JP7791673B2 - 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 - Google Patents

Description

This invention relates to a technique for evaluating the shape of a crystal surface of a semiconductor substrate, and in particular to a technique for evaluating the three-dimensional shape of a crystal surface.

Wide band gap semiconductors, such as stable phase gallium oxide (β-Ga ₂ O ₃ ), 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.

These wide-gap semiconductors have high thermal and chemical stability, so crystal growth during substrate manufacturing must be carried out at high temperatures of 1000°C to 2400°C. This means that thermal stresses can occur due to temperature gradients during crystal growth and in the cooling stage after crystal growth, which can cause the crystal planes of the manufactured substrate to curve. Furthermore, because flattening the substrate is not easy, mechanical stresses applied during the flattening process can also cause the crystal planes of the substrate to curve.

Such curvature of the crystal plane can cause warping and cracking of the substrate. Furthermore, when epitaxial growth is performed on a substrate with a curved crystal plane, the local crystal orientation varies depending on the position within the plane, which can lead to uneven impurity concentrations within the plane. As such, curvature of the crystal plane can cause a variety of problems. For this reason, there is a strong demand for reducing the curvature of the crystal plane, but in order to do so, it is necessary to evaluate the curvature of the crystal plane using a non-destructive method. Accordingly, 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).

JP 2015-004639 A

In Patent Document 1, the radius of curvature of the substrate is calculated based on the width of the rocking curve, but because 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 is capable of measuring the radius of curvature of the substrate, it is not able to evaluate the three-dimensional shape of the crystal planes, which provides information useful for reducing the curvature of the crystal planes.

The present invention was made to solve the above-mentioned conventional problems, and aims to provide a technology for evaluating the three-dimensional shape of crystal planes in semiconductor substrates using a non-destructive method.

To achieve at least part of the above objectives, the present invention can be realized in the following forms or application examples.

[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 incident 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 incident X-rays and a traveling direction of diffracted X-rays obtained by diffracting the incident X-rays at a reference plane that is a crystal plane when the incident X-rays are 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 incident 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 reference Bragg angle, which is a Bragg angle on the reference plane 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 first topographic image group and the angle of the incident angle direction of each X-ray topographic image. acquiring a first Bragg angle shift , which is a shift in the apparent Bragg angle obtained by measurement from the first and second Bragg angle shifts; acquiring a second Bragg angle shift, which is a shift in 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; 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; 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 calculating, from the normal vector, a displacement of the crystal plane from the reference plane at each position on the semiconductor substrate.

Typically, the Bragg angle shift due to curvature of the crystal plane in a direction perpendicular to the diffraction plane is negligibly small compared to the Bragg angle shift due to 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, allowing the three-dimensional shape of the crystal plane to be accurately evaluated.

[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 image pickup element by an image pickup element arranged in the traveling direction of the diffracted X-rays.

According to this application example, an X-ray topography image of the entire surface of a semiconductor substrate can be obtained by photographing with an imaging element, making it possible to obtain X-ray topography images used to evaluate the three-dimensional shape of crystal surfaces in a shorter time.

[Application Example 3]
A shape evaluation method according to Application Example 1, wherein a beam diameter of the incident X-rays is such that the semiconductor substrate is irradiated with points, and the steps of acquiring the first and second topography image groups include the steps of: scanning an irradiation position of the incident X-rays 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 acquiring the intensity of the diffracted X-rays by changing the angle of the incident angle direction for each irradiation position using an X-ray detector arranged in the traveling direction of the diffracted X-rays.

In this application example, the beam diameter of the incident X-rays is 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.

[Application Example 4]
A shape evaluation method according to Application Example 1, wherein a beam diameter of the incident X-rays is such that the semiconductor substrate is irradiated with points, and the steps of acquiring the first and second topography image groups each include the steps of: changing an angle of the incident angle direction; 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 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.

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.

[Application Example 5]
A shape evaluation method according to any one of Application Examples 1 to 4, wherein the step of acquiring the Bragg angle shift from the rocking curve includes the steps of fitting a peak shape function to the rocking curve and calculating a peak shift that is a difference between a peak position of the fitted peak shape function and a peak position of the peak shape function on the reference plane , the peak shift corresponding to the Bragg angle shift.

