Analysis device, analysis method, and analysis program

Abstract

Provided are an analysis device, an analysis method, and an analysis program which are capable of accurately analyzing a scatterer having a complicated cross-sectional shape and improving robustness of analysis. The present invention is provided with: an initial information setting unit 124c that sets an initial cross-sectional shape when fitting is repeated by changing the cross-sectional shape of a layer under the condition that a scatterer is formed by laminating, in the thickness direction of a plate-shaped sample, a layer having a constant cross-sectional shape represented by an angle and a radius centered about the origin; an intensity calculation unit 126 that calculates, on the basis of the cross-sectional shape of the layer, the scattering intensity of X-rays scattered by the plate-shaped sample; a fitting unit 127 that fits the calculated scattering intensity to the measured scattering intensity; and a parameter determination unit 128 that determines, according to the result of the fitting, the angle and radius representing the cross-sectional shape of the layer. The fitting unit repeats fitting by changing the cross-sectional shape of the layer.

Description

Analysis device, analysis method, and analysis program

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

[0002] As a method for analyzing the shape of a microfabrication pattern using a periodic arrangement of long scatterers in the thickness direction of a plate-like sample, a method is known in which the scatterers are sliced ​​at each position in the depth direction and the position of the center of gravity and the size of each sliced ​​layer are calculated (see Patent Document 1). Unlike an analysis that determines parameters representing a predetermined model such as an elliptical cylinder, this method introduces an analysis that can arbitrarily express the position of the center of gravity and size in the depth direction.

[0003] Patent No. 7100897

[0004] However, in the method described in Patent Document 1, the cross-sectional shape of each layer of the scatterer is approximated by a predetermined shape such as a circle, ellipse, or rectangle. This type of analysis cannot obtain accurate analysis results when the scatterer has an arbitrary shape whose cross section cannot be expressed by a predetermined shape (circle, ellipse, or rectangle) or a shape whose cross section varies along the depth direction. For example, the processed shapes of semiconductor devices have become more complex in recent years, and in transmission CD-SAXS, there are an increasing number of situations in which the processed shapes cannot be analyzed using simple shape models. Particularly during the product development stage, scatterers with complex cross-sectional shapes may be formed, whether intentional or not. In such situations, it is important to accurately recognize the shape of the scatterer.

[0005] The present invention has been made in consideration of the above circumstances, and aims to provide an analysis device, an analysis method, and an analysis program that can accurately analyze scatterers with complex cross-sectional shapes and improve the robustness of the analysis.

[0006] (1) In order to achieve the above object, the analytical device of the present invention is an analytical device for the microstructure of a plate-shaped sample formed by a periodic arrangement of scatterers that are long in the thickness direction, and includes: a measurement data memory unit that stores data on the scattering intensity of X-rays scattered from the plate-shaped sample measured by transmitting X-rays at multiple ω rotation angles; an initial information setting unit that sets an initial cross-sectional shape when repeating fitting by changing the cross-sectional shape of the layer under the condition that the scatterers are formed by layers having a constant cross-sectional shape represented by an angle and a radius about the origin as the center and that are stacked in the thickness direction of the plate-shaped sample; an intensity calculation unit that calculates the scattering intensity of X-rays scattered by the plate-shaped sample based on the cross-sectional shape of the layer; a fitting unit that performs the fitting of the calculated scattering intensity to the measured scattering intensity; and a parameter determination unit that determines the angle and radius that represent the cross-sectional shape of the layer based on the results of the fitting, wherein the fitting unit repeats the fitting by changing the cross-sectional shape of the layer.

[0007] (2) In the analysis device described in (1) above, the intensity calculation unit calculates the scattering intensity under the condition that the shapes of the layers constituting the scatterer are similar to each other.

[0008] (3) In the analysis device described in (1) or (2) above, the initial information setting unit sets a predetermined shape as the initial cross-sectional shape of the layer.

[0009] (4) In the analysis device described in (1) or (2) above, the initial information setting unit is characterized in that it sets a shape designated by a user as the initial cross-sectional shape of the layer.

[0010] (5) Furthermore, the analysis device described in (4) above is characterized by further comprising an input information conversion unit that converts a shape specified by the user using a freeform tool into an initial cross-sectional shape of the layer.

[0011] (6) Furthermore, in the analysis device described in (1) or (2) above, the initial information setting unit is characterized in that it uses a shape set using image data of the plate-shaped sample as the initial cross-sectional shape of the layer.

[0012] (7) In the analysis device described in (1) or (2) above, the initial information setting unit is characterized in that it uses a shape determined by parameters obtained by model-based analysis as the initial cross-sectional shape of the layer.

[0013] (8) Furthermore, in the analysis device described in any one of (1) to (7) above, the parameter determination unit is characterized in that it calculates the center of gravity position of the cross-sectional shape of each of the layers in a relative position with respect to the origin.

[0014] (9) In addition, in the analysis device described in any one of (1) to (8) above, the parameter determination unit is characterized in that it determines conditions for using a model-based analysis in which the cross-sectional shape of the layer is assumed to be constant, based on the determined angle and radius representing the cross-sectional shape of the layer.

