 is also referred to as "interference of diffracted X-rays in the up and down directions." The pitch of diffraction grating 80 is also simply referred to as "pitch."

[0033] Although FIG. 4 shows only one maximum point of the diffraction signal, the diffraction signal may have many peaks due to the effect of interference. D -θ S The maximum point of the diffraction signal on the plane is θ S In some cases, multiple maximum points may be separated in the axial direction. In such a case, correction data 43n, which will be described later, may be obtained around the maximum point that is closest to the line T.

[0034] [Pitch measurement principle using the θ / 2θ method] Next, a method for measuring the pitch by the θ / 2θ method will be described. First, the diffraction of X-rays generated by GI-SAXS will be explained using a three-dimensional space. First, the conditions under which diffraction occurs due to the diffraction grating 80 will be considered in a reciprocal space formed by reciprocal lattice vectors.

[0035] FIG. 6 is an explanatory diagram illustrating the movement of the diffraction spot when the diffraction grating on which the X-rays are incident is rotated in the positive direction. FIG. 7 is an explanatory diagram illustrating the movement of the diffraction spot when the diffraction grating on which the X-rays are incident is rotated in the negative direction. In FIG. 6 and FIG. 7, k i is the wave vector of the incident X-ray, and k f is the wave vector of the scattered X-ray, and q is the scattering vector. The diffraction spot S is located at the intersection of a reciprocal lattice rod R (GTR: grating truncation rod) on the reciprocal lattice plane F and the Ewald sphere. As shown in Figures 6 and 7, the X-ray incident on the surface of the diffraction grating 80 is diffracted on the surface, and a point (diffraction spot) where the intensity of the X-ray is maximum is generated at a position where the optical path difference is an integer multiple of the wavelength. This integer value is called the order, and the position where the diffraction spot appears varies depending on the order.

[0036] When the diffraction grating 80 rotates, the reciprocal lattice plane F also rotates by the same angle as the rotation angle of the diffraction grating 80. Here, the rotation direction in FIG. 6 is the positive direction, and the rotation direction in FIG. 7 is the negative direction. As shown in FIG. 6, when the diffraction grating 80 is rotated by +δ, the reciprocal lattice plane F also rotates by +δ, so that the diffraction spot S on the negative y-axis side moves downward and the diffraction spot S on the positive y-axis side moves upward, centered on the position H where the reflected X-ray appears. As shown in FIG. 7, when the diffraction grating 80 is rotated by -δ, the reciprocal lattice plane F also rotates by -δ, so that the diffraction spot S on the negative y-axis side moves upward and the diffraction spot S on the positive y-axis side moves downward, centered on the position H.

[0037] FIG. 8 is an explanatory diagram illustrating the vertical movement of the diffraction spots S of each order as viewed from the diffraction grating 80 side, accompanying the rotation of the diffraction grating 80. In FIG. As shown in FIG. 8, when the diffraction grating 80 is rotated by +δ, the arc on which the diffraction spots S of each order are plotted rotates counterclockwise around position H. When the diffraction grating 80 is rotated by -δ, the arc on which the diffraction spots S of each order are plotted rotates clockwise around position H. When the diffraction grating 80 is rotated, the higher the order of the diffraction spots S, the faster they move. The dashed line indicated by the symbol "Y" is also called the Yoneda band, and is the line where the intensity of the diffraction signal is maximum. In other words, the intensity of the diffraction signal is maximum at the same height as position H.

[0038] Next, a method for measuring the pitch by the θ / 2θ method will be described with reference to Figs. 9 to 12. Fig. 9 shows various conditions (diffraction spot position, θ D , θ S ) is a graph illustrating an example. FIG. 10 shows the information in FIG. D -θ S 10 is a diagram showing an example of conversion into information on a plane. In FIG. 10, the rotation angle (θ D ) is taken on the horizontal axis, and the rotation angle (θ S ) is on the vertical axis. FIG. 11 shows the rotation angle (θ D 11 is a diagram showing an example of the intensity distribution based on the relationship between the rotation angle (θ D ) is plotted on the horizontal axis and the intensity of the diffraction signal is plotted on the vertical axis. Fig. 12 is a diagram showing data illustrating the positions of the maximum points of each order extracted by applying Gaussian approximation to the intensity distribution of Fig. 11. In Fig. 12, the horizontal axis represents the order of the diffraction signal, and the horizontal axis represents the rotation angle (θ D ) is on the vertical axis. Figures 9 and 10 show that the θ / 2θ method is based on the principle of S :θ D = 1:2" and does not represent data derived by actual calculation.

[0039] First, by rotating the first rotating stage 33 and the second rotating stage 35 at an angular ratio of 1:2, the diffraction grating 80 and the detector 32b are also rotated at an angular ratio of 1:2, while X-rays are emitted from the X-ray diffraction device 10 to the diffraction grating 80, and multiple maximum points of the diffraction signal as shown in Figure 11 are detected by the detector 32b.

[0040] Now, referring to FIG. 9, θ S :θ D The reason why the intensity of the diffraction signal (FIG. 11) becomes maximum when the first rotation stage 33 and the second rotation stage 35 are rotated so that θ = 1:2 will be described.S Looking at the arc of θ = φ, the +1st order diffraction spot S (hatched circle) is on the Yoneda band. D Since θ = 2φ (the angle at which the +1st order diffracted X-rays occur is 2φ), S :θ D =1:2. S Looking at the arc of θ = 2φ, the +2nd order diffraction spot S (hatched square) is on the Yoneda band. D = 4φ, so θ S :θ D =1:2. S The same is true for the diffraction spot S (hatched diamond) on the arc of θ = 3φ. In other words, when the Yoneda band and the diffraction spot S intersect, the S :θ D When the measurement is performed under this condition, the intensity of the diffraction signal (FIG. 11) becomes maximum. D -θ S It is drawn on a flat surface.

[0041] Next, the positions of the maximum points of each order are extracted by approximating the intensity distribution as shown in FIG. 11 with a Gaussian distribution function, and the positions of the maximum points of each order are extracted as shown in FIG. 12. D The diffraction angle φ can be obtained by plotting the maximum points of each order on the coordinate system and deriving the slope of the approximation line based on the plotted maximum points of each order. In other words, the slope of the approximation line is 2φ, so the diffraction angle φ is the slope of the approximation line divided by 2.

[0042] The pitch (d) can be calculated by applying the diffraction angle φ calculated above to the Bragg condition shown in the following formula (1). In formula (1), n ​​is the diffraction order and λ is the wavelength of the X-ray. Note that n is set to 1 when calculating the pitch (d).

[0043]

number

[0044] [Actual state of measurement using the θ / 2θ method] Next, with reference to FIGS. 13 to 16, the influence of interference of X-rays scattered at the top and bottom surfaces of the grating on measurement data using the θ / 2θ method will be described. Figure 13 shows the intensity distribution of the diffraction signal affected by interference at θ D -θ S This is a diagram converted into information on a plane. FIG. 14 is a partially enlarged view of the intensity distribution of FIG. FIG. 15 shows the relationship between the rotation angle (θ D 13 is a diagram showing an example of an intensity distribution based on the relationship between the diffraction signal intensity and the diffraction light intensity. FIG. 16 is a graph illustrating the positions of the maximum points of each order extracted by applying Gaussian approximation to the intensity distribution of FIG.

