Analysis device, analysis method, and analysis program

Abstract

To provide an analysis device capable of highly accurately measuring only an inclination of two directional components of columnar scatterers periodically aligned in a plate-like sample at high speed, an analysis method and an analysis program.SOLUTION: An analysis device 120 includes: a measurement data storage part 123 for storing data of scattering intensity from a plate-like sample measured by X-ray transmission in one-time ω scan; a coordinate conversion part 125 for converting coordinates of a scattering vector into coordinates of an inclination of the scatterer, regarding a waveform based on the intensity of the two directional components of a specific diffraction point by using the data of the measured scattering intensity; a peak position specification part 126 for specifying a peak position of the intensity waveform relative to the converted coordinates of the inclination; and an inclination calculation part 127 for calculating a difference between the specified peak position and a peak position determined assuming that the scatterer is not inclined from a direction perpendicular to a surface of the plate-like sample, as the inclination of the scatterer in the two direction components.SELECTED DRAWING: Figure 4

Description

[Technical Field]

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

[0002] Conventionally, small-angle transmission X-ray scattering (tSAXS) has been used to non-destructively and easily measure the pattern shape of semiconductor devices, which are undergoing three-dimensional miniaturization through deep groove patterns. As applications of this measurement method, methods are known for precisely identifying the shape of columnar scatterers periodically arranged within a plate-like sample, based on a complex shape model with high adaptability, requiring time for measurement and analysis (see Patent Document 1), and for measuring in a short time but with lower accuracy, based on a simple shape model (see Patent Document 2). Furthermore, a method has been proposed to calculate the tilt of the scatterers from measurement results obtained by scanning in two directions without a shape model (see Patent Document 3). [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Patent No. 7100897 [Patent Document 2] Patent No. 7168985 [Patent Document 3] International Publication No. 2020 / 028412 [Overview of the project] [Problems that the invention aims to solve]

[0004] In actual semiconductor inspection processes, the need for analyzing complex shapes, as described in Patent Document 1 is effective, is not the only issue. For example, there are situations where it is necessary to measure only the inclination of a columnar scatterer relative to the sample surface in a short time while maintaining accuracy. The technologies described in Patent Documents 2 and 3 are characterized by their simplicity and can meet this need to some extent. However, it is difficult to measure the inclination of the two directional components of a columnar scatterer with high accuracy while also completing the measurement and analysis in a short time.

[0005] This invention has been made in view of these circumstances, and aims to provide an analytical device, analytical method, and analytical program that can measure only the inclination of the two directional components of columnar scattering bodies periodically arranged within a plate-shaped sample at high speed and with high precision. [Means for solving the problem]

[0006] (1) To achieve the above objective, the present invention provides an analytical device for analyzing the microstructure of a plate-shaped sample formed by periodically arranging columnar scattering bodies that are long in the thickness direction, and is characterized by comprising: a measurement data storage unit that stores scattering intensity data from a plate-shaped sample measured by X-ray transmission in one ω scan; a coordinate transformation unit that uses the measured scattering intensity data to transform the coordinates of the scattering vector to the coordinates of the tilt of the scattering body for a waveform based on the intensity of two directional components of a specific diffraction point; a peak position identification unit that identifies the peak position of the intensity waveform with respect to the coordinates of the transformed tilt; and a tilt calculation unit that calculates the difference between the identified peak position and the peak position obtained assuming that the scattering body is not tilted from a direction perpendicular to the surface of the plate-shaped sample as the tilt of the scattering body using the two directional components.

[0007] (2) Furthermore, in the analysis apparatus described in (1) above, the coordinate transformation unit is characterized in that it performs a coordinate transformation to the coordinate of the inclination of at least one of the two directional components of the scattering vector by a single analysis using a diffraction point where one of the coordinates of the two directional components is 0.

[0008] (3) Furthermore, in the analysis apparatus described in (1) above, the coordinate transformation unit is characterized in that it performs a coordinate transformation to the coordinate of the tilt of the scattering body of the two directional components by loop analysis using diffraction points in which neither of the coordinates of the scattering vectors of the two directional components is zero.

[0009] (4) Furthermore, in the analytical apparatus described in any of (1) to (3) above, the two-directional components are characterized in that they are in a direction parallel to the surface of the plate-like sample and are components in the x-direction in which the unit cell is oriented and in the y-direction perpendicular to the x-direction.

[0010] (5) Furthermore, in the analytical apparatus described in any of (1) to (3) above, the two-directional components are characterized in that they are in a direction parallel to the surface of the plate-shaped sample and are components in the a0 direction, which is the scanning direction of the ω scan, and in the a1 direction, which is perpendicular to the a0 direction.

[0011] (6) Furthermore, in the analysis apparatus described in any of (1) to (5) above, the coordinate transformation unit is characterized in that it uses a waveform obtained by integrating multiple diffraction points as a waveform based on the intensity of the two-directional components of the specific diffraction point.

