Method for evaluating surface shape

Abstract

This invention provides a surface shape evaluation method that quantitatively describes the direction of inclination of lines and regions set on the surface when evaluating the surface shape of a target object for measurement. [Solution] A surface shape evaluation method for evaluating the direction of inclination of the surface shape of a target to be measured, comprising the steps of: acquiring height shape data along an arbitrary line set on the surface of the target to be measured or in an arbitrary region set on the surface of the target to be measured; and quantifying the direction of inclination based on the acquired height data along the line or in the region, using a parameter obtained by differentiating the height data in the case of height data along the line, or a parameter obtained by partially differentiating the height data in the X-axis direction and Y-axis direction after setting XY coordinates in the region, and identifying the direction of inclination along the line or in the region from the sign of the obtained numerical value.

Description

[Technical Field]

[0001] The present invention relates to a method for evaluating surface shape. [Background technology]

[0002] Among the surface features of a substrate, waviness, which is a long-wavelength component, and roughness, which is the component remaining after removing waviness from the surface shape, are important characteristics of the substrate surface and its manufacturing process. Roughness affects the properties of friction and the reflection and scattering behavior of light. Furthermore, in processes such as grinding and polishing during manufacturing, the roughness before and after processing is an important indicator of processing quality. Moreover, because roughness affects the reflection and scattering behavior of light, it also significantly impacts the results of various optical inspections. The surface shape itself and waviness can also affect the success rate and strength of bonding between substrate surfaces. In addition, the roughness of processing materials such as polishing pads used in the substrate manufacturing process also affects the roughness of the substrate, so the roughness of the processing materials is equally important.

[0003] There are various parameters for evaluating roughness, waviness, and shape. Focusing on dimensions, linear data such as data measured linearly, data obtained by cutting planar data at a specific virtual cross-section, and data obtained by observation from the actual cross-sectional direction are called roughness curves, waviness curves, cross-sectional curves, etc., and these are collectively called contour curves. For example, the parameter that represents the roughness curve is linear roughness. Similarly, the parameters for the roughness, waviness, and shape of the entire surface are called surface roughness, surface waviness, and surface shape, respectively. There are various parameters within these as well. In particular, when analyzing differences in friction and light scattering behavior depending on the direction, the influence of the processing direction, and the orientation suitable for bonding, parameters that can quantify the direction of roughness are important.

[0004] Furthermore, surface roughness and surface waviness are components extracted from the surface shape at specific wavelengths. Therefore, surface roughness and surface waviness are sometimes collectively referred to as surface shape.

[0005] As parameters for quantifying shape, for example, JIS B 0601 specifies various parameters for one-dimensional roughness curves, waviness curves, and cross-sectional curves. Taking roughness as an example, typical examples include arithmetic mean roughness, which is the average of the absolute values ​​of the distance from the reference line, and root mean square height, which indicates the standard deviation of surface roughness. In addition, as a complex parameter, there is root mean square slope, which is the root mean square of the local slope.

[0006] Furthermore, ISO 25178 specifies surface roughness parameters that extend the JIS B 0601 standard to include surface roughness. In addition, it specifies parameters that indicate the direction and intensity of roughness, such as the surface texture direction (Std), which indicates the direction of the surface texture knots, and the surface texture aspect ratio (Str), which are specific to two-dimensional surface roughness.

[0007] Furthermore, Patent Document 1 discloses a technique for evaluating haze, which is the light scattering behavior of a semiconductor wafer surface, using parameters such as root mean square roughness and root mean square slope, which are specified in JIS B 0601. [Prior art documents] [Patent Documents]

[0008] [Patent Document 1] Japanese Patent Application Publication No. 2-74051 [Overview of the project] [Problems that the invention aims to solve]

[0009] However, the parameters described in JIS B 0601 lacked a parameter to describe the direction of the slope of the shape. Similarly, the parameters described in ISO 25178 included the direction of the nodes in the shape and the root mean square of the local slope, but lacked a parameter to describe the direction of the slope. Furthermore, the technology described in Patent Document 1 lacked the ability to consider the direction of the slope when evaluating haze based on the slope.

[0010] The present invention has been made in view of the above problems, and an object thereof is to provide a method for evaluating a surface shape that quantitatively describes the directionality of the inclination of a linear shape and a planar shape in the evaluation of the surface shape of a measurement object.