[0045] As shown in Fig. 9, the diffraction signals appearing for each order are affected by the interference of the diffracted X-rays in the up and down directions. D -θ S When plotted on a plane, the positions of the maximum points of the diffraction signal are shifted as in the examples of Figures 13 and 14. Figure 13 shows an example in which the maximum points of the -2nd and +2nd order diffraction intensity distributions are shifted. In measurement using the conventional θ / 2θ method, measurement is performed on a straight line with a slope of 1 / 2, so real peak J, which is the maximum point of the -2nd and +2nd order two-dimensional intensity distribution, cannot be detected, and virtual peak K is detected.

[0046] If the peak in the ideal case where there is no influence of interference from diffracted X-rays in the vertical direction is taken as ideal peak R, and the positional relationship between real peak J and virtual peak K is shown in Figure 14. If there is no influence of interference from diffracted X-rays in the vertical direction, the maximum point should appear at the position of ideal peak R, but as a result of being influenced by interference from the diffracted signal, the signal intensity becomes maximum at the position of real peak J. Therefore, if measurement is performed in this state along a straight line T with a slope of 1 / 2 based on the θ / 2θ method, the maximum of the signal intensity will be detected at the position of virtual peak K. Therefore, when the rotation angle (θ D) When the intensity of the diffraction signal with respect to () is graphed, an intensity distribution deviated from the ideal is drawn as shown in Fig. 15.

[0047] Figs. 13 and 15 are diagrams showing an example in the case where the maximum points of the -2nd and +2nd order diffraction intensity distributions are shifted, and θ between the actual peak J of the -3rd order and the virtual peak K of the -2nd order D The axial distance P1 between the virtual peak K of the -2nd order and the actual peak J of the -1st order is θ D It shows an example where it becomes shorter than the axial distance P2, and the same applies to the +3rd order and +2nd order.

[0048] When approximating the intensity distribution as shown in Fig. 15 with a Gaussian distribution function, the positions of the maximum points of the -2nd order and +2nd order are shifted. As shown in Fig. 16, the approximate straight lines based on the maximum points of each order extracted are shifted from the correct approximate straight line (ideal straight line). In Fig. 16, as in Figs. 13 and 15, θ D It shows the case where the interval between the maximum points in the axial direction is shifted (see "Q1<Q2" in the figure), and thereby, the slope of the approximate straight line becomes larger than the slope of the straight line in the ideal case.

[0049] As described above, when obtaining the pitch (d) by the θ / 2θ method, the diffraction angle φ is obtained from the slope of the approximate straight line, and the obtained diffraction angle φ is applied to the Bragg's condition formula. That is, the deviation of the approximate straight line derived by the θ / 2θ method from the ideal straight line means that the slope of the approximate straight line deviates from the ideal, which becomes a factor of error in pitch measurement. More specifically, as shown in Fig. 16, when the slope of the derived approximate straight line becomes larger than the slope of the ideal straight line, the measurement result of the pitch becomes smaller than the reference value. Therefore, the pitch calculation device 40 in the present embodiment performs correction processing on the pre-correction pitch dm, which is the value of the pitch obtained by the θ / 2θ method, to obtain the post-correction pitch d, which is the value of the pitch with the influence of the interference of the diffracted X-rays in the vertical direction alleviated. The post-correction pitch d is a value corrected to reduce the error due to the interference of the diffracted X-rays in the vertical direction included in the pre-correction pitch dm, and as the value of the pitch, it is a more accurate value than the pre-correction pitch dm.

[0050] An example of the functional configuration of pitch calculation device 40 and a method of calculating pitch by pitch calculation device 40 will be described with reference to FIGS. FIG. 17 is a block diagram showing an example of the functional configuration of pitch calculation device 40. As shown in FIG. The pitch calculation device 40 has a communication unit 41, a storage unit 43, an input unit 44, a display unit 45, and a control unit 50. The communication unit 41 is an interface for the control unit 50 to communicate with external devices such as the X-ray diffraction apparatus 10 in a wired or wireless manner.

[0051] Various information is stored in the storage unit 43 in addition to operation programs of the control unit 50, such as a pitch measurement program 43p. The storage unit 43 can be configured with a RAM (Random Access Memory) and a ROM (Read Only Memory), a PROM (Programmable ROM) such as a flash memory, or an HDD (Hard Disk Drive), etc. The input unit 44 includes, for example, a keyboard and a pointing device such as a mouse or a trackball. The input unit 44 accepts an input operation by a user and transmits an operation signal to the control unit 50 according to the content of the input operation. The display unit 45 is, for example, a liquid crystal display (LCD), and displays various information according to instructions from the control unit 50. Note that pitch calculation device 40 may have a touch panel including a display panel that displays characters or images, and detection means that is stacked on the display panel and detects a touch operation, instead of input unit 44 and display unit 45. Pitch calculation device 40 may have both a touch panel and a mouse or a keyboard, etc.

[0052] The control unit 50, in accordance with a pitch measurement program 43p described below, comprehensively controls the operation of the entire pitch measurement system 100. The control unit 50 includes a diffraction signal acquisition unit 51, a pitch calculation unit 52, a distribution information acquisition unit 53, a correction data acquisition unit 54, and a pitch correction unit 55. The control unit 50 can be configured by a calculation device such as a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit), and a pitch measurement program 43p that cooperates with the calculation device to realize the above-mentioned various functions. That is, the pitch measurement program 43p is a program that causes the control unit 50 as a computer and the storage unit 43 to function as a diffraction signal acquisition unit 51, a pitch calculation unit 52, a distribution information acquisition unit 53, a correction data acquisition unit 54, and a pitch correction unit 55.

[0053] Here, the main cause of the two-dimensional intensity distribution of the diffraction spot and its surroundings is the interference of X-rays scattered from each grating constituting the diffraction grating. S The phenomenon occurring in the axial direction includes the effect of interference of X-rays scattered at the top and bottom surfaces of the diffraction grating (interference of diffracted X-rays in the up and down directions), so θ D Function expressing the intensity distribution in the axial direction and θ S This is strictly different from the function that represents the axial intensity distribution (Figure 4 shows such a situation, where θ D Axis・θ S The axial intensity distribution is divided into two parts by different functions f D (θ D )f S (θ S However, empirically, functions such as Gaussian functions are expressed as θ D Axial direction and θ S In some cases, the axis direction can be applied to either direction. D Axial direction and θ S A universal method that can be applied even when different functions are required for the θ axis direction and θ D Axial direction and θ S We will explain separately the method for handling special cases where the same function can be assumed for both the θ axis direction and the θ D The axial direction is called the "second axial direction", and θ S The axial direction is also called the "first axial direction."

[0054] [Common processing regardless of assumed function] First, θD Axial direction and θ S A common process when assuming different functions for the axis direction and when assuming the same function will be outlined below.

[0055] The diffraction signal acquisition unit 51 acquires a diffraction signal based on the diffracted X-rays detected by the detection unit 32 while the first rotation stage 33 and the second rotation stage 35 are rotated in conjunction with each other so that the ratio of the rotation angle of the first rotation stage 33 to the rotation angle of the second rotation stage 35 is 1:2. More specifically, the diffraction signal acquisition unit 51 acquires a signal of X-rays scattered on the surface of the diffraction grating 80, which rotates in conjunction with the driving of the first rotation stage 33, via the detection unit 32, which rotates in conjunction with the driving of the second rotation stage 35, which operates independently of the first rotation stage 33. The diffraction grating 80 rotates in conjunction with the driving of the first rotation stage 33 while placed on the sample stage 31. The detection unit 32 is mounted on the arm unit 34, and therefore rotates in conjunction with the operation of the arm unit 34, which rotates in conjunction with the driving of the second rotation stage 35.

