JP2023142687A - Polarizing microscope device and in-visual field correction analysis method - Google Patents

Abstract

To provide a polarizing microscope device and an in-visual field correction analysis method which can highly accurately measure a magnetization characteristic in a visual field.SOLUTION: A polarizing microscope device 1 according to an embodiment comprises: a light source 10 which generates illumination light 21; a polarizer 12 on which the illumination light 21 is incident and which transmits the illumination light 21 including linear polarization in a first polarization direction; an objective lens 14 which illuminates a sample 20 with the illumination light 21 including the linear polarization and transmits reflection light 22 obtained with reflection of the illumination light 21 on the sample 20; an analyzer 17 which transmits a component of the linear polarization in the second polarization direction in the reflection light 22; an image acquisition unit 19 which acquires an image of the reflection light 22; a magnet 16 which generates an external magnetic field to be applied to the sample 20; and an image processing unit 30 which processes the acquired image. The image processing unit 30 calculates a device constant number including a polarization rotation angle distribution for each ROI in a visual field and a square distribution of an ellipticity, and calculates a rotation angle of Kerr rotation for each ROI from analysis using the device constant number and a hysteresis loop.SELECTED DRAWING: Figure 6

Description

The present invention relates to a polarizing microscope device and an intra-field correction analysis method.

Kerr effect microscopes and magnetic domain observation microscopes are based on classical polarizing microscopes, and have already been commercialized by multiple manufacturers. This is described in, for example, Non-Patent Document 1.

US Patent No. 4,410,277 Japanese Patent Application Publication No. 2009-042040

Meguro, “Development of a Kerr effect microscope capable of detecting local magnetization and its application to spatial magnetic field detection”, Microscopy, Vol52, No3 (2017). P. Wolniansky, et.al, "Magneto-optical measurements of hysteresis loop and anisotropy energy constants on amorphous TbxFe1-x alloys", Applied Physics 60, 346 (1986).

The Kerr effect microscope uses laser light to enter a sample containing a magnetic material such as a magnetic thin film while sweeping an external magnetic field, and measures the amount of change in the polarization component of the reflected light. A hysteresis loop can be obtained. On the other hand, a magnetic domain observation microscope applies an external magnetic field to a sample containing a magnetic material such as a magnetic thin film, and converts the light from an incoherent light source into polarized light using a polarizer.The polarized light component of the reflected light when it enters the sample This method records changes in the brightness of the image sensor as changes in the brightness of the image sensor, making it possible to record magnetic domain patterns within the field of view.

Even with a magnetic domain observation microscope, you can obtain a hysteresis loop for each pixel by recording the brightness for each pixel while sweeping an external magnetic field, but with a magnetic domain observation microscope, variations in polarization characteristics within the field of view are sensitive to polarization changes occurring in the sample. big. Therefore, it is difficult to quantitatively evaluate the hysteresis loop within the field of view, and the magnetization characteristics cannot be measured with high precision.

The present invention has been made in view of the above problems, and provides a polarizing microscope device and an intra-field correction analysis method that can measure magnetic properties with high precision.

A polarizing microscope device according to the present invention includes: a light source that generates illumination light; a polarizer that receives the illumination light generated by the light source and transmits the illumination light that includes linearly polarized light in a first polarization direction; an objective lens that illuminates the sample with the illumination light including the linearly polarized light, and that transmits reflected light that is reflected by the illumination light on the sample; and an objective lens that transmits the linearly polarized component of the reflected light in a second polarization direction. The image processing unit includes an analyzer, an image acquisition unit that acquires an image of the reflected light, a magnet that generates an external magnetic field to be applied to the sample, and an image processing unit that processes the acquired image. , while rotating the angle between the first polarization direction and the second polarization direction within a predetermined range in predetermined increments, the non-magnetic sample or the sample containing a magnetic material is subjected to a magnetic field. The polarization rotation for each region of interest within a field of view including a plurality of regions of interest is obtained from the plurality of images obtained by illuminating the sample with the illumination light, which can be regarded as a non-magnetic mirror surface when used in a state where no voltage is applied. When calculating device constants including the angular distribution and the square distribution of ellipticity due to ovalization, and setting the angle between the first polarization direction and the second polarization direction as the first angle, A hysteresis loop of the brightness value for each region of interest is determined from a plurality of images acquired while illuminating the magnetic body part of the sample containing the magnetic body with the illumination light and sweeping the external magnetic field. and when the angle between the first polarization direction and the second polarization direction is set to a second angle, the illumination is applied to the portion of the magnetic material of the sample containing the magnetic material. A hysteresis loop of the luminance value for each region of interest is acquired from a plurality of images acquired while illuminating the light and sweeping the external magnetic field, and the device constant, the hysteresis loop at the first angle, and the first From the analysis using the hysteresis loop at two angles, the rotation angle of Kerr rotation occurring in the sample is calculated for each region of interest.

In the polarizing microscope device, the analyzer may be rotated in the predetermined range with respect to the polarizer based on a crossed Nicol arrangement.

In the polarizing microscope device, the image processing section may calculate the device constant including the angular distribution and the square distribution for each region of interest using Malus' law.

In the polarizing microscope device, the device constant may include a brightness distribution, and the image processing unit may calculate the device constant including the brightness distribution for each region of interest.

In the polarizing microscope device, the image processing unit fits the hysteresis loop at the first angle and the hysteresis loop at the second angle to an empirical approximation function, thereby determining the magnetization contrast for each region of interest; Coercive force and slope may also be calculated. Magnetization contrast represents the brightness contrast defined by the maximum and minimum brightness when the brightness is recorded while sweeping an external magnetic field across the sample.

In the polarizing microscope device, the image processing unit may rotate the rotation for each region of interest based on the first angle, the second angle, the magnetization contrast at the first angle, and the magnetization contrast at the second angle. You may also calculate the angle.

The intra-field correction analysis method according to the present invention includes a light source that generates illumination light, and a polarizer that receives the illumination light generated by the light source and that transmits the illumination light that includes linearly polarized light in a first polarization direction. and an objective lens that illuminates the sample with the illumination light including the linearly polarized light and transmits reflected light reflected by the illumination light on the sample, and a linearly polarized component of the reflected light in a second polarization direction. A polarizing microscope device comprising: an analyzer for transmitting light; an image acquisition section for acquiring an image of the reflected light; a magnet for generating an external magnetic field to be applied to the sample; and an image processing section for processing the acquired image. An in-field correction analysis method using the non-magnetic sample while rotating the angle formed by the first polarization direction and the second polarization direction in a predetermined step within a predetermined range. , or a plurality of regions of interest are obtained from the plurality of images obtained by illuminating the sample with the illumination light on a sample that can be regarded as a non-magnetic mirror surface by using the sample containing a magnetic substance without applying a magnetic field. a first step of calculating device constants including the polarization rotation angle distribution for each of the regions of interest in the field of view and the square distribution of ellipticity due to ovalization; and the first polarization direction and the second polarization direction. When the angle formed by the magnetic substance is set to a first angle, a plurality of images obtained while illuminating the illumination light and sweeping the external magnetic field are applied to a portion of the magnetic substance of the sample containing the magnetic substance. A hysteresis loop of the luminance value for each region of interest is obtained from the image, and when the angle formed by the first polarization direction and the second polarization direction is set to a second angle, the magnetic material is A step of illuminating the magnetic material portion of the sample with the illumination light and acquiring a hysteresis loop of the brightness value for each region of interest from a plurality of images acquired while sweeping the external magnetic field. and a third step of calculating a rotation angle of Kerr rotation occurring in the sample for each region of interest from an analysis using the device constant, the hysteresis loop at the first angle, and the hysteresis loop at the second angle. and.

In the intra-field correction analysis method, in the first step, the analyzer may rotate the predetermined range with respect to the polarizer based on a crossed Nicol arrangement.

In the intra-field of view correction analysis method, in the first step, the device constant including the angular distribution and the square distribution for each region of interest may be calculated using Malus' law.

In the intra-visual field correction analysis method, in the first step, the device constant may include a brightness distribution, and the device constant including the brightness distribution for each region of interest may be calculated.

In the intra-field of view correction analysis method, in the second step, the hysteresis loop at the first angle and the hysteresis loop at the second angle are fitted to an empirical approximation function to determine the contrast of each region of interest. , coercive force and slope may be calculated.

In the intra-field correction analysis method, in the third step, the first angle, the second angle, the magnetization contrast at the first angle, and the magnetization contrast at the second angle are used for each region of interest. The rotation angle may be calculated.

The present invention provides a polarizing microscope device and an intra-field correction analysis method that can measure magnetization characteristics within a field of view with high precision.

