Polarizing microscope apparatus and in-field correction analysis method

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

Technical Field

[0001] The present invention relates to a polarized microscope apparatus and an in-field correction analysis method.

Background Art

[0002] The Kerr effect microscope and the magnetic domain observation microscope are based on the classical polarized microscope and have already been commercialized by a plurality of manufacturers. This is described in, for example, Non-Patent Document 1.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Patent Document 2

Non-Patent Documents

[0004]

Non-Patent Document 1

Non-Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0005] A Kerr effect microscope can obtain a magnetic hysteresis loop at a single point on a sample containing a magnetic material such as a magnetic thin film by irradiating it with laser light while sweeping an external magnetic field and measuring the change in the polarization component of the reflected light. 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 records the change in the polarization component of the reflected light when light from an incoherent light source is polarized by a polarizer and incident on the sample, as a change in brightness of an image sensor, making it possible to record magnetic domain patterns within the field of view.

[0006] While a hysteresis loop can be obtained for each pixel by recording brightness while sweeping an external magnetic field using a magnetic domain microscope, the variation in polarization characteristics within the field of view is large compared to the polarization changes occurring in the sample. Therefore, it is difficult to quantitatively evaluate the hysteresis loop within the field of view, and it is not possible to measure magnetization characteristics with high precision.

[0007] This invention has been made in view of the above problems, and provides a polarizing microscope device and an in-field correction analysis method that can measure magnetic properties with high precision. [Means for solving the problem]

[0008] The polarizing microscope apparatus according to the present invention comprises a light source that generates illumination light, a polarizer that receives the illumination light generated by the light source and transmits the illumination light including linear polarization in a first polarization direction, an objective lens that illuminates a sample with the illumination light including linear polarization and transmits the reflected light reflected by the sample, an analyzer that transmits the linear polarization component in a second polarization direction of 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, and an image processing unit that processes the acquired image, wherein the image processing unit rotates the angle between the first polarization direction and the second polarization direction in predetermined increments within a predetermined range, and from a plurality of images acquired by illuminating a non-magnetic sample, or a sample that can be considered as a non-magnetic mirror surface by using a sample containing a magnetic material without applying a magnetic field, the image processing unit acquires the image of the field of view including a plurality of areas of interest. The device constants, including the polarization rotation angle distribution for each region of interest and the squared distribution of ellipticity due to ellipticization, are calculated. When the angle between the first polarization direction and the second polarization direction is set as the first angle, the illumination light is used to illuminate the portion of the magnetic material in the sample containing the magnetic material, and a hysteresis loop of the brightness value for each region of interest is obtained from multiple images acquired while sweeping the external magnetic field. When the angle between the first polarization direction and the second polarization direction is set as the second angle, the illumination light is used to illuminate the portion of the magnetic material in the sample containing the magnetic material, and a hysteresis loop of the brightness value for each region of interest is obtained from multiple images acquired while sweeping the external magnetic field. The rotation angle of Kerr rotation generated in the sample for each region of interest is calculated from an analysis using the device constants, the hysteresis loop at the first angle, and the hysteresis loop at the second angle.

[0009] In the polarizing microscope apparatus described above, the analyzer may be rotated within the predetermined range relative to the polarizer with respect to the crossed nicol arrangement.

[0010] In the polarizing microscope apparatus described above, the image processing unit may use Malus's law to calculate the angular distribution for each region of interest, as well as the apparatus constants including the squared distribution.

[0011] In the polarizing microscope apparatus described above, the apparatus constant may include the luminance distribution, and the image processing unit may calculate the apparatus constant including the luminance distribution for each area of ​​interest.

[0012] In the polarizing microscope apparatus described above, the image processing unit may calculate the magnetization contrast, coercivity, 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 magnetization contrast represents the luminance contrast, which is defined by the maximum and minimum luminance when the luminance is recorded while sweeping an external magnetic field over the sample.

[0013] In the polarizing microscope apparatus described above, the image processing unit may calculate the rotation angle 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.

[0014] The in-field correction analysis method according to the present invention is an in-field correction analysis method using a polarizing microscope apparatus comprising: a light source that generates illumination light; a polarizer that receives the illumination light generated by the light source and transmits the illumination light including linear polarization in a first polarization direction; an objective lens that illuminates a sample with the illumination light including the linear polarization and transmits the reflected light reflected by the sample; an analyzer that transmits the linear polarization component in a second polarization direction of 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; and an image processing unit that processes the acquired image, wherein the method involves rotating the angle between the first polarization direction and the second polarization direction in predetermined increments within a predetermined range, and illuminating a non-magnetic sample, or a sample that can be considered a non-magnetic mirror surface by using a sample containing a magnetic material without applying a magnetic field, with the illumination light, and from a plurality of images acquired, each of the multiple areas of interest within the field of view includes a plurality of areas of interest. The method comprises: a first step of calculating an instrument constant including the polarization rotation angle distribution and the squared distribution of ellipticity due to ellipticization; a second step of obtaining a hysteresis loop of the brightness value for each region of interest from a plurality of images acquired while illuminating the portion of the magnetic material of the sample containing the magnetic material with the illumination light and sweeping the external magnetic field when the angle between the first polarization direction and the second polarization direction is set to the first angle; a third step of calculating the rotation angle of Kerr rotation generated in the sample for each region of interest from an analysis using the instrument constant, the hysteresis loop at the first angle and the hysteresis loop at the second angle.

[0015] In the above-described in-field correction analysis method, in the first step, the analyzer may be rotated within the predetermined range with respect to the polarizer, using the crossed nicol arrangement as a reference.

[0016] In the above-described in-field correction analysis method, in the first step, the device constants, including the angular distribution and the squared distribution for each region of interest, may be calculated using Malus's law.

[0017] In the above-described in-field correction analysis method, in the first step, the device constant may include the luminance distribution, and the device constant may be calculated to include the luminance distribution for each of the areas of interest.

[0018] In the above-described in-field correction analysis method, in the second step, the contrast, coercivity, and slope for each area of ​​interest may be calculated by fitting the hysteresis loop at the first angle and the hysteresis loop at the second angle to an empirical approximation function.

[0019] In the above-described in-field correction analysis method, in the third step, the rotation angle for each region of interest may be calculated based on the first angle, the second angle, the magnetization contrast at the first angle, and the magnetization contrast at the second angle. [Effects of the Invention]

[0020] The present invention provides a polarizing microscope apparatus and a field-of-view correction analysis method that can measure the magnetization characteristics within a field of view with high precision. [Brief explanation of the drawing]

