Method and apparatus for evaluating the shape of a crystal surface of a semiconductor substrate, and computer program for evaluating the shape of a crystal surface of a semiconductor substrate

Abstract

To provide a technique for evaluating a three-dimensional shape of a crystal plane in a semiconductor substrate by a non-destructive method.SOLUTION: Topography image groups including a plurality of X-ray topography images IT1, IT2 are acquired respectively in two arrangement states where directions of diffraction surfaces are orthogonal within a plane of a reference plane being a crystal plane when there is no curve. Rocking curves which are obtained from the acquired two topography image groups and are expressed by an X-ray intensity and an angle in an incident angle direction at the same position on a semiconductor substrate are used, so as to acquire two kinds of Bragg angle shifts at the respective positions on the semiconductor substrate 10. Inclination angles of the crystal plane in each one of the two orthogonal directions are acquired from the two kinds of Bragg angle shifts, so as to determine normal vectors of the crystal plane from the inclination angles. Then, displacements from the reference plane of the crystal plane at the respective positions on the semiconductor substrate 10 are calculated from the determined normal vectors of the crystal plane.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a technique for evaluating the shape of a crystal plane of a semiconductor substrate, and more particularly to a technique for evaluating the three-dimensional shape of a crystal plane. [Background technology]

[0002] Wide-bandgap semiconductors, such as stable gallium oxide (β-Ga2O3), silicon carbide (SiC), and gallium nitride (GaN), have a high breakdown field and are suitable as power device materials for realizing high-voltage, low-loss power devices.

[0003] These wide-gap semiconductors have high thermal and chemical stability, so crystal growth during substrate fabrication must be carried out at high temperatures of 1000°C to 2400°C. This can lead to thermal stresses caused by temperature gradients during crystal growth and in the cooling stage after crystal growth, potentially resulting in curvature of the crystal planes of the fabricated substrate. Furthermore, since flattening the substrate is not easy, mechanical stresses applied during the flattening process can also lead to curvature of the crystal planes of the substrate.

[0004] Such curvature of the crystal plane can cause warping or cracking of the substrate. Furthermore, when epitaxial growth is performed on a substrate with a curved crystal plane, the local crystal orientation changes depending on the position within the plane, which can lead to unevenness in the impurity concentration, etc. within the plane. As such, curvature of the crystal plane can cause various problems. Therefore, there is a strong demand for reducing the curvature of the crystal plane, but in order to reduce the curvature of the crystal plane, it is necessary to evaluate the curvature of the crystal plane using a non-destructive method. Therefore, various methods have been proposed for non-destructively measuring the warpage of single crystal substrates, including the curvature of the crystal plane (see, for example, Patent Document 1). [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Laid-Open No. 2015-004639 Summary of the Invention [Problem to be solved by the invention]

[0006] In Patent Document 1, the radius of curvature of the substrate is calculated based on the width of the rocking curve, but since the width of the rocking curve is also affected by variations in the interplanar spacing of the crystal planes, it is not easy to measure the radius of curvature with sufficient accuracy. Furthermore, while the method disclosed in Patent Document 1 can measure the radius of curvature of the substrate, it cannot evaluate the three-dimensional shape of the crystal planes, which provides information useful for reducing the curvature of the crystal planes.

[0007] The present invention has been made to solve the above-mentioned conventional problems, and aims to provide a technique for evaluating the three-dimensional shape of a crystal plane in a semiconductor substrate by a non-destructive method. [Means for solving the problem]

[0008] In order to achieve at least part of the above objects, the present invention can be realized in the following forms or application examples.

[0009] [Application example 1] A shape evaluation method for evaluating a shape of a crystal plane of a semiconductor substrate, the method comprising the steps of: acquiring a first group of topographic images including a plurality of X-ray topographic images of the crystal plane having different angles of incidence angle direction in an arrangement state in which a direction in the plane of a reference plane of a diffraction plane including a traveling direction of an incident X-ray and a traveling direction of a diffracted X-ray obtained by diffracting the incident X-ray at a reference plane that is a crystal plane when the incident X-ray is not curved is a first direction; acquiring a second group of topographic images including a plurality of X-ray topographic images of the crystal plane having different angles of incidence angle direction in an arrangement state in which a direction in the plane of the reference plane of the diffraction plane is a second direction orthogonal to the first direction; and calculating a rocking curve represented by X-ray intensity at the same position on the semiconductor substrate in each of the plurality of X-ray topographic images included in the first group of topographic images and the angle of the incidence angle direction of each X-ray topographic image. , is the deviation of the apparent Bragg angle obtained by measurement from the reference Bragg angle, which is the Bragg angle on the reference plane. a step of acquiring a first Bragg angle shift; and calculating a Bragg angle shift at each position on the semiconductor substrate from a rocking curve represented by the X-ray intensity at the same position on the semiconductor substrate in each of the plurality of X-ray topographic images included in the second topographic image group and the angle of the incident angle direction of each X-ray topographic image. , the deviation of the apparent Bragg angle from the reference Bragg angle a step of acquiring a second Bragg angle shift; a step of acquiring, for each position on the semiconductor substrate, an inclination angle of the crystal plane with respect to the reference plane in each of the first and second directions from the first and second Bragg angle shifts; a step of determining, for each position on the semiconductor substrate, a normal vector of the crystal plane from the inclination angle of the crystal plane in the first and second directions; and a step of calculating, from the normal vector, a displacement of the crystal plane from the reference plane at each position on the semiconductor substrate.

[0010] Typically, the Bragg angle shift due to the curvature of the crystal plane in a direction perpendicular to the diffraction plane is negligibly small compared to the Bragg angle shift due to the curvature of the crystal plane in a direction parallel to the diffraction plane. Therefore, according to this application example, the normal vector of the crystal plane used to calculate the shape of the crystal plane can be more accurately determined from the first and second Bragg angle shifts, and the three-dimensional shape of the crystal plane can be accurately evaluated.

[0011] [Application example 2] A shape evaluation method according to Application Example 1, wherein a beam diameter of the incident X-rays is large enough to irradiate the entire surface of the semiconductor substrate, and the steps of acquiring the first and second topography image groups each include the steps of changing the angle of incidence direction and capturing X-ray topography images formed on an imaging element by an imaging element arranged in the traveling direction of the diffracted X-rays.

[0012] According to this application example, an X-ray topography image of the entire surface of the semiconductor substrate can be obtained by photographing with the imaging element, so that the X-ray topography image used to evaluate the three-dimensional shape of the crystal plane can be obtained in a shorter time.

[0013] [Application example 3] In the shape evaluation method according to Application Example 1, a beam diameter of the incident X-ray is a thickness that irradiates the semiconductor substrate in a point-like manner, and the steps of acquiring the first and second topography image groups include the steps of scanning an irradiation position of the incident X-ray on a surface of the semiconductor substrate by moving the semiconductor substrate in first and second movement directions that are parallel to the reference plane and perpendicular to each other, and scanning the incident X-ray for each irradiation position. corner and changing the angle of the direction to acquire the intensity of the diffracted X-rays using an X-ray detector arranged in the direction of propagation of the diffracted X-rays.