FIG. 2 is a configuration diagram illustrating a polarizing microscope device such as a magnetic domain microscope according to a comparative example. FIG. 2 is a schematic diagram illustrating the Kerr effect in a polarizing microscope device such as a magnetic domain microscope according to a comparative example. It is a graph illustrating hysteresis loops in five regions of interest within the field of view measured by a polarizing microscope device such as a magnetic domain microscope according to a comparative example, where the horizontal axis represents the external magnetic field and the vertical axis represents the brightness value. Hysteresis loops in five ROIs in the field of view measured with a polarizing microscope device such as a magnetic domain microscope according to a comparative example are normalized by the average of the brightness values of each ROI, and further normalized by the average in the ROI at the center of the field of view. This is a graph illustrating hysteresis loops in five ROIs within the field of view measured with a spot measuring device according to a comparative example, where the horizontal axis represents the external magnetic field and the vertical axis is normalized by the average value in the ROI at the center of the field of view. Indicates the rotation angle of Kerr rotation of physical quantity. 1 is a configuration diagram illustrating a polarizing microscope device according to Embodiment 1. FIG. 3 is a flowchart diagram illustrating an intra-field correction analysis method according to the first embodiment; FIG. 3 is a flowchart diagram illustrating an intra-field correction analysis method according to the first embodiment; FIG. 3 is a flowchart diagram illustrating an intra-field correction analysis method according to the first embodiment; FIG. 1 is a diagram illustrating an image acquired by the polarizing microscope device according to Embodiment 1. FIG. FIG. 3 is a diagram illustrating converting a plurality of images acquired by the polarizing microscope device according to the first embodiment into analyzer transmission angle data for each ROI. It is a graph illustrating analyzer transmission angle data acquired by the polarizing microscope device according to Embodiment 1, in which the horizontal axis indicates the angle of the polarization direction of the analyzer, and the vertical axis indicates the brightness value. (a) to (c) show the distribution of brightness unevenness a(x, y), the distribution of polarization rotation angle Θ ₀ (x, y), and the ellipticity η in the polarizing microscope device 1 according to the first embodiment. FIG. 2 is a diagram illustrating a distribution of squared η ² (x, y). (a) is a diagram illustrating an image including a plurality of ROIs acquired by the polarizing microscope device according to Embodiment 1, and (b) is a diagram illustrating each ROI from the image acquired by the polarizing microscope device according to Embodiment 1. It is a graph illustrating an extracted hysteresis loop, in which the horizontal axis represents an external magnetic field, and the vertical axis represents a brightness value. It is a graph illustrating a hysteresis loop and a fitting function acquired by the polarizing microscope device according to Embodiment 1, in which the horizontal axis represents an external magnetic field, and the vertical axis represents a brightness value. 3 is a diagram illustrating a mathematical formula used in the intra-field correction analysis method according to the first embodiment; FIG. 2 is a graph illustrating definitions of contrast C(x, y), coercive force Hc(x, y), and slope (x, y) acquired by the polarizing microscope device according to Embodiment 1. FIG. 2 is a graph illustrating definitions of contrast C(x, y), coercive force Hc(x, y), and slope (x, y) acquired by the polarizing microscope device according to Embodiment 1. FIG. FIG. 2 is a diagram illustrating rotation and ellipticalization of the plane of polarization when no external magnetic field is applied in the polarizing microscope device according to the first embodiment. FIG. 7 is a diagram illustrating an optical path of reflected light reflected by a sample until it reaches an imaging surface of an image acquisition unit in a state where there is no beam splitter. FIG. 7 is a diagram illustrating an optical path of reflected light reflected by a sample until it reaches an imaging surface of an image acquisition unit in a state where a beam splitter is present. FIG. 3 is a diagram illustrating rotation and ellipticalization of the plane of polarization when an external magnetic field is applied in the polarizing microscope device according to the first embodiment. (a) shows the height difference range of the hysteresis loop when the angle of the polarization direction of the analyzer is set to +4 degrees, normalized to the gray level at the center of the visual field, and (b) shows the difference range of the hysteresis loop when the angle of the polarization direction of the analyzer is set to +4 degrees. The contrast is simply divided by the average brightness value and normalized based on the value at the center of the visual field, and (c) illustrates the distribution of magnetization contrast of the sample obtained by the polarizing microscope device according to Embodiment 1. (d) is a diagram illustrating the distribution of magnetization contrast acquired by the spot measuring device. (a) to (c) are diagrams illustrating the results of quantitative analysis of the polarizing microscope device 1 according to the first embodiment, and (d) to (f) are diagrams illustrating the results of spot measurement. 2 is a diagram illustrating features of a polarizing microscope device and an intra-field correction analysis method according to Embodiment 1. FIG.

For clarity of explanation, the following description and drawings are omitted and simplified as appropriate. Further, in each drawing, the same elements are denoted by the same reference numerals, and redundant explanation will be omitted as necessary.

(Comparative example)
Before explaining the polarizing microscope device according to the first embodiment, a polarizing microscope according to a comparative example and its problems will be explained. This makes the polarizing microscope of this embodiment more clear. Note that the configuration and problems of the comparative example are also included in the scope of the technical idea of the embodiment.

FIG. 1 is a configuration diagram illustrating a polarizing microscope device such as a magnetic domain microscope according to a comparative example. As shown in FIG. 1, the polarizing microscope device 101 according to the comparative example includes a light source 10, a lens 11, a polarizer 12, a beam splitter 13, an objective lens 14, It includes a sample stage 15, a magnet 16, an analyzer 17, an imaging lens 18, and an image acquisition unit 19. A sample 20 is placed on the sample stage 15 .

Here, for convenience of explanation of the polarizing microscope device 101, an XYZ orthogonal coordinate axis system will be introduced. For example, the direction perpendicular to the top surface of the sample stage 15 is the Z-axis direction, and the plane parallel to the top surface of the sample stage 15 is the XY plane. Each configuration will be explained below.

Light source 10 generates illumination light 21 . The light source 10 is, for example, a halogen lamp, a white LED (Light Emitting Diode), or the like. The illumination light 21 may be white light. The light source 10 emits the generated illumination light 21 to the polarizer 12 . A lens 11 may be placed between the light source 10 and the polarizer 12. Illumination light 21 converted into parallel light by lens 11 enters polarizer 12 .

The polarizer 12 is placed at or near the illumination pupil 23 of the illumination light 21 . Illumination light 21 generated by the light source 10 is incident on the polarizer 12 . The polarizer 12 converts the incident illumination light 21 into illumination light 21 containing linearly polarized light. For example, the polarizer 12 transmits illumination light containing linearly polarized light in a first polarization direction. For example, the first polarization direction is the Z-axis direction. In this case, the polarizer 12 converts the illumination light 21 to include linearly polarized light in the Z-axis direction. That is, the transmission axis of the polarizer 12 is in the Z-axis direction. Illumination light 21 converted by polarizer 12 to include linearly polarized light enters beam splitter 13 .

The beam splitter 13 reflects a part of the incident illumination light 21 toward the objective lens 14 . The illumination light 21 reflected by the beam splitter 13 includes, for example, linearly polarized light in the X-axis direction. Objective lens 14 is arranged between beam splitter 13 and sample 20. It is arranged at or near the pupil plane 24 of the objective lens 14 . The objective lens 14 focuses the illumination light 21 reflected by the beam splitter 13 onto the sample. The objective lens 14 illuminates the sample 20 with illumination light 21 containing linearly polarized light. Incidentally, the magnetic thin film sample in the present invention is a non-patterned thin film sample or an island pattern of a sufficiently large size (for example, several 100 um in diameter).

The sample 20 includes a magnetic material such as a magnetic thin film. The sample 20 may be, for example, a magnetic thin film formed on a wafer. Further, the sample 20 may be a magnetic thin film used in MRAM (Magnetoresistive Random Access Memory). For example, an external magnetic field in the Z-axis direction may be applied to the magnetic body of the sample 20 placed on the sample stage 15. When the direction of the external magnetic field changes upward or downward, the magnetization direction of the magnetic body may change upward or downward. Note that the sample 20 in the calibration described below may be a non-magnetic sample 20.

Magnet 16 is placed between sample 20 and objective lens 14 . The magnet 16 is, for example, an electromagnet that can modulate the strength and direction of the magnetic field on the sample. Note that the magnet 16 may be a permanent magnet. Magnet 16 generates an external magnetic field that is applied to sample 20. Thereby, the magnet 16 applies an external magnetic field to the sample 20. For example, when inspecting a free layer made of a perpendicular magnetic anisotropic material of an MRAM, a Polar Kerr effect (referred to as a polar Kerr effect) is detected. Therefore, the magnet 16 applies a magnetic field perpendicular to the surface of the sample 20. When the magnet 16 is an electromagnet, an external magnetic field in a predetermined range from the +Z direction to the -Z direction is applied to the sample 20 by controlling the value and direction of the current flowing through the electromagnet.

Furthermore, in order to detect the polar Kerr effect, the incident light that enters the sample 20 needs to be linearly polarized light that is perpendicular to the surface of the sample 20 and whose electric field oscillates in the XY plane. The polarization state of the sample 20 changes slightly due to the Kerr effect depending on the magnetic field strength (H) of the external magnetic field. The Kerr effect includes rotation of the polarization axis (called Kerr rotation) and Kerr ellipticity.

