JP5969915B2 - Method and apparatus for measuring cross-sectional shape of fine pattern - Google Patents

Description

  The present invention relates to a method for measuring or inspecting the cross-sectional shape of a repetitive pattern formed on a substrate with a spacing of several micrometers or less, for example, an optical element such as a diffraction grating or a fine pattern of an electronic device such as a semiconductor. The present invention relates to a method and an apparatus for measuring a cross-sectional shape.

  In the semiconductor field, measuring the cross-sectional shape of a pattern by a so-called scatterometry technique is generally performed in recent years. Scatterometry is a technique for measuring the cross-sectional shape of the same repetitive pattern based on the reflectance of the sample surface on which the fine repetitive pattern is formed. Is described.

  Patent Document 1 describes a technique for measuring a cross-sectional shape of a pattern based on spectral reflectance and ellipso parameters on a sample surface. Further, Patent Document 2 uses optical simulation to extract data closest to the actually detected spectral reflectance from a spectral reflectance library calculated in advance under various cross-sectional shape conditions, and the extracted data. A method is described in which the shape condition at the time of calculating is output as a measured shape.

  Japanese Patent Application Laid-Open No. 2004-228561 describes a method of performing analysis by creating a bilaterally symmetric model using a Gaussian distribution in a method for obtaining a cross-sectional shape of a repeated pattern by scatterometry.

  Further, Patent Document 4 describes performing modeling of a symmetrical cross-sectional shape using Fourier series expansion.

  Furthermore, Patent Document 5 describes the analysis by representing the initial shape of the cross section with a symmetrical trapezoidal model.

US Pat. No. 5,432,607 US Pat. No. 5,607,800 US Pat. No. 6,704,661 US Pat. No. 7,031,894 US Pat. No. 7,280,230

  As a method for measuring the cross-sectional shape of a minute repetitive pattern using the scatterometry technique, the so-called library matching method that extracts the closest data from the library and the spectral reflectance etc. are calculated using the shape as a parameter. In addition, there is a so-called model fitting method in which a shape parameter is obtained so as to coincide with a spectral reflectance actually detected using an optimization method such as nonlinearity. In any method, in order to calculate the spectral reflectance and the like by optical simulation, it is necessary to model the cross-sectional shape of the pattern.

  For example, modeling will be described by taking an example of measuring a semiconductor pattern. FIG. 1 schematically shows a cross-sectional shape 101 of a semiconductor pattern. It is assumed that a pattern having such a cross-sectional shape is repeatedly placed on the sample surface. As shown in Patent Documents 3 to 5, a model 201 in which a plurality of trapezoids are stacked in the vertical direction as shown in FIG. 2 is assumed for this cross-sectional shape (indicated by a dotted line in the figure). With such a method, the cross-sectional shape can be modeled as a relatively simple shape. For example, the height of the pattern can be obtained as a total value of the heights of the trapezoids.

  On the other hand, for example, in the case of the diffraction grating pattern 301 shown in FIG. 3, compared with FIG. 1, it is asymmetrical, has a comparatively gentle shape, has rounded convex portions and concave portions, and has concave and convex portions on the slope portion, etc. A number of features differ from the case of a symmetrical cross-sectional shape. In the case of modeling such a cross-sectional shape by stacking trapezoids in the vertical direction in the same manner as in FIG. 2, if an error between the actual shape and the model shape is to be reduced, a large number of trapezoids are formed as shown in FIG. Must be laminated structure 401 (indicated by a dotted line in the figure).

  However, when many trapezoids are combined as shown in FIG. 4, the parameters for determining the shape increase. For example, in the case of FIG. 2, the number of parameters is the same for the lower base and the upper base of the trapezoid in contact with each other, so the number of parameters is 7, which is 4 in width and 3 in height. On the other hand, in the case of FIG. 4, since it is composed of seven trapezoids, the width is 8, the height is 7, and the shape is non-target, so 6 parameters for each relative position are required. , The total number of parameters is greatly increased to 21.

  When the parameters increase, in the case of library matching, an increase in the library and an increase in calculation time become problems in model fitting. For example, in the case of library matching, assuming that the number of variable levels of each parameter is 10, in the case of FIG. 2, the number of operations of spectral reflectance included in the library is 10 7 to 10 million. This is a sufficiently large number, but in the case shown in FIG. 4, it is a very large number of 10 to the 21st power.

  In this way, in the case of the left-right asymmetric cross-sectional shape as shown in FIG. 4, the number of parameters is large and the calculation time of the library is enormous compared to the case shown in FIG. It becomes. Alternatively, when the number of parameters is reduced to shorten the calculation time, there is a problem that the shape measurement accuracy must be lowered because the model needs to be simplified.

  None of Patent Documents 1 to 5 describes the modeling of such a left-right asymmetric pattern shape.

  The present invention solves the above-described problem, and even if the pattern has a cross-sectional shape that is asymmetrical on the left and right sides, the number of parameters can be reduced to reduce the calculation time of the library and to ensure high shape measurement accuracy. It is an object of the present invention to provide a method and an apparatus for measuring a cross-sectional shape of a fine pattern that can be compatible with each other.

In order to solve the above problems, the present invention irradiates a sample having a fine repetitive pattern whose cross-sectional shape is asymmetric on the surface and spectrally detects the light reflected by the surface of the sample. The cross-section of the pattern to obtain the cross-sectional shape of the fine repetitive pattern formed on the sample surface using the data on the spectral reflectance of the sample surface obtained or the data on the ellipso parameters of the sample surface and the data stored in advance In the shape measurement method, the data stored in advance is the data related to the spectral reflectance of the surface of the sample of the same type as the data obtained by spectral detection or the data related to the ellipso parameter of the surface of the sample and the spectral detection. associated with the data relating to the ellipsometric parameters of the data or the surface of the sample relating to the spectral reflectance of the same type of surface of the sample and the resulting data Digit is data that models the cross-sectional shape of the fine repetitive pattern, data obtained by modeling the cross-sectional shape, one function or by using the data relating to ellipsometric parameters of the data or the surface of the sample relating to the spectral reflectance of the surface of the sample It is data formed by a left-right asymmetric curve expressed by combining a plurality of functions.

