X-ray dark-field in-line inspection for semiconductor samples

Abstract

An x-ray imaging/inspection system includes an x-ray source having a plurality of sub-sources in thermal communication with a substrate. The system further includes a first grating positioned to receive at least some of the x-rays from the x-ray source, a stage configured to hold a sample positioned to receive at least some of the x-rays from the x-ray source, at least one x-ray detector, and a second grating having periodic structures. The x-ray source, the first grating, and the second grating are configured such that a ratio of a pitch p.sub.0 of the plurality of sub-sources to a pitch p.sub.2 of the periodic structures of the second grating is substantially equal to a ratio of a distance d.sub.S-G1 between the plurality of sub-sources and the first grating and a distance d.sub.G1-G2 between the first grating and the second grating: (p.sub.0/p.sub.2)=(d.sub.S-G1/d.sub.G1-G2).

Claims

1. An x-ray imaging/inspection system comprising: an x-ray source comprising a plurality of sub-sources in thermal communication with a substrate and that are configured to emit x-rays when bombarded by electrons configured to generate x-rays by electron bombardment of the target material; a first grating positioned to receive at least some of the x-rays from the x-ray source, the first grating comprising periodic structures configured to absorb at least some of the x-rays received from the x-ray source; a stage configured to hold a sample positioned to receive at least some of the x-rays from the x-ray source, the sample configured to scatter and emit a first portion of the x-rays and to emit without scattering a second portion of the x-rays; at least one x-ray detector; and a second grating positioned to receive at least some of the first portion of the x-rays and at least some of the second portion of the x-rays, the second grating comprising periodic structures configured to substantially block transmission of the second portion of the x-rays from reaching the at least one x-ray detector while substantially allowing transmission of the first portion of the x-rays to the at least one x-ray detector, wherein the x-ray source, the first grating, and the second grating are configured such that a ratio of a pitch p.sub.0 of the plurality of sub-sources to a pitch p.sub.2 of the periodic structures of the second grating is substantially equal to a ratio of a distance d.sub.S-G1 between the plurality of sub-sources and the first grating and a distance d.sub.G1-G2 between the first grating and the second grating: (p.sub.0/p.sub.2)=(d.sub.S-G1/d.sub.G1-G2), wherein the second grating is positioned such that x-rays that directly propagate from the x-ray source and that are collimated by the first grating are substantially blocked by the second grating from reaching the at least one x-ray detector, while scattered x-rays from the sample are not substantially blocked by the second grating from reaching the at least one x-ray detector.

2. The x-ray imaging/inspection system of claim 1, wherein the plurality of sub-sources comprises one or more arrays of metal microstructures.

3. The x-ray imaging/inspection system of claim 2, wherein the microstructures comprise an atomic element selected from the group consisting of: W, Rh, Mo.

4. The x-ray imaging/inspection system of claim 2, wherein the substrate comprises diamond and the microstructures are on or embedded in the substrate.

5. The x-ray imaging/inspection system of claim 4, wherein the plurality of sub-sources further comprises a diffusion barrier between the microstructures and the substrate.

6. The x-ray imaging/inspection system of claim 1, wherein the first grating comprises an array of x-ray absorptive structures that is periodic in a single dimension or is periodic in two dimensions.

7. The x-ray imaging/inspection system of claim 6, wherein the array of x-ray absorptive structures is periodic in two dimensions and comprises a checkerboard, honeycomb, mesh, or grid of x-ray absorptive material.

8. The x-ray imaging/inspection system of claim 1, wherein the at least one detector comprises a spatially resolving detector.

9. The x-ray imaging/inspection system of claim 1, wherein the at least one detector comprises a non-spatially resolving detector.

10. The x-ray imaging/inspection system of claim 1, wherein the second grating comprises a second array of x-ray absorptive structures that is periodic in a single dimension or that is periodic in two dimensions.