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 easier to evaluate the three-dimensional shape of the crystal plane while maintaining high evaluation accuracy of the three-dimensional shape of the crystal plane.

The present invention can be realized in various forms. For example, it can be realized as a method and apparatus for evaluating the shape of a crystal surface in a semiconductor substrate, a computer program for implementing at least some of the functions of the method or apparatus, a recording medium on which the computer program is recorded, or a data signal containing the computer program and embodied in a carrier wave.

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. FIG. 1 is an explanatory diagram showing how incident X-rays are diffracted on a curved crystal plane. 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. 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. 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. 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. 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. FIG. 10 is an explanatory diagram showing how the Bragg angle shift is obtained from a group of topographic images. FIG. 10 is an explanatory diagram showing an image in which feature amounts of fitted peak shape functions are mapped. FIG. 10 is an explanatory diagram showing an image in which feature amounts of fitted peak shape functions are mapped. 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. 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 acquired. 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 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 planes:
A4. Evaluation of crystal face shape:
A5. Example of the first embodiment:
B: Second embodiment:
B1. Acquisition of X-ray topography image in the second embodiment:
B2. Example of the second embodiment:
C. Variations:

A. First embodiment:
A1. Overview of X-ray topography:
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.

As shown in Figure 1(a), in X-ray topography, as indicated 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.

The incident X-rays BXI irradiated onto the substrate 10 are diffracted by the crystal planes of the substrate 10. The diffracted X-ray beam (diffracted X-rays) BXD then travels from the substrate 10 towards the image sensor 20, as indicated by the two-dot chain line, and is irradiated onto the image sensor 20. In this way, the incident X-rays BXI irradiated onto the substrate 10 are diffracted by the crystal planes of the substrate 10, and the diffracted X-rays BXD are irradiated onto the image sensor 20, thereby forming an X-ray topography image IT1 of the crystal planes of the substrate 10 on the image sensor 20.

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 position of the image sensor 20 in the ω direction are adjusted appropriately 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.

By capturing the X-ray topography image IT1 formed on the image sensor 20 in this manner using the image sensor 20, an image representing the X-ray topography image IT1 is obtained. Note that an image representing the X-ray topography image IT1 can also be considered an X-ray topography image IT1, and therefore, hereinafter, unless a distinction is particularly necessary, an image representing the X-ray topography image IT1 will also be referred to as the X-ray topography image IT1.

In the example of Figure 1(a), the reference plane of the substrate 10 is the xy plane, and the Cartesian coordinate system (x, y, z) is set so that 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 Figure 1(a), i.e., the plane containing 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 Figure 1(a) will be used in the following explanation.

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

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 rotates in-plane. Other points are the same as Figure 1(a), so their description will be omitted here.

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

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 diffraction plane (y-z plane) is perpendicular to 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.

The multiple images representing the X-ray topography images IT1 and IT2, or the group of topography images including the multiple 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 described below, to generate evaluation results for the shape of the crystal planes of the substrate 10.

Therefore, the technology for evaluating the three-dimensional shape of crystal surfaces 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 topography images supplied as image data and performing the various processing steps described below.

The three-dimensional shape evaluation technology for crystal surfaces according to the present invention can also be implemented as a shape evaluation device having a functional unit that acquires topography images and a functional unit that performs the various processes described below. In this case, at least a portion of each functional unit can be implemented using hardware.

A2. Diffraction on curved crystal faces:
Figure 2 is an explanatory diagram showing how incident X-rays BXI are diffracted at a curved crystal surface S. Figure 2(a) shows how incident X-rays BXI are diffracted at the curved crystal surface S projected onto the diffraction plane PDF, and Figure 2(b) shows the geometric configuration of g-vectors g _hkl that define the diffraction conditions at the crystal surface S. 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.

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

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 (grad) 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.

Here, vector i, vector j, and vector k represent unit vectors in the x, y, and z directions, respectively.

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

The displacement z at any point P _C (x _C , y _C ) on the reference plane PRF is given by the following equation (3), and therefore the shape of the crystal plane S is uniquely determined by the normal vector N of the crystal plane S.

Note that the above equation (3) indicates that the displacement z at point _PC ( _xC , _yC ) is given by integrating the gradient of the function f(x, y), i.e., the normal vector N( _P ( _x , _y )), along any path C from the starting point _P0 ( _x0 , _y0 ) to point PC(xC, yC).