[0014] According to this application example, since the beam diameter of the incident X-ray is narrowed, the required level of parallelism for the incident X-ray is lowered, and therefore, X-ray topography images used for evaluating the three-dimensional shape of crystal surfaces can be obtained more easily.

[0015] [Application example 4] In the shape evaluation method according to Application Example 1, a beam diameter of the incident X-ray is a diameter that irradiates the semiconductor substrate in a point-like manner, and the steps of acquiring the first and second topography image groups each include: corner changing the angle of the incident light; corner and scanning the irradiation position of the incident X-rays on the surface of the semiconductor substrate by moving the semiconductor substrate in first and second movement directions that are parallel to the reference plane and perpendicular to each other, for each angle of the direction, and acquiring the intensity of the diffracted X-rays with an X-ray detector arranged in the traveling direction of the diffracted X-rays.

[0016] In this application example, the beam diameter of the incident X-rays is also narrowed, which reduces the required level of parallelism for the incident X-rays, making it easier to obtain X-ray topography images used to evaluate the three-dimensional shape of crystal surfaces.

[0017] [Application example 5] In the shape evaluation method according to any one of Application Examples 1 to 4, the step of acquiring the Bragg angle shift from the rocking curve includes fitting a peak shape function to the rocking curve and calculating a value of the fitted peak shape function. The difference between the peak position and the peak position of the peak shape function at the reference plane and calculating a peak shift corresponding to the Bragg angle shift.

[0018] According to this application example, even if the number of multiple X-ray topography images included in the topography image group is reduced, the resolution of the peak shift corresponding to the Bragg angle shift can be increased, making it possible to more easily evaluate the three-dimensional shape of the crystal plane while maintaining high evaluation accuracy of the three-dimensional shape of the crystal plane.

[0019] The present invention can be realized in various forms, such as a method and apparatus for evaluating the shape of a crystal plane in a semiconductor substrate, a computer program for implementing at least some of the functions of the method and apparatus, a recording medium on which the computer program is recorded, a data signal including the computer program and embodied in a carrier wave, and the like. [Brief explanation of the drawings]

[0020] [Figure 1] FIG. 1 is an explanatory diagram showing an overview of X-ray topography used to evaluate the shape of a crystal plane of a substrate. [Figure 2] An explanatory diagram showing how incident X-rays are diffracted on a curved crystal plane. [Figure 3] FIG. 1 is an explanatory diagram showing how the apparent Bragg angle deviates from the reference Bragg angle due to curvature of the crystal plane. [Figure 4] FIG. 1 is an explanatory diagram showing how the apparent Bragg angle deviates from the reference Bragg angle due to curvature of the crystal plane. [Figure 5] FIG. 1 is an explanatory diagram showing how the apparent Bragg angle deviates from the reference Bragg angle due to curvature of the crystal plane. [Figure 6] FIG. 1 is an explanatory diagram showing how the apparent Bragg angle deviates from the reference Bragg angle due to curvature of the crystal plane. [Figure 7] FIG. 1 is an explanatory diagram showing how the apparent Bragg angle deviates from the reference Bragg angle due to curvature of the crystal plane. [Figure 8] FIG. 10 is an explanatory diagram showing how the Bragg angle shift is obtained from a group of topographic images. [Figure 9] FIG. 10 is an explanatory diagram showing an image in which feature amounts of fitted peak shape functions are mapped. [Figure 10] FIG. 10 is an explanatory diagram showing an image in which feature amounts of fitted peak shape functions are mapped. [Figure 11] FIG. 10 is an explanatory diagram showing the results of evaluation of the shape of a crystal plane in an example of the first embodiment. [Figure 12]FIG. 2 is an explanatory diagram showing how an X-ray topography image used for evaluating the shape of a crystal plane of a substrate is obtained. [Figure 13] FIG. 10 is an explanatory diagram showing the results of evaluation of the shape of a crystal plane in an example of the second embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0021] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described in detail below with reference to the following examples. A: First embodiment: A1. Overview of X-ray topography: A2. Diffraction on curved crystal faces: A3. Bragg angle shift due to curvature of crystal plane: A4.Evaluation of crystal face shape: A5. Example of the first embodiment: B: Second embodiment: B1. Acquisition of X-ray topography images in the second embodiment: B2. Example of the second embodiment: C. Variations:

[0022] A. First embodiment: A1. Overview of X-ray topography: Figure 1 is an explanatory diagram showing an overview of X-ray topography used to evaluate the shape of a crystal plane of a substrate 10. Figures 1(a) and 1(b) show how images used to evaluate the three-dimensional shape of a crystal plane (hereinafter simply referred to as "shape") are captured by X-ray topography. Here, the crystal plane of the substrate 10 refers to a specific crystal plane (hereinafter simply referred to as "crystal plane") on the surface portion of the substrate 10.

[0023] 1(a), in X-ray topography, as shown by the dashed-dotted line, an X-ray beam (incident X-ray) BXI is irradiated onto the substrate 10, which has high parallelism and monochromaticity and a wide beam diameter so that the entire surface of the substrate 10 can be irradiated. As the incident X-ray BXI irradiated onto the substrate 10 in this manner, it is preferable to use synchrotron X-rays, which have high parallelism, monochromaticity, and brightness, a wide beam diameter, and a wavelength that can be tuned over a wide wavelength range. However, it is also possible to use X-rays other than synchrotron X-rays as the incident X-rays, as long as the X-ray beam has sufficiently high parallelism and monochromaticity and a sufficiently wide beam diameter.

[0024] The incident X-rays BXI irradiated onto the substrate 10 are diffracted by the crystal plane of the substrate 10. Then, the diffracted X-ray beam (diffracted X-rays) BXD travels from the substrate 10 towards the imaging element 20 as indicated by the two-dot chain line, and is irradiated onto the imaging element 20. In this way, the incident X-rays BXI irradiated onto the substrate 10 are diffracted by the crystal plane of the substrate 10, and the diffracted X-rays BXD are irradiated onto the imaging element 20, whereby an X-ray topography image IT1 of the crystal plane of the substrate 10 is formed on the imaging element 20.

[0025] The wavelength of the incident X-rays BXI, the angle of the reference plane of the substrate 10 in the ω direction (incident angle direction), and the arrangement of the image sensor 20 in the ω direction are adjusted as appropriate so that the diffracted X-rays BXD travel toward the image sensor 20. Here, the reference plane of the substrate 10 refers to the crystal plane of the substrate 10 when it is not curved.