11. The x-ray imaging/inspection system of claim 10, wherein the second array of x-ray absorptive structures is periodic in two dimensions and comprises a checkerboard, honeycomb, mesh, or grid of x-ray absorptive material.

12. The x-ray imaging/inspection system of claim 1, wherein the sample is positioned behind the first grating such that the sample receives at least some of the x-rays from the first grating and the second grating is positioned behind the sample to receive at least some of the first portion of the x-rays from the sample and at least some of the second portion of the x-rays from the sample.

13. The x-ray imaging/inspection system of claim 1, further comprises at least one mask positioned in front of the sample, the at least one mask comprising x-ray absorptive portions and x-ray transmissive portions, the x-ray transmissive portions corresponding to features of the sample under inspection, the x-ray absorptive portions configured to substantially prevent the x-rays from irradiating portions of the sample between the features under inspection.

14. The x-ray imaging/inspection system of claim 13, wherein the x-ray absorptive portions comprise an x-ray absorptive material and the x-ray transmissive portions comprise openings in the at least one mask.

15. The x-ray imaging/inspection system of claim 13, wherein the x-ray transmissive portions are in registry with features of the sample under inspection.

16. The x-ray imaging/inspection system of claim 1, wherein x-ray source, the first grating, and the second grating are configured such that a ratio of a distance d.sub.S-G1 between the x-ray source and the first grating and a spacing w.sub.0 between adjacent sub-sources of the plurality of sub-sources is greater than a pitch p.sub.1 of the first grating divided by a wavelength λ of the x-rays: (d.sub.S-G1/w.sub.0)>(p.sub.1/λ).

17. The x-ray imaging/inspection system of claim 1, wherein the x-ray source, the first grating, and the second grating satisfy the Lau condition but do not satisfy the Talbot condition.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIGS. 1A and 1B schematically illustrate an example system in accordance with certain implementations described herein.

(2) FIG. 1C schematically illustrates an example system comprising at least one mask in accordance with certain implementations described herein.

(3) FIGS. 2A-2C show an absorption image, a differential phase contrast image, and a dark-field image, respectively, of a portion of a semiconductor sample comprising a plurality of microbumps under inspection in accordance with certain implementations described herein.

DETAILED DESCRIPTION

(4) Current inspection techniques center around analyzing the x-ray absorption across a two-dimensional (2D) region of the sample. However, the sensitivity of such techniques to voids decreases rapidly for smaller voids because the x-ray absorption by a sample region comprising such smaller voids is only slightly less than the absorption by a sample region without such smaller voids. Three-dimensional (3D) x-ray inspection schemes have been posited, but they are too slow for 100% inspection and they increase the radiation dose applied to the sample, which can be problematic for NAND flash memory by introducing defects caused by the increased radiation. Some inspection schemes use laminography (a “2.5 dimensional” technique), which offers some improvements in sensitivity.

(5) X-ray dark-field (e.g., x-ray scattering) contrast is of interest because it is particularly sensitive to features (e.g., voids; cracks) with dimensions at the micron to submicron scale. X-ray dark-field contrast is fundamentally different than absorption contrast, which forms the basis of current x-ray imaging techniques and instead is based on measuring small angle x-ray scattering (SAXS). However, conventional SAXS is typically performed with systems that utilize long flight paths for collimation and that are not ideal for in-line semiconductor use.

(6) Talbot-Lau interferometry is another inspection technique that simultaneously acquires absorption, phase, and dark-field contrasts using grating-based interferometry. A standard Talbot-Lau interferometer uses a large extended x-ray source coupled to a G.sub.0 grating (e.g., source grating) having a 1:2 or 1:3 duty cycle, such that more than half of the x-rays produced by the x-ray source are absorbed by the absorptive struts of the G.sub.0 grating. The G.sub.0 grating effectively creates a linear or 2D array of periodic sub-sources of x-rays from the x-ray source that are transmitted through the G.sub.0 grating. A G.sub.1 grating (e.g., beam-splitting grating), which can be either an absorbing grating or a phase shifting grating, can be positioned downstream from the G.sub.0 grating to diffract the x-rays such that a Talbot carpet of x-rays is formed which irradiates the sample being inspected. A G.sub.2 grating (e.g., detector grating) can be typically positioned in front of (e.g., upstream from) a large pixel x-ray detector configured to detect the fringes of x-rays from the sample being inspected to determine absorption, phase, and dark-field (e.g., scattering) contrasts.