Means for Solving the Problems

[0011] The present invention has been made to achieve the above object, and is a method for evaluating a surface shape that evaluates the directionality of the inclination of the surface shape of a measurement object, acquiring height-direction shape data along an arbitrary line set on the surface of the measurement object or in an arbitrary region set on the surface of the measurement object; based on the height data along the line or in the region acquired above, in the case of the height data along the line, a parameter obtained by differentiating the height data, in the case of the height data in the region, setting XY coordinates in the region and using a parameter obtained by partially differentiating the height data in the X-axis direction and the Y-axis direction, quantifying the directionality of the inclination using the above, and specifying the directionality of the inclination along the line or in the region from the positive or negative sign of the obtained numerical value; A method for evaluating a surface shape including the above is provided.

[0012] According to such a method for evaluating a surface shape, it is possible to quantitatively evaluate the directionality of the inclination of the surface shape of a measurement object.

[0013] At this time, in the step of specifying the directionality of the inclination, when specifying the directionality of the inclination along the line based on the height data along the line, when the coordinate of the position along the line is x and the height at the coordinate x is z(x), Σ(dz(x) / dx) , if = 0, it is specified that there is no directionality in the inclination, Σ(dz(x) / dx) 2 if ≠ 0, the directionality of the inclination is

Number

[0014] Thereby, the evaluation of the surface shape along an arbitrary line set on the surface can be performed with higher accuracy.

[0015] At this time, in the step of specifying the directionality of the inclination, when specifying the directionality of the inclination of the said region based on the height data in the said region, When the coordinates of the position in the said region are (x, y) and the height at the coordinates (x, y) is z(x, y), Σ(∂z(x,y) / ∂x) 2 =Σ(∂z(x,y) / ∂y) 2 = 0, the vector quantity P1 is (0, 0) ··· (Equation 2) represented as, and it is specified that there is no directionality in the inclination within the said region, Σ(∂z(x,y) / ∂x) 2 = 0, Σ(∂z(x,y) / ∂y) 2 ≠ 0, the vector quantity P2 is

Number

Number

number

[0016] This allows for more accurate evaluation of the surface shape of any area set on the surface.

[0017] In this case, the surface shape evaluation method can be implemented in which, in the step of determining the direction of the slope, the derivative of dz(x) / dx and the partial derivatives of ∂z(x,y) / ∂x and ∂z(x,y) / ∂y are calculated using the 7-point numerical differentiation formula, excluding the three points at each end of the data.

[0018] This reduces the impact of noise in the data, allowing for more accurate evaluation of the surface shape of any line or region set on the surface.

[0019] In this case, the process of acquiring the shape data can be a surface shape evaluation method that measures the surface shape using an electron microscope or an atomic force microscope.

[0020] This allows for even more accurate evaluation of surface shape.

[0021] In this case, the method for evaluating the surface shape of a semiconductor substrate can be used as the object to be measured.

[0022] The surface shape evaluation method according to the present invention is particularly effective for evaluating the surface shape of semiconductor substrates. [Effects of the Invention]

[0023] As described above, the surface shape evaluation method of the present invention makes it possible to quantitatively evaluate the direction of the inclination of the surface shape of the object to be measured. [Brief explanation of the drawing]

[0024] [Figure 1] This is a schematic diagram of a hypothetical contour curve consisting of line segments AB and BC. [Figure 2] This is a binarized image of a cross-sectional transmission electron microscope image of 3C-SiC / Si, with noise removed. [Figure 3] This is an atomic force microscope image of a silicon epitaxial substrate with the (100) plane as the main plane. [Figure 4] Figure 3 is an image with dotted lines connecting the vertices of the nodes added. [Modes for carrying out the invention]

[0025] The present invention will be described in detail below, but the present invention is not limited to these descriptions.

[0026] As described above, in evaluating the surface shape of a measurement target, there was a need for a surface shape evaluation method that could quantitatively describe the direction of the inclination of the lines and surfaces set on the surface.

