Systems and methods for color scanning electron microscopy (SEM)

Abstract

A scanning electron microscopy (SEM) system performs color SEM using a probe and detector. The probe directs incoming probe electrons at a sample. The detector detects electrons scattered by the sample. The system determines materials of the sample using the detected scattered electrons. The system generates a color SEM image of the sample using the detected scattered electrons, determining colors in the image based on determined materials. The system may determine an electron distribution, e.g., electron count relative to detection angle, and may determine materials by comparing a sample's electron distribution to electron distributions for a group of materials. The system may be a focused ion beam scanning electron microscopy (FIB-SEM) system that directs a FIB at samples to separate layers thereof. For each of multiple layers, the system detects scattered electrons, to generate a three-dimensional color SEM image of the sample having thicker than individual layers.

Description

[0001] Attorney Docket No. : Y0087. 70178WOOO

[0002] - 1 -

[0003] SYSTEMS AND METHODS FOR COLOR SCANNING ELECTRON MICROSCOPY (SEM)

[0004] CROSS-REFERENCE TO RELATED APPLICATIONS

[0005] This application claims the benefit under 35 USC 119(e) of U.S. Application Serial No. 63 / 713,533, filed October 29, 2024, under attorney docker number Y0087.70178US00, and titled "SYSTEMS AND METHODS FOR COLOR SCANNING ELECTRON MICROSCOPY (SEM)", which is hereby incorporated herein by reference in its entirety.

[0006] BACKGROUND

[0007] Scanning electron microscopy (SEM) may be used for imaging in biological and other environments. Conventional SEM images may be overlaid with low resolution color data obtained using a different image technology, resulting in low quality color images.

[0008] SUMMARY

[0009] According to aspects of the disclosure, there is provided a color scanning electron microscopy (SEM) system, comprising: a probe configured to direct incoming probe electrons at a sample; a detector configured to detect electrons scattered by the sample; and at least one processor configured to determine a material of the sample based on the detected electrons scattered by the sample.

[0010] In some embodiments, the at least one processor is further configured to generate a color SEM image of the sample based on the detected electrons scattered by the sample.

[0011] In some embodiments, generating the color SEM image of the sample comprises determining at least one color in the color SEM image based on the determined material of the sample.

[0012] In some embodiments, detecting the electrons scattered by the sample comprises detecting an electron profile dimension of the electrons scattered by the sample with respect to a spatial dimension.

[0013] In some embodiments, the spatial dimension comprises angle.

[0014] In some embodiments, the electron profile dimension comprises electron count.

[0015] #14520034v4 In some embodiments, determining the material of the sample based on the detected electrons scattered by the sample comprises generating an electron distribution for the sample, the electron distribution representing electron count with respect to angle.

[0016] In some embodiments, determining the material of the sample based on the detected electrons scattered by the sample further comprises: comparing the electron distribution for the sample to respective electron distributions for a plurality of materials; and selecting the material of the sample from the plurality of materials based on a result of the comparing.

[0017] In some embodiments, comparing the electron distribution for the sample to the respective electron distributions for the plurality of materials comprises inputting the electron distribution for the sample into a rules-based model; and selecting the material of the sample from the plurality of materials based on the result of the comparing comprises selecting the material based on an output of the rules-based model.

[0018] In some embodiments, comparing the electron distribution for the sample to the respective electron distributions for the plurality of materials comprises inputting the electron distribution for the sample into a trained statistical model; and selecting the material of the sample from the plurality of materials based on the result of the comparing comprises selecting the material based on an output of the trained statistical model.

[0019] In some embodiments, the electron profile dimension comprises electron energy; and determining the material of the sample based on the detected electrons scattered by the sample comprises generating an electron distribution for the sample, the electron distribution representing electron energy with respect to angle.

[0020] In some embodiments, the detector comprises a three-dimensional detection surface.

[0021] In some embodiments, the at least one processor is further configured to generate a three- dimensional color SEM image of the sample based on the detected electrons scattered by the sample.

[0022] In some embodiments, the SEM system is a focused ion beam scanning electron microscopy (FIB-SEM) system comprising a focused ion beam (FIB) emitter configured to direct a FIB at the sample to separate layers of the sample.

[0023] In some embodiments, the FIB-SEM system is further configured to: for a first layer of the sample having a sample layer thickness, detect electrons scattered by the sample; using the FIB, separate the first layer of the sample from a second layer of the sample; for the second layer of the sample, detect electrons scattered by the sample; and generate a three-dimensional color SEM image of the sample based on the detected electrons scattered by the sample, the three- dimensional color SEM image having a thickness greater than the sample layer thickness.

[0024] #14520034v4 In some embodiments, the at least one processor further configured to: determine a two- dimensional energy profile map of the detected electrons; and determine the material of the sample based on the two-dimensional energy profile map.

[0025] In some embodiments, the two-dimensional energy profile map of the detected electrons comprises: a map having at least two spatial dimensions; and for a plurality of points in the map, a two-dimensional energy profile comprising: an electron count along a first profile dimension; and an electron energy along a second profile dimension.

[0026] In some embodiments, determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function and a second parameter affecting a mode of the function; comparing the determined first parameter and the determined second parameter to, for two or more known materials, a known one of the first parameter of the function and a known one of the second parameter of the function; and determining the material of the sample based on the comparing.

[0027] In some embodiments, determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function, a second parameter affecting a mode of the function, and a third parameter affecting a width of the function; comparing the determined first parameter, the determined second parameter, and the determined third parameter to, for two or more known materials, a known one of the first parameter of the function, a known one of the second parameter of the function, and a known one of the third parameter of the function; and determining the material of the sample based on the comparing.

[0028] In some embodiments, fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function, a second parameter affecting a mode of the function, and a third parameter affecting a width of the function comprises: fitting the electron angular distribution to a Power Sine function by determining a first parameter ho defining an amplitude of the function, a second parameter (p defining a mode of the function, and a third parameter p defining a width of the function.

[0029] In some embodiments, determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; determining a ratio between electron count at a first angle and electron count at a second angle; comparing the determined ratio to, for two or more

[0030] #14520034v4 known materials, a known one of the first ratio between electron count at the first angle and electron count at the second angle; and determining the material of the sample based on the comparing.

[0031] In some embodiments, the first angle is between 15 and 45° and the second angle is between 45 and 85°.

[0032] In some embodiments, determining an electron angular distribution of the electrons scattered by the sample comprises: determining the electron angular distribution without electrons having energies less than a threshold energy, wherein the threshold energy is 0.05 keV or greater.

[0033] In some embodiments, the threshold energy is 50% of the energy of the incoming probe electrons or greater.

[0034] In some embodiments, determining an electron angular distribution of the electrons scattered by the sample comprises: determining the electron angular distribution without electrons having energies less than a lower threshold energy and without electrons having energies greater than an upper threshold energy, wherein the lower threshold energy is 0.05 keV or greater; and wherein the upper threshold energy is 100% of an energy of the incoming probe electrons or lower.

[0035] In some embodiments, the upper threshold energy is 95% of the energy of the incoming probe electrons or lower.

[0036] In some embodiments, determining an electron angular distribution of the electrons scattered by the sample comprises: determining the electron angular distribution without electrons having energies less than a lower threshold energy and without electrons having energies greater than an upper threshold energy, wherein the lower threshold energy is 90% of the energy of the incoming probe electrons or greater; and wherein the upper threshold energy is 100% of an energy of the incoming probe electrons or lower.

[0037] According to aspects of the disclosure, there is provided a method of performing color scanning electron microscopy (SEM), comprising: directing incoming probe electrons at a sample; detecting electrons scattered by the sample; and determining a material of the sample based on the detected electrons scattered by the sample.

[0038] In some embodiments, the method further comprises generating a color SEM image of the sample based on the detected electrons scattered by the sample.

[0039] In some embodiments, generating the color SEM image of the sample comprises determining at least one color in the color SEM image based on the determined material of the sample.

[0040] #14520034v4 In some embodiments, detecting the electrons scattered by the sample comprises detecting an electron profile dimension of the electrons scattered by the sample with respect to a spatial dimension.

[0041] In some embodiments, the spatial dimension comprises angle.

[0042] In some embodiments, the electron profile dimension comprises electron count.

[0043] In some embodiments, determining the material of the sample based on the detected electrons scattered by the sample comprises generating an electron distribution for the sample, the electron distribution representing electron count with respect to angle.

[0044] In some embodiments, determining the material of the sample based on the detected electrons scattered by the sample further comprises: comparing the electron distribution for the sample to respective electron distributions for a plurality of materials; and selecting the material of the sample from the plurality of materials based on a result of the comparing.

[0045] In some embodiments, comparing the electron distribution for the sample to the respective electron distributions for the plurality of materials comprises inputting the electron distribution for the sample into a rules-based model; and selecting the material of the sample from the plurality of materials based on the result of the comparing comprises selecting the material based on an output of the rules-based model.

[0046] In some embodiments, comparing the electron distribution for the sample to the respective electron distributions for the plurality of materials comprises inputting the electron distribution for the sample into a trained statistical model; and selecting the material of the sample from the plurality of materials based on the result of the comparing comprises selecting the material based on an output of the trained statistical model.

[0047] In some embodiments, the electron profile dimension comprises electron energy; and determining the material of the sample based on the detected electrons scattered by the sample comprises generating an electron distribution for the sample, the electron distribution representing electron energy with respect to angle.

[0048] In some embodiments, detecting the electrons scattered by the sample comprises detecting the electrons using a three-dimensional detection surface.

[0049] In some embodiments, the method further comprises generating a three-dimensional color SEM image of the sample based on the detected electrons scattered by the sample.

[0050] In some embodiments, the method further comprises directing a focused ion beam (FIB) at the sample to separate layers of the sample.

[0051] In some embodiments, the method further comprises: for a first layer of the sample having a sample layer thickness, detecting electrons scattered by the sample; using the FIB,

[0052] #14520034v4 separating the first layer of the sample from a second layer of the sample; for the second layer of the sample, detecting electrons scattered by the sample; and generating a three-dimensional color SEM image of the sample based on the detected electrons scattered by the sample, the three-dimensional color SEM image having a thickness greater than the sample layer thickness.

[0053] In some embodiments, the method further comprises: determining a two-dimensional energy profile map of the detected electrons; and determining the material of the sample based on the two-dimensional energy profile map.

[0054] In some embodiments, the two-dimensional energy profile map of the detected electrons comprises: a map having at least two spatial dimensions; and for a plurality of points in the map, a two-dimensional energy profile comprising: an electron count along a first profile dimension; and an electron energy along a second profile dimension.

[0055] In some embodiments, determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function and a second parameter affecting a mode of the function; comparing the determined first parameter and the determined second parameter to, for two or more known materials, a known one of the first parameter of the function and a known one of the second parameter of the function; and determining the material of the sample based on the comparing.

[0056] In some embodiments, determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function, a second parameter affecting a mode of the function, and a third parameter affecting a width of the function; comparing the determined first parameter, the determined second parameter, and the determined third parameter to, for two or more known materials, a known one of the first parameter of the function, a known one of the second parameter of the function, and a known one of the third parameter of the function; and determining the material of the sample based on the comparing.

[0057] In some embodiments, fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function, a second parameter affecting a mode of the function, and a third parameter affecting a width of the function comprises: fitting the electron angular distribution to a Power Sine function by determining a first parameter ho defining an amplitude of the function, a second parameter (p defining a mode of the function, and a third parameter p defining a width of the function.

[0058] #14520034v4 In some embodiments, determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; determining a ratio between electron count at a first angle and electron count at a second angle; comparing the determined ratio to, for two or more known materials, a known one of the first ratio between electron count at the first angle and electron count at the second angle; and determining the material of the sample based on the comparing.

[0059] In some embodiments, the first angle is between 15 and 45° and the second angle is between 45 and 85°.

[0060] In some embodiments, determining an electron angular distribution of the electrons scattered by the sample comprises: determining the electron angular distribution without electrons having energies less than a threshold energy, wherein the threshold energy is 0.05 keV or greater.

[0061] In some embodiments, the threshold energy is 50% of the energy of the incoming probe electrons or greater.

[0062] In some embodiments, determining an electron angular distribution of the electrons scattered by the sample comprises: determining the electron angular distribution without electrons having energies less than a lower threshold energy and without electrons having energies greater than an upper threshold energy, wherein the lower threshold energy is 0.05 keV or greater; and wherein the upper threshold energy is 100% of an energy of the incoming probe electrons or lower.