(7) Talbot-Lau interferometry utilizes configurations that satisfy at least the following two conditions: 1. Talbot (coherence) condition to form fringes: Coherence is related to the width (w.sub.0) of openings of the G.sub.0 grating divided by the distance d.sub.G0-G1 between the G.sub.0 grating and the G.sub.1 grating. Under the Talbot (coherence) condition, this quantity is smaller than the pitch p.sub.1 of the G.sub.1 grating divided by the wavelength λ of the x-ray energy: (d.sub.G0-G1×λ)/w.sub.0≅p.sub.1. 2. Lau condition: A geometric relation in which the ratio of the pitch (p.sub.0) of the G.sub.0 grating to the pitch p.sub.2 of the G.sub.2 grating is equivalent to the ratio of the distance d.sub.G0-G1 between the G.sub.0 grating and the G.sub.1 grating and the distance d.sub.G1-G2 between the G.sub.1 grating and the G.sub.2 grating: (p.sub.0/p.sub.2)=(d.sub.G0-G1/d.sub.G1-G2). When the Lau condition is satisfied, the Talbot fringes downstream of the G.sub.1 grating from an opening (e.g., micron-sized sub-source) of the G.sub.0 grating is shifted by exactly one period, and from the nth neighbor opening of the G.sub.0 grating is shifted by n number of periods. Therefore, the Talbot fringes from all the openings of the G.sub.0 grating completely overlap, which is an important innovation, attributed to Lau, that enables the use of large extended x-ray sources with a G.sub.0 grating.

(8) However, Talbot-Lau interferometry utilizes phase-stepping (e.g., relative motion of the G.sub.1 grating and the G.sub.2 grating) so that the Talbot fringes can be sampled multiple times (e.g., at least three times if not more), and the time needed for such phase-stepping can adversely increase the overall time of the inspection. In addition, the absorption and phase contrast of Talbot-Lau interferometry are not necessary for defect detection and inspection. Furthermore, the Talbot condition sets a minimum to the distance d.sub.G0-G1 between the G.sub.0 grating and the G.sub.1 grating, which can limit throughput.

(9) Certain implementations described herein advantageously provide a dark-field-only inspection (e.g., imaging) system for semiconductor samples (e.g., a system that does not utilize absorption or phase contrast). Certain implementations described herein satisfy only the Lau condition (e.g., do not satisfy the Talbot condition). Certain implementations described herein utilize at least first and second absorption gratings in a magnifying arrangement (e.g., as in a projection microscope) in which the second absorption grating blocks x-rays passed by the first absorption grating in the absence of a sample from reaching the x-ray detector. Small angle scattering (e.g., due to edges and/or interfaces within the sample) provide x-rays that pass through the openings of the second absorption grating to be detected by an area x-ray detector positioned downstream from the second absorption grating. In certain implementations, the sample is positioned between the first and second absorption gratings.

(10) FIGS. 1A and 1B schematically illustrate an example system 10 that utilizes only dark-field contrast and satisfies only the Lau condition in accordance with certain implementations described herein. The example system 10 comprises an x-ray source 20 comprising a plurality of sub-sources 22 (e.g., one or more arrays of metal microstructures) in thermal communication with a substrate 24 (e.g., embedded or on a diamond substrate) and that are configured to emit x-rays 26 when bombarded by electrons (not shown). Examples of x-ray sources 20 with a plurality of sub-sources 22 compatible with certain implementations described herein are disclosed (in conjunction with other systems different from those described herein) in U.S. Pat. Nos. 9,390,881; 9,448,190; 9,449,781; 9,570,265; 9,543,109; 9,594,036; 9,719,947; 9,823,203; 9,874,531; 10,269,528; 10,295,485; 10,297,359; 10,304,580; 10,349,908; 10,352,880; 10,401,309, each of which is incorporated in its entirety by reference herein. Such x-ray sources 20 do not utilize a G.sub.0 grating (e.g., source grating), which is different from conventional sources that combine a G.sub.0 grating with an extended x-ray source.