[0026] An image representing the X-ray topography image IT1 is obtained by capturing the X-ray topography image IT1 formed on the image pickup element 20 in this manner using the image pickup element 20. Note that an image representing the X-ray topography image IT1 can also be considered as an X-ray topography image IT1, and therefore, hereinafter, unless a particular distinction is required, an image representing the X-ray topography image IT1 will also be referred to as the X-ray topography image IT1.

[0027] 1(a), a Cartesian coordinate system (x, y, z) is set so that the reference plane of the substrate 10 is the xy plane, and the propagation directions of the incident X-rays BXI and diffracted X-rays BXD are parallel to the yz plane. Therefore, the yz plane in the example of FIG. 1(a), i.e., the plane including the propagation directions of the incident X-rays BXI and diffracted X-rays BXD, is also referred to as the "diffraction plane." Note that the same coordinate system as FIG. 1(a) will be used in the following description.

[0028] In the first embodiment, as shown by the dashed line in Fig. 1(a), the angle of the substrate 10 in the ω direction is sequentially changed to acquire a group of topography images including a plurality of X-ray topography images IT1 with different angles in the ω direction. The group of topography images acquired in this manner is used to evaluate the shape of the crystal plane of the substrate 10, as will be described in detail later.

[0029] Figure 1(b) shows how a group of topography images is acquired by rotating the substrate 10 by 90° in-plane, i.e., by 90° in the φ direction, from the state shown in Figure 1(a). Figure 1(b) differs from Figure 1(a) in that the substrate 10 is rotated by 90° in-plane and that the X-ray topography image IT2 formed on the imaging element 20 changes as the substrate 10 is rotated in-plane. Other points are the same as Figure 1(a), so a description thereof will be omitted here.

[0030] 1, the crystal plane of the substrate 10, from which the incident X-rays BXI are diffracted, is parallel to the surface of the substrate 10, that is, the orientation of the crystal plane is selected so that the diffraction of the incident X-rays BXI is symmetrically reflected. Therefore, in FIG. 1(b), X-ray topography is performed with the substrate 10 rotated 90° in-plane, but if the crystal plane and the surface of the substrate 10 are not parallel, the substrate 10 is rotated appropriately in the y-axis direction so that the direction of the reference plane matches the state in FIG. 1(a).

[0031] In the crystal plane shape evaluation method of the first embodiment, as shown in Figures 1(a) and 1(b), a group of topography images is acquired in each of two arrangement states in which the directions of the diffraction plane (yz plane) are orthogonal within the reference plane. Then, as will be described in detail later, the group of topography images in these two arrangement states can be used to evaluate the shape of the crystal plane of the substrate 10.

[0032] The plurality of images representing the X-ray topography images IT1 and IT2, or a group of topography images including the plurality of X-ray topography images IT1 and IT2, are supplied as image data to a computer (not shown). The computer then performs processing on the supplied group of topography images, as will be described later, to generate an evaluation result of the shape of the crystal plane of the substrate 10.

[0033] Therefore, the evaluation technique for the three-dimensional shape of a crystal face according to the present invention can be realized as a computer program that causes a computer to execute the steps of acquiring a group of topographic images supplied as image data and performing the various processing steps described below.

[0034] Furthermore, the technique for evaluating the three-dimensional shape of a crystal plane according to the present invention can be realized as a shape evaluation device having a functional unit for acquiring a group of topographic images and a functional unit for performing each process described below. In this case, at least a part of each functional unit can be realized by hardware.

[0035] A2. Diffraction on curved crystal faces: FIG. 2 is an explanatory diagram showing how incident X-ray BXI is diffracted at a curved crystal plane S. FIG. 2(a) shows how incident X-ray BXI is diffracted at the curved crystal plane S projected onto the diffraction plane PDF, and FIG. 2(b) shows how g-vector g hkl As shown in Figure 2, vectors are represented by bold symbols in drawings and formulas, but in the text of this specification, vectors are represented by adding the word "vector" before the symbol.

[0036] Here, let us consider how incident X-rays BXI are diffracted by a curved crystal plane S as shown in Figure 2(a). First, the crystal plane S from which incident X-rays BXI are diffracted is generally expressed as a set of points P(x,y,z) such that the scalar function f(P) for point P(x,y,z) in a three-dimensional Cartesian coordinate system (x,y,z) satisfies the following equation (1):

number

[0037] In this way, since the crystal plane S is defined by the scalar function f(P), the scalar function f(P) can be considered to represent the crystal plane S. The gradient of the scalar function f(P) expressed by the following equation (2) is the normal vector N of the crystal plane S at point P.

number

[0038] As can be seen from the above formula (2), the normal vector N depends on the point P(x, y, z), but does not depend on the way the Cartesian coordinate system (x, y, z) is used. Therefore, in this specification, as shown in Figures 1 and 2, the reference plane PRF of the substrate 10 (Figure 1) is defined as the xy plane, and the diffraction plane PDF is defined as the yz plane. By using the Cartesian coordinate system (x, y, z) in this way, as shown in Figure 2(a), z (= f(x, y)) at the point P(x, y, z) represents the displacement of the crystal plane S from the reference plane PRF (hereinafter, also simply referred to as "displacement").

[0039] Then, at any point P on the reference plane PRF C (x C ,y C ) is given by the following equation (3), so the shape of the crystal plane S is uniquely determined by the normal vector N of the crystal plane S.

number

[0040] The above equation (3) is C (x C ,y C ) is the displacement z from the origin P0(x0,y0) to the point P C (x C ,y C ) along any path C leading to the vector N(P(x,y)), i.e., the gradient of the function f(x,y) is given by integrating the normal vector N(P(x,y)).

[0041] In this way, the shape of the crystal surface S is determined by the normal vector N(P(x,y)), so the shape of the crystal surface S can be evaluated by obtaining the normal vector N(P(x,y)).

[0042] In the first embodiment, as described above, X-ray topography obtained by diffraction of incident X-rays BXI is used to evaluate the shape of the crystal plane S. The Bragg condition (also called "Bragg's law"), which is a diffraction condition of such X-rays, is given by the wave vector k of the incident X-rays BXI. i , wave vector k of the diffracted X-rays BXD d and g vector g hkl Using this, it is expressed by the following equation (4).

number

[0043] The g vector g in the above equation (4) hkl is the reciprocal lattice vector of the crystal plane S, and its direction coincides with the normal direction of the crystal plane (hkl) where diffraction occurs, i.e., the direction of the normal vector N of the specific crystal plane S at the surface portion of the substrate 10 (FIG. 1).

[0044] As described above, the incident X-rays BXI irradiating the substrate 10 have sufficiently high parallelism and monochromaticity, so the wave vector ki is constant at each position on the substrate 10 irradiated with the incident X-rays BXI. On the other hand, the wave vector k d is determined by the arrangement of the image sensor 20 in the ω direction, as shown in FIG.