[0012] (7) The present invention also provides an analysis method for analyzing the microstructure of a plate-shaped sample formed by periodically arranging columnar scattering bodies that are long in the thickness direction, and is characterized by including the steps of: preparing scattering intensity data from the plate-shaped sample measured by X-ray transmission in one ω scan; using the measured scattering intensity data, transforming the coordinates of the scattering vector to the coordinates of the tilt of the scattering body for a waveform based on the intensity of two directional components of a specific diffraction point; identifying the peak position of the intensity waveform with respect to the coordinate-transformed tilt coordinates; and calculating the difference between the identified peak position and the peak position obtained assuming that the scattering body is not tilted from a direction perpendicular to the surface of the plate-shaped sample, as the tilt of the scattering body using the two directional components.

[0013] (8) Furthermore, the analysis program of the present invention is an analysis program for analyzing the microstructure of a plate-shaped sample formed by periodically arranging columnar scattering bodies that are long in the thickness direction, and is characterized in that it causes a computer to perform the following steps: preparing scattering intensity data from the plate-shaped sample measured by X-ray transmission in one ω scan; using the measured scattering intensity data, transforming the coordinates of the scattering vector to the coordinates of the tilt of the scattering body for a waveform based on the intensity of two directional components of a specific diffraction point; identifying the peak position of the intensity waveform with respect to the coordinates of the transformed tilt; and calculating the difference between the identified peak position and the peak position obtained assuming that the scattering body is not tilted from a direction perpendicular to the surface of the plate-shaped sample as the tilt of the scattering body using the two directional components. [Brief explanation of the drawing]

[0014] [Figure 1] This is a perspective view showing a transmission-type CD-SAXS measurement system. [Figure 2] (a) and (b) are diagrams showing the unit cell of the hole pattern and the relationship between the silicon wafer and the lattice vector, respectively. [Figure 3] This graph shows the scattering intensity profile of the diffraction point (11) with respect to Qz. [Figure 4] This is a block diagram showing the measurement system of the present invention. [Figure 5] This is a plan view showing the configuration of the measuring device. [Figure 6] This flowchart shows the measurement and analysis procedures for the present invention. [Figure 7] (a) and (b) are flowcharts showing single-step analysis and loop analysis, respectively. [Figure 8] This graph shows the QZ waveform based on the intensity of the diffraction point at QY=0nm-1 with respect to θX. [Figure 9] This graph shows the QZ waveform based on the intensity of the diffraction point at QX = 0 nm - 1 with respect to θY. [Figure 10] This graph shows the QZ waveform based on the intensity of the diffraction point with respect to θX where QX ≠ 0 nm-1. [Figure 11] This graph shows the QZ waveform based on the intensity of the diffraction point with respect to θY where QY ≠ 0 nm-1. [Figure 12] (a) and (b) are graphs and tables showing the optimization of the XY components of the slope, respectively. [Figure 13] (a) and (b) are graphs showing the diffraction pattern for a single analysis of θX and the QZ waveform based on the intensity of the diffraction point at QY=0nm-1 relative to θX, respectively. [Figure 14] (a) and (b) are graphs showing the diffraction pattern for a single analysis of θY and the QZ waveform based on the intensity of the diffraction point at QX=0nm-1 relative to θY, respectively. [Figure 15] (a) and (b) are graphs showing the diffraction pattern and QZ waveform based on the intensity of the diffraction point against θX, respectively, which are the subjects of loop analysis. [Figure 16] (a) and (b) are graphs showing the diffraction pattern and QZ waveform based on the intensity of the diffraction point against θY, respectively, which are the subjects of loop analysis. [Figure 17] (a) and (b) are graphs showing the diffraction pattern for a single analysis of θX and the QZ waveform based on the intensity of the diffraction point at QY=0nm-1 relative to θX, respectively. [Figure 18] This is the diffraction pattern that will be analyzed in a single step for θY. [Figure 19] (a) and (b) are graphs showing the diffraction pattern and QZ waveform based on the intensity of the diffraction point against θX, respectively, which are the subjects of loop analysis. [Figure 20] (a) and (b) are graphs showing the diffraction pattern and QZ waveform based on the intensity of the diffraction point against θY, respectively, which are the subjects of loop analysis. [Figure 21] This is a diffraction pattern that is the subject of a single-step analysis. [Figure 22] This graph shows the diffraction pattern and the QZ waveform based on the intensity of the diffraction points relative to a0, which are the subjects of a single-step analysis. [Figure 23] This graph shows the diffraction pattern and the QZ waveform based on the intensity of the diffraction points relative to a1, which are the subjects of a single-step analysis. [Figure 24] This graph shows the diffraction pattern and QZ waveform based on the intensity of the diffraction points relative to a0, which are the subjects of loop analysis. [Figure 25] This graph shows the diffraction pattern and QZ waveform based on the intensity of the diffraction points relative to a1, which are the subjects of loop analysis. [Modes for carrying out the invention]

[0015] Next, embodiments of the present invention will be described with reference to the drawings. To facilitate understanding of the description, the same reference numerals are used for identical components in each drawing, and redundant descriptions are omitted.