(11) The example system 10 further comprises a first grating 30 (e.g., “G.sub.1 grating”) positioned to receive at least some of the x-rays 26 from the x-ray source 20 (e.g., positioned downstream from the x-ray source 20), the first grating 30 comprising periodic structures configured to absorb at least some of the x-rays 26 received from the x-ray source 20. For example, the first grating 30 comprises an array of x-ray absorptive structures 32 that is periodic in a single dimension (e.g. lines of x-ray absorptive material). For another example, the first grating 30 comprises an array of x-ray absorptive structures 32 that is periodic in two dimensions (e.g., checkerboard, honeycomb, mesh, or grid of x-ray absorptive material). Examples of a first grating 30 (e.g., “G.sub.1 grating”) with periodic structures 32 compatible with certain implementations described herein are disclosed (in conjunction with other systems different from those described herein) in U.S. Pat. Nos. 9,719,947; 9,874,531; 10,304,580; 10,349,908; 10,352,880, each of which is incorporated in its entirety by reference herein.

(12) The example system 10 further comprises a stage 42 configured to hold a sample 40, the sample 40 positioned to receive at least some of the x-rays 26 from the x-ray source 20 (e.g., positioned downstream from the x-ray source 20). The sample 40 is configured to scatter and emit a first portion 44 of the x-rays 26 and to emit without scattering (e.g., transmit) a second portion 46 of the x-rays 26. Examples of a stage 42 compatible with certain implementations described herein are disclosed (in conjunction with other systems different from those described herein) in U.S. Pat. Nos. 9,719,947; 9,874,531; 10,349,908; 10,352,880, each of which is incorporated in its entirety by reference herein.

(13) The example system 10 further comprises a second grating 50 (e.g., “G.sub.2 grating” or “G.sub.D grating”) positioned to receive at least some of the first portion 44 of the x-rays 26 and at least some of the second portion 46 of the x-rays 26 (e.g., downstream from the sample 40). The example system 10 further comprises at least one x-ray detector 60 positioned to receive at least some of the first portion 44 of the x-rays from the second grating 50 (e.g., positioned downstream from the second grating 50). For example, the at least one detector 60 can comprise a spatially resolving detector (e.g., CCD or linear sensitivity detector). For another example, the at least one detector 60 can comprise a non-spatially resolving detector that simply measures the amount of scattered x-rays and is configured to monitor only changes in the dark-field scattered signal as an inspection technique. Examples of detectors 60 compatible with certain implementations described herein are disclosed (in conjunction with other systems different from those described herein) in U.S. Pat. Nos. 9,719,947; 9,874,531; 10,349,908; 10,352,880, each of which is incorporated in its entirety by reference herein.

(14) As schematically illustrated by FIG. 1B, the second grating 50 comprises periodic structures configured to substantially block transmission of the second portion 46 of the x-rays 26 from reaching the at least one x-ray detector 60 while substantially allowing transmission of the first portion 44 of the x-rays 26 to the at least one x-ray detector 60. For example, the second grating 50 comprises an array of x-ray absorptive structures 52 that is periodic in a single dimension (e.g. lines of x-ray absorptive material). For another example, the second grating 50 comprises an array of x-ray absorptive structures 52 that is periodic in two dimensions (e.g., checkerboard, honeycomb, mesh, or grid of x-ray absorptive material). Examples of a second grating 50 (e.g., “G.sub.2 grating” or “G.sub.D grating”) with periodic structures 32 compatible with certain implementations described herein are disclosed (in conjunction with other systems different from those described herein) in U.S. Pat. Nos. 9,719,947; 9,874,531; 10,304,580; 10,349,908; 10,352,880, each of which is incorporated in its entirety by reference herein.