[0021] [Figure 1] This is a diagram illustrating the configuration of a polarizing microscope device, such as a magnetic domain microscope, related to a comparative example. [Figure 2] This is a schematic diagram illustrating the Kerr effect in a polarizing microscope device such as a magnetic domain microscope, as described in the comparative example. [Figure 3] This graph illustrates hysteresis loops in five areas of interest within the field of view, measured using a polarizing microscope such as a magnetic domain microscope, as shown in the comparative example. The horizontal axis represents the external magnetic field, and the vertical axis represents the luminance value. [Figure 4]The hysteresis loops in the five ROIs within the field of view, measured using a polarizing microscope such as a magnetic domain microscope in the comparative example, were normalized by the average of the brightness values ​​of each ROI, and then further normalized by the average of the ROI at the center of the field of view. [Figure 5] This graph illustrates hysteresis loops in five ROIs within the field of view measured by a spot measuring instrument related to the comparative example. The horizontal axis represents the external magnetic field, and the vertical axis represents the rotation angle of the Kerr rotation, a physical quantity normalized by the average value in the ROI at the center of the field of view. [Figure 6] This is a diagram illustrating a polarizing microscope apparatus according to Embodiment 1. [Figure 7] This is a flowchart illustrating the in-field correction analysis method according to Embodiment 1. [Figure 8] This is a flowchart illustrating the in-field correction analysis method according to Embodiment 1. [Figure 9] This is a flowchart illustrating the in-field correction analysis method according to Embodiment 1. [Figure 10] This figure illustrates an image acquired by the polarizing microscope apparatus according to Embodiment 1. [Figure 11] This figure illustrates the process of converting multiple images acquired by the polarizing microscope apparatus according to Embodiment 1 into analyzer transmission angle data for each ROI. [Figure 12] This graph illustrates the analyzer transmission angle data acquired by the polarizing microscope apparatus according to Embodiment 1. The horizontal axis represents the angle of polarization of the analyzer, and the vertical axis represents the luminance value. [Figure 13] Figures (a) to (c) illustrate the distribution of brightness unevenness a(x, y), the distribution of polarization rotation angle Θ0(x, y), and the distribution of ellipticity η²(x, y) in the polarizing microscope apparatus 1 according to Embodiment 1. [Figure 14] (a) is a diagram illustrating an image containing multiple ROIs acquired by the polarizing microscope apparatus according to Embodiment 1, and (b) is a graph illustrating hysteresis loops extracted for each ROI from the image acquired by the polarizing microscope apparatus according to Embodiment 1, where the horizontal axis represents the external magnetic field and the vertical axis represents the brightness value. [Figure 15]This graph illustrates the hysteresis loop and fitting function acquired by the polarizing microscope apparatus according to Embodiment 1, with the horizontal axis representing the external magnetic field and the vertical axis representing the luminance value. [Figure 16] This figure illustrates the mathematical formulas used in the in-field correction analysis method according to Embodiment 1. [Figure 17] This graph illustrates the definitions of contrast C(x, y), coercivity Hc(x, y), and slope (x, y) obtained by the polarizing microscope apparatus according to Embodiment 1. [Figure 18] This graph illustrates the definitions of contrast C(x, y), coercivity Hc(x, y), and slope (x, y) obtained by the polarizing microscope apparatus according to Embodiment 1. [Figure 19] This figure illustrates the rotation and ellipticization of the polarization plane in the polarizing microscope apparatus according to Embodiment 1 when no external magnetic field is applied. [Figure 20] This diagram illustrates the optical path from the reflected light from the sample to the imaging surface of the image acquisition unit in the absence of a beam splitter. [Figure 21] This diagram illustrates the optical path from the reflected light from the sample to the imaging surface of the image acquisition unit, when a beam splitter is present. [Figure 22] This figure illustrates the rotation and ellipticization of the polarization plane when an external magnetic field is applied in the polarizing microscope apparatus according to Embodiment 1. [Figure 23] (a) is the high-low gray level difference range of the hysteresis loop normalized to the gray level at the center of the field of view when the polarization direction angle of the analyzer is set to +4 degrees; (b) is the contrast of the hysteresis loop simply divided by the average brightness value and normalized based on the value at the center of the field of view; (c) is a diagram illustrating the distribution of magnetization contrast of a sample acquired by the polarizing microscope apparatus according to Embodiment 1; and (d) is a diagram illustrating the distribution of magnetization contrast acquired by the spot measuring instrument. [Figure 24]Figures (a) to (c) illustrate the results of quantitative analysis of the polarizing microscope apparatus 1 according to Embodiment 1, and figures (d) to (f) illustrate the results of spot measurement. [Figure 25] This figure illustrates the features of the polarizing microscope apparatus and in-field correction analysis method according to Embodiment 1. [Modes for carrying out the invention]

[0022] For clarity of explanation, the following descriptions and drawings have been omitted and simplified as appropriate. Furthermore, the same elements are denoted by the same reference numerals in each drawing, and redundant explanations have been omitted where necessary.

[0023] (Comparative example) Before describing the polarizing microscope apparatus according to Embodiment 1, a comparative example of a polarizing microscope and its problems will be described. This will clarify the polarizing microscope of this embodiment. Note that the configuration and problems of the comparative example are also included within the scope of the technical concept of the embodiment.

[0024] Figure 1 is a diagram illustrating the configuration of a polarizing microscope apparatus, such as a magnetic domain microscope, according to a comparative example. As shown in Figure 1, the polarizing microscope apparatus 101 according to the comparative example comprises a light source 10, a lens 11, a polarizer 12, a beam splitter 13, an objective lens 14, a 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.

[0025] Here, for the sake of explaining the polarizing microscope apparatus 101, we introduce an XYZ Cartesian coordinate system. For example, the direction perpendicular to the upper surface of the sample stage 15 is defined as the Z-axis direction, and the plane parallel to the upper surface of the sample stage 15 is defined as the XY plane. The various components will be explained below.

[0026] The light source 10 generates illumination light 21. The light source 10 is, for example, a halogen lamp, a white LED (Light Emitting Diode), etc. The illumination light 21 may also be white light. The light source 10 emits the generated illumination light 21 towards the polarizer 12. A lens 11 may be placed between the light source 10 and the polarizer 12. The illumination light 21, converted into parallel light by the lens 11, is incident on the polarizer 12.

[0027] The polarizer 12 is positioned 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 that includes linear polarization. For example, the polarizer 12 transmits illumination light that includes linear polarization 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 linear polarization in the Z-axis direction. That is, the transmission axis of the polarizer 12 is the Z-axis direction. The illumination light 21 that has been converted by the polarizer 12 to include linear polarization is incident on the beam splitter 13.

[0028] The beam splitter 13 reflects a portion of the incident illumination light 21 off 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. The objective lens 14 is positioned between the beam splitter 13 and the sample 20. It is positioned at or near the position of 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 including linearly polarized light. In this invention, the magnetic thin film sample is either a non-patterned thin film sample or an island pattern of a sufficiently large size (e.g., Φ several hundred μm).

[0029] Sample 20 includes a magnetic material such as a magnetic thin film. Sample 20 may be, for example, a magnetic thin film deposited on a wafer. Alternatively, Sample 20 may be a magnetic thin film used in MRAM (Magnetoresistive Random Access Memory). The magnetic material of Sample 20 placed on the sample stage 15 may have an external magnetic field applied to it in the Z-axis direction, for example. When the direction of the external magnetic field changes upward or downward, the magnetization direction of the magnetic material may change upward or downward. Note that Sample 20 in the calibration described later may be a non-magnetic sample 20.

[0030] The magnet 16 is positioned between the sample 20 and the objective lens 14. The magnet 16 is, for example, an electromagnet whose magnetic field strength and direction can be modulated onto the sample. The magnet 16 may also be a permanent magnet. The magnet 16 generates an external magnetic field to be applied to the sample 20. In this way, the magnet 16 applies an external magnetic field to the sample 20. For example, when inspecting the free layer of an MRAM composed of perpendicular magnetic anisotropy material, the Polar Kerr Effect is detected. Therefore, the magnet 16 applies a magnetic field perpendicular to the surface of the sample 20. If the magnet 16 is an electromagnet, an external magnetic field within a predetermined range from the +Z direction to the -Z direction is applied to the sample 20 by controlling the current value and direction flowing through the electromagnet.

[0031] Furthermore, in order to detect the polar Kerr effect, the incident light incident on sample 20 must be perpendicular to the surface of sample 20 and linearly polarized with the direction of electric field vibration in the XY plane. The polarization state of sample 20 changes slightly due to the Kerr effect depending on the magnetic field strength (H) of the external magnetic field. The Kerr effect involves rotation of the polarization axis (called Kerr rotation) and Kerr ellipticity.

[0032] Figure 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 Figure 2, the Kerr effect includes the rotation angle ΔΘ of the polarization axis (also called the rotation angle ΔΘ of the polarization direction) and ellipticization including the change in ellipticity Δη. The change in ellipticity Δη is, for example, tan -1 (OB / OA), where OA is the minor axis and OB is the major axis. The reflected light 22 reflected by sample 20 is modulated in polarization state by the Kerr effect caused by sample 20.

[0033] Returning to Figure 1, the reflected light 22 from the sample 20 enters the objective lens 14. The objective lens 14 transmits the reflected light 22, which is the illumination light 21 that was reflected from the sample 20. The reflected light 22 passes through the objective lens 14 and the beam splitter 13 and enters the analyzer 17.

