RU2657000C1 - Method of quantitative three-dimensional reconstruction of a sample surface in a scanning- electron microscope - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: invention relates to scanning electron microscopy. Invention uses the principle of photogrammetric processing of images obtained in a scanning electron microscope at various inclination angles the test sample. On the surface of the test sample, spherical structural elements generating a contrast in the image are preliminarily formed, the results of photogrammetric image processing are corrected for the values of the individual height of the structural elements determined from the images.

EFFECT: technical result is increased three-dimensional reconstruction accuracy.

1 cl, 2 dwg

Description

The invention relates to the field of scanning electron microscopy and can be used to control the dimensional parameters of products of micro- and nanoelectronics, microsystem technology, in materials science.

A scanning electron microscope (SEM), which has a high spatial resolution and a large depth of focus, is the most commonly used device for obtaining images of the surfaces of micro- and nano-objects. The ease of use of the SEM is explained by the high speed of image acquisition and a wide range of magnifications.

However, SEM images themselves are two-dimensional and provide only qualitative information about the Z coordinate, since the video signal level for each image point is a complex function of the compositional and topographic features of the sample surface, as well as the collection coefficient of secondary electrons. Nevertheless, in practice it is often necessary to carry out three-dimensional reconstruction of objects, including silicon, with a high aspect ratio, which include many products of micro- and nanoelectronics and microsystem technology. Moreover, the restoration of the three-dimensional profile of these objects by traditional methods, such as atomic force microscopy, can be difficult.

The known method [1] for quantitative three-dimensional reconstruction of objects from stereo images obtained in a scanning electron microscope when the table of objects is tilted at angles ± Δϕ relative to its horizontal position. This method uses the principles of photogrammetric image processing, determining the height difference between two points A and B (point B is at the origin) on the surface of the object based on mathematical calculations by the formula (provided that the tilt of the object’s table is carried out around the X axis)

where indices 1 and 2 correspond respectively to the Y-coordinates of point A in the 1st image (when the object is tilted by an angle -Δϕ) and the 2nd image (when the object is tilted by an angle + Δϕ), the value of _1- y ₂ is the change the distance along the Y axis between two points A and B (the so-called parallax) when the object is tilted at an angle of 2Δϕ around the X axis.

The process of photogrammetric processing of stereo images (obtained when the object is tilted at angles + Δϕ and -Δϕ) includes several stages:

- finding an array of contrasting elements for each of the stereo images;

- definition of an array of pairs of homologous points, where inside each pair, homologous points representing contrasting elements from different images correspond to one location on the surface of the object;

- determination of the three-dimensional coordinates of the surface points of the investigated object in accordance with the formula (1).

This method has the following disadvantages that affect the accuracy of the results of quantitative three-dimensional reconstruction:

- it is not always possible to isolate on the surface of the object under study a sufficient number of contrasting elements that can be uniquely identified on each stereo image, while the blurriness of these points or their insufficient contrast against the background of the noise of the video signal (causing the error in identifying homological points) will degrade the accuracy of the results of quantitative three-dimensional reconstruction;

- image distortion in a scanning electron microscope, leading to a distortion of two-dimensional coordinates, affects the error of the results of three-dimensional reconstruction.

In the patent [2], a method is described for reconstructing the surface of an object under study in a SEM, which is realized with a stationary table of objects by changing the angle at which the electron probe falls on the object for three or more values of the specified angle. This proposal can be implemented by introducing additional deflecting elements into the electron-optical column, forming a double deflection of the electron beam, while the place of incidence of the electron probe on the sample should remain unchanged. Registration of an informative signal from electrons emitted by the test sample as a result of exposure to the sample by a primary electron probe is carried out by a set of electron detectors located in different angular positions relative to the electron-optical axis. Although this improvement accelerates the process of three-dimensional reconstruction of the surface of the object under study, the spatial resolution of the SEM is deteriorated due to the introduction of additional deflecting elements into the SEM column, which means that the accuracy of the results of three-dimensional reconstruction is reduced.

The disadvantages inherent in the method of three-dimensional reconstruction of the surface of an object in the SEM described in [1] are partially solved in the patent [3], which can be selected as a prototype. This patent describes a method of three-dimensional reconstruction of a surface in a scanning electron microscope, which includes recording the signal of the electrons emitted by the sample when the electron beam is scanned by the test object for its two angular positions. To facilitate the stereo-alignment of SEM images obtained at two angles of inclination of the sample, reference markers are formed on the surface of the test sample, and the need for their formation is evaluated by a computer program after preliminary scanning of the sample in the SEM and determining the presence of the required number of characteristic details in the image. In case of detection of sample areas where there are no characteristic image details necessary for performing the stereo image alignment procedure, reference markers are formed in such areas.