(15) In certain implementations, the example system 10 is configured to meet the Lau condition in which the ratio of the pitch p.sub.0 of the plurality of sub-sources 22 to the pitch p.sub.2 of the array of x-ray absorptive structures 52 of the second grating 50 (e.g., G.sub.2 grating) is substantially equal to the ratio of the distance d.sub.S-G1 between the plurality of sub-sources 22 of the x-ray source 20 and the first grating 30 (e.g., G.sub.1 grating) and the distance d.sub.G1-G2 between the first grating 30 (e.g., G.sub.1 grating) and the second grating 50 (e.g., G.sub.2 grating): (p.sub.0/p.sub.2)=(d.sub.S-G1/d.sub.G1-G2). In addition, the second grating 50 of certain implementations is positioned such that x-rays 26 that directly propagate from the x-ray source 20 and that are collimated by the first grating 30 are substantially blocked by the second grating 50 from reaching the at least one x-ray detector 60, while scattered x-rays 26 are not substantially blocked by the second grating 50 from reaching the at least one x-ray detector 60.

(16) In certain other implementations, as schematically illustrated by FIGS. 1A and 1B, the sample 40 is positioned behind (e.g., downstream from) the first grating 30 such that the sample 40 receives at least some of the x-rays 26 from (e.g., transmitted through) the first grating 30 and the second grating 50 is positioned behind (e.g., downstream from) the sample 40 to receive at least some of the first portion 44 of the x-rays 26 from the sample 40 and at least some of the second portion 46 of the x-rays 26 from the sample 40 (e.g., positioned downstream from the sample 40). Certain such implementations can be advantageous by protecting the sample 40 from being exposed to an unnecessary dose of x-rays. In certain implementations, the distance between the first grating 30 and the sample 40 and the distance between the second grating 50 and the at least one x-ray detector 60 are selected to be as small as practical as other operative constraints (e.g., compatibility for use in inspection of samples 40 while on a production/fabrication line) will allow. For example, for two-dimensional imaging, the distance between the first grating 30 and the sample 40 can be less than 10 mm. In certain implementations, the distance between the second grating 50 and the at least one x-ray detector 60 is selected to minimize the overall length of the system 10 (e.g., to provide a more compact form factor).

(17) Sensitivity to larger voids can be increased in certain implementations by using larger distances between the sample 40 and the at least one x-ray detector 60, since the minimum angle of small angle x-ray detection is directly proportional to the opening width of the second grating 50 divided by the distance between the first grating 30 and the second grating 50. However, since increasing geometric magnification can reduce sensitivity due to smearing and can result in larger form factors, certain implementations limit the geometric magnification. For example, the geometric magnification of the sample 40 can be in the range of four to six and can be configured to improve sensitivity to larger voids (which have smaller scattering) and to use larger pixel sizes.

(18) In certain implementations, the x-ray source 20, the first grating 30, and the second grating 50 are configured to satisfy the Lau condition, such that a ratio of a pitch p.sub.0 of the plurality of sub-sources 22 to a pitch p.sub.2 of the periodic structures 52 of the second grating 50 is substantially equal to a ratio of a distance d.sub.S-G1 between the plurality of sub-sources 22 and the first grating 30 and a distance d.sub.G1-G2 between the first grating 30 and the second grating 50: (p.sub.0/p.sub.2)=(d.sub.S-G1/d.sub.G1-G2). In certain such implementations, the x-ray source 20, the first grating 30, and the second grating 50 are further configured to not satisfy the Talbot condition, such that a ratio of a distance d.sub.S-G1 between the x-ray source 20 and the first grating 30 and a spacing w.sub.0 between adjacent sub-sources 22 of the plurality of sub-sources 22 is greater than a pitch p.sub.1 of the first grating 30 divided by a wavelength λ of the x-rays 26: (d.sub.S-G1/w.sub.0)>(p.sub.1/λ). In certain implementations, the x-ray source 20, the first grating 30, and the second grating 50 are further configured such that the distance between the first grating 30 and the sample 40 is small to maximize throughput (e.g., d.sub.S-G1 is in a range of less than 3 mm or in a range of less than 50 mm).