[0016] [First Embodiment] [Transparent CD-SAXS] This invention is suitable for analyzing the microstructure of plate-like samples formed by periodically arranged columnar scattering bodies that are long in the thickness direction, and can be applied to calculating the inclination of the scattering bodies in a sample using a transmission-type 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 three-dimensional NAND and DRAM. This invention is effective for non-destructive and simple measurement of deep groove microfabrication patterns with very large aspect ratios, and is suitable for analyzing structures embedded in the substrate. There is a high demand for measurement of deep groove patterns in recent three-dimensional semiconductor devices, and this invention can greatly contribute to in-line measurement of three-dimensional semiconductor devices.

[0017] Figure 1 is a perspective view showing the measurement system of a transmission-type CD-SAXS. In transmission-type CD-SAXS, the sample is rotated (ω rotation) with respect to the direction in which X-rays are incident perpendicular to the sample surface, and the dependence of the integrated intensity of each diffraction line on the sample rotation angle is measured. The sample rotation is performed based on the scattering vector Q. Z This is to obtain information in the depth direction by changing the value.

[0018] [Scattering vector and sample structure] Figs. 2(a) and 2(b) are diagrams showing the unit cell of the hole pattern and the relationship between the silicon wafer and the lattice vectors, respectively. When there is a unit cell with lattice constants a and b and a lattice angle γ, the diffraction condition for diffraction indices (h,k) is given using the scattering vectors Q X , Q Y , Q Z .<--> <-->

Equation

[0019] <--> For example, in the case of a silicon wafer sample, a mark called a notch is attached, and measurements are often performed with the XY direction of the sample aligned with the directions of the scattering vectors Q X , Q Y . Hereinafter, in principle, it will be described assuming that the XY direction of the sample coincides with the directions of the scattering vectors Q X , Q Y .<--> <-->

[0020] <--> In addition, when the a-axis is rotated by φ with respect to the notch, the tilt angles (θ WX , θ WY ) with respect to the wafer reference can be calculated as follows.<--> <-->

Equation

[0021] <--> [Tilt Angle and Q Z Waveform]<--> When a cylindrical scatterer has a central axis in a direction perpendicular to the surface of the sample, the shape factor of the cylindrical scatterer is expressed as follows.<--> <-->

Equation

[0022] <--> Also, with respect to the surface, in the Q X direction and the Q Yθ in each direction X and θ Y The shape factor of a scatterer of a cylinder tilted by a certain amount can be expressed as follows:

number

[0023] Considering the dashed lines in the above equations (2) and (3), Q for the surface of the sample X Direction and Q Y θ in each direction X and θ Y When it is tilted by only Q, Z The waveform in the direction will be shifted by the following amount.

number

[0024] θ X and θ Y The following equation can be derived as an expression for .

number

number

[0025] In fact, there is a difference in Q between a sample with no tilt and a sample with a tilt in the scattering material. Z The waveform positions are different. Figure 3 is a graph showing the scattering intensity profile of the diffraction point (11) against Qz. The circle plot represents the Qz scattering by a cylindrical scatterer with a central axis perpendicular to the surface of the sample. Z The waveform is shown, and the square plot represents the Q scattering by a cylindrical scatterer with a central axis tilted perpendicular to the surface of the sample. ZThis represents the waveform. In the example shown in Figure 3, the Q of each is Z The waveform difference ΔQz is 0.0022 nm. -1 That is the case.

[0026] [Measurement system configuration] Next, the configuration of the measurement system 100 of the present invention will be described. Figure 4 is a block diagram of the measurement system 100. The measurement system 100 comprises a measuring device 110 and an analysis device 120, and enables the measurement and analysis of transmission-type CD-SAXS by irradiating a plate-shaped sample with X-rays and measuring the scattering intensity. The analysis device 120 controls the measuring device 110 and manages the measurement data together with the control data, enabling data analysis. The specific configuration will be described below.

[0027] [Configuration of the measuring device] Figure 5 is a plan view showing the configuration of the measuring device 110. The measuring device 110 includes an X-ray source 111, a mirror 112, slits S1, S2, GS, sample stage 115, vacuum path 116, beam stopper 118, and 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.

[0028] MoKα can be used for the X-ray source 111. The mirror 112 spectrally analyzes the X-rays emitted from the X-ray source 111 and irradiates the spectrally analyzed X-rays in the direction of the sample S0. The slits S1 and S2 are made of a material capable of shielding X-rays and constitute slit sections that focus the spectrally analyzed X-rays. With this configuration, it is possible to irradiate the surface of the plate-shaped sample S0 with X-rays at multiple rotation angles ω that are close to perpendicular to the surface. It is preferable to select a specific angle in the range of -10° to 10° for the multiple rotation angles ω. The slit GS can limit the X-ray spot size on the sample surface to tens of micrometers or less. Basically, the beam size is determined by the slits S1 and S2. slit Parasitic scattering generated at slits S1 and S2 is removed using GS. However, when creating very small spots, slit The beam can also be made smaller using GS.