In addition, to eliminate the errors of three-dimensional reconstruction associated with image distortion, the patent [3] proposes to use reference plates on which reference markers are formed at given points. SEM images of reference plates at two tilt values of the SEM objects table allow you to determine the correction factors associated with image distortion. The resulting correction coefficients are used in the future to convert images from the object under study at two tilt angles to compensate for image distortion.

However, in practice, very often the main contribution to the error of three-dimensional reconstruction is not the distortion of the image, but the procedure of combining characteristic points on stereo images [4]. For example, for a sample, the surface portion of which has a smoothly varying relief, the image contrast will be absent in this region, since the specified contrast will not exceed the noise value of the video path and the combination of the characteristic points in stereo images is impossible due to their absence in the images. In the patent [3], it is proposed to form reference markers on the surface of the test sample, which will provide contrast in the image at the points where the markers are located. Reference markers must have finite dimensions in order to provide contrast in the image, therefore, reconstruction of the surface relief takes into account the height of the markers themselves.

In the described invention [3] it is proposed that the reference markers may be conical contamination formations that occur when the electron probe is fixed at a given point for a certain period of time. The growth mechanism of such contamination formations is due to [5]:

- polymerization on the surface of the sample under the influence of an electron beam of hydrocarbon compounds, which are part of the residual atmosphere of the chamber of the SEM samples;

- surface diffusion and polymerization under an electron beam of hydrocarbon compounds adsorbed on the surface of the sample.

From the available literature data on the growth rate of cone-shaped contamination formations [6] it is known that the time required for the formation of one specified contamination formation is approximately 1 minute. Therefore, the formation of reference markers in a quantity sufficient for constructing a three-dimensional map of the surface relief is problematic. In addition, on inclined sections of the surface relief, such a reference marker will have different sizes compared to flat sections of the surface due to an increase in the yield of secondary electrons from the inclined surface. With a change in the composition of the sample on individual surface areas, the growth conditions of contamination formations will also change. The uneven overall dimensions of the reference markers creates an additional systematic error of three-dimensional reconstruction.

The objective of the invention is to improve the accuracy of the results of quantitative three-dimensional reconstruction of the surface of the sample in a scanning electron microscope. This problem is solved by forming structural elements on the surface of the test sample that create contrast on SEM images and taking into account the sizes of these structural elements to determine the true surface shape of the test sample.

The problem is solved using the method of three-dimensional reconstruction of the surface of the sample, which includes mounting the sample on a SEM stage with the possibility of tilting it into two angular positions relative to the electron-optical axis, irradiating the sample with a focused beam of accelerated electrons, detecting the signal of secondary electrons emitted by the sample, obtaining two images when scanning an electron beam of a sample in two angular positions of the stage.

диаметра D структурного элемента, который определяют по изображению для каждого структурного элемента и по результатам предварительной трехмерной реконструкции определяют угол локального наклона поверхности α относительно горизонтальной плоскости в месте расположения каждого структурного элемента;A feature of the proposed method is that pre-formed on the sample are structural elements of a spherical shape that create contrast on SEM images, three-dimensional reconstruction is carried out in 2 stages by photogrammetric processing of the obtained images using the coordinates of the centers of structural elements in the images, and at the first stage, preliminary three-dimensional reconstruction, for which the results of photogrammetric processing in the form of a Z-coordinate for the center of each structural element are reduced by a parameter equal to

the diameter D of the structural element, which is determined by the image for each structural element and the results of preliminary three-dimensional reconstruction determine the angle of the local inclination of the surface α relative to the horizontal plane at the location of each structural element;

at the second stage of three-dimensional reconstruction, the results of photogrammetric processing in the form of the Z-coordinate for the center of each structural element are reduced by a parameter equal to D / (2⋅cosα).

An implementation option of the proposed method may be the use of spherical elements made of tin as structural elements on the surface of the test sample.

The proposed method is illustrated by micrographs and drawings.

In FIG. Figure 1 shows an image of a structural element of a spherical shape on a surface section of a test sample having a local slope α relative to a horizontal plane.

, соответствующие краям сферического структурного элемента на РЭМ-изображении - точки С и D. На фиг. 2 приведена микрофотография структурных элементов сферической формы из олова на графитовой подложке.Shown electron beam positions

corresponding to the edges of the spherical structural element in the SEM image — points C and D. In FIG. Figure 2 shows a micrograph of the structural elements of a spherical shape made of tin on a graphite substrate.