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)).

As described above, the first embodiment utilizes X-ray topography obtained by diffraction of incident X-rays BXI to evaluate the shape of crystal plane S. The Bragg condition (also called "Bragg's law"), which is a diffraction condition of such X-rays, is expressed by the following equation (4) using the wave vector k _i of incident X-rays BXI and the wave vector k _d and g vector g _hkl of diffracted X-rays BXD.

The g vector g _hkl in the above formula (4) 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 on the surface portion of the substrate 10 ( FIG. 1 ).

As described above, the incident X-rays BXI irradiating the substrate 10 have sufficiently high parallelism and monochromaticity, so the wave vector k _i of the incident X-rays BXI 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 of the diffracted X-rays BXD is determined by the arrangement of the image sensor 20 in the ω direction, as shown in FIG. 1 .

In this way, since the wave vectors k _i and k _d of the incident X-ray BXI and the diffracted X-ray BXD are known, the g vector g _hkl is given as a vector function g _hkl (x, y) of the point P(x, y) on the reference plane PRF. Then, by treating the vector function g _hkl (x, y) as the normal vector N(P(x, y)), the shape of the crystal plane S can be obtained, as explained in the above formula (3).

Then, for the reference plane PRF, i.e., the crystal plane S of the uncurved substrate 10, the Bragg condition corresponding to the g vector _g is expressed by the following equation (5) using the lattice spacing d, the diffraction order n, and the Bragg angle θ _B.

On the other hand, as shown in FIG. 2(b), if the angle that the g vector g _hkl (x, y) at point P(x, y) makes with the vector g' _hkl (x, y) that is its projection onto the diffraction plane PDF is χ, and the angle that the vector g' _hkl (x, y) makes with the g vector g ₀ of the reference plane PRF is Δω, the Bragg condition corresponding to the g vector g _hkl (x, y) at point P(x, y) is expressed by the following equation (6) using the interplanar spacing d, the diffraction order n, and the apparent Bragg angle θ _B (x, y) obtained by measurement using X-ray diffraction.

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 apparent Bragg angle θ _B (x, y) corresponding to the g vector g _hkl (x, y) at point P(x, y) deviates by Δω from the Bragg angle θ _B0 corresponding to the g vector g ₀ .

On the other hand, when the crystal plane S is curved in a direction perpendicular to the diffraction plane PDF and the g vector g _hkl (x, y) is not parallel to the diffraction plane PDF, the apparent Bragg angle θ _B (x, y) shifts according to the factor cos χ in equation (6). However, in practice, cos χ ≈ 1, and therefore the shift of the apparent Bragg angle θ _B (x, y) according to the factor cos χ is negligibly small compared to the shift Δω.

In this way, since the shift in the apparent Bragg angle θ _B (x, y) due to the factor cos χ is negligibly small, if we set cos χ = 1, as can be seen from the above equations (5) and (6), the angle Δω between the vector g' _hkl (x, y) and the g vector g ₀ is given as the Bragg angle θ _B defined by the g vector g ₀ of the reference plane PRF, that is, the angle obtained by subtracting the apparent Bragg angle θ _B (x, y) from the Bragg angle (reference Bragg angle) θ _B0 on the reference plane PRF.

As can be seen from the above explanation, the vector g' _hkl (x, y) is the projection of the g vector g _hkl (x, y) on the crystal plane S onto the diffraction plane PDF, and therefore the angle Δω between the vector g' _hkl (x, y) and the g vector g ₀ 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.

A3. Bragg angle shift due to curvature of crystal planes:
3 to 7 are explanatory diagrams showing how the apparent Bragg angle θ _B (x, y) deviates from the reference Bragg angle θ _B0 due to the curvature of the crystal plane. In FIGS. 3 to 7, the diagrams with subnumbers (a) show the shape of the curved crystal plane, and the diagrams with subnumbers (b) show the normal vector N(P(x, y)) of the curved crystal plane. Furthermore, in FIGS. 3 to 7, the diagrams with subnumbers (c) show the deviation (θ B (x, y)) of the apparent Bragg angle θ _B (x, y) from the reference Bragg angle θ _B0 (θ _B (x, y) - θ _B0 ). Note that, hereinafter, this deviation (θ _B (x, y) - _{θ B0} ) will also be referred to as the "Bragg angle deviation."