[0029] The sample stage 115 supports the sample S0 on the stage, and the orientation of the plate-shaped sample S0 can be adjusted by a drive mechanism under the control of the analysis device 120. Specifically, as shown in Figure 1 Q Y In addition to the ω rotation angle, the χ and φ rotation angles can also be adjusted. This adjustment allows the incident angle of the spectrally dispersed X-rays onto the sample S0 to be changed, enabling the measurement of scattering intensity according to the diffraction angle.

[0030] Sample S0 is formed in a plate shape, with scattering elements periodically arranged in a direction parallel to the main surface of the sample. Examples of scattering elements include holes. In other words, a typical sample is a silicon wafer substrate, in which case the scattering elements are holes formed by etching. As the integration density increases, it becomes increasingly important to confirm the formation of holes with precise specifications.

[0031] The scattering material is not limited to holes as described above, but may also be pillars. In other words, the present invention can also be applied to silicon substrate samples in which cylinders are periodically formed on the surface. Furthermore, samples in which line patterns (space patterns) such as long molecular arrangements are formed may also be used.

[0032] The vacuum path 116 maintains a vacuum in the path of the scattered beam to increase the camera length and prevent beam attenuation. The beam stopper 118 absorbs the direct beam. The detector 119 is, for example, a two-dimensional semiconductor detector that can move along the circumference from the sample position and can detect the scattering intensity of X-rays. The measuring device 110 and the analysis device 120 are connected, and the detected scattering intensity data is sent to the analysis device 120.

[0033] Furthermore, it is preferable that the measuring device 110 has a laser light source and a detector for reflected light. By utilizing the reflection of laser light, it is possible to adjust the orientation of the plate-shaped sample 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 a reference, in which case ω = χ = 0°.

[0034] [Configuration of the analysis device] The analysis device 120 is composed of, for example, a PC having memory and a processor, and each process can be executed by running 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 arranged long scattering particles in the thickness direction.

[0035] The analysis device 120 includes a computer 121, an input device 128, and an output device 129. The computer 121 also includes a measurement control unit 122, a measurement data storage unit 123, a formula storage unit 124, a coordinate transformation unit 125, a peak position identification unit 126, and a slope calculation unit 127. The computer 121 may be a PC terminal or a cloud server. Each unit can send and receive information via the control bus L.

[0036] The measurement control unit 122 controls the measuring device 110 and manages control data and measurement data. For example, the measurement control unit 122 controls the sample stage 115 by a drive mechanism and adjusts the orientation of the sample S0.

[0037] The measurement data storage unit 123 stores the measured X-ray intensity data. The measured intensity data is obtained by measuring at an ω rotation angle near the perpendicular direction to the surface of the plate-shaped sample, scattering from the plate-shaped sample as the X-rays are transmitted, and detecting it with the detector. Data measured in one ω scan is sufficient. The formula storage unit 124 stores formulas for fitting to the scattering intensity and for coordinate transformation.

[0038] The coordinate transformation unit 125 uses the measured scattering intensity data to transform the coordinates of the scattering vector to the coordinates of the tilt of the scattering body for a waveform based on the intensity of the two directional components of a specific diffraction point.

[0039] The coordinate transformation unit 125 first transforms the Q of each diffraction point. Z The waveform is acquired. It is preferable to use a waveform obtained by integrating the intensities of the two-directional components of a specific diffraction point across multiple diffraction points. This allows for highly accurate identification of the peak position.

[0040] The coordinate transformation unit 125 is used for user selection and Q Z Depending on the presence or absence of a waveform, a single-pass analysis or loop analysis is performed. Details of single-pass and loop analysis will be described later. The coordinate transformation unit 125 selects the diffraction points to be analyzed for single-pass or loop analysis, either by user selection or automatically. θ X In a single analysis of Q, Y =0nm -1 Select the diffraction point, θ Y In a single analysis of Q, X =0nm -1 Select the diffraction point. In loop analysis, Q X ≠0nm -1 Katsu Q Y ≠0nm -1 Select the diffraction point. In either case, it is preferable to select the diffraction point with high intensity. Note that the analysis device 120 can perform both single-pass analysis and loop analysis, but a device capable of only one of these may also be used.

[0041] When a single-step analysis is performed, the coordinate transformation unit 125 uses diffraction points where one of the coordinates of the two-directional scattering vectors is 0 to perform a coordinate transformation to the tilt coordinate of at least one of the two-directional scattering vectors. This allows for a single-step coordinate transformation. The two-directional components are components in two directions parallel to the surface of the plate-like sample. Preferably, the two-directional components are in directions parallel to the surface of the plate-like sample and are components in the x-direction oriented towards the unit cell and the y-direction perpendicular to the x-direction. This makes it easy to calculate the tilt angles of the two components for samples where the orientation of the unit cell is known.