[0034] The analyzer 17 is positioned between the beam splitter 13 and the image acquisition unit 19. The analyzer 17 transmits the linearly polarized component of the reflected light 22 in a second polarization direction. The second direction is, for example, the Y-axis direction. In this case, the analyzer 17 transforms the reflected light 22 to include linearly polarized light in the Y-axis direction. That is, the transmission axis of the analyzer 17 is the Y-axis direction. The direction of linearly polarized light transmitted by the analyzer 17 (transmission axis) may be positioned orthogonal to the direction of linearly polarized light transmitted by the polarizer 12 (transmission axis). For example, the direction of linearly polarized light transmitted by the polarizer 12 may be the X-axis direction, and the direction of linearly polarized light transmitted by the analyzer 17 may be the Y-axis direction. This arrangement, where the transmission axis of the analyzer 17 is orthogonal to the transmission axis of the polarizer 12, is called a cross Nicole arrangement. The cross Nicole arrangement can detect changes in polarized light, including linearly polarized light, as changes in brightness with high sensitivity. The reflected light 22, which contains polarized light that is slightly rotated and elliptic from the sample 20, is transmitted through the analyzer 17 at an intensity equal to the square of the amplitude projected onto the transmission axis. The reflected light 22 that has passed through the analyzer 17 is incident on the image acquisition unit 19, for example, via the imaging lens 18.

[0035] The image acquisition unit 19 detects changes in the polarization component of the reflected light 22 as changes in intensity. This allows the image acquisition unit 19 to acquire 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 also 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 image sensor, as long as it can acquire an image. The imaging surface 26 of the image acquisition unit 19 is in an image conjugate relationship with the measurement surface 25 of the sample 20.

[0036] Here, the rotation angle ΔΘ of the polarization direction rotation occurring in the aforementioned sample 20 for MRAM is typically 0.1 degrees or less. Furthermore, the change in ellipticity Δη is also a slight change, similar to the rotation angle ΔΘ. Ellipticity η is the ellipticity angle (angle quantity) defined by the arctan of the flattening of the ellipse. A magnetic domain microscope focuses on magnetic domains (patterns) within its field of view. Therefore, it is sufficient for a magnetic domain microscope to be able to visualize magnetic domains within its field of view, and it does not focus on the quantitative values ​​of the rotation angle ΔΘ and the change in ellipticity Δη. Also, a magnetic domain microscope does not focus on the quantitative analysis error of the visibility between locations within the field of view (pattern contrast).

[0037] As shown in the upper right of Figure 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 error caused by the instrument (tool), making it difficult to detect the Kerr effect generated in the sample. 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 instrument (tool), so the Kerr effect can be detected.

[0038] First, in the following explanation, we will describe the standard device: spot measurement using laser light. This is also a well-known device, and many products are available on the market. Below, we will refer to the device that performs spot measurement as a spot measuring instrument.

[0039] The spot detector measures using differential polarization. The spot detector irradiates the sample with laser light containing linearly polarized light and sweeps the magnetic field applied to the sample. While sweeping the magnetic field, the spot detector splits the reflected light, which contains the modulated polarized light from the sample, into s-polarized and p-polarized light using a polarization separation prism. This allows the spot detector's two photodetectors to perform lock-in differential processing, measuring the rotation angle of the Kerr rotation generated in the sample. Therefore, by plotting the magnetic field on the horizontal axis and the rotation angle on the vertical axis, a hysteresis loop can be obtained. Generally, this is what is referred to as a MOKE (Magneto-optical Kerr Effect) device or Kerr effect measurement device. Since the obtained hysteresis loop measures a physical quantity, it is possible to evaluate the quantitative characteristics of magnetic thin films. Furthermore, because the evaluation position is changed while the sample is moved, and only the center of the optical system is used, and the entire reflected light beam is detected by the photodetector, instrument error is not included in the evaluation position.

[0040] Incidentally, in the aforementioned magnetic domain microscope, when acquiring an image while sweeping the 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 way roughly correlates with the hysteresis loop obtained by spot measurement using laser light. A magnetic domain microscope can also obtain a hysteresis loop as one of its functions. However, the function of obtaining a hysteresis loop in a magnetic domain microscope is only a guideline. For example, the inventors have found that hysteresis loops acquired at multiple different measurement coordinates within the field of view of a magnetic domain microscope show large differences (errors) between the measurement coordinates. This will be explained using Figure 3 below.

[0041] Figure 3 is a graph illustrating hysteresis loops in five regions of interest (hereinafter referred to as ROIs) within the field of view, measured using a polarizing microscope such as a magnetic domain microscope in a comparative example. The horizontal axis represents the external magnetic field, and the vertical axis represents the luminance value. In Figure 3, the five ROIs include the center of the field of view CE, the upper right UR, the upper left UL, the lower right LR, and the lower left LL within the field of view.

[0042] Figure 4 shows the hysteresis loops in five ROIs within the field of view, measured using a polarizing microscope such as a magnetic domain microscope in the comparative example. These loops are normalized by the average luminance value of each ROI, and then further normalized by the average luminance value of the ROI at the center CE of the field of view. Figure 4 shows the normalized values ​​in a table. Specifically, it shows the difference between the maximum and minimum luminance values ​​for each ROI, and the ratio of the average luminance value of each ROI to the center CE of the field of view.

[0043] Figure 5 is a graph illustrating hysteresis loops in five ROIs within the field of view measured by a spot measuring instrument related to the comparative example. The horizontal axis represents the external magnetic field, and the vertical axis represents the rotation angle of the Kerr rotation, a physical quantity normalized by the average value in the ROI at the field center CE. Figure 5 shows the normalized values ​​in a table, specifically the rotation angle of the Kerr rotation in each ROI and its ratio to the field center CE.

[0044] As shown in Figure 4, in a magnetic domain microscope, the magnetization contrast of each ROI within the field of view has a variation of approximately ±20%. On the other hand, as shown in Figure 5, in a spot measuring instrument, the rotation angle of each ROI within the field of view has a variation of approximately ±5%. Thus, in a magnetic domain microscope, the variation in the magnetization contrast of each ROI within the field of view makes it difficult to quantitatively detect and evaluate hysteresis loops.

[0045] Therefore, if the variation (error) in magnetization contrast can be corrected for each position (ROI coordinate or image height) within the field of view of the magnetic domain microscope, local hysteresis loops within the field of view can be quantitatively measured. Thus, measurement of local hysteresis loops in a plane (2D) using a magnetic domain microscope becomes feasible. This means that the processing time is greatly improved compared to spot measuring instruments using laser light. This embodiment performs measurement of local hysteresis loops in a plane (2D) using a polarizing microscope device such as a magnetic domain microscope. Hereafter, such measurements will be referred to as Imaging MOKE.

[0046] (Embodiment 1) Next, a polarizing microscope apparatus and an in-field correction analysis method according to Embodiment 1 will be described. Figure 6 is a configuration diagram illustrating a polarizing microscope apparatus according to Embodiment 1. As shown in Figure 6, the polarizing microscope apparatus 1 of this embodiment further includes an image processing unit 30 in addition to the configuration of the polarizing microscope apparatus 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 the in-field correction analysis method using the polarizing microscope apparatus 1 shown below.

[0047] Figures 7 to 9 are flowcharts illustrating the in-field correction analysis method according to Embodiment 1. The in-field correction analysis method of this embodiment has three components: (i) pre-calibration without magnetic field sweeping shown in Figure 7, (ii) image acquisition by magnetic field sweeping on a sample containing a magnetic material and analysis for each ROI shown in Figure 8, and (iii) correction processing of the Kerr effect using the measurement data from (i) and (ii) and a physical model equation shown in Figure 9. In the following description, the rotation direction is defined as clockwise (CW) as "+" and counterclockwise (CCW) as "-" when viewed from the direction of light propagation.

[0048] <(i) Pre-calibration without magnetic field sweep> In the pre-calibration, first, a mirror-finish sample is placed on the sample stage 15 (step S11 in Figure 7). The mirror-finish sample may be an unpatterned magnetized thin film or a silicon wafer, etc. Thus, a non-magnetic sample 20 may be placed as the mirror-finish sample, or an unpatterned magnetic thin film may be placed as the non-magnetic mirror-finish sample 20 under illumination light 21 without applying a magnetic field.