[0015] (10) The analytical method of the present invention is a method for analyzing the microstructure of a plate-shaped sample formed by periodically arranging long scatterers in the thickness direction, and is characterized by including the steps of: preparing data on the scattering intensity of X-rays scattered from the plate-shaped sample measured by transmitting X-rays at multiple ω rotation angles; setting an initial cross-sectional shape when repeating fitting by changing the cross-sectional shape of the layer under the condition that the scatterers are formed by layers having a constant cross-sectional shape represented by an angle and a radius about the origin as the center and stacked in the thickness direction of the plate-shaped sample; calculating the scattering intensity of X-rays scattered by the plate-shaped sample based on the cross-sectional shape of the layer; fitting the calculated scattering intensity to the measured scattering intensity; and determining the angle and radius representing the cross-sectional shape of the layer based on the fitting result.

[0016] (11) Furthermore, the analysis program of the present invention is an analysis program for the microstructure of a plate-shaped sample formed by a periodic arrangement of long scatterers in the thickness direction, and is characterized in that it causes a computer to execute the following processes: a process for preparing data on the scattering intensity of X-rays scattered from the plate-shaped sample measured by transmitting X-rays at multiple ω rotation angles; a process for setting an initial cross-sectional shape when repeating fitting by changing the cross-sectional shape of the layer under the condition that the scatterers are formed by layers having a constant cross-sectional shape represented by an angle and a radius about the origin as the center and stacked in the thickness direction of the plate-shaped sample; a process for calculating the scattering intensity of X-rays scattered by the plate-shaped sample based on the cross-sectional shape of the layer; a process for fitting the calculated scattering intensity to the measured scattering intensity; and a process for determining the angle and radius representing the cross-sectional shape of the layer based on the result of the fitting.

[0017] 1 is a perspective view showing a transmission type CD-SAXS measurement system. (a) and (b) are XY cross-sectional view and XZ cross-sectional view, respectively, showing a plate-shaped sample in terms of electron number density distribution. (a) and (b) are diagrams showing hole shapes in the XZ plane and YZ plane, respectively, showing analysis conditions. (a) and (b) are diagrams showing the cross-sectional shape of a slice layer containing a scatterer. (b) are diagrams showing the cross-sectional shape where Rk is expressed as a multi-valued function of θk. (c) is a block diagram showing the configuration of a measurement system according to the present invention. (d) is a plan view showing the configuration of a measurement device. (e) is a diagram showing an example in which a shape obtained by model-free analysis is approximated by an elliptical model. (f) is a flowchart showing a measurement and analysis method according to the present invention. (g) is a flowchart showing the selection of a cross-sectional shape setting method according to the present invention. (g) is a diagram showing the magnification for each slice layer of a scatterer. (h) is a diagram showing the shape of each cross section of a scatterer set as the true shape. (h) is a diagram showing a shape set using a free form tool. Ｚ 1 is a graph showing a scattering profile fitted with a constant ellipse as a cross-sectional shape to an actually measured scattering profile in the Q direction. Ｚ 10A and 10B are graphs showing scattering profiles fitted to a model-free shape as a cross-sectional shape relative to an actually measured scattering profile in the Q direction. Ｒ1 is a graph showing scattering profiles fitted with a constant ellipse and a model-free shape as cross-sectional shapes in the Q direction; FIG. 2 is a diagram showing the cross-sectional shape of a scatterer for i=5 fitted with a constant ellipse and a model-free shape as cross-sectional shapes; FIG. 3 is a diagram showing the cross-sectional shape of a scatterer for i=15 fitted with a constant ellipse and a model-free shape as cross-sectional shapes; FIG. 4 is a diagram showing the cross-sectional shape of a scatterer for i=25 fitted with a constant ellipse and a model-free shape as cross-sectional shapes; and FIG. 5 is a diagram showing the shapes of each cross section of a scatterer set as the true shape. Ｚ 1 is a graph showing a scattering profile fitted with a constant circle as a cross-sectional shape to an actually measured scattering profile in the Q direction. Ｚ 10A and 10B are graphs showing scattering profiles fitted to a model-free shape as a cross-sectional shape relative to an actually measured scattering profile in the Q direction. Ｒ 10 is a graph showing scattering profiles fitted with a constant circle and a model-free shape as cross-sectional shapes in the direction, respectively.

[0018] Next, an embodiment of the present invention will be described with reference to the drawings. To facilitate understanding of the description, the same reference numerals are used to designate the same components in the drawings, and duplicated descriptions will be omitted.

[0019] [Principle] (Transmission CD-SAXS) In this invention, the shape of the scatterers in a sample is analyzed using a transmission CD-SAXS that can be performed at the laboratory level. This method is particularly suitable for analyzing the shape of semiconductor devices with deep groove microfabrication patterns, such as 3D NAND and DRAM. This invention is based on an analysis method in which the sample is finely sliced ​​in the depth direction and diameter and positional fluctuations are assigned as parameters to each depth.

[0020] FIG. 1 is a perspective view showing a measurement system of a transmission-type CD-SAXS. In a transmission-type CD-SAXS, the sample is rotated (ω rotation) based on the direction of incidence of X-rays perpendicular to the sample surface, and the dependence of the integrated intensity of each diffraction line on the sample rotation angle is measured. The ω axis is the sample rotation axis perpendicular to the direction of incidence of X-rays, and the Q ＹThe axis coincides with the ω axis. The sample rotation is performed by the scattering vector Q Ｚ This is because the information in the depth direction can be obtained by changing the ΔQ Ｚ is the reflective ΔQ Ｚ Since it is extremely small, 1 / 100 to 1 / 1000 times smaller than the conventional method, it is effective for analyzing deep holes or deep grooves.