[0042] If loop analysis is being performed, The coordinate transformation unit 125 is, Loop analysis using diffraction points where the coordinates of both directional scattering vectors are non-zero is performed to transform the coordinates of the tilt of the scattering body in both directions. This allows for the calculation of the tilt angle with high accuracy using a large number of diffraction points.

[0043] The peak position identification unit 126 uses Q, which is the waveform of the intensity relative to the coordinate of the coordinate-transformed slope. Z Identify the peak position in the waveform.

[0044] The peak position identification unit 126 obtains a mathematical formula for fitting from the formula storage unit 124, and Q is determined by fitting. Z The peak position of the waveform is calculated. The peak position identification unit 126 checks whether the fitted is optimal and changes the parameters until it is optimal. The peak position θ of the obtained waveform is taken. X and θ Y The converged results are the X component T of the scatterer's inclination. X and Y component T Y That is the case.

[0045] The tilt calculation unit 127 calculates the tilt of the scattering body as a two-directional component by taking the difference between the identified peak position and the peak position obtained assuming that the scattering body is not tilted from a direction perpendicular to the surface of the plate-shaped sample. This shortens the measurement and analysis time and allows for the calculation of the two-directional tilt angle with high analytical accuracy.

[0046] The input device 128 is, for example, a keyboard or mouse, and accepts input to the computer 121. The user can select the type of analysis and the diffraction points via the input device 128. The output device 129 is, for example, a display, and outputs the selection screen and the analysis results.

[0047] [Measurement and analysis methods] (Overall flow) Next, we will describe the measurement and analysis method using the system configuration described above. Figure 6 is a flowchart of the measurement and analysis procedure. As shown in Figure 6, first, the plate-shaped sample is placed and its position is adjusted (step S101). Then, the scattering intensity is measured with one ω scan (step S102). This completes the measurement.

[0048] In the analysis, first, the Q of each diffraction point is determined based on the measurement data. Z The waveform is acquired (step S103). Then, the user's selection is accepted, Q X and Q YIt is determined whether a single analysis that analyzes and independently has been selected (step S104). If a single analysis is not selected (i.e., a loop analysis has been selected), the loop analysis is performed (step S105), and the process proceeds to step S108.

[0049] If single analysis is selected, Q X =0nm -1 and Q Y =0nm -1 Both Q Z The system determines whether a waveform exists or not. If it does not exist, it proceeds to step S105. If it does exist, a single analysis is performed (step S107). The analysis results are then output (step S108), and the series of procedures is completed.

[0050] Figures 7(a) and 7(b) are flowcharts for single-step analysis and loop analysis, respectively. As shown in Figure 7(a), in single-step analysis, Q Y =0nm -1 Using the diffraction point, the X component of the tilt angle is θ X Determine the peak position of Q (step S201). Then, Q X =0nm -1 Using the diffraction point, the Y component of the tilt angle is θ Y The peak position is determined (step S202), and the single analysis is terminated.

[0051] Furthermore, as shown in Figure 7(b), in loop analysis, Q X ≠0nm -1 The diffraction point and a reasonable θ Y Using θ X The peak position is determined (step S301). Then, θ X , θ Y It is determined whether or not the function has converged (step S302). The convergence determination is, for example, θ X , θ Y This can be done by checking whether the difference or change is below a threshold. If convergence is achieved, the loop analysis is terminated. If convergence is not achieved, the process proceeds to step S303.

[0052] Next, QY ≠0 nm -1 and the determined θ at the diffraction point where it is -1 X are used to determine the peak position of θ (step S303). Then, it is determined whether θ Y , θ has converged (step S304). If it has converged, the loop analysis is terminated. If it has not converged, proceed to step S301. In this way, the finally converged θ X , θ Y are respectively the X component and the Y component of the tilt angle. In the above analysis, although there is an order in the analysis of θ X , θ Y , it may be in the reverse order. Also, each process in the above analysis can be performed by executing a program.

[0053] (Single - pass analysis) The details of single - pass analysis will be described with examples. Single - pass analysis is an analysis method in which when the Q X =0 nm<00​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​The intensity is integrated as shown above, and the peak position as the X component of the tilt angle is determined by peak search for the waveform representing the upper integration in Figure 8.

[0055] Meanwhile, Q Z For a waveform, Q X =0nm -1 Using only the diffraction points, Q can be calculated using the following formula. Z The horizontal axis of the waveform is θ. Y The coordinates are transformed. Figure 9 is Q X =0nm -1 θ of the diffraction point Y This graph shows waveforms based on intensity.

number

[0056] In such a single analysis, Q X and Q Y θ independently without correlation X , θ Y Q can be calculated. On the other hand, as diffraction points to be used for analysis, X =0nm -1 Q Y =0nm -1 It is necessary to prepare diffraction points.

