Analysis device, analysis method, and analysis program
Patent Information
- Application Number
- JP2023171642
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2023-10-02
- Publication Date
- 2026-01-06
Smart Images
Figure 00000000_0000_ABST
Abstract
Description
[Technical field]
[0001] The present invention relates to an apparatus, method and program for analyzing the microstructure of a plate-shaped sample in which scatterers long in the thickness direction are periodically arranged. [Background technology]
[0002] As a method for analyzing the shape of a microfabricated pattern based on 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 center of gravity position and size of each sliced layer are calculated (see Patent Document 1). Unlike an analysis that determines parameters that represent a pre-defined model such as an elliptical cylinder, this method introduces an analysis that can arbitrarily express the center of gravity position and size in the depth direction. [Prior art documents] [Patent documents]
[0003] [Patent Document 1] Patent No. 7100897 Summary of the Invention [Problem to be solved by the invention]
[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, an ellipse, or a rectangle. In such an analysis, if the scatterer has an arbitrary shape whose cross section cannot be expressed by a predetermined shape (circle, ellipse, rectangle) or a shape whose cross section of the predetermined shape changes along the depth direction, a correct analysis result cannot be obtained. For example, the processed shapes of semiconductor devices in recent years have become more complex, and there are an increasing number of cases in which the processed shapes cannot be analyzed by a simple shape model in transmission CD-SAXS. Especially in the product development stage, scatterers having complex cross-sectional shapes may be formed, regardless of whether they are intended or not. In such cases, 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. [Means for solving the problem]
[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 long scatterers 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 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, 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, and the fitting unit is characterized in that it changes the cross-sectional shape of the layer and repeats the fitting.
[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 is characterized in that it sets a predetermined shape as an 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 an initial cross-sectional shape of the layer.
[0010] (5) Furthermore, the analysis device described in (4) above is characterized in that it further comprises 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 uses a shape determined by parameters obtained by model-based analysis as the initial cross-sectional shape of the layer.
[0013] (8) 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 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) Furthermore, the analysis method of the present invention is a method for analyzing the microstructure of a plate-shaped sample formed by a periodic arrangement of 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 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.
[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 stacking layers having a certain 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. [Brief description of the drawings]
[0017] [Figure 1] FIG. 1 is a perspective view showing a transmission type CD-SAXS measurement system. [Diagram 2] (a) and (b) are XY and XZ cross-sectional views, respectively, showing the electron number density distribution of a plate-shaped sample. [Diagram 3] 13A and 13B are diagrams showing hole shapes on the XZ plane and the YZ plane, respectively, illustrating the analysis conditions. [Figure 4] FIG. 13 is a diagram showing a cross-sectional shape of a slice layer having a scatterer. [Diagram 5] FIG. 13 is a diagram showing a cross-sectional shape in which Rk is expressed as a multi-valued function of θk. [Figure 6] 1 is a block diagram showing a configuration of a measurement system according to the present invention. [Figure 7] FIG. 2 is a plan view showing the configuration of a measuring device. [Figure 8] FIG. 13 is a diagram showing an example in which a shape obtained by model-free analysis is approximated by an elliptical model. [Figure 9] 2 is a flow chart illustrating a measurement and analysis method according to the present invention. [Figure 10] 10 is a flowchart showing a selection of a cross-sectional shape setting method according to the present invention. [Figure 11] FIG. 1 is a diagram showing the magnification of each slice layer of a scatterer. [Figure 12] FIG. 13 is a diagram showing a shape set by a free form tool. [Figure 13] FIG. 13 is a diagram showing the shapes of the cross sections of a scatterer that are set as the true shape. [Figure 14] 13 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 QZ direction. [Figure 15] 13 is a graph showing a scattering profile fitted with a model-free shape as a cross-sectional shape to an actually measured scattering profile in the QZ direction. [Figure 16] Graphs showing scattering profiles fitted with a constant ellipse and a model-free shape as cross-sectional shapes in the QR direction (a) and (b), respectively. [Figure 17] FIG. 13 shows the cross-sectional shape of a scatterer for i=5 fitted with a constant ellipse and a model-free shape as the cross-sectional shape. [Figure 18]FIG. 13 shows the cross-sectional shape of a scatterer i=15 fitted with a constant ellipse and a model-free shape as the cross-sectional shape. [Figure 19] FIG. 13 shows the cross-sectional shape of a scatterer i=25 fitted with a constant ellipse and a model-free shape as the cross-sectional shape. [Figure 20] FIG. 13 is a diagram showing the shapes of the cross sections of a scatterer that are set as the true shape. [Figure 21] 13 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 QZ direction. [Figure 22] 13 is a graph showing a scattering profile fitted with a model-free shape as a cross-sectional shape to an actually measured scattering profile in the QZ direction. [Figure 23] Graphs showing scattering profiles fitted with a constant circle and a model-free shape as cross-sectional shapes in the QR direction (a) and (b), respectively. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0018] Next, an embodiment of the present invention will be described with reference to the drawings. In order to facilitate understanding of the description, the same reference numerals are used to refer to the same components in each drawing, and duplicated description will be omitted.