[0027] The inventors of the present invention have conducted thorough studies on the above problem, A method for evaluating surface shape, which evaluates the direction of the inclination of the surface shape of a target to be measured, A step of acquiring height-direction shape data along an arbitrary line set on the surface of the object to be measured or in an arbitrary area set on the surface of the object to be measured, Based on the height data obtained along the line or in the region, In the case of height data along the aforementioned line, the parameter obtained by differentiating the aforementioned height data is In the case of height data in the aforementioned region, XY coordinates are set for the region, and the parameters obtained by partially differentiating the height data in the X-axis direction and the Y-axis direction are A step of quantifying the direction of the slope using and determining the direction of the slope along the line or in the region from the sign of the obtained numerical value, We have completed the present invention by discovering that a surface shape evaluation method including [specific method] makes it possible to quantitatively evaluate the direction of the inclination of the surface shape of the object being measured.

[0028] The following explanation will be given with reference to the drawings.

[0029] First, in order to discuss the direction of the slope, it is necessary to define the direction of the slope. Therefore, we define a positive direction of slope when there is a large area of ​​positive slope from the starting point to the ending point (a large amount of slope components that increase in elevation), and a negative direction of slope when there is a large area of ​​negative slope from the starting point to the ending point (a large amount of slope components that decrease in elevation). Furthermore, we define that the larger the proportion of the slope region with that sign, the larger the absolute value of the direction of the slope. Note that if coordinate axes are set on the surface, the origin can be set as the starting point as described above. In other words, the evaluation of the direction of slope is not an evaluation of the average slope of the object, but an evaluation that takes into account the asymmetry of the slope directions of each of the multiple irregularities in a given direction when multiple irregularities exist.

[0030] [Method for evaluating surface shape] The present invention involves a step of acquiring shape data in the height direction along an arbitrary line set on the surface of the object to be measured or in an arbitrary region set on the surface of the object to be measured. Based on the height data obtained along the line or in the region, In the case of height data along the aforementioned line, the parameter obtained by differentiating the aforementioned height data is In the case of height data in the aforementioned region, XY coordinates are set for the region, and the parameters obtained by partially differentiating the height data in the X-axis direction and the Y-axis direction are A step of quantifying the direction of the slope using and determining the direction of the slope along the line or in the region from the sign of the obtained numerical value, This provides a method for evaluating surface shape, including the surface shape.

[0031] As described above, by quantifying the direction of the slope using parameters obtained by differentiating or partially differentiating height data along a line or within a region, and evaluating based on the sign of the obtained numerical value, it becomes possible to quantify the asymmetry and discuss the direction of the slope, even if, for example, the average slope in the X-axis direction as a whole is 0, but there is an asymmetry in the slope state between the positive and negative directions of the X-axis (see, for example, the explanation using Figure 1 described later).

[0032] In this invention, when x is the coordinate of a position along an arbitrary line on the surface to be evaluated, and z(x) is the height at that coordinate x,

number

[0033] Here, Σ(dz(x) / dx) 2 If the value is 0, there is no local slope at all, so the direction of the slope can be described as 0 (the slope has no direction).

[0034] Furthermore, if the local slopes dz(x1) / dx1 and dz(x2) / dx2 of adjacent points x1 and x2 are symmetrical, then dz(x1) / dx1 can be written as -dz(x2) / dx2, and dz(x1) / dx1|dz(x1) / dx1|+dz(x2) / dx2|dz(x2) / dx2| becomes 0. Therefore, if all slopes are symmetrical, (Equation 1) becomes 0, demonstrating that the slopes have no directional characteristics (the slopes have no directionality).

[0035] Furthermore, since the sign of dz(x) / dx|dz(x) / dx| is equal to the sign of dz(x) / dx, dz(x) / dx|dz(x) / dx| contains information about the direction of the local slope. Also, if the slope contains asymmetry, Σdz(x) / dx|dz(x) / dx| will not be 0. On the other hand, Σ(dz(x) / dx) 2 This value is 0 if there is no slope, and positive otherwise. Therefore, if the contour curve has an asymmetric local slope, (Equation 1) will have a sign corresponding to the distribution of that local slope, and thus contains information about the direction of the contour curve's slope.

[0036] Furthermore, if the numerator is assumed to be Σdz(x) / dx, it will always be 0 if the heights of the starting and ending points are equal. Therefore, even if the contour curve has an asymmetrical slope, it will be impossible to properly represent the direction of the slope.

[0037] Furthermore, when the heights of the starting and ending points of the linear shape are equal, if there are many points where dz(x) / dx is positive, then |dz(x) / dx| at each point is small, and therefore Σdz(x) / dx|dz(x) / dx| becomes negative. Thus, by multiplying by a negative number as shown in (Equation 1), it is possible to make the parameter take a positive value when there are many points where the slope is positive.