[0056] The pitch calculation unit 52 calculates a pre-correction pitch dm, which is the value of the pitch of the diffraction grating before correction, by the θ / 2θ method, based on the diffraction signal acquired by the diffraction signal acquisition unit 51. More specifically, in response to an input operation by a user, the X-ray diffraction device 10 is controlled by the diffraction signal acquisition unit 51 to emit X-rays to the diffraction grating 80, rotate the first rotating stage 33, and rotate the second rotating stage 35. At this time, the diffraction signal acquisition unit 51 controls the first rotating stage 33 and the second rotating stage 35 to rotate at an angle ratio of 1:2. At this time, the diffraction signal acquisition unit 51 acquires multiple maximum points of the diffraction signal from the detector 32b. That is, the diffraction signal acquisition unit 51 acquires an intensity distribution as shown in FIG. 11, approximates it with a Gaussian distribution function, etc., and extracts the positions of the maximum points of each order.

[0057] Next, the pitch calculation unit 52 calculates the order -θ DThe maximum points of each order are plotted on the coordinate system, and the diffraction angle φ is obtained from the gradient of an approximation line based on the plotted maximum points of each order. Then, the pitch calculation unit 52 calculates the pre-correction pitch dm by calculation based on the equation (2) obtained by modifying the equation (1) by setting d to "dm" and the diffraction order n to "1". The pre-correction pitch dm calculated by the pitch calculation unit 52 includes an error due to interference of diffracted X-rays in the upward and downward directions. The pitch calculation unit 52 stores the calculated pre-correction pitch dm in the memory unit 43.

[0058]

number

[0059] Next, a method for obtaining a corrected pitch d in which the influence of interference of diffracted X-rays in the upward and downward directions is alleviated by performing a correction process on the uncorrected pitch dm obtained based on the θ / 2θ method will be described. As shown in FIG. 14, if the position where the diffraction signal maximum appears in an ideal case is the ideal peak R, the position of this maximum will shift due to interference from diffracted X-rays in the upward and downward directions. The diffraction signal has a two-dimensional intensity distribution around the maximum. Therefore, if measurement is performed using the θ / 2θ method with the maximum shifted to the position of real peak J, the point where the diffraction signal becomes maximum on a line with a slope of 1 / 2, that is, virtual peak K, will be detected. However, since this position is different from the ideal peak R, the peaks of the diffraction signals for each order will shift, for example, as shown by the dashed line in FIG. 15. As a result, the order-θ D The straight line fitting results of the maximum points of each order on the coordinate system also shift as shown by the dashed lines in Fig. 16. As a result, the diffraction angle calculated from the slope of the straight line shifts from the ideal value, and the pre-correction pitch dm ends up including an error. In other words, the error in the pre-correction pitch dm depends on the shift of the maximum point appearance position from the ideal peak R to the actual peak J, and on the spread of the two-dimensional intensity distribution.

[0060] FIG. 18 shows the deviation of the maximum point appearance position shown in FIG. 14 (θ D ,θ S ) coordinate values. In Figure 18, the coordinates of the real peak J, the ideal peak R, and the virtual peak K are (θDО ,θ SО ), (θ DО ,1 / 2(θ DО )), (θ′ DО ,1 / 2(θ′ DО )) is shown. 4 and 18 show the two-dimensional distribution of the diffraction signal (θ D ,θ S ) coordinate values, two ways of expressing the spread of the distribution are shown. One is to express the spread of the two-dimensional intensity distribution as θ D axis, θ S A method of expressing functions on the axis, each function is f D (θ D )f S (θ S The other is the spread of the two-dimensional intensity distribution, expressed as θ D Direction, and θ S This is a method to express the FWHM (Full Width at Half Maximum) around the maximum point in the direction. Each FWHM is expressed as Δθ D, Δθ S It is expressed as:

[0061] In the above discussion, the order of the diffraction signal was not specified, but from now on, the diffraction order will be expressed by the subscript n. As a result, the coordinates of the real peak J, ideal peak R, and virtual peak K of the nth order diffraction signal are respectively (θ DО,n ,θ SО,n ), (θ DО,n ,1 / 2(θ DО,n )), (θ′ DО,n ,1 / 2(θ′ DО,n )) and the spread of the two-dimensional intensity distribution of the nth order diffraction signal is expressed as θ D axis, θ S When expressed as a function of the axis, f D,n (θ D )f S,n (θ S ), and when expressed as a half-width, Δθ D,n, Δθ S,n It becomes.

[0062] As described above, the uncorrected pitch dm is affected by the shift of the maximum point of the diffraction signal due to the interference of the diffracted X-rays in the upward and downward directions and the spread of the two-dimensional intensity distribution of the diffraction signal, and it is necessary to reduce these effects when deriving the corrected pitch d. The most natural method is to reduce or remove the effects of the maximum point shift and two-dimensional intensity distribution of the diffraction signal contained in the uncorrected pitch dm to obtain the corrected pitch d, but as will be described later, this method may not be able to improve the accuracy. Therefore, in this method, the corrected pitch d is determined by the reverse approach of adopting as the corrected pitch d the pitch of the diffraction grating that gives the uncorrected pitch dm when calculated by adding the effects of the maximum point shift and two-dimensional intensity distribution of the diffraction signal.

[0063] First, we will discuss the relationship that the corrected pitch d must satisfy. As described above, the corrected pitch d is a value in which the effects of the maximum point shift of the diffraction signal and the two-dimensional intensity distribution are reduced or eliminated. Therefore, by modifying equation (1) when the order n is set to 1, it is possible to obtain the diffraction angle φ in which the effects of the maximum point shift of the diffraction signal and the two-dimensional intensity distribution are reduced or eliminated, as shown below.

[0064]

number

[0065] As described above, this method takes the opposite approach of correcting the corrected pitch d so that the calculation result obtained by taking into account the effects of the maximum point shift of the diffraction signal and the two-dimensional intensity distribution on the quantities calculated from the corrected pitch d is the uncorrected pitch dm. Therefore, many of the quantities derived in the process of inversely calculating the uncorrected pitch dm from the corrected pitch d are functions of the corrected pitch d. For this reason, the diffraction angle is also treated as a function of the corrected pitch d, and is expressed as φ(d) in the above equation.

[0066] By using the above diffraction angle φ(d) while referring to the matters explained above using FIG. 9 and to FIGS. 10 and 11, it is possible to simulate the results of the θ / 2θ method measurement in which the effects of the maximum point shift of the diffraction signal and the two-dimensional intensity distribution are reduced or eliminated. The detector rotation angle θ at each order where the diffraction signal is maximized can be calculated. DО,n (d) can be found as follows:

[0067]

number

[0068] Next, the diffraction grating rotation angle θ at each order where the diffraction signal is maximized SО,n We will also describe a method for evaluating the two-dimensional intensity distribution of the diffraction signal. DО,n As described above, (d) was calculated from the theoretically corrected pitch d. In contrast, the diffraction grating rotation angle θ at each order where the diffraction signal is maximized SО,n The two-dimensional intensity distribution is experimentally measured using the same diffraction grating as that used to determine the uncorrected pitch dm, in the following procedure. It is preferable to use the same pitch measurement system as that used to determine the uncorrected pitch dm during the measurement, but a different pitch measurement system may be used for this measurement as long as it has the same specifications as the system used to determine the uncorrected pitch dm.