[0049] Next, the polarizer 12 and the analyzer 17 are positioned in a crossed nicol configuration (step S12 in Figure 7). Typically, on the upper surface of the sample stage 15, the polarization direction of the polarized light contained in the illumination light 21 is aligned with either the X-axis or Y-axis direction, for example, the X-axis direction.

[0050] Next, the polarization direction of the polarizer 12 is fixed. For example, the polarization direction of the polarizer 12 is fixed so that it is in the X-axis direction on the upper surface of the sample stage 15. In this case, the brightness of the image acquired by the image acquisition unit 19 will be low at the position of the analyzer 17 which is arranged in a crossed nicol configuration. The position of the analyzer 17 at this time is set as the zero point. Below is the angle Θ of the polarization direction of the analyzer 17 at the zero point. a We define this as 0 degrees. Note that the angle Θ a The 'a' in 'a' is a subscript for Θ.

[0051] Next, the illumination light 21 is shone onto the mirror surface sample 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. This allows for the acquisition of multiple images (step S13 in Figure 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 increment is, for example, 1 degree. In this case, 21 images are acquired while rotating within a range of approximately ±10 degrees in 1-degree increments. Note that the predetermined range is not limited to approximately ±10 degrees. Also, the predetermined increment is not limited to 1 degree. Furthermore, the number of images acquired is not limited to 21.

[0052] Figure 10 is an example of an image acquired by the polarizing microscope apparatus 1 according to Embodiment 1. For simplicity, Figure 10 shows 11 images. As shown in Figure 10, the polarization direction angle Θ of the analyzer 17 at the zero point. a In principle, the luminance value is minimized when the cross-nicol configuration is set to 0.

[0053] Next, from the acquired images, a set of analyzer data (through angle of analyzerdata) is calculated for each ROI in the field of view that contains multiple ROIs, and calculation processing is performed (step S14 in Figure 7).

[0054] Figure 11 illustrates the process of converting multiple images acquired by the polarizing microscope apparatus 1 according to Embodiment 1 into analyzer transmission angle data for each ROI. As shown in Figure 11, the multiple images are converted into analyzer transmission angle data for each ROI. Here, it is desirable to bin the ROI into, for example, a rectangle (10 pixels × 10 pixels) or a circle (φ20 pixels) rather than a single pixel, in order to reduce noise. Note that some reference numerals have been omitted to avoid making the figure too complex.

[0055] Figure 12 is a graph illustrating the analyzer transmission angle data acquired by the polarizing microscope apparatus 1 according to Embodiment 1. The horizontal axis represents the polarization direction angle Θa of the analyzer 17, and the vertical axis represents the average luminance value (Gray Level) within the ROI. As shown in Figure 12, the smaller the polarization direction angle Θa of the analyzer 17, the smaller the luminance value tends to be. However, the position where the luminance value is smallest for each ROI shifts from angle Θa=0 for each ROI. a This is called the polarization rotation angle Θ0.

[0056] 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 Malus's law or a similar one, which is well known in the field of polarization optics (step S15 in Figure 7).

[0057] Figures 13(a) to (c) show the distribution of brightness unevenness a(x, y), the distribution of polarization rotation angle Θ0(x, y), and the square of ellipticity η in the polarizing microscope apparatus 1 according to Embodiment 1. 2 This figure illustrates the distribution of (x, y). As shown in Figure 13, by fitting the analyzer transmission angle data for each ROI with a predetermined function, the distribution of brightness unevenness a(x, y), the distribution of polarization rotation angle Θ0(x, y), and the square of the ellipticity η can be obtained for each ROI. 2 The distribution of (x, y) can be calculated (step S16 in Figure 7). This includes the distribution of brightness unevenness a(x, y) for each ROI, the distribution of polarization rotation angle Θ0(x, y), and the square of the ellipticity η. 2 In the following explanation, the distribution of (x, y) will be referred to as the apparatus function or apparatus constant.

[0058] In this way, the image processing unit 30 acquires multiple images by illuminating a non-magnetic sample 20, or a sample used as a non-magnetic mirror surface sample without applying a magnetic field to a sample 20 containing a magnetic material, with 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. The image processing unit 30 then calculates from the acquired multiple images the brightness uniformity distribution for each ROI within the field of view, which includes multiple ROIs, the polarization rotation angle distribution, and the squared distribution of ellipticity due to ellipticization, as well as instrument constants.

[0059] In this case, the analyzer 17 may be rotated within a predetermined range relative to the polarizer 12 with respect to the crossed nicol configuration. The image processing unit 30 may also calculate the instrument constant (instrument function) for each ROI using Malus's law. Furthermore, it goes without saying that it is equivalent to fixing the orientation of the analyzer 17 and rotating the polarizer 12 within a predetermined range to acquire data.

[0060] <(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 described. First, a sample 20 containing a 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.

[0061] Next, the polarizer 12 and the analyzer 17 are adjusted to a cross Nicol arrangement and set to the zero point (step S22 in FIG. 8). Then, the angle Θ of the polarization direction of the analyzer 17 a is set to any angle β1 within the angle range of the aforementioned calibration (step S23 in FIG. 8). The angle β1 is usually, for example, about 5 degrees.

[0062] 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, the image is acquired with sufficient time 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 associated with a time stamp. The increment of image acquisition is set such that the exposure time, frame rate, and magnetic field sweep time per image are set so that several measurement points are included in the rising / falling slope of the hysteresis loop.

[0063] FIG. 14(a) is a diagram illustrating an image including a plurality of ROIs acquired by the polarization microscope apparatus 1 according to Embodiment 1. FIG. 14(b) is a graph illustrating hysteresis loops extracted for each ROI from the image acquired by the polarization microscope apparatus 1 according to Embodiment 1. The horizontal axis represents the external magnetic field, and the vertical axis represents the luminance value. As shown in FIGS. 11(a) and (b), for each ROI of the acquired image, a group of magnetic field sweep data (Through Magnetic field) of the data obtained by sweeping the magnetic field is subjected to arithmetic processing (step S25 in FIG. 8). It is desirable that the ROI coordinates and the pixel binning processing within the ROI be aligned with the calibration. By plotting the magnetic field on the horizontal axis and the luminance value on the vertical axis for the arithmetic processed data group, an uncorrected hysteresis loop can be obtained for each ROI as shown in FIG. 14(b).

[0064] Next, the hysteresis loop for each ROI is fitted with an approximation function. Figure 15 is a graph illustrating the hysteresis loop measurement values ​​and their fitting function curves acquired by the polarizing microscope apparatus 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 Figure 15, the acquired hysteresis loop for each ROI is fitted with an approximation function. The approximation function may be an empirical function. The approximation function does not have to be a physical model equation.

[0065] Figure 16 is a diagram illustrating the mathematical formula used in the in-field correction analysis method according to Embodiment 1. As shown in Figure 16, in this embodiment, the hysteresis loop for each ROI shown in Figures 14 and 15 is fitted using the following equation (0).

[0066] I = D + Rtanh(α(H ± Hc)) (0)

[0067] This fitting allows us to obtain an in-field map for each ROI using magnetization indices such as contrast (C(x,y)), coercivity (Hc(x,y)), and slope (α(x,y)) from the shape of the hysteresis loop (step S26 in Figure 8).

[0068] Figures 17 and 18 are graphs illustrating the definitions of contrast C(x, y), coercivity Hc(x, y), and slope α(x, y) obtained by the polarizing microscope apparatus 1 according to Embodiment 1. As shown in Figure 17, contrast C(x, y) can be calculated from the range R and brightness D obtained by fitting equation (0) to the hysteresis loop using the formula contrast C = 0.5 * (R / D). Here, range R is the difference between the brightness value of the positive saturation magnetization state and the brightness value of the negative saturation magnetization state. Brightness D is the average brightness value of the positive and negative saturation magnetization states.