FIG. 2 is a schematic diagram illustrating the Kerr effect in a polarizing microscope device such as a magnetic domain microscope according to a comparative example. As shown in FIG. 2, the Kerr effect includes a rotation angle ΔΘ of rotation of the polarization axis (also referred to as a rotation angle ΔΘ of rotation of the polarization direction) and ovalization including a change in ellipticity Δη. The change in ellipticity Δη is, for example, tan ⁻¹ (OB/OA). Here, OA is the minor axis and OB is the major axis. The reflected light 22 reflected by the sample 20 has its polarization state modulated by the Kerr effect caused by the sample 20.

Returning to FIG. 1, the reflected light 22 reflected by the sample 20 enters the objective lens 14. The objective lens 14 transmits reflected light 22 from the illumination light 21 reflected by the sample 20. The reflected light 22 passes through the objective lens 14 and the beam splitter 13 and enters the analyzer 17 .

The analyzer 17 is arranged between the beam splitter 13 and the image acquisition section 19. The analyzer 17 transmits the linearly polarized component of the reflected light 22 in the second polarization direction. The second direction is, for example, the Y-axis direction. In this case, the analyzer 17 converts the reflected light 22 to include linearly polarized light in the Y-axis direction. That is, the transmission axis of the analyzer 17 is in the Y-axis direction. The direction of the linearly polarized light transmitted by the analyzer 17 (transmission axis) may be arranged to be orthogonal to the direction of the linearly polarized light transmitted by the polarizer 12 (transmission axis). For example, the direction of the linearly polarized light transmitted by the polarizer 12 may be the X-axis direction, and the direction of the linearly polarized light transmitted by the analyzer 17 may be the Y-axis direction. An arrangement in which the transmission axis of the analyzer 17 is orthogonal to the transmission axis of the polarizer 12 in this manner is called a cross Nicole arrangement. The crossed Nicol arrangement can detect changes in polarized light including linearly polarized light as changes in brightness with high sensitivity. The reflected light 22 containing polarized light slightly rotated and ovalized by the sample 20 transmits the square intensity of the amplitude projected onto the transmission axis of the analyzer 17. The reflected light 22 that has passed through the analyzer 17 enters the image acquisition unit 19 via the imaging lens 18, for example.

The image acquisition unit 19 detects a change in the polarization component of the reflected light 22 as a change in intensity. Thereby, the image acquisition unit 19 acquires an image of the reflected light 22. For example, the image acquisition unit 19 acquires an image within the field of view. The image acquisition unit 19 is, for example, a camera. The image acquisition unit 19 may be, for example, an image sensor including a PD (Photodiode) array. Note that the image acquisition unit 19 is not limited to a camera or an image sensor as long as it can acquire an image. The imaging surface 26 of the image acquisition unit 19 has an image conjugate relationship with the measurement surface 25 of the sample 20.

Here, the rotation angle ΔΘ of the rotation of the polarization direction that occurs in the sample 20 for MRAM described above is typically 0.1 degree or less. Further, the change in ellipticity Δη is also a slight change on the same level as the rotation angle ΔΘ. The ellipticity η is an ellipticity angle (angle amount) defined by the flatness of an ellipse in terms of arctan. A magnetic domain microscope is a microscope that focuses on magnetic domains (Pattern) within a field of view. Therefore, with a magnetic domain microscope, it is sufficient to be able to visually recognize the magnetic domains within the field of view, and the focus is not on the quantitative values of the rotation angle ΔΘ and the change in ellipticity Δη. Furthermore, the magnetic domain microscope does not focus on quantitative analysis errors in visibility (pattern contrast) between locations within the field of view.

As shown in the upper right of FIG. 1, in the case of MRAM sample 20, the rotation angle ΔΘ and the change in ellipticity Δη are more than an order of magnitude smaller than the errors caused by the device (Tool), and are due to the Kerr effect generated in the sample. This is because it is difficult to detect. On the other hand, in the case of a normal magnetic sample, the Kerr effect generated in the sample is larger than the error caused by the device (tool), so the Kerr effect can be detected.

First, in the following description, spot measurement using a laser beam, which is a reference device, will be explained. This is also a well-known device and there are many products on the market as well. Hereinafter, a device that performs spot measurement will be referred to as a spot measuring device.

The spot measuring device measures by differential polarization method. A spot measuring instrument makes a laser beam containing linearly polarized light enter a sample, and sweeps a magnetic field applied to the sample. Then, while sweeping the magnetic field, the spot measuring device splits the reflected light, including the polarized light modulated by the sample, into s-polarized light and p-polarized light using a polarization splitting prism. Thereby, the rotation angle in the Kerr rotation generated in the sample is measured by lock-in difference processing by the two photo detectors of the spot measuring instrument. Therefore, a hysteresis loop can be obtained by plotting the magnetic field on the horizontal axis and the rotation angle on the vertical axis. Generally speaking, this is referred to as a MOKE device (Magneto-optical Kerr Effect) or a Kerr effect measuring device. Since the obtained hysteresis loop measures a physical quantity, it is possible to evaluate the quantitative characteristics of the magnetic thin film. In addition, since this method changes the evaluation position while moving the sample, only the center of the optical system is used, and all reflected light flux is detected by a photodetector, the evaluation position does not include equipment errors. .

By the way, in the above-described magnetic domain microscope, when an image is acquired while sweeping an external magnetic field, a hysteresis loop can be obtained by plotting the external magnetic field on the horizontal axis and the brightness value on the vertical axis. The hysteresis loop obtained in this manner roughly correlates with the hysteresis loop in spot measurement using laser light. A magnetic domain microscope can also provide a hysteresis loop as one function. However, the ability to obtain a hysteresis loop in a magnetic domain microscope is only a guideline. For example, the inventor discovered that in a magnetic domain microscope, hysteresis loops obtained at a plurality of different measurement coordinates within the field of view have a large difference (error) between the measurement coordinates. This will be explained using FIG. 3 below.

FIG. 3 is a graph illustrating hysteresis loops in five regions of interest (hereinafter referred to as ROI) within a field of view measured by a polarizing microscope device such as a magnetic domain microscope according to a comparative example, and the horizontal axis is , indicates the external magnetic field, and the vertical axis indicates the brightness value. In FIG. 3, the five ROIs include a visual field center CE, an upper right visual field UR, an upper left visual field UL, a lower right visual field LR, and a lower left visual field LL within the visual field.

Figure 4 shows the hysteresis loops in five ROIs within the field of view measured with a polarizing microscope device such as a magnetic domain microscope according to a comparative example, normalized by the average of the brightness values of each ROI, and further normalized by the average in the ROI at the center of the field of view CE. This is what I did. FIG. 4 shows the values after normalization in a table. That is, it shows the difference between the maximum and minimum brightness values in each ROI, and the ratio of the average brightness value of each ROI to the visual field center CE.

FIG. 5 is a graph illustrating hysteresis loops in five ROIs within the field of view measured with a spot measuring device according to a comparative example, in which the horizontal axis represents the external magnetic field, and the vertical axis represents the average in the ROI at the center of the field of view CE. Indicates the rotation angle of the Kerr rotation of the physical quantity normalized by the value. FIG. 5 shows the values after normalization in a table. That is, the rotation angle of Kerr rotation in each ROI and the ratio to the visual field center CE are shown.

As shown in FIG. 4, in the magnetic domain microscope, the magnetization contrast of each ROI within the field of view has a variation of about ±20%. on the other hand. As shown in FIG. 5, in the spot measuring instrument, the rotation angle of each ROI within the field of view has a variation of about ±5%. As described above, in a magnetic domain microscope, variations in the magnetization contrast of each ROI within the field of view make it difficult to quantitatively detect and evaluate a hysteresis loop.

Therefore, if variations (errors) in magnetization contrast can be corrected for each position (ROI coordinates or image height) within the field of view of a magnetic domain microscope, local hysteresis loops within the field of view can be quantitatively handled. Therefore, measurement of a local hysteresis loop in a plane (two-dimensional) using a magnetic domain microscope is established. This means that the treatment time is greatly improved compared to spot measuring instruments that use laser light. In this embodiment, a local hysteresis loop is measured in a plane (two-dimensional) using a polarizing microscope device such as a magnetic domain microscope. Hereinafter, such measurement will be referred to as imaging MOKE.

(Embodiment 1)
Next, a polarizing microscope device and an intra-field correction analysis method according to the first embodiment will be described. FIG. 6 is a configuration diagram illustrating a polarizing microscope device according to the first embodiment. As shown in FIG. 6, the polarizing microscope device 1 of this embodiment further includes an image processing section 30 in addition to the configuration of the polarizing microscope device 101 of the comparative example. The image processing unit 30 processes the image acquired by the image acquisition unit 19. For example, the image processing unit 30 performs image processing in an intra-field correction analysis method using the polarizing microscope device 1 described below.