[0063] In some embodiments, the upper threshold energy is 95% of the energy of the incoming probe electrons or lower.

[0064] In some embodiments, determining an electron angular distribution of the electrons scattered by the sample comprises: determining the electron angular distribution without electrons having energies less than a lower threshold energy and without electrons having energies greater than an upper threshold energy, wherein the lower threshold energy is 90% of the energy of the incoming probe electrons or greater; and wherein the upper threshold energy is 100% of an energy of the incoming probe electrons or lower.

[0065] According to aspects of the disclosure, there is provided at least one non-transitory computer-readable storage medium having instructions encoded thereon that, when executed by at least one processor, cause the at least one processor to perform a method of performing color scanning electron microscopy (SEM), comprising: directing incoming probe electrons at a

[0066] #14520034v4 sample; detecting electrons scattered by the sample; and determining a material of the sample based on the detected electrons scattered by the sample.

[0067] In some embodiments, the method further comprises generating a color SEM image of the sample based on the detected electrons scattered by the sample.

[0068] In some embodiments, generating the color SEM image of the sample comprises determining at least one color in the color SEM image based on the determined material of the sample.

[0069] In some embodiments, detecting the electrons scattered by the sample comprises detecting an electron profile dimension of the electrons scattered by the sample with respect to a spatial dimension.

[0070] In some embodiments, the spatial dimension comprises angle.

[0071] In some embodiments, the electron profile dimension comprises electron count.

[0072] In some embodiments, determining the material of the sample based on the detected electrons scattered by the sample comprises generating an electron distribution for the sample, the electron distribution representing electron count with respect to angle.

[0073] In some embodiments, determining the material of the sample based on the detected electrons scattered by the sample further comprises: comparing the electron distribution for the sample to respective electron distributions for a plurality of materials; and selecting the material of the sample from the plurality of materials based on a result of the comparing.

[0074] In some embodiments, comparing the electron distribution for the sample to the respective electron distributions for the plurality of materials comprises inputting the electron distribution for the sample into a rules-based model; and selecting the material of the sample from the plurality of materials based on the result of the comparing comprises selecting the material based on an output of the rules-based model.

[0075] In some embodiments, comparing the electron distribution for the sample to the respective electron distributions for the plurality of materials comprises inputting the electron distribution for the sample into a trained statistical model; and selecting the material of the sample from the plurality of materials based on the result of the comparing comprises selecting the material based on an output of the trained statistical model.

[0076] In some embodiments, the electron profile dimension comprises electron energy; and determining the material of the sample based on the detected electrons scattered by the sample comprises generating an electron distribution for the sample, the electron distribution representing electron energy with respect to angle.

[0077] #14520034v4 In some embodiments, detecting the electrons scattered by the sample comprises detecting the electrons using a three-dimensional detection surface.

[0078] In some embodiments, the method further comprises generating a three-dimensional color SEM image of the sample based on the detected electrons scattered by the sample.

[0079] In some embodiments, the method further comprises directing a focused ion beam (FIB) at the sample to separate layers of the sample.

[0080] In some embodiments, the method further comprises: for a first layer of the sample having a sample layer thickness, detecting electrons scattered by the sample; using the FIB, separating the first layer of the sample from a second layer of the sample; for the second layer of the sample, detecting electrons scattered by the sample; and generating a three-dimensional color SEM image of the sample based on the detected electrons scattered by the sample, the three-dimensional color SEM image having a thickness greater than the sample layer thickness.

[0081] In some embodiments, the method further comprises: determining a two-dimensional energy profile map of the detected electrons; and determining the material of the sample based on the two-dimensional energy profile map.

[0082] In some embodiments, the two-dimensional energy profile map of the detected electrons comprises: a map having at least two spatial dimensions; and for a plurality of points in the map, a two-dimensional energy profile comprising: an electron count along a first profile dimension; and an electron energy along a second profile dimension.

[0083] In some embodiments, determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function and a second parameter affecting a mode of the function; comparing the determined first parameter and the determined second parameter to, for two or more known materials, a known one of the first parameter of the function and a known one of the second parameter of the function; and determining the material of the sample based on the comparing.

[0084] In some embodiments, determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function, a second parameter affecting a mode of the function, and a third parameter affecting a width of the function; comparing the determined first parameter, the determined second parameter, and the determined third parameter to, for two or more known materials, a known one of the first parameter of the

[0085] #14520034v4 function, a known one of the second parameter of the function, and a known one of the third parameter of the function; and determining the material of the sample based on the comparing.

[0086] In some embodiments, fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function, a second parameter affecting a mode of the function, and a third parameter affecting a width of the function comprises: fitting the electron angular distribution to a Power Sine function by determining a first parameter ho defining an amplitude of the function, a second parameter (p defining a mode of the function, and a third parameter p defining a width of the function.

[0087] In some embodiments, determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; determining a ratio between electron count at a first angle and electron count at a second angle; comparing the determined ratio to, for two or more known materials, a known one of the first ratio between electron count at the first angle and electron count at the second angle; and determining the material of the sample based on the comparing.

[0088] In some embodiments, the first angle is between 15 and 45° and the second angle is between 45 and 85°.

[0089] In some embodiments, determining an electron angular distribution of the electrons scattered by the sample comprises: determining the electron angular distribution without electrons having energies less than a threshold energy, wherein the threshold energy is 0.05 keV or greater.

[0090] In some embodiments, the threshold energy is 50% of the energy of the incoming probe electrons or greater.

[0091] In some embodiments, determining an electron angular distribution of the electrons scattered by the sample comprises: determining the electron angular distribution without electrons having energies less than a lower threshold energy and without electrons having energies greater than an upper threshold energy, wherein the lower threshold energy is 0.05 keV or greater; and wherein the upper threshold energy is 100% of an energy of the incoming probe electrons or lower.

[0092] In some embodiments, the upper threshold energy is 95% of the energy of the incoming probe electrons or lower.

[0093] In some embodiments, determining an electron angular distribution of the electrons scattered by the sample comprises: determining the electron angular distribution without electrons having energies less than a lower threshold energy and without electrons having

[0094] #14520034v4 energies greater than an upper threshold energy, wherein the lower threshold energy is 90% of the energy of the incoming probe electrons or greater; and wherein the upper threshold energy is 100% of an energy of the incoming probe electrons or lower.

[0095] BRIEF DESCRIPTION OF DRAWINGS

[0096] FIGs. 1A-1B show an exemplary embodiment of a scanning electron microscopy (SEM) system;

[0097] FIG. 1C shows an exemplary process flow of a method of determining color SEM information for use with an SEM system;

[0098] FIG. 2A shows first exemplary data of an SEM system for determining material and / or color information of an SEM image;

[0099] FIG. 2B shows second exemplary data of an SEM system for determining material and / or color information of an SEM image;

[0100] FIG. 3 shows third exemplary data of an SEM system for determining material and / or color information of an SEM image;

[0101] FIG. 4 shows fourth exemplary data of an SEM system for determining material and / or color information of an SEM image;

[0102] FIG. 5 shows fifth exemplary data of an SEM system for determining material and / or color information of an SEM image;

[0103] FIG. 6 shows sixth exemplary data of an SEM system for determining material and / or color information of an SEM image;

[0104] FIG. 7 shows seventh exemplary data of an SEM system for determining material and / or color information of an SEM image;

[0105] FIG. 8 shows eight exemplary data of an SEM system for determining material and / or color information of an SEM image;

[0106] FIG. 9 shows ninth exemplary data of an SEM system for determining material and / or color information of an SEM image;

[0107] FIG. 10 shows tenth exemplary data of an SEM system for determining material and / or color information of an SEM image;

[0108] FIG. 11 shows eleventh exemplary data of an SEM system for determining material and / or color information of an SEM image;

[0109] FIG. 12 shows twelfth exemplary data of an SEM system for determining material and / or color information of an SEM image;

[0110] FIG. 13 A shows a first exemplary embodiment of a detector of an SEM system;

[0111] #14520034v4 FIG. 13B shows a second exemplary embodiment of a detector of an SEM system;

[0112] FIG. 13C shows a third exemplary embodiment of a detector of an SEM system;

[0113] FIG. 14 shows an exemplary block diagram of a special purpose computer system that can be improved over conventional implementations based on implementations and / or execution of methods discussed herein;

[0114] FIG. 15 shows an exemplary embodiment of an operating space of an SEM system;

[0115] FIG. 16 shows an exemplary process flow of a method of determining subvoxel information for use with an SEM system;

[0116] FIG. 17A shows an exemplary SEM system voxel and subvoxels thereof;

[0117] FIG. 17B shows a first exemplary sample for an SEM system;

[0118] FIG. 17C shows first exemplary data of an SEM system for the sample of FIG. 17A;

[0119] FIG. 18A shows a second exemplary sample for an SEM system;

[0120] FIG. 18B shows second exemplary data of an SEM system for the sample of FIG. 18 A;

[0121] FIG. 19A shows a third exemplary sample for an SEM system;

[0122] FIG. 19B shows third exemplary data of an SEM system for the sample of FIG. 19 A;

[0123] FIG. 20A shows a fourth exemplary sample for an SEM system;

[0124] FIG. 20B shows fourth exemplary data of an SEM system for the sample of FIG. 20 A;

[0125] FIG. 21 A shows a fifth exemplary sample for an SEM system;

[0126] FIG. 21B shows fifth exemplary data of an SEM system for the sample of FIG. 21 A;

[0127] FIG. 22A shows a sixth exemplary sample for an SEM system;

[0128] FIG. 22B shows sixth exemplary data of an SEM system for the sample of FIG. 22A;

[0129] FIG. 23 A shows a seventh exemplary sample for an SEM system;

[0130] FIG. 23B shows seventh exemplary data of an SEM system for the sample of FIG. 23 A;

[0131] FIG. 24A shows an eighth exemplary sample for an SEM system;

[0132] FIG. 24B shows eight exemplary data of an SEM system for the sample of FIG. 24 A;

[0133] FIG.25A shows a fourth exemplary embodiment of a detector of an SEM system;

[0134] FIGs. 25B and 25C show an exemplary embodiment of an SEM system that includes detectors according to the fourth exemplary embodiment of a detector shown in FIG. 25 A;

[0135] FIGs. 26A, 26B, 26C, 26D, 26E, 26F, 26G, 26H, and 261 show further exemplary data of an SEM system for determining material and / or color information of an SEM image;

[0136] FIGs. 27A and 27B show comparisons of the exemplary data of an SEM system for determining material and / or color information of an SEM image from FIGs. 26A, 26B, 26C, 26D, 26E, 26F, 26G, 26H, and 261;

[0137] #14520034v4 FIGs. 28A and 28B show further exemplary data of an SEM system for determining material and / or color information of an SEM image;

[0138] FIGs. 29A, 29B, 29C, 29D, 29E, and 29F show parameters of an SEM system for determining material and / or color information of an SEM image;

[0139] FIGs. 30 A, 3 OB, 30C, 30D, 30E, and 3 OF show further parameters of an SEM system for determining material and / or color information of an SEM image.

[0140] DETAILED DESCRIPTION

[0141] According to aspects of the disclosure, a scanning electron microscopy (SEM) system performs color SEM using a probe and detector. The probe directs incoming probe electrons at a sample. The detector detects electrons scattered by the sample. The system determines materials of the sample using the detected scattered electrons. The system generates a color SEM image of the sample using the detected scattered electrons, determining colors in the image based on determined materials. The system may determine an electron distribution, e.g., electron count relative to detection angle, and may determine materials by comparing a sample’s electron distribution to electron distributions for a group of materials. The system may be a focused ion beam scanning electron microscopy (FIB-SEM) system that directs a FIB at samples to separate layers thereof. For each of multiple layers, the system detects scattered electrons, to generate a three-dimensional color SEM image of the sample having thicker than individual layers. _ Color Scanning Electron Microscopy

[0142] The disclosure provides scanning electron microscopy (SEM) systems that perform color SEM imaging. Compared with conventional color microscopy systems, the system provides increased resolution, higher accuracy, and does not require alignment of data from multiple different imaging systems.

[0143] For example, an SEM system may determine the material of a sample based on detected electrons scattered. In some embodiments, the system may determine an electron angular distribution based on collected information, fit the electron angular distribution to a function, and compare the fitted function to know parameters to determine the material. For example, the system may fit the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function, a second parameter affecting a mode of the function, and / or a third parameter affecting a width of the function. The system may then compare the first, second, and third parameters to, for two or more known materials, known ones of the first, second, and third parameters of the function and determine the material of the sample based on

[0144] #14520034v4 the comparing. For example, the function may comprise a Power Sine function. In some embodiments, the system may determine the material by determining a ratio between electron count at a first angle and electron count at a second angle and comparing the determined ratio to known ones of the first ratio.