In order to solve the above problems, in the present invention, a pattern cross-sectional shape measuring apparatus includes a light irradiation system for irradiating a sample having a fine repetitive pattern whose cross-sectional shape is asymmetric on the surface, and a light A spectroscopic detection system that spectroscopically detects light reflected by the sample irradiated with light from the irradiation system, a storage unit that stores data, and a surface of the sample obtained by spectroscopically detecting the reflected light using the spectroscopic detection system A data processing system for calculating a cross-sectional shape of a fine repetitive pattern formed on the sample surface using data on the spectral reflectance of the sample or data on the ellipsometric parameters of the sample surface and data stored in the storage unit configure Te, data stored in the storage unit, ellipsometry data or the surface of the samples for the spectral reflectance of the surface of the same type of sample data obtained by the spectrum detection by the spectral detection system parameter Models and data about the data, the cross-sectional shape of the fine repetitive pattern associated with the data relating to ellipsometric parameters of spectral reflectance on the data or the surface of the sample of the same type of surface of the sample and the data obtained by the spectrum detection by spectroscopic detection system The data obtained by modeling the cross-sectional shape is asymmetry that is expressed by combining a single function or a plurality of functions using data on the spectral reflectance of the sample surface or data on the ellipsometric parameters of the sample surface. The data is formed by a simple curve.

Furthermore, in order to solve the above-described problems, in the present invention, a sample having a fine repetitive pattern whose cross-sectional shape is asymmetric on the surface is irradiated with light, and the light reflected on the surface of the sample is spectrally detected. The cross-sectional shape of the minute repetitive pattern formed on the sample surface using the data on the spectral reflectance of the sample surface obtained by spectroscopic detection or the data on the ellipso parameters of the sample surface and the data stored in advance. In the method to obtain, the data stored in advance was obtained by spectroscopic detection and data on the spectral reflectance of the surface of the same type of sample as that obtained by spectroscopic detection or data on the ellipso parameters of the surface of the sample . data that fine that associated with the data relating to the ellipsometric parameters of the data or the surface of the sample relating to the spectral reflectance of the same type of surface of the sample Ri returns a data sectional shape was modeled pattern data that models the cross-sectional shape in the measurement object forming process by using the data relating to ellipsometric parameters of the data or the surface of the sample relating to the spectral reflectance of the surface of the sample The present invention is characterized in that the data is formed by a left-right asymmetric curve represented by a combination of a single function or a plurality of functions whose distribution shapes are selected or constructed based on physical phenomena and process conditions.

Furthermore, in order to solve the above problems, in the present invention, a pattern cross-sectional shape measuring apparatus is
A light irradiation system that irradiates a sample with a microscopic repetitive pattern whose cross-sectional shape is asymmetric on the surface, and spectral detection that spectrally detects light reflected by the sample irradiated with light by this light irradiation system System, storage unit for storing data, data on the spectral reflectance of the surface of the sample obtained by spectroscopic detection of the reflected light by the spectroscopic detection system, or data on the ellipso parameters of the surface of the sample And a data processing system for calculating a cross-sectional shape of a fine repetitive pattern formed on the sample surface using the data stored in the storage unit, and the data stored in the storage unit is a spectroscopic detection system. the same type and data in related ellipsometric parameters of spectral reflectance on the data or the surface of the sample of the same type of surface of the sample and spectrum detection-obtained data, and data obtained by the spectrum detection by spectroscopic detection system A data modeling the cross-sectional shape of the fine repetitive pattern associated with the data related to the ellipsometric parameters of the data or the surface of the sample relating to the spectral reflectance of the surface of the sample, the data obtained by modeling the cross-sectional shape of the surface of the sample A function or combination of functions that select or construct a distribution shape based on physical phenomena and process conditions in the formation process of the object to be measured using data on spectral reflectances or data on ellipso parameters of the surface of the sample. The data is formed by a left-right asymmetric curve.

  By using the present invention, for example, the cross-sectional shape including features such as asymmetric and round like the diffraction grating, the parameters can be reduced as compared with the conventional modeling method. Shape measurement by model fitting can be enabled. Alternatively, modeling with a smaller shape error is possible with a smaller number of parameters, and the shape measurement accuracy can be improved.

  Furthermore, in the case of a diffraction grating, if a sinusoidal waveform, that is, a Fourier series expansion is used as the distribution shape, correlation with the diffraction efficiency, which is one of the diffraction grating performances, can be obtained by modeling with a small order. Can be evaluated.