7 to 9 are flowcharts illustrating the intra-field correction analysis method according to the first embodiment. The intra-field of view correction analysis method of this embodiment includes (i) pre-calibration without magnetic field sweep as shown in FIG. 7, and (ii) image acquisition by magnetic field sweep on a sample containing a magnetic material and It has three configurations: (iii) (i) and (ii) shown in FIG. In the following description, the rotation direction will be defined as "+" for clockwise (CW) and "-" for counterclockwise (CCW) when viewed from the direction in which the light travels.

<(i) Pre-calibration without magnetic field sweep>
In pre-calibration, first, a mirror sample is placed on the sample stage 15 (step S11 in FIG. 7). The mirror sample may be an unpatterned magnetized thin film, a silicon wafer, or the like. In this way, the non-magnetic sample 20 may be placed as a mirror sample, or the sample 20 may be placed as a non-magnetic mirror sample using an unpatterned magnetic thin film with no magnetic field applied to the illumination light 21. It's okay.

Next, the positions of the polarizer 12 and the analyzer 17 are adjusted so that they form a crossed Nicol arrangement (step S12 in FIG. 7). Typically, on the upper surface of the sample stage 15, the polarization direction of the polarized light included in the illumination light 21 is made to match either the X-axis direction or the Y-axis direction, for example, the X-axis direction.

Next, the polarization direction of the polarizer 12 is fixed. For example, the polarization direction of the polarizer 12 is fixed on the upper surface of the sample stage 15 so that it is in the X-axis direction. In this case, the brightness of the image acquired by the image acquisition unit 19 becomes low at the position of the analyzer 17 in the crossed Nicol arrangement. The position of the analyzer 17 at this time is set as the zero point. Hereinafter, the angle Θ _a of the polarization direction of the analyzer 17 at the zero point is defined as 0 degrees. Note that a of the angle Θ _a is a subscript of Θ.

Next, the mirror surface sample is illuminated with the illumination light 21 while rotating the angle between the polarization direction of the polarizer 12 and the polarization direction of the analyzer 17 within a predetermined range in predetermined increments. As a result, a plurality of images are acquired (step S13 in FIG. 7). The predetermined range of the angle between the polarization direction of the polarizer 12 and the polarization direction of the analyzer 17 is, for example, within a range of approximately ±10 degrees, and the predetermined increments are, for example, 1 degree. In that case, 21 images are acquired while rotating in 1 degree increments within a range of approximately ±10 degrees. Note that the predetermined range is not limited to approximately ±10 degrees. Further, the predetermined increment is not limited to one time. Furthermore, the number of images to be acquired is not limited to 21.

FIG. 10 is a diagram illustrating an image acquired by the polarizing microscope device 1 according to the first embodiment. In FIG. 10, 11 images are shown for simplicity. As shown in FIG. 10, in the case of a crossed Nicol arrangement in which the angle Θ _a of the polarization direction of the analyzer 17 at the zero point is 0, the luminance value is theoretically minimized.

Next, from the plurality of acquired images, a data group of analyzer transmission angle data (Through angle of analyzer data) transmitted through the analyzer 17 is calculated for each ROI in a field of view including a plurality of ROIs, and arithmetic processing is performed. (Step S14 in FIG. 7).

FIG. 11 is a diagram illustrating converting a plurality of images acquired by the polarizing microscope device 1 according to the first embodiment into analyzer transmission angle data for each ROI. As shown in FIG. 11, multiple images are converted into analyzer transmission angle data for each ROI. Here, it is preferable that the ROI is not a single pixel, but is subjected to binning processing, for example, into a rectangle (10 pixels x 10 pixels) or a circle (φ20 pixels), etc., in order to reduce noise. Note that some symbols are omitted to avoid cluttering the diagram.

FIG. 12 is a graph illustrating analyzer transmission angle data acquired by the polarizing microscope device 1 according to Embodiment 1, in which the horizontal axis indicates the angle Θa of the polarization direction of the analyzer 17, and the vertical axis indicates the angle Θa of the polarization direction of the analyzer 17. The average brightness value (Gray Level) is shown. As shown in FIG. 12, the smaller the angle Θa of the polarization direction of the analyzer 17, the smaller the brightness value tends to be. However, the position where the brightness value is the smallest for each ROI is shifted from the angle Θa=0 for each ROI. The angle Θ _a that is the smallest is called the polarization rotation angle Θ ₀ .

Next, the analyzer transmission angle data for each ROI is fitted to a predetermined function. As will be described later, the function used for fitting is the Malus law, which is well known in the field of polarization optics, or a function similar thereto (step S15 in FIG. 7).

13(a) to (c) show the distribution of brightness unevenness a(x, y), the distribution of polarization rotation angle Θ ₀ (x, y), and the ellipticity in the polarizing microscope device 1 according to the first embodiment. FIG. 2 is a diagram illustrating the distribution of η squared η ² (x, y). As shown in FIG. 13, by fitting the analyzer transmission angle data for each ROI with a predetermined function, the distribution of brightness unevenness a (x, y) for each ROI and the polarization rotation angle Θ ₀ (x, y) can be determined. The distribution and the distribution of the square of the ellipticity η ² (x, y) can be calculated (step S16 in FIG. 7). In the following explanation, the distribution of brightness unevenness a(x, y), polarization rotation angle Θ ₀ (x, y), and square of ellipticity η ² (x, y) for each ROI will be explained. , called a device function or device constant.

In this way, the image processing unit 30 rotates the angle between the polarization direction of the polarizer 12 and the polarization direction of the analyzer 17 within a predetermined range in predetermined increments, while rotating the non-magnetic sample 20 or A plurality of images are acquired by illuminating a sample 20 containing a magnetic material with illumination light 21, which is used as a non-magnetic mirror sample without applying a magnetic field. Then, the image processing unit 30 calculates a luminance unevenness distribution for each ROI in a field of view including a plurality of ROIs, a polarization rotation angle distribution, and an apparatus constant including a square distribution of ellipticity due to ovalization from the plurality of acquired images. Calculate.

At this time, the analyzer 17 may be rotated within a predetermined range with respect to the polarizer 12 based on the crossed Nicol arrangement. Further, the image processing unit 30 may calculate an apparatus constant (apparatus function) for each ROI using Malus' law. Furthermore, it goes without saying that it is equivalent to obtain data by fixing the orientation of the analyzer 17 and rotating the polarizer 12 within a predetermined range.

<(ii) Image acquisition by magnetic field sweep and analysis for each ROI>
Next, image acquisition by magnetic field sweeping and analysis for each ROI will be explained. First, the sample 20 containing the magnetic material to be evaluated is placed on the sample stage 15 (step S21 in FIG. 8). The sample 20 is, for example, a wafer on which a magnetic thin film is formed.

Next, the polarizer 12 and analyzer 17 are adjusted to a crossed nicol arrangement and set to the zero point (step S22 in FIG. 8). Thereafter, the angle Θ _a of the polarization direction of the analyzer 17 is set to any angle β ₁ within the above-described calibration angle range (step S23 in FIG. 8). The angle β ₁ is usually about 5 degrees, for example.

Next, an image is acquired while sweeping the magnetic field at about ±10 times the coercive force Hc of the sample 20 to be evaluated (a level that reaches saturation magnetization with a margin) (step S24 in FIG. 8). At this time, images are acquired with sufficient temporal resolution. When the magnet 16 is an electromagnet, the control value of the magnetic field and the imaging time of the image acquisition unit 19 are linked by a timestamp. Image acquisition steps are determined by adjusting the exposure time, frame rate, and magnetic field sweep per image so that several measurement points fall within the rising/falling slope of the hysteresis loop. Set the time.

FIG. 14A is a diagram illustrating an image including a plurality of ROIs acquired by the polarizing microscope device 1 according to the first embodiment. FIG. 14(b) is a graph illustrating a hysteresis loop extracted for each ROI from an image acquired by the polarizing microscope device 1 according to Embodiment 1, where the horizontal axis represents the external magnetic field and the vertical axis represents the brightness. Show value. As shown in FIGS. 11A and 11B, a magnetic field sweep data (Through Magnetic field) group of data obtained by sweeping the magnetic field of the acquired image is processed for each ROI (step S25 in FIG. 8). It is desirable that the ROI coordinates and pixel binning processing within the ROI be the same as the calibration. By plotting the magnetic field on the horizontal axis and the brightness value on the vertical axis of the arithmetic-processed data group, it is possible to obtain an uncorrected hysteresis loop for each ROI, as shown in FIG. 14(b). .

Next, a hysteresis loop for each ROI is fitted using an approximation function. FIG. 15 is a graph illustrating the hysteresis loop measurement value and its fitting function curve acquired by the polarizing microscope device 1 according to Embodiment 1, where the horizontal axis represents the external magnetic field and the vertical axis represents the brightness value. As shown in FIG. 15, the hysteresis loop for each obtained ROI is fitted with an approximation function. The approximation function may be an empirical function. The approximate function does not have to be a physical model formula.