[0038] また、Σ(dz(x) / dx) 2 If it is not 0, then Σdz(x) / dx|dz(x) / dx| becomes Σ(dz(x) / dx) 2 Dividing by this number allows it to be normalized to a dimensionless number. This makes it possible to evaluate the strength of the slope direction independently of the height of the shape.

[0039] In this way, by quantitatively obtaining the direction of the gradient, it becomes possible to link the direction of the gradient with other surface properties. For example, if the direction of the gradient is large, the scattering behavior changes when light is incident from one direction compared to when it is incident from the opposite direction. Therefore, when applying inspection using light scattering behavior, it becomes possible to quantitatively obtain the direction of roughness of a representative sample in advance, and then, if it exceeds a certain threshold, measure from two directions, and if it is below that threshold, measure from only one direction of light.

[0040] Furthermore, in the step of determining the direction of the inclination of the present invention, when determining the direction of the inclination of the region based on height data in the set region, when (x,y) is an arbitrary coordinate on the surface to be evaluated and z(x,y) is the height at coordinate (x,y), then Σ(∂z(x,y) / ∂x) 2 and Σ(∂z(x,y) / ∂y) 2 If both are 0, then the vector quantity P1 is, (0,0)... (Formula 2) This can be expressed as Σ(∂z(x,y) / ∂x) 2 If it is 0, then Σ(∂z(x,y) / ∂y) 2 If it is not 0, then the vector quantity P2 is

number

number

number

[0041] Here, in the above vector quantities P2, P3, and P4, if the component of the vector is 0, it is determined that there is no directionality in the slope in the direction of the component. In the above vector quantities P2, P3, and P4, if the component of the vector is a positive value, it is determined that there is a large slope component that rises in the positive direction of the component with a positive value from the origin of the XY coordinate system (it has a positive directionality of slope). In the above vector quantities P2, P3, and P4, if the component of the vector is a negative value, it can be determined that there is a large slope component that rises in the negative direction of the component with a negative value from the origin of the XY coordinate system (it has a negative directionality of slope).

[0042] That is, Σ(∂z(x,y) / ∂x) 2 If is 0, there is no local slope in the x direction, so the direction of the slope in the x direction can be described as 0. Also, Σ(∂z(x,y) / ∂y) 2 If the value is 0, there is no local slope in the y direction, so the direction of the slope in the y direction can be described as 0 (i.e., the slope has no direction).

[0043] Furthermore, the vectors in (Equation 5) are extensions of (Equation 1) to a surface in the x and y directions, respectively, and, as with the linear shape, can indicate the direction of the inclination of the surface shape.

[0044] Furthermore, the calculation of the derivative of dz(x) / dx, and the partial derivatives of ∂z(x,y) / ∂x and ∂z(x,y) / ∂y, can be performed using the 7-point numerical differentiation formula, except for the three points at each end of the data. Using the 7-point numerical differentiation formula can reduce the influence of measurement noise and other factors. At the ends of the data points, the 7-point formula cannot be applied because there are not enough data points on one side. In this case, the slope is calculated using the 3-point numerical differentiation formula, the 5-point formula, or simply the difference with adjacent data points.

[0045] Furthermore, shape data in the height direction (surface shape) can be obtained by measurement using an electron microscope. In particular, when discussing the linear shape of cross-sectional curves, selecting an electron microscope with a magnification corresponding to the wavelength component of the object being analyzed allows for appropriate evaluation.

[0046] In addition, the shape data (surface shape) in the height direction can be measured with an atomic force microscope. Since an atomic force microscope generally has high resolution and can evaluate a height shape on the order of sub-nanometers, it is suitable when height information with such high resolution is required.

[0047] In addition, the measurement object that is the evaluation target of the surface shape of the present invention can be the surface of a semiconductor substrate. Semiconductor devices are used everywhere in modern society, and various optical inspections are performed in the inspection of semiconductor substrates that are the materials thereof. In recent years, the number of cases where devices are manufactured by bonding substrates together has been increasing. When analyzing such inspections and processes, by using the parameter indicating the direction of the inclination according to the present invention, it becomes possible to perform analysis using the quantitative directionality of the inclination.