[0145] In some embodiments, the SEM system may use energy thresholding when determining electron angular distribution, e.g., by not detecting electrons or by excluding detected electrons with energies less than a lower threshold energy (e.g., 0.05 or 5 keV) and / or greater than an upper threshold energy (e.g., 95% or 100% of the energy of the electrons beam). Energy thresholding may provide greater differences in angular distributions for different materials, which may increase the accuracy of the SEM system when differentiating between different materials during detection.

[0146] The inventors have recognized and appreciated that material composition information (and therefore the color information associated with that material composition information) is encoded in the backscattered electrons of an SEM system. While conventional SEM systems may simply measure backscattered electron count at the probe location, and determine only intensity data (i.e., no color data), the systems described herein overcome these limitations. Moreover, conventional methods of obtaining color microscopy images are cumbersome and do not produce high resolution and accurate images. As an example, one conventional method uses correlative light-electron microscopy (CLEM), taking two images: one with a fluorescence microscope and one with an electron microscope. Such an approach provides subpar results, as the color information obtained from the fluorescence microscope is of much lower resolution than the electron microscope image. Moreover, the process of staining and dehydration of the sample for fluorescence image causes changes to the shape and size of features of a sample, leading to a poorly aligned composite image.

[0147] Accordingly, the SEM systems described herein provide a high resolution and accurate color SEM image that uses only one image to obtain both color and intensity information. The SEM system, for example, includes a probe that directs incoming probe electrons at a sample and a detector detects electrons scattered by the sample. The system determines materials of the sample using the detected scattered electrons. The system generates a color SEM image of the sample using the detected scattered electrons, determining colors in the image based on determined materials. The system may determine an electron distribution, e.g., electron count relative to detection angle, and may determine materials by comparing a sample’s electron distribution to electron distributions for a group of materials.

[0148] #14520034v4 As one example, described in more detail below, a difference of angular distributions between backscattered electrons from silver and gold allows for easy distinction between the two elements. The electron distributions for these materials may be prepared as an electron count along a range of angles, which may be detected by the detectors described herein. The electron distribution may then be compared to electron distributions of known materials to determine the material of the sample. The comparison may be performed using rules-based models or trained statistical models, or using other models.

[0149] The disclosure enables SEM systems to provide structural and elemental information at the same spatial resolution, overcoming fundamental limitations that have constrained the capability of SEM since its birth more than 80 years ago. The elemental information may be determined using properties of the backscattered electrons (e.g., angular and energy distributions) to retrieve both the elemental and structural information of a sample in a single scan. The detection architecture harvests and decodes the intrinsic and important backscattered electron information. The elemental information may be collected in both 2D and 3D using volume SEM techniques, such as FIB-SEM, serial block face SEM, serial section SEM, and other imaging techniques. The systems described herein maintain a same resolution as the SEM micrograph and reduces or eliminates the need for aligning multiple 3D volumes.

[0150] Color SEM systems described herein are configured to combine grayscale images with specific protein or elemental characteristics of specimens, allowing biological, material science, and semiconductor, and other samples to be analyzed more precisely at the nanoscale. Systems described herein provide the following benefits, among others. First, the systems may use only a single scan: color SEM systems described herein may use only one scan to simultaneously capture both structural and elemental information, greatly improving data acquisition efficiency, eliminating the need for multiple 3D volumes registration, and simplifying post-processing and analysis. Second, high resolution: the systems maintain the high spatial resolution characteristic of traditional SEM, ensuring detailed visualization. Third, 3D capability: the systems described herein may be integrated with existing volume SEM technologies such as FIB-SEM, serial block face SEM, and serial section SEM, enabling the extension from 2D to 3D imaging.

[0151] Electron microscopy (EM) provides resolution superior to optical microscopy, enabling the visualization of structures down to atomic levels. EM is a powerful technique in biological studies, revealing details from individual molecules to entire organisms. EM images, generated from electron counts, are displayed in grayscale, offering structural details through contrast variations. In biological EM, substances like lipids and proteins are often stained with heavy metals to enhance this contrast. However, EM's primary limitation is that it detects just structural

[0152] #14520034v4 attributes (e.g., size and shape) and does not show the composition of the observed elements. This is particularly challenging for biological specimens, where many proteins, despite having similar shapes and sizes, perform vastly different functions. Therefore, only a small fraction of proteins can be identified in EM based on their location clues within the cellular context. For instance, ribosomes can be identified by their size and association with the endoplasmic reticulum (ER) membranes, but distinguishing other cellular proteins and biomolecules remains a formidable challenge.

[0153] Conventional approaches to color microscopy have significant drawbacks. Conventional approaches include electron energy loss spectroscopy (EELS), energy dispersive X-ray spectrometry (EDS), immuno-EM, and correlative light and electron microscopy (CLEM). There are limitations associated with each of those approaches.

[0154] Electron energy loss spectroscopy (EELS) is a technique used in transmission electron microscopy (TEM) that measures the energy loss of the incoming electrons as they pass through a thin specimen. This energy loss varies characteristically among different atoms in the specimen, allowing EELS to provide detailed elemental composition information. However, EELS depends on the properties of transmitted electrons specific to TEM configurations. In contrast, scanning electron microscopy (SEM) uses backscattered or secondary electrons for detection and lacks the capability for EELS.

[0155] Elemental analysis through Energy Dispersive X-ray Spectroscopy (EDS) utilizes spectroscopic data from emitted X-rays when incoming electrons interact with a specimen. The requirement for high-energy electrons to induce X-ray emissions results in a large interaction volume. This substantially degrades spatial resolution to hundreds of nanometers in all three dimensions, making it challenging to identify cellular proteins and other biomolecules that are on the order of a few nanometers.

[0156] Immuno-electron microscopy (Immuno-EM) is labor-intensive and tailored specifically for biological specimens. It operates on the principle of antibody binding to target proteins. In the pre-embed labeling technique, detergents disrupt cell membranes to permit antibody access to intracellular proteins. However, this approach compromises the fine cellular structure, rendering it unsuitable for ultrastructural visualization.

[0157] In the Correlative Light and Electron Microscopy (CLEM) approach for biological specimens, proteins are first labeled with fluorophores and imaged using fluorescence microscopy. The specimen then undergoes preparation for electron microscopy, which includes heavy metal staining, dehydration, and resin embedding. These EM preparation steps often cause significant changes to the specimen's shape and size, potentially altering it by microns.

[0158] #14520034v4 Correlating the lower-resolution light microscopy images with the high-resolution electron microscopy data presents substantial challenges in accurately aligning the volumes from both microscopy techniques.

[0159] Accordingly, the inventors have recognized and appreciated a crucial need for SEM systems that can simultaneously provide structural and elemental information during SEM measurements, thereby eliminating the need for correlating 3D volumes, and achieve spatial resolution for elemental data that is similar or equivalent with that of SEM. In various embodiments, SEM systems described herein may provide multiple color in SEM images. Therefore, color SEM systems described herein may be referred to as multi-color scanning electron microscopy (MC-SEM) systems.

[0160] Systems described herein may determine the elemental makeup of samples. Biological specimens, composed primarily of low atomic number elements like Hydrogen, Carbon, Nitrogen, Oxygen, Phosphorus, and Sulfur, may inherently produce low contrast in EM. To enhance this contrast, conventional EM sample preparation involves staining biomolecules with heavy metals such as Osmium, Uranium, Lead, and Tungsten. Since these metals may bind non- selectively, all stained biomolecules are visible in electron micrographs, providing a comprehensive visualization of the entire cellular content. However, the identification of individual biomolecules relies mostly on their size, shape, and location. Optical microscopy has overcome the challenge of protein identification by using fluorophores, such as fluorescent dyes or proteins, to tag specific proteins. This allows for distinct identification through the color of the labels.

[0161] Color SEM systems described herein detect elemental information and therefore enable a similar selective identification of proteins together with their cellular contexts, but with the significantly higher spatial resolution characteristic of electron microscopy. In SEM, the backscattered electrons carry the signature of the elements that the incoming electrons interact with. By collecting the angular and energy distributions of the backscattered electrons, the elemental information of each scanned pixels can be retrieved. Specifically, the SEM systems described herein may measure both angular and energy distributions of backscattered electrons. As described herein, models using simulations and experimental data may identify the elements in each detected pixel. For example, the angular distribution of backscattered electrons alone can be used to distinguish between silver and gold, described in more detail below. Moreover additional elements may be used, such as 10 heavy metals used for EM staining (molybdenum, ruthenium, silver, tungsten, osmium, iridium, platinum, gold, lead, and uranium).

[0162] #14520034v4 Additionally, selectively staining elements not usable with conventional SEM may be used by the systems described herein. Furthermore, certain elements such as selenium can selectively label intracellular proteins. Since selenium has a low atomic number, it is nearly invisible in traditional electron microscopy when specimens are stained with heavy metals. However, with the color SEM systems described herein, proteins may be readily visualized when labeled with selenium, even when using conventional heavy-metal staining protocols for EM sample preparation. Indeed the systems described herein provide advantages by allowing identification of the selenium labeled proteins within the complex cellular content that is revealed by nonselective binding metals. As described below, systems described herein may identify selenium using the clear difference in the angular distribution of backscattered electrons between selenium and other commonly used heavy metals for EM staining, such as osmium and uranium.

[0163] In addition to biological specimens, the color SEM systems described herein can be applied to other applications in material science and the semiconductor industry, providing valuable insights and advancements in each of these fields.

[0164] Referring now to FIG. 1 A, an exemplary embodiment of an SEM system 100 is provided. SEM system 100 comprises a probe 102 and a detector 104. SEM system may be configured to image a sample 106. The probe 102 may be configured to direct incoming probe electrons 108 at the sample 106. As further discuss below, the incoming probe electrons 108 may have an energy and a direction. The detector 104 may be configured to detect electrons 110 scattered by the sample. The detector 104 may further be configured to generate a two- dimensional (or otherwise multi-dimensional) energy profile map 112, illustrated in FIG. IB, using the detected electrons. In some embodiments, two-dimensional electron information of two-dimensional energy profile map 112 may be electron information from one or more of FIGs. 2A, 2B, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17C, 18B, 19B, 20B, 21B, 22B, 23B, and 24B (discussed in more detail below), or other electron information.

[0165] FIG. 1 A illustrates one exemplary embodiment of incoming electrons li and resulting scattered electrons Io. Incoming probe electrons L may have an energy of E and incident angle of 6 relative to a z-axis. Further, scattered electrons Iomay have energy e (e <= E) with a direction defined by (p and ip. In some embodiments, the SEM system 100 derives a direction of scattered electrons 110 (e.g., (p and / i) from spatial location of pixels of the detector 104, relative to the sample 106, for example, as shown in FIG. 1 A. Additionally, a voltage bias of V is applied to the specimen or sample. For a given structure, resulting scattered electrons form specific angular and energy distributions which may be functions of E, 0, and V. A two-dimensional electron

[0166] #14520034v4 energy profile may encode a combination of features in X, Y and Z directions that are smaller than a probe size and have a distinctive signature pattern reflecting unique scattering events of individual electrons. In some embodiments, a specimen can rotate around z axis at an angle of a> to produce a reflection tomography.

[0167] According to some embodiments, a direct electron detector may be used to detect an electron energy profile, No(E, 0, m, V). In some embodiments, TEM cameras may be used to generate a two-dimensional mapping of electrons. For example, a TEM detector may have an acquisition rate of about 5,000 frames per second (fps). In some embodiments, a TEM detector may not measure energy. Accordingly, aspects of the disclosure provide an SEM system configured to perform an energy filtering scheme to capture energy measurements. An acquisition rate of the SEM system may in some embodiments be substantially improved by reducing a number of pixels. Such a detector may be included in a color and / or subvoxel SEM system.

[0168] FIG. 1C shows an exemplary process flow 150 of performing color scanning electron microscopy (SEM) for use with an SEM system. Process flow 150 includes act 152, act 154, and act 156. At act 152, the process flow 150 may include directing incoming probe electrons at a sample. At act 154, the process flow 150 may include detecting electrons scattered by the sample. At act 156, the process flow 150 may include determining a material of the sample based on the detected electrons scattered by the sample.