[0069] The distribution information acquisition unit 53 acquires distribution information of the diffracted X-rays in a two-dimensional coordinate system of the first and second axes, where the value of the rotation angle of the diffraction grating is taken on the first axis and the value of the rotation angle of the detection unit 32 is taken on the second axis, for each order based on the diffraction signal based on the diffracted X-rays detected by the detection unit 32 while the first rotation stage 33 and the second rotation stage 35 are rotated separately. That is, the distribution information acquisition unit 53 acquires distribution information of the diffracted X-rays in a two-dimensional coordinate system of the first and second axes, where the value of the rotation angle of the diffraction grating is taken on the first axis and the value of the rotation angle of the detection unit 32 is taken on the second axis, for each order based on the diffraction signal based on the diffracted X-rays detected by the detection unit 32 while the first rotation stage 33 and the second rotation stage 35 are rotated separately. S Axial direction and θ D The diffraction grating rotation angle θ at each order where the diffraction signal is maximized is scanned independently in the axial direction. SО,n , detector rotation angle θ DО,nIn addition, a two-dimensional intensity distribution for each order is acquired. Specifically, the distribution information acquisition unit 53 calculates the distribution information θ from the maximum point position of the diffraction signal for each order when the uncorrected pitch dm is calculated. S By scanning the angle only in the axial direction, S The maximum point of the diffraction signal on the axis is determined. However, as shown in Fig. 4 and Fig. 14, the maximum point of the diffraction signal at a certain order n when the uncorrected pitch dm is obtained is at the position of the white circle indicated by the virtual peak K, and the θ S In the angle scan in the axial direction, the black circle of the actual peak J does not pass through. Therefore, for example, the distribution information acquisition unit 53 calculates an angle θ S Scan the axis direction one-dimensionally to find the maximum point on the line, and then measure θ D By one-dimensional scanning in the axial direction, the θ of the black circle of the actual peak J D θ S Find the coordinates and calculate the θ of the real peak J of the corresponding order. D θ S Coordinates are (θ DО,n ,θ SО,n ) The above is merely an example, and the method for obtaining the maximum point of the black circle is not limited to the above. The distribution information acquisition unit 53 may perform the above one-dimensional scan in a different order. S -θ D It may be determined by a two-dimensional scan in a plane.

[0070] Next, the θ of the real peak J of a certain order n determined in this way D θ S Coordinates (θ DО,n ,θ SО,n ) at the center, θ D θ S An axial angle scan is performed to obtain data related to the spread of the two-dimensional intensity distribution. As mentioned above, the spread of the two-dimensional intensity distribution is expressed as θ D axis, θ S There are two ways to express the value: as a function of the axis or as a half-width. You can obtain data for at least one of these as needed. In the former case, the actual peak J is centered on θ D θS Scan the angle in the axial direction and measure θ S Axial intensity distribution f S (θ S ), θ D Axial intensity distribution f D (θ D ) is calculated, and in the latter case, θ D θ S Scan the angle in the axial direction and find the θ value where the signal intensity is half the signal intensity of the actual peak J. D θ S Determine the coordinate point, and calculate the half-width Δθ D , Δθ S Determine.

[0071] In addition, when determining the actual peak J, the above θ S Axial angle scan, or θ D If you have already performed an axial angle scan, use θ S θ D There is no need to perform both axial and angular scans, but by performing additional scans only for the missing data on the already scanned axes and the unscanned axes, the f S (θ S ), f D (θ D ) and Δθ D , Δθ S may be determined. In addition, θ S Axial intensity distribution f S (θ S ), θ D Axial intensity distribution f D (θ D ) in determining θ S Axial direction, θ D When the step of the axial angle scan is rough, function fitting and interpolation can be performed based on the scan results to obtain f S (θ S ), f D (θ D ) may be determined.

[0072] The above process is performed for each order to evaluate the spread of the two-dimensional intensity distribution of the diffraction signal for each order. Specifically, the spread of the two-dimensional intensity distribution is evaluated by the following equation: D axis, θ S When expressing the half-width relative to the axis, the half-width Δθ calculated above is used. D , Δθ S Add the subscript of the corresponding order n to Δθ D,n , Δθ S,n This is used as a parameter that represents the spread of the two-dimensional intensity distribution of the diffraction signal at each order. The spread of the two-dimensional intensity distribution is expressed as θ D axis, θ S When expressed as a function of the axis, the intensity distribution function f D (θ D ), f S (θ S ) with the subscript of the corresponding degree n, and D,n (θ D ), f S,n (θ S ) and θ D f is a function of coordinates only D,n (θ D ) of the actual peak J D Coordinate value θ DО,n , and θ of the actual peak J D Coordinate value θ DО,n Relative coordinate θ D -θ DО,n Convert it to a function of f D,n (θ DО,n ,θ D -θ DО,n ) and θ S f is a function of coordinates only S,n (θ S ) can be converted in the same way to f S,n (θ SО,n ,θ S -θ SО,n ) and the product of the two functions, f D,n (θ DО,n ,θ D -θ DО,n )×f S,n (θ SО,n ,θ S -θ SО,n ) is a function that describes the spread of the two-dimensional intensity distribution.

[0073] In the above process, the θ D θ S Coordinates (θ DО,n ,θ SО,n ) has been experimentally determined, and in principle, this θ DО,n is the rotation angle θ of the detector at which the diffraction signal peaks of each order are detected in the ideal case where there is no interference between the diffracted X-rays in the upward and downward directions. D Therefore, θ DО,n For each order, plot as shown in Figure 12, fit a line to find φ from the slope of the line, and substitute it into the Bragg condition equation in equation (1) to find the pitch d. This should enable highly accurate evaluation of d. Unfortunately, however, the θ determined in this way DО,n does not necessarily improve the measurement accuracy of the actual pitch d.

[0074] The inventor of the present application has newly discovered that the accuracy of measuring the pitch of a diffraction grating can be improved by correcting the corrected pitch d so that the result of back-calculating the uncorrected pitch dm from the corrected pitch d becomes equal to the uncorrected pitch dm based on the actual measurement value, and by calculating the corrected pitch d determined in this way as the pitch of the diffraction grating. The key point of this process is the actual measurement value θ of the detector rotation angle at the actual peak J. DО,n Instead of θ, the pitch after correction d is calculated using the above formula (2-2). DО,n This is the process of using (d). D θ S The actual coordinate value (θ DО,n ,θ SО,n ) is the inversely calculated θ from the corrected pitch d D Coordinate value including coordinate value (θ DО,n (d),θ SО,n ) is replaced by the function I n is expressed as the following equation (2-3).

