Method for determining surface map and imaging system therefor
By positioning the sample surface at a defocused distance and using a backpropagation algorithm, the method enhances the effective dynamic range of imaging systems to accurately capture samples with varying reflectivities.
Patent Information
- Application Number
- JP2024202688
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2024-01-29
- Filing Date
- 2024-11-20
- Publication Date
- 2025-08-08
AI Technical Summary
Imaging systems have a limited dynamic range, leading to saturation or insufficient light reception in regions of different reflectivity, making it impossible to take reliable images of samples with varying reflectance.
Position the sample surface at a defocused position relative to the imaging system's focus measurement plane to acquire a defocused image, then apply a backpropagation algorithm to convert the defocused image into a focused image with an increased effective dynamic range.
Enables determination of a surface map with a wider range of reflectances by blending bright and dark regions, overcoming saturation and insufficient light issues in imaging systems.
Smart Images
Figure 2025116812000001_ABST
Abstract
Description
Summary of the Invention
[0001] The present invention relates to a method for determining a surface map, e.g., a height map, of a surface of a sample having a first region with a first reflectivity and a second region with a second reflectivity.
[0002] The present invention further relates to an imaging system for determining a surface map of a sample surface having a first region with a first reflectivity and a second region with a second reflectivity. The present invention also relates to a digital data storage medium containing a computer program that, when executed on a processor of the imaging system according to the present invention, causes the imaging system to perform the method according to the present invention. Determining a surface map of a sample surface may be required, for example, for inspection at different stages of the sample's manufacturing. For example, the sample may be a semiconductor, and it may be important to monitor the growth of structures thereon. In the semiconductor industry, in-line structural inspection of surface structures made of silicon and precious metals may be important for different stages of lithography and metal bonding.
[0003] In general, the sample surface may be illuminated, for example, using a dedicated light source in an interferometer or using background light, and the light may be reflected by the sample surface and captured by an imaging system.
[0004] Imaging systems generally have a limited dynamic range so that samples that reflect too much or too little light cannot be effectively measured.
[0005] To prevent the image of the sample surface captured by the imaging system from becoming saturated, for example, to prevent excessive light from falling on the imaging system, e.g., its optical sensor, the intensity of the light projected onto the sample surface can be reduced. Equivalently, the overall integration time of the imaging system can be reduced. A drawback of this approach is that when the sample surface has regions of different reflectivity, the regions with lower reflectivity may not reflect enough light to allow for proper measurement thereof.
[0006] Thus, some regions of the image (e.g., regions corresponding to regions of the sample surface having higher reflectivity) may be saturated, for example, when the overall light intensity is higher, or some regions of the image (e.g., regions corresponding to regions of the sample surface having lower reflectivity) may be too dark. In other words, using known approaches, some parts of the imaging system, e.g., pixels, may receive too much or too little light depending on the measurement parameters, making it impossible to take a reliable image of the field of view of the imaging system.
[0007] The present invention aims to provide a method for determining a surface map of a sample surface that has an increased effective dynamic range, i.e., such that sample surfaces with a wider range of reflectances can still be adequately determined by the imaging system.
[0008] The object of the present invention is achieved by a method according to claim 1.
[0009] The method is for determining a surface map of a sample surface. For example, the surface map may be a height map of the sample surface. For example, the height map may be based on a phase map of the sample surface. The sample may be, for example, a semiconductor in a manufacturing process.
[0010] The sample surface has a first region having a first reflectance and a second region having a second reflectance. The first reflectance is different from the second reflectance. In an example, the sample surface may have multiple regions with different reflectances. For example, the first region may be the region with the lowest reflectance and the second region may be the region with the highest reflectance. For example, the difference in reflectance between the first and second regions may be the difference in the highest reflectance between regions of the sample surface.
[0011] The different reflectivities may be the result of material differences between the regions or different orientations, eg tilt, of the surface relative to the imaging system.
[0012] The method utilizes an imaging system to determine or measure an image of the sample surface.