[0169] SEM systems described herein may obtain electron information for multiple layers of a sample, which may be used in order to generate three-dimensional color and / or subvoxel information for the sample. For example, the SEM system may measure a sample layer each having a sample layer thickness to obtain energy and direction of incoming probe electrons and generate a two-dimensional energy profile map of detected electrons, before using a FIB to separate the layer from another layer of the sample, which may in turn be measured to obtain the energy and direction of incoming probe electrons and generate a two-dimensional energy profile map of detected electrons for that other layer. The SEM system may then generate three- dimensional color and / or subvoxel volume information of the sample, with the vertical dimension of the three-dimensional color and / or subvoxel volume being greater than the thickness of a single sample layer. If multiple layers are measured, the vertical dimension of the three-dimensional color and / or subvoxel volume may be equal to the thickness of the multiple layers.

[0170] Aspects of the disclosure also provide color and / or subvoxel FIB-SEM systems. Such FIB-SEM systems may be configured to provide new high-resolution large volume EM, which

[0171] #14520034v4 may reveal new structure-function relationships in biology. As described above, electron angular and energy distributions may encode color and / or subvoxel features in X, Y and Z. According to aspects of the disclosure, SEM architectures are provided that exploit comprehensive electron properties, and use physics and mathematical models to reconstruct color and / or subvoxel information that is encoded in said electron angular and energy distributions. Conventional systems and approaches do not exploit the color and / or subvoxel information that is encoded in said electron angular and energy distributions. In contrast, some conventional systems may instead focus on highly stable FIB-SEM architectures with high effective reliability at the fine isotropic resolutions, such as 4 nm.

[0172] As discussed above, the systems herein provide color and / or subvoxel FIB-SEM functionality as a novel technological approach that bridges the resolution and volume gap between conventional imaging schema, such as cryo-ET and FIB-SEM. SEM systems configured for whole cell mapping at near-atomic resolutions may be applied to technical fields such as EM, physiology, cell biology, and structural biology, and provide illumination to vistas in life science and therapeutic development that are inaccessible with conventional imaging systems.

[0173] According to various embodiments, a probe directs electrons towards a sample and the incoming beam of electrons interacts with atoms in the sample. When the electrons interact with atoms of the specimen, inelastic scattering and / or elastic scattering may occur. In an inelastic scattering event, an incoming electron may lose its energy, and may only slightly deviate from its original path. In an elastic scattering event, an incoming electron may experience larger changes to its travel path and may have little to no energy loss. According to various embodiments, in order to train a model for an SEM system (described in more detail below), electron scattering events, such as inelastic scattering and / or elastic scattering, may be simulated using Monte Carlo calculations in order to build a set of training data for an SEM system. The Monte Carlo calculations may be used to effectively predict the electron travel trajectory. According to aspects of the disclosures, refined physical models and accumulated experimental measurements may be used to perform advanced Monte Carlo simulations to calculate the training data. The training data may in turn be used by SEM systems or training systems to analyze interactions between electrons and samples and provide models for providing color and / or subvoxel information based on scattered election information. According to some embodiments, electron data from Monte Carlo simulations (or other electron data) may be used to generate a large amount of ground truth, which can be used to train a deep learning model (or other model). The model may be configured to classify patterns of electron data in order to

[0174] #14520034v4 reconstruct color and / or subvoxel features of samples. In some embodiments, a model generated using Monte Carlo simulation data may thereafter be refined using experimental data.

[0175] According to aspects of the disclosure, Monte Carlo simulations may be used to provide backscattered electron (BSE) energy and angular (or positional) distributions. According to merely one example, a sample may include a 5 nm gold cube embedded in epoxy resin cube with a size of 10 mm, with the epoxy including carbon, hydrogen, and oxygen. According to one embodiment, a probe may direct an incoming electron beam with an energy of E = 1 kV, and the probe may be sized to provide a beam diameter of 10 nm that radiates perpendicularly towards a sample. As may be appreciated, the beam diameter of 10 nm is of equal size to the epoxy cube, and as such, conventional SEM systems may not be able to measure the smaller 5 nm gold cube within the epoxy.

[0176] In some embodiments, the sample (which, as described above, may be simulated) may scatter electrons. Each BSE may have an energy e, with e <= E, and may have a scattered direction defined by ip and (p (e.g., as illustrated in FIG. 1 A). As such, the data encoded by a BSE may be visualized as a single dot in a 3D space defined by ip, (p, and e. In some embodiments, an SEM system or training system may obtain simulations of multiple electrons, in order to generate a plurality of dots in the 3D space, and may form an “electron cloud.” When measured by an SEM system, unique samples, made up of color and / or subvoxel features having varying sizes and materials, may each encode a different electron cloud. Each such electron cloud may have identifiable properties, including shape, density, distribution, among other properties. In some embodiments, detectors of various shapes may be used to capture the electron cloud of samples. As described in more detail above, the detectors may include hemisphere detectors, circular detectors, donut-shaped detector, or detectors of multiple planar surfaces, among other configurations.

[0177] FIGs. 2A, 2B, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 show various exemplary samples of SEM systems and various exemplary data for samples of such SEM systems. FIGs. 2A and 2B show differences in spatial distributions of scattered electrons for different materials. In the illustrated embodiments of FIGs. 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12, the samples may each correspond to an exemplary 10 nm block of a respective material. By using the different data for each of the different samples, an SEM system may be able to determine the material of the block, and may also therefore determine a color of the sample. While FIGs. 2A and 2B illustrate angle along one axis of a detector (such as hemisphere detector), FIGs. 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 may represent various data for a hemisphere detection surface. In various embodiments, the electron information, such as the data of FIGs. 2A, 2B, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 (which may be

[0178] #14520034v4 used as training data) may be generated by real-world experimental processes, using Monte Carlo simulations, or by other suitable methods.

[0179] FIG. 2A shows electron information 200a that may be obtained by an SEM system based on detecting electrons scattered by a sample. FIG. 2A shows a plot of electron information 200a obtained at IkV, with an angle of 0, and 50,000 incoming electrons. The electron information 200a is provided along a horizontal axis of angle < >, and a vertical axis of electron count at each angle (p. FIG. 2A shows electron information 200a for two materials, silver and gold. As may be appreciated from FIG. 2A, silver and gold scatter the electrons with different spatial distributions, providing different electron counts at different angles. By comparing detected scattered electrons for a sample with known information for materials, the material of the sample may be determined. For example, if the electron information closely matches the illustrated electron information of gold, it may be determined that the sample includes gold. Thereafter, a color of the sample may be determined, such as by determined that the sample has a color of gold. This process may be repeated for different locations of the sample, such as for each voxel measured by an SEM system. In some embodiments, color may also be determined for subvoxels, which are described in more detail below.

[0180] FIG. 2B shows electron information 200b that may be obtained by an SEM system based on detecting electrons scattered by a sample. FIG. 2B shows a plot of electron information 200b obtained at IkV, with an angle of 0, and 50,000 incoming electrons. The electron information 200b is provided along a horizontal axis of angle < >, and a vertical axis of electron count at each angle (p. FIG. 2B shows electron information 200b for three materials, osmium, uranium, and selenium. As may be appreciated from FIG. 2B, osmium, uranium, and selenium scatter the electrons with different spatial distributions, providing different electron counts at different angles. The SEM system may use the distributions to determine the material and / or color of a sample.

[0181] FIG. 3 shows an exemplary sample 300a for an SEM system as well as third exemplary data that may be gathered by the SEM system for the sample 300a. The SEM system may be the SEM system 100 of FIG. 1 A, and it includes a probe 102 configured to direct incoming probe electrons 108 at a sample 300a, and a detector (not illustrated) configured to detect electrons scattered by the sample 300a, in order to measure electron information 300b. Sample 300a comprises a 10 nm cube of molybdenum in a 100 nm epoxy cube. As shown in FIG. 3, the SEM system may obtain electron information 300b based on detecting electrons scattered by sample 300a. FIG. 3 may represent data with 8855 detected BSE, 8856 total BSE, and 50000 incoming electrons. FIG. 3 includes nine plots showing the electron information 300b plotted for different

[0182] #14520034v4 spatial distributions of electrons. The SEM system may use the distributions to determine the material and / or color of a sample, such as by comparing the distributions to known distributions of materials, or using a trained statistical model.

[0183] FIG. 4 shows an exemplary sample 400a for an SEM system as well as fourth exemplary data that may be gathered by the SEM system for the sample 400a. The SEM system may be the SEM system 100 of FIG. 1 A, and it includes a probe 102 configured to direct incoming probe electrons 108 at a sample 400a, and a detector (not illustrated) configured to detect electrons scattered by the sample 400a, in order to measure electron information 400b. Sample 400a comprises a 10 nm cube of rubidium in a 100 nm epoxy cube. As shown in FIG. 4, the SEM system may obtain electron information 400b based on detecting electrons scattered by sample 400a. FIG. 4 may represent data with 8224 detected BSE, 8224 total BSE, and 50000 incoming electrons. FIG. 4 includes nine plots showing the electron information 400b plotted for different spatial distributions of electrons. The SEM system may use the distributions to determine the material and / or color of a sample, such as by comparing the distributions to known distributions of materials, or using a trained statistical model.

[0184] FIG. 5 shows an exemplary sample 500a for an SEM system as well as fifth exemplary data that may be gathered by the SEM system for the sample 500a. The SEM system may be the SEM system 100 of FIG. 1 A, and it includes a probe 102 configured to direct incoming probe electrons 108 at a sample 500a, and a detector (not illustrated) configured to detect electrons scattered by the sample 500a, in order to measure electron information 500b. Sample 500a comprises a 10 nm cube of silver in a 100 nm epoxy cube. As shown in FIG. 5, the SEM system may obtain electron information 500b based on detecting electrons scattered by sample 500a. FIG. 5 may represent data with 8983 detected BSE, 8991 total BSE, and 50000 incoming electrons. FIG. 5 includes nine plots showing the electron information 500b plotted for different spatial distributions of electrons. The SEM system may use the distributions to determine the material and / or color of a sample, such as by comparing the distributions to known distributions of materials, or using a trained statistical model.

[0185] FIG. 6 shows an exemplary sample 600a for an SEM system as well as sixth exemplary data that may be gathered by the SEM system for the sample 600a. The SEM system may be the SEM system 100 of FIG. 1 A, and it includes a probe 102 configured to direct incoming probe electrons 108 at a sample 600a, and a detector (not illustrated) configured to detect electrons scattered by the sample 600a, in order to measure electron information 600b. Sample 600a comprises a 10 nm cube of tungsten in a 100 nm epoxy cube. As shown in FIG. 6, the SEM system may obtain electron information 600b based on detecting electrons scattered by sample

[0186] #14520034v4 600a. FIG. 6 may represent data with 8872 detected BSE, 8873 total BSE, and 50000 incoming electrons. FIG. 6 includes nine plots showing the electron information 600b plotted for different spatial distributions of electrons. The SEM system may use the distributions to determine the material and / or color of a sample, such as by comparing the distributions to known distributions of materials, or using a trained statistical model.

[0187] FIG. 7 shows an exemplary sample 700a for an SEM system as well as seventh exemplary data that may be gathered by the SEM system for the sample 700a. The SEM system may be the SEM system 100 of FIG. 1 A, and it includes a probe 102 configured to direct incoming probe electrons 108 at a sample 700a, and a detector (not illustrated) configured to detect electrons scattered by the sample 700a, in order to measure electron information 700b. Sample 700a comprises a 10 nm cube of osmium in a 100 nm epoxy cube. As shown in FIG. 7, the SEM system may obtain electron information 700b based on detecting electrons scattered by sample 700a. FIG. 7 may represent data with 8373 detected BSE, 8376 total BSE, and 50000 incoming electrons. FIG. 7 includes nine plots showing the electron information 700b plotted for different spatial distributions of electrons. The SEM system may use the distributions to determine the material and / or color of a sample, such as by comparing the distributions to known distributions of materials, or using a trained statistical model.

