Method for determining surface map and imaging system for determining surface map

Abstract

The invention relates to a method for determining a surface map, such as a height map, of a sample surface having a first region and a second region, the first region having a first reflectance and the second region having a second reflectance. The invention also relates to an imaging system for determining a surface map of a sample surface having a first region and a second region, the first region having a first reflectance and the second region having a second reflectance. The invention also relates to a digital data carrier comprising a computer program which, when executed on a processor of an imaging system according to the invention, causes the imaging system to perform a method according to the invention.

Description

Technical Field

[0001] The present invention relates to a method for determining a surface map (e.g., a height map) of a sample surface having a first region and a second region, wherein the first region has a first reflectivity and the second region has a second reflectivity. The present invention also relates to an imaging system for determining a surface map of a sample surface having a first region and a second region, wherein the first region has a first reflectivity and the second region has a second reflectivity. The present invention also relates to a digital data carrier comprising a computer program which, when run on a processor of an imaging system according to the present invention, causes the imaging system to perform the method according to the present invention. Background Art

[0002] For example, inspections carried out at different stages of sample manufacturing may require determining a surface map of a sample surface. For example, the sample may be a semiconductor, and it may be important to monitor the development of structures thereon. In the semiconductor industry, inline structural examination of surface structures made of silicon and precious metals may be important for different stages of lithography and metal bonding.

[0003] Generally, the sample surface can be irradiated, for example, using a dedicated light source in an interferometer or using background light, and the light can be reflected by the sample surface and captured by an imaging system. The imaging system typically has a limited dynamic range, such that it may not be possible to effectively measure samples that reflect too much or too little light. To prevent the image of the sample surface captured by the imaging system from saturating (e.g., too much light 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 total integration time of the imaging system can be reduced. The disadvantage of this method is that when the sample surface has regions with different reflectivities, regions with lower reflectivities may not reflect enough light to allow for their proper measurement. Thus, for example, when the overall light intensity is high, some regions of the image (e.g., corresponding to regions of the sample surface with higher reflectivities) may be saturated, or some regions of the image (e.g., corresponding to regions of the sample surface with lower reflectivities) may be too dark. In other words, in the case of using known methods, depending on the measurement parameters, some parts (e.g., pixels) of the imaging system receive too much light or too little light and may not be able to capture a reliable image of the field of view of the imaging system. Summary of the Invention

[0004] The present invention aims to provide a method for determining a surface map of a sample surface with an increased effective dynamic range, i.e., such that a sample surface with a wider range of reflectivities can still be properly determined by an imaging system.

[0005] The object of the present invention is achieved by the method according to claim 1.

[0006] The method is a method for determining a surface map of a sample surface. For example, the surface map can be a height map of the sample surface. For example, the height map can be based on a phase map of the sample surface. The sample can be, for example, a semiconductor during a manufacturing process.

[0007] The sample surface has a first region and a second region, the first region having a first reflectivity and the second region having a second reflectivity. The first reflectivity is different from the second reflectivity. In an example, the sample surface can have a plurality of regions having different reflectivities. For example, the first region is the region with the lowest reflectivity and the second region is the region with the highest reflectivity. For example, the reflectivity difference between the first region and the second region can be the highest reflectivity difference between the regions of the sample surface. The different reflectivities can be the result of a material difference between the regions or the result of different orientations (e.g., slopes) of the surface relative to the imaging system.

[0008] The method uses an imaging system to determine or measure an image of the sample surface. The imaging system has a focus measurement plane. The image of the sample surface can include pixels of the imaging system, and the pixel values after measuring the light reflected from the sample surface allow the determination of the surface map. The imaging system can be an interferometer, such as a digital holographic interferometer, or other suitable type of imaging system. The focus measurement plane can be perpendicular to the optical axis of the imaging system. The focus measurement plane can be determined as the plane where the object is within the focus range of the imaging system.