[0045] Thus, the wave vectors k of the incident X-ray BXI and the diffracted X-ray BXD i ,k d is known, so the g vector g hkl is the vector function g of the point P(x,y) on the reference plane PRF hkl (x,y) and the vector function g hkl By treating (x, y) as the normal vector N(P(x, y)), the shape of the crystal plane S can be determined as explained in the above formula (3).

[0046] For the reference plane PRF, i.e., the crystal plane S of the uncurved substrate 10, the Bragg condition corresponding to the g vector g0 is the lattice spacing d, the diffraction order n, and the Bragg angle θ B0 Using this, it is expressed by the following equation (5).

number

[0047] On the other hand, as shown in Figure 2(b), the g vector g at point P(x,y) hkl (x,y) is the vector g' whose projection onto the diffraction surface PDF hkl Let the angle formed by (x,y) be χ, and the vector g' hkl If the angle that (x, y) makes with the g vector g0 of the reference plane PRF is Δω, then the g vector g at point P(x, y) is hkl The Bragg condition corresponding to (x,y) is the interplanar spacing d, the diffraction order n, and the apparent Bragg angle θ obtained by measurement using X-ray diffraction. B Using (x, y), it is expressed by the following equation (6).

number

[0048] As can be seen from the above equations (5) and (6), when the crystal plane S is curved in the direction of the diffraction plane PDF as shown in Figure 2(a), the g vector g at point P(x, y) hkl Apparent Bragg angle θ corresponding to (x,y) B (x,y) is the Bragg angle θ corresponding to the g vector g0 B0 It deviates by Δω from

[0049] On the other hand, the crystal plane S is curved in the direction perpendicular to the diffraction plane PDF, and the g vector g hkl If (x,y) is not parallel to the diffraction plane PDF, the apparent Bragg angle θ B (x, y) is shifted according to the factor cos χ in equation (6). However, in practice, cos χ ≒ 1, so the apparent Bragg angle θ B The deviation of (x, y) is negligibly small compared to the deviation of Δω.

[0050] Thus, the apparent Bragg angle θ due to the factor cos χ B Since the deviation of (x, y) is negligibly small, if we set cos χ=1, as can be seen from the above equations (5) and (6), the vector g' hkl The angle Δω between (x, y) and the g vector g0 is the Bragg angle θ defined by the g vector g0 of the reference plane PRF. B , that is, the Bragg angle (reference Bragg angle) θ at the reference plane PRF B0 From this, the apparent Bragg angle θ B It is given as an angle subtracted from (x,y).

[0051] As can be seen from the above explanation, the vector g' hkl (x,y) is the g vector g on the crystal plane S hkl Since (x,y) is projected onto the diffraction surface PDF, the vector g' hkl The angle Δω between (x, y) and the g vector g0 coincides with the tilt angle of the crystal plane S with respect to the reference plane PRF in the direction of the diffraction plane PDF.

[0052] A3. Bragg angle shift due to curvature of crystal plane: 3 to 7 show that the apparent Bragg angle θ B (x, y) is the reference Bragg angle θ B0 3 to 7, the diagrams with sub-numbers (a) show the shape of the curved crystal plane, and the diagrams with sub-numbers (b) show the normal vector N(P(x,y)) of the curved crystal plane. Also, the diagrams with sub-numbers (c) show the apparent Bragg angle θ B Reference Bragg angle θ of (x,y) B0 Deviation from (θ B (x,y)-θ B0 ) is shown. In the following, the deviation (θ B (x,y)-θ B0 ) is also called the "Bragg angle shift."

[0053] 3 to 7, the shape of the curved crystal plane is an ellipsoid with radii of curvature a, b, and c in the yz, zx, and xy planes, respectively. Therefore, the displacement z of the crystal plane from the reference plane PRF (FIG. 2) is given by the following equation (7):

number

[0054] Then, the radii of curvature a, b, and c were appropriately set, and the shape of the crystal plane was calculated when the outer shape of the substrate was a square with sides of 50 mm (sub-number (a) in Figures 3 to 7). Based on the calculated shape of the crystal plane, the normal vector N(P(x, y)) of the curved crystal plane was calculated (sub-number (b) in Figures 3 to 7). Next, the reference Bragg angle θ B0 is set to 30°, and the apparent Bragg angle θ B (x, y) and the Bragg angle shift (θ B (x,y)-θ B0 ) was calculated (sub-number (c) in Figures 3 to 7).

[0055] Figure 3 shows the shape of the crystal plane (Fig. 3(a)), the normal vector N(P(x,y)) (Fig. 3(b)), and the Bragg angle shift (θ B (x,y)-θ B0 ) (Fig. 3(c)). In the example of Fig. 3, the radii of curvature a, b, and c are set to 10 km, 10 m, and 10 m, respectively.

[0056] In this case, as shown in FIG. 3(a), the height z of the crystal plane at the end in the y direction (y=±25 mm) (i.e., the displacement z of the crystal plane S in FIG. 2 from the reference plane PRF) is about 31 μm higher than the center in the y direction (y=0 mm), which is the valley. As shown in FIG. 3(b), the x-direction component of the normal vector N(P(x,y)) is zero (0). By curving the crystal plane in this way, the Bragg angle deviation (θ B (x,y)-θ B0 ) is 0° (deg) at the center in the y direction (y=0 mm), and its absolute value is approximately 0.14° at the ends in the y direction (y=±25 mm).

[0057] Figure 4 shows the shape of the crystal plane (Fig. 4(a)), the normal vector N(P(x,y)) (Fig. 4(b)), and the Bragg angle shift (θ B (x,y)-θ B0 ) (Fig. 4(c)). In the example of Fig. 4, the curvature radii a, b, and c are set to 10 m, 10 km, and 10 m, respectively.

[0058] In this case, as shown in Figure 4(a), the height z of the crystal plane at the end in the x direction (x = ±25 mm) is about 31 μm higher than the center in the x direction (x = 0 mm), which is the valley. And, as shown in Figure 4(b), the y-direction component of the normal vector N(P(x, y)) becomes zero. By curving the crystal plane in this way, the Bragg angle shift (θ B (x,y)-θ B0) is 0 arcsec at the center of the x direction (x = 0 mm). And even at the end of the x direction (x = ±25 mm) where the absolute value of the Bragg angle shift is maximum, the Bragg angle shift (θ B (x,y)-θ B0 ) is at most about 0.37 arc seconds.

[0059] This is because, as mentioned above, the g vector g hkl When (x,y) is not parallel to the diffraction plane PDF (Fig. 2), the apparent Bragg angle θ B (x,y) is a g vector g hkl Although there is a shift according to the factor cos χ corresponding to the deviation from the diffraction plane PDF of (x, y), cos χ ≒ 1, so the apparent Bragg angle θ according to the factor cos χ B This is because the (x,y) shift is negligibly small. B (x,y)-θ B0 ) for g vector g hkl Since the effect of deviation from the (x, y) diffraction surface PDF is small, curvature in the direction perpendicular to the diffraction surface is usually not detected.