[0075]

number

[0076] If the corrected pitch d can be set so that the pre-correction pitch dm can be calculated inversely, the calculated θ DО,n (d) shows the diffraction signal θ with the effect of interference from the diffracted X-rays in the upward and downward directions removed. D The coordinate maximum point can be reproduced with higher accuracy. This, together with the θ of the actual peak J determined by actual measurement, S Coordinate θ SО,n It is determined by the set of (θ DО,n (d),θ SО,n ) is newly defined as the coordinate point of actual peak J. The one-dimensional distribution function f D,n , f S,n By using this, the function I on the right side of the above equation (2-3) can be n This makes it possible to reproduce with high accuracy the two-dimensional intensity distribution of the diffraction signal, which also simulates the effect of interference of diffracted X-rays in the upward and downward directions.

[0077] In the following, the spread of the two-dimensional intensity distribution is expressed as θ D axis, θ S First, we describe the case where the two-dimensional intensity distribution is expressed as a function of the axis, and then we explain how the two-dimensional intensity distribution spreads with respect to the θ D direction, θ S The following describes the process of expressing the half-width in the θ direction. D Axial direction and θ S This is a universal method that can be applied even when it is necessary to assume different functions for the axis direction. D Axial direction and θ S This is a method for handling special cases where the same function can be assumed in both the axial and axial directions.

[0078] [θ D Axial direction and θ S [When different functions are assumed for the axis direction (separate function assumption case)] In this case, the f on the right side of the above equation (2-3) D,n , f S,nWithout assuming a specific functional form for , the two-dimensional intensity distribution function of the diffraction signal around the actual peak J at each order is simulated as shown in equation (2-3), and the maximum point at each order is calculated when an angle scan is performed according to the θ / 2θ method on such a two-dimensional intensity distribution function of the diffraction signal.

[0079] In the θ / 2θ method, θ S =θ D Since the scan is performed while maintaining the angle condition of θ / 2, the detector rotation angle θ D The diffraction signal for is obtained by modifying equation (2-3) as follows:

[0080]

number

[0081] If the maximum value of the above equation (2-4) is found using a numerical solution such as the gradient method, the detector rotation angle θ when an angle scan is performed according to the θ / 2θ method is D For example, as shown by the dashed line in Figure 15, a graph simulating a state in which the detection position of the maximum point is shifted due to interference from diffracted X-rays in the upward and downward directions can be drawn. The detector rotation angle θ of each maximum point shown by this dashed line D is a simulation of the shift of the maximum points of the diffraction signal due to the interference of the diffracted X-rays in the upward and downward directions, using the corrected pitch d and the actual measured value. The detector rotation angle θ D is the θ of the virtual peak K in Fig. 14 D The coordinate equivalent, i.e., θ′ in Fig. 4 DО Since it is a significant quantity and a function of d, θ′ DО,n (d) Let this be the degree-θ for n at each degree. DWhen plotted on a graph, it looks like Figure 16. In Figure 16, the result of fitting the data points for each order to a straight line is, as shown by the solid line, a simulation of the effect of interference of diffracted X-rays in the upward and downward directions. Half the slope of this line with respect to the order is an amount equivalent to the diffraction angle φ mentioned earlier, and as mentioned above, it correlates with d. However, since it is different from the function φ(d) defined in equation (2-1), in the following, for the sake of distinction, a different function notation will be used, φ'(d).

[0082] Next, if the pitch of the diffraction grating (the intermediate pitch obtained in the process of calculating the corrected pitch) obtained from the diffraction angle (the intermediate diffraction angle obtained in the process of calculating the corrected pitch) φ′(d) obtained above is dm′, the following equation (2-5) is derived.

[0083]

number

[0084] As mentioned above, the solution to be found is the corrected pitch d, which allows the uncorrected pitch dm to be calculated inversely. To do this, we need to find d when dm' on the left side of the above equation (2-5) is replaced with dm, and mathematically, this can be achieved by solving the following equation (2-6).

[0085]

number

[0086] However, as mentioned above, the derivation of φ'(d) involves linear approximation of data at each order, and since it is impossible to analytically determine the inverse function of φ'(d), the corrected pitch d is derived, for example, by a numerical method such as the following. Note that the following is merely an example, and the corrected pitch d may be derived by other methods.

[0087] Here, a method for numerically determining the corrected pitch d by the bisection method will be illustrated. (1): First, the uncorrected pitch dm obtained based on the θ / 2θ method is used as the corrected pitch d as is, and the process for obtaining dm' described above is carried out to obtain dm', and dm'-dm is calculated.

[0088] (2): If the result of (1) is dm'-dm=0, then d=dm and the calculation of the corrected pitch d is terminated.

[0089] (3): If the result of (1) is dm'-dm<0, then the first candidate for corrected pitch d1 is set to d1=dm'. The second candidate for corrected pitch d2 is set to d2=dm-(dm'-dm), and the above-mentioned process for finding dm' is carried out on d2 to find the corresponding dm'. If dm'-dm<0, then d2-(dm'-dm) is set as the new second candidate for corrected pitch d2, and the process for d2 is repeated until dm'-dm>0. Note that if dm'-dm=0 during this calculation, then d=dm is set and the calculation of corrected pitch d is terminated.

[0090] (4): If the result of (1) is dm'-dm>0, then the second candidate for corrected pitch d2 is set to d2=dm'. Also, the first candidate for corrected pitch d1 is set to d1=dm-(dm'-dm), and the above-mentioned process for finding dm' is carried out on d1 to find the corresponding dm'. If dm'-dm>0, then d1-(dm'-dm) is set as the second candidate for corrected pitch d2, and the process for d1 is repeated until dm'-dm<0. Note that if dm'-dm=0 during this calculation, then d=dm is set and the calculation of corrected pitch d is terminated.

[0091] (5): Calculate the midpoint d3=1 / 2(d1+d2) between d1 and d2, and perform the above-mentioned process to find dm' for d3 to find the corresponding dm'. If dm'-dm>0, set d3 as the second candidate d2 for the new corrected pitch, and if dm'-dm<0, set d3 as the first candidate d1 for the new corrected pitch. Note that if dm'-dm=0, set d=dm and end the calculation of the corrected pitch d.

[0092] (6) Repeat the step in (5) until dm′ - dm = 0. Set d = dm using dm at the end of the step, and finish the calculation of the corrected pitch d. In the above (3) and (4), the method for obtaining the first candidate d1 and the second candidate d2 of the corrected pitch was described. However, this is just an example. As long as the condition d1 < dm < d2 is satisfied, the selection method can be based on any method. Also, in (2), (3), (4), and (6), the condition for finishing the calculation of the corrected pitch d was set as dm′ - dm = 0. However, this is just an ideal case. Considering the calculation resources and the burden in terms of calculation time, it is desirable to set the end condition according to the required determination accuracy of the corrected pitch d. For example, if the determination accuracy of the corrected pitch d is d ± Δd, the end condition may be |dm′ - dm| < Δd.

[0093] When numerically obtaining the corrected pitch d, a method other than the above bisection method may be adopted. For example, within the interval containing the pitch dm before correction, a large number of candidate values of the corrected pitch d are defined at the step of the determination accuracy Δd of the corrected pitch d. Using the process of obtaining dm′ described above, calculate dm′ for each candidate value, select the dm′ closest to dm, and adopt the candidate value of the corrected pitch d corresponding to this as the calculation result of the corrected pitch d.