[0019] [principle] (Transmission CD-SAXS) In this invention, the shape of the scatterers in the sample is analyzed by transmission CD-SAXS that can be performed at the laboratory level. It is particularly suitable for analyzing the shape of semiconductor devices with deep groove microfabrication patterns, such as 3D NAND and DRAM. This invention is premised on an analysis method in which the sample is finely sliced in the depth direction, and the diameter and position fluctuation are given as parameters to each depth.
[0020] FIG. 1 is a perspective view showing a measurement system for transmission CD-SAXS. In transmission 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 Y The axis coincides with the ω axis. The sample is rotated by the scattering vector Q Z This is to obtain information in the depth direction by changing ΔQ Z is the reflective ΔQ Z Since the measurement 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] (X-ray small angle scattering intensity) As described above, in transmission CD-SAXS, which is less affected by refraction and multiple reflections, 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] Figures 2(a) and (b) are XY and XZ cross-sectional views, respectively, of a plate-shaped sample, which show the electron number density distribution. When the scatterer has a periodic pattern structure as shown in Figures 2(a) and (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. The Laue function can then be used to determine Q, which satisfies the diffraction condition. X , Q Y is derived.
[0023] (Shape of scatterer) In Fig. 2(a), independent sites in 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 expresses the scattering amplitude within the unit cell can be described as the product of the scatterer shape factor F, which is the integral for 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 calculation 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 specified 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 X-ray scattering intensity of 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 hole depth is used as a parameter and the sample is sliced into N equal layers in the depth direction. Figures 3(a) and (b) show the hole shapes in the XZ and YZ planes, respectively, which show 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 every 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 j-th slice layer, the density ρ[j], thickness t[j], and the 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 j-th 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 origin representing the cross-sectional shape is the center, and the position of the center of gravity of the cross-sectional shape. This makes it possible to express complex shapes. For example, when the position of 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 position of the center of gravity (X, Y) and the parameters of the angle and radius (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 that the user is not allowed to specify such shapes as the initial cross-sectional shape.
[0029] FIG. 5 is a diagram showing a cross-sectional shape in which Rk is expressed by a multi-valued function of θk. As shown in FIG. 5, a shape in which multiple radii Rk occur at a specific θk with respect to a certain origin is not included as an initial shape. However, depending on how the origin is taken, there may be cases in which Rk is expressed by a multi-valued function of θk and cases in which Rk is not expressed by a multi-valued function of θk. By taking the origin separately 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 by a multi-valued function of θk. In this case, the position of the center of gravity or the origin can be expressed by the relative position of the other. The origin position and the center of gravity position may be made to coincide. In that 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 by applying such a continuity constraint. This makes it easier for the simulation results to converge, and results close to the actual shape can be obtained while reducing the calculation burden. For example, there is a method of adding weights to minimize the path integral of the cross section using the least squares method. In addition, in order to determine the cross-sectional shape in the analysis, multiple diffraction image data are obtained by rotating the sample.
[0031] [System Wide] 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. A specific configuration will be described below.
[0032] [Measuring equipment] 7 is a plan view showing the configuration of the measurement device 110. The measurement device 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 rays. 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 a material capable of blocking X-rays and constitute a slit section that narrows the split X-rays. This configuration enables irradiation of X-rays 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 in the range of -10° to 10° for the multiple rotation angles ω. The slit GS can limit the spot size of the X-rays on the sample surface to several tens of μm or less. Basically, 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, when making a very small spot, the beam can also be made smaller by the GS.
[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. Y In addition to the ω rotation angle, the χ and φ rotation angles can also be adjusted. By adjusting these angles, the incident angle of the dispersed X-rays on 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. An example of the scatterers is holes. That is, a typical sample is a silicon wafer substrate, and in this case, the scatterers are holes formed by etching. The higher the integration level, the more important it is to be able to confirm the formation of hole shapes that meet the specifications.