[0009] The method includes: when the sample surface is arranged in the focus measurement plane of the imaging system (e.g., when the sample surface is within the focus range of the imaging system), determining that the image of the sample surface obtained by the imaging system is saturated. For example, the image of the sample surface can be taken with the imaging system (e.g., taken using measurement parameters such as the light intensity and integration time of the imaging system), and it can be observed or determined that one or more pixels of the imaging system are saturated. The sample surface can be arranged to be substantially aligned with and substantially at the focus measurement plane. Determining that the image of the sample surface obtained by the imaging system is saturated can be performed in various ways. For example, the determination can be based on a measurement of the light intensity of the light reflected from the sample surface using a presensor, i.e., no image of the sample surface is taken with the imaging system. The image of the sample surface can be taken using a computer program or a human observer, and the determination of saturation can be performed using a computer program or a human observer.

[0010] In response to determining that an image of a sample surface obtained with an imaging system is saturated when the sample surface is disposed in a focus measurement plane of the imaging system, the sample surface is disposed in an out-of-focus position at 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 with the imaging system is no longer saturated. By disposing the sample surface in the out-of-focus position, the image obtained with the imaging system may be out of focus. Thus, the image obtained with the imaging system is blurred in the case where the sample surface is out of focus, such that brighter and darker regions are mixed. This results in a relative increase in the light intensity in the darker regions of the image and a relative decrease in the light intensity in the brighter regions of the image depending on the out-of-focus distance Z at which the sample surface is disposed. By providing the sample surface further away from the focus measurement plane, more mixing between the brighter and darker regions can occur, and the brightest regions (i.e., regions with higher reflectivity) may appear darker in the out-of-focus image. By moving the sample surface sufficiently out of focus, the image may no longer be saturated because the saturated regions may have been sufficiently mixed with the darker regions.

[0011] The distance Z can be determined by gradually moving the image away from the focus measurement plane and observing the effect on the saturation of the obtained image or the reflected light intensity determined with a front sensor. The distance Z can also be determined using calculations, for example, based on the reflectivity and light intensity of the sample surface.

[0012] The imaging system can include a sample holder that is movable relative to the focus measurement plane such that the sample surface can be disposed at a desired distance Z by moving the sample holder.

[0013] The method includes obtaining an out-of-focus image of the sample surface with the imaging system when the sample surface is disposed in an out-of-focus position (e.g., at a desired distance Z from the focus measurement plane). The out-of-focus image can include information about the amplitude and phase of the light reflected from the sample surface (e.g., for each pixel of the imaging system). According to embodiments disclosed herein, the out-of-focus image can be obtained by the imaging system and subsequently provided to a processor for further processing.

[0014] Based on a defocused image, a focused image is determined by applying a backpropagation algorithm to the defocused image to backpropagate the defocused image by a distance Z. For example, the backpropagation algorithm can use the defocus phase and defocus amplitude of each pixel of the defocused image to determine the focus phase and / or amplitude of the focused image. The distance Z can be an explicit input to the backpropagation algorithm. As a result, the focused image can have pixel values outside the dynamic range of the imaging system. Thus, this method allows for the determination of an image of a sample surface having an effective dynamic range greater than the dynamic range of the imaging system. For example, the backpropagation algorithm can be a numerical propagation algorithm such as an angular spectrum algorithm or a Fresnel propagation algorithm.

[0015] This allows for the determination of a surface map of a sample surface having different reflectivities, otherwise at least some regions of the image would saturate or be too dark. For example, the surface map can be a height map of the sample surface, such as a height map based on the focus phase of the sample surface. The surface map can also be directly represented by the focused image.

[0016] In an embodiment of the method, the imaging system is configured to determine the phase and amplitude of an image of a sample surface, wherein obtaining the defocused image includes determining the defocus phase and defocus amplitude of the defocused image, and wherein the backpropagation algorithm is based on the determined defocus phase and the determined defocus amplitude of the defocused image. For example, the defocus phase and / or amplitude can be determined based on a carrier fringe method, a phase-shift method, a heterodyne method, or a method based on Lissajous phase extraction.