(19) In certain implementations, as schematically illustrated by FIG. 1C, the system 10 comprises at least one mask 70 positioned in front of (e.g., upstream from) the sample 40. The at least one mask 70 comprises x-ray absorptive portions 72 (e.g., x-ray absorptive material) and x-ray transmissive portions 74 (e.g., openings), the x-ray transmissive portions 74 corresponding to (e.g., in registry with) the features of the sample 40 (e.g., vias; microbumps) under inspection. By substantially preventing x-rays from irradiating portions of the sample 40 between the features under inspection, and which would otherwise not contribute useful signal but would add to the radiation dosage received by the sample 40, certain implementations utilizing the at least one mask 70 advantageously reduce the background x-ray signal received by the at least one x-ray detector 60. Certain implementations utilizing the at least one mask 70 can advantageously improve image resolution by reducing (e.g., avoiding) photoelectron creation in regions of the x-ray detector 60 that do not correspond to the features under inspection and having these photoelectrons “bleed through” to the regions that do correspond to the features under inspection, with such photoelectrons reducing image resolution by contributing to the blurriness of the images. Certain implementations utilizing the at least one mask 70 advantageously protect the sample 40 from unnecessary x-ray dosage which could otherwise cause damage to the sample 40.

(20) In certain implementations, only a relatively small fraction of the area of the at least one x-ray detector 60 receives scattered x-rays that are transmitted through the second grating 50. In certain such implementations, the x-ray source 20 can be configured to be controllably moved (e.g., in a direction parallel to a surface of the substrate 24) such that different regions of the at least one x-ray detector 60 receive the scattered x-rays (e.g., making use of parallax). In certain implementations, the x-ray detector 60 is not an imaging detector but is configured to provide information regarding the scattered x-rays corresponding to the features under inspection.

(21) In certain implementations in which the sample 40 is moving during the inspection process (e.g., while the sample 40 travels along a production line), the x-ray source 20, the first and second gratings 30, 50, and the at least one mask 70 (for systems 10 comprising at least one mask 70) can be configured to be controllably moved along with the moving sample 40 to maintain the desired configuration. Alignment of the various components can be assured by using appropriate fiducials and servo-controlled alignment aids. In certain implementations, the sample 40 is rotated to acquire three-dimensional dark-field images.

(22) Parameters of Example Implementations

(23) In certain implementations, the x-ray source 20 comprises a plurality of sub-sources 22 that comprise microstructures that comprise tungsten, rhodium, molybdenum, or other high-Z elements. In certain implementations, the microstructures comprise a diffusion barrier between the microstructures and the substrate 24 (e.g., diamond).

(24) In certain implementations, the x-rays 26 generated by the x-ray source 20 have a mean x-ray energy in a range of 20 keV to 30 keV, in a range of 30 keV to 50 keV, or in a range of 50 keV to 80 keV. The x-ray source 20 of certain implementations can comprise a filter configured to remove x-rays having energies below a predetermined value. In certain implementations, the substrate 24 is on a window (e.g., diamond window; beryllium window) at least partially bounding a vacuum region within the x-ray source 20 from a non-vacuum region outside the x-ray source 20. In certain other implementations, the substrate 24 is within an x-ray tube in a reflection geometry with the window (e.g., diamond window; beryllium window).