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

Then, by appropriately setting the radii of curvature a, b, and c, the shape of the crystal plane was calculated when the outer shape of the substrate was a square with sides of 50 mm (subscript (a) in Figures 3 to 7), and based on the calculated shape of the crystal plane, the normal vector N(P(x, y)) of the curved crystal plane was calculated (subscript (b) in Figures 3 to 7). Next, with the reference Bragg angle θ _B0 set to 30°, the apparent Bragg angle θ _B (x, y) was calculated using the above formula (6), and the Bragg angle shift (θ _B (x, y) - θ _B0 ) was calculated (subscript (c) in Figures 3 to 7).

Figure 3 shows the shape of the crystal plane (Figure 3(a)), the normal vector N(P(x,y)) (Figure 3(b)), and the Bragg angle shift (θ B (x,y)-θ _B0 ) (Figure 3(c)) when the shape of the crystal plane is a cylindrical plane curved in the _y direction, that is, a cylindrical plane whose curvature direction is parallel to the diffraction plane (yz plane). In the example of Figure 3, the radii of curvature a, b, and c are set to 10 km, 10 m, and 10 m, respectively.

In this case, as shown in Figure 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 Figure 2 from the reference plane PRF) is about 31 µm higher than at the center in the y direction (y = 0 mm), which is the valley. And, as shown in Figure 3(b), the x-direction component of the normal vector N (P(x, y)) is zero (0). Because the crystal plane is curved in this way, the Bragg angle shift (θ _B (x, y) - θ _B0 ) is 0° (deg) at the center in the y direction (y = 0 mm), and its absolute value is about 0.14° at the end in the y direction (y = ±25 mm).

Figure 4 shows the shape of the crystal plane (Figure 4(a)), the normal vector N(P(x,y)) (Figure 4(b)), and the Bragg angle shift (θ B (x,y)-θ _B0 ) (Figure 4(c)) when the shape of the crystal plane is a cylindrical plane curved in the x direction, that is, a cylindrical _plane whose curvature direction is perpendicular to the diffraction plane (y-z plane). In the example of Figure 4, the radii of curvature a, b, and c are set to 10 m, 10 km, and 10 m, respectively.

In this case, as shown in Figure 4(a), the height z of the crystal plane at the x-direction end (x = ±25 mm) is approximately 31 μm higher than at the center in the x-direction (x = 0 mm), which is the valley. As shown in Figure 4(b), the y-direction component of the normal vector N(P(x, y)) is zero. Because the crystal plane is curved in this way, the Bragg angle shift (θ _B (x, y) - θ _B0 ) is 0 arcsec at the center in the x-direction (x = 0 mm). Even at the x-direction end (x = ±25 mm), where the absolute value of the Bragg angle shift is maximum, the absolute value of the Bragg angle shift (θ _B (x, y) - θ _B0 ) remains at most approximately 0.37 arcsec.

This is because, as described above, when the g-vector g _hkl (x, y) is not parallel to the diffraction plane PDF (FIG. 2), the apparent Bragg angle θ _B (x, y) shifts depending on the factor cos χ, which corresponds to the deviation of the g-vector g _hkl (x, y) from the diffraction plane PDF, but since cos χ ≈ 1, the deviation of the apparent Bragg angle θ _B (x, y) depending on the factor cos χ is negligibly small. In this way, since the effect of the deviation of the g-vector g _hkl (x, y) from the diffraction plane PDF on the Bragg angle shift (θ _B (x, y) - θ _B0 ) is small, curvature in the direction perpendicular to the diffraction plane is usually not detected.

Figure 5 shows the shape of the crystal plane (Figure 5(a)), the normal vector N(P(x,y)) (Figure 5(b)), and the Bragg angle shift (θ _B (x,y)-θ _B0 ) (Figure 5(c)) when the shape of the crystal plane is spherical and curved in the x and y directions. In the example of Figure 5, the radii of curvature a, b, and c are set to 10 m, 10 m, and 10 m, respectively.