[0188] FIG. 8 shows an exemplary sample 800a for an SEM system as well as eighth exemplary data that may be gathered by the SEM system for the sample 800a. The SEM system may be the SEM system 100 of FIG. 1 A, and it includes a probe 102 configured to direct incoming probe electrons 108 at a sample 800a, and a detector (not illustrated) configured to detect electrons scattered by the sample 800a, in order to measure electron information 800b. Sample 800a comprises a 10 nm cube of iridium in a 100 nm epoxy cube. As shown in FIG. 8, the SEM system may obtain electron information 800b based on detecting electrons scattered by sample 800a. FIG. 8 may represent data with 8466 detected BSE, 8467 total BSE, and 50000 incoming electrons. FIG. 8 includes nine plots showing the electron information 800b plotted for different spatial distributions of electrons. The SEM system may use the distributions to determine the material and / or color of a sample, such as by comparing the distributions to known distributions of materials, or using a trained statistical model.

[0189] FIG. 9 shows an exemplary sample 900a for an SEM system as well as ninth exemplary data that may be gathered by the SEM system for the sample 900a. The SEM system may be the SEM system 100 of FIG. 1 A, and it includes a probe 102 configured to direct incoming probe electrons 108 at a sample 900a, and a detector (not illustrated) configured to detect electrons scattered by the sample 900a, in order to measure electron information 900b. Sample 900a

[0190] #14520034v4 comprises a 10 nm cube of platinum in a 100 nm epoxy cube. As shown in FIG. 9, the SEM system may obtain electron information 900b based on detecting electrons scattered by sample 900a. FIG. 9 may represent data with 8692 detected BSE, 8697 total BSE, and 50000 incoming electrons. FIG. 9 includes nine plots showing the electron information 900b plotted for different spatial distributions of electrons. The SEM system may use the distributions to determine the material and / or color of a sample, such as by comparing the distributions to known distributions of materials, or using a trained statistical model.

[0191] FIG. 10 shows an exemplary sample 1000a for an SEM system as well as tenth exemplary data that may be gathered by the SEM system for the sample 1000a. The SEM system may be the SEM system 100 of FIG. 1 A, and it includes a probe 102 configured to direct incoming probe electrons 108 at a sample 1000a, and a detector (not illustrated) configured to detect electrons scattered by the sample 1000a, in order to measure electron information 1000b. Sample 1000a comprises a 10 nm cube of gold in a 100 nm epoxy cube. As shown in FIG. 10, the SEM system may obtain electron information 1000b based on detecting electrons scattered by sample 1000a. FIG. 10 may represent data with 9008 detected BSE, 9011 total BSE, and 50000 incoming electrons. FIG. 10 includes nine plots showing the electron information 1000b plotted for different spatial distributions of electrons. The SEM system may use the distributions to determine the material and / or color of a sample, such as by comparing the distributions to known distributions of materials, or using a trained statistical model.

[0192] FIG. 11 shows an exemplary sample 1100a for an SEM system as well as eleventh exemplary data that may be gathered by the SEM system for the sample 1100a. The SEM system may be the SEM system 100 of FIG. 1 A, and it includes a probe 102 configured to direct incoming probe electrons 108 at a sample 1100a, and a detector (not illustrated) configured to detect electrons scattered by the sample 1100a, in order to measure electron information 1100b. Sample 1100a comprises a 10 nm cube of lead in a 100 nm epoxy cube. As shown in FIG. 11, the SEM system may obtain electron information 1100b based on detecting electrons scattered by sample 1100a. FIG. 11 may represent data with 10481 detected BSE, 10486 total BSE, and 50000 incoming electrons. FIG. 11 includes nine plots showing the electron information 1100b plotted for different spatial distributions of electrons. The SEM system may use the distributions to determine the material and / or color of a sample, such as by comparing the distributions to known distributions of materials, or using a trained statistical model.

[0193] FIG. 12 shows an exemplary sample 1200a for an SEM system as well as twelfth exemplary data that may be gathered by the SEM system for the sample 1200a. The SEM system may be the SEM system 100 of FIG. 1 A, and it includes a probe 102 configured to direct

[0194] #14520034v4 incoming probe electrons 108 at a sample 1200a, and a detector (not illustrated) configured to detect electrons scattered by the sample 1200a, in order to measure electron information 1200b. Sample 1200a comprises a 10 nm cube of uranium in a 100 nm epoxy cube. As shown in FIG. 12, the SEM system may obtain electron information 1200b based on detecting electrons scattered by sample 1200a. FIG. 12 may represent data with 9692 detected BSE, 9697 total BSE, and 50000 incoming electrons. FIG. 12 includes nine plots showing the electron information 1200b plotted for different spatial distributions of electrons. The SEM system may use the distributions to determine the material and / or color of a sample, such as by comparing the distributions to known distributions of materials, or using a trained statistical model.

[0195] Electron information collected by an SEM system for electrons scattered by a sample may comprise various types of electron information. As shown in 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12, electron information 300b, 400b, 500b, 600b, 700b, 800b, 900b, 1000b, 1100b, and 1200b include various types of electron information.

[0196] Electron information may be collected having multi-dimensional electron profile information. Multi-dimensional electron profile information may in turn be collected at a set of points arranged in multiple spatial dimensions. For example, electron profile information may be collected along an electron profile dimension in that it includes one or more of an electron count along a first profile dimension or an electron energy along a second profile dimension, or another electron measurement.

[0197] Electron profile information may also be collected in one or more spatial dimensions. The spatial dimensions may be for example, on a two-dimensional surface, or on a three- dimensional surface. The surface may comprise a plurality of pixels. Each pixel on a two- dimensional surface may have two spatial coordinates associated with which it is associated. Each pixel on a three-dimensional surface therefore have three spatial coordinates associated with which it is associated.

[0198] Each pixel may collect electron information in two dimensions, e.g., electron count and electron energy, as described above. Therefore, in total, each pixel of a two-dimensional surface may have four pieces of associated information (in each sampling period): two spatial coordinates, electron count, and electron energy. In total, each pixel of a three-dimensional surface may have five pieces of associated information (in each sampling period): three spatial coordinates, electron count, and electron energy.

[0199] At the first row, first column, the electron information shows a first plot of hemisphere detector (which may have a radius of about 800-1200 pm, or a radius of about 1000 pm) counts, with electrons plotted as points, and with a horizontal axis for X position of the hemisphere

[0200] #14520034v4 detector pixel in pm and a vertical axis for Y position of the hemisphere detector pixel in pm. In some embodiments, the center of the sample top surface may correspond to a location at the origin (e.g., X = 0 pm, Y = 0 pm, and Z = 0 pm). The plot at the first row, first column may correspond to a parallel projection of the electron profile (from the hemisphere detector) along the Z axis onto the X-Y plane at Z = 0 pm. At the first row, second column, the electron information shows a second plot at ip between 45° and 135° (e.g., a “north” quadrant) with electron counts plotted on the vertical axis, and with a horizontal axis for (p in degrees. At the first row, third column, the electron information shows a third plot with 2D stereographic projection counts, with electrons plotted as points, and with a horizontal axis for X position in pm and a vertical axis for Y position in pm. The third plot at the first row, third column may correspond to a projection of the electron profile from the point X = 0 pm, Y = 0 pm, and Z = 1000 pm (1000 pm below the origin) on to the X-Y plane at Z = -1000 pm (the top of the hemisphere detector, 1000 pm above the origin).

[0201] While the exemplary detector may have a size of about 1000 pm as discussed above, detectors in various embodiments may have other dimensions. For example, detectors may have a size ranging from about a few millimeters to several centimeters. Detectors may be sized based on sample size or based on a desired sample space size.

[0202] At the second row, first column, the electron information shows a second plot at ip between 135° and -135° (e.g., a “west” quadrant) with electron counts plotted on the vertical axis, and with a horizontal axis for (p in degrees. At the second row, second column, the electron information shows a second plot at ip between -180° and 180° (e.g., a sum of all four quadrants) with electron counts plotted on the vertical axis, and with a horizontal axis for (p in degrees. At the second row, third column, the electron information shows a second plot at ip between -45° and 45° (e.g., a “east” quadrant) with electron counts plotted on the vertical axis, and with a horizontal axis for (p in degrees.

[0203] At the third row, first column, the electron information shows a seventh plot with 2D flattened detector counts, with electrons plotted as points, and with a horizontal axis for ip in degrees and a vertical axis for (p in degrees. At the third row, second column, the electron information shows a second plot at ip between -135° and -45° (e.g., a “south” quadrant) with electron counts plotted on the vertical axis, and with a horizontal axis for (p in degrees. At the third row, third column, the electron information shows a ninth plot with 2D energy profile, with energy in kV on the vertical axis, and with horizonal axes for ip and (p in degrees.

[0204] SEM systems provided herein may include detectors having various configurations. For example, detectors of SEM systems may be arranged with different shapes, with different

[0205] #14520034v4 positions relative to probes or samples, and / or with different orientations relative to probes or samples. FIGs. 13A-13C show a various exemplary embodiment of detectors of SEM systems.

[0206] FIG. 13A shows an SEM system 1300a with a detector 104a, as well as a probe 102 and a sample 106. In FIG. 13 A, detector 104a includes a hemisphere detection surface.

[0207] FIG. 13B shows an SEM system 1300b with a detector 104b, as well as a probe 102 and a sample 106. In FIG. 13B, detector 104b includes a planar detection surface that is a circular detection surface.

[0208] FIG. 13C shows an SEM system 1300c with a detector 104c, as well as a probe 102 and a sample 106. In FIG. 13C, detector 104c includes a plurality of planar detection surfaces 104c- 1, 104c-2, 104c-3, and 104c-4. In FIG, 13C, the planar detection surfaces 104c-l, 104c-2, 104c- 3, and 104c-4 are angled towards the sample 106 (and away from the probe 102 and its axis of electron emission) and are positioned in different quadrants above the sample 106 (and therefore also positioned in different quadrants relative to the probe 102 and its axis).

[0209] According to various embodiments, detectors of SEM systems may comprise one or more three-dimensional detection surfaces, and / or one or more planar detection surfaces. For example, detectors may include three-dimensional detection surfaces, such as a concave detection surface, a partial sphere detection surface, or a hemisphere detection surface.

[0210] In some embodiments, detectors may include planar detection surfaces, such as circular detection surfaces. In some embodiments, the planar detection surface may be a single planar detection surface of the detector. In other embodiments, the detector may comprise a plurality of planar detection surfaces.

[0211] Detection surfaces may also be arranged relative to the probe and / or sample position of the SEM system. For example, the detection surfaces may be arranged at different distances along the axis of the probe of the SEM system, where the probe axis is the axis along which the probe emits electrons. The detection surfaces may also be arranged at different distances along directions perpendicular to the probe axis. Further, the detection surfaces may be arranged at different angles relative to the probe axis and / or the sample position. For example, a detector may include three or more planar detection surfaces that are arranged around an axis of the probe, where the normal vectors of the three or more planar detection surfaces are angled relative to the axis. FIG. 13C shows one such exemplary arrangement. In FIG. 13C, the detector 104c includes four planar detection surfaces 104c-l, 104c-2, 104c-3, and 104c-4. that are arranged around the axis in four different quadrants relative to the sample 106, with their normal vectors facing the sample 106.

[0212] #14520034v4 The detection surfaces may be arranged to gather sufficient data from electrons such that subvoxel features may be measured without necessarily capturing every single scattered electron. For example, the detection surfaces may be arranged in positions configured to capture a majority of or a statistically sufficient portion of the electrons scattered by the sample. For example, tests or simulations may be used to determine optimal positioning of the one or more detection surfaces, in order to ensure that a statistically sufficient portion of scattered electrons are captured. The statistically sufficient portion of electrons may correspond to an amount of scattered electrons sufficient for the SEM system to determine subvoxel features of the sample using the measured electron data. In various embodiments, detector size and position may be different based on desired performance or cost. For example, a bigger or more complexly shaped detector may cost more but capture more electrons and therefore provide more accurate measurements or require less model training. In other embodiments, a smaller or most simply shaped detection may cost less and capture fewer electrons, therefore requiring more model training in order to provide similar accuracy measurements of bigger or more complexly shaped detectors.

[0213] In various embodiments, a detector may include a gap. The gap may comprise an open space between the probe 102 and the sample. The probe may direct electrons through the gap, along its emission axis. In some embodiments, the gap may comprise a hole in a detection surface, though the gap may also include an open space between two or more different detection surfaces. In FIG. 13A, detector 104a comprises a gap 1302a that is an opening in the hemisphere detection surface. In FIG. 13B, detector 104b comprises a gap 1302b that is an opening in the planar, circular detection surface. As such, the detector 104b may form a donut shape. In FIG. 13C, detector 104c includes gap 1302c which is an open space between the plurality of planar detection surfaces 104c-l, 104c-2, 104c-3, and 104c-4.