[0021] (Small-angle X-ray scattering intensity) In transmission CD-SAXS, which is less affected by refraction and multiple reflections as described above, the small-angle X-ray scattering intensity I(Q) can be calculated using the Born approximation (the square of the absolute value of the Fourier transform of the electron number density distribution ρ(r) in the entire system).

[0022] 2(a) and (b) are XY and XZ cross-sectional views, respectively, of a plate-shaped sample, which are expressed by the electron number density distribution. When the scatterer has a periodic pattern structure as shown in FIGS. 2(a) and 2(b), the amplitude of the scattered X-rays can be described by the product of the integral over the unit cell and the Laue function L. Then, Q, which satisfies the diffraction condition, is calculated from the Laue function. Ｘ , Q Ｙ is derived.

[0023] 2(a), independent sites of each unit cell are indicated by hatched circles. When the electron density distribution and shape are common regardless of the site, the integral within the unit cell that represents the scattering amplitude within the unit cell can be described as the product of the scatterer shape factor F, which is the integral of one scatterer, and the structure factor S.

[0024] When the pattern structure of the scatterer is determined by the mask pattern, such as in semiconductor devices, it is important to determine the shape of the scatterer (electron number density distribution). The factor related to the shape of the scatterer is nothing other than the shape factor F, which is the shape integral of the scatterer.

[0025] Since the shape of an actual scatterer cannot be approximated by a simple shape such as a cylinder, it is effective to slice it in the depth direction and analyze it using shape factors that are incorporated into the parameters of each slice layer. The shape can be determined by refining the model parameters so that the calculated data, which uses the model parameters as variables, matches the experimental data. In this case, an analysis that assumes the cross-sectional shape of each layer to be a predetermined shape such as a circle, ellipse, or rectangle is called a model-based analysis, while an analysis that allows for arbitrariness in the cross-sectional shape of each layer is called a model-free analysis.

[0026] [Model-free analysis] The scattering intensity of X-rays from a plate-shaped sample can be calculated under the condition that the scatterers are formed by stacking layers with different cross-sectional shapes (XY cross-sectional shapes) in the thickness direction of the plate-shaped sample. For example, the depth of the hole is used as a parameter, and the sample is sliced ​​into N equal layers in the depth direction. Figures 3(a) and 3(b) show the hole shapes in the XZ plane and the YZ plane, respectively, showing the analysis conditions.

[0027] In model-free analysis, one rotation (2π) is divided into N equal parts, and the distance Rk to the boundary surface is given as a variable for each θk = 2πk / N, to express any XY cross-sectional shape. In analysis, any XY cross-sectional shape can be obtained by optimizing Rk. For the jth slice layer, the density ρ[j], thickness t[j], and origin position of the scatterer (ΔX[j], ΔY[j]) can be given as variables. Note that x[j] and y[j] in Figure 3 indicate the center of gravity position of the jth slice layer.

[0028] FIG. 4 is a diagram showing the cross-sectional shape of a certain slice layer of a scatterer. Each slice layer of a scatterer is specified by the angle and radius when the center of gravity of the cross-sectional shape is the origin. This allows complex shapes to be represented. For example, if the center of gravity is expressed as (X, Y), the position and shape of a hole are given by the origin position (X + ΔX, Y + ΔY) relative to the center of gravity (X, Y) and the angle and radius parameters (θk, Rk). Note that cross-sectional shapes where Rk is expressed as a multi-valued function of θk are not handled, and it is preferable to prevent the user from specifying such shapes as the initial cross-sectional shape.

[0029] FIG. 5 is a diagram showing a cross-sectional shape in which Rk is expressed as a multi-valued function of θk. As shown in FIG. 5, shapes in which multiple radii Rk occur at a specific θk relative to a certain origin are not considered as initial shapes. However, depending on how the origin is selected, Rk may be expressed as a multi-valued function of θk or may not be expressed as a multi-valued function of θk. By selecting an origin separate from the center of gravity of the cross-sectional shapes of each layer, the initial shape can be set so that Rk is not expressed as a multi-valued function of θk. In this case, the position of the center of gravity or the origin can be expressed as the relative position of the other. The origin position and the center of gravity position may also be coincident. In this case, the amount of information to be processed can be reduced.

[0030] In reality, sliced ​​layers adjacent to each other in the stacking direction are continuously connected to each other. Therefore, it is preferable to perform fitting while imposing such a continuity constraint. This makes it easier for the simulation results to converge, reducing the calculation burden and obtaining results that are close to the actual shape. For example, one method is to use the least squares method and add weights that minimize the path integral of the cross section. In order to determine the cross-sectional shape during analysis, multiple diffraction image data are obtained by rotating the sample.

[0031] [Overall System] Figure 6 is a block diagram showing the configuration of measurement system 100. Measurement system 100 includes a measurement device 110 and an analysis device 120, and enables transmission CD-SAXS measurement by irradiating a plate-shaped sample with X-rays and measuring the scattering intensity. Analysis device 120 controls measurement device 110 and manages measurement data together with control data, enabling data analysis. The specific configuration is described below.