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. Due to the curvature of the crystal plane in this way, the absolute value of the Bragg angle shift (θ _B (x, y) - θ _B0 ) at the end in the y direction (y = ±25 mm) is approximately 0.14°. On the other hand, as mentioned above, the deviation of the g vector g _hkl (x, y) from the diffraction surface PDF has almost no effect on the Bragg angle shift (θ _B (x, y) - θ _B0 ), so the Bragg angle shift (θ _B (x, y) - θ _B0 ) is approximately constant in the x direction, and the Bragg angle shift (θ _B (x, y) - θ _B0 ) shown in Figure 5(c) is the same as when the curvature direction is a cylindrical surface parallel to the diffraction surface (Figure 3(c)).

6A and 6B show the shape of the crystal plane (FIG. 6A), the normal vector N(P(x,y)) (FIG. 6B), and the Bragg angle shift (θ B (x,y)-θ _B0 ) (FIG. 6C) when the shape of the crystal plane is curved in the y direction and made ellipsoidal with an extremely larger curvature in the _x direction than in the y direction. In the example of FIG. 6, the radii of curvature a, b, and c are set to 2 m, 10 m, and 10 m, respectively.

In this case, as shown in Figure 6(a), the height z of the crystal plane at the end in the x direction (x = ±25 mm) is about 800 μm higher than the center in the x direction (x = 0 mm), which is the valley. Due to this curvature of the crystal plane, the Bragg angle shift (θ _B (x, y) - θ _B0 ) becomes detectable in the x direction as well, as shown in Figure 6(c).

FIG. 7 shows the shape of the crystal face (FIG. 7(a)), the normal vector N(P(x,y)) (FIG. 7(b)), and the Bragg angle shift (θ B (x,y)-θ _B0 ) (FIG. 7(c)) when the shape of the crystal face is curved in the x and y directions and is made into a _saddle -shaped face with the convex direction of curvature reversed between the x and y directions. In the example of FIG. 7, the radii of curvature a, b, and c are set to 10 m, 10 im, and 10 m, respectively. Here, i is the imaginary unit, i.e., the square root of -1.

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 is lowest in the x direction at the center (x = 0 mm), while being highest in the y direction at the center (y = 0 mm). Even when the crystal plane is curved in this way, the curvature in the x direction, which is orthogonal to the diffraction plane, has almost no effect on the Bragg angle shift (θ _B (x,y) - θ _B0 ), so the Bragg angle shift (θ _B (x,y) - θ _B0 ) is approximately constant in the x direction. On the other hand, in the y direction, the shape of the crystal plane is downward convex in the example of Figure 3, whereas the shape of the crystal plane is upward convex in the example of Figure 7. Therefore, the Bragg angle shift (θ _B (x,y) - θ _B0 ) shown in Figure 7(c) is the inverse of that in Figure 3(c) in the y direction.

A4. Evaluation of crystal face shape:
Figure 8 is an explanatory diagram showing how the Bragg angle shift (θ _B (x, y) - θ _B0 ) is obtained from the topography image group SIT. Figure 8(a) shows the topography image group SIT obtained by sequentially changing the angle in the ω direction of the substrate 10 (Figure 1) and capturing X-ray topography images IT1/IT2 formed on the imaging element 20, as described above, and Figure 8(b) shows how the Bragg angle shift (θ _B (x, y) - θ _B0 ) is obtained from the rocking curve obtained from the topography image group SIT.

8A, the topography image group SIT includes (2M+1) X-ray topography images IT1/IT2. To obtain the Bragg angle shift (θ _B (x, y)-θ _B0 ) from the topography image group SIT, first, the X-ray intensity at the hatched pixels (i.e., the same positions on the substrate 10) is obtained for each of the X-ray topography images IT1/IT2 included in the topography image group SIT.

Next, the rocking curve shown by the black circle in Fig. 8(b) is obtained by correlating the angle _ωi (-M≦i≦+M) in the ω direction when each of the X-ray topography images IT1/IT2 was captured with the X-ray intensity at the angle _ωi 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.

The difference between the peak position of the fitted peak shape function in this way and the peak position of the peak shape function on the reference plane indicated by the dashed line (i.e., ω ₀ ) is the Bragg angle shift (θ _B (x, y) - θ _B0 ). As described above, the angle Δω formed by the vector g' hkl (x, y), which is the projection of the g vector g _hkl (x, y) corresponding to the normal vector N(P(x, y)) onto the diffraction plane _PDF ( FIG. 2 ), and the g vector g ₀ is given as the value (θ _B0 - θ _B (x, y)) obtained by inverting the Bragg angle shift (θ _B (x, y) - _{θ B0} ).