It is sectional drawing of the pattern which shows an example of the cross-sectional shape of a semiconductor pattern. It is sectional drawing of the pattern which shows an example which modeled the cross-sectional shape of the semiconductor pattern. It is sectional drawing of the diffraction grating which shows an example of the cross-sectional shape of a diffraction grating. It is sectional drawing of the diffraction grating which shows an example which modeled the cross-sectional shape of the diffraction grating with the conventional method. It is a block diagram which shows the structure of the pattern cross-sectional shape measuring apparatus in Example 1 of this invention. FIG. 2 is a block diagram illustrating a configuration of a spectral detection optical system of a pattern cross-sectional shape measuring apparatus in Example 1. FIG. 3 is a block diagram illustrating a configuration of an illumination optical system of a spectral detection optical system of the pattern cross-sectional shape measuring apparatus in Example 1. 3 is a block diagram illustrating an example of the configuration of an XY stage in Embodiment 1. FIG. 3 is a block diagram illustrating an example of a configuration of an XZθ stage in Embodiment 1. FIG. FIG. 3 is a flowchart showing a procedure for measuring a cross-sectional shape in Example 1. FIG. 6 is a flowchart showing a procedure for library matching in the first embodiment. FIG. 6 is a flowchart showing a procedure of library operations in the first embodiment. It is a schematic diagram of the cross section of the pattern which shows an example which approximated the pattern to the laminated structure by effective medium approximation. It is sectional drawing of the diffraction grating which shows an example which modeled the cross-sectional shape of the diffraction grating using several Gaussian distribution. It is a figure which shows the list of input data in the case of modeling the cross-sectional shape of a diffraction grating using multiple Gaussian distribution. It is a figure which shows an example of the list | wrist of the data which show the result of having modeled the cross-sectional shape of the diffraction grating using multiple Gaussian distribution. It is the schematic which shows the method of forming a pattern in a positive resist by mask exposure. It is sectional drawing of the pattern formed in the positive resist by mask exposure. It is the schematic which shows the method of forming an asymmetrical pattern in a positive resist by mask exposure. It is sectional drawing of the asymmetrical pattern formed in the positive resist by mask exposure. It is sectional drawing of an example of an asymmetric pattern. FIG. 5 is a cross-sectional view of a positive resist pattern showing an example of modeling a case where an asymmetric pattern cross-sectional shape is formed by moving exposure light having a Gaussian distribution by equal pitches and exposing multiple times to a positive resist. . It is a schematic diagram which shows the relationship between exposure amount and exposure intensity distribution. It is a figure which shows an example of the list | wrist of the data which show the result of having modeled the cross-sectional shape of the diffraction grating by using several Gaussian distributions as a variable. It is a figure which shows an example of the list | wrist of the data which show the result of having modeled the cross-sectional shape of the diffraction grating by using height and a position as a variable using multiple Gaussian distribution. It is the schematic which shows the method of forming the pattern in the case of a negative resist. FIG. 6 is a cross-sectional view of a negative resist pattern showing an example of modeling a case where an asymmetric pattern cross-sectional shape is formed by moving exposure light having a Gaussian distribution by equal pitches to a negative resist to expose it multiple times. . It is sectional drawing of the diffraction grating which shows an example which modeled the cross-sectional shape of the diffraction grating using Fourier series expansion | deployment. It is a figure which shows an example of the input data list in the case of modeling the cross-sectional shape of a diffraction grating using a Fourier series expansion | deployment. It is sectional drawing of the diffraction grating which showed an example of modeling by the Fourier series to 2 term | term. It is sectional drawing of the diffraction grating which showed an example of modeling by the Fourier series to 3 term | terms. It is sectional drawing of the diffraction grating which showed an example of the modeling by a Fourier series to four terms. It is the graph which showed an example of the relationship between the number of terms of a Fourier series, and diffraction efficiency. It is a schematic diagram of a surface. It is a block diagram which shows the structure of the pattern cross-sectional shape measuring apparatus in Example 2 of this invention. 6 is a diagram illustrating a configuration of a spectroscopic ellipso optical system in Example 2. FIG. FIG. 10 is a flowchart showing a procedure for library matching in the second embodiment. FIG. 10 is a flowchart showing the procedure of library operations in the second embodiment.

  The present invention is a fine pattern that makes it possible to reduce the number of parameters and reduce the calculation time of the library and ensure high shape measurement accuracy even for a pattern having an asymmetrical cross-sectional shape. The present invention relates to a pattern cross-sectional shape measuring method and apparatus.

  Embodiments of the present invention will be described below with reference to the drawings, taking as an example the measurement of the cross-sectional shape of a diffraction grating.

  In the present embodiment, an example of an apparatus that detects the spectral reflectance of the sample surface and measures the cross-sectional shape of a fine repetitive pattern formed on the sample surface based on the detected spectral reflectance will be described.

  FIG. 5 shows a configuration diagram of the apparatus. The apparatus performs spectral detection by controlling at least a spectral reflectance detection optical system 901 for detecting spectral reflectance, a sample stage 902 for installing a sample 905 and a reference sample 906, and a spectral reflectance detection optical system 901. The control unit 903 for controlling the operation of the stage and the stage, the arithmetic unit 904 for calculating the cross-sectional shape based on the detected spectral reflection intensity, the interface 907 for setting conditions and displaying results, and the data necessary for the operation are stored in the arithmetic unit 904 The data storage unit 908 is configured to be configured.

  FIG. 6A shows an example of the configuration of the spectral reflectance detection optical system 901. The optical system includes at least a light source 1001 that irradiates light including a number of wavelengths, an optical system 1002 that irradiates the sample surface with light emitted from the light source, and a spectroscopic detector 1003 that splits reflected light from the sample surface. Is done.

  This figure shows a case where a general optical microscope is applied. By using a xenon lamp as the light source 1001, light from ultraviolet light to infrared light can be emitted. If deep ultraviolet light is required, a deuterium lamp may be used, and if ultraviolet light is unnecessary, a halogen lamp may be used. It is also conceivable to use a laser light source that emits light including a plurality of wavelengths or a plurality of laser light sources having different wavelengths.

  For example, the optical system 1002 includes an illumination optical system 1004, a half mirror (or beam splitter) 1005, an objective lens 1006, an imaging lens 1007, and a field stop 1008.

  As shown in FIG. 6B, the illumination optical system 1004 includes a condensing lens 10041, a first slit plate 10042, a collimator lens 10043, and a second slit plate 10044.

  In such a configuration, the illumination optical system 1004 condenses the light emitted from the light source 1001 by the condensing lens 10041, and the first slit provided in the vicinity of the portion where the condensed light is narrowed down. The disturbance light is shielded by a hole provided in the plate 10042 to transmit the collected light, and the light having passed through the hole of the first slit plate and whose diameter is enlarged is converted into parallel light by the collimator lens 10043. Out of the light converted into parallel light, the surrounding light is shielded by the second slit plate 10044, and the light in the vicinity of the center where the intensity is relatively uniform is passed through the hole provided in the second slit plate 10044. The light that has passed through the second slit plate 10044 is incident on the half mirror 1005, and half of the light is reflected toward the objective lens 1006 and irradiated on the sample 905.

  The reflected light from the sample 905 is guided again to the spectroscopic detector 1003 through the objective lens 1006 and the half mirror 1005, and this time through the imaging lens 1007 and the field stop 1008. The surface of the sample 905 and the surface provided with the field stop 1008 are optically conjugate, and the field stop 1008 allows only reflected light in a specific region on the surface of the sample 905 to pass therethrough. .

  The stage 902 has three axes of so-called XYZ, which is two axes in the horizontal direction and one axis in the vertical direction (FIG. 7A), or one axis in the horizontal direction and one axis in the vertical direction. It is desirable to provide (FIG. 7B).

  The control unit 903 controls the spectral reflectance detection optical system 901 and the stage 902 so as to detect the spectral reflectance at an arbitrary position on the surface of the sample 905.

  A series of operations for measuring the cross-sectional shape will be described with reference to FIG. First, the stage 902 is operated to move the reference sample 906 to a position where the spectral reflectance detection optical system 901 can perform spectral detection (S1201). Here, the spectral reflection intensity Ir of the reference sample 906 is detected (S1202). Next, the stage 902 is operated to move the sample 905 to a position where the spectral reflectance detection optical system 901 can perform spectral detection (S1203). Similarly, the spectral reflection intensity Is of the sample 905 is detected (S1204). When detecting the spectral reflection intensity, the Z-axis is adjusted as necessary so that the surface of the sample 905 becomes the focus position of the spectral reflectance detection optical system 901. Next, the arithmetic unit 904 calculates the ratio (Is / Ir) of the two detected spectral reflection intensities (S1205).