, где D=CD - диаметр сферического элемента.From FIG. 1 it follows that as a result of determining the edges of the spherical element - points C and D, the center of the spherical element, defined in the image plane - point O will have a height relative to the surface of the sample equal to the length of the segment OA. From the geometric constructions of FIG. 1 it follows that

where D = CD is the diameter of the spherical element.

. Данная коррекция заключается в уменьшении значения Z-координаты (при условии, что ось Z направлена вверх) на величину

. Поскольку в общем случае в каждой точке значение угла наклона α неизвестно, на первом этапе производится предварительная трехмерная реконструкция, где коррекция результатов заключается в уменьшении значения Z-координаты на величину D/2, полагая что угол α мал и cosα≈1.Therefore, when using for the three-dimensional reconstruction of the coordinates of the centers of spherical elements on SEM images, the results of this reconstruction in the form of the Z-coordinates of points corresponding to the centers of the spherical elements should be adjusted by the value

. This correction consists in decreasing the value of the Z coordinate (provided that the Z axis is directed upwards) by

. Since in the general case at each point the value of the angle of inclination α is unknown, at the first stage a preliminary three-dimensional reconstruction is performed, where the correction of the results consists in decreasing the Z-coordinate value by D / 2, assuming that the angle α is small and cosα≈1.

As a result of preliminary three-dimensional reconstruction, a set of X _i Y _i Z _{i of} approximate coordinates of the surface points of the test sample at the locations of the structural elements is obtained. The error in determining the Z coordinate for the inclined sections of the test sample at the first stage is due to the fact that cosα = 1 is assumed in the calculation of the correction factor.

The local slope α of the sample surface at the point X _i Y _i Z _i can be determined using additional coordinates of the two nearest points X _i-1 Y _i-1 Z _i-1 , and X _{i + 1} Y _{i + 1} Z _{i + 1} such that the indicated 3 points do not lie on one straight line. Using formulas of analytic geometry, for the local slope of α,

где

Where

Literature

1. Piazzesi G. Photogrammetry with the scanning electron microscope // J. Phys. E: Sci. Instrum. 1973. V. 6. No. 4. PP 392-396.

2. G.F. Lorusso, R.A. Watts, A.J. Gubbens, L.S. Hordon. SEM Profile and Surface Reconstruction using multiple data sets. US Patent No. US 6,930,308 B1.

3. N. Kochi, H. Koike. Electron beam device and method for stereoscopic measurements. US Patent No. US 6852974 B2.

4. Kuzin A.Yu., Vasiliev A.L., Mityukhlyaev V.B., Mikhutkin A.A., Todua P.A., Filippov M.N. Analysis of factors affecting the error of three-dimensional reconstruction of the surface of objects with a submicron relief, according to stereo images obtained in SEM // Measuring technique. 2016. No3, p. 20-23.

5. Zhdanov G.S. On the rate of hydrocarbon pollution of objects in microprobe systems // Surface. 1983, No. 1. S. 65-72.

6. N. Yoshimura. Vacuum Technology. Practice for Scientific Instruments. Springer-Verlag Berlin Heidelberg. 2008. P.p. 175-203.

Claims (4)

1. A method for quantitative three-dimensional reconstruction of the surface of a sample in a scanning electron microscope (SEM), including mounting the sample on a SEM stage with the possibility of tilting it into two angular positions relative to the electron-optical axis, irradiating the sample with a focused beam of accelerated electrons, detecting the signal of secondary electrons emitted a sample, obtaining two images when scanning an electron beam of a sample in two angular positions of the stage, characterized in that in order to increase the accuracy of three-dimensional reconstruction, spherical structural elements are formed on the sample that create contrast on SEM images, three-dimensional reconstruction is carried out in 2 stages by photogrammetric processing of the obtained images using the coordinates of the centers of structural elements in the images, and the first stage is a preliminary three-dimensional reconstruction, for which the results of photogrammetric processing in the form of Z-coordinates for prices traces of each structural element are reduced by a parameter equal to

the diameter D of the structural element, which is determined by the image for each structural element and the results of preliminary three-dimensional reconstruction determine the angle of the local inclination of the surface α relative to the horizontal plane at the location of each structural element; at the second stage of three-dimensional reconstruction, the results of photogrammetric processing in the form of the Z-coordinate for the center of each structural element are reduced by a parameter equal to D / (2⋅cosα). 2. The method according to p. 1, characterized in that as structural elements on the surface of the test sample form spherical structural elements of tin.

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