[0032] 7 is a plan view showing the configuration of the measurement apparatus 110. The measurement apparatus 110 includes an X-ray source 111, a mirror 112, slits S1, S2, GS, a sample stage 115, a vacuum path 116, a beam stopper 118, and a detector 119. The distance L0 from the X-ray source 111 to the sample S0 and the camera length L can be set to, for example, 1000 mm and 3000 mm, respectively.

[0033] The X-ray source 111 can use MoKα radiation. The mirror 112 splits the X-rays emitted from the X-ray source 111 and irradiates the split X-rays toward the sample S0. The slits S1 and S2 are made of an X-ray-shielding material and form a slit section that focuses the split X-rays. This configuration enables X-ray irradiation at multiple rotation angles ω close to the perpendicular direction to the surface of the plate-shaped sample S0. It is preferable to select specific angles between -10° and 10° for the multiple rotation angles ω. The slit GS can limit the X-ray spot size on the sample surface to several tens of μm or less. Essentially, the beam size is determined by the slits S1 and S2, and the GS is used to remove parasitic scattering occurring in the slits S1 and S2. However, to create a very small spot, the GS can also be used to reduce the beam size.

[0034] The sample stage 115 supports the sample S0 on the stage, and can adjust the orientation of the plate-shaped sample S0 by a driving mechanism under the control of the analysis device 120. Specifically, the Q Ｙ In addition to the ω rotation angle, the χ rotation angle and the φ rotation angle can also be adjusted. By adjusting these angles, the incident angle of the dispersed X-rays onto the sample S0 can be changed, and the scattering intensity can be measured according to the diffraction angle.

[0035] The sample S0 is formed in a plate shape, and scatterers are periodically arranged in a direction parallel to the main surface of the sample. Examples of scatterers include holes. A typical sample is a silicon wafer substrate, in which case the scatterers are holes formed by etching. The higher the integration level, the more important it is to be able to confirm that the hole shapes are formed accurately according to the specifications.

[0036] In such a case, even if the length of the scatterer is 200 nm or more and 20 μm or less, the shape of the scatterer that is long in the thickness direction can be identified by irradiating X-rays perpendicularly to the sample surface and utilizing the scattering that occurs as the X-rays pass through, as shown in Figure 7.

[0037] The scatterers are not limited to holes as described above, but may be pillars. That is, the present invention can be applied to a silicon substrate sample on whose surface circular columns are periodically formed. Furthermore, the present invention can also be applied to a sample on which a line pattern (space pattern) such as a long molecular array is formed.

[0038] The vacuum path 116 maintains a vacuum on the path of the scattered beam to prevent beam attenuation while increasing the camera length. The beam stopper 118 absorbs the direct beam. The detector 119 is, for example, a semiconductor two-dimensional detector that can move along a circumference from the sample position and can detect the scattering intensity of X-rays. The measurement device 110 and the analysis device 120 are connected, and the detected scattering intensity data is sent to the analysis device 120.

[0039] The measuring device 110 preferably includes a laser light source and a detector for reflected light. The orientation of the plate-shaped sample can be adjusted by using the reflection of the laser light so that the surface of the plate-shaped sample is perpendicular to the direction of incidence of the X-rays. The orientation adjusted in this way can be used as the reference, where ω = χ = 0°.

[0040] When evaluating the cross-sectional shape of a sample, analysis itself can be performed without a reference. However, the cross-sectional shape determined in this way is merely based on an appropriate origin of the ω-axis and χ-axis of the goniometer. In many cases where cross-sectional shape evaluation is required, it is required to evaluate the cross-sectional shape based on the surface. In such cases, it is desirable to determine the surface reference before measurement and analysis.

[0041] [Analysis Device] The analysis device 120 is configured, for example, with a PC having a memory and a processor, and is capable of executing various processes by running programs. By processing the measurement data obtained from the measurement device 110, it is possible to analyze the microstructure of a plate-shaped sample formed by a periodic arrangement of scatterers long in the thickness direction. The analysis device 120 is capable of not only model-free analysis but also model-based analysis. The configuration described in Patent Document 1 can be used for model-based analysis.

[0042] The analysis device 120 includes a control unit 121, a mathematical formula storage unit 122, a measurement data storage unit 123, a basic information setting unit 124a, a setting method selection unit 124b, an initial information setting unit 124c, an input information conversion unit 125, an intensity calculation unit 126, a fitting unit 127, and a parameter determination unit 128. Each unit can send and receive information via a control bus L. The input device 210 and the output device 220 are connected to the CPU via an appropriate interface.

[0043] The analysis device 120 is a device equipped with a CPU and memory, and may be a PC terminal or a server on the cloud. Furthermore, not only the entire device, but also some of the devices or some of the functions within the device may be provided on the cloud. The input device 210 is, for example, a keyboard or a mouse, and receives selections and specifications from the user, and inputs them to the analysis device 120. The output device 220 is, for example, a display, and displays the scattering profile output from the analysis device 120, a UI for setting initial information, and the like.