[0094] Figure 19 graphs an example of the calculation results. In Figure 19, when plotting each of the large number of defined candidate values of the corrected pitch d and dm′ for each candidate value as the horizontal and vertical axis coordinates, it shows that an oblique solid line in the figure is obtained. In this case, the pitch dm before correction is 99.27 [nm], and the corresponding corrected pitch d is calculated to be 99.90 [nm]. The reference value of the pitch of the diffraction grating used as the measurement object is 99.98 [nm]. It can be seen that the accuracy of the measured value of the pitch is improved by the processing of this method. Note that the same corrected pitch d = 99.90 [nm] is obtained by the bisection method described above.

[0095] [θ S Axial direction and θD [When the same function is assumed in both the axial and axial directions (identical function assumption case)] In the following, θ S Axial direction and θ D We will now describe a special case where the same function can be assumed for both the axial and axial directions. This method is based on the premise that the two-dimensional intensity distribution of the diffraction signal is centered on the maximum position of the intensity distribution and is scaled by θ S Axial direction and θ D In the case where the diffraction signal is symmetric with respect to the axis, the two-dimensional intensity distribution of the diffraction signal is expressed as θ S Axial direction, θ D Axial half-width Δθ S , Δθ D The correction data acquisition unit 54 calculates this θ S Direction half-width (first peak width) Δθ S and the actual position θ S0 and θ D Half-width in the direction (second peak width) Δθ D and are acquired as correction data.

[0096] One function that satisfies the above conditions is the Gaussian function, θ D Axial direction and θ S The case where the intensity distribution of the diffraction signal in the axial direction is a Gaussian function will be illustrated. In this case, the function f D,n (θ DО,n ,θ D -θ DО,n ) and f S,n (θ SО,n ,θ S -θ SО,n ) is defined as follows:

[0097]

number

[0098]

number

[0099] Substituting the above into equation (2-3), we obtain the function I nThe rotation angle of the detector when measuring with the θ / 2θ method is specified as θ. D and the diffraction grating rotation angle θ S The angle condition, θ S =θ D / 2, the detector signal intensity when the angle scan is performed according to the θ / 2θ method is expressed as the detector rotation angle θ D An equation equivalent to equation (2-4), which shows the dependency, is derived.

[0100] θ D Axial direction and θ S In the analysis assuming a different function in the axial direction, a numerical solution such as the gradient method is used to calculate the detector rotation angle θ′ at each order where the detector signal intensity is maximized in the θ / 2θ method measurement. DО,n (d) was calculated, and like the Gaussian function, the two-dimensional intensity distribution of the diffraction signal was centered on the maximum position of the intensity distribution, and D Axial direction and θ S Symmetrical with respect to the axis, the two-dimensional intensity distribution θ D direction, θ S Direction half-width Δθ D , Δθ S In this case, the contour of the two-dimensional intensity distribution of the diffraction signal is calculated by simulating the shift of the maximum point of the diffraction signal due to the interference of the diffracted X-rays in the upward and downward directions using the corrected pitch d and the actual measured value. DО,n (d),θ SО,n ) is the center, and θ S direction, θ D The length of the diameter in each direction is the half-width Δθ D , Δθ S When the contour line is an ellipse, the θ of the virtual peak K in Fig. 14 is D The coordinate equivalent, i.e., θ′ in Fig. 4 DО A considerable amount of θ′ DО,n (d) can be calculated using the following formula:

[0101]

number

[0102] θ′ calculated above DО,n(d) is a simulation of the shift of the maximum point of the diffraction signal due to the interference of diffracted X-rays in the upward and downward directions. D The coordinate equivalent, i.e., θ′ in Fig. 4 DО This is a considerable amount. Therefore, we use the order-θ for n at each order. D When plotted on a graph, it looks like Figure 16, and the straight line fitting result of the data points of each order simulates the effect of interference of diffracted X-rays in the up and down directions, as shown by the solid line. The 1 / 2 slope of this straight line with respect to the order is an amount equivalent to the diffraction angle φ explained using Figure 12, and corresponds to φ'(d) shown in formula (2-5).

[0103] The corrected pitch d is calculated using the above φ′(d), and the numerical processing used at that time is performed in the same manner as in the case of the individual function assumption, using the bisection method described above or a numerical solution other than the bisection method.

[0104] As described above, the corrected pitch d can be calculated using either the same function assumption case or the individual function assumption case. The control unit 50 may be configured to selectively execute both the same function assumption case and the individual function assumption case, or may be configured to execute only one of the same function assumption case and the individual function assumption case. When using the former configuration, the user may be allowed to select between the different types of calculation.

[0105] Next, referring to the flowchart of FIG. 20, in the pitch calculation method according to the present embodiment, D Axial direction and θ S An example of operation when different functions are assumed in the axial direction will be described. Figure 20 shows the D Axial direction and θ S 13 is a flowchart showing an example of operation when different functions are assumed in the axial direction.

[0106] In step (hereinafter, referred to as S) 11, the diffraction signal acquisition unit 51 acquires a diffraction signal based on the diffracted X-rays detected by the detection unit 32 while the first rotation stage 33 and the second rotation stage 35 are rotated in conjunction with each other so that the ratio of the rotation angle of the first rotation stage 33 to the rotation angle of the second rotation stage 35 is 1:2. Then, the pitch calculation unit 52 calculates a pre-correction pitch dm, which is the pre-correction value of the pitch of the diffraction grating, by the θ / 2θ method based on the diffraction signal acquired by the diffraction signal acquisition unit 51.

[0107] In S12, the distribution information acquisition unit 53 acquires distribution information of the diffracted X-rays in a two-dimensional coordinate system of the first and second axes, where the value of the rotation angle of the diffraction grating is taken as the first axis and the value of the rotation angle of the detection unit 32 is taken as the second axis, for each order based on the diffraction signal based on the diffracted X-rays detected by the detection unit 32 while the first rotation stage 33 and the second rotation stage 35 are rotated individually.

[0108] In S13, the correction data acquisition unit 54 acquires the distribution information of the diffracted X-rays acquired for each order by dividing it into a first function corresponding to the first axis direction along the first axis and a second function corresponding to the second axis direction along the second axis. S Axial direction and θ D An intensity distribution in the axial direction is generated and used as correction data 43n by a first function f S (θ S ) and the second function f D (θ D ,d) and For example, in the case of this individual function assumption, the correction data acquisition unit 54 calculates "f D,n (θ DО,n (d),θ D -θ DО,n (d))" and "f S,n (θ SО,n ,θ S -θ SО,n ))" are obtained, but the specific function obtained varies depending on the case.

[0109] In S14, the pitch correction unit 55 calculates the second rotation angle θ at which the equation (2-4) becomes maximum for each diffraction order signal. D Virtual position θ′ D0 is required.

[0110] In S15, the pitch correction unit 55 calculates the order and the virtual position θ′ D0 On the coordinate plane corresponding to the virtual position θ′ of each order D0 is plotted and approximated by a straight line, and the diffraction angle φ' corresponding to the slope of the approximate line obtained by the straight line approximation is obtained as a function of the corrected pitch d.

[0111] In S16, the pitch correction unit 55 determines the corrected pitch d by numerically solving equation (2-5) using the determined diffraction angle φ'(d) and the uncorrected pitch dm determined in S11.

[0112] Next, referring to the flowchart of FIG. 21, in the pitch calculation method of this embodiment, D Axial direction and θ S An example of operation when it is assumed that the same function is used in the axial direction will be described. Figure 21 shows the D Axial direction and θ S 13 is a flowchart showing an example of operation when the same function is assumed in the axial direction.