  In the arithmetic unit 904, the cross-sectional shape is calculated by library matching or model fitting using the calculated spectral reflectance (S1206).

  By repeating the above operation as necessary, the cross-sectional shape of the pattern at an arbitrary position on the surface of the sample 905 can be measured (S1207).

  Next, a method for calculating the cross-sectional shape executed in S1206 will be described. As an example, a library matching method will be described with reference to FIG.

  In order to measure the shape by library matching in the arithmetic unit 904, the detected spectral reflectance data is prepared (S1301), while the spectral reflectance data calculated by the optical simulation is stored in the data storage unit 908. It is extracted from the library (database) that is stored (S1302), these data are compared to calculate an error (S1303), and comparison with the already calculated error is performed to determine the minimum value of the error (S1304). This is performed for all data stored in the library of the unit 908 (S1305), and the spectral reflectance is calculated using the shape condition when the spectral reflectance with the smallest error from the spectral reflectance detected in S1304 is calculated as the shape measurement value. And the shape condition are extracted from the stored library (S130). ).

In S1303, as a method of calculating an error between the detected spectral reflectance and the spectral reflectance calculated by the simulation extracted from the database, for example, it is conceivable to use the mean square error shown in (Equation 1). In the same equation, R _s indicates the spectral reflectance detected, and R _m indicates the spectral reflectance calculated by simulation.

  In many cases, the spectral reflectance actually detected is not evenly spaced data depending on the specifications of the spectral detector. In that case, the wavelength of the data detected by interpolation etc. and the wavelength of the calculated data are made to correspond.

  As described above, in the method based on library matching, it is necessary to create a spectral reflectance library by calculation in advance. Next, a calculation method of the spectral reflectance library will be described with reference to FIG.

  First, in order to grasp the cross-sectional shape of the measurement target to some extent, a rough shape is detected (a rough shape is detected) (S1401). This operation can be realized by measuring the target shape with another means, observing the cross section with an SEM, or the like. Next, this cross-sectional shape is modeled (S1402).

  Next, a shape parameter for calculating the library is selected (S1403). The cross-sectional shape of the pattern formed on the surface of the sample varies depending on the conditions of the formation process. In this change, the cross-sectional shape of the measurement object measured by another method in S1401 or the cross-sectional shape observed by the SEM does not simply change in a similar manner. Therefore, it is necessary to consider a cross-sectional shape model that can represent all the shapes that can be changed with a small number of parameters.

  Finally, compute the library. In order to calculate the library, it is necessary to determine the calculation conditions of the parameters constituting the model (S1404). The parameter calculation conditions include, for example, a method of setting a calculation range and resolution. The calculation range may be set so as to cover the shape that can be changed, and the resolution may be set large enough to obtain the necessary shape measurement accuracy. The library is calculated under the set parameter calculation conditions (S1405).

  As a means for calculating the spectral reflectance, an RCWA (Rigorous Coupled Wave Analysis) method is used (RCWA is a known technique in the art). When the size of the target pattern is small and is about one tenth or less of the wavelength used for detection, the target pattern is approximated to a layer structure using effective medium approximation as shown in FIG. It is also possible to use the Fresnel coefficient formula based on the layer structure (the effective medium approximation and the Fresnel coefficient are known techniques in the art).

  As a method of calculating the reflectance using the effective medium approximation and the Fresnel coefficient, the method described in Patent Document 5 may be used.

  As described above, the spectral reflectance on the surface of the sample can be detected, and the cross-sectional shape of the fine repetitive pattern formed on the sample surface can be measured based on the detected spectral reflectance.

  Next, a method for modeling the cross-sectional shape in S1402 will be described. As a first method, a method of using a distribution shape by a distribution function such as a Gaussian distribution for modeling a cross-sectional shape will be described. As described above, in the conventional modeling, a model 401 in which trapezoids are vertically stacked as shown in FIG. In this method, when a complicated shape is to be modeled, the number of trapezoids to be divided in the vertical direction must be increased, resulting in an increase in the number of parameters.

  In contrast, in the present embodiment, as shown in FIG. 12A, for example, a plurality of Gaussian distributions are arranged in the horizontal direction, and modeling is realized by adding them together. That is, as shown in the figure, a modeled shape 503 is formed by adding two Gaussian distributions 501 and 502 arranged in the water direction (indicated by a dotted line in the figure).

  In the case of the example shown in FIG. 12A, the number of parameters is the number obtained by multiplying the number of Gaussian distributions and the number 3 of parameters of the Gaussian distribution function that defines the Gaussian distribution (center position p, height h, and half width w). 6 can be greatly reduced compared to 21 in the case of stacking conventional trapezoids. In addition, the shape error between the cross-sectional shape and the model can be reduced, and the shape can be measured with higher accuracy.

  When a cross-sectional shape model is created using two Gaussian distributions as shown in FIG. 12A, the input data includes three data that characterize the Gaussian distribution: height, half-value width, and position, as shown in FIG. 12B. What is necessary is just to input as each Gaussian distribution data. Further, as a result of calculation based on the input data of FIG. 12B, as error data between the cross-sectional shape model 503301 shown by the solid line in FIG. 12A and the data 503 obtained by combining the two Gaussian distributions 501 and 502 shown by the dotted line, As shown in FIG. 12C, the result of calculating the peak position error, height error, maximum error, etc. is output (displayed on the screen). The operator can adjust the data input in FIG. The input data shown in FIG. 12B and the output data shown in FIG. 12C are displayed on the screen of the interface 907 together with the graph of FIG. 12A.

  FIG. 12A shows a case where two Gaussian distributions are used as an example, and the number of Gaussian distributions used is not limited to two. You may create combining 3 or more.

  Similarly, in FIG. 12A, the Gaussian distribution is used as the distribution function representing the distribution shape, but the distribution function is not limited to the Gaussian distribution, and a Lorentz distribution, a SINC function, or the like may be used.

  The use of a Gaussian distribution is described in [0074] of Patent Document 3, but this document does not disclose that a plurality of Gaussian distributions are arranged in the horizontal direction or that an asymmetric shape is measured.