In this way, the vector g' _hkl (x, y) which is the projection of the normal vector N(P(x, y)) (i.e., the g vector g _hkl (x, y)) onto the diffraction plane PDF ( FIG. 2 ) is determined. Therefore, by using a topography image group SIT including X-ray topography images IT1/IT2 obtained for two arrangement states in which the direction of the diffraction plane PDF is orthogonal within the reference plane, the normal vector N(P(x, y)) of the crystal plane S can be determined. 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. Therefore, according to the first embodiment, the shape of the crystal plane S can be evaluated.

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-Ga ₂ O ₃ substrate was prepared as a sample, and the shape of the crystal plane was obtained. Specifically, a rectangular β-Ga ₂ O ₃ 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 [010] axis (b-axis) and [100] axis (a-axis), respectively. Furthermore, both sides of the substrate were subjected to chemical mechanical polishing to flatten its surface.

X-ray topography was performed by irradiating the substrate surface with a monochromatic X-ray beam with a wavelength of λ = 1.9265 Å at an incident angle of 20°, using symmetric reflection with a g-vector of g = 002. By rotating the substrate by 90° in-plane, the diffraction plane, i.e., the direction of travel of the X-ray beam, can be made parallel to the [010] or [100] direction.

For 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 the 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, and a group of topography images containing 201 X-ray topography images was obtained.

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

Figures 9 and 10 are explanatory diagrams showing images in which the feature quantities of the fitted peak shape function are mapped. In Figures 9 and 10, the figures with subnumbers (a) show images in which the maximum intensity is mapped, the figures with subnumbers (b) show images in which the full width at half maximum (FWHM) is mapped, and the figures with subnumbers (c) show images in which the Bragg angle shift is mapped. Furthermore, Figure 9 shows an image in which the X-ray beam propagation direction is parallel to the [100] direction, and Figure 10 shows an image in which the X-ray beam propagation direction is parallel to the [010] direction.

As shown in Figures 9(a) and 10(a), the maximum intensity is higher in the central portion of the substrate, indicating that the crystal quality of the substrate is higher in the central portion and lower in the peripheral portion. Furthermore, as shown in Figures 9(b) and 10(b), the half-width averaged approximately 20 arc seconds and was generally uniform across the entire substrate.

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-Ga ₂ O ₃ substrate used as the sample is curved. Note that although variations in the interplanar spacing of the crystal plane affect the half-width, their 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 precision.

Next, from the Bragg angle shift thus obtained, the normal vector N(P(x, y)) of the crystal plane at point P(x, y) on the substrate is obtained. As described above, the angle Δω calculated from the Bragg angle shift is the angle between the vector g' _hkl (x, y), which is the projection of the g vector g _hkl (x, y) of the crystal plane S (FIG. 2) onto the diffraction plane PDF, and the g vector g ₀ of the reference plane PRF, i.e., the angle between the g vector g _hkl (x, y) and the g vector g ₀ on the diffraction plane PDF.

9 and 10 , the Bragg angle shifts used to calculate the angle Δω are obtained for each of two orientations in which the diffraction planes are orthogonal to each other within the reference plane. Therefore, the angle Δω is calculated for two orthogonal diffraction planes with respect to the reference plane. Therefore, by treating the angle Δω calculated for each of the two orthogonal diffraction planes as a component parallel to both the diffraction plane and the reference plane, the g vector g _hkl (x, y) of the crystal plane, i.e., the normal vector N(P(x, y)), can be determined. The shape of the crystal plane can then be obtained by integrating the normal vector N(P(x, y)) thus determined.

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).

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, Figure 11(a) only depicts normal vectors N(P(x,y)) for 20 grid points in the x direction and 30 grid points in the y direction.

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).

As such, according to the first embodiment, a group of topography images containing multiple X-ray topography images is acquired in each of two arrangement states in which the diffraction plane (y-z plane) is 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 topography images. This makes it possible to evaluate the three-dimensional shape of the crystal plane, as shown in Figure 11(b).

B: Second embodiment:
B1. Acquisition of X-ray topography image in the second embodiment:
12 is an explanatory diagram showing how an X-ray topography image used in the second embodiment for evaluating the shape of a crystal plane of a substrate 10 is acquired. 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 having a single detection element corresponding to the narrow beam of diffracted X-rays BXDa.