[0060] Figure 5 shows the shape of the crystal plane (Fig. 5(a)), the normal vector N(P(x,y)) (Fig. 5(b)), and the Bragg angle shift (θ B (x,y)-θ B0 ) (Fig. 5(c)). In the example of Fig. 5, the curvature radii a, b, and c are set to 10 m, 10 m, and 10 m, respectively.

[0061] In this case, as shown in Figure 5(a), the height z of the crystal plane at the four corners ((x, y) = (±25 mm, ±25 mm)) is approximately 63 μm higher than the center of the xy plane ((x, y) = (0 mm, 0 mm)), which is the bottom. By curving the crystal plane in this way, the Bragg angle shift (θ B (x,y)-θ B0 ) has an absolute value of approximately 0.14° at the end of the y direction (y = ±25 mm). On the other hand, as mentioned above, the g vector g hklThe deviation of (x,y) from the diffraction plane PDF is the Bragg angle shift (θ B (x,y)-θ B0 ), so that the Bragg angle shift (θ B (x,y)-θ B0 ) is almost constant, and the Bragg angle shift (θ B (x,y)-θ B0 ) is the same as the case where the curvature direction is a cylindrical surface parallel to the diffractive surface (FIG. 3(c)).

[0062] Figure 6 shows the shape of the crystal plane (Figure 6(a)), the normal vector N(P(x,y)) (Figure 6(b)), and the Bragg angle shift (θ B (x,y)-θ B0 ) (Fig. 6(c)). In the example of Fig. 6, the curvature radii a, b, and c are set to 2 m, 10 m, and 10 m, respectively.

[0063] In this case, as shown in Figure 6(a), the height z of the crystal plane at the end (x = ±25 mm) in the x direction is about 800 μm higher than the center (x = 0 mm) in the x direction, which is the valley. Due to the curvature of the crystal plane in this way, the Bragg angle shift (θ B (x,y)-θ B0 ) becomes detectable.

[0064] Figure 7 shows the shape of the crystal plane (Figure 7(a)), the normal vector N(P(x,y)) (Figure 7(b)), and the Bragg angle shift (θ B (x,y)-θ B0 ) (Fig. 7(c)). In the example of Fig. 7, the radii of curvature a, b, and c are set to 10 m, 10 m, and 10 m, respectively. Here, i is the imaginary unit, i.e., the square root of -1.

[0065] In this case, as shown in Figure 7(a), the height z of the crystal plane ranges from approximately -31 μm to +31 μm, and in the x direction, it is lowest at the center (x = 0 mm), while in the y direction, it is highest at the center (y = 0 mm). Even when the crystal plane is curved in this way, the curvature in the x direction, which is perpendicular to the diffraction plane, does not change the Bragg angle shift (θ B (x,y)-θ B0 ), so that the Bragg angle shift (θ B (x,y)-θ B0 ) is approximately constant. On the other hand, in the y direction, the shape of the crystal plane is convex downward in the example of FIG. 3, whereas the shape of the crystal plane is convex upward in the example of FIG. 7. Therefore, the Bragg angle shift (θ B (x,y)-θ B0 ) is a form obtained by inverting FIG. 3(c) in the y direction.

[0066] A4.Evaluation of crystal face shape: Figure 8 shows the Bragg angle shift (θ B (x,y)-θ B0 8(a) shows the topography image group SIT obtained by sequentially changing the angle of the substrate 10 (FIG. 1) in the ω direction and capturing the X-ray topography images IT1 / IT2 formed on the image sensor 20, as described above, and FIG. 8(b) shows the Bragg angle shift (θ B (x,y)-θ B0 ) is acquired.

[0067] As shown in FIG. 8(a), the topography image group SIT includes (2M+1) X-ray topography images IT1 / IT2. The Bragg angle shift (θ B (x,y)-θ B0 ), first, for each of the X-ray topography images IT1 / IT2 included in the topography image group SIT, the X-ray intensities at the hatched pixels (i.e., the same positions on the substrate 10) are obtained.

[0068] Next, the angle ω in the ω direction when each X-ray topography image IT1 / IT2 was taken i (-M≦i≦+M) and angle ω i 8(b) is obtained by correlating the X-ray intensity at the same position on the substrate 10 with the X-ray intensity at the same position on the substrate 10. Then, a peak shape function (e.g., Gaussian or Lorentzian) is fitted to the obtained rocking curve using a well-known fitting method such as the least squares method.

[0069] The difference between the peak position of the fitted peak shape function and the peak position of the peak shape function on the reference plane (i.e., ω0) shown by the dashed line is the Bragg angle shift (θ B (x,y)-θ B0 ) As mentioned above, the g vector g corresponding to the normal vector N(P(x,y)) hkl Vector g', which is the projection of (x,y) onto the diffraction plane PDF (Figure 2) hkl The angle Δω between (x, y) and the g vector g0 is the Bragg angle shift (θ B (x,y)-θ B0 ) with the inverted sign (θ B0 -θ B (x,y)

[0070] In this way, the normal vector N(P(x,y)) (i.e., the g vector g hkl (x,y)) onto the diffraction plane PDF (Figure 2), which is the vector g' hkl Since (x, y) is determined, the normal vector N(P(x, y)) of the crystal plane S can be determined by using a topography image group SIT including X-ray topography images IT1 / IT2 obtained for two arrangement states in which the directions of the diffraction plane PDF are orthogonal within the reference plane. Then, by integrating the normal vector N(P(x, y)), the displacement z of the crystal plane S from the reference plane PRF can be calculated, and therefore, according to the first embodiment, the shape of the crystal plane S can be evaluated.

[0071] A5. Example of the first embodiment: To demonstrate that the crystal plane shape can be properly evaluated using the crystal plane shape evaluation method of the first embodiment, a β-Ga2O3 substrate was prepared as a sample, and the shape of the crystal plane was obtained. Specifically, a rectangular β-Ga2O3 substrate with a (001) surface orientation was prepared as the sample. The prepared substrate measured 10 mm × 15 mm and was 0.65 mm thick, with the short and long sides of the substrate parallel to the <0010> axis (b-axis) and the <0100> axis (a-axis), respectively. Furthermore, both sides of the substrate were subjected to chemical mechanical polishing to flatten the surface.

[0072] X-ray topography was performed by irradiating the substrate surface with a monochromatic X-ray beam of wavelength λ = 1.9265 Å at an incident angle of 20° and using symmetric reflection with a g-vector g = 002. By rotating the substrate by 90° in-plane, the diffraction plane, i.e., the propagation direction of the X-ray beam, can be made parallel to the

[0010] or

[0100] direction.