FIG. 16 is a diagram illustrating formulas used in the intra-field correction analysis method according to the first embodiment. As shown in FIG. 16, in this embodiment, the following equation (0) is used to fit the hysteresis loop for each ROI shown in FIGS. 14 and 15.

I=D+Rtanh(α(H±Hc)) (0)

Through this fitting, the magnetization indices Contrast: C (x, y), Coercive force: Hc (x, y), and Slope: α (x, y) are determined for each ROI from the shape of the hysteresis loop. An intra-field map can be obtained (Step S26 in FIG. 8).

17 and 18 illustrate definitions of contrast C(x, y), coercive force Hc(x, y), and slope α(x, y) acquired by the polarizing microscope device 1 according to Embodiment 1. This is a graph. As shown in FIG. 17, the contrast C(x, y) is calculated from the range R and brightness D when formula (0) is fitted to the hysteresis loop, and the contrast C=0.5*(R/D). be able to. Here, the range R is the difference between the brightness value in the saturated magnetization state on the plus side and the brightness value in the saturated magnetization state on the negative side. Brightness D is the average brightness value of the saturated magnetization state on the plus side and the minus side.

As shown in FIGS. 17 and 18, the coercive force Hc (x, y) is determined from the intersection of the hysteresis loop and the intermediate value of the two saturation magnetizations of the hysteresis loop. The slope α(x, y) is determined from the rising slope of the hysteresis loop, as shown in FIGS. 17 and 18. Note that the slope is also called steepness.

As described above, in (ii) of the present embodiment, the image processing unit 30 detects the magnetic material when the angle between the polarization direction of the polarizer 12 and the polarization direction of the analyzer 17 is set to angle β ₁ . A plurality of images are acquired while illuminating the magnetic material portion of the sample 20 with illumination light 21 and sweeping an external magnetic field. Then, the image processing unit 30 acquires a hysteresis loop of brightness values for each ROI from the plurality of acquired images. The image processing unit 30 further fits the hysteresis loop to an empirical approximation function for each ROI (x, y), thereby calculating the contrast C (x, y) and coercive force Hc for each ROI (x, y). (x, y) and slope α(x, y). The contrast C (x, y), the coercive force Hc (x, y), and the slope α (x, y) when the angle β ₁ of the polarization direction of the analyzer 17 is expressed as the contrast C ₁ (x, y), respectively. ), coercive force Hc ₁ (x, y), and slope α ₁ (x, y).

Next, the angle Θ _a of the polarization direction of the analyzer 17 is set to an angle β ₂ different from the angle β ₁ (step S27). β ₂ is any angle within the angular range of the calibration described above. For example, β ₂ =-β ₁ , but there is no particular limitation as long as it is within the calibration angle range. Next, as in the case of angle β ₁ , an image is acquired while sweeping the magnetic field at about ±10 times the coercive force Hc of the sample 20 to be evaluated (step S28 in FIG. 8). At this time, image acquisition operations are performed in the same way as in the case of angle β ₁ , such as acquiring images with sufficient temporal resolution. Then, the acquired image is subjected to arithmetic processing on the magnetic field sweep data group for each ROI (step S29 in FIG. 8). Then, by fitting the hysteresis loop for each ROI with an approximation function, the contrast C (x, y), coercive force Hc (x, y), and slope α (x, y) can be obtained for each ROI ( Step S30 in FIG. 8).

In this way, in (ii) of the present embodiment, the image processing unit 30 can detect the magnetic material even when the angle between the polarization direction of the polarizer 12 and the polarization direction of the analyzer 17 is set to angle β ₂ . A plurality of images are acquired while illuminating the magnetic material portion of the sample 20 containing the magnetic material with the illumination light 21 and sweeping an external magnetic field. Then, the image processing unit 30 acquires a hysteresis loop of brightness values for each ROI from the plurality of acquired images. The image processing unit 30 further fits the hysteresis loop to an empirical approximation function for each ROI (x, y), thereby calculating the contrast C (x, y) and coercive force Hc for each ROI (x, y). (x, y) and slope α(x, y) are calculated. The contrast C (x, y), the coercive force Hc (x, y), and the slope α (x, y) in the case of the angle β ₂ of the polarization direction of the analyzer 17 are respectively expressed as the contrast C ₂ (x, y ), coercive force Hc ₂ (x, y), and slope α ₂ (x, y).

The contrast C(x,y), the coercive force Hc(x,y), and the slope α(x,y) show important and characteristic shapes of the hysteresis loop. All of these are, for example, indicators related to the final performance (operating speed, power consumption, reliability) as a MRAM device. Note that other indicators may be defined in addition to these three indicators. According to the analysis by the inventor, the coercive force Hc (x, y), which is an index of the external magnetic field in which magnetization reversal occurs, provides results that are almost similar to spot measurement without correction. However, although the saturation magnetization amount Ms(x, y) is a characteristic quantity that correlates with the magnetization contrast, as explained in FIGS. 3 and 4 in the above-mentioned comparative example, the deviation from the spot measurement is large and correction is necessary. be. Further, the slope α(x, y) is an index that is a mixture of the coercive force Hc(x, y) and Ms(x, y), and therefore requires correction.

<(iii) Correction processing using measurement data and physical model formula>
Next, a rotation angle ΔΘ(x, y) of rotation of the polarization direction is calculated for each ROI (x, y) using a physical model equation (step S31 in FIG. 9). Specifically, the image processing unit 30 calculates the rotation angle ΔΘ(x, y) of Kerr rotation for each ROI from an analysis using device constants, a hysteresis loop at angle β ₁ , and a hysteresis loop at angle β ₂ . The physical model equations are shown in equations (1) and (2) in FIG. Further, equations (1) and (2) are shown below, but due to space constraints, equation (1) is divided into equations (1-1) to (1-4).

2ΔΘ(x,y)=(P1-P2)/P3 (1-1)
P1=C ₂ (x, y) {(1-2η ² (x, y)) sin ² (β ₂ -Θ(x, y))+η ² (x, y)}
(1-2)
P2=AC ₁ (x, y) {(1-2η ² (x, y)) sin ² (β ₁ -Θ(x, y))+η ² (x, y)}
(1-3)
P3=(1−2η ² (x, y)) {sin(2(β ₂ −Θ(x, y))−A sin(2(β ₁ −Θ(x, y))}
(1-4)

Here, A in equation (1), equations (1-3), and equations (1-4) is the following equation (2).

A={1+cos(2(β ₁ - Θ(x, y)})/{1+cos(2(β ₂ - Θ(x, y)}
(2)

Explanation and derivation of Equations (1) and (2) will be shown in Examples. In (ii), at least the polarization direction of the analyzer 17 is set to two angles β ₁ and β ₂ , and images are captured while sweeping the magnetic field. Then, by analyzing the hysteresis loop for each ROI in the image, two contrast values C ₁ (x, y) and C ₂ (x, y) are calculated for each ROI.

Therefore, the image processing unit 30 calculates the calibration results of the device constants in (i) above, the set values of the angles β ₁ and β ₂ of the polarization direction of the analyzer 17 in (ii), and the contrast C in (ii). By substituting ₁ (x, y) and C ₂ (x, y) into the above physical model equations (1) and (2), the measured value of the rotation angle ΔΘ (x, y) of the corrected Kerr rotation is obtained. can be obtained.

In equations (1) and (2), the values measured in <(i) pre-calibration>, <(ii) image acquisition by magnetic field sweep and analysis for each ROI>, and the set angle β ₁ , _β2 . Therefore, the rotation angle ΔΘ(x,y) of the Kerr rotation generated in the sample 20 in the ROI(x,y) becomes a corrected quantitative value.

<Propagation of polarization error generated in the polarizing microscope itself to Kerr rotation>
Next, it will be explained that the polarization error (device constant) generated in the polarization microscope itself, which was the problem discussed above, propagates to the Kerr rotation generated by the sample 20.

First, consider the case where no external magnetic field is applied to the sample 20. Also, consider ROI (x, y) as one arbitrary coordinate. The polarizer 12 has an ideal crossed Nicol arrangement in which the polarization direction is the X-axis direction and the analyzer 17 is the Y-axis direction. At this time, the linearly polarized light having an amplitude in the X-axis direction that has passed through the polarizer 12 passes through the optical system of the polarizing microscope device 1, so that the plane of polarization is rotated by Θ and becomes elliptical with an ellipticity η.