[0017] In an embodiment, the imaging system is an interferometer including a light source, and wherein the defocused image is a defocused interferogram, wherein the focused image is a focused interferogram, and wherein the surface map is a height map, such as a height map based on a phase map of the sample surface. For example, the interferometer can include:

[0018] A light source for emitting a light beam;

[0019] A beam splitter for splitting the light beam into a reference beam propagating along a reference path and a sample beam propagating along a sample path;

[0020] An optical sensor having a focal measurement plane;

[0021] A reference mirror for reflecting the reference beam towards the imaging system;

[0022] A sample holder for holding the sample, wherein the sample holder is movable relative to the optical sensor in a direction parallel to the sample path, for example, wherein the sample holder includes a component for moving the sample holder relative to the imaging system in a direction parallel to the sample path; and

[0023] A processor connected to an imaging system.

[0024] In a further embodiment, the method further comprises:

[0025] Determining an average intensity of a sample beam reflected from the sample surface; and

[0026] Providing a reference surface such that an average intensity of a reflected reference beam is equal to the average intensity of the reflected sample beam.

[0027] In a further embodiment, the interferometer is a digital holographic interferometer.

[0028] In an embodiment, the distance Z depends on a reflectivity difference between a first reflectivity and a second reflectivity, e.g., such that the distance Z is greater for a larger reflectivity difference and smaller for a smaller reflectivity difference. If other relevant parameters (e.g., such as incident light intensity, reflection region size, and imaging system characteristics) are the same or similar, the distance Z can be greater for a larger reflectivity difference and smaller for a smaller reflectivity distance. As a result, the distance Z can be determined by determining the reflectivity difference between the first region and the second region and, e.g., based on a single image of the sample surface taken by the imaging system.

[0029] In an embodiment, the distance Z depends on the dynamic range of the imaging system such that if the dynamic range is smaller, the distance Z is greater, and such that if the dynamic range is larger, the distance Z is smaller. For example, the distance Z in these embodiments can be determined based on the dynamic range of the imaging system. For example, an approximate distance Z can be determined based on the dynamic range of the imaging system and, e.g., other parameters such as the reflectivity difference and the incident light intensity.

[0030] In an embodiment, the distance Z is such that a difference between a highest intensity and a lowest intensity of a defocused image is below a predetermined intensity threshold, e.g., for a predetermined beam intensity. For example, the predetermined intensity threshold can depend on the dynamic range of the imaging system.

[0031] In an embodiment, the backpropagation algorithm is one of an angular spectrum algorithm and a Fresnel propagation algorithm.

[0032] In an embodiment, a surface map is determined from a focused image using one of a carrier fringe method, a phase shift method, a heterodyne method, and a Lissajous phase extraction method.

[0033] The present invention also relates to an imaging system for determining a surface map of a sample surface having a first region and a second region, the first region having a first reflectivity and the second region having a second reflectivity, wherein the imaging system comprises a processor, and wherein the imaging system is configured to determine an image of the sample surface, wherein the imaging system has a focus measurement plane, and wherein the imaging system (e.g., its processor) is configured to:

[0034] When the sample surface is disposed in the focal measurement plane of the imaging system, it is determined that the image of the sample surface obtained with the imaging system is saturated;

[0035] Along an axis perpendicular to the focal measurement plane, the sample surface is disposed (e.g., using a movable sample holder) in a defocused position at a distance Z from the focal measurement plane of the imaging system such that the image of the sample surface obtained with the imaging system is no longer saturated;

[0036] An out-of-focus image of the sample surface disposed in the defocused position is obtained;

[0037] A focused image is determined by applying a backpropagation algorithm to the out-of-focus image to backpropagate the out-of-focus image a distance Z; and

[0038] A surface map of the sample surface is determined based on the focused image.

[0039] The imaging system of the present invention can be used to perform the method of the present invention. The imaging system allows increasing its effective dynamic range, e.g., the effective dynamic range of its optical sensor, by performing measurements of the sample surface at a distance Z and obtaining a focused image using a backpropagation algorithm.

[0040] In an embodiment of the imaging system, the imaging system (e.g., its processor) is configured to determine the phase and amplitude of the image of the sample surface, and wherein the backpropagation algorithm is based on the defocused phase and defocused amplitude of the out-of-focus image.

[0041] In an embodiment of the imaging system, the imaging system is an interferometer, e.g., a digital holographic interferometer, e.g., the interferometer described herein, which includes a light source, and wherein the out-of-focus image is an out-of-focus interferogram, wherein the focused image is a focused interferogram, and wherein the surface map is a height map.