(25) In certain implementations, the sub-sources 22 have a size (e.g., lateral dimension along a direction parallel to a surface of the substrate 24) in a range of 0.3 micron to 1 micron, in a range of 1 micron to 3 microns, or in a range of 3 microns to 10 microns. In certain implementations, the pitch p.sub.0 is in a range that is comparable to the range of sizes of the sub-sources 22 (e.g., the pitch p.sub.0 is in a range of 0.3 micron to 1 micron, in a range of 1 micron to 3 microns, or in a range of 3 microns to 10 microns). In certain implementations, a ratio of the size of the sub-sources 22 to the size of the space between adjacent sub-sources 22 is in a range of 1:1 to 1:2 or in a range of 1:2 to 1:3 (e.g., the ratio can be substantially equal to 1:3).

(26) In certain implementations, the pitch p.sub.1 for the first grating 30 (e.g., distance from a position on a first x-ray absorptive structure 32a to the equivalent position on a second x-ray absorptive structure 32b adjacent to the first x-ray absorptive structures 32a) can be in a range of 0.3 micron to 1 micron, in a range of 1 micron to 3 microns, in a range of 3 microns to 10 microns, or in a range of 10 microns to 50 microns. In certain implementations, the x-ray absorptive structures 32 of the first grating 30 are configured to block the spaces between adjacent x-ray absorptive structures 52 of the second grating 50 in a projection geometry. In certain such implementations, the first grating 30 has a first ratio of open to blocked areas and the second grating 50 has a second ratio of open to blocked areas that is larger than or equal to the first ratio (e.g., the first ratio equal to 1:1 and the second ratio in a range of 1:1 to 1:0.9 or in a range of 1:1 to 1:0.7). In certain implementations, the pitch p.sub.2 for the second grating 50 (e.g., distance from a position on a first x-ray absorptive structure 52a to the equivalent position on a second x-ray absorptive structure 52b adjacent to the first x-ray absorptive structures 52a) can be in a range of 1 micron to 10 microns, in a range of 10 microns to 40 microns, in a range of 40 microns to 60 microns, in a range of 60 microns to 80 microns, or in a range of 80 microns to 200 microns. In certain implementations, the pitch p.sub.2 is substantially equal to the pitch p.sub.1 multiplied by (d.sub.S-G2/d.sub.S-G1), where d.sub.S-G2 is the distance between the sub-sources 22 and the second grating 50 and d.sub.S-G1 is the distance between the sub-sources 22 and the first grating 30.

(27) In certain implementations, the distance d.sub.S-G1 between the sub-sources 22 of the x-ray source 20 and the first grating 30 is in a range of 2 mm to 4 mm, in a range of 4 mm to 10 mm, in a range of 10 mm to 30 mm, in a range of 30 mm to 100 mm, or in a range of 100 mm to 500 mm. In certain implementations, the distance d.sub.G1-G2 between the first grating 30 and the second grating 50 is in a range of 30 mm to 100 mm, in a range of 100 mm to 500 mm, or in a range of 500 mm to 1500 mm.

(28) In certain implementations, the system 10 is configured to be used for inspection for defects in semiconductor packaging or other two-dimensional samples (e.g., as the samples are processed along the production line). In certain implementations, the system 10 is configured for dark-field imaging for medical use (e.g., clinical medical 2D x-ray). In certain implementations, the system 10 is configured to be used for laminography (e.g., 2.5D) in addition to 2D, or for dark-field tomography acquisition, or for three-dimensional imaging. For in-line semiconductor imaging implementations, the sample 40 can be placed on a conveyer belt such that a seconds-long dark-field image is obtained while the sample 40 is moving. For three-dimensional or laminography imaging implementations, the sample 40 can be placed in front of the first grating 30 (which is placed near the second grating 50 and the at least one x-ray detector 60) such that large samples 40 can be rotated. In certain implementations in which only small voids are of interest, the distance between the first grating 30 and the second grating 50 can be small and the overall size of the system 10 can be compact.