[0057] (Loop analysis) Loop analysis is Q X =0nm -1 and Q Y =0nm -1 Q Z If no waveform exists, θ X , θ Y This analysis method allows for the determination of the tilt angle by repeatedly calculating and converging the values. An example of loop analysis will be given to illustrate this.

[0058] First, θ Y A reasonable numerical value is given as an initial value. For example, θY It is preferable to assume that = 0. Furthermore, Q X ≠0nm -1 Using the diffraction point, Q Z The horizontal axis of the waveform is defined by equation (5) θ X Convert to Q. Figure 10 shows Q. X ≠0nm -1 θ of the diffraction point X Q based on intensity Z This is a graph showing waveforms. For the multiple waveforms shown at the bottom of Figure 10, the horizontal axis is θ. X The intensity is integrated above, and the waveform representing the upper integration in Figure 10 is subjected to peak search θ X Determine the peak position.

[0059] Next, θ X The numerical value of the determined peak position is given to Q. Y ≠0nm -1 Using the diffraction point, Q Z The horizontal axis of the waveform is defined by equation (6) θ Y Convert to Q. Figure 11 shows Q. Y ≠0nm -1 θ of the diffraction point Y Q based on intensity Z This is a graph showing waveforms. For the multiple waveforms shown at the bottom of Figure 11, the horizontal axis is θ. Y The intensity is integrated above, and the waveform representing the upper integration in Figure 11 is subjected to peak search θ Y Determine the peak position of θ. X , θ Y Until the peak position converges, the above θ X , θ Y The process of determining the peak position is repeated.

[0060] The axis of rotation is Q X or Q Y If the measurement is performed under conditions consistent with the direction, Q Y =0nm -1 or Q X =0nm -1 Q ZIn some cases, a waveform may not exist. In such cases, the X and Y components of the tilt angle cannot be determined independently, but loop analysis can be used to determine them. Loop analysis uses Q X =0nm -1 or Q Y =0nm -1 It can be used even at diffraction spots where there is a certain property, and many diffraction spots can be used.

[0061] Figures 12(a) and (b) show the optimization of the XY components of the slope, respectively, as graph and table. X and θ Y The respective peak positions are T X and T Y This is how it is expressed. In the examples shown in Figures 12(a) and (b), the values ​​converge in about 4 cycles of loop analysis.

[0062] [Example 1] The following describes an example. First, Q X =0nm -1 and Q Y =0nm -1 Both Q Z As an example of application when a waveform is present, the silicon wafer sample is rotated 45° around an axis perpendicular to the wafer surface relative to the notch, and the axis in the X-Y diagonal 45° direction Rotate ω around the axis Measurements were taken. The tilt angle was then calculated based on the obtained measurement data.

[0063] Figures 13(a) and (b) show θ, respectively. X The diffraction pattern and Q are the targets of the single-step analysis. Y =0nm -1 θ of the diffraction point X Q based on intensity Z These are graphs showing waveforms. Figures 14(a) and (b) show θ, respectively. Y The diffraction pattern and Q are the targets of the single-step analysis. X =0nm -1 θ of the diffraction point Y Q based on intensity Z This is a graph showing the waveform.

[0064] Figures 15(a) and (b) show the diffraction pattern and the θ of the diffraction point, respectively, which are the subject of loop analysis. X Q based on intensity Z This is a graph showing the waveform. Figures 16(a) and (b) show the diffraction pattern and the θ of the diffraction point, respectively, which are the subject of loop analysis. Y Q based on intensity Z This is a graph showing the waveform.

[0065] The loop analysis showed that the values ​​converged in 4 cycles. Figures 15(b) and 16(b) show the Q values ​​at 3.5 and 4 cycles, respectively. Z The waveforms are shown. These represent the Q factor at convergence. Z This is a waveform. In a single analysis, the X component T of the tilt angle is obtained. X and the Y component T of the tilt angle Y The values ​​obtained were -0.865 degrees and 1.082 degrees, respectively. In the loop analysis, the X component T of the tilt angle was obtained. X and the Y component T of the tilt angle Y The results obtained were -0.864 degrees and 1.080 degrees, respectively. Thus, the results of each analysis agreed with high accuracy.

[0066] [Example 2] Next, Q X =0nm -1 or Q Y =0nm -1 Q Z As an example of application when no waveform exists, the Y-axis (Q) of the silicon wafer sample used in Example 1 Y The sample was rotated ω around the axis (parallel to the axis) and measurements were taken. The tilt angle was then calculated based on the acquired measurement data.

[0067] Figures 17(a) and (b) show θ, respectively. X The diffraction pattern and Q are the targets of the single-step analysis. Y =0nm -1 θ of the diffraction point X Q based on intensity Z This is a graph showing the waveform. Figure 18 shows θ Y This is the diffraction pattern that will be analyzed in a single run. The axis of rotation and QY Because the directions are aligned, Q X =0nm -1 Q of the diffraction point Z The dependency could not be obtained. Therefore, θ Y A single-run analysis was not possible.