[0073] In each of these two directions, the angle in the ω direction was changed sequentially, and X-ray topography images with different angles in the ω direction were formed on an image sensor (CCD). The angle in the ω direction was changed in increments of 0.0002 degrees. The X-ray topography images formed on the image sensor were then photographed to obtain a group of 201 topography images.

[0074] After acquiring the topography images, a peak shape function was fitted to the rocking curve, which is expressed as the angle ω and the X-ray intensity, for each pixel corresponding to the same position on the substrate for 201 X-ray topography images. Three feature quantities of the fitted peak shape function, namely, the maximum intensity, the half-width (full width at half maximum: FWHM), and the peak shift (Bragg angle shift), were then calculated for each pixel of the X-ray topography image.

[0075] 9 and 10 are explanatory diagrams showing images in which feature quantities of fitted peak shape functions are mapped. In Fig. 9 and Fig. 10, the figures with sub-numbers (a) show images in which maximum intensity is mapped, the figures with sub-numbers (b) show images in which full width at half maximum (FWHM) is mapped, and the figures with sub-numbers (c) show images in which Bragg angle shift is mapped. Furthermore, Fig. 9 shows an image in which the X-ray beam propagation direction is parallel to the

[0100] direction, and Fig. 10 shows an image in which the X-ray beam propagation direction is parallel to the

[0010] direction.

[0076] As shown in Figures 9(a) and 10(a), the maximum intensity was higher in the center of the substrate, indicating that the crystalline quality of the substrate was higher in the center and lower in the peripheral area. Also, as shown in Figures 9(b) and 10(b), the half-width was approximately 20 arcsec on average and was nearly uniform across the entire substrate.

[0077] As shown in Figures 9(c) and 10(c), the Bragg angle shift varied in the range of -11 to 8 arc seconds on the substrate. This indicates that the crystal plane of the β-Ga2O3 substrate used as the sample is curved. Although the variation in the interplanar spacing of the crystal plane affects the half-width, its effect on the Bragg angle shift is minor. Therefore, the Bragg angle shifts shown in Figures 9(c) and 10(c) represent the curvature of the crystal plane with high accuracy.

[0078] Next, the normal vector N(P(x,y)) of the crystal plane at point P(x,y) on the substrate is obtained from the Bragg angle shift thus obtained. As mentioned above, the angle Δω calculated from the Bragg angle shift is calculated by the g vector g of the crystal plane S (Figure 2). hkl Vector g' is the projection of (x,y) onto the diffraction plane PDF. hkl The angle between (x, y) and the g vector g0 of the reference plane PRF, that is, the g vector g hkl This is the angle between (x,y) and the g vector g0.

[0079] As shown in Figures 9 and 10, the Bragg angle shifts used to calculate the angle Δω are obtained for each of the two arrangements where the diffraction plane directions are orthogonal within the reference plane, and are therefore obtained for two diffraction planes that are orthogonal to the reference plane. Therefore, if the angle Δω calculated for each of the two orthogonal diffraction planes is treated as a component parallel to both the diffraction plane and the reference plane, the g vector g of the crystal plane can be calculated as follows: hkl (x, y), i.e., the normal vector N(P(x, y)), can be determined. Then, by integrating the normal vector N(P(x, y)) thus determined, the shape of the crystal plane can be obtained.

[0080] Figure 11 is an explanatory diagram showing the results of evaluating the shape of the crystal plane in an example of the first embodiment. Figure 11(a) shows the projection onto the xy plane of the normal vector N(P(x,y)) determined from the Bragg angle shift, and Figure 11(b) shows the shape of the crystal plane calculated from the normal vector N(P(x,y)) shown in Figure 11(a).

[0081] As shown in Figure 11(a), the normal vector N(P(x,y)) at point P(x,y) on the substrate corresponding to each pixel can be determined from the Bragg angle shift shown in the map images of Figures 9(c) and 10(c). Note that although the normal vector N(P(x,y)) is determined for each pixel in the map images of Bragg angle shift shown in Figures 9(c) and 10(c), for convenience of illustration, in Figure 11(a), normal vectors N(P(x,y)) are drawn only for 20 grid points in the x direction and 30 grid points in the y direction.

[0082] By integrating the normal vector N(P(x, y)) shown in Figure 11(a) (see equation (3) above), the height z of the crystal plane for each pixel, i.e., the shape of the crystal plane, can be obtained, as shown in Figure 11(b). Note that the starting point P0(x0, y0) of the path C used to integrate the normal vector N(P(x, y)) was the point at the left end of Figure 11(b) where (x, y) = (0 mm, 0 mm).

[0083] As described above, according to the first embodiment, a group of topographic images including a plurality of X-ray topographic images is acquired in each of two arrangement states in which the directions of the diffraction plane (yz plane) are orthogonal within the reference plane, and the Bragg angle shift, normal vector, and height of the crystal plane are sequentially determined from the group of topographic images, thereby making it possible to evaluate the three-dimensional shape of the crystal plane as shown in FIG. 11(b).

[0084] B: Second embodiment: B1. Acquisition of X-ray topography images in the second embodiment: 12 is an explanatory diagram showing how an X-ray topography image used to evaluate the shape of a crystal plane of a substrate 10 is acquired in the second embodiment. The second embodiment differs from the first embodiment in that it uses incident X-rays BXIa with a narrow beam diameter that are irradiated in a point-like manner onto the substrate 10, and in that it uses an X-ray detector 20a with a single detection element corresponding to the narrow beam of diffracted X-rays BXDa.

[0085] In this way, in the second embodiment, the beam diameter of the incident X-rays BXIa is narrowed, so if the monochromaticity is sufficiently high, the parallelism can be made lower than that of the incident X-rays BXI in the first embodiment. Therefore, an X-ray beam obtained by monochromatizing an X-ray beam from a general X-ray source using a monochromator can be used as the incident X-rays BXIa.

[0086] In the second embodiment, the substrate 10 is irradiated with the incident X-rays BXIa in a point-like manner, and therefore the substrate 10 is moved in the X and Y directions parallel to the xy plane, whereby the surface of the substrate 10 is scanned with the incident X-rays BXIa.

[0087] Then, at each position (irradiation position) on the substrate 10 where the incident X-ray BXIa is irradiated in a point form, the angle of the substrate 10 in the ω direction is sequentially changed, and the intensity of the diffracted X-ray BXDa is acquired by the X-ray detector 20a. As a result, a group of rocking curves including rocking curves at each position on the substrate 10 is acquired.

[0088] The acquired rocking curves include the intensities of the diffracted X-rays BXDa at each angle in the ω direction for each position on the substrate 10. Therefore, the rocking curves include an X-ray topography image that represents the intensities of the diffracted X-rays BXDa for each position on the substrate 10.