[0044] The control unit 121 controls the measurement device 110 and manages control data and measurement data. For example, the control unit 121 controls the sample stage using a drive mechanism to adjust the orientation of the sample. The mathematical formula storage unit 122 stores mathematical formulas for calculating scattering intensity for specific shape models or analysis conditions. The measurement data storage unit 123 stores intensity data of X-rays scattered from the plate-shaped sample as the X-rays pass through, measured at multiple ω rotation angles near the perpendicular direction to the surface of the plate-shaped sample.

[0045] The basic information setting unit 124a sets basic information, for example, by providing initial values ​​of density ρ[j], thickness t[j], and origin position (ΔX[j], ΔY[j]) of the scatterer for each layer sliced ​​at each depth.

[0046] The setting method selection unit 124b selects a model-based analysis in which the cross-sectional shape is a predetermined shape or a model-free analysis in which the cross-sectional shape is arbitrary based on the user's selection information. Also, based on the user's selection information, in the model-free analysis, selects whether to set an initial shape for all layers or to set the cross-sectional shape of one layer and the magnification of each layer.

[0047] The initial information setting unit 124c sets the initial cross-sectional shape of each layer when repeating fitting by changing the cross-sectional shape of each layer under specific conditions. The specific conditions are conditions in which a scatterer is formed by stacking layers each having a constant cross-sectional shape in the thickness direction of the plate-shaped sample. Note that the constant cross-sectional shape is expressed by an angle and a radius when the origin is the center. If the angle is specified as the kth angle when 360° is divided by a predetermined number, the amount of information can be reduced and processing efficiency can be improved.

[0048] When repeating fitting by changing the cross-sectional shape of each layer, the initial information setting unit 124c can set a predetermined shape as the initial cross-sectional shape of each layer. This makes it possible to set a predetermined shape, such as an oval or an oval, as the initial shape, making setting easier.

[0049] The initial information setting unit 124c can also set a shape that is set using image data of a plate-shaped sample as the initial cross-sectional shape of each layer. This allows the initial scatterer shape to be specified using, for example, an electron microscope image. In this case, the measurement data can be used to eliminate arbitrariness in the setting.

[0050] The initial information setting unit 124c can set a shape determined by parameters obtained by model-based analysis as the initial cross-sectional shape of each layer. That is, the cross-sectional shape of each layer can be first fixed to a standard shape and analyzed, and the obtained results can be used as the initial conditions. This allows a cross-sectional shape with a certain degree of validity to be used for the initial setting, and appropriate parameters that are easy to converge can be prepared.

[0051] The input information conversion unit 125 converts the shape specification information received from the user using the freeform tool into shape setting information as the initial cross-sectional shape of each layer, thereby reducing the workload of the user who has to input N points one by one to specify the cross-sectional shape.

[0052] The intensity calculation unit 126 calculates the scattering intensity of X-rays scattered by the plate-shaped sample under specific conditions. The intensity calculation unit 126 acquires a formula for calculating scattering for a desired shape model or analysis conditions from the formula storage unit 122, and calculates the scattering intensity of X-rays using the formula and the values ​​of various set parameters. By using the acquired formula, the scattering intensity of X-rays scattered by the plate-shaped sample under specific conditions can be calculated.

[0053] The fitting unit 127 fits the scattering intensity calculated by the intensity calculation unit 126 to the scattering intensity of X-rays actually measured by the measurement device 110. The fitting unit 127 checks whether the fitting is optimal, and if not, changes the parameters and calculates the scattering intensity again by simulation.

[0054] The parameter determination unit 128 determines the parameters of the scatterers in the plate-like sample using the fitting results. Specifically, it determines the angles and radii that represent the cross-sectional shape of each layer. In this way, it is possible to determine the shape of scatterers that are long in the thickness direction, and it is possible to accurately analyze scatterers with complex cross-sectional shapes, thereby improving the robustness of the analysis.

[0055] The parameter determination unit 128 may calculate the center of gravity of the cross-sectional shape of each layer relative to the origin. This allows a point independent of the center of gravity of the cross-sectional shape of the scatterer to be used as the origin, making it possible to handle a variety of cross-sectional shapes without making the radius a multi-valued function of the angle.

[0056] The parameter determination unit 128 can also determine the conditions for using a model-based analysis that assumes a fixed cross-sectional shape, based on the determined angles and radii that represent the cross-sectional shapes of each layer. This allows models to be set for similar cases, enabling efficient analysis.

[0057] For example, the XY cross-sectional shape obtained by the model-free analysis can be fitted with the shape used in the model-based analysis, and the obtained shape can be used as the initial value for the model-based analysis. Figure 8 is a diagram showing an example in which the shape obtained by the model-free analysis is approximated with an ellipse model. The shape obtained by the model-free analysis is shown with a dashed line, and the ellipse obtained by fitting is shown with a solid line. In the example shown in Figure 8, the model-based analysis is performed using the ellipse represented by the solid line as a constant cross-sectional shape, thereby making the processing more efficient.

[0058] [Measurement Method and Analysis Method] (Overall Flow) Next, a measurement and analysis method using the above-described system configuration will be described. FIG. 9 is a flowchart showing the measurement and analysis method. As shown in FIG. 9, first, a plate-shaped sample is placed (step S101). At this time, the normal to the sample surface is aligned parallel to the X-ray. Then, the scattering intensity at multiple ω rotation angles is measured to obtain a transmission CD-SAXS waveform (step S102).