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.

In the second embodiment, the incident X-rays BXIa are irradiated onto the substrate 10 in a point-like manner, and the substrate 10 is moved in the X and Y directions parallel to the xy plane. As a result, the surface of the substrate 10 is scanned with the incident X-rays BXIa.

Then, at each position (irradiation position) on the substrate 10 where the incident X-rays BXIa are irradiated in a point-like manner, the angle of the substrate 10 in the ω direction is sequentially changed, and the intensity of the diffracted X-rays BXDa is acquired by the X-ray detector 20a. This allows a group of rocking curves to be acquired, including rocking curves at each position on the substrate 10.

The acquired rocking curves contain the intensities of diffracted X-rays BXDa for each position on the substrate 10 at each angle in the ω direction. Therefore, the rocking curves contain X-ray topography images that represent the intensities of diffracted X-rays BXDa for each position on the substrate 10.

In this way, the group of rocking curves acquired in the second embodiment includes X-ray topography images at each of multiple angles in the ω direction, and is therefore equivalent to a group of topography images including multiple X-ray topography images at different angles in the ω direction. Furthermore, 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).

In the second embodiment, the rocking curves at each position on the substrate 10 have already been acquired at the time the topography image group is acquired. Therefore, it is possible to omit the process 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.

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 diffraction plane directions are orthogonal within the reference plane, and the Bragg angle shift is determined from the group of topography images for 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.

In the second embodiment, to obtain a group of topography images (group of rocking curves), the irradiation position on the substrate 10 is scanned and rocking curves are obtained at each position on the substrate 10, but it is also possible to obtain a group of topography images by other methods.

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

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 lower. Therefore, if the incident X-rays BXIa are monochromated, an X-ray beam from a general X-ray source can be used, making it easier to obtain X-ray topography images used to evaluate the shape of the crystal surface S. In this respect, the second embodiment is preferable to the first embodiment.

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 to evaluate 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.

B2. Example of the second embodiment:
In the second embodiment, a GaN substrate was prepared as a sample, and the shape of the crystal plane was obtained to demonstrate that the shape of the crystal plane can be properly evaluated. 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).

In the second embodiment, a group of rocking curves was obtained in both an arrangement state in which the direction of the diffraction plane was parallel to the orientation flat and an arrangement state in which the direction of the diffraction plane was perpendicular to the orientation flat. Next, from the obtained 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)).

Figure 13 is an explanatory diagram showing the results of evaluating the shape of a 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).

As such, according to the second embodiment, even when the incident X-rays BXIa, which have a narrow beam diameter, are 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) acquired by moving the substrate 10 parallel to the reference plane (x-y plane) and scanning the irradiation position of the incident X-rays BXIa.

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.

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 a peak shape function fitted to a rocking curve. However, the Bragg angle shift can also be obtained by other methods. For example, the peak shift corresponding to the Bragg angle shift can also be obtained by directly detecting the angle _ωi in the ω direction at which the X-ray intensity is maximized from the rocking curve. In this way, it becomes easier to obtain the peak shift corresponding to the Bragg angle shift.

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, making it easier to evaluate the shape of the crystal plane while maintaining high evaluation accuracy of the three-dimensional shape of the crystal plane.

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

C2. Variation 2:
In the above examples, the present invention is applied to the shape evaluation of the crystal plane of a β-Ga ₂ O ₃ substrate or a GaN substrate, but the present invention can be applied to the shape evaluation 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).

REFERENCE SIGNS LIST 10... Substrate 20... Image pickup element 20a... X-ray detector BXD, BXDa... Diffracted X-rays BXI, BXIa... Incident X-rays PDF... Diffraction plane PRF... Reference plane S... Crystal plane SIT... Topography image group IT1, IT2... X-ray topography images

Claims (7)

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. 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. 2. The shape evaluation method according to claim 1,
a beam diameter of the incident X-rays is such that the X-rays irradiate the semiconductor substrate 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. 2. The shape evaluation method according to claim 1,
a beam diameter of the incident X-rays is such that the X-rays irradiate the semiconductor substrate 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. 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. A shape evaluation device for evaluating the shape of a crystal plane of a semiconductor substrate, comprising:
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: 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.