[0089] In this way, the group of rocking curves acquired in the second embodiment includes X-ray topography images at each of a plurality of angles in the ω direction, and is therefore equivalent to a group of topography images including a plurality of X-ray topography images at different angles in the ω direction. Also in the second embodiment, as in the first embodiment, the Bragg angle shift at each position on the substrate 10 can be determined from the group of acquired topography images (i.e., the group of rocking curves).

[0090] In the second embodiment, at the time when the topography image group is acquired, the rocking curve has already been acquired at each position on the substrate 10. Therefore, it is possible to omit the step of acquiring the X-ray intensity at the same position on the substrate 10 from each X-ray topography image included in the topography image group to obtain the rocking curve.

[0091] Also in the second embodiment, as shown in Figures 12(a) and 12(b), a group of topography images (i.e., a group of rocking curves) is acquired for each of two arrangement states in which the directions of the diffraction planes are orthogonal within the reference plane, and the Bragg angle shift is determined from the group of topography images in each of the two arrangement states. As in the first embodiment, this allows the normal vector N(P(x, y)) at each position on the substrate 10 to be determined, and the determined normal vector N(P(x, y)) can be used to evaluate the shape of the crystal plane of the substrate 10.

[0092] In the second embodiment, in order to acquire a group of topography images (group of rocking curves), the irradiation position on the substrate 10 is scanned and rocking curves are acquired at each position on the substrate 10, but it is also possible to acquire a group of topography images by other methods.

[0093] For example, it is possible to obtain an X-ray topography image by scanning the irradiation position on the substrate 10 while fixing the angle in the ω direction and obtaining the intensity of the diffracted X-rays BXDa at each position on the substrate 10. In this case, by changing the angle in the ω direction and obtaining an X-ray topography image at each angle in the ω direction, it is possible to obtain a group of topography images similar to those in the first embodiment.

[0094] In the second embodiment, the beam diameter of the incident X-rays BXIa is narrowed, so the required level of parallelism for the incident X-rays BXIa is lowered. Therefore, an X-ray beam from a general X-ray source can be used as the incident X-rays BXIa as long as it is monochromatic, so that an X-ray topography image used for evaluating the shape of the crystal plane S can be obtained more easily. In this respect, the second embodiment is preferable to the first embodiment.

[0095] On the other hand, in the first embodiment, X-ray topography images IT1 and IT2 of the entire surface of the substrate 10 can be acquired by imaging with the image sensor 20 without scanning with the incident X-rays BXI. Therefore, the X-ray topography images IT1 and IT2 used for evaluating the shape of the crystal plane S can be acquired in a shorter time. In this respect, the first embodiment is preferable to the second embodiment.

[0096] B2. Example of the second embodiment: In the second embodiment, a GaN substrate was prepared as a sample to demonstrate that the shape of the crystal plane can be properly evaluated, and the shape of the crystal plane was obtained. Specifically, a round GaN substrate with a diameter of 2 inches and a thickness of 350 μm was prepared as the sample. The surface orientation of the prepared substrate was (0001), and the orientation of the orientation flat formed on the substrate was (1-100).

[0097] In the second embodiment, a group of rocking curves was acquired in both an arrangement state where the direction of the diffraction plane was parallel to the orientation flat and an arrangement state where the direction of the diffraction plane was perpendicular to the orientation flat. Next, from the acquired group of rocking curves, the normal vector N(P(x,y)) of the crystal plane at each position on the substrate was determined, and the shape of the crystal plane was evaluated by integrating the determined normal vector N(P(x,y)).

[0098] Figure 13 is an explanatory diagram showing the results of evaluating the shape of the crystal plane in an example of the second embodiment. Figure 13(a) shows the projection of the normal vector N(P(x,y)) onto the xy plane, and Figure 13(b) shows the shape of the crystal plane obtained from the normal vector N(P(x,y)) shown in Figure 13(a).

[0099] As described above, according to the second embodiment, even when the incident X-ray BXIa having a narrow beam diameter is irradiated in a point-like manner, it is possible to evaluate the three-dimensional shape of the crystal plane as shown in Figure 13(b) by using a group of rocking curves (group of topography images) obtained by moving the substrate 10 parallel to the reference plane (xy plane) and scanning the irradiation position of the incident X-ray BXIa.

[0100] C. Variations: The present invention is not limited to the above-described embodiments and examples, and can be implemented in various forms without departing from the spirit of the invention. For example, the following modifications are also possible.

[0101] C1. Variation 1: In each of the above embodiments, the Bragg angle shift used to evaluate the shape of the crystal plane S is obtained as a peak shift, which is a feature quantity of the peak shape function fitted to the rocking curve, but the Bragg angle shift can also be obtained by other methods. For example, the peak shift corresponding to the Bragg angle shift can be obtained by obtaining the peak shift from the rocking curve at the angle ω in the ω direction at which the X-ray intensity is maximum. i It is also possible to directly detect and obtain the peak shift corresponding to the Bragg angle shift.

[0102] On the other hand, if the Bragg angle shift is acquired as in each of the above embodiments, the resolution of the peak shift corresponding to the Bragg angle shift can be increased even if the amount of change when changing the angle in the ω direction is increased, so that the shape of the crystal plane can be more easily evaluated while maintaining high evaluation accuracy of the three-dimensional shape of the crystal plane.

[0103] Furthermore, by acquiring the Bragg angle shift as in each of the above embodiments, even if noise is superimposed on the X-ray intensity, it is possible to more accurately acquire the peak shift corresponding to the Bragg angle shift.

[0104] C2. Variation 2: In the above examples, the present invention is applied to the evaluation of the shape of the crystal plane of a β-Ga2O3 substrate or a GaN substrate. However, the present invention can be applied to the evaluation of the shape of the crystal plane of not only wide-gap semiconductor substrates such as SiC and aluminum nitride (AlN), but also other semiconductor substrates such as silicon (Si) and gallium arsenide (GaAs). [Explanation of symbols]

[0105] 10...Substrate 20...Image sensor 20a...X-ray detector BXD, BXDa...diffracted X-rays BXI,BXIa…Incoming X-ray PDF… Diffractive Surface PRF…Reference plane S...Crystal plane SIT...Topography images IT1, IT2...X-ray topography images