[0069] The coercivity Hc(x, y) is determined from the intersection of the hysteresis loop and the midpoint of the two saturation magnetizations of the hysteresis loop, as shown in Figures 17 and 18. The slope α(x, y) is determined from the incline of the rising edge of the hysteresis loop, as shown in Figures 17 and 18. The slope is also called the steepness.

[0070] Thus, in (ii) of this embodiment, the image processing unit 30 sets the angle between the polarization direction of the polarizer 12 and the polarization direction of the analyzer 17 to angle β1, illuminates the magnetic portion of the sample 20 containing the magnetic material with illumination light 21, and acquires multiple images while sweeping the external magnetic field. The image processing unit 30 then obtains a hysteresis loop of the brightness value for each ROI from the acquired multiple images. The image processing unit 30 further calculates the contrast C(x,y), coercivity Hc(x,y), and slope α(x,y) for each ROI(x,y) by fitting the hysteresis loop for each ROI(x,y) to an empirical approximation function. The contrast C(x,y), coercivity Hc(x,y), and slope α(x,y) when the polarization angle β1 of the analyzer 17 are referred to as contrast C1(x,y), coercivity Hc1(x,y), and slope α1(x,y), respectively.

[0071] Next, the polarization direction angle Θ of the analyzer 17 aThe angle is set to angle β2, which is different from angle β1 (step S27). β2 is any angle within the angle range of the calibration described above. For example, β2 = -β1, but there are no particular limitations as long as it is within the angle range of the calibration. Next, as with angle β1, an image is acquired while sweeping the magnetic field at approximately ±10 times the coercivity Hc of the sample 20 to be evaluated (step S28 in Figure 8). At this time, the image acquisition operation is the same as with angle β1, such as acquiring the image with sufficient temporal resolution. Then, the acquired images are processed for each ROI, and the magnetic field sweep data set is calculated (step S29 in Figure 8). Then, by fitting the hysteresis loop for each ROI with an approximation function, the contrast C(x,y), coercivity Hc(x,y), and slope α(x,y) can be obtained for each ROI (step S30 in Figure 8).

[0072] Thus, in (ii) of this embodiment, even when the angle between the polarization direction of the polarizer 12 and the polarization direction of the analyzer 17 is set to angle β2, the image processing unit 30 illuminates the magnetic portion of the sample 20 containing the magnetic material with illumination light 21 and acquires multiple images while sweeping the external magnetic field. The image processing unit 30 then obtains a hysteresis loop of the brightness value for each ROI from the acquired multiple images. The image processing unit 30 further calculates the contrast C(x,y), coercivity Hc(x,y), and slope α(x,y) for each ROI(x,y) by fitting the hysteresis loop for each ROI(x,y) to an empirical approximation function. The contrast C(x,y), coercivity Hc(x,y), and slope α(x,y) when the polarization angle β2 of the analyzer 17 are referred to as contrast C2(x,y), coercivity Hc2(x,y), and slope α2(x,y), respectively.

[0073] The contrast C(x,y), coercivity Hc(x,y), and slope α(x,y) indicate important and characteristic shapes of the hysteresis loop. All of these are indicators related to the final performance of the MRAM device (operating speed, power consumption, reliability), for example. In addition to these three indicators, other indicators may also be defined. According to the inventor's analysis, the coercivity Hc(x,y), which is an indicator of the external magnetic field that causes magnetization reversal, yields results that are almost similar to spot measurements without correction. However, the saturation magnetization Ms(x,y) is a characteristic quantity that correlates with magnetization contrast, but as explained in Figures 3 and 4 of the comparative example above, it deviates significantly from spot measurements and requires correction. Also, the slope α(x,y) is an indicator that is a mixture of coercivity Hc(x,y) and Ms(x,y), and therefore also requires correction.

[0074] (iii) Correction process using measurement data and physical model equations Next, the rotation angle ΔΘ(x,y) of the rotation in the polarization direction is calculated for each ROI(x,y) using the physical model equation (step S31 in Figure 9). Specifically, the image processing unit 30 calculates the rotation angle ΔΘ(x,y) of the Kerr rotation for each ROI from analysis using the device constants, the hysteresis loop at angle β1, and the hysteresis loop at angle β2. The physical model equations are shown in equations (1) and (2) in Figure 16. Equations (1) and (2) are also shown below, but due to space limitations, equation (1) is divided into equations (1-1) to (1-4).

[0075] 2ΔΘ(x, y) = (P1 - P2) / P3 (1-1) P1 = C2(x, y) {(1-2η) 2 (x, y) sin 2 (β2-Θ(x,y))+η 2 (x, y)} (1-2) P2 = AC1(x, y) {(1-2η) 2 (x, y) sin 2 (β1-Θ(x,y))+η 2 (x, y)} (1-3) P3=(1-2η 2(x, y)){sin(2(β2-Θ(x, y))-Asin(2(β1-Θ(x, y))} (1-4)

[0076] Here, A in equations (1), (1-3), and (1-4) is the following equation (2).

[0077] A={1+cos(2(β1-Θ(x, y)} / {1+cos(2(β2-Θ(x, y)} (2)

[0078] The explanation and derivation of equations (1) and (2) are shown in the examples. In (ii), the polarization direction of at least the analyzer 17 is set to two angles β1 and β2, and an image is acquired while sweeping the magnetic field. Then, by analyzing the hysteresis loop for each ROI in the image, two contrast values ​​C1(x,y) and C2(x,y) are calculated for each ROI.

[0079] Therefore, the image processing unit 30 can obtain the measured value of the corrected Kerr rotation angle ΔΘ(x,y) by substituting the calibration result of the device constants in (i) above, the set values ​​of the polarization direction angles β1 and β2 of the analyzer 17 in (ii), and the contrasts C1(x,y) and C2(x,y) in (ii) into the above physical model equations (1) and (2).

[0080] In equations (1) and (2), all values ​​are those measured by <(i) pre-calibration> and <(ii) image acquisition by magnetic field sweep and analysis for each ROI>, as well as the set angles β1 and β2. Therefore, the rotation angle ΔΘ(x,y) of the Kerr rotation generated by sample 20 at ROI(x,y) is a corrected quantitative value.

[0081] <Propagation of polarization errors generated by the polarizing microscope itself to car rotation> Next, we will explain how the polarization error (instrument constant) generated by the polarizing microscope itself, which was the problem mentioned above, propagates into the Kerr rotation generated by the sample 20.

[0082] First, consider the case where no external magnetic field is applied to the sample 20. Also, consider ROI(x,y) as an arbitrary single coordinate. Assume an ideal crossed nicol configuration where the polarization direction of the polarizer 12 is the X-axis direction and the polarization direction of the analyzer 17 is the Y-axis direction. In this case, the linearly polarized light with amplitude in the X-axis direction that has passed through the polarizer 12 passes through the optical system of the polarizing microscope 1, causing the plane of polarization to rotate Θ and become elliptic with ellipticity η.

[0083] Figure 19 illustrates the rotation and ellipticization of the polarization plane in the polarizing microscope apparatus 1 according to Embodiment 1 when no external magnetic field is applied. The orientation of the incident linearly polarized light is the X-axis, and the orientation of the analyzer is the Y-axis. As shown in Figure 19, the polarization orientation OA of the reflected light 22 undergoes Θ rotation and ellipticization (ellipse major axis OA, minor axis OB) from the X-axis as it passes through the polarizing microscope apparatus 1. This Θ rotation and ellipticization are caused by the amplitude difference (ellipticization) of s-polarized and p-polarized light generated by the curvature of the objective lens 14, the anti-reflective coating, and the coating of the beam splitter 13, as well as the phase difference (rotation of the polarization plane) of s-polarized and p-polarized light. The image acquisition unit detects the sum of the projection components of OA and OB onto the Y-axis. Furthermore, since the optical path to reach the coordinates (image position) of the image sensor in the image acquisition unit 19 differs for each image position, the amount of change in polarization varies depending on the image position.