[0068] Figures 19(a) and (b) show the diffraction pattern and the θ of the diffraction point, respectively, which are the subject of loop analysis. X Q based on intensity Z This is a graph showing the waveform. Figures 20(a) and (b) show the diffraction pattern and the θ of the diffraction point, respectively, which are the subject of loop analysis. Y Q based on intensity Z This is a graph showing the waveform.

[0069] The loop analysis showed that the values ​​converged in 4 cycles. Figures 19(b) and 20(b) show the Q values ​​at 3.5 and 4 cycles, respectively. Z The waveforms are shown. These represent the Q factor at convergence. Z This is a waveform. In a single analysis, the X component T of the tilt angle is obtained. X -0.864 degrees was obtained. In loop analysis, the X component T of the tilt angle was obtained. X and the Y component T of the tilt angle Y The values ​​obtained were -0.864 degrees and 1.082 degrees, respectively. Thus, the X component T of the tilt angle X They matched with high accuracy.

[0070] [Second Embodiment] The two directional components do not necessarily have to be the X and Y components. Alternatively, the two directional components can be the a0 direction, which is parallel to the surface of the plate-like sample and is the scanning direction of the ω scan, and the a1 direction, which is perpendicular to the a0 direction. In this case, even if the orientation of the sample is unknown, the tilt angles of the two components can be calculated based on the scanning direction.

[0071] (Single analysis) In this embodiment, a single-run analysis is possible. First, tanθ hk The diffraction point in the scanning direction (θ) where is 0. hk =0, θhk Using only (π), a0 is determined independently by the following equation (10). Note that ω0 is Q Z =0nm -1 This is the rotation angle of the sample corresponding to θ. hk This is the angular displacement of the diffraction point at the exponent (hk).

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[0072] Next, we determine a1 using equation (11).

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[0073] Here, the diffraction point in the scanning direction (θ hk =0, θ hk (θ) = π and diffraction spots in the direction perpendicular to the scan hk If you select =±π / 2), then tanθ hk The value diverges to 0 or infinity. Therefore, diffraction points are selected excluding diffraction points in the scanning direction and diffraction points in the direction perpendicular to the scan. Then, using the selected diffraction points, a1 is determined using a0 determined above. In this way, a0 and a1 can be determined in a single step without looping, as components of the scatterer's tilt in the scanning direction and the direction perpendicular to it.

[0074] Then, using the following equation (12), the peak positions of converged a0 and a1 are obtained. against The a0 and a1 direction components of the tilt angle are converted to the direction β determined by the notch in the silicon wafer sample.

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[0075] (Loop analysis) The following loop analysis is also possible. Using all diffraction points except those perpendicular to the scan direction (θhk = ±π / 2), an appropriate value (e.g., 0) is given as an initial value for a1, and the coordinate transformation Q is performed using equation (10). ZThe peak position of a0 is determined from the waveform using all diffraction points.

[0076] Also, Q obtained by the coordinate transformation in equation (11) Z Based on the waveform, the diffraction point (θ) in the scanning direction is determined. hk =0, θ hk (θ) = π and diffraction spots in the direction perpendicular to the scan hk Using all diffraction points except for those at ±π / 2, the peak position of a1 is determined using a0 determined above.

[0077] The calculation to determine the peak positions of a0 and a1 is repeated until the peak positions of a0 and a1 converge. Once the values ​​converge, equation (12) is used to convert the converged peak positions of a0 and a1 into the a0 and a1 direction components of the tilt angle in the direction β determined by the notch in the silicon wafer sample.

[0078] [Example 3] Using the sample from Example 1, single-pass analysis was performed with reference to the a0 and a1 directions. Figure 21 shows the diffraction pattern subject to single-pass analysis. Figure 22 shows the diffraction pattern subject to single-pass analysis and the Q based on the intensity of the diffraction points relative to a0. Z This is a graph showing the waveform. Figure 23 shows the diffraction pattern and the Q based on the intensity of the diffraction points relative to a1, which are the subject of the single-step analysis. Z This is a graph showing the waveform. Note that a 0p a 1p These represent the peak positions of a0 and a1, respectively.

[0079] The analysis revealed that the X component T of the tilt angle... X and the Y component T of the tilt angle Y The results obtained were -0.864 degrees and 1.082 degrees, respectively. The obtained results are in high agreement with the results of Examples 1 and 2.

[0080] [Example 4] Loop analysis was performed using the sample from Example 1, with reference to the a0 and a1 directions. The diffraction pattern targeted for loop analysis is the same as that targeted for single-pass analysis. Figure 24 shows the diffraction pattern targeted for loop analysis and the Q based on the intensity of the diffraction points relative to a0. Z This is a graph showing the waveform. Figure 25 shows the diffraction pattern and the Q based on the intensity of the diffraction points relative to a1, which are the subject of loop analysis. Z This is a graph showing the waveform.