[0013] The imaging system has a focus measurement plane. An image of the sample surface may include pixels of the imaging system, and the pixel values after measuring light reflected from the sample surface allow a surface map to be determined. The imaging system may be an interferometer, such as a digital holographic interferometer, or another type of suitable imaging system. The focus measurement plane may be perpendicular to the optical axis of the imaging system. The focus measurement plane may be determined to be the plane in which the object is at the focus of the imaging system.
[0014] The method includes determining that an image of the sample surface obtained by the imaging system is saturated when the sample surface is positioned within a focal measurement plane of the imaging system (e.g., when the sample surface is at the focus of the imaging system). For example, an image of the sample surface may be taken with the imaging system using measurement parameters such as, for example, the light intensity and integration time of the imaging system, and one or more pixels of the imaging system may be observed or determined to be saturated.
[0015] The sample surface may be substantially aligned with and positioned substantially at the focus measurement plane. The determination of whether an image of the sample surface obtained using the imaging system is saturated may be performed in various ways. For example, the determination may be based on measuring the light intensity of light reflected from the sample surface using a pre-sensor, i.e., without capturing an image of the sample surface using the imaging system. An image of the sample surface may be captured, and an explicit determination of saturation may be made, for example, using a computer program or a human observer.
[0016] In response to determining that an image of the sample surface acquired by the imaging system is saturated when the sample surface is positioned within the focus measurement plane of the imaging system, the sample surface is positioned at a defocus position a distance Z from the focus measurement plane of the imaging system along an axis perpendicular to the focus measurement plane of the imaging system so that the image of the sample surface acquired by the imaging system is no longer saturated. By positioning the sample surface at a defocus position, the image acquired by the imaging system may be out of focus. As a result, an image acquired by the imaging system of an out-of-focus sample surface may be blurred, blending bright and dark regions. This results in a relative increase in light intensity in darker regions of the image and a relative decrease in light intensity in brighter regions of the image, depending on the distance Z by which the sample surface is positioned out of focus. By positioning the sample surface farther from the focus measurement plane, more blending between brighter and darker regions may occur, and the brightest regions, i.e., regions with higher reflectivity, may appear darker in the defocused image. By moving the sample surface sufficiently far from the focus, the saturated regions may be sufficiently blended with the darker regions so that the image may no longer be saturated.
[0017] The distance Z can be determined by gradually moving the image away from the focal measurement plane and observing the effect on the saturation of the resulting image or the reflected light intensity determined using a pre-sensor. The distance Z may also be determined using calculations, depending, for example, on the reflectivity and light intensity of the sample surface.
[0018] The imaging system includes a sample holder that is movable relative to the focus measurement plane, and the sample surface can be positioned at a desired distance Z by moving the sample holder.
[0019] The method includes acquiring a defocused image of the sample surface using an imaging system when the sample surface is positioned at a defocused position, e.g., a desired distance Z, from a focus measurement plane. The defocused image may include, e.g., for each pixel of the imaging system, information about the amplitude and phase of light reflected from the sample surface. The defocused image may be acquired by the imaging system and then provided to a processor for further processing according to embodiments disclosed herein.
[0020] A focused image is determined based on the defocused image by backpropagating the defocused image by a distance Z by applying a backpropagation algorithm to the defocused image. For example, the backpropagation algorithm can use the defocus phase and defocus amplitude of each pixel in the defocused image to determine the focus phase and / or focus amplitude for the defocused image. The distance Z may be an explicit input to the backpropagation algorithm. As a result, the focused image may have pixel values outside the dynamic range of the imaging system. Therefore, this method allows for determining an image of the sample surface with an effective dynamic range greater than the dynamic range of the imaging system. For example, the backpropagation algorithm may be a numerical propagation algorithm, such as an angular spectrum algorithm or a Fresnel propagation algorithm.
[0021] This allows for determining a surface map of sample surfaces with different reflectivities, otherwise at least some regions of the image would be saturated or too dark. For example, the surface map may be a height map of the sample surface, for example, based on the in-focus phase of the sample surface. The surface map may also be directly represented by the in-focus image.