[0059] Based on the obtained measurement data, the Q of each diffraction point Ｚ The waveform is acquired (step S103). Then, the depth direction is appropriately divided into slices (step S104), and initial values ​​of the density ρ[j], thickness t[j], and origin position (ΔX[j], ΔY[j]) of the scatterer are assigned to each slice layer (step S105).

[0060] Next, a method for setting the cross-sectional shape is selected (step S106). Specifically, a type of model-free analysis or a model-based analysis is selected as a method for setting the cross-sectional shape of the scatterer. Details will be described later.

[0061] Under these conditions, the X-ray scattering intensity is calculated assuming physical parameters (step S107). The calculated scattering intensity is then fitted to the measured scattering intensity (step S108). It is checked whether the fitting is optimal (step S109). If it is not optimal, the parameters are changed (step S110), and the process returns to step S107. The parameters include the density, thickness, origin, angle, and radius of each cross-sectional shape. If the fitting is optimal, the parameters are determined using the values ​​at that time (step S111), and the process ends.

[0062] (Selection of Cross-Section Shape Setting Method) Of the above series of steps, the selection of the cross-section shape setting method will be particularly described. Fig. 10 is a flowchart showing the selection of the cross-section shape setting method. The selection in this flowchart is basically based on information input by the user, but may also be made automatically in accordance with some kind of flag.

[0063] First, it is determined whether or not a model-free analysis has been selected (step S201). If a model-free analysis has not been selected, a model-based analysis is performed, and a predetermined cross-sectional shape is selected as a shape model for each layer (step S202). Predetermined cross-sectional shapes include ellipses, polygons, teardrops, ovals, snowmen, and dumplings. These shapes also include corners with a constant curvature.

[0064] Then, initial values ​​of the shape model are set (step S203), and the selection of the cross-sectional shape setting method is completed. For example, if an ellipse is selected, the center, major axis, minor axis, and rotation orientation of the major axis of the ellipse are set as initial values. Also, if a rectangle is selected, the center, major side, minor side, and rotation orientation of the major side of the rectangle are set as initial values.

[0065] On the other hand, if model-free analysis is selected in step S201, it is determined whether or not the setting of all layers when the scatterer is sliced ​​at each Z position has been selected (step S204). If the setting of all layers has not been selected, a scatterer is set in which the cross-sectional shapes of all layers are similar to each other. That is, the shape data of the first layer and the magnification in the depth direction are set as initial information (step S205). The shape data is expressed as the position of the origin and the angle and radius when the origin is the center. Furthermore, the shape data of a specific layer, not just the first layer, may be set as a reference, and the magnifications of other layers may be set.

[0066] If setting all layers is selected in step S204, the initial values ​​of the shape data for all layers are set (step S206). Since the initial values ​​of the shape data are set for all layers, when the cross-sectional shape of the scatterer changes depending on the depth or when the scatterer has a complex shape, the shape can be analyzed accurately.

[0067] (Setting by Similar Shapes) A ​​scatterer in which the cross-sectional shapes of all layers are similar to one another can also be set as initial information. In this case, the user simply specifies the cross-sectional shape of a specific layer and the magnifications of the other layers as initial conditions. Figure 11 is a diagram showing the magnifications for each slice layer of a scatterer. For example, as shown in Figure 11, different magnifications are set for layers at each Z position with the first layer as the reference.

[0068] In this case, the intensity calculation unit 126 calculates the scattering intensity under the condition that the shapes of the layers constituting the scatterer are similar to each other. This makes it possible to analyze the shape of the scatterer by reducing the number of parameters when the shapes of the scatterers in adjacent layers are almost the same.

[0069] For example, analysis can be performed using parameters such as Rk of the outermost X-Y cross section and the magnification of each slice excluding the surface. If it is assumed that the X-Y cross sections are similar, the number of parameters can be reduced, thereby shortening the analysis time. If the X-Y cross section shape is completely model-free, even in the depth direction, the number of parameters is the number of divisions of the X-Y cross section shape x the number of divisions in the depth direction. However, if it is assumed that the X-Y cross section shape is similar in the depth direction, the number of parameters is the number of divisions of the X-Y cross section shape + the number of divisions in the depth direction - 1.

[0070] (Setting using the freeform tool) The freeform tool may be made available when initially setting the cross-sectional shape. Setting the radius of each angle is a burden for the user. Setting all layers is particularly burdensome. In such cases, setting using the freeform tool is effective.

[0071] FIG. 12 is a diagram showing a shape set using the freeform tool. As shown in FIG. 12, a curve can be specified along the dashed arrow by clicking the mouse at an inflection point while moving the pointer. The specified curve can be converted into radius information at each angle, thereby specifying the initial information for the cross-sectional shape. Note that various methods for specifying a curve can be adopted as a freeform tool. The mouse can be clicked only at the start and end points, and the intermediate portion can be specified by simply moving the pointer, or the clicked points can be connected by a straight line. The mouse can also be clicked by touching with a finger.

[0072] The model-free analysis according to the present invention as described above can be applied particularly to the field of semiconductor devices, and enables highly robust analysis of any shape of a microfabricated pattern formed on a wafer surface from experimental data acquired using transmission CD-SAXS.