[0081] The loop analysis showed that the values ​​converged in 4 cycles. Figures 24 and 25 show the Q values ​​at cycles 3.5 and 4, respectively. Z The waveforms are shown. These represent the Q factor at convergence. Z This is a waveform. Analysis revealed the X component T of the tilt angle. X and the Y component T of the tilt angle Y The results obtained were -0.864 degrees and 1.082 degrees, respectively. The obtained results are in high agreement with the results of Examples 1 and 2. [Explanation of Symbols]

[0082] 100 Measurement Systems 110 Measuring device 111 X-ray source 112 Mirror 115 Sample stage 116 Vacuum path 118 Beam Stopper 119 Detectors 120 Analysis equipment 121 Computer 122 Measurement Control Unit 123 Measurement data storage unit 124 Formula Memory Unit 125 Coordinate Transformation Unit 126 Peak position identification unit 127. Slope calculation unit 128 Input Devices 129 Output device GS Slit Q X Q Y Q Z Scatter vector S0 sample S1, S2 Slit T X X component of tilt angle T Y Y component of tilt angle

Claims

1. An analytical device for analyzing the microstructure of a plate-like sample formed by periodically arranging columnar scattering bodies that are long in the thickness direction, A measurement data storage unit that stores scattering intensity data from a plate-shaped sample measured by X-ray transmission in a single ω scan, A coordinate transformation unit that uses the measured scattering intensity data to transform the coordinates of the scattering vector to the coordinates of the tilt of the scattering body for a waveform based on the intensity of the two-directional components of a specific diffraction point, A peak position identification unit that identifies the peak position of the intensity waveform with respect to the coordinates of the coordinate-transformed slope, An analytical apparatus characterized by comprising: a tilt calculation unit that calculates the difference between the identified peak position and the peak position obtained assuming that the scattering body is not tilted from a direction perpendicular to the surface of the plate-shaped sample, as the tilt of the scattering body using the two directional components.

2. The analysis apparatus according to claim 1, characterized in that the coordinate transformation unit performs a coordinate transformation to the coordinate of the inclination of at least one of the two directional components of the scattering vector by a single analysis using a diffraction point where one of the coordinates of the two directional components is 0.

3. The analysis apparatus according to claim 1, characterized in that the coordinate transformation unit performs a coordinate transformation to the coordinate of the tilt of the scattering body of the two directional components by loop analysis using diffraction points where the coordinates of either of the two directional component scattering vectors are not zero.

4. The analytical apparatus according to any one of claims 1 to 3, characterized in that the two directional components are in a direction parallel to the surface of the plate-like sample and are components in the X direction in which the unit cell is oriented and in the Y direction perpendicular to the X direction.

5. The aforementioned two-directional component is in a direction parallel to the surface of the plate-like sample and is the scanning direction of the ω scan. ０ Direction and the a ０ a perpendicular to the direction １ The analytical apparatus according to any one of claims 1 to 3, characterized in that it is a directional component.

6. The analysis apparatus according to any one of claims 1 to 3, characterized in that the coordinate transformation unit uses a waveform obtained by integrating a plurality of diffraction points as a waveform based on the intensity of the two-directional components of the specific diffraction point.

7. An analytical method for analyzing the microstructure of a plate-like sample formed by periodically arranging columnar scattering bodies that are long in the thickness direction, The steps include: preparing scattering intensity data from a plate-shaped sample measured by X-ray transmission in a single ω scan; Using the measured scattering intensity data, the steps include: transforming the coordinates of the scattering vector to the coordinates of the tilt of the scattering body for a waveform based on the intensity of the two-directional components of a specific diffraction point; The steps include identifying the peak position of the intensity waveform with respect to the coordinates of the transformed slope, The analysis method is characterized by comprising the step of calculating the difference between the identified peak position and the peak position obtained assuming that the scattering body is not tilted in a direction perpendicular to the surface of the plate-shaped sample, as the tilt of the scattering body using the two directional components.

8. An analysis program for analyzing the microstructure of a plate-like sample formed by periodically arranged columnar scattering bodies that are long in the thickness direction, A process to prepare scattering intensity data from a plate-shaped sample measured by X-ray transmission in a single ω scan, Using the measured scattering intensity data, a process is performed to transform the coordinates of the scattering vector to the coordinates of the tilt of the scattering body for a waveform based on the intensity of the two directional components of a specific diffraction point. A process to identify the peak position of the intensity waveform with respect to the coordinates of the slope that have been transformed, An analysis program characterized by causing a computer to perform the following steps: calculate the difference between the identified peak position and the peak position obtained assuming that the scattering body is not tilted from a direction perpendicular to the surface of the plate-shaped sample, using the two-directional components as the tilt of the scattering body.

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