[0084] Figure 20 illustrates the optical path from the reflected light 22 reflected by the sample 20 to the imaging surface 26 of the image acquisition unit 19 in the absence of the beam splitter 13. Figure 21 illustrates the optical path from the reflected light 22 reflected by the sample 20 to the imaging surface 26 of the image acquisition unit 19 in the presence of the beam splitter 13. As shown in Figures 20 and 21, with the beam splitter 13, the optical path to the imaging surface 26 of the image acquisition unit 19 differs for each image position. Furthermore, it is shown that the angles at which the three rays are incident on the beam splitter 13 differ depending on the object position (sample position). In a typical beam splitter 13, reflectivity and transmittance are controlled by a dielectric multilayer film, but polarization dependence is not taken into consideration. Therefore, the degree of rotation and ellipticization of the plane of polarization changes according to this angle difference. As an example, the dielectric multilayer film of the beam splitter 13 was cited, but the same principle applies to anti-reflective coatings on each surface of the objective lens that constitutes the optical path. The fluctuation in the polarization component of the entire optical path leading to the image position differs depending on the image position. Therefore, the amount of change in the polarization direction changes depending on the image position. This is unavoidable to varying degrees.

[0085] Energy, OA 2 +OB 2 When = 1, the projection components of OA and OB onto analyzer 17 are √(1-η) 2 )sinΘ and ηcosΘ. These have mutually orthogonal planes of vibration and are therefore non-interfering. Thus, the intensity transmitted through analyzer 17 is (1-η 2 )sin 2 Θ+η 2 cos 2 This becomes Θ, and by further transformation, we obtain the following equation and equation (3) in Figure 16.

[0086] I(Θ,η)=(1-2η) 2 )sin 2 Θ+η 2 (3)

[0087] This equation is known as Malus's law, which represents the light intensity transmitted through analyzer 17. Therefore, in the aforementioned (i) pre-calibration, the angle Θ of analyzer 17 aWhen the brightness value is recorded by the image acquisition unit 19 while shaking the device, the following equation and equation (4) in Figure 16 are obtained.

[0088] I(Θ,η) = a[(1-2η) 2 )sin 2 (Θ a -Θ)+η 2 (4)

[0089] Here, I, a, η 2 Θ has different values ​​for each position (x, y) within the field of view. That is, it is I(x, y). Below, the notation (x, y) will be omitted. Also, it will be expressed as I(Θ, η). a is a coefficient multiplied by the total energy of 1, and corresponds to the so-called brightness unevenness. sin 2 Amplitude 1-2η 2 And the DC component η 2 The ratio of η 2 / (1-2η 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 in the field of view. In this way, a(x, y), η can be obtained for each ROI from fitting using equation (4). 2 (x, y) and Θ(x, y) are obtained as device constants. In the inventor's tests, the field of view variation a(x, y) was approximately ±10%, η 2 (x, y) is approximately ±20%, and Θ(x, y) is approximately ±0.5 degrees (see Figure 13). Also, Θ(x, y), η 2 The absolute value of (x, y) is an order of magnitude larger than the Kerr rotation and Kerr ellipticization occurring in the magnetic thin film being measured.

[0090] Next, we consider the small Kerr rotation and Kerr ellipticization in the sample 20 containing a magnetic material such as a magnetic thin film when an external magnetic field is swept. Figure 22 is a diagram illustrating the rotation and ellipticization of the polarization plane when an external magnetic field is applied in the polarizing microscope apparatus 1 according to Embodiment 1. As shown in Figure 22, the Kerr rotation is assumed to be modulated by ±ΔΘ around Θ, and the ellipticity by ±Δη around η. In both cases, it is sufficient to consider the ±saturation magnetic field during the sweep of the external magnetic field. The apparatus constants are considered in the same way as in (i) pre-calibration, and are given below and in equation (5) of Figure 16.

[0091] I ± =a[(1-2(η±Δη) 2 )sin 2 (Θ a -(Θ±ΔΘ))+(η±Δη) 2 ] (5)

[0092] Since ΔΘ << Θ and Δη << η, we perform approximations and algebraic manipulations, and for simplicity, Θ a We write -Θ=Θ and omit a. Then we get the following and equation (6) in Figure 16.

[0093] I ± ≒[(1-2(η 2 (±2ηΔη) 2 )sin 2 (Θ±ΔΘ)]+η 2 [±2ηΔη] (6)

[0094] The quantitative evaluation indicator is ΔI = I + -I - Therefore, we denote it as ΔI from equation (6) and rearrange it.

[0095] ΔI = (1 - 2η) 2 +4ηΔη)sin(2Θ)sin(2ΔΘ)+4ηΔη(1+cos(2(Θ+ΔΘ))) (7)

[0096] From this equation, it can be seen that 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 impossible to derive each of them in a single measurement.

[0097] Therefore, as the simplest way to change the state, we will measure the angle β of the analyzer 17 twice at two levels (Θ1=β1-Θ, Θ2=β2-Θ). Incidentally, up to equation (7), the light intensity is dimensionless, but what is actually recorded is the pixel value (luminance value: gray level) of the image sensor of the image acquisition unit 19. Therefore, we introduce a dimensionless contrast value obtained by dividing equation (7) by equation (4). In this case, a in equation (4) also applies to equation (7), so they cancel each other out. That is, the contrast C is defined by the following equations (8-1) to (8-4) and equation (8) in Figure 16.

[0098] 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)

[0099] In actual measurement data, this corresponds to the difference in height (luminance difference) of the hysteresis loop during the sweep of the external magnetic field / the average value. Contrast C is the contrast in Figure 17. Taking the contrasts derived from the hysteresis loop at two levels of analyzer 17 as contrasts C1 and C2, and eliminating Δη from the two simultaneous equations of (8) to derive ΔΘ, we obtain the following equations (9-1) to (9-4) and equation (9) in Figure 16.

[0100] U1=U2 (9-1) U1=(1-2η 2 )(C2sin 2 Θ2-C1sin 2 Θ(1)+η 2 (C2-C1) (9-2) U2=(1-2η 2 )[sin(2Θ2)sin(2ΔΘ)-sin(2Θ1)sin(2ΔΘ)·U3] (9-3) U3=(1+cos(2Θ2)cos(2ΔΘ)) / (1+cos(2Θ1)cos(2ΔΘ)) (9-4)

[0101] Here, since ΔΘ is a sufficiently small quantity, we approximate sin(2ΔΘ)≈2ΔΘ and cos(2ΔΘ)≈1 and rearrange the equations. Doing so gives us equations (1) and (2) in Figure 16.

[0102] Furthermore, Δη(x, y) can be derived as shown in equations (10-1) to (10-4) below and equation (10) in Figure 16.

[0103] 2Δη(x, y)=(V1-V2) / V3 (10-1) V1=C1{(1-2η 2 (x, y) sin 2 (β1-Θ(x,y))+η 2 (x, y)} (10-2) V2=(1-2η 2 (x, y)) sin(2(β1-Θ(x, y))×2ΔΘ(x, y) (10-3) V3=2η(x, y){1+cos(2(β1-Θ(x, y)))} (10-4)

[0104] However, it is necessary to identify the sign of η(x, y) in the denominator. This requires another measurement using a λ / 4 wave plate. Furthermore, the above formulas and the representation in Figure 16 can be modified as appropriate, as long as they do not deviate from the intended purpose. For example, if the essential physical phenomenon is expressed, approximate notations such as sinΘ≒Θ may be used. Specifically, the above explanation and the series of formulas shown in Figure 16 use notations that avoid approximations as much as possible, but the essential physical notation does not change even if approximate notations are used according to the order of magnitude of the measured and set values ​​entered.

[0105] 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 the same accuracy as spot measurement. For example, Patent Document 2 describes a polarizing microscope for analyzing polarization characteristics such as Kerr rotation angle, but it does not describe correcting for variations within the field of view. The polarizing microscope apparatus 1 of this embodiment can achieve measurement with the same accuracy as spot measurement (Φ several tens of μm) for surface measurement (~ several Φ 1000 μm) through measurement and correction, and can significantly reduce processing time.

[0106] <Example 1> Next, we will explain the results of actually obtaining the instrument constants by pre-calibration in the method of the above embodiment, and performing image acquisition by magnetic field sweep and analysis for each ROI. Specifically, the magnetization contrast C was evaluated using imaging MOKE measured at the angles β1 and β2 of the two polarization directions of the analyzer 17.