[0022] In an embodiment of the method, the imaging system is configured to determine a phase and an amplitude of an image of the sample surface, and acquiring the defocused image includes determining a defocus phase and a defocus amplitude of the defocused image, and the backpropagation algorithm is based on the determined defocus phase and the determined defocus amplitude of the defocused image.
[0023] For example, the defocus phase and / or defocus amplitude may be determined based on a carrier fringe method, a phase shift method, a heterodyne method, or a method based on Lissajous phase extraction.
[0024] In an embodiment, the imaging system is an interferometer with a light source, the defocused image is a defocused interferogram, the focused image is a focused interferogram, and the surface map is, for example, a height map based on a phase map of the sample surface. For example, an interferometer a light source for emitting a light beam; a beam splitter that splits the light beam into a reference light beam propagating along a reference path and a sample light beam propagating along a sample path; an optical sensor having a focus measuring surface; a reference mirror for reflecting the reference light beam towards the imaging system; a sample holder for holding a sample, the sample holder being movable relative to the optical sensor in a direction parallel to the sample path, e.g., the sample holder including means for moving the sample holder relative to the imaging system in a direction parallel to the sample path; and a processor connected to the imaging system; may include:
[0025] In a further embodiment, the method further comprises determining an average intensity of the sample light beam reflected from the specimen surface, and providing a reference surface such that the average intensity of the reflected reference light beam is equal to the average intensity of the reflected sample light beam.
[0026] In a further embodiment, the interferometer is a digital holographic interferometer.
[0027] In an embodiment, distance Z depends on the reflectance difference between the first and second reflectances, such that distance Z is larger for larger reflectance differences and smaller for smaller reflectance differences. Distance Z can be larger for larger reflectance differences and smaller for smaller reflectance differences, provided that other relevant parameters, such as incident light intensity, reflective area size, and imaging system characteristics, are the same or similar. As a result, distance Z can be determined by determining the reflectance difference between the first and second areas, for example, based on a single image of the sample surface captured by an imaging system.
[0028] In embodiments, the distance Z depends on the dynamic range of the imaging system, such that when the dynamic range is small, the distance Z is large, and when the dynamic range is large, the distance Z is small. For example, the distance Z in these embodiments may be determined based on the dynamic range of the imaging system. For example, the approximate distance Z may be determined based on the dynamic range of the imaging system and other parameters, such as the reflectivity difference and the incident light intensity.
[0029] In an embodiment, the distance Z is such that the difference between the maximum intensity of the defocused image and the minimum intensity of the defocused image is below a predetermined intensity threshold, e.g., a predetermined light beam intensity. For example, the predetermined intensity threshold may depend on the dynamic range of the imaging system.
[0030] In an embodiment, the back propagation algorithm is one of an angular spectrum algorithm and a Fresnel propagation algorithm.
[0031] In an embodiment, the surface map is determined from the focused image using one of a carrier fringe method, a phase shifting method, a heterodyne method, and a Lissajous phase extraction method.
[0032] The present invention further relates to an imaging system for determining a surface map of a sample surface having a first region with a first reflectivity and a second region with a second reflectivity, the imaging system comprising a processor and configured to determine an image of the sample surface, the imaging system having a focus measurement plane, the imaging system, for example, the processor of the imaging system, being configured to perform the following steps: determining that an image of the sample surface obtained by the imaging system is saturated when the sample surface is positioned within a focal measurement plane of the imaging system; positioning the sample surface at a defocused position a distance Z from the focus measurement plane of the imaging system along an axis perpendicular to the focus measurement plane, e.g., using a movable sample holder, such that the image of the sample surface obtained by the imaging system is no longer saturated; acquiring a defocused image of a sample surface positioned at a defocused position; determining a focused image by backpropagating the defocused image by a distance Z by applying a backpropagation algorithm to the defocused image; and Determining a surface map of the sample surface based on the in-focus image.
[0033] The imaging system of the present invention can be used to implement the method of the present invention, which performs measurements of the sample surface at a distance Z and uses a back-propagation algorithm to acquire focused images, thereby increasing its effective dynamic range (e.g., the effective dynamic range of its optical sensor).