FIG. 19 is a diagram illustrating rotation and ellipticalization of the plane of polarization when no external magnetic field is applied in the polarization microscope device 1 according to the first embodiment. The direction of the incident linearly polarized light is the X axis, and the direction of the analyzer is the Y axis. As shown in FIG. 19, the polarization direction OA of the reflected light 22 is rotated by Θ from the X axis and made into an ellipse (ellipse major axis OA, minor axis OB) by passing through the polarizing microscope device 1. This Θ rotation and ovalization are caused by the amplitude difference (elliptization) between s-polarized light and p-polarized light caused by the curvature of the objective lens 14, the anti-reflection film, and the coating of the beam splitter 13, and the This is caused by a phase difference (rotation of the plane of polarization). The image acquisition unit detects the sum of projected components of OA and OB onto the Y axis. Further, since the optical path to reach the coordinates (image position) of the image sensor of the image acquisition unit 19 differs depending on the image position, the amount of change in polarization changes depending on the image position.

FIG. 20 is a diagram illustrating the optical path of the reflected light 22 reflected by the sample 20 until it reaches the imaging surface 26 of the image acquisition unit 19 in a state where the beam splitter 13 is not present. FIG. 21 is a diagram illustrating an optical path of the reflected light 22 reflected by the sample 20 until it reaches the imaging surface 26 of the image acquisition unit 19 in a state where the beam splitter 13 is present. As shown in FIGS. 20 and 21, when the beam splitter 13 is provided, the optical path to reach the imaging surface 26 of the image acquisition unit 19 differs depending on the image position. It also shows that the angles at which the three light rays enter the beam splitter 13 differ depending on the object position (sample position). In a general beam splitter 13, reflectance and transmittance are controlled using a dielectric multilayer film, but polarization dependence is not taken into account. Therefore, the degree of rotation and ellipticalization of the plane of polarization changes depending on this angular difference. The dielectric multilayer film of the beam splitter 13 was given as an example, but the same applies to anti-reflection coatings on each surface of the objective lens that make up the optical path, and the polarization component of the entire optical path leading to the image position varies depending on the image position. different. Therefore, the amount of change in the polarization direction changes depending on the image position. This is inevitable to varying degrees.

When energy is OA ² +OB ² =1, the projected components of OA and OB onto the analyzer 17 are √(1−η ² )sinΘ and ηcosΘ, respectively. These have non-interfering vibration planes that are perpendicular to each other. Therefore, the intensity transmitted through the analyzer 17 is (1-η ² )sin ² Θ+η ² cos ² Θ, which is further transformed to obtain equation (3) below and in FIG. 16.

I (Θ, η) = (1-2η ² ) sin ² Θ+η ² (3)

This equation is known as Malus' law, which expresses the intensity of light transmitted through the analyzer 17. Therefore, in the above-mentioned (i) pre-calibration, when the image acquisition unit 19 records the brightness value while changing the angle _Θa of the analyzer 17, the following and equation (4) in FIG. 16 are obtained.

I (Θ, η) = a [(1-2η ² ) sin ² (Θ _a - Θ) + η ² ] (4)

Here, I, a, η ² , and Θ have different values for each position (x, y) within the field of view. That is, I(x,y). In the following, the notation of (x, y) will be omitted. Further, it is expressed as I(Θ, η). a is a coefficient applied to the total energy 1, and corresponds to so-called brightness unevenness. The ratio η ² /(1-2η ² ) between the amplitude 1−2η ² of sin ² and the DC component η ² corresponds to the so-called extinction ratio. (i) In pre-calibration, according to the inventor's verification, this experimental curve differs for each ROI within the field of view. In this way, a(x, y), η ² (x, y), and Θ(x, y) are obtained as device constants from fitting using equation (4) for each ROI. In tests conducted by the inventor, the variation within the visual field a(x, y) was approximately ±10%, η ² (x, y) was approximately ±20%, and Θ(x, y) was approximately ±0.5 degrees. (See Figure 13). Moreover, the absolute values of Θ(x, y) and η ² (x, y) are larger than the Kerr rotation and Kerr ellipticization that occur in the magnetic thin film to be measured by at least one order of magnitude.

Next, consider adding a minute Kerr rotation and Kerr ellipse in the sample 20 containing a magnetic material such as a magnetic thin film when an external magnetic field is swept. FIG. 22 is a diagram illustrating rotation and ellipticalization of the plane of polarization when an external magnetic field is applied in the polarizing microscope device 1 according to the first embodiment. As shown in FIG. 22, it is assumed that the Kerr rotation is modulated as ±ΔΘ with Θ as the center, and the ellipticity is modulated as ±Δη with η as the center. In either case, it is sufficient to consider the ±saturation magnetic field in the sweep of the external magnetic field. The device constant is considered as in the case of (i) pre-calibration, and is expressed by the equation (5) below and in FIG. 16.

I _± = a[(1-2(η±Δη) ² ) sin ² (Θ _a -(Θ±ΔΘ))+(η±Δη) ² ]
(5)

Since ΔΘ<<Θ and Δη<<η, approximation and formula transformation are performed, and for simplicity, it is written as Θ _a −Θ=Θ, and a is omitted. Then, the following and equation (6) in FIG. 16 are obtained.

I _± ≒ [(1-2(η ² ±2ηΔη) ² ) sin ² (Θ±ΔΘ)]+η ² ±2ηΔη]
(6)

Since the index for quantitative evaluation is ΔI=I ₊ −I ₋ , it is expressed as ΔI from equation (6) and transformed.

ΔI=(1-2η ² +4ηΔη) sin(2Θ) sin(2ΔΘ)+4ηΔη(1+cos(2(Θ+ΔΘ)))
(7)

From this equation, ΔΘ and Δη are multiplied by the device constant as a coefficient and cannot be separated. Furthermore, since there are two undetermined coefficients, ΔΘ and Δη, it is understood that it is impossible to derive each of them in one measurement.

Therefore, as the simplest means to change the state, it is assumed that the angle β of the analyzer 17 is measured twice at two levels (Θ ₁ =β ₁ -Θ, Θ ₂ =β ₂ -Θ). Incidentally, although the equations up to equation (7) represent dimensionless light intensity, what is actually recorded is the pixel value (luminance value: gray level) of the image sensor of the image acquisition unit 19. Therefore, a dimensionless contrast value obtained by dividing equation (7) by equation (4) is introduced. At this time, a in equation (4) is also multiplied by equation (7), so it is canceled out. That is, the contrast C is defined by the following equations (8-1) to (8-4) and equation (8) in FIG.

C=(Q1+Q2)/Q3 (8-1)
Q1=(1-2η ² +4ηΔη) sin(2Θ) sin(2ΔΘ)) (8-2)
Q2=4ηΔη(1+cos(2(Θ+ΔΘ))) (8-3)
Q3=[(1-2η ² )sin ² (Θ)+η ² ] (8-4)

In actual measurement data, this corresponds to the height difference (brightness difference)/average value of the hysteresis loop when sweeping the external magnetic field. Contrast C is the contrast in FIG. 17. The contrasts derived from the hysteresis loop at two levels of the analyzer 17 are taken as contrasts C ₁ and C ₂ , and ΔΘ is derived by eliminating Δη from the two simultaneous equations (8), as follows (9-1). ) to (9-4) and equation (9) in FIG.

U1=U2 (9-1)
U1=(1-2η ² )(C ₂ sin ² Θ ₂ -C ₁ sin ² Θ ₁ )+η ² (C ₂ -C ₁ )
(9-2)
U2=(1-2η ² )[sin(2Θ ₂ )sin(2ΔΘ)−sin(2Θ ₁ )sin(2ΔΘ)・U3]
(9-3)
U3=(1+cos( _2Θ2 )cos(2ΔΘ))/(1+cos( _2Θ1 )cos(2ΔΘ))
(9-4)

Here, since ΔΘ is a sufficiently small amount, the equation is transformed by approximating sin(2ΔΘ)≒2ΔΘ and cos(2ΔΘ)≒1. Then, equations (1) and (2) in FIG. 16 are obtained.

Further, Δη(x, y) is also derived as in the following equations (10-1) to (10-4) and equation (10) in FIG.

2Δη(x,y)=(V1-V2)/V3 (10-1)
V1=C ₁ {(1-2η ² (x, y)) sin ² (β ₁ -Θ(x, y))+η ² (x, y)}
(10-2)
V2=(1-2η ² (x, y)) sin(2(β ₁ -Θ(x, y))×2ΔΘ(x, y)
(10-3)
V3=2η(x,y) {1+cos(2(β ₁ -Θ(x,y)))}
(10-4)

However, it is necessary to identify the sign of η(x,y) in the denominator. This requires another measurement using a λ/4 wavelength plate. Further, the above-mentioned mathematical expressions and the expression in FIG. 16 can be changed as appropriate without departing from the spirit. For example, if an essential physical phenomenon is expressed, an approximate notation such as sinΘ≒Θ may be used. Specifically, the above explanation and the series of mathematical formulas shown in FIG. 16 are expressed using approximations as little as possible; The essential physical notation remains the same.