[0048] In addition, the measurement object that is the evaluation target of the surface shape of the present invention can be the surface of a polishing pad. Since the roughness of the polishing pad surface can be transferred to the polishing target, for example, in the case of a polishing pad for polishing a semiconductor substrate, it is important to perform analysis using the quantitative directionality of the inclination as in the case of a semiconductor substrate.

[0049] Here, the significance of the parameter of the present invention will be described in detail using a virtual linear shape (the shape along an arbitrary line set on the surface of the measurement object). FIG. 1 shows a schematic diagram of a contour curve represented by two line segments, line segment AB and line segment BC. Let the coordinates of point A be (-0.5, 0), the coordinates of point B be (a, b) (-0.5 < a < 0.5), the coordinates of point C be (0.5, 0), and the height of a point on line segment AB or line segment BC be z(x). Here, on line segment AB, the height z(x) = z1(x), and on line segment BC, the height z(x) = z2(x). At this time, dz1(x) / dx is 2b / (2a + 1), and dz2(x) / dx is 2b / (2a - 1). Also, (Equation 1) is, in the limit where the interval between data points becomes 0, when b ≠ 0,

Equation

[0050] Therefore, the parameter indicating the direction of the slope of the contour curve of the present invention in the contour curve of Figure 1 is,

number

[0051] Here, with the positive x-direction being to the right, the case where a>0 is called the rightward slope component, and the case where a<0 is called the leftward slope component.

[0052] Furthermore, if we were to change the numerator of (Equation 1) to Σdz(x) / dx, the numerator of the lower part of (Equation 7) in the limit where the interval between measurement points becomes 0 would be:

number

[0053] Furthermore, when using only the numerator of (Equation 1), in the limit where the interval between measurement points becomes 0,

number

[0054] For simplicity, a contour curve consisting of two line segments is given as a specific example here, but the parameter indicating the direction of the slope of the contour curve in this invention can be applied to any contour curve in which the height z(x) is uniquely determined with respect to the coordinate x.

[0055] Furthermore, by extending the parameter indicating the direction of the slope of the contour curve to a plane (region) with extension in two directions, x and y, and setting XY coordinates, and calculating for the x and y directions respectively, the direction of the slope of the surface shape can be indicated as vector components in the x and y directions, as shown in (Equations 2) to (Equations 5).

[0056] Here, the parameter indicating the direction of the inclination of the surface shape can be applied to any surface shape in which the height z(x,y) is uniquely determined with respect to the surface coordinates (x,y).

[0057] Next, the flow of embodiments of the present invention will be described, but the present invention is not limited thereto.

[0058] First, data is prepared for the contour curve or surface shape of the surface to be evaluated (a step to acquire shape data in the height direction). The data to be acquired can be any data as long as it is shape data in the height direction along an arbitrary line set on the surface of the object to be measured or in an arbitrary area set on the surface of the object to be measured. In the case of a contour curve, the contour curve can be any contour curve as long as the height z(x) is uniquely determined for a given coordinate x. Examples of such contour curves include, but are not limited to, the shape of a line scanned with a contact probe, the shape of a line scanned with a laser, and the shape of a curve represented by a non-diverging function f(x).

[0059] Furthermore, even if the shape is obtained by a measurement method in which the height z(x) is not necessarily uniquely determined for each coordinate x, it can still be evaluated if the actually obtained shape is a contour curve in which the height z(x) is uniquely determined for each coordinate x. Such measurement methods include, but are not limited to, optical microscopy and electron microscopy of cross-sectional samples.

[0060] Furthermore, if the contour curve obtained by cutting the surface shape with an arbitrary virtual cross-section has a shape in which the height z(x) is uniquely determined with respect to the coordinate x, then this contour curve can also be analyzed.

[0061] In the case of shape data in the height direction of a surface (arbitrary region), the shape of the surface can be any surface shape as long as the height z(x,y) is uniquely determined for the coordinates (x,y) of the XY coordinate set for the target region. Examples of such surface shapes include, but are not limited to, the shape of a surface scanned with a contact probe, the shape of a surface scanned with a non-contact probe, the shape of a surface scanned with a laser, and the shape of a curved surface represented by a non-divergent function f(x,y).

[0062] On the other hand, even in measurement methods for evaluating roughness, data obtained using methods that do not allow for the acquisition of contour curves and surface shapes cannot be analyzed using the parameters of the present invention. An example of such a measurement method is light scattering type roughness measurement.