[0107] Furthermore, the rotation angle of the Kerr rotation within the field of view was measured in advance using spot measurement, and this was used as ground truth data for comparison. Sample 20 has a free CoFeB layer, which is commonly used in MRAM. Specifically, sample 20 comprises a free CoFeB layer, layers arranged above and below the free layer to introduce perpendicular magnetic anisotropy, and a metal layer laminated as a cap layer on the outermost layer.

[0108] The external magnetic field was set to a level sufficient to reach saturation magnetization, with a coercivity (Hc) of more than 10 times the coercivity. Furthermore, the ROI coordinates within the imaging MOKE's field of view were identical to those of the spot measurement. The magnetic field sweep speed (in Oe / sec) for both spot measurement and imaging MOKE was also the same.

[0109] Figure 23(a) shows the gray level difference range of the hysteresis loops of each ROI, normalized to the gray level difference range at the center of the field of view, when the polarization direction angle of analyzer 17 is set to +4 degrees. Figure 23(a) is the uncorrected raw data. In this case, the spatial variability was 9.7% in σ / AVE.

[0110] Figure 23(b) shows the contrast of the hysteresis loop, simply divided by the average luminance value of each ROI and normalized based on the value at the center of the field of view. In this case, the spatial variability is 11.4%, but this deviates significantly from the raw data in (a) and the correct distribution in (d) obtained from spot measurements.

[0111] Figure 23(c) is an example of the contrast distribution of a sample 20 acquired by the polarizing microscope apparatus 1 according to Embodiment 1. As shown in Figure 23(c), the contrast distribution of this embodiment was derived from the results of two measurements with the polarization direction angles of the analyzer 17 set to β1 = +4 degrees and β2 = -4 degrees. In this case, the spatial variability is 3.2%. It can be seen that characteristic patterns (fingerprints) that appear to be caused by apparatus constants, as shown in Figures 23(a) and (b), but are not present in the correct distribution in (d), have been well removed.

[0112] Figure 23(d) illustrates the contrast distribution acquired by the spot measurement device. As shown in Figure 23(d), the results obtained by spot measurement show reduced variability and no characteristic patterns that appear to be caused by the device constants.

[0113] Figures 24(a) to (c) illustrate the results of quantitative analysis of the polarizing microscope apparatus 1 according to Embodiment 1, and (d) to (f) illustrate the results of spot measurement. Figures 24(a) to (c) show the distribution of saturation magnetization Ms (∝Δ2Θ), coercivity Hc, and slope α within the field of view. Figures 24(d) to (f) show the results of spot measurement at the same locations as in (a) to (c).

[0114] As shown in Figures 24(a) to (c), this embodiment can quantitatively analyze all the hysteresis loop indicators shown in Figure 18. Furthermore, although the numerical values ​​of the distribution of each indicator in this embodiment are scaled, they correlate with the distribution obtained from spot measurements. Since coefficient control is possible in the field of semiconductor manufacturing, there are no practical problems.

[0115] As shown in Figure 24(b), the coercivity Hc is not affected by the scaling in the magnetization direction, which is an instrument constant. Therefore, no correction is necessary. As shown in Figure 24(c), the slope α can be corrected by multiplying the scaling coefficient in the magnetization direction applied at saturated magnetization Ms by R in the empirical model equation (0) of Figure 16. Specifically, ΔΘ(x,y) is normalized with respect to the center of the field of view to calculate the relative distribution ΔΘ'(x,y) (step S32 in Figure 9). Next, the uncorrected range R(x,y) is normalized with respect to the center of the field of view to calculate the relative distribution (step S33 in Figure 9). Then, the Y-axis correction coefficient of the slope is calculated for each ROI. The slope distribution is corrected by ΔΘ'(x,y) / R(x,y)Slope(x,y) (step S34 in Figure 9).

[0116] Next, the effects of this embodiment will be described. The polarizing microscope device 1 of this embodiment can measure the polarization characteristic distribution within the field of view with the same accuracy as spot measurement, and can achieve quantitative surface measurement.

[0117] Figure 25 illustrates the effect of the in-field correction analysis method according to Embodiment 1. As shown in Figure 25, the in-field correction analysis method of this embodiment acquires a gray level difference range image (raw data) when an external magnetic field is swept over the sample 20, by setting the polarization direction angle β of the analyzer 17 to, for example, -4 degrees and +4 degrees. In this case, the raw data has variations of approximately σ = 8.6% and σ = 10%, respectively. By normalizing each data, contrasts C1(x, y) and C2(x, y) are obtained, but each contrast contains errors caused by the device. These C1 and C2 are correction results based on the so-called conventional approach of normalization by luminance.

[0118] In this embodiment, such device-induced errors are corrected using pre-acquired device constants. This reduces the variation to approximately σ = 3.2% (Figure 25, 3). Characteristic gradient distributions caused by device constants are also eliminated. This brings the results closer to those of spot measurements. Furthermore, the polarizing microscope apparatus 1 of this embodiment enables large-scale measurements in a short time, making it effective for managing the magnetization characteristics of magnetic films in MRAMs.

[0119] In magnetic domain observation microscopes that use a polarizing microscope as a base, such as the magnetic domain polarizing microscope in the comparative example, the function is limited to observing magnetic domains. On the other hand, according to this embodiment, it is possible to quantitatively evaluate hysteresis loops within the field of view.

[0120] Furthermore, while the Kerr effect measuring device and spot measuring instrument in the comparative example perform point measurements, this embodiment performs surface measurements. Moreover, this embodiment can quantitatively analyze the hysteresis loop for each ROI within the field of view. In addition, performance indicators directly related to the final performance of the MRAM device, such as saturation magnetization Ms, coercivity Hc, and slope α, can be quantitatively evaluated across the surface based on the shape of the hysteresis loop. Therefore, it is possible to dramatically increase the number of evaluation points, enabling yield management using volume data.

[0121] The present invention is not limited to Embodiment 1 and the examples described above, and can be modified as appropriate without departing from the spirit of the invention. For example, the configurations of Embodiment 1 and the examples can be combined with each other.

[0122] Furthermore, the image processing unit 30 described above may be, for example, an information processing device such as a personal computer. The image processing unit 30 is not limited to a personal computer; it may be a server, tablet, mobile terminal, or even a cloud-based device, as long as it performs information processing. The image processing unit 30 may also include a processor, memory, storage device, and communication device (not shown in the diagram). The storage device may store the processing performed by the image processing unit 30 as a program. The processor may load the program from the storage device into memory and execute it. In this way, the processor realizes the functions of the image processing unit 30.

[0123] The image processing unit 30 may be implemented with dedicated hardware. Alternatively, part or all of the image processing unit 30 may be implemented by general-purpose or dedicated circuits, processors, etc., or a combination thereof. These may be configured on a single chip or on multiple chips connected via a bus. Part or all of the image processing unit 30 may be implemented by a combination of the aforementioned circuits, etc., and a program. Furthermore, a CPU (Central Processing Unit), GPU (Graphics Processing Unit), FPGA (field-programmable gate array), quantum processor (quantum computer control chip), etc., can be used as the processor.

[0124] Furthermore, if part or all of the image processing unit 30 is implemented by multiple information processing devices or circuits, these devices may be centrally located or distributed. For example, the information processing devices or circuits may be implemented in a form in which each is connected via a communication network, such as a client-server system or a cloud computing system. In addition, the functions of the image processing unit 30 may be provided in SaaS (Software as a Service) format.

[0125] Furthermore, the following in-field correction analysis program, which loads the above-described in-field correction analysis method into a computer and executes it, is also within the scope of the technical concept of the embodiment. The in-field correction analysis program may be stored in a non-temporary computer-readable medium or a physical storage medium. Examples, but not limited, of the computer-readable medium or physical storage medium include random-access memory (RAM), read-only memory (ROM), flash memory, solid-state drive (SSD) or other memory technologies, CD-ROM, digital versatile disc (DVD), Blu-ray® disc or other optical disc storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage devices. The in-field correction analysis program may be transmitted over a temporary computer-readable medium or a communication medium. Examples, but not limited, of the temporary computer-readable medium or communication medium include electrically, optically, acoustically, or otherwise propagating signals.