According to this embodiment, variations within the field of view can be corrected and the distribution of polarization characteristics within the field of view can be measured with accuracy equivalent to spot measurement. For example, Patent Document 2 describes a polarizing microscope that analyzes polarization characteristics such as Kerr rotation angle, but does not describe correcting variations within the field of view. Through measurement and correction, the polarizing microscope device 1 of this embodiment can achieve measurement with the same accuracy as spot measurement (a few 10 μm in diameter) with surface measurement (up to several 1000 μm in diameter), and significantly shorten processing time. can do.

<Example 1>
Next, the results of actually acquiring device constants through pre-calibration in the method of the above embodiment, image acquisition by magnetic field sweep, and analysis for each ROI will be described. That is, the magnetization contrast C was evaluated by imaging MOKE, which is measured at angles β ₁ and β ₂ of the two polarization directions of the analyzer 17.

In addition, the rotation angle of Kerr rotation within the visual field was measured in advance by spot measurement, and this was compared as correct data. Sample 20 has a free layer of CoFeB, which is commonly used in MRAM. Specifically, sample 20 was laminated with a CoFeB free layer, layers arranged above and below the free layer for producing perpendicular magnetic anisotropy, and a cap layer on the outermost layer. It includes a metal layer.

The external magnetic field was set at a level that was at least 10 times the coercive force Hc and sufficiently reached saturation magnetization. Further, the ROI coordinates within the field of view of the imaging MOKE were made the same as the measurement spot coordinates of the spot measurement. Furthermore, the magnetic field sweep speed (unit: Oe/sec) is the same for spot measurement and imaging MOKE.

FIG. 23A shows the gray level difference range of the hysteresis loop of each ROI normalized by the gray level difference range at the center of the visual field when the angle of the polarization direction of the analyzer 17 is set to +4 degrees. FIG. 23(a) is uncorrected raw data. In this case, the spatial variation in σ/AVE was 9.7%.

In FIG. 23(b), the contrast of the hysteresis loop is simply divided by the average brightness value of each ROI and normalized using the value at the center of the visual field as a reference. In this case, the spatial variation is 11.4%, but there is a large deviation from the raw data in (a) and the correct answer distribution in (d) obtained by spot measurement.

FIG. 23(c) is a diagram illustrating the contrast distribution of the sample 20 acquired by the polarizing microscope device 1 according to the first embodiment. As shown in FIG. 23(c), the contrast distribution of this embodiment is based on the results of two measurements in which the angle of the polarization direction of the analyzer 17 is set to β ₁ = +4 degrees and β ₂ = -4 degrees. This is what was derived. In this case, the spatial variation is 3.2%. It can be seen that the characteristic patterns (fingerprints) that appear to be caused by device constants as shown in Figures 23(a) and (b), but not in the correct distribution in (d), have been successfully removed. .

FIG. 23(d) is a diagram illustrating the contrast distribution acquired by the spot measuring device. As shown in FIG. 23(d), the results obtained by spot measurement have reduced variations, and there is no characteristic pattern that is considered to be caused by the device constants.

24(a) to (c) are diagrams illustrating the results of quantitative analysis of the polarizing microscope device 1 according to Embodiment 1, and (d) to (f) are diagrams illustrating the results of spot measurement. be. FIGS. 24(a) to 24(c) show the distributions of saturation magnetization Ms (∝Δ2Θ), coercive force Hc, and slope α within the field of view. FIGS. 24(d) to 24(f) show the results of spot measurement at the same locations as in FIGS. 24(a) to 24(c).

As shown in FIGS. 24(a) to 24(c), this embodiment can quantitatively analyze all the indicators of the hysteresis loop shown in FIG. 18. Moreover, although scaling is applied to the numerical values of the distribution of each index in this embodiment, there is a correlation with the distribution obtained by spot measurement. In the field of semiconductor manufacturing, it is possible to manage coefficients, so there is no problem in practice.

As shown in FIG. 24(b), the coercive force Hc does not include scaling in the magnetization direction, which is a device constant. Therefore, no correction is necessary. As shown in FIG. 24(c), the slope α can be corrected by multiplying R in the empirical model equation (0) in FIG. 16 by the scaling coefficient of the magnetization direction applied by the saturation magnetization Ms. . Specifically, ΔΘ(x, y) is normalized with respect to the center of the visual field to calculate the relative distribution ΔΘ'(x, y) (step S32 in FIG. 9). Next, the uncorrected range R(x, y) is normalized with respect to the center of the visual field to calculate the relative distribution (step S33 in FIG. 9). Then, a slope Y-axis correction coefficient is calculated for each ROI. The slope distribution is corrected by ΔΘ'(x, y)/R(x, y)Slope(x, y) (step S34 in FIG. 9).

Next, the effects of this embodiment will be explained. The polarizing microscope device 1 of this embodiment can measure the polarization characteristic distribution within the field of view with an accuracy equivalent to spot measurement, and can realize quantitative surface measurement.

FIG. 25 is a diagram illustrating the effect of the intra-field correction analysis method according to the first embodiment. As shown in FIG. 25, the intra-field correction analysis method of this embodiment sets the angle β of the polarization direction of the analyzer 17 to, for example, −4 degrees and +4 degrees, and applies an external magnetic field to the sample 20. Obtain the gray level difference range image (raw data) when sweeping. The raw data in this case has variations of approximately σ=8.6% and σ=10%, respectively. Contrasts C ₁ (x, y) and C ₂ (x, y) are obtained by normalizing each data, but each contrast includes errors caused by the apparatus. These C ₁ and C ₂ are correction results based on the so-called conventional concept of normalization based on brightness.

In this embodiment, such errors caused by the device are corrected using device constants obtained in advance. In this case, the variation can be reduced to about σ=3.2% (3) in FIG. 25. The characteristic slope distribution caused by device constants can also be removed. This makes it possible to approximate the result of spot measurement. The polarizing microscope device 1 of this embodiment is capable of performing mass measurements in a short period of time, and is effective for managing the magnetization characteristics of the magnetic film of MRAM.

In a magnetic domain observation microscope based on a polarization microscope, such as the magnetic domain polarization microscope of the comparative example, the function is limited to observation of magnetic domains. On the other hand, according to this embodiment, the hysteresis loop within the visual field can be quantitatively evaluated.

Further, while the Kerr effect measuring device and the spot measuring device of the comparative example use point measurement, the present embodiment uses surface measurement. Furthermore, in this embodiment, the hysteresis loop can be quantitatively analyzed for each ROI within the field of view. Furthermore, from the shape of the hysteresis loop, performance indicators directly connected to the final performance of the MRAM device, such as saturation magnetization Ms, coercive force Hc, and slope α, can be quantitatively evaluated in terms of surface. Therefore, since it is possible to dramatically increase the evaluation score, yield management can be performed using volume data (Volume date).

The present invention is not limited to the first embodiment and examples described above, and can be modified as appropriate without departing from the spirit. For example, the configurations of Embodiment 1 and Examples can be combined with each other.

Further, the image processing section 30 described above may be an information processing device such as a personal computer, for example. Note that the image processing unit 30 is not limited to a personal computer, but may be a server, a tablet, a mobile terminal, etc. as long as it performs information processing, or may be a device on the cloud. The image processing unit 30 may include a processor, a memory and storage device, and a communication device as components not shown. Further, the storage device may store the processing performed by the image processing unit 30 as a program. Further, the processor may read a program from the storage device into the memory and execute the program. Thereby, the processor realizes the functions of the image processing section 30.

The image processing section 30 may be realized by dedicated hardware. Further, part or all of the image processing unit 30 may be realized by a general-purpose or dedicated circuit, a processor, etc., or a combination thereof. These may be configured by a single chip or multiple chips connected via a bus. A part or all of the image processing section 30 may be realized by a combination of the above-mentioned circuits and the like and a program. Further, as the processor, a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), an FPGA (field-programmable gate array), a quantum processor (quantum computer control chip), etc. can be used.

Further, when part or all of the image processing unit 30 is realized by a plurality of information processing devices, circuits, etc., the plurality of information processing devices, circuits, etc. may be centrally arranged or distributed. Good too. For example, information processing devices, circuits, etc. may be realized as a client server system, a cloud computing system, or the like, in which each is connected via a communication network. Furthermore, the functions of the image processing unit 30 may be provided in a SaaS (Software as a Service) format.

Further, the following intra-field correction analysis program that causes a computer to read and execute the above-described intra-field correction analysis method is also within the scope of the technical idea of the embodiment. The intra-field correction analysis program may be stored on a non-transitory computer-readable medium or a tangible storage medium. By way of example and not limitation, computer readable or tangible storage media may include random-access memory (RAM), read-only memory (ROM), flash memory, solid-state drive (SSD) or other memory technology, CD -Includes ROM, digital versatile disc (DVD), Blu-ray disc or other optical disc storage, magnetic cassette, magnetic tape, magnetic disc storage or other magnetic storage device. The intra-field correction analysis program may be transmitted on a transitory computer-readable medium or communication medium. By way of example and not limitation, transitory computer-readable or communication media includes electrical, optical, acoustic, or other forms of propagating signals.