[0063] Next, the height data obtained from the measurement may be processed using methods commonly used for each measurement, as needed. The processing will vary depending on the measurement method, but examples include binarization of the microscope image in the case of an electron microscope, and scan correction to correct for deviations between scan lines in the case of a scanning measurement method. However, data processing (correction) is not limited to these. By applying such corrections, it is possible to remove the effects of the measurement method itself and evaluate the results.

[0064] Next, the aforementioned data may be further corrected as needed, using corrections commonly used for shape evaluation such as roughness and waviness. Examples of such corrections include, but are not limited to, noise reduction and tilt correction. By applying such corrections, the influence of measurement-related factors can be removed and the evaluation can be performed. In particular, if the entire sample is tilted during measurement, tilt correction is important because it has a significant impact on the parameter indicating the direction of tilt in the present invention.

[0065] Furthermore, when evaluating roughness or waviness, filters commonly used for roughness and waviness evaluation are applied to the aforementioned data. Examples of such filters include, but are not limited to, 2CR filters and Gaussian filters. Noise reduction and slope correction can also be performed through filtering. By applying such filters, it is possible to extract only the roughness and waviness components of the wavelength to be evaluated, or to remove only the unwanted wavelength components for evaluation.

[0066] Next, as a step to determine the direction of the slope, the parameters of the present invention are calculated for the height data mentioned above, in accordance with the contour curve and surface shape. If the acquired shape data is height data along a line, these parameters are obtained by differentiating the height data. If the acquired shape data is height data in a region, XY coordinates are set for the region, and the parameters are obtained by partially differentiating the height data in the X-axis and Y-axis directions.

[0067] In cases where the number of data points is small, or the shape can be represented by a simple function, the calculation can be done manually. However, when the number of data points is large, or the shape can be represented by a complex function, it is preferable to use a computer for the calculation.

[0068] When calculating the aforementioned parameters, the local slopes dz(x) / dx, ∂z(x,y) / ∂x, and ∂z(x,y) / ∂y are given by, when the data interval is h,

number

[0069] However, the 7-point formula for numerical differentiation cannot be used unless there are at least 3 data points before and after the given point. Therefore, if there are not enough data points, such as at the edges of the data points, you can use the 3-point formula, the 5-point formula for numerical differentiation, or the slope calculated from the difference with adjacent data points as needed.

[0070] Furthermore, when the shape is represented by a differentiable function, the local slopes dz(x) / dx, ∂z(x,y) / ∂x, and ∂z(x,y) / ∂y used to calculate the parameters can be obtained by differentiating or partially differentiating the said differentiable function. In such cases, the interval between data points can be considered infinitesimally small, and therefore it is possible to express it in integral form as shown in (Equation 6).

[0071] Based on the parameters already described, the direction of the inclination of the surface shape of the object being measured can be quantitatively evaluated. [Examples]

[0072] The present invention will be described in detail below with reference to examples, but this is not intended to limit the present invention.

[0073] (Example 1) First, a 3C-SiC / Si substrate was prepared by epitaxially growing 3C-SiC on a silicon single crystal substrate having a (111) surface.

[0074] Next, cross-sectional thin sections were prepared from the substrate using a FIB-SEM (FEI Corporation, Nova600). These cross-sectional thin sections were observed using a transmission electron microscope (Hitachi High-Tech Corporation, HT7700) at an acceleration voltage of 100kV, and cross-sectional transmission electron microscope images were obtained.

[0075] Next, the cross-sectional transmission electron microscope image was binarized and noise was removed to obtain the image shown in Figure 2. In the image, the white area represents the cross-section of the substrate, and the black area represents the background. After performing tilt correction on this image, the X-axis was set to positive on the right and the Z-axis to positive on the top, and a parameter indicating the direction of the slope of the cross-sectional curve was calculated based on (Equation 1). For the calculation of local slope, the difference between adjacent points was divided by the interval for points at the edges of the image, the 3-point formula for numerical differentiation was used for the second point from the edge, the 5-point formula for numerical differentiation was used for the third point from the edge, and the 7-point formula for numerical differentiation was used for all other points. As a result, the parameter indicating the direction of the slope of the cross-sectional curve of the present invention was approximately -0.58, indicating that there was a large slope component that was higher in the leftward direction (from the end point to the starting point).

[0076] (Example 2) First, a silicon epitaxial substrate with the (100) plane as the main surface was prepared.