(29) FIGS. 2A-2C show an absorption image, a differential phase contrast image, and a dark-field image, respectively, of a portion of a semiconductor sample comprising a plurality of microbumps under inspection in accordance with certain implementations described herein. The dark-field image of FIG. 1C shows regions (e.g., “white spots”) at the centers of the microbumps that are indicative of voids. In addition, the dark-field images of certain implementations can show cracks and other features (e.g., substrate defects) that are not seen in conventional absorption imaging.

(30) Although commonly used terms are used to describe the systems and methods of certain implementations for ease of understanding, these terms are used herein to have their broadest reasonable interpretations. Although various aspects of the disclosure are described with regard to illustrative examples and implementations, the disclosed examples and implementations should not be construed as limiting. Conditional language, such as “can,” “could,” “might,” or “may,” unless specifically stated otherwise, or otherwise understood within the context as used, is generally intended to convey that certain implementations include, while other implementations do not include, certain features, elements, and/or steps. Thus, such conditional language is not generally intended to imply that features, elements, and/or steps are in any way required for one or more implementations. In particular, the terms “comprises” and “comprising” should be interpreted as referring to elements, components, or steps in a non-exclusive manner, indicating that the referenced elements, components, or steps may be present, or utilized, or combined with other elements, components, or steps that are not expressly referenced.

(31) Conjunctive language such as the phrase “at least one of X, Y, and Z,” unless specifically stated otherwise, is to be understood within the context used in general to convey that an item, term, etc. may be either X, Y, or Z. Thus, such conjunctive language is not generally intended to imply that certain implementations require the presence of at least one of X, at least one of Y, and at least one of Z.

(32) Language of degree, as used herein, such as the terms “approximately,” “about,” “generally,” and “substantially,” represent a value, amount, or characteristic close to the stated value, amount, or characteristic that still performs a desired function or achieves a desired result. For example, the terms “approximately,” “about,” “generally,” and “substantially” may refer to an amount that is within ±10% of, within ±5% of, within ±2% of, within ±1% of, or within ±0.1% of the stated amount. As another example, the terms “generally parallel” and “substantially parallel” refer to a value, amount, or characteristic that departs from exactly parallel by ±10 degrees, by ±5 degrees, by ±2 degrees, by ±1 degree, or by ±0.1 degree, and the terms “generally perpendicular” and “substantially perpendicular” refer to a value, amount, or characteristic that departs from exactly perpendicular by ±10 degrees, by ±5 degrees, by ±2 degrees, by ±1 degree, or by ±0.1 degree. The ranges disclosed herein also encompass any and all overlap, sub-ranges, and combinations thereof. Language such as “up to,” “at least,” “greater than,” less than,” “between,” and the like includes the number recited. As used herein, the meaning of “a,” “an,” and “said” includes plural reference unless the context clearly dictates otherwise. While the structures and/or methods are discussed herein in terms of elements labeled by ordinal adjectives (e.g., first, second, etc.), the ordinal adjectives are used merely as labels to distinguish one element from another, and the ordinal adjectives are not used to denote an order of these elements or of their use.

(33) Various configurations have been described above. It is to be appreciated that the implementations disclosed herein are not mutually exclusive and may be combined with one another in various arrangements. Although this invention has been described with reference to these specific configurations, the descriptions are intended to be illustrative of the invention and are not intended to be limiting. Various modifications and applications may occur to those skilled in the art without departing from the true spirit and scope of the invention. Thus, for example, in any method or process disclosed herein, the acts or operations making up the method/process may be performed in any suitable sequence and are not necessarily limited to any particular disclosed sequence. Features or elements from various implementations and examples discussed above may be combined with one another to produce alternative configurations compatible with implementations disclosed herein. Various aspects and advantages of the implementations have been described where appropriate. It is to be understood that not necessarily all such aspects or advantages may be achieved in accordance with any particular implementation. Thus, for example, it should be recognized that the various implementations may be carried out in a manner that achieves or optimizes one advantage or group of advantages as taught herein without necessarily achieving other aspects or advantages as may be taught or suggested herein.