[0034] In an embodiment of the imaging system, the imaging system, for example a processor thereof, is configured to determine the phase and amplitude of an image of the sample surface, and the back-propagation algorithm is based on the defocus phase and defocus amplitude of the defocused image.
[0035] In an embodiment of the imaging system, the imaging system is an interferometer, e.g., a digital holographic interferometer, e.g., an interferometer as described herein, that includes a light source, the defocused image is a defocused interferogram, the focused image is a focused interferogram, and the surface map is a height map.
[0036] The invention further relates to a digital data storage medium comprising a computer program which, when executed on a processor of an imaging system according to the invention, causes the imaging system to carry out the method according to the invention.
[0037] Embodiments of the present invention will now be described, by way of example, with reference to the accompanying drawings in which corresponding reference symbols indicate corresponding parts and in which: [Brief explanation of the drawings]
[0038] [Figure 1] FIG. 1 illustrates an imaging system. [Figure 2] 1 shows a flowchart of a method for determining a surface map.
[0039] 1 shows an imaging system 1 embodied as an interferometer comprising a light source 4, an optical sensor 5 and a reference surface 6. The imaging system 1 further comprises a movable sample holder 7 for holding a sample 2 and enabling movement of the sample 2 relative to the focus measurement plane 3 in a direction perpendicular to the focus measurement plane 3.
[0040] In FIG. 1, the sample surface is at a distance Z from the focus measurement plane 3 so that a defocused image taken of the sample surface by the optical sensor 5 is not saturated even though the sample surface is in the focus measurement plane 3 .
[0041] The sample 2 has a first region 2a with a first reflectivity and a second region 2b with a second reflectivity, the difference in reflectivity being such that the incident light from the light source 4 reflected by the first region 2a saturates the optical sensor 5, while the incident light reflected by the second region 2b is too small to allow proper determination of a surface map of the sample surface.
[0042] The imaging system 1 comprises an optical sensor emitting a light beam that is split by a beam splitter into a reference light beam that reflects from a reference surface 6 to the optical sensor 5 and a sample light beam that reflects from the sample 2 to the optical sensor 5. The two light beams interfere to produce an interferogram that makes it possible to determine the phase and / or amplitude of the light reflected from the sample 2.
[0043] The imaging system is configured to perform the method of the present invention shown in FIG. 2: determining 101 that an image of the sample surface obtained by the imaging system is saturated when the sample surface is positioned within a focal measurement plane of the imaging system; step 102 of positioning the sample surface at a defocus position a distance Z from the focus measurement plane of the imaging system along an axis perpendicular to the focus measurement plane, such that the image of the sample surface obtained by the imaging system is no longer saturated; Step 103: acquiring a defocused image of the sample surface placed at the defocused position by the imaging system; determining 104 a focused image by backpropagating the defocused image by a distance Z by applying a backpropagation algorithm to the defocused image; and Step 105 of determining a surface map of the sample surface based on the in-focus image.
[0044] As explained above, the present invention makes it possible to determine a surface map of a sample 2 having first and second regions 2a and 2b with different reflectivities when the surface map using known methods would be corrupted either due to a saturated image of the sample 2 or due to too little light collected by the imaging system 1. This is done by positioning the sample 2 at a distance Z from the focus measurement plane 3 of the imaging system 1, so that the resulting defocused image of the sample 2 is not saturated, since brighter regions may blend with darker regions of the sample 2. Then, by applying a backpropagation algorithm to the defocused image, a focused image of the sample 2 can be determined, which may have regions that are outside the dynamic range of the imaging system 1.
[0045] In an embodiment, the average intensity of the sample light beam reflected by the sample 2 may be determined and the reference surface 6 may be provided, for example a mirror with a desired reflectivity, such that the average intensity of the reference light beam is substantially equal to the average intensity of the reflected sample light beam.