[0042] The present invention further relates to a digital data carrier comprising a computer program which, when run on a processor of an imaging system according to the present invention, causes the imaging system to perform the method according to the present invention. Description of the Drawings

[0043] Embodiments of the present invention will now be described by way of example with reference to the drawings, in which corresponding reference numerals indicate corresponding parts, and wherein:

[0044] Figure 1 An imaging system is shown; and

[0045] Figure 2 A flowchart of a method for determining a surface map is shown. Detailed Description

[0046] Figure 1Shows an imaging system 1 embodied as an interferometer, which includes a light source 4, an optical sensor 5, and a reference surface 6. The imaging system 1 also includes a movable sample holder 7 for holding the sample 2 and allowing the sample 2 to move in a direction perpendicular to the focal measurement plane 3 relative to the focal measurement plane 3.

[0047] In Figure 1 , the sample surface is at a distance Z from the focal measurement plane 3, such that even if the sample surface were in the focal measurement plane 3 the image would saturate, the defocused image taken from the sample surface with the optical sensor 5 is not saturated.

[0048] The sample 2 has a first region 2a and a second region 2b, the first region 2a having a first reflectivity and the second region 2b having a second reflectivity. The difference in reflectivities may cause the incident light from the light source 4 reflected from the first region 2a to saturate the optical sensor 5, while at the same time the incident light reflected from the second region 2b is too little to allow an appropriate determination of the surface map of the sample surface.

[0049] The imaging system 1 includes an optical sensor 4 that emits a light beam, the light beam being split by a beam splitter into a reference beam and a sample beam, the reference beam being reflected from the reference surface 6 to the optical sensor 5 and the sample beam being reflected from the sample 2 to the optical sensor 5. The interference of the two beams produces an interference pattern that allows the determination of the phase and / or amplitude of the light reflected from the sample 2.

[0050] The imaging system is configured to perform Figure 2 the method of the present invention as shown:

[0051] When the sample surface is arranged in the focal measurement plane of the imaging system, determine 101 that the image of the sample surface obtained with the imaging system is saturated;

[0052] Along an axis perpendicular to the focal measurement plane, arrange 102 the sample surface at a defocused position at a distance Z from the focal measurement plane of the imaging system, such that the image of the sample surface obtained with the imaging system is no longer saturated;

[0053] Obtain 103 a defocused image of the sample surface arranged at the defocused position with the imaging system;

[0054] Determine 104 the focused image by applying a backpropagation algorithm to the defocused image to backpropagate the defocused image a distance Z; and

[0055] Determine 105 the surface map of the sample surface based on the focused image.

[0056] As described above, in the case of using known methods, the present invention allows to determine the surface map of a sample 2 having a first region 2a and a second region 2b with different reflectivities, and this surface map would be impaired by a saturated image of the sample 2 or by too little light collected by the imaging system 1. This is done by placing the sample 2 at a distance Z from the focal measurement plane 3 of the imaging system 1 such that the resulting defocused image of the sample 2 is not saturated because the brighter regions can blend with the darker regions of the sample 2. By subsequently applying a backpropagation algorithm to the defocused image, a focused image of the sample 2 can be determined, and this focused image can have regions outside the dynamic range of the imaging system 1.

[0057] In an embodiment, the average intensity of the sample beam reflected by the sample 2 can be determined, and a reference surface 6 (e.g., a mirror with a desired reflectivity) can be provided such that the average intensity of the reference beam is substantially equal to the average intensity of the reflected sample beam.

[0058] The distance Z of the sample 2 from the focal measurement plane 3 can depend on one or more of the following: the light intensity emitted by the light source 4, the reflectivity of the first region 2a, the reflectivity of the second region 2b, the reflectivity difference between the first region 2a and the second region 2b, and the dynamic range of the imaging system 1. The sample surface is arranged at the distance Z such that, for example, according to one or more of the above parameters, the defocused image is not saturated. This allows backpropagating the defocused image to a focused image (e.g., outside the dynamic range of the imaging system 1), such that it can be said that the effective dynamic range of the imaging system 1 is increased.