The use of a plurality of Gaussian distribution functions can be said to be a reasonable modeling consistent with a physical phenomenon, for example, when an asymmetric cross-sectional shape is formed by exposing a resist a plurality of times.
[Modification 1]
As a modification of the method of modeling the cross-sectional shape, for example, a mask having a simple slit-like opening is used, and the pattern is asymmetrical by performing exposure multiple times by changing the mask position and exposure amount. Think about forming. The principle of pattern formation will be described with reference to FIG. The figure schematically shows exposure to the resist 2004.

  By the light 2001 emitted from the light source, an image of a mask 2002, in this case, a slit-shaped opening having a width a, is transferred to the resist 2004 on the substrate 2005. This figure shows a slit image, that is, an exposure intensity distribution 2006 toward the substrate 2005 in the depth direction with the resist surface as the origin. When the width of the slit-shaped opening is close to the wavelength of light used for exposure, the intensity distribution of exposure transferred to the resist is not a rectangular distribution but a distribution as shown by a dotted line in FIG.

  If a sample that has been exposed only once is developed, a groove shape 2101 is obtained as shown in FIG. 14 according to the exposure intensity distribution 2006 and the characteristics of the resist 2004 and development conditions. This figure shows an example of a positive resist.

  As shown in FIG. 14, an asymmetric shape cannot be formed by one exposure. Therefore, an asymmetric shape is formed by changing the position of the mask and the exposure amount, and performing a plurality of times to form a shape model based on the physical phenomenon of the process. FIG. 15 shows an example in which an asymmetric shape is formed by five exposures. In the case of the same figure, an example is shown in which the asymmetric exposure distribution shape 2202 is formed by shifting the position of the mask 2002 at equal intervals (shown only in the case of the center position in FIG. 15) and changing the respective exposure amounts 2201. Yes. By developing this, an asymmetric pattern shape 2301 as shown in FIG. 16 can be realized.

  When measuring the asymmetric pattern shape 2301 as shown in FIG. 16 with a shape model formed based on the physical phenomenon of the process in which a plurality of distribution shapes developed in the horizontal direction described above are superimposed, the above-described measurement target pattern Information on the formation process can be used.

  FIG. 17 shows an asymmetric pattern 2601 formed in the resist 2602 on the substrate 2603. This is modeled by a Gaussian distribution as shown in FIG. This figure shows an example in which five upside-down Gaussian distributions are modeled. The modeled shape 2701 (dotted line) is obtained by subtracting a value obtained by superimposing five Gaussian distributions 2701 to 2705 from the resist surface 2706. In this case, 3 × 5 = 15 parameters are necessary as parameters for determining the model shape because three parameters of width, height, and position that define the Gaussian distribution are required for each of the five gausses. It can be subtracted from the process conditions to be formed.

  For example, the interval between the multiple exposures is known from the process conditions and depends on the exposure apparatus, but is positioned with an accuracy of several nanometers or less, so that the center position of each distribution can be determined from the process conditions.

  Further, when performing multiple exposures, the same mask is used in FIG. FIG. 19 schematically shows exposure distribution shapes 2401 to 2403 when three types of exposure amounts are changed using the same slit-shaped mask. In the figure, the widths indicated by arrows 2404 are the respective half-value widths, and the half-value width 2404 of each distribution is constant regardless of the amount of exposure. From this, it is considered that the half widths of the five Gaussian distributions shown in FIG. 18 are the same. Therefore, when the same mask is used, the width (half width) of the distribution shape in each exposure can be handled as the same value.

  Also, the distribution shape width (half width) by multiple exposures can be set as one parameter with the same value, or the half width of all distributions can be set as a fixed value if the half width can be evaluated in advance.

  Even if the mask widths for multiple exposures are all different, there is a correlation between the mask width and the half width of the distribution shape, so the half width of the exposure distribution shape is determined by calculation or actually evaluated. Thus, the half width of the distribution shape can be determined.

  Since the height of the distribution also has a correlation with the exposure amount, it can be excluded from the parameters at the time of the library calculation as a fixed value from the exposure amount.

  All of the above mentioned that it can be handled as a fixed value on the assumption that the process conditions are stable, but since there are variations in the process, if library operations are performed using only parameters that can cause variation, Good. For example, when various pattern shapes are to be formed by exposing the same mask with the same mask as shown in FIG. 16 and varying the exposure amount of each exposure, the position and half of the distribution used in the model are used. If the value width is fixed and only the exposure amount is used as a parameter, the number of parameters is originally 3 × 5 = 15 parameters, but a model shape can be constructed with only 5 parameters for each exposure amount (FIG. 20A).

  Alternatively, if only the half width of the distribution used for the model is fixed and the position of the distribution and the exposure amount are used as parameters, the number of necessary parameters becomes 2 × 5 = 10 parameters, and the model shape is constructed with 10 parameters. (FIG. 20B).

  As described above, the number of parameters for library operation can be reduced by using the process conditions at the time of pattern formation. If the parameters can be reduced, the number of libraries can be reduced, and the calculation time required for pattern shape measurement can be shortened. Alternatively, a more detailed library can be calculated for each parameter, and more accurate measurement can be realized.

In the examples described above with reference to FIGS. 13 to 16 and FIGS. 18 to 20B, so-called positive type resists have been described, but so-called negative types can also be handled in the same manner. That is, the exposed portion remains in the positive type, but the unexposed portion remains in the negative type. In the positive type, for example, as described with reference to FIG. 15, the distribution shape is defined toward the substrate with the pattern surface as the origin, but in the negative case, as shown in FIG. 21, for example, as shown in FIG. The distribution shape 2501 may be defined in the film thickness direction with the interface of.
In the case of using a negative type resist, in order to form an asymmetric pattern 2601 by the resist 2602 as shown in FIG. 17 on the substrate 2603, the case of using the positive type resist described in FIG. Modeled by a Gaussian distribution as shown in FIG. This figure shows an example of modeling using five Gaussian distributions as in the case of FIG.

  The modeled shape 2906 (dotted line) is obtained as a value obtained by superimposing five Gaussian distributions 2901 to 2905. In this case, as the parameters for determining the model shape, as in the case of FIG. 18, three parameters of width, height, and position that define the Gaussian distribution are required for each of the five Gaussians, so that 3 × 5 = 15 parameters. However, it can be subtracted from the process conditions for forming the target pattern, and the model shape can be constructed with 5 or 10 parameters, as described in the case of using a positive resist. The above has described a method using five Gaussian distributions as an example, but the number of distributions is not limited to five, and the distribution shape may be appropriately selected depending on the object.