[0046] The distance Z of the sample 2 from the focal measurement plane 3 may depend on one or more of the light intensity emitted by the light source 4, the reflectivity of the first region 2a, the reflectivity of the second region 2b, the difference in reflectivity between the first region 2a and the second region 2b, and the dynamic range of the imaging system 1. The sample surface is positioned at a distance Z such that the defocused image does not saturate, e.g., depending on one or more of the parameters mentioned above. This allows the defocused image to be back-propagated to a focused image that is, for example, outside the dynamic range of the imaging system 1, and as a result, it can be said that the effective dynamic range of the imaging system 1 is increased.
Claims
1. 1. A method for determining a surface map of a sample surface having a first region with a first reflectivity and a second region with a second reflectivity, the method comprising: the first reflectance is different from the second reflectance, and an imaging system is used to determine an image of the sample surface; the imaging system has a focus measurement plane; The method comprises: determining that an image of the sample surface obtained by the imaging system is saturated when the sample surface is located in the focus measurement plane of the imaging system; positioning the sample surface at a defocused position a distance Z from the focus measurement plane of the imaging system along an axis perpendicular to the focus measurement plane such that an image of the sample surface obtained by the imaging system is no longer saturated; acquiring a defocused image of a sample surface placed at a defocused position by the imaging system; determining a focused image by backpropagating the defocused image a distance Z by applying a backpropagation algorithm to the defocused image; determining the surface map of the sample surface based on the focused image; A method comprising:
2. the imaging system is configured to determine the phase and amplitude of an image of a sample surface; acquiring the defocused image includes determining a defocus phase and a defocus amplitude of the defocused image; the back-propagation algorithm is based on the determined defocus phase and the determined defocus amplitude of the defocused image. The method of claim 1.
3. the imaging system is an interferometer including a light source; the defocused image is a defocused interferogram, the focused image is a focused interferogram; the surface map is a height map; 3. The method according to claim 1 or 2.
4. determining an average intensity of the sample light beam reflected from the sample surface; providing a reference surface such that the average intensity of the reflected reference light beam is equal to the average intensity of the reflected sample light beam; The method of claim 3.
5. the interferometer is a digital holographic interferometer; The method of claim 3.
6. The distance Z depends on the reflectance difference between the first reflectance and the second reflectance.
3. The method according to claim 1 or 2.
7. the distance Z depends on the dynamic range of the imaging system such that the distance Z is large when the dynamic range of the imaging system is small, and the distance Z is small when the dynamic range is large.
3. The method according to claim 1 or 2.
8. the distance Z is such that the difference between the maximum intensity of the defocused image and the minimum intensity of the defocused image is below a predetermined intensity threshold.
3. The method according to claim 1 or 2.
9. the back propagation algorithm is one of an angular spectrum algorithm and a Fresnel propagation algorithm; 3. The method according to claim 1 or 2.
10. the surface map is determined from the focused image using one of a carrier fringe method, a phase shifting method, a heterodyne method, or a Lissajous phase extraction method; 3. The method according to claim 1 or 2.
11. 1. An imaging system for determining a surface map of a sample surface having a first region with a first reflectivity and a second region with a second reflectivity, comprising: the imaging system includes a processor; the imaging system is configured to determine an image of the sample surface; The imaging system has a focus measurement plane, and the processor determining that an image of the sample surface obtained by the imaging system is saturated when the sample surface is located in the focus measurement plane of the imaging system; positioning the sample surface at a defocused position a distance Z from the focus measurement plane of the imaging system along an axis perpendicular to the focus measurement plane such that an image of the sample surface obtained by the imaging system is no longer saturated; acquiring a defocused image of a sample surface disposed at a defocused position; determining a focused image by backpropagating the defocused image a distance Z by applying a backpropagation algorithm to the defocused image; determining the surface map of the sample surface based on the focused image; An imaging system configured to:
12. the processor is configured to determine the phase and amplitude of an image of the sample surface; the backpropagation algorithm is based on a defocus phase and a defocus amplitude of the defocused image; The imaging system according to claim 11 .
13. the imaging system is an interferometer including a light source; the defocused image is a defocused interferogram and the focused image is a focused interferogram; the surface map is a height map; The imaging system according to claim 11 or 12.
14. A computer program product that, when executed on a processor of an imaging system according to claim 9, causes the imaging system to carry out the method of claim 1.