[0214] FIG.25A shows a fourth exemplary embodiment of a detector 2502 and FIGs. 25B and 25C show an exemplary embodiment of an SEM system 2500 that includes the detector 2502. Detector 2502 may comprise one of the other detectors described herein, such as detector 104, detector 104a, 104b, or 104c. As shown in FIG. 25A, the detector 2502 includes a sensor 2504, and a sample may be arranged in a sensing region 2506. FIGs. 25B and 25C show one example of a detector arrangement in the detector system 2500. For example, the detector 2502 may comprise a Medipix3 detector. Sensor 2504 of detector 2502 may have sensor area of about 14.1 x 14.1 mm2. In some embodiments, sensor 2504 has an array of 256 x 256 pixels. Each pixel of the sensor may have an area of about 55 x 55 gm2.

[0215] #14520034v4 In some embodiments, two or more detectors 2502 may be arranged with the planes of their sensors 2504 not parallel. For example, the sensors 2504 may be arranged at an angle to each other. For example, each detector 2052 may be angled at 45° relative to the incoming probe electron beam 2508, forming the illustrative “rooftop” configuration illustrated in FIGs. 25B and 25C. An exemplary sample is arranged in the sensing region 2506 and is represented by a cube. In some embodiments, the two detectors 2052 are positioned inside an SEM system (e.g., directly below the objective lens of the electron column). In the figures, the detectors 2502 are displayed with transparency and added shadows, for illustrative purposes.

[0216] In some embodiments, the sample may be moved (e.g., up and down along a vertical direction aligned with the electron column). The SEM system moving the sample may allow the two detectors 2502 to capture electrons with larger backscattering angles (e.g., between 20° and 70°) relative to the incoming probe electrons. Movement of the sample thus may provide for measurement of backscattered electrons over a wide range of angles.

[0217] Some exemplary experimental and / or simulated experimental results and SEM system parameters are described with respect to the SEM system 2500. For example, the exemplary experimental and / or simulated experimental results and SEM system parameters may provide extracted elemental information using the angular distributions of backscattered electrons detected using the SEM system 2500. In some embodiments, experimental and / or simulated experimental results are provided for the moving sample techniques.

[0218] In some embodiments, SEM systems may perform energy thresholding. For example, detectors may detect electrons and / or output data of electrons having energies about a threshold energy. In some embodiments, a detector such as a Medipix3 detector may detect electrons and / or output data of electrons with energy thresholding.

[0219] For example, some detectors, such as a Medipix3 detector may detect electrons that have energies greater than or equal to 5 keV. According to some exemplary embodiments, experimental and / or simulated experimental data is provided with respect to energy thresholding and the effects thereof on angular distributions. For example, exemplary Monte Carlo simulations are provided using 10 keV incoming probe electron beams scattered from nine different bulk materials (with Z representing the atomic number of the element): carbon (Z=6); silicon (Z=14); vanadium (Z=23); copper (Z=29); niobium (Z=41); silver (Z=47); neodymium (Z=60); tantalum (Z=73); and gold (Z=79).

[0220] FIGs. 26A, 26B, 26C, 26D, 26E, 26F, 26G, 26H, and 261 show further exemplary data of an SEM system for determining material and / or color information of an SEM image. These figures represent simulated experimental data. For example, FIG. 26A shows a plot 2600a for

[0221] #14520034v4 carbon (Z=6); FIG. 26B shows a plot 2600b for copper (Z=29); FIG. 26C shows a plot 2600c for neodymium (Z=60); FIG. 26D shows a plot 2600d for silicon (Z=14); FIG. 26E shows a plot 2600e for niobium (Z=41); FIG. 26F shows a plot 2600f for tantalum (Z=73); FIG. 26g shows a plot 2600g for vanadium (Z=23); FIG. 26H shows a plot 2600h for silver (Z=47); and FIG. 261 shows a plot 2600i for gold (Z=79). FIGs 26A, 26B, 26C, 26D, 26E, 26F, 26G, 26H, and 261 show angular distributions of backscattered electrons for the nine different bulk materials, with angle along the horizontal axis and electron count along the vertical axis. In each of FIGs. 26A, 26B, 26C, 26D, 26E, 26F, 26G, 26H, and 261, the solid lines represent all backscattered electrons (e.g., without energy thresholding), and dotted lines represent electrons that retain at least 90% of initial energy (e.g., with energy thresholding). The illustrative simulated experimental data is provided using a 10 keV incoming probe electron beam. In FIGs. 26A, 26B, 26C, 26D, 26E, 26F, 26G, 26H, and 261, the electron counts may be normalized.

[0222] FIGs. 27A and 27B show comparisons of the exemplary data of an SEM system for determining material and / or color information of an SEM image from FIGs. 26A, 26B, 26C, 26D, 26E, 26F, 26G, 26H, and 261. FIG. 27A shows an exemplary overlay of the normalized angular distributions of the nine different bulk materials without energy thresholding. As may be appreciated from FIG. 27A, the angular distributions of different materials without energy thresholding show more similar profiles, increasing the difficulty of differentiating different materials and / or elements (and thus colors). FIG. 27B shows an exemplary overlay of the normalized angular distributions with an energy threshold of 90% incoming probe electron energy. As may be appreciated from FIG. 27B, the angular distributions of different materials with energy thresholding show substantially different profiles, increasing the ease of detecting different materials and / or elements (and thus colors).

[0223] Accordingly, as may be appreciated by comparing the exemplary simulated data illustrated in FIGs. 27A to that of FIG. 27B, performance of energy thresholding by an SEM system may affect the angular distribution of electron counts. In some embodiments, an SEM system may apply energy thresholding to generate more pronounced differences in electron distributions, e.g., using a threshold (e.g., a lower threshold) of 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 85%, 90%, 95%, 98%, or 99% of the initial energy of the electron beam, where electrons having energies below the lower threshold are not used in the electron distribution. In some embodiments, the SEM system may use an upper threshold, where electrons having energies above the upper threshold are not used in the electron distribution. For example, an upper threshold may be 50%, 80%, 90%, 95%, 98%, 99%, 100%, 101%, 102%, 105%, 110%, 120%, or 150% of the initial energy of the electron beam. In some embodiments, an SEM

[0224] #14520034v4 system may use one of the listed lower thresholds in combination with one of the listed upper thresholds, which may be used to generate an electron distribution for a band of electrons having energies between the upper and lower thresholds. In some embodiments, an SEM system may use one, two, three, or more of such bands to analyze electron information and determine one or more materials of a sample. Some groups of elements having lower or higher atomic numbers or having other properties may be more differentiable through the use of particular electron energy bands.

[0225] As such, SEM systems may store parameters and / or training data generated based on energy distribution information obtained using energy thresholding. Such parameters and / or training data may be generated based on the distinctions in the energy distributions for different elements, (e.g., for high energy incoming probe electrons). It may also be appreciated that distributions of the same material may differ between the bulk materials at 10 keV (e.g., as illustrated in FIGs. 26A, 26B, 26C, 26D, 26E, 26F, 26G, 26H, and 261) and a small 10-nm cube embedded in a 100 * 100 * 100 nm3 epoxy resin at 1 keV, (e.g., as described with respect to FIGs. 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12). As such, SEM systems may have parameters and / or training data generated based on differences in scattering behavior provided by differences in sample size and energy.

[0226] FIGs. 28A and 28B show further exemplary data of an SEM system for determining material and / or color information of an SEM image. FIG. 28A shows exemplary experimental data for two bulk materials, silicon and copper which may be compared with the Monte Carlo simulation data of FIG. 28B. FIG. 28 A shows plot 2800a of angular distributions of bulk silicon (at left of plot 2800a, the top curve) and copper (at left of plot 2800a, the bottom curve). The data of FIG. 28 A is for example representative of a 10 keV, 5 nA incoming electron beam. Data may be representative of two different working distances of 20 mm (solid lines) and 30 mm (dash lines) joined, and normalized. As may be appreciated from FIG. 28A, different materials (here copper and silicon) exhibit distinct angular distributions when measured. For example, the differences may be determined based on differences in shape, width, and angle of maximum intensity. The characteristics in angular distribution for different materials may be used by an SEM system to differentiate between the multiple materials (here, two elements). For example, the differentiation may be performed independent of total electron count.

[0227] FIG. 28B shows plot 2800b of angular distributions of bulk silicon (at left of plot 2800b, the bottom curve) and copper (at left of plot 2800b, the top curve). FIG. 28B shows simulated data comprising Monte Carlo simulations of backscattered electron angular distributions for bulk silicon and copper. For example, FIG. 28B is representative of a simulation using 10 million

[0228] #14520034v4 incoming electrons at 10 keV energy with a detection threshold of 9 keV (90% of initial energy). As may be appreciated from FIG. 28B, the angular distributions electrons of silicon and copper differ, e.g., having distinct shapes and intensities. As may be appreciated from FIGs. 28A and 28B, simulations provide a good qualitative match with experimental data. In some embodiments, an SEM system may be trained on simulation data, experimental data, or a combination of the two. For example, an SEM system may be trained at least in part on Monte Carlo simulations, the simulations used for predicting behavior of backscattered electrons.

[0229] According to various embodiments, SEM systems may store and / or use parameters for different materials (e.g., elements). The SEM systems may collect data for a sample and compare the collected data to known parameters for different materials, and based on a comparison result, determine one or more materials are present in the sample. For example, the parameters may define a known electron distribution (e.g., angular distribution) for two or more materials. In some embodiments, the SEM systems may calculate parameters for a collected electron distribution and compare the calculated parameters to the known parameters and determine material with the least error (e.g., using a lookup table or a technique such as least squares). In some embodiments, the SEM systems may compare points in a collected electron distribution to a curve defined by the known parameters and determine material with the least error (e.g., using a technique such as least squares).

[0230] Exemplary fitting functions for backscattered electron angular distributions are now described. In some embodiments, backscattered electron angular distributions represent the probability of detecting electrons at a backscattered angle ranging from 0 to 90° relative to the incoming probe electron beam. SEM systems described herein may use a variety of different techniques to extract elemental information from such angular distribution curves. In some embodiments, a system may use a fitting function that reduces the curves to a few parameters. Such a technique provides an effective method for performing straightforward comparisons among angular distributions from different elements. Various functions can be used to fit the angular distributions, non-limiting examples of which are now provided.

[0231] In some embodiments, an SEM system may use a polynomial function that describes a distribution curve using, e.g., three parameters, such as: f(cp; a, b, c) = cup5+ bcp3+ ccp

[0232] In some embodiments, an SEM system may use a Power Sine function that is defined by three parameters: ho, which affects the amplitude, cpo, which affects the location of the peak

[0233] #14520034v4 (e.g., the mode), and p, which affects the distribution width. The Power Sine function may be represented by: fPS.<p; h0,<p0,p') = h0(sin(p'ypwhere 0’ is a piecewise function, and may be defined by:

[0234] FIGs. 29A, 29B, and 29C show parameters of an SEM system for determining material and / or color information of an SEM image. For example, FIGs. 29A, 29B, and 29C show how each of the three parameters affect the Power Sine function. Lighter traces indicate smaller parameter values, and the darker traces indicate larger parameter values for the respective parameters. As ho is changed (plot 2900a of FIG. 29A), the amplitude of the distribution changes, and the width and mode of the distribution may be constant. As 0o changes (plot 2900b of FIG. 29B), the mode of the distribution shifts either to higher or lower angles, which may have a moderate effect on the width of the distribution and may not affect the amplitude. As p changes (plot 2900c of FIG. 29C), the width of the distribution increases or decreases and the amplitude and mode may be unchanged.

[0235] In some embodiments, an SEM system may use a Power Trig function. A Power Trig function may be similar to a Power Sine function, but may not use piecewise functions. A Power Trig function may be defined by three parameters: ho, which affects the amplitude and p and q which control the peak width and the location of the location of the peak (e.g., the mode). A Power Trig function may be defined as fPT<p; h0, p, q) = h0N cos <p)psin <p)q+1where A is a normalization factor that configured to normalize based on how p and q affect amplitude of a distribution. N may be defined by: l(p + q + 1)P+£?+1N~ J pp(q + 1)£?+1

[0236] A Power Trig function may not have an explicit parameter for mode of the distribution, but the mode may be provided by:

[0237] COS .0 = l - V -

[0238] Ip + q + 1

[0239] FIGs. 29D, 29E, and 29F show parameters of an SEM system for determining material and / or color information of an SEM image. For example, FIGs. 29D, 29E, and 29F show how

[0240] #14520034v4 each of the three parameters affect the Power Trig function. Lighter traces indicate smaller parameter values, and darker traces indicate larger parameter values for the respective parameters. For the Power Trig equation, ho affects the amplitude and may have effect on the distribution width or mode (plot 2900d of FIG. 29D). The parameter p affects both the peak width and mode, shifting the distribution toward smaller angles and decreasing the width as p is increased (plot 2900e of FIG. 29E). The parameter q shifts the distribution toward larger angles while decreasing the width (plot 2900f of FIG. 29F). By changing both p and q, the effects of p and q may be combined, allowing for the width and mode of the distribution to be varied freely. It should be appreciated that the normalization factor may be configured to normalize amplitude. For example, without the normalization factor, increasing p and / or q may decrease the amplitude of the distribution.