[0113] In S21 and S22, the same processes as in S11 and S12 in FIG. 20 are performed, respectively. In S23, the correction data acquisition unit 54 calculates the first rotation angle θ using the distribution information acquired in S22. S and the second rotation angle θ D More specifically, the correction data acquisition unit 54 obtains the correction data 43n for each order associated with both the first peak width Δθ S and the actual position θ S0 and the second peak width Δθ D and are obtained as the correction data 43n.

[0114] In S24, the virtual position θ′ for each order is calculated by the above-mentioned formula (3). D0 as a function of the corrected pitch d. In S25 and S26, the same processes as in S15 and S16 in FIG. 20 are performed, respectively.

[0115] As described above, according to this embodiment, the pitch measurement system 100 is configured such that the distribution information acquisition unit acquires distribution information of the diffracted X-rays, the correction data acquisition unit obtains correction data based on this distribution information, and the pitch correction unit corrects the pre-correction pitch using the correction data to obtain the corrected pitch. This allows the pitch measurement system 100 to perform more accurate pitch measurement of the diffraction grating with reduced influence of interference. The diffraction grating 80 is often used as a standard sample for scale calibration and magnification calibration of semiconductor inspection equipment. In this regard, according to the pitch measurement system 100 of the present embodiment, a highly accurate measurement value of the pitch of the diffraction grating 80 can be obtained by a correction process using the correction data 43n. Therefore, since a more accurate pitch measurement can be realized than the conventional θ / 2θ method, reliability can be improved and the user's sense of security can be increased.

[0116] Second embodiment FIG. 22 is a diagram showing an entire pitch measurement system 100A of the second embodiment. In FIG. 22, the same components of the pitch measurement system 100A as those of the pitch measurement system 100 in FIG. 1 are designated by the same reference numerals, and the description thereof will be omitted.

[0117] In the X-ray diffraction apparatus 10A in this embodiment, the detection unit 32A is composed of an analyzer 132a and a detector 32b. The analyzer 132a narrows the line width of the diffracted X-rays generated by the diffraction grating 80 (for example, a Ge(220) 4-bounce channel-cut analyzer). The analyzer 132a is made of a single crystal such as germanium, and the angle at which reflection (= diffraction) occurs on the crystal surface of the analyzer 132a is uniquely determined by the X-ray wavelength.

[0118] Here, when the diffracted X-rays are generated as parallel light having a certain spatial width, the detector 32b in the above-mentioned detection unit 32 detects the diffracted X-rays containing information on that width through the slit 32a. That is, the diffracted X-rays detected by the detector 32b have a thickness equal to the width of the diffracted X-rays, even though the slit 32a is in front of the detector. Therefore, the measurement result of the diffraction spot by the detector 32b is D It becomes thicker by an amount corresponding to the slit width. In this manner, the slit 32a is affected by the spatial width of the diffracted X-rays.

[0119] In contrast, the detector 32A using the analyzer 132a is not affected by the spatial width of the diffracted X-rays, so the detector 32b can detect only the diffraction angle information from the detected diffracted X-rays. Therefore, the diffraction signal based on the diffracted X-rays by the detector 32b becomes relatively narrow.

[0120] In this embodiment, the diffraction signal generated from the diffraction grating 80 passes through the analyzer 132a and is detected by the detector 32b. The detector 32b detects the intensity of the diffracted X-rays that have passed through the analyzer 132a and transmits a diffraction signal indicating the detection result to the pitch calculation device 40. That is, the detector 32b inputs the diffracted X-rays that have passed through the analyzer 132a, detects the intensity of the diffracted X-rays, and transmits a diffraction signal, which is information on the detection result, to the pitch calculation device 40. The X-rays that are incident on the surface of the diffraction grating 80 are divided into reflected X-rays that travel straight without any deviation to the left or right, and diffracted X-rays that are generated due to the unevenness of the diffraction grating 80. The diffracted X-rays generated on the surface of the diffraction grating 80 pass through the analyzer 132a and are detected as a diffraction signal by the detector 32b.

[0121] As described above, the detection unit 32A in this embodiment has the analyzer 132a that narrows the diffracted X-rays generated by the diffraction grating 80, and the detector 32b that detects the intensity of the diffracted X-rays that have passed through the analyzer 132a and transmits a diffraction signal that is the detection result to the pitch calculation device 40. Therefore, the detector 32b can transmit a diffraction signal in which the influence of the width of the diffracted X-rays is mitigated to the pitch calculation device 40, thereby improving the calculation accuracy.

[0122] (Variations) The present disclosure is not limited to the above-described embodiment, and various modifications and variations are possible, and these are also within the scope of the present disclosure.

[0123] (1) In each embodiment, the optical mechanism 20 may be an external component of the X-ray diffraction apparatus 10. In other words, the X-ray diffraction apparatus 10 may be configured with only the support mechanism 30, without including the optical mechanism 20.

[0124] (2) In each embodiment, the pitch calculation device 40 may be configured such that the control unit 50 acquires the pre-correction pitch dm to be corrected from the outside, and the control unit 50 may not be provided with the pitch calculation unit 52. However, it should be noted that the pre-correction pitch dm and the distribution information on which the correction data 43n is based must be measured under the same conditions. In reality, it is not easy to measure the pre-correction pitch dm by an external device under the same conditions as when the correction data 43n is measured by the pitch calculation device 40. Therefore, as shown in FIG. 17, it is preferable to provide the pitch calculation unit 52 in the control unit 50, operate the first rotation stage 33, the second rotation stage 35, and the detector 32b under the same conditions, and have the pitch calculation device 40 obtain both the pre-correction pitch dm and the distribution information. Note that the interval between the timing of measuring the pre-correction pitch dm and the timing of measuring the distribution information can be arbitrarily changed. In the above, the first peak width Δθ S and the second peak width Δθ D In the above example, the half-width method is used to calculate the first peak width Δθ. However, the present invention is not limited to this. The pitch calculation device 40 may calculate the first peak width Δθ by a method such as a tangent method or an area height method. S and the second peak width ΔθD That is, the peak width is not limited to the half-width.

[0125] (3) In each embodiment, the order of each process in the pitch calculation method can be changed as appropriate. For example, in the case of assuming the same function, when calculating each element of the correction data 43n, the first peak width Δθ S and actual position θ S0 may be obtained first, and the second peak width Δθ D In addition, in the case of assuming individual functions, when determining each element of the correction data 43n, the first function may be determined first, or the second function may be determined first.