Claims

1. A shape evaluation method for evaluating a shape of a crystal plane of a semiconductor substrate, comprising: a step of acquiring a first group of topographic images including a plurality of X-ray topographic images of the crystal plane having different angles of incidence angle directions in an arrangement state in which a direction in the plane of a reference plane of a diffraction plane including a traveling direction of an incident X-ray and a traveling direction of a diffracted X-ray obtained by diffracting the incident X-ray at a reference plane that is a crystal plane when there is no curvature is a first direction; acquiring a second group of topographic images including a plurality of X-ray topographic images of the crystal plane having different angles of incidence angle directions in an arrangement state in which the direction of the diffraction plane in the plane of the reference plane is a second direction orthogonal to the first direction; acquiring a first Bragg angle shift, which is a deviation of an apparent Bragg angle obtained by measurement at each position on the semiconductor substrate from a reference Bragg angle, which is the Bragg angle on the reference plane, from a rocking curve represented by X-ray intensity at the same position on the semiconductor substrate in each of the plurality of X-ray topographic images included in the first topographic image group and the angle of the incident angle direction of each X-ray topographic image; obtaining a second Bragg angle shift, which is a shift of the apparent Bragg angle from the reference Bragg angle at each position on the semiconductor substrate, from a rocking curve represented by X-ray intensity at the same position on the semiconductor substrate in each of the plurality of X-ray topographic images included in the second topographic image group and the angle of the incident angle direction of each X-ray topographic image; obtaining, for each position on the semiconductor substrate, a tilt angle of the crystal plane relative to the reference plane in each of the first and second directions from the first and second Bragg angle shifts; determining, for each location on the semiconductor substrate, a normal vector of the crystal plane from the tilt angles of the crystal plane in the first and second directions; calculating a displacement of the crystal plane from the reference plane at each position on the semiconductor substrate from the normal vector; A shape evaluation method comprising:

2. 2. The shape evaluation method according to claim 1, a beam diameter of the incident X-rays is large enough to irradiate the entire surface of the semiconductor substrate; the step of acquiring the first and second topographic image groups includes a step of capturing X-ray topographic images formed on an image pickup element by changing the angle of incidence direction, the image pickup element being disposed in the traveling direction of the diffracted X-rays; Shape evaluation method.

3. 2. The shape evaluation method according to claim 1, a beam diameter of the incident X-rays is such that the semiconductor substrate is irradiated with the X-rays in a point-like manner; The steps of acquiring the first and second sets of topographic images each include: scanning the irradiation position of the incident X-rays on the surface of the semiconductor substrate by moving the semiconductor substrate in first and second movement directions that are parallel to the reference plane and perpendicular to each other; a step of changing the angle of the incident angle direction for each irradiation position and acquiring the intensity of the diffracted X-rays using an X-ray detector arranged in the traveling direction of the diffracted X-rays; Including, Shape evaluation method.

4. 2. The shape evaluation method according to claim 1, a beam diameter of the incident X-rays is such that the semiconductor substrate is irradiated with the X-rays in a point-like manner; The steps of acquiring the first and second sets of topographic images each include: changing the angle of the incident angle direction; a step of scanning the irradiation position of the incident X-rays on the surface of the semiconductor substrate by moving the semiconductor substrate in first and second movement directions that are parallel to the reference plane and perpendicular to each other for each angle of the incident angle direction, and acquiring the intensity of the diffracted X-rays using an X-ray detector arranged in the traveling direction of the diffracted X-rays; Including, Shape evaluation method.

5. 5. The shape evaluation method according to claim 1, The step of obtaining the Bragg angle shift from the rocking curve comprises: fitting a peak shape function to the rocking curve; calculating a peak shift, which is the difference between the peak position of the fitted peak shape function and the peak position of the peak shape function at the reference plane, and which corresponds to the Bragg angle shift; Including, Shape evaluation method.

6. A shape evaluation device for evaluating the shape of a crystal plane of a semiconductor substrate, a first topography image group acquisition unit that acquires a first topography image group including a plurality of X-ray topography images of the crystal plane having different angles of incidence angle directions in an arrangement state in which a diffraction plane including a traveling direction of an incident X-ray and a traveling direction of diffracted X-rays obtained by diffracting the incident X-ray at a reference plane that is a crystal plane when there is no curvature is in a first direction; a second topography image group acquisition unit that acquires a second topography image group including a plurality of X-ray topography images of the crystal plane having different angles of the incident angle direction in an arrangement state in which a direction of the diffraction surface in the plane of the reference plane is a second direction orthogonal to the first direction; a first Bragg angle shift acquisition unit that acquires a first Bragg angle shift, which is a shift of an apparent Bragg angle obtained by measurement at each position on the semiconductor substrate from a reference Bragg angle, which is the Bragg angle on the reference plane, from a rocking curve represented by X-ray intensity at the same position on the semiconductor substrate in each of the plurality of X-ray topography images included in the first topography image group and the angle of the incident angle direction of each X-ray topography image; a second Bragg angle shift acquisition unit that acquires a second Bragg angle shift, which is a deviation of the apparent Bragg angle from the reference Bragg angle at each position on the semiconductor substrate, from a rocking curve represented by X-ray intensity at the same position on the semiconductor substrate in each of the plurality of X-ray topography images included in the second topography image group and the angle of the incident angle direction of each X-ray topography image; a tilt angle acquisition unit that acquires, for each position on the semiconductor substrate, a tilt angle of the crystal plane relative to the reference plane in each of the first and second directions from the first and second Bragg angle shifts; a normal vector determination unit that determines a normal vector of the crystal plane from the tilt angles of the crystal plane in the first and second directions for each position on the semiconductor substrate; a reference plane displacement calculation unit that calculates a displacement of the crystal plane at each position on the semiconductor substrate from the reference plane based on the normal vector; A shape evaluation device comprising:

7. A computer program for evaluating the shape of a crystal plane of a semiconductor substrate, comprising: acquiring a first group of topographic images including a plurality of X-ray topographic images of the crystal plane having different angles of incidence angle directions in an arrangement state in which a diffraction plane including a propagation direction of an incident X-ray and a propagation direction of a diffracted X-ray obtained by diffracting the incident X-ray at a reference plane that is a crystal plane when there is no curvature is in a first direction; acquiring a second group of topographic images including a plurality of X-ray topographic images of the crystal plane having different angles of the incident angle direction in an arrangement state in which the direction of the diffraction plane in the plane of the reference plane is a second direction orthogonal to the first direction; obtaining a first Bragg angle shift, which is a shift of an apparent Bragg angle obtained by measurement at each position on the semiconductor substrate from a reference Bragg angle, which is the Bragg angle on the reference plane, from a rocking curve represented by X-ray intensity at the same position on the semiconductor substrate in each of the plurality of X-ray topographic images included in the first topographic image group and the angle of the incident angle direction of each X-ray topographic image; obtaining a second Bragg angle shift, which is a shift of the apparent Bragg angle from the reference Bragg angle at each position on the semiconductor substrate, from a rocking curve represented by X-ray intensity at the same position on the semiconductor substrate in each of the plurality of X-ray topographic images included in the second topographic image group and the angle of the incident angle direction of each X-ray topographic image; obtaining, for each position on the semiconductor substrate, a tilt angle of the crystal plane relative to the reference plane in each of the first and second directions from the first and second Bragg angle shifts; determining, for each location on the semiconductor substrate, a normal vector of the crystal plane from the tilt angles of the crystal plane in the first and second directions; calculating a displacement of the crystal plane from the reference plane at each position on the semiconductor substrate from the normal vector; to the computer, Computer program.

Images