[0077] Next, the central part of the substrate was measured using an atomic force microscope (ParkSystems, XE-Wafer) with a field of view of □1 μm and 256 × 256 measurement points. The roughness component was extracted by processing with scan correction and a Gaussian filter. The atomic force microscope image at that time is shown in Figure 3.

[0078] Next, after performing tilt correction on the roughness data, the parameters indicating the direction of the surface roughness slope were calculated based on (Equation 5), with the X-axis set to positive on the right, the Y-axis set to positive on the top, and the Z-axis set to positive on the plane of the paper. For the calculation of local slope, the difference between adjacent points was divided by the interval for points at the edges of the image, the 3-point numerical derivative formula was used for the second point from the edge, the 5-point numerical derivative formula was used for the third point from the edge, and the 7-point numerical derivative formula was used for all other points. As a result, the parameters indicating the direction of the slope of the cross-sectional curve of the present invention were (-0.02, -0.06), indicating that there is a large amount of slope component that is slightly higher to the left (from the end point to the starting point of the X-axis) and somewhat higher downwards (from the end point to the starting point of the Y-axis).

[0079] (Comparative Example 1) For the binarized image shown in Figure 2 in Example 1, the same tilt correction as in Example 1 was performed, and the root mean square slope of the cross-sectional curve was calculated. As a result, a value of approximately 1.13 was obtained, but this value does not contain information about the direction of the slope.

[0080] (Comparative Example 2) The direction of the inclination was visually confirmed in the binarized image of Figure 2 shown in Example 1. The inclination between the convex and concave parts was shorter for the rightward-sloping inclination due to its steeper angle, and longer for the leftward-sloping inclination. In addition, the concave parts were generally sloped upward to the left. The convex parts were generally flat. From these results, it can be said that the inclination is roughly to the left, but this is a subjective judgment and could not be quantified by visual inspection alone.

[0081] (Comparative Example 3) Regarding the measurement results of Example 2 described above, the aspect ratio of the surface shape, the direction of the surface texture, and the root mean square slope were calculated. As a result, values ​​of approximately 0.16, approximately 3°, and approximately 3.2 were obtained, respectively, but these values ​​do not contain information about the direction of the slope. Here, although the direction of the surface texture indicates the direction of the node, it does not contain information about the direction of the slope, such as how much the slope forming the node is biased relative to the node's apex. Furthermore, the direction of the surface texture is a value with the right side set to 0°, which at first glance seems to contradict the fact that the parameter indicating the direction of the slope of the cross-sectional curve in the above example had a relatively large value in the downward direction. However, the parameter indicating the direction of the slope in the present invention indicates the direction of the slope forming the node, and is therefore orthogonal to the direction of the surface texture, which indicates the direction of the node itself. Therefore, there is no contradiction between the direction of the surface texture and the parameter indicating the direction of the slope in the present invention.

[0082] (Comparative Example 4) Regarding the measurement results of Example 2, the direction of the inclination was visually confirmed from the image in Figure 3. There are nodes that curve in the left-right direction, and the color change is steeper in the downward direction than in the upward direction relative to the apex of the white nodes. Therefore, it is expected that the proportion of the downward component of the vertical inclination that constitutes the nodes is large. However, it is not possible to quantify the degree of this by visual inspection. Also, as shown in Figure 4, by connecting the white apex of the nodes, it can be confirmed that there are nodes with longer wavelengths. However, the direction of the inclination that forms these nodes cannot be read from the image. From the results of Example 2, it is expected that the leftward inclination component is stronger than the rightward inclination component.

[0083] As described above, according to the embodiment of the present invention, it was possible to quantitatively evaluate the direction of the inclination of the surface shape of the object to be measured.

[0084] This specification includes the following embodiments: [1]: A method for evaluating the direction of the inclination of the surface shape of a surface object to be measured, A step of acquiring height-direction shape data along an arbitrary line set on the surface of the object to be measured or in an arbitrary area set on the surface of the object to be measured, Based on the height data obtained along the line or in the region, In the case of height data along the aforementioned line, the parameter obtained by differentiating the aforementioned height data is In the case of height data in the aforementioned region, XY coordinates are set for the region, and the parameters obtained by partially differentiating the height data in the X-axis direction and the Y-axis direction are A step of quantifying the direction of the slope using and determining the direction of the slope along the line or in the region from the sign of the obtained numerical value, A method for evaluating surface shape, including the surface shape. [2]: In the step of determining the direction of the slope, if the direction of the slope along the line is determined based on height data along the line, When the coordinate of the position along the aforementioned line is x, and the height at that coordinate x is z(x), Σ(dz(x) / dx)2 If = 0, it is determined that the slope has no direction. Σ(dz(x) / dx) 2 If ≠0, the direction of the slope is,

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[0085] It should be noted that the present invention is not limited to the embodiments described above. The embodiments described above are illustrative, and any configuration that is substantially identical to the technical idea described in the claims of the present invention and achieves similar effects is included within the technical scope of the present invention.