  As described above, the distribution shape used in the shape model can be measured with sufficiently high accuracy by using a distribution shape such as Gaussian. However, the actual distribution shape is not exactly a relatively simple distribution shape such as Gauss, but a shape determined by resist characteristics, development conditions, and the like.

  Therefore, in order to realize measurement with higher accuracy, it is only necessary to actually measure the distribution. If a model is constructed based on the measured shape, more accurate measurement is possible.

For example, when a model is constructed with five distribution shapes, an error due to the distribution shape occurs between the actual shape and an error of five cycles may occur. In this case, the error can be reduced by performing the moving average process with a width of one cycle.
It is also possible to obtain an accurate distribution shape by calculation based on a physical phenomenon.

  In the above, a model is constructed by horizontally unfolding and superimposing a plurality of distribution shapes, but depending on the measurement object, it is also conceivable to superimpose distributions unfolded vertically or obliquely. It is also conceivable to combine the horizontal direction, the vertical direction and the oblique direction.

  Conventionally, it is common to use a model in which trapezoids and rectangles are stacked as the shape of a model for simulation as described above. The feature of this model is that the target shape is divided and replaced with a relatively simple shape (region division model). On the other hand, the model of this embodiment has a feature that a complicated target shape is constructed by superimposing relatively simple distribution shapes based on a physical phenomenon (distribution superposition model).

[Modification 2]
Next, a method of using Fourier series expansion for cross-sectional shape modeling will be described as a second modification of the method for modeling cross-sectional shape in S1402. FIG. 23A shows a shape modeled by Fourier series expansion of the cross-sectional shape 301 shown in FIG. 3 (indicated by a dotted line 601 in the figure). A shape that matches the cross-sectional shape 503 indicated by the solid line can also be obtained by Fourier series expansion. FIG. 23B shows an example of data to be input when modeling by Fourier series expansion. The input data includes phase and amplitude, and the number of terms in the Fourier series used for modeling. FIG. 23C shows another example of data to be input. As shown in FIG. 23C, input data may be input in terms of two items of amplitude and phase. FIG. 23C shows an example when the number of terms is two. Enter the amplitude and phase for the number of terms. Further, as the calculation result, information similar to that shown in FIG. 12C is output. The input data of FIG. 23B or FIG. 23C and the output data similar to FIG. 12C are displayed on the screen of the interface 907 together with the graph of FIG. 23A.

  Here, the diffraction efficiency of the diffraction grating having the cross-sectional shape shown in FIG. 3 is considered. 24A to 24C show shapes obtained by modeling the cross-sectional shape 501 of the diffraction grating with Fourier series up to n terms (n = 2, 3 and 4). That is, FIG. 24A shows a model shape 701 (dotted line) with a Fourier series up to two terms superimposed on a cross-sectional shape 501 indicated by a solid line. FIG. 24B shows a model shape 702 based on Fourier series up to three terms superimposed on the cross-sectional shape 501. Further, FIG. 24C shows a model shape 702 based on Fourier series up to four terms superimposed on the cross-sectional shape 501. As shown in FIGS. 24A to 24C, when the order is small (FIG. 24A), an error from the original shape is large.

  Here, attention is focused on diffraction efficiency, which is one of the diffraction grating performances. In FIG. 25, the number n of terms used for modeling is plotted on the horizontal axis, and the diffraction efficiency in a shape modeled by a Fourier series up to n terms is calculated on the vertical axis. From the figure, it can be seen that the diffraction efficiency is almost the same as that when the number of terms is large before the number of terms reaches a sufficiently small error. That is, the diffraction efficiency of the diffraction grating can be evaluated without calculating the number of terms with which the shape error is sufficiently small.

Although the use of Fourier series expansion is described in [0197] of Patent Document 4, it does not disclose modeling an asymmetric shape or taking a correlation with diffraction efficiency.
[Modification 3]
Next, a third modification of the method for modeling the cross-sectional shape in S1402 will be described. When the modeling equations in the first method and the first and second modified examples are generalized, they can be expressed by (Expression 2). This expression is an expression obtained by adding a plurality of distribution shapes f (x) arranged in the horizontal direction. In the case of the above two methods, the distribution shapes are (Equation 3) and (Equation 4), respectively.

  In the third modification, the distribution formula f (x) in the generalized expression represented by (Expression 2) is the same as that described in the first method represented by (Expression 3) (Expression 4). ) Expressed by the second method are combined and weighted and modeled. In this case, as described above, the distribution shape is not limited to the Gaussian distribution, and a Lorentz distribution, a SINC function, or the like may be used. In short, an appropriate distribution may be selected as the shape model.

  According to the present embodiment, it is possible to calculate model data having a cross-sectional shape that is asymmetrical from the data obtained by detecting the spectral reflectance of the sample surface using a plurality of distribution functions and using fewer parameters. As a result, it is possible to reduce the calculation time of the library while maintaining high shape measurement accuracy as compared with the case of creating cross-sectional model data by combining conventional trapezoidal patterns.

  In the present embodiment, an example of an apparatus that detects an ellipso parameter on a sample surface and measures a cross-sectional shape of a fine repetitive pattern formed on the sample surface based on the detected ellipso parameter will be described.

  FIG. 26 shows a configuration diagram of an apparatus according to the present embodiment. The configuration of the apparatus according to the present embodiment is the same as that described with reference to FIG. 5 in the first embodiment, but includes a spectral ellipso optical system 1601 instead of the spectral reflectance detection optical system 901 for detecting the spectral reflectance. Has been.

  FIG. 27 shows an example of the configuration of the spectroscopic ellipso optical system 1601. The spectroscopic ellipso optical system 1601 includes at least a light source 1701 that emits light including a plurality of wavelengths, a polarizer 1702, a rotation stage 1706 that rotates the polarizer around the optical axis, a compensator 1703, an analyzer 1704, and A spectroscopic detector 1705 is provided. If necessary, the incident optical system from the light source 1701 to the compensator 1703 and the detection optical system from the analyzer 1704 to the spectroscopic detector 1705 are arranged at the same angle (elevation angle) relative to the sample. You may make it provide the adjustment mechanism (not shown) which can adjust an angle. The stage 912 on which the sample 905 is placed has a configuration as shown in FIG. 7A or 7B, similarly to the stage 902 described in the first embodiment.