[0126] The embodiments and modifications may be used in appropriate combination, but detailed description thereof will be omitted. The present disclosure is not limited to the embodiments described above. [Explanation of symbols]

[0127] 10 X-ray Diffraction Equipment 10A X-ray Diffraction Instrument 20 Optical mechanism section 21 X-ray source 22 Condenser mirror 23 Monochromator 30 Support mechanism section 31 Sample stage 32, 32A Detector 32a Slit 32b Detector 33 First Rotation Stage 34 Arm section 35 2nd Rotation Stage 40 Pitch Calculation Device 41 Communications Department 43 Storage section 43n correction data 43p Pitch measurement program 44 Input section 45 Display section 50 Control section 51 Diffraction signal acquisition unit 52 Pitch calculation section 53 Distribution information acquisition unit 54 Correction data acquisition section 55 Pitch correction section 80 Diffraction Grating 100, 100A Pitch Measurement System 132a Analyzer

Claims

1. a first rotation stage that is rotatable with a diffraction grating to be measured attached thereto; an X-ray source that irradiates the diffraction grating with X-rays; a detection unit that detects at least the diffracted X-rays diffracted by the diffraction grating; a second rotation stage to which the detection unit is attached and which is rotatable together with the detection unit; a diffraction signal acquisition unit that acquires a diffraction signal based on the diffracted X-rays detected by the detection unit while the first rotation stage and the second rotation stage are rotated in conjunction with each other so that a ratio of a rotation angle of the first rotation stage to a rotation angle of the second rotation stage is 1:2; a pitch calculation unit that calculates a pre-correction pitch, which is a pre-correction value of the pitch of the diffraction grating, by a θ / 2θ method based on the diffraction signal acquired by the diffraction signal acquisition unit; a distribution information acquisition unit that acquires distribution information of the diffracted X-rays in a two-dimensional coordinate system of a first axis and a second axis, where a value of a rotation angle of the diffraction grating is taken as a first axis and a value of a rotation angle of the detection unit is taken as a second axis, based on a diffraction signal based on the diffracted X-rays detected by the detection unit while the first rotation stage and the second rotation stage are rotated individually; a correction data acquisition unit that determines correction data to be used for correcting the pre-correction pitch based on the distribution information; a pitch correction unit that corrects the pre-correction pitch using the correction data to obtain a corrected pitch; A pitch measurement system comprising:

2. 2. The pitch measurement system according to claim 1, the correction data acquisition unit acquires distribution information of the diffracted X-rays acquired for each order by dividing the information into a first function corresponding to a first axis direction that is a direction along the first axis and a second function corresponding to a second axis direction that is a direction along the second axis, The pitch correction unit calculates the corrected pitch by using the first function and the second function.

3. 2. The pitch measurement system according to claim 1, the correction data acquisition unit acquires, for each order of the diffracted X-rays, a first peak width which is a peak width of the diffracted X-rays in a first axis direction which is a direction along the first axis, an actual position which is a position of a maximum point of the diffracted X-rays in the first axis direction, and a second peak width which is a peak width of the diffracted X-rays in a second axis direction which is a direction along the second axis; The pitch correction unit calculates the corrected pitch using the first peak width, the actual position, and the second peak width.

4. In the pitch measurement system according to any one of claims 1 to 3, the pitch correction unit determines the corrected pitch by numerically analyzing, for the corrected pitch, an arithmetic equation including the pre-corrected pitch, a diffraction angle during correction obtained in a process in which the pitch correction unit calculates the corrected pitch, and the pitch during correction obtained in the process of the calculation.

5. 5. The pitch measurement system according to claim 4, The pitch correction unit determines an actual position, which is the position of the maximum point of the diffracted X-ray in a second axial direction, which is a direction along the second axis, from the uncorrected pitch and Bragg's condition equation, and corrects the uncorrected pitch in calculating the corrected pitch.

6. In the pitch measurement system according to any one of claims 1 to 3, The detection unit includes an analyzer that narrows the line width of the diffracted X-rays generated by the diffraction grating.

7. a first rotation stage that is rotatable with a diffraction grating to be measured attached thereto; an X-ray source that irradiates the diffraction grating with X-rays; a detection unit that detects at least the diffracted X-rays diffracted by the diffraction grating; a second rotation stage to which the detection unit is attached and which is rotatable together with the detection unit; a diffraction signal acquisition unit that acquires a diffraction signal based on the diffracted X-rays detected by the detection unit while the first rotation stage and the second rotation stage are rotated in conjunction with each other so that a ratio of a rotation angle of the first rotation stage to a rotation angle of the second rotation stage is 1:2; a pitch calculation unit that calculates a pre-correction pitch, which is a pre-correction value of the pitch of the diffraction grating, by a θ / 2θ method based on the diffraction signal acquired by the diffraction signal acquisition unit; a distribution information acquisition unit that acquires distribution information of the diffracted X-rays in a two-dimensional coordinate system of a first axis and a second axis, where a value of a rotation angle of the diffraction grating is taken as a first axis and a value of a rotation angle of the detection unit is taken as a second axis, based on a diffraction signal based on the diffracted X-rays detected by the detection unit while the first rotation stage and the second rotation stage are rotated individually; a correction data acquisition unit that determines correction data to be used for correcting the pre-correction pitch based on the distribution information; a pitch correction unit that corrects the pre-correction pitch using the correction data to obtain a corrected pitch; A pitch measurement device comprising:

8. a first rotation stage that is rotatable with a diffraction grating to be measured attached thereto; an X-ray source that irradiates the diffraction grating with X-rays; a detection unit that detects at least the diffracted X-rays diffracted by the diffraction grating; a second rotation stage to which the detection unit is attached and which is rotatable together with the detection unit; A pitch measurement method in a pitch measurement system or a pitch measurement device comprising: a diffraction signal acquiring unit acquiring a diffraction signal based on the diffracted X-rays detected by the detection unit in a state in which the first rotation stage and the second rotation stage are rotated in conjunction with each other so that a ratio of a rotation angle of the first rotation stage to a rotation angle of the second rotation stage is 1:2; A pitch calculation unit calculates a pre-correction pitch, which is a value of the pitch of the diffraction grating before correction, by a θ / 2θ method; a distribution information acquisition unit acquiring distribution information of the diffracted X-rays in a two-dimensional coordinate system of a first axis and a second axis, where the rotation angle of the diffraction grating is a first axis and the rotation angle of the detection unit is a second axis, for each order based on a diffraction signal based on the diffracted X-rays detected by the detection unit while the first rotation stage and the second rotation stage are rotated separately; a correction data acquisition unit determining correction data to be used for correcting the pre-correction pitch based on the distribution information; a pitch correction unit correcting the pre-correction pitch using the correction data to obtain a corrected pitch; The pitch measurement method comprises:

9. a first rotation stage that is rotatable with a diffraction grating to be measured attached thereto; an X-ray source that irradiates the diffraction grating with X-rays; a detection unit that detects at least the diffracted X-rays diffracted by the diffraction grating; a second rotation stage to which the detection unit is attached and which is rotatable together with the detection unit; A pitch measurement program for use in a pitch measurement system or a pitch measurement device comprising: On the computer, a diffraction signal acquiring unit acquiring a diffraction signal based on the diffracted X-rays detected by the detection unit in a state in which the first rotation stage and the second rotation stage are rotated in conjunction with each other so that a ratio of a rotation angle of the first rotation stage to a rotation angle of the second rotation stage is 1:2; A pitch calculation unit calculates a pre-correction pitch, which is a value of the pitch of the diffraction grating before correction, by a θ / 2θ method; a distribution information acquisition unit acquiring distribution information of the diffracted X-rays in a two-dimensional coordinate system of a first axis and a second axis, where the rotation angle of the diffraction grating is a first axis and the rotation angle of the detection unit is a second axis, for each order based on a diffraction signal based on the diffracted X-rays detected by the detection unit while the first rotation stage and the second rotation stage are rotated separately; a correction data acquisition unit determining correction data to be used for correcting the pre-correction pitch based on the distribution information; a pitch correction unit correcting the pre-correction pitch using the correction data to obtain a corrected pitch; Pitch measurement program for executing the above.

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