Claims

1. A method for determining a surface map of a sample surface, the sample surface having a first region and a second region, the first region having a first reflectivity and the second region having a second reflectivity, wherein, The first reflectivity is different from the second reflectivity, wherein an imaging system for determining an image of the sample surface is used, wherein the imaging system has a focus measurement plane, and wherein the method includes: Determining that an image of the sample surface obtained with the imaging system is saturated when the sample surface is disposed in the focus measurement plane of the imaging system; Disposing the sample surface in a defocused position at 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 with the imaging system is no longer saturated; Obtaining a defocused image of the sample surface disposed in the defocused position with the imaging system; Determining a focused image by applying a backpropagation algorithm to the defocused image to backpropagate the defocused image the distance Z; and Determining the surface map of the sample surface based on the focused image.

2. The method according to claim 1, wherein The imaging system is configured to determine the phase and amplitude of the image of the sample surface, wherein obtaining the defocused image includes determining the defocused phase and defocused amplitude of the defocused image, and wherein the backpropagation algorithm is based on the determined defocused phase and determined defocused amplitude of the defocused image.

3. The method according to one or more of the preceding claims, wherein, The imaging system is an interferometer including a light source, and wherein the defocused image is a defocused interferogram, wherein the focused image is a focused interferogram, and wherein the surface map is a height map, the height map being based, for example, on a phase map of the sample surface.

4. The method according to claim 3, wherein, The method further includes: Determining an average intensity of a sample beam reflected from the sample surface; and Providing a reference surface such that an average intensity of a reflected reference beam is equal to the average intensity of the reflected sample beam.

5. The method according to one or more of claims 3-4, wherein, The interferometer is a digital holographic interferometer.

6. The method according to one or more of the preceding claims, wherein, The distance Z depends on a reflectivity difference between the first reflectivity and the second reflectivity, such that the distance Z is greater for a larger reflectivity difference and smaller for a smaller reflectivity difference.

7. The method according to one or more of the preceding claims, wherein, The distance Z depends on a dynamic range of the imaging system such that if the dynamic range is smaller, the distance Z is greater, and if the dynamic range is larger, the distance Z is smaller.

8. The method according to one or more of the preceding claims, wherein, The distance Z is such that a difference between a highest intensity and a lowest intensity of the defocused image is below a predetermined intensity threshold, for example, for a predetermined beam intensity.

9. The method according to one or more of the preceding claims, wherein, The backpropagation algorithm is one of an angular spectrum algorithm and a Fresnel propagation algorithm.

10. The method according to one or more of the preceding claims, wherein, The surface map is determined from the in-focus image using one of a carrier fringe method, a phase-shifting method, a heterodyne method, and a Lissajous phase extraction method.

11. An imaging system for determining a surface map of a sample surface, the sample surface having a first region and a second region, the first region having a first reflectivity and the second region having a second reflectivity, wherein, The imaging system includes a processor, and wherein the imaging system is configured to determine an image of the sample surface, wherein the imaging system has a focus measurement plane, and wherein the imaging system, for example, its processor, is configured to: Determine that an image of the sample surface obtained with the imaging system is saturated when the sample surface is disposed in the focus measurement plane of the imaging system; The sample surface is arranged at a defocused position at 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 with the imaging system is no longer saturated; Obtain a defocused image of the sample surface arranged at the defocused position; Determine a focused image by applying a backpropagation algorithm to the defocused image to backpropagate the defocused image by the distance Z; and Determine the surface map of the sample surface based on the focused image.

12. The imaging system according to claim 11, wherein, The imaging system, such as its processor, is configured to determine the phase and amplitude of the image of the sample surface, and wherein the backpropagation algorithm is based on the defocused phase and defocused amplitude of the defocused image.

13. The imaging system according to one or more of claims 11-12, wherein, The imaging system is an interferometer including a light source, such as a digital holographic interferometer, and wherein the defocused image is a defocused interferogram, wherein the focused image is a focused interferogram, and wherein the surface map is a height map.

14. A digital data carrier comprising a computer program which, when run on a processor of an imaging system according to one or more of claims 9 - 13, causes the imaging system to perform the method according to one or more of claims 1 - 8.

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