[0073] [Examples] Analyses were performed under different conditions on a plate-shaped sample model in which scatterers long in the depth direction were periodically arranged in a direction parallel to the surface. In all cases, a true shape was assumed instead of actual measurements, and the scattering profile calculated from this assumption was used as the actual measurement value. In Example 1, a model-free analysis in which the cross-sectional shape of each layer is changed was compared with a model-based analysis in which the cross-sectional shape of all layers is fixed to a predetermined shape. In Example 2, a model-free analysis in which the cross-sectional shape of all layers is set to a similar shape to an initially set shape was compared with a model-based analysis in which the cross-sectional shape of all layers is fixed to a predetermined shape. The R-factor indicates the degree of discrepancy between the calculated value and the actual measurement value.

[0074] (Example 1) Assuming a true shape, a shape in which the XY cross-sectional shape changes successively as Z increases from ellipse, oval, rectangle, oval, ellipse, egg, teardrop, egg, ellipse, snowman, dumpling, snowman, and ellipse was assumed. Fig. 13 is a diagram showing the shapes of each cross section of the scatterer set as the true shape. The XY plane shows the overlap of the cross-sectional shapes of each layer of the scatterer. The ZY plane and ZX plane show the cross-sectional shapes of the center of the scatterer, respectively.

[0075] For this true shape, a model-based analysis was performed by fixing the cross-sectional shape to a constant ellipse. Ｚ 14 is a graph showing a scattering profile fitted with a constant ellipse as a cross-sectional shape to the actually measured scattering profile in the Q direction. As shown in FIG. 14, in the model-based analysis, the scattering profiles are slightly different from each other, and Ｚ The directional R factor is R(Q Ｚ ) = 17.131% was obtained.

[0076] Next, the initial cross-sectional shape was set to a constant ellipse, and a model-free analysis was performed. Ｚ 15 is a graph showing a scattering profile fitted to a model-free shape as a cross-sectional shape for an actually measured scattering profile in the Q direction. As shown in FIG. 15, in the model-free analysis, the scattering profiles almost perfectly match, and Ｚ The directional R factor is R(Q Ｚ ) = 0.098% was obtained.

[0077] 16(a) and (b) show the Q Ｒ 10 is a graph showing scattering profiles fitted with a uniform ellipse and a model-free shape as cross-sectional shapes in the Q direction, respectively. Ｒ In the model-based analysis in which a certain ellipse is fixed as the cross-sectional shape, the scattering profiles diverge, and Q Ｒ The directional R factor is R(Q Ｒ On the other hand, in the case of the model-free analysis, the scattering profiles are almost perfectly consistent, and Q Ｒ The directional R factor is R(Q Ｒ) = 0.049% is obtained.

[0078] In fact, when comparing the shape obtained by the model-based analysis with the shape obtained by the model-free analysis for a layer with a characteristic cross-sectional shape, there was a clear difference. Figure 17 shows the cross-sectional shape of a scatterer at i=5, fitted with a fixed ellipse and a model-free shape as the cross-sectional shape. i indicates the number of the slice layer stacked in the Z direction. In the model-based analysis, which fixed the shape to a fixed ellipse, only a portion of the ellipse obtained by the analysis overlaps with the rectangle representing the true shape. However, the shape obtained by the model-free analysis is a rectangle that is almost identical to the true shape.

[0079] Figure 18 shows the cross-sectional shape of a scatterer at i = 15, fitted with a constant ellipse and a model-free shape. The model-based analysis yields an ellipse that is close to the teardrop shape representing the true shape, but it is ultimately an ellipse. However, the shape obtained by the model-free analysis is a teardrop shape that is almost identical to the true shape.

[0080] Figure 19 shows the cross-sectional shape of a scatterer at i=25, fitted with a constant ellipse and a model-free shape. In the model-based analysis, which fixed the cross-sectional shape to a constant ellipse, the obtained ellipse only overlaps the true round-shaped shape at both ends. However, the shape obtained in the model-free analysis is almost the same round-shaped shape as the true shape.

[0081] (Example 2) It was assumed that the true shape was a triangle (rice ball shape) with corners of constant curvature, with only the size changing in the depth direction (Z direction). In other words, the XY cross-sectional shapes at different depths are similar to each other. Figure 20 is a diagram showing the shapes of each cross section of the scatterer set as the true shape. The XY plane shows the overlap of the cross-sectional shapes of each layer of the scatterer. The ZY plane and ZX plane each show the cross-sectional shape of the center of the scatterer. As shown in Figure 20, the XY cross-sectional shapes of each layer are similar to each other.

[0082] For this true shape, a model-based analysis was performed with the cross-sectional shape fixed to a constant circle. Ｚ21 is a graph showing a scattering profile fitted with a constant circle as a cross-sectional shape to the actually measured scattering profile in the Q direction. As shown in FIG. 21, in the model-based analysis, the scattering profiles are slightly different from each other, and Ｚ The directional R factor is R(Q Ｚ ) = 20.335% was obtained.

[0083] Next, the initial cross-sectional shape was set to a constant circle, and a model-free analysis was performed under the condition that the cross-sectional shapes of each layer were similar. Ｚ 22 is a graph showing a scattering profile obtained by fitting a model-free shape as a cross-sectional shape to an actually measured scattering profile in the Q direction. As shown in FIG. 22, in the model-free analysis, the scattering profiles almost completely matched each other, and Ｚ The directional R factor is R(Q Ｚ ) = 0.002% was obtained.