[0036] In such a case, even if the length of the scatterer is between 200 nm and 20 μm, 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 penetrate, as shown in Figure 7.
[0037] The scatterer is not limited to the above-mentioned holes, but may be a pillar. That is, the present invention can be applied to a silicon substrate sample on which cylinders are periodically formed on the surface. Also, the scatterer may be a sample on which a line pattern (space pattern) such as a long molecular array is formed.
[0038] The vacuum path 116 maintains the path of the scattered beam in a vacuum 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 on a circumference from the sample position, and can detect the scattering intensity of X-rays. The measuring device 110 and the analyzing device 120 are connected, and the detected scattering intensity data is sent to the analyzing device 120.
[0039] The measuring device 110 preferably has a laser light source and a detector for reflected light. It is possible to adjust the orientation of the plate-shaped sample by utilizing 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 thus adjusted can be used as the reference, where ω=χ=0°.
[0040] When evaluating the cross-sectional shape of a sample, the 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 shapes are evaluated, 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 performing measurement and analysis.
[0041] [Analysis equipment] The analysis device 120 is composed of, for example, a PC having a memory and a processor, and can execute various processes by executing a program. 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 periodically arranging scatterers long in the thickness direction. The analysis device 120 is capable of not only model-free analysis but also model-based analysis. For model-based analysis, the configuration described in Patent Document 1 can be used.
[0042] The analysis device 120 includes a control unit 121, a 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 transmit 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. In addition to the entire device, some of the devices or some 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 by a 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 measuring device 110 and manages control data and measurement data. For example, the control unit 121 controls the sample stage by a driving mechanism to adjust the orientation of the sample. The formula storage unit 122 stores a formula for calculating the scattering intensity for a specific shape model 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 penetrate the sample, measured at multiple ω rotation angles in the vicinity of 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 that the scatterer is formed by stacking layers each having a constant cross-sectional shape in the thickness direction of the plate-shaped sample. The constant cross-sectional shape is expressed by the angle and 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 ellipse or an oval, as the initial shape, making it easier to set.
[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 setting shape of the scatterer to be specified using, for example, an image from an electron microscope. In this case, arbitrariness in setting can be eliminated by using measurement data.
[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 is first fixed to a standard shape and analyzed, and the obtained results can be used as the initial conditions. This makes it possible to use a cross-sectional shape with a certain degree of validity for the initial setting, and to prepare appropriate parameters that are easy to converge.
[0051] The input information conversion unit 125 converts shape designation information received from the user using a freeform tool as the initial cross-sectional shape of each layer into shape setting information, thereby reducing the workload of the user who inputs N points one by one to designate the cross-sectional shape.
[0052] The intensity calculation unit 126 calculates the scattering intensity of the 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 the X-rays using the formula and the values of various parameters that have been set. By using the acquired formula, it is possible to calculate the scattering intensity of the X-rays scattered by the plate-shaped sample under specific conditions.
[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 or not, and if it is not optimal, changes the parameters and recalculates the scattering intensity by simulation.
[0054] The parameter determination unit 128 determines the parameters of the scatterers in the plate-shaped 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 the 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, and various cross-sectional shapes can be handled 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 a model 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 applied to the initial value of the model-based analysis. FIG. 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 FIG. 8, the model-based analysis is performed with the ellipse represented by the solid line as a constant cross-sectional shape, making it possible to make the processing more efficient.
[0058] [Measurement and analysis methods] (Overall flow) Next, a measurement and analysis method using the above system configuration will be described. Fig. 9 is a flow chart 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 made parallel to the X-rays. Then, the scattering intensity is measured at multiple ω rotation angles to obtain a transmission CD-SAXS waveform (step S102).
[0059] Based on the obtained measurement data, the Q Z The waveform is acquired (step S103). Then, the depth direction is appropriately sliced (step S104), and the initial values of density ρ[j], thickness t[j], and origin position (ΔX[j], ΔY[j]) of the scatterer are given 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). Then, the calculated scattering intensity is fitted to the measured scattering intensity (step S108). It is confirmed whether the fitting is optimal (step S109), and 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 at the values at that time (step S111), and the series of procedures is terminated.