  In the configuration shown in FIG. 27, the light emitted from the light source 1701 is irradiated to the sample placed on the stage 912 via the polarizer 1702 and the compensator 1703, and the reflected light is spectrally separated via the analyzer 1704. Spectroscopic detection is performed by a detector 1705. Note that the analyzer 1704 and the polarizer 1702 may have the same configuration (a ¼ wavelength plate or a ½ wavelength plate or a combination thereof).

  The control unit 1602 in FIG. 26 controls the compensator rotating stage 1706, the spectral detector 1705, and the stage 902, detects the spectral intensity at an arbitrary position on the surface of the sample 905, and calculates the spectral unit based on the detected spectral intensity. In step 1603, ellipso parameters are calculated.

  Specifically, the angle of the compensator 1703 is rotated by the compensator rotating stage 1706, and the spectral reflection intensity is detected by the spectral detector 1705. Based on the detected spectral reflection intensity data of the compensator angle, Δ and Ψ, which are ellipso parameters, are calculated. Since calculating the ellipso parameter based on the spectral intensity data is a known technique in the technical field, details of the calculation are omitted.

  FIG. 28 shows a method for calculating a cross-sectional shape by library matching in the second embodiment. This figure corresponds to the flowchart shown in FIG.

  In the procedure for calculating the cross-sectional shape by library matching based on the ellipso parameter, first, the stage 912 is driven to move the sample to the measurement position (S1801). Next, the reflected light from the surface of the sample 905 is detected by the spectroscopic detector 1705 while rotating the compensator rotating stage 1706 controlled by the control unit 1602 to change the angle of the compensator 1704, and spectral reflection intensity data is obtained. Obtain (S1802). Next, Δ and Ψ, which are ellipso parameters, are calculated using the spectral reflection intensity data obtained in S1802 (S1803). Next, the cross-sectional shape is calculated by library matching or model fitting using the calculated ellipso parameters (Δ and Ψ) (S1804).

  By repeating the above operation as necessary, the cross-sectional shape of the repetitive pattern at an arbitrary position on the surface of the sample 905 can be measured (S1805).

Next, a method for calculating the cross-sectional shape executed in S1804 will be described. As an example, a method by library matching will be described with reference to FIG.
In order to measure the shape by library matching, ellipso parameters (Δ and Ψ) calculated in S1803 from prepared spectral reflection intensity data are prepared (S1901), while ellipso parameter data calculated by optical simulation is stored in the library ( The data is extracted from the database (S1902), the error is calculated by comparing these data (S1903), and the minimum error determination is performed by comparing with the already calculated error (S1904). This is performed for all the data (S1905), and the ellipso parameters and the shape conditions are extracted from the stored library in association with the shape conditions when the ellipso parameters with the smallest error detected in S1904 are calculated. (S1906).

  In S1903, as a method of calculating the error between the detected ellipso parameter and the ellipso parameter calculated by the simulation drawn from the database, the equation representing the mean square error shown in (Equation 5) or (Equation 6) is similarly used. Can be considered. In this equation, as an example, a case is shown in which Δ and Ψ are normalized within the variable range and added together.

  In many cases, the ellipso parameters actually detected are not evenly spaced data depending on spectroscopic detector specifications. In that case, the wavelength of the data detected by interpolation etc. and the wavelength of the calculated data are made to correspond.

  As described above, in the library matching method, it is necessary to calculate an ellipso parameter library in advance.

Since the method for calculating the library is the same as the method described with reference to FIG. 10 in the first embodiment, the description thereof is omitted. Ellipso parameters can be calculated by using Fresnel's equation using RCWA or effective medium approximation.
By the above method, the cross-sectional shape of the fine repetitive pattern formed on the sample surface can be measured.

  According to this embodiment, it is possible to calculate model data having a cross-sectional shape that is asymmetrical from the data obtained by detecting ellipso parameters on the sample surface using a plurality of distribution functions and using fewer parameters. Therefore, it is possible to reduce the calculation time of the library while maintaining high shape measurement accuracy as compared with the case where cross-sectional model data is created by combining conventional trapezoidal patterns.

DESCRIPTION OF SYMBOLS 101 ... Cross-sectional shape of semiconductor pattern 901 ... Spectral reflectance detection optical system 902 ... Sample stage 903 ... Control unit 904 ... Arithmetic unit 905 ... Sample 906 ... Reference sample 907 .. Interface 1001 ... Light source 1002 ... Optical system 1003 ... Spectral detector 1004 ... Illumination optical system 1005 ... Half mirror or beam splitter 1006 ... Objective lens 1007 ... Imaging lens DESCRIPTION OF SYMBOLS 1008 ... Field stop 1101 ... X stage 1102 ... Y stage 1103 ... Z stage 1104 ... θ stage 1501 ... Cross sectional shape 1601 ... Spectroscopic ellipso optical system 1602 ... Control unit 1603 ... Calculation unit 1701 ... Light source 1702 ... Polarizer 1703 ... Compensator 1704 ... Analyzer 1705 ... Spectral detector 1706 ... Rotary stage 2001 ... Light emitted from the light source 2002 ... Mask 2003: Exposure optical system 2004: Resist 2005 ... Substrate 2006 ... Exposure intensity distribution 2101 ... Pattern shape 2201 ... Exposure intensity 2202 ... Asymmetric exposure intensity distribution 2301 Asymmetric patterns 2401 to 2403... Exposure intensity distribution 2404... Half-value width 2501... Exposure intensity distribution 2601... Asymmetric pattern 2602 ... resist 2603 ... substrate 2701 to 2705 ... Gaussian distribution 2706 ... Resist surface 270 ... modeling shape

Claims (12)