[0241] In some embodiments, SEM systems may extract the elemental information without fitting an angular distribution to a specific function. For example, SEM system may determine a ratio of electron counts at two different angles. The relationship between electron counts at different angles may provide quicker processing in certain operating environments. In some embodiments, the ratio of electron counts may be determined as a ratio of count at a first angle and count at a second angle. The first angle may be, for example, greater than 15°, 20°, or 25°, less than 30, 35, 40, or 45° and / or between 15 and 45°, between 20° and 40°, between 20 and 30°, or may be about 25°. The second angle may be, for example, greater than 45°, 55°, 60°, 65, less than 75°, 80°, 85°, and / or between 45 and 85°, between 50 and 80°, between 60 and 80°, between 65 and 75°, or may be about 65°, about 70°, or about 75°. For example, exemplary ratios for 25° and 65° (1^=25 / 1^=65) and 25° and 75° (1^=25 / 1^=75) are discussed in more detail below with respect to Table 1.

[0242] The simulated experimental data represented by FIGs. 26A, 26B, 26C, 26D, 26E, 26F, 26G, 26H, and 261 (e.g., Monte Carlo simulations) demonstrate techniques for elemental detection using backscattered electron angular distributions. For at least some materials, trends of changes may not be immediately apparent when electrons of all energies are counted. However, as described herein, SEM systems may use energy thresholding to filter collected data signals, thereby enhancing detection of different materials. In some embodiments, energy thresholding may improve detection because high-energy backscattered electrons undergo fewer collisions, e.g., such that these electrons have preserved signatures that distinguish different elements.

[0243] FIGs. 30 A, 30B, 30C, 30D, 30E, and 3 OF show further parameters of an SEM system for determining material and / or color information of an SEM image. These figures, along with

[0244] #14520034v4 Table 1, provide additional demonstration of relationships between angular distribution and elemental information. For example, FIGs. 30A, 30B, 30C, 30D, 30E, and 30F, and Table 1 show exemplary Power Sine fitting parameters for different atomic number Z. Each column shows the values for one of the three parameters that define the Power Sine function. FIGs. 30A, 30C, and 30E show each parameter for the Power Sine function after fitting electron distribution data (e.g., fitting of a full simulated angular distribution), while FIGs. 30B, 30D, and 30F show each parameter for the Power Sine function after fitting electron distribution data with energy thresholding (e.g., filtering out backscattered electrons with less than 90% of the primary energy). As such, FIGs. 30A, 30B, 30C, 30D, 30E, and 30F provide exemplary parameters for Power Sine fits of electron angular distributions as a function of atomic number. Values for FIGs. 30B, 30D, and 30F (using energy thresholding) are also shown in Table 1.

[0245] Table 1 : First exemplary parameters for SEM systems.

[0246] According to some first exemplary embodiments, Table 1 shows parameters for power Sine fits (parameters ho,p, and o). In the example of Table 1, the parameters are determined from fits of simulated distributions of bulk materials at Ao = 10 keV with energy thresholding at 90% Eo. Exemplary intensity ratios of angular distributions are provided in in the last two columns, for a 25° to 65° ratio and a 25° to 75° ratio.

[0247] Referring back to In FIG. 30 A, 30C, and 30E, it may be appreciated how the Power Sine parameter values change with atomic number Z for a fit of the full angular distribution to the Power Sine function. In plot 3000a of FIG. 30 A, a trend for ho provides for ho to increase (e.g., monotonically) as Z increases. In some embodiments, the ho trend may plateau at larger Z values. Similarly, a comparable trend is observed in the backscatter coefficient of different elements, which also increases monotonically with Z. This behavior underlies the material contrast in conventional electron microscopy, including TEM and SEM. In some embodiments, the plateau at large Z may be due to reduced distinction between heavy elements. In plot 3000c

[0248] #14520034v4 of FIG. 30C, a trend for p provides for p to tend to decrease as Z increases, though in some embodiments, the trend may not be monotonic with increasing Z. In plot 3000e of FIG. 30E, a trend for < >o provides for < >o to tend to decrease as Z increases, though in some embodiments, the trend may not be monotonic with increasing Z.

[0249] Referring back to FIG. 30B, 30D, and 30F, it may be appreciated how the Power Sine parameter values change with atomic number Z for a fit of the energy thresholding distribution to the Power Sine function (e.g., when only backscattered electrons that retain 90% of their initial energy are considered). In plot 3000b of FIG. 30B, a trend for parameter ho provides for ho to increase (e.g., monotonically) with Z, and this trend may be more linear than in plot 3000a and may be without plateauing. In some embodiments, the ho in plot 300b may be due to high-Z materials ejecting backscattered electrons at high energies, e.g., due those materials increased propensity for large-angle deflections. In plot 3000d of FIG. 30D, a trend for p provides for p to decrease (e.g., monotonically) as Z increases. In plot 3000f of FIG. 30F, a trend for (po provides for (po to decrease (e.g., monotonically) as Z increases. In some embodiments, trends for p and (po may be more monotonic when energy filtering is applied because high energy backscattered electrons retain the strongest signature of the sample material. As such, SEM systems may use energy information of backscattered electrons (e.g., by using energy thresholding) to more accurately determine elemental composition (e.g., at high incoming probe electron energies).

[0250] As may be appreciated from FIGs. 30A, 30B, 30C, 30D, 30E, and 30F and Table 1, an SEM system may use energy filtering to collect electron distribution information and determine materials of a sample. For example, the collected distribution may be fitted with Power Sine parameters to predict an atomic number of a material. As an example, if a material’s parameters (using energy thresholding) are fitted top = 1.2 and (po = 59°, an SEM system can compare these fitted parameters to known parameters similar to those of FIGs. 30B, 30D, and 30F and / or Table 1. Based on a result of the comparison, the SEM system can predict atomic number and / or material, which may be either a material with known parameters or a material with parameters inferred or implied based on other materials with known parameters. Returning to the example, the system may predict the atomic number to be around 30, and may determine that the material is copper with Z=29, with copper having known parameters. In some embodiments, the system may determine that the material is zinc (Z=30), with zinc not having known parameters but instead having inferred or implied parameters.

[0251] In some embodiments, an SEM system may use ratios of electron counts at different angles to determine materials. Ratio techniques also provide for trends based on atomic number Z. The intensity ratios of 25° over 65° (1^=25 / 1^=65) and 25° over 75° (1^=25 / 1^=75) may each

[0252] #14520034v4 increase consistently with atomic number. Accordingly, in some embodiments, an SEM system may use a simpler detector configuration with two or more detectors capable of measuring backscattered electrons at two or more angles, which can provide sufficient information to distinguish between different elements. The angle ratio techniques may provide a more efficient system with a simplified detector arrangement and reduced computational complexity.

[0253] Parameters may also be fitted with experimentally collected data. Table 2 provides parameters for Power Sine functions fitted with experimentally collected angular distributions of several bulk materials. Table 2 shows parameters for four materials: carbon (Z = 6); silicon (Z = 14); copper (Z = 29); and indium (Z = 49). Table 2 may represent parameters determined using 10 keV incoming probe electrons. Table 2 also provides average and standard deviation of the Power Sine parameters p and o. As may be appreciated from Table 2, trends for p and o are provided, where p and o decrease as the atomic number increases, similar to the Monte Carlo simulation results described above.

[0254] Table 2: Second exemplary parameters for SEM systems.

[0255] SEM systems described herein may be configured to detect different materials. For example, in some embodiments, SEM systems may store fitting parameters or training data used to identify different ranges of materials. For example, in one embodiment, the SEM systems may store information for differentiating between two or more of Carbon, Silicon, Copper, Iridium and / or additional materials. In another embodiment, the SEM systems may store information for differentiating between two or more of Beryllium, Boron, Carbon, Magnesium, Aluminum, Silicon, Phosphorus, Titanium, Vanadium, Chromium, Manganese, Iron, Cobalt, Nickel, Copper, Zinc, Gallium, Germanium, Arsenic, Selenium, Yttrium, Zirconium, Niobium, Molybdenum, Ruthenium, Rhodium, Palladium, Silver, Cadmium, Indium, Tin, Antimony, Hafnium, Tantalum, Tungsten, Osmium, Iridium, Platinum, Gold, Lead, Bismuth, Uranium, Silicon Carbide, Silicon Nitride, Silicon dioxide, Gallium Arsenide and / or other materials. In yet another embodiment, the SEM systems may store information for differentiating between two or more of the materials comprising elements with atomic numbers between 1 (Hydrogen) and 92 (Uranium) and / or other materials.

[0256] #14520034v4 SEM systems describe herein may use different incoming probe electron energy Eo). In some embodiments, incoming probe electron energy Eo) may be greater than 0.05, 5, or 7.5 keV, less than 25 or 30 keV, and / or between 7.5 and 25 keV, between 5 to 25 keV, or between 0.05 to 30 keV. SEM systems describe herein may use different energy thresholds. In some embodiments, energy thresholds may be greater than 0%, 20%, or 40%, less than 90% or 99%, and / or between 0% and 90%, between 20% and 99%, and between 0% and 99%. SEM systems may use different numbers of fitting parameters. In some embodiments, the number of fitting parameters used may be greater than 2, less than 3 or 5, and / or between 2 and 3 or 2 and 5.

[0257] Furthermore, SEM systems collecting color information may also collect subvoxel information, e.g., spatial information of sample having dimensions smaller than a dimension of the SEM probe. The SEM systems described herein may collect both color information and subvoxel information in the same scan. In some embodiments, the SEM systems may determine a plurality of subvoxels but collect color information for each voxel, or may determine a plurality of subvoxels and collect color information for each voxel. SEM systems for performing subvoxel microcopy are now described.

[0258] II. Subvoxel SEM Based Volume Electron Microscopy

[0259] A scanning electron microscopy (SEM) system performs subvoxel microscopy with a probe and detector. The probe directs incoming probe electrons at a sample with an energy and a direction. The detector detects electrons scattered by the sample and generates a two- dimensional energy profile map of the detected electrons. The system may determine subvoxel information including features of the sample smaller than a size of the probe using the energy and direction and the two-dimensional energy profile map. The system may determine three- dimensional subvoxel information of the sample. The system may be a focused ion beam scanning electron microscopy (FIB-SEM) system with an emitter directing a FIB at the sample to separate layers thereof. For each of multiple layers, the system may obtain the energy and direction and generate the two-dimensional energy profile map. The system may generate three- dimensional subvoxel volume information of the sample thicker than individual layers.

[0260] Provided is a scanning electron microscopy (SEM) system configured to transcend a resolution limit of conventional SEM systems that has persisted for 80 years. In conventional SEM systems, resolution may be one order of magnitude worse than that of transmission electron microscopy (TEM) systems, and may generally be limited by the scanning electron probe diameter. Conventional SEM architectures for image formation involves scanning the surface pixel-by-pixel and only counting the backscattered and / or secondary electrons. When

[0261] #14520034v4 pixel size is smaller than the probe size, the electron counts obtained from adjacent pixels leads to oversampling without substantial additional information. As such, electron probe diameter provides a limit of conventional SEM resolution. Conventional approaches for reducing probe size have focused on aberration mitigation by attempting to improve electron source and lens design. However, smaller conventional probes may induce larger diffraction errors worsen resolution. Accordingly, some conventional practical SEM systems may only provide resolution capped at 1-2 nm on gold on carbon calibration specimens, and 4 nm on block face biological specimens.