[0126] (Note 1) A light source that generates illumination light, The illumination light generated by the light source is incident on a polarizer that transmits the illumination light, including 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 the reflected light reflected by the sample from the illumination light, An analyzer that transmits the linearly polarized component in the second polarization direction of 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, A field-of-view correction analysis program using a polarizing microscope equipped with the following: The first step involves illuminating a non-magnetic sample, or a sample that can be considered a non-magnetic mirror surface by using a sample containing a magnetic material without applying a magnetic field, with polarized illumination light, while rotating the angle between the first polarization direction and the second polarization direction in predetermined increments within a predetermined range, and calculating instrument constants including the polarization rotation angle distribution for each of the multiple areas of interest within a field of view, and the squared distribution of ellipticity due to ellipticization, from a plurality of images obtained by this illumination. When the angle between the first polarization direction and the second polarization direction is set to the first angle, polarized illumination light is used to illuminate the portion of the magnetic material in the sample containing the magnetic material, and a hysteresis loop of the brightness value for each region of interest is obtained from a plurality of images acquired while sweeping the external magnetic field. When the angle between the first polarization direction and the second polarization direction is set to the second angle, the polarized illumination light is used to illuminate the portion of the magnetic material in the sample containing the magnetic material, and a hysteresis loop of the brightness value for each region of interest is obtained from a plurality of images acquired while sweeping the external magnetic field. A third step involves calculating the rotation angle of the Kerr rotation for each region of interest from an analysis using the device constants, the hysteresis loop at the first angle, and the hysteresis loop at the second angle. A field-of-view correction analysis program that is executed by a computer. (Note 2) In step 1 above, The analyzer rotates the polarizer within the predetermined range with respect to the crossed nicol configuration. The in-field correction analysis program described in Appendix 1. (Note 3) In step 1 above, Using Malus's law, the device constants, including the angular distribution and the squared distribution for each region of interest, are calculated. The in-field correction analysis program described in Appendix 1 or 2. (Note 4) In step 1 above, The aforementioned device constants include the luminance distribution, The device constants, including the luminance distribution for each of the regions of interest, are calculated. The in-field correction analysis program described in any one of the appendices 1 to 3. (Note 5) In the second step above, The contrast, coercivity, and slope for each region of interest are calculated by fitting the hysteresis loop at the first angle and the hysteresis loop at the second angle to an empirical approximation function. A field-of-view correction analysis program described in any one of the following appendices 1 to 4. (Note 6) In the third step above, Based on the first angle, the second angle, the luminance contrast at the first angle, and the luminance contrast at the second angle, the rotation angle for each area of ​​interest is calculated. The in-field correction analysis program described in Appendix 5. [Explanation of symbols]

[0127] 1. 101 Polarizing microscope apparatus 10 light source 11 lenses 12 polarizers 13 Beam Splitter 14 Objective lens 15 Sample stage 16 Magnets 17. Analyzer 18 Imaging Lenses 19 Image acquisition unit 20 samples 21 Illumination light 22 Reflected light 23 Illumination Eye 24 Pupil plane 25 Measuring surface 26 Imaging surface 30 Image Processing Unit

Claims

1. A light source that generates illumination light, The illumination light generated by the light source is incident on a polarizer that transmits the illumination light, including 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 the reflected light reflected by the sample from the illumination light, An analyzer that transmits the linearly polarized component in the second polarization direction of 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 aforementioned image processing unit, While rotating the angle between the first polarization direction and the second polarization direction in predetermined increments within a predetermined range, the polarization rotation angle distribution for each of the multiple areas of interest within the field of view, and the squared distribution of ellipticity due to ellipticization are calculated from a plurality of images obtained by illuminating a non-magnetic sample, or a sample containing a magnetic material that can be considered a non-magnetic mirror surface by using it without applying a magnetic field, with the polarized illumination light. When the angle between the first polarization direction and the second polarization direction is set to the first angle, polarized illumination light is used to illuminate the portion of the magnetic material in the sample containing the magnetic material, and a hysteresis loop of the brightness value for each region of interest is obtained from a plurality of images acquired while sweeping the external magnetic field. When the angle between the first polarization direction and the second polarization direction is set to the second angle, the polarized illumination light is used to illuminate the portion of the magnetic material in the sample containing the magnetic material, and a hysteresis loop of the brightness value for each region of interest is obtained from a plurality of images acquired while sweeping the external magnetic field. The rotation angle of the Kerr rotation is calculated for each region of interest from the analysis using the device constants, the hysteresis loop at the first angle, and the hysteresis loop at the second angle. Polarizing microscope device.

2. The analyzer rotates the polarizer within the predetermined range with respect to the crossed nicol configuration. The polarizing microscope apparatus according to claim 1.

3. The image processing unit calculates the device constants, including the polarization rotation angle distribution and the squared distribution for each region of interest, using the Malus law. The polarizing microscope apparatus according to claim 1 or 2.

4. The aforementioned device constants include the luminance uniformity distribution, The image processing unit calculates the device constants, including the brightness uniformity distribution for each area of ​​interest. A polarizing microscope apparatus according to any one of claims 1 to 3.

5. The image processing unit calculates the contrast, coercivity, 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. A polarizing microscope apparatus according to any one of claims 1 to 4.

6. The image processing unit calculates the rotation angle for each area 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 apparatus according to claim 5.

7. A light source that generates illumination light, The illumination light generated by the light source is incident on a polarizer that transmits the illumination light, including 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 the reflected light reflected by the sample from the illumination light, An analyzer that transmits the linearly polarized component in the second polarization direction of 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, A field-of-view correction analysis method using a polarizing microscope equipped with the following: The first step involves calculating device constants, including the polarization rotation angle distribution for each of the multiple areas of interest within a field of view, and the squared distribution of ellipticity due to ellipticization, from a plurality of images obtained by illuminating a non-magnetic sample, or a sample containing a magnetic material that can be considered a non-magnetic mirror surface by using it without applying a magnetic field, while rotating the angle between the first polarization direction and the second polarization direction in predetermined increments within a predetermined range; When the angle between the first polarization direction and the second polarization direction is set to the first angle, polarized illumination light is used to illuminate the portion of the magnetic material in the sample containing the magnetic material, and a hysteresis loop of the brightness value for each region of interest is obtained from a plurality of images acquired while sweeping the external magnetic field. When the angle between the first polarization direction and the second polarization direction is set to the second angle, the polarized illumination light is used to illuminate the portion of the magnetic material in the sample containing the magnetic material, and a hysteresis loop of the brightness value for each region of interest is obtained from a plurality of images acquired while sweeping the external magnetic field. A third step involves calculating the rotation angle of the Kerr rotation for each region of interest from an analysis using the device constants, the hysteresis loop at the first angle, and the hysteresis loop at the second angle. A field-of-view correction analysis method equipped with the following features.

8. In the first step described above, The analyzer rotates the polarizer within the predetermined range with respect to the crossed nicol configuration. The in-field correction analysis method according to claim 7.

9. In the first step described above, Using Malus's law, the polarization rotation angle distribution for each region of interest and the device constants including the squared distribution are calculated. The in-field correction analysis method according to claim 7 or 8.

10. In the first step described above, The aforementioned device constants include the luminance uniformity distribution, The apparatus constants, including the luminance unevenness distribution for each of the regions of interest, are calculated. The in-field correction analysis method according to any one of claims 7 to 9.

11. In the second step described above, The contrast, coercivity, and slope for each region of interest are calculated by fitting the hysteresis loop at the first angle and the hysteresis loop at the second angle to an empirical approximation function. The in-field correction analysis method according to any one of claims 7 to 10.

12. In step 3, Based on the first angle, the second angle, the luminance contrast at the first angle, and the luminance contrast at the second angle, the rotation angle for each area of ​​interest is calculated. The in-field correction analysis method according to claim 11.

Images