[0084] 23(a) and (b) show the Q Ｒ 10 is a graph showing scattering profiles fitted with a constant circle and a model-free shape as cross-sectional shapes in the Q direction, respectively. Ｒ In the model-based analysis in which a certain circle is fixed as the cross-sectional shape, the scattering profiles diverge, and Q Ｒ The directional R factor is R(Q Ｒ On the other hand, in the case of the model-free analysis, the scattering profiles are almost perfectly consistent, and Q Ｒ The directional R factor is R(Q Ｒ ) = 0.001% is obtained.

[0085] 100 Measurement system 110 Measurement device 111 X-ray source 112 Mirror 115 Sample stage 116 Vacuum path 118 Beam stopper 119 Detector 120 Analysis device 121 Control unit 122 Formula storage unit 123 Measurement data storage unit 124a Basic information setting unit 124b Setting method selection unit 124c Initial information setting unit 125 Input information conversion unit 126 Intensity calculation unit 127 Fitting unit 128 Parameter determination unit 210 Input device 220 Output device GS Slit S0 Sample S1, S2 Slit

Claims

1. An apparatus for analyzing the microstructure of a plate-shaped sample formed by a periodic arrangement of long scatterers in the thickness direction, comprising: a measurement data memory unit that stores data on the scattering intensity of X-rays scattered from the plate-shaped sample measured by transmitting X-rays at multiple ω rotation angles; an initial information setting unit that sets an initial cross-sectional shape when repeating fitting by changing the cross-sectional shape of the layer under the condition that the scatterers are formed by layers having a constant cross-sectional shape represented by an angle and radius about the origin as the center and being stacked in the thickness direction of the plate-shaped sample; an intensity calculation unit that calculates the scattering intensity of X-rays scattered by the plate-shaped sample based on the cross-sectional shape of the layer; a fitting unit that performs the fitting of the calculated scattering intensity to the measured scattering intensity; and a parameter determination unit that determines the angle and radius representing the cross-sectional shape of the layer based on the result of the fitting, wherein the fitting unit changes the cross-sectional shape of the layer and repeats the fitting.

2. The analysis device according to claim 1, wherein said intensity calculation section calculates said scattering intensity under the condition that the shapes of the layers constituting said scatterer are similar to each other.

3. The analysis device according to claim 1 or 2, wherein the initial information setting section sets a predetermined shape as the initial cross-sectional shape of the layer.

4. The analysis device according to claim 1 or 2, wherein the initial information setting section sets a shape designated by a user as the initial cross-sectional shape of the layer.

5. The analysis device according to claim 4, further comprising an input information conversion unit that converts a shape designated by the user using a freeform tool into an initial cross-sectional shape of the layer.

6. An analytical device according to claim 1 or 2, characterized in that the initial information setting section uses a shape set using image data of the plate-like sample as the initial cross-sectional shape of the layer.

7. The analysis device according to claim 1 or 2, wherein said initial information setting section uses a shape determined by parameters obtained by model-based analysis as the initial cross-sectional shape of said layer.

8. The analysis device according to claim 1 or 2, characterized in that the parameter determination section calculates the position of the center of gravity of the cross-sectional shape of each of the layers relative to the origin.

9. An analysis device as described in claim 1 or claim 2, characterized in that the parameter determination unit determines the conditions for using a model-based analysis that assumes the cross-sectional shape of the layer to be constant, based on the determined angle and radius representing the cross-sectional shape of the layer.

10. A method for analyzing the microstructure of a plate-shaped sample formed by a periodic arrangement of long scatterers in the thickness direction, comprising the steps of: preparing data on the scattering intensity of X-rays scattered from the plate-shaped sample measured by transmitting X-rays at multiple ω rotation angles; setting an initial cross-sectional shape when repeating fitting by changing the cross-sectional shape of the layer under the condition that the scatterers are formed by stacking layers having a constant cross-sectional shape represented by an angle and radius about the origin as the center in the thickness direction of the plate-shaped sample; calculating the scattering intensity of X-rays scattered by the plate-shaped sample based on the cross-sectional shape of the layer; fitting the calculated scattering intensity to the measured scattering intensity; and determining the angle and radius representing the cross-sectional shape of the layer based on the result of the fitting.

11. A program for analyzing the microstructure of a plate-shaped sample formed by a periodic arrangement of long scatterers in the thickness direction, comprising: a process for preparing data on the scattering intensity of X-rays scattered from the plate-shaped sample measured by transmitting X-rays at multiple ω rotation angles; a process for setting an initial cross-sectional shape when repeating fitting by changing the cross-sectional shape of the layer under the condition that the scatterers are formed by stacking layers having a constant cross-sectional shape represented by an angle and radius about the origin as the center in the thickness direction of the plate-shaped sample; a process for calculating the scattering intensity of X-rays scattered by the plate-shaped sample based on the cross-sectional shape of the layer; a process for fitting the calculated scattering intensity to the measured scattering intensity; and a process for determining the angle and radius representing the cross-sectional shape of the layer based on the result of the fitting.

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