[0062] (Selection of cross-sectional shape setting method) Among the above series of steps, the selection of the cross-sectional shape setting method will be particularly described. Fig. 10 is a flowchart showing the selection of the cross-sectional shape setting method. The selection in this flowchart is basically based on information input by the user, but the selection may be made automatically according to some 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 predetermined cross-sectional shape is selected as a shape model for each layer as a model-based analysis (step S202). The predetermined cross-sectional shapes include an ellipse, a polygon, a teardrop shape, an egg shape, a snowman shape, and a dumpling shape. These shapes also include corners with a certain curvature.
[0064] Then, the initial values of the shape model are set (step S203), and the selection of the cross-sectional shape setting method is completed. For example, when 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. When 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 whose cross-sectional shapes of all layers are similar to each other is set. 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 represented by the position of the origin and the angle and radius when the origin is the center. Also, the shape data of a specific layer, not limited to the first layer, may be set as a reference, and the magnifications of other layers may be set.
[0066] If the setting of all layers is selected in step S204, the initial values of the shape data of 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 similarity) A scatterer in which the cross-sectional shapes of all layers are similar to each other can also be set as the initial information. In that case, the user only needs to specify the cross-sectional shape of a specific layer and the magnifications of the other layers as the initial conditions. Figure 11 shows 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 based on the first layer.
[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 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 XY cross section and the magnification of each slice excluding the surface. If it is assumed that the XY cross sections are similar, the number of parameters can be reduced, thereby shortening the analysis time. If the XY cross section shape is completely model-free even in the depth direction, the number of parameters is the number of divisions of the XY cross section shape x the number of divisions in the depth direction. However, if the condition is that the XY cross section shape is similar in the depth direction, the number of parameters is the number of divisions of the XY cross section shape + the number of divisions in the depth direction - 1.
[0070] (Setting with the Freeform tool) A free-form tool may be made available during the initial setting of the above cross-sectional shape. Setting the radius of each angle is a burden for the user. In particular, setting all layers is a heavy burden. In such cases, setting using the free-form tool is effective.
[0071] FIG. 12 is a diagram showing a shape set with the freeform tool. As shown in FIG. 12, a curve can be specified along the dashed arrow by clicking the mouse at the inflection point while moving the pointer. The specified curve can be converted into radius information at each angle to specify initial information on 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 point and end point, and the intermediate part can be specified by simply moving the pointer, or the clicked points can be connected with 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 particularly applied to the field of semiconductor devices, and makes it possible to analyze with high robustness any shape of a microfabricated pattern formed on a wafer surface, based on experimental data acquired by transmission CD-SAXS.
[0073] [Example] Analysis was 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 each case, a true shape was assumed instead of actual measurement, and the scattering profile calculated from the 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 is fixed to a predetermined shape across all layers. In Example 2, a model-free analysis in which a similar shape to an initially set shape is used for the cross-sectional shape of all layers was compared with a model-based analysis in which the cross-sectional shape is fixed to a predetermined shape across all layers. The R factor indicates the degree of deviation of the calculated value from the actual measurement value.
[0074] Example 1 Assuming that the true shape is a shape in which the XY cross-sectional shape changes successively from ellipse, oval, rectangle, oval, ellipse, egg, teardrop, egg, ellipse, snowman, dumpling, snowman, and ellipse as Z increases. Figure 13 shows 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 and ZX planes 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. Z15 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 each other, and Z The directional R factor is R(Q Z )=0.098% was obtained.
[0077] Figure 16(a) and (b) show the Q R 3 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 from each other, and Q R The directional R factor is R(Q R ) = 8.246%. On the other hand, in the case of the model-free analysis, the scattering profile almost perfectly matches, 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 and 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, which was fitted with a constant 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 was fixed to a constant ellipse, only a part of the ellipse obtained as a result of the analysis overlaps with the rectangle that represents 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, which is fitted with a certain ellipse and a model-free shape as the cross-sectional shape. In the model-based analysis, an ellipse close to the teardrop shape representing the true shape is obtained, but it is still an ellipse. However, the shape obtained in 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 as the cross-sectional shape. In the model-based analysis, which fixes the cross-sectional shape to a constant ellipse, the obtained ellipse simply overlaps the true dumpling shape at both ends. However, the shape obtained by the model-free analysis is almost the same dumpling shape as the true shape.