Claims

1. A method for evaluating surface shape, which evaluates the direction of the inclination of the surface shape of a target to be measured, A step of acquiring height-direction shape data along an arbitrary line set on the surface of the object to be measured or in an arbitrary area set on the surface of the object to be measured, Based on the height data obtained along the line or in the region, In the case of height data along the aforementioned line, the parameter obtained by differentiating the aforementioned height data is In the case of height data in the aforementioned region, XY coordinates are set for the region, and the parameters obtained by partially differentiating the height data in the X-axis direction and the Y-axis direction are A step of quantifying the direction of the slope using and determining the direction of the slope along the line or in the region from the sign of the obtained numerical value, A method for evaluating surface shape, characterized by including the following:

2. In the step of determining the direction of the slope, if the direction of the slope along the line is determined based on height data along the line, When the coordinate of the position along the aforementioned line is x, and the height at that coordinate x is z(x), Σ(dz(x) / dx) ２ If the value is 0, it is determined that the slope has no direction. Σ(dz(x) / dx) ２ If ≠ 0, the direction of the slope is, [Math 1] Expressed as a relational expression, If the above (Equation 1) is a positive value, it is determined that there is a large slope component in the line that increases in the direction in which the coordinate x increases. If the above (Equation 1) is a negative value, it is determined that there is a large slope component in the line that increases in the direction in which the coordinate x decreases. The method for evaluating surface shape according to feature 1.

3. In the step of determining the direction of the slope, if the direction of the slope of the region is determined based on the height data of the region, When the coordinates of the position within the aforementioned region are (x, y) and the height at the aforementioned coordinates (x, y) is z(x, y), Σ(∂z(x,y) / ∂x) ２ =Σ(∂z(x,y) / ∂y) ２ If = 0, the vector quantity P1 is, (0,0) ... (Formula 2) This is expressed as follows, and it is determined that there is no directionality in the slope within the aforementioned region. Σ(∂z(x,y) / ∂x) ２ =0, Σ(∂z(x,y) / ∂y) ２ If ≠ 0, the vector quantity P2 is, [Math 2] It is expressed as, Σ(∂z(x,y) / ∂x) ２ ≠0, Σ(∂z(x,y) / ∂y) ２ If = 0, the vector quantity P3 is, [Math 3] It is expressed as, Σ(∂z(x, y) / ∂x) ２ ≠ 0, Σ(∂z(x, y) / ∂y) ２ If ≠ 0, then the vector quantity P4 is [Math 4] It is expressed as, In the aforementioned vector quantities P2, P3, and P4, if the component of the vector is 0, it is determined that there is no directionality in the slope in the direction of the component. In the aforementioned vector quantities P2, P3, and P4, if the components of the vectors have positive values, it is determined that there are many slope components that rise in the positive direction of the component having a positive value, starting from the origin of the XY coordinate system. In the aforementioned vector quantities P2, P3, and P4, if the components of the vectors have negative values, it is determined that there are many slope components that increase in the negative direction of the component having a negative value, starting from the origin of the XY coordinate system. The method for evaluating surface shape according to feature 1.

4. The method for evaluating the surface shape according to claim 2 or 3, characterized in that, in the step of determining the direction of the slope, the derivative of dz(x) / dx and the partial derivatives of ∂z(x,y) / ∂x and ∂z(x,y) / ∂y are calculated using the seven-point formula for numerical differentiation, excluding the three points at each end of the data.

5. The method for evaluating surface shape according to claim 1, characterized in that, in the step of acquiring the shape data, the surface shape is measured using an electron microscope or an atomic force microscope.

6. The method for evaluating the surface shape according to any one of claims 1 to 3, characterized in that the object to be measured is a semiconductor substrate.

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