[0262] SEM systems described herein provide image resolution higher than conventional SEM system resolution limit. SEM systems according to the disclosure have a new architecture for forming SEM images. According to aspects of the disclosure, SEM systems may treat an SEM scanning electron probe as an illumination source with a controllable profile and record a solid angle and energy of each electron to form a two-dimensional electron energy map. A resulting two-dimensional electron energy profile may encode a combination of features in X, Y and Z directions that are smaller than a probe size of the system. This map may further have a distinctive signature pattern reflecting the unique scattering events of individual electrons. The SEM system may then use the available electron properties to mathematically reconstruct subvoxel biomolecule or other structures that are finer than the size of the electron probe.

[0263] Aspects of the disclosure provide a novel SEM detector configured to captures the two- dimensional electron energy map with high efficiency.

[0264] According to aspects of the disclosure, there is provided an apparatus, comprising a scanning electron microscopy (SEM) system, comprising a probe configured to direct incoming probe electrons at a sample, the incoming probe electrons having an energy and a direction, and a detector configured to detect electrons scattered by the sample and generate a two-dimensional energy profile map of the detected electrons.

[0265] In some embodiments, the two-dimensional energy profile map of the detected electrons comprises a map having at least two spatial dimensions (e.g., a first spatial dimension and a second spatial dimension) and, for a plurality of points in the map, a two-dimensional energy profile comprising an electron count along a first profile dimension and an electron energy along a second profile dimension.

[0266] In some embodiments, the detector is further configured to detect energy and direction of the detected electrons and generate the two-dimensional energy profile map of the detected electrons based on the detected energy and direction of the detected electrons.

[0267] #14520034v4 In some embodiments, the SEM system is further configured to determine subvoxel information of the sample using the energy of the incoming probe electrons, the direction of the incoming probe electrons, and the two-dimensional energy profile map of the detected electrons.

[0268] In some embodiments, the subvoxel information comprises features of the sample that are smaller than a size of the probe.

[0269] In some embodiments, the SEM system is further configured to determine three- dimensional subvoxel information of the sample.

[0270] In some embodiments, the SEM system is a focused ion beam scanning electron microscopy (FIB-SEM) system comprising an emitter configured to direct a FIB at the sample and separate layers of the sample using the FIB.

[0271] In some embodiments, FIB-SEM system is further configured to for a first layer of the sample having a sample layer thickness, obtain energy and direction of incoming probe electrons and generate a two-dimensional energy profile map of detected electrons, using the FIB, separate the first layer of the sample from a second layer of the sample, for the second layer of the sample, obtain energy and direction of incoming probe electrons and generate a two- dimensional energy profile map of detected electrons, and generate three-dimensional subvoxel volume information of the sample, the three-dimensional subvoxel volume information having a volume information thickness greater than the sample layer thickness.

[0272] In some embodiments, the detector is further configured to, for each of the first layer and the second layer, detect the energy and direction of the detected electrons and generate the two- dimensional energy profile map of the detected electrons based on the detected energy and direction of the detected electrons.

[0273] In some embodiments, the detector comprises a three-dimensional detection surface. In some embodiments, the detector comprises a concave detection surface. In some embodiments, the detector comprises a partial sphere detection surface. In some embodiments, the detector comprises a hemisphere detection surface.

[0274] In some embodiments, the detector comprises at least one planar detection surface. In some embodiments, the detector comprises a single planar detection surface. In some embodiments, the detector comprises a circular detection surface. In some embodiments, the detector comprises a plurality of planar detection surfaces.

[0275] In some embodiments, the detector comprises three or more planar detection surfaces and the three or more planar detection surfaces are arranged around an axis of the probe and normals of the three or more planar detection surfaces are angled relative to the axis. In some

[0276] #14520034v4 embodiments, the three or more planar detection surfaces comprises four planar detection surfaces arranged in respective quadrants around the axis.

[0277] In some embodiments, the detector further comprises a gap and the probe is configured to direct incoming probe electrons at the sample through the gap. In some embodiments, a detection surface of the detector comprises an opening and the probe is configured to direct incoming probe electrons at the sample through the opening.

[0278] According to aspects of the disclosure, there is provided a method of determining subvoxel information for use with a scanning electron microscopy (SEM) system, the method comprising obtaining an energy of incoming probe electrons and a direction of the incoming probe electrons, obtaining a two-dimensional energy profile map of detected electrons, and determining subvoxel information of a sample using the energy of incoming probe electrons, the direction of the incoming probe electrons, and the two-dimensional energy profile map of the detected electrons.

[0279] In some embodiments, obtaining the two-dimensional energy profile map of the detected electrons comprises obtaining a map having at least two spatial dimensions (e.g., a first spatial dimension and a second spatial dimension) and, for a plurality of points in the map, obtaining a two-dimensional energy profile comprising an electron count along a first profile dimension and an electron energy along a second profile dimension.

[0280] In some embodiments, the method further comprises detecting energy and direction of the detected electrons and generating the two-dimensional energy profile map of the detected electrons based on the detected energy and direction of the detected electrons.

[0281] In some embodiments, the method further comprises determining subvoxel information of the sample using the energy of the incoming probe electrons, the direction of the incoming probe electrons, and the two-dimensional energy profile map of the detected electrons.

[0282] In some embodiments, the subvoxel information comprises features of the sample that are smaller than a size of a probe of the SEM system.

[0283] In some embodiments, the method further comprises determining three-dimensional subvoxel information of the sample.

[0284] In some embodiments, the method further comprises separating layers of the sample.

[0285] In some embodiments, the method further comprises, for a first layer of the sample having a sample thickness, obtaining energy and direction of incoming probe electrons and generating a two-dimensional energy profile map of detected electrons, separating the first layer of the sample from a second layer of the sample, for the second layer of the sample, obtaining energy and direction of incoming probe electrons and generating a two-dimensional energy

[0286] #14520034v4 profile map of detected electrons, and generating three-dimensional subvoxel volume information of the sample, the three-dimensional subvoxel volume information having a volume information thickness greater than the sample layer thickness.

[0287] In some embodiments, the method further comprises, for each of the first layer and the second layer, detecting the energy and direction of the detected electrons and generating the two-dimensional energy profile map of the detected electrons based on the detected energy and direction of the detected electrons.

[0288] According to aspects of the disclosure, there is provided at least one non-transitory computer-readable storage medium having instructions encoded thereon that, when executed by at least one processor, cause the at least one processor to perform a method of determining subvoxel information for use with a scanning electron microscopy (SEM) system, the method comprising obtaining an energy of incoming probe electrons and a direction of the incoming probe electrons, obtaining a two-dimensional energy profile map of detected electrons, and determining subvoxel information of a sample using the energy of the incoming probe electrons, the direction of the incoming probe electrons, and the two-dimensional energy profile map of the detected electrons.

[0289] In some embodiments, obtaining the two-dimensional energy profile map of the detected electrons comprises obtaining a map having at least two spatial dimensions (e.g., a first spatial dimension and a second spatial dimension) and, for a plurality of points in the map, obtaining a two-dimensional energy profile comprising an electron count along a first profile dimension and an electron energy along a second profile dimension.

[0290] In some embodiments, the method further comprises detecting energy and direction of the detected electrons and generating the two-dimensional energy profile map of the detected electrons based on the detected energy and direction of the detected electrons.

[0291] In some embodiments, the method further comprises determining subvoxel information of the sample using the energy of the incoming probe electrons, the direction of the incoming probe electrons, and the two-dimensional energy profile map of the detected electrons.

[0292] In some embodiments, the subvoxel information comprises features of the sample that are smaller than a size of a probe of the SEM system.

[0293] In some embodiments, the method further comprises determining three-dimensional subvoxel information of the sample.

[0294] In some embodiments, the method further comprises separating layers of the sample.

[0295] In some embodiments, the method further comprises, for a first layer of the sample having a sample layer thickness, obtaining energy and direction of incoming probe electrons and

[0296] #14520034v4 generating a two-dimensional energy profile map of detected electrons, separating the first layer of the sample from a second layer of the sample, for the second layer of the sample, obtaining energy and direction of incoming probe electrons and generating a two-dimensional energy profile map of detected electrons, and generating three-dimensional subvoxel volume information of the sample, the three-dimensional subvoxel volume information having a volume information thickness greater than the sample layer thickness.

[0297] In some embodiments, the method further comprises, for each of the first layer and the second layer, detecting the energy and direction of the detected electrons and generating the two-dimensional energy profile map of the detected electrons based on the detected energy and direction of the detected electrons.

[0298] Aspects of the disclosure relate to a physics and mathematical model configured to reconstruct subvoxel structure.

[0299] In various embodiments, SEM system may obtain a two-dimensional electron energy map and use that to recover subvoxel information with an inverse scattering function. For example, formation of a two-dimensional electron energy map may be considered as a forward transformation of incident electrons scattered by subvoxel structures of a specimen. The forward model and the inverse scattering function are optimized through iterative progression with experimental data. In some embodiments, a library is generated and provided based on simulation and then refined through experimental measurements. The library may be used to speed up the subvoxel features prediction based on the electron energy profiles. In various embodiments, the system is configured to use artificial intelligence, including one or more trained statistical models, to enhance the accuracy of inverse scattering functions and models. For example, the system may use both an improved or optimized forward model and an improved or optimized inverse scattering function. The improved or optimized models may be obtained using Al-based training, for example, by training a statistical model using training datasets. Use of the trained statistical models may improve the overall performance of the inverse scattering function.

[0300] Aspects of the disclosure relate to subvoxel SEM architecture that transcends conventional SEM system resolution limit that has persisted since the birth of SEM system 80 years ago.

[0301] In some embodiments, an SEM system’s detector’s pixel number, energy detection resolution, and spatial arrangement relative to the specimen and electron column are improved or optimized to enable a more or most efficient detection of electron energy profiles, which are used to reconstruct subvoxels. In some embodiments the reconstruction model constructed based

[0302] #14520034v4 on a configuration of a detector, and the model is tuned based on configuration of the detector’s pixel number, energy detection resolution, and spatial arrangement relative to the specimen and electron column, or other properties. The detector and reconstruction model are included in the SEM system and provide a subvoxel SEM system configured to image with a higher resolution than allowed by conventional SEM probe size in the last 80 years.

[0303] Aspects of the disclosure relate to subvoxel FIB-SEM.

[0304] In some embodiments, subvoxel SEM systems described herein are integrated with a focused ion beam to provide a subvoxel FIB-SEM system. In some embodiments, subvoxel FIB- SEM systems may image specimen with near-atomic resolution for whole cell imaging. Conventional systems do not provide near-atomic resolution for whole cell imaging. Accordingly, SEM systems described herein may bridge a resolution and imageable volume gap between conventional imaging schema such as cryo-ET and enhanced FIB-SEM.

[0305] FIG. 15 shows an exemplary embodiment of SEM system in an operating space 1500. The operating space 1500 is defined by isotropic voxel resolution (on the y-axis) and imaging volume (on the x-axis). As illustrated in FIG. 15, subvoxel FIB-SEM systems described herein bridge the fields of structural biology and cell biology. FIG. 15 shows an operating environment of exemplary subvoxel FIB-SEM systems. This operating environment connects the fields of structural biology and cell biology by bridging a resolution and image volume gap of cryo-ET and enhanced FIB-SEM. Accordingly, SEM systems described herein may probe structure and function across scales from protein domains to proteins to organelles to cells, in an isolated form, but also in native tissue environments and within the holistic milieu of whole cells.

[0306] Aspects of the disclosure relate to subvoxel volume SEM.

[0307] According to some embodiments, SEM systems further provide an expanded subvoxel SEM architecture integrated with other volume electron microscopy technologies. These SEM systems substantially expand a horizon of other conventional volume SEM technologies, such as serial block face SEM and serial section SEM, and other imagine schema, to provide resolutions higher than the resolution limits of these conventional imaging schema, thus providing a profound impact on biology.

[0308] Aspects of the disclosure provide the following improvements over conventional systems.

[0309] First, there is provided a novel SEM detector that is configured to record angular and energy distributions of scattered electrons. A resulting two-dimensional electron energy profile encodes a combination of features in X, Y and Z directions that are smaller than a probe size of

[0310] #14520034v4 an SEM system and has a distinctive signature pattern that reflects unique scattering events of individual electrons.

[0311] Second, there is provided a mathematical and physical model configured to have inputted the above-described novel electron properties to reconstruct and output subvoxel structures having finer resolution than the size of the electron probe.

[0312] Third, there is provided subvoxel SEM systems that image with a higher resolution than conventional SEM resolution limits that have persisted since the birth of conventional SEM systems 80 years ago. The subvoxel SEM systems provided herein image with resolution beyond the electron probe diameter by collecting electron information of additional dimensions, followed