[0081] Example 2 Assuming that the true shape is a triangle (rice ball shape) whose corners always have a constant curvature, and only the size changes 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 overlapping 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. Z 21 is a graph showing a scattering profile fitted with a certain 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 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. 22, in the model-free analysis, the scattering profiles almost perfectly match each other, and Z The directional R factor is R(Q Z )=0.002% was obtained.
[0084] Figure 23(a) and (b) show the Q R 3 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 from each other, and Q R The directional R factor is R(Q R ) = 11.784%. On the other hand, in the case of the model-free analysis, the scattering profiles almost perfectly matched, and Q R The directional R factor is R(Q R )=0.001% is obtained. [Explanation of symbols]
[0085] 100 Measurement System 110 Measuring Equipment 111 X-ray source 112 Mirror 115 Sample stage 116 Vacuum Path 118 Beam Stopper 119 Detector 120 Analysis equipment 121 Control Unit 122 Formula Memory Section 123 Measurement data storage unit 124a Basic information setting section 124b Setting method selection section 124c Initial information setting section 125 Input information conversion unit 126 Strength calculation section 127 Fitting section 128 Parameter Determination Unit 210 Input Device 220 Output Device GS Slit S0 sample S1, S2 slits
Claims
1. An apparatus for analyzing the microstructure of a plate-shaped sample in which long scatterers are periodically arranged in the thickness direction, a measurement data storage unit that stores data on the scattering intensity of X-rays scattered from the plate-shaped sample, the data being measured by transmitting X-rays at a plurality of 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 scatterer is formed by stacking layers having a constant cross-sectional shape represented by the arbitrary shape expressed by an angle and a radius when the center is an origin, in the thickness direction of the plate-like 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; a parameter determination unit that determines an angle and a radius that represent a cross-sectional shape of the layer based on a result of the fitting, The analysis device is characterized in that the fitting unit repeats the fitting by changing the cross-sectional shape of the layer.
2. 2. The analysis device according to claim 1, wherein 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.
3. 3. The analysis device according to claim 1, wherein the initial information setting unit sets a predetermined shape as the initial cross-sectional shape of the layer.
4. 3. The analysis device according to claim 1, wherein the initial information setting unit sets a shape designated by a user as the initial cross-sectional shape of the layer.
5. 5. The analysis device according to claim 4, further comprising an input information conversion unit that converts the shape specified by the user using a freeform tool into an initial cross-sectional shape of the layer.
6. 3. The analysis device according to claim 1, wherein the initial information setting unit uses a shape set using image data of the plate-like sample as the initial cross-sectional shape of the layer.
7. 3. The analysis device according to claim 1, wherein the initial information setting unit uses a shape determined by parameters obtained by model-based analysis as the initial cross-sectional shape of the layer.
8. 3. The analysis device according to claim 1, wherein the parameter determination unit calculates the position of the center of gravity of the cross-sectional shape of each of the layers relative to the origin.
9. 3. The analysis device according to claim 1, wherein the parameter determination unit 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.
10. A method for analyzing the microstructure of a plate-shaped sample formed by periodically arranging long scatterers in the thickness direction, comprising: preparing data on the scattering intensity of X-rays scattered from the plate-shaped sample, the data being measured by transmitting X-rays at a plurality of ω rotation angles; a step of setting an initial cross-sectional shape when repeating fitting by changing the cross-sectional shape of the layer under the condition that the scatterer is formed by stacking layers having a constant cross-sectional shape represented by the arbitrary shape in terms of an angle and a radius when the center is the origin, in the thickness direction of the plate-like sample; calculating the scattering intensity of the X-rays scattered by the plate-shaped sample based on the cross-sectional shape of the layer; fitting the calculated scattering intensities to the measured scattering intensities; and determining angles and radii representing the cross-sectional shape of the layer based on the results of the fitting.
11. A program for analyzing the microstructure of a plate-shaped sample formed by periodically arranging long scatterers in the thickness direction, preparing data on the scattering intensity of X-rays scattered from the plate-shaped sample, the data being measured by transmitting X-rays at a plurality of ω rotation angles; a process of setting an initial cross-sectional shape when repeating fitting by changing the cross-sectional shape of the layer under the condition that the scatterer is formed by stacking layers having a constant cross-sectional shape represented by the angle and radius when the center is the origin, and the scatterer is formed by stacking layers having a constant cross-sectional shape represented by the shape with arbitrariness in the thickness direction of the plate-like sample; a process of calculating the scattering intensity of the 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 an angle and a radius representing a cross-sectional shape of the layer based on the result of the fitting.