Irradiate the sample with a fine repeating pattern whose cross-sectional shape is asymmetrical on the surface,
The light reflected from the surface of the sample is spectrally detected, and the data relating to the spectral reflectance of the surface of the sample obtained by the spectral detection or the data relating to the ellipsometric parameters of the surface of the sample and the data stored in advance are stored. A method for obtaining a cross-sectional shape of a fine repetitive pattern formed on the surface of the sample by using the data stored in advance on the surface of the sample of the same type as the data obtained by the spectral detection Data relating to spectral reflectance or data relating to ellipso parameters of the surface of the sample, data relating to spectral reflectance of the surface of the sample of the same type as data obtained by the spectral detection, or data relating to ellipso parameters of the surface of the sample This is data obtained by modeling the cross-sectional shape of the associated minute repetitive pattern, and the data obtained by modeling the cross-sectional shape. It data is data formed by asymmetric curve represented by combining one function or multiple functions using data on ellipsometric parameters of the data or the surface of the samples for the spectral reflectance of the surface of the sample A method for measuring a cross-sectional shape of a fine pattern characterized by Data modeling the cross-sectional shape, a fine of claim 1 Symbol mounting, characterized in that the data formed by the asymmetric curve represented by combining a plurality of either Gaussian or Lorentzian distribution or SINC function Method for measuring the cross-sectional shape of a pattern. Data modeling the cross-sectional shape, for asymmetrical curve represented by a Fourier series expansion, according to claim 1 Symbol placing a fine pattern, characterized in that the data which is formed by changing the phase and amplitude Cross-sectional shape measurement method. A light irradiation system for irradiating a sample having a fine repetitive pattern with a cross-sectional shape asymmetric on the surface, and light reflected from the sample irradiated with the light by the light irradiation system is detected by spectroscopy. Spectral detection system, storage unit for storing data, data on spectral reflectance of the surface of the sample obtained by spectrally detecting the reflected light by the spectral detection system, or data on ellipso parameters on the surface of the sample And a data processing system for calculating a cross-sectional shape of a fine repetitive pattern formed on the sample surface using the data stored in the storage unit, and the data stored in the storage unit is the spectral detection data relating ellipsometric parameters of the surface of the data or the samples for spectral reflectance of the same type of the surface of the sample with data obtained by the spectrum detection in the system, spectroscopic detection Be data that models the cross-sectional shape of the fine repetitive pattern associated with the data relating to ellipsometric parameters of spectral reflectance on the data or the surface of the sample of the same type of the surface of the sample with data obtained by the spectrum detection in The data obtained by modeling the cross-sectional shape is a left-right asymmetric curve represented by combining one function or a plurality of functions using data on the spectral reflectance of the sample surface or data on the ellipsometric parameters of the sample surface. An apparatus for measuring a cross-sectional shape of a fine pattern, characterized in that the data is formed by the above method. The data obtained by modeling the cross-sectional shape stored in the storage unit is data formed by a left-right asymmetric curve expressed by combining a plurality of Gaussian distributions, Lorentz distributions, or SINC functions. 4. Symbol placement of the cross-sectional shape measuring device of a fine pattern. The data obtained by modeling the cross-sectional shape to be stored in the storage unit, according to claim 4, characterized in that the asymmetrical curve represented by a Fourier series expansion, a data formed by changing the phase and amplitude sectional shape measuring apparatus of the serial mounting of the fine pattern. Light is irradiated to a sample having a microscopic repetitive pattern whose cross-sectional shape is asymmetric on the surface, and the light reflected on the surface of the sample is spectrally detected, and spectral reflection of the surface of the sample obtained by the spectral detection is performed. A method for obtaining a cross-sectional shape of a fine repetitive pattern formed on the sample surface using data relating to a rate or data relating to an ellipso parameter of the surface of the sample and data stored in advance, The same data as the data obtained by the spectral detection and the data on the spectral reflectance of the surface of the sample of the same type as the data obtained by the spectral detection or the data on the ellipsometric parameters of the surface of the sample. the fine that associated with the data relating to the ellipsometric parameters of the data or the surface of the samples for the spectral reflectance of the surface of the type of the sample Ri returns a data sectional shape was modeled pattern, data modeling the the cross-sectional shape of the measurement object by using the data relating to ellipsometric parameters of the data or the surface of the samples for the spectral reflectance of the surface of the sample A fine pattern characterized by data formed by a left-right asymmetric curve represented by one function or a combination of functions selected or constructed based on physical phenomena and process conditions in the formation process Cross-sectional shape measurement method. The modeled data sectional shape, claim, characterized in that determining the parameter representing the distribution shape on the basis of the process conditions in the measurement target formation process to a fixed value or variable during library operation 7 The method for measuring the cross-sectional shape of the fine pattern described. 8. The method for measuring a cross-sectional shape of a fine pattern according to claim 7, wherein the data obtained by modeling the cross-sectional shape is constructed by superimposing a plurality of distribution shapes developed horizontally, vertically and obliquely. A light irradiation system for irradiating a sample having a fine repetitive pattern with a cross-sectional shape asymmetric on the surface, and light reflected from the sample irradiated with the light by the light irradiation system is detected by spectroscopy. Spectral detection system, storage unit for storing data, data on spectral reflectance of the surface of the sample obtained by spectrally detecting the reflected light by the spectral detection system, or data on ellipso parameters on the surface of the sample And a data processing system for calculating a cross-sectional shape of a fine repetitive pattern formed on the sample surface using the data stored in the storage unit, and the data stored in the storage unit is the spectral detection data relating ellipsometric parameters of the surface of the data or the samples for spectral reflectance of the same type of the surface of the sample with data obtained by the spectrum detection in the system, spectroscopic detection Be data that models the cross-sectional shape of the fine repetitive pattern associated with the data relating to ellipsometric parameters of spectral reflectance on the data or the surface of the sample of the same type of the surface of the sample with data obtained by the spectrum detection in The data obtained by modeling the cross-sectional shape is a distribution shape based on physical phenomena and process conditions in the forming process of a measurement object using data on spectral reflectance of the surface of the sample or data on ellipso parameters on the surface of the sample. An apparatus for measuring a cross-sectional shape of a fine pattern, which is data formed by a left-right asymmetric curve expressed by combining one function or a plurality of functions selected or constructed. The data obtained by modeling the cross-sectional shape stored in the storage unit determines whether to change the parameter expressing the distribution shape based on the process conditions in the formation process of the measurement target or to use a fixed value during the library calculation. 11. The apparatus for measuring a cross-sectional shape of a fine pattern according to claim 10 . 11. The cross-section of a fine pattern according to claim 10, wherein the data obtained by modeling the cross-sectional shape stored in the storage unit is constructed by superimposing a plurality of distribution shapes developed horizontally, vertically, and obliquely. Shape measuring device.

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