(Additional note 1)
a light source that generates illumination light;
a polarizer into which the illumination light generated by the light source is incident and which transmits the illumination light containing linearly polarized light in a first polarization direction;
an objective lens that illuminates a sample with the illumination light including the linearly polarized light and transmits reflected light that is reflected by the illumination light on the sample;
an analyzer that transmits a component of linearly polarized light in a second polarization direction in the reflected light;
an image acquisition unit that acquires an image of the reflected light;
a magnet that generates an external magnetic field to be applied to the sample;
an image processing unit that processes the acquired image;
An in-field correction analysis program using a polarizing microscope device equipped with
Applying a magnetic field to the non-magnetic sample or the sample containing a magnetic material while rotating the angle formed by the first polarization direction and the second polarization direction in predetermined increments within a predetermined range. The polarized light for each region of interest within a field of view including a plurality of regions of interest is obtained from the plurality of images obtained by illuminating the polarized illumination light onto a sample that can be regarded as a non-magnetic mirror surface when used in a non-magnetic state. A first step of calculating device constants including a rotation angle distribution and a square distribution of ellipticity due to ovalization;
When the angle between the first polarization direction and the second polarization direction is set to a first angle, the illumination light polarized with respect to the magnetic body part of the sample containing the magnetic body from a plurality of images acquired while illuminating the area and sweeping the external magnetic field, acquiring a hysteresis loop of the brightness value for each region of interest,
When the angle formed by the first polarization direction and the second polarization direction is set to a second angle, the polarized illumination light is applied to the magnetic material portion of the sample containing the magnetic material. a second step of acquiring a hysteresis loop of the brightness value for each region of interest from a plurality of images acquired while illuminating the area and sweeping the external magnetic field;
a third step of calculating a rotation angle of Kerr rotation for each region of interest from an analysis using the device constant, the hysteresis loop at the first angle, and the hysteresis loop at the second angle;
An intra-field correction analysis program that allows a computer to execute the following.
(Additional note 2)
In the first step,
The analyzer rotates the predetermined range with respect to the polarizer based on a crossed Nicol arrangement.
The intra-field correction analysis program described in Appendix 1.
(Additional note 3)
In the first step,
calculating the angular distribution for each region of interest and the device constant including the square distribution using Malus'law;
The intra-field correction analysis program described in Supplementary note 1 or 2.
(Additional note 4)
In the first step,
The device constant includes a brightness distribution,
calculating the device constant including the brightness distribution for each region of interest;
The intra-field correction analysis program according to any one of Supplementary Notes 1 to 3.
(Appendix 5)
In the second step,
calculating the contrast, coercive force, and slope for each region of interest by fitting the hysteresis loop at the first angle and the hysteresis loop at the second angle to an empirical approximation function;
The intra-field correction analysis program according to any one of Supplementary Notes 1 to 4.
(Appendix 6)
In the third step,
Calculating the rotation angle for each region of interest based on the first angle, the second angle, the brightness contrast at the first angle, and the brightness contrast at the second angle;
The intra-field correction analysis program described in Appendix 5.

1, 101 Polarizing microscope device 10 Light source 11 Lens 12 Polarizer 13 Beam splitter 14 Objective lens 15 Sample stage 16 Magnet 17 Analyzer 18 Imaging lens 19 Image acquisition section 20 Sample 21 Illumination light 22 Reflected light 23 Illumination pupil 24 Pupil plane 25 Measurement Surface 26 Imaging surface 30 Image processing section

Claims (12)

a light source that generates illumination light;
a polarizer into which the illumination light generated by the light source is incident and which transmits the illumination light containing linearly polarized light in a first polarization direction;
an objective lens that illuminates a sample with the illumination light including the linearly polarized light and transmits reflected light that is reflected by the illumination light on the sample;
an analyzer that transmits a component of linearly polarized light in a second polarization direction in the reflected light;
an image acquisition unit that acquires an image of the reflected light;
a magnet that generates an external magnetic field to be applied to the sample;
an image processing unit that processes the acquired image;
Equipped with
The image processing unit includes:
Applying a magnetic field to the non-magnetic sample or the sample containing a magnetic material while rotating the angle formed by the first polarization direction and the second polarization direction in predetermined increments within a predetermined range. From the plurality of images obtained by illuminating the polarized illumination light onto a sample that can be regarded as a non-magnetic mirror surface when used in a non-magnetic state, polarization rotation for each region of interest within a field of view including a plurality of regions of interest is obtained. Calculate device constants including the angular distribution and the square distribution of ellipticity due to ovalization,
When the angle between the first polarization direction and the second polarization direction is set to a first angle, the illumination light polarized with respect to the magnetic body part of the sample containing the magnetic body from a plurality of images acquired while illuminating the area and sweeping the external magnetic field, acquiring a hysteresis loop of the brightness value for each region of interest,
When the angle formed by the first polarization direction and the second polarization direction is set to a second angle, the polarized illumination light is applied to the magnetic material portion of the sample containing the magnetic material. from a plurality of images acquired while illuminating the area and sweeping the external magnetic field, acquiring a hysteresis loop of the brightness value for each region of interest;
calculating a rotation angle of Kerr rotation for each region of interest from an analysis using the device constant, the hysteresis loop at the first angle, and the hysteresis loop at the second angle;
Polarized light microscope equipment. The analyzer rotates the predetermined range with respect to the polarizer based on a crossed Nicol arrangement.
The polarizing microscope device according to claim 1. The image processing unit calculates the angular distribution for each region of interest and the device constant including the square distribution using Malus' law.
The polarizing microscope device according to claim 1 or 2. The device constant includes a brightness distribution,
the image processing unit calculates the device constant including the brightness distribution for each region of interest;
A polarizing microscope device according to any one of claims 1 to 3. The image processing unit calculates the contrast, coercive force, and slope for each region of interest by fitting the hysteresis loop at the first angle and the hysteresis loop at the second angle to an empirical approximation function. ,
The polarizing microscope device according to any one of claims 1 to 4. The image processing unit calculates the rotation angle for each region of interest based on the first angle, the second angle, the brightness contrast at the first angle, and the brightness contrast at the second angle.
The polarizing microscope device according to claim 5. a light source that generates illumination light;
a polarizer into which the illumination light generated by the light source is incident and which transmits the illumination light containing linearly polarized light in a first polarization direction;
an objective lens that illuminates a sample with the illumination light including the linearly polarized light and transmits reflected light that is reflected by the illumination light on the sample;
an analyzer that transmits a component of linearly polarized light in a second polarization direction in the reflected light;
an image acquisition unit that acquires an image of the reflected light;
a magnet that generates an external magnetic field to be applied to the sample;
an image processing unit that processes the acquired image;
An in-field correction analysis method using a polarizing microscope device equipped with
Applying a magnetic field to the non-magnetic sample or the sample containing a magnetic material while rotating the angle formed by the first polarization direction and the second polarization direction in predetermined increments within a predetermined range. From the plurality of images obtained by illuminating the polarized illumination light onto a sample that can be regarded as a non-magnetic mirror surface when used in a non-magnetic state, polarization rotation for each region of interest within a field of view including a plurality of regions of interest is obtained. A first step of calculating device constants including an angular distribution and a square distribution of ellipticity due to ovalization;
When the angle between the first polarization direction and the second polarization direction is set to a first angle, the illumination light polarized with respect to the magnetic body part of the sample containing the magnetic body from a plurality of images acquired while illuminating the area and sweeping the external magnetic field, acquiring a hysteresis loop of the brightness value for each region of interest,
When the angle formed by the first polarization direction and the second polarization direction is set to a second angle, the polarized illumination light is applied to the magnetic material portion of the sample containing the magnetic material. a second step of acquiring a hysteresis loop of the brightness value for each region of interest from a plurality of images acquired while illuminating the area and sweeping the external magnetic field;
a third step of calculating a rotation angle of Kerr rotation for each region of interest from an analysis using the device constant, the hysteresis loop at the first angle, and the hysteresis loop at the second angle;
An intra-field correction analysis method with In the first step,
The analyzer rotates the predetermined range with respect to the polarizer based on a crossed Nicol arrangement.
The intra-field correction analysis method according to claim 7. In the first step,
calculating the device constants including the angle distribution and the square distribution for each region of interest using Malus'law;
The intra-field correction analysis method according to claim 7 or 8. In the first step,
The device constant includes a brightness distribution,
calculating the device constant including the brightness distribution for each region of interest;
The intra-field correction analysis method according to any one of claims 7 to 9. In the second step,
calculating the contrast, coercive force, and slope for each region of interest by fitting the hysteresis loop at the first angle and the hysteresis loop at the second angle to an empirical approximation function;
The intra-field correction analysis method according to any one of claims 7 to 10. In the third step,
calculating the rotation angle for each region of interest based on the first angle, the second angle, the brightness contrast at the first angle, and the brightness contrast at the second angle;
The intra-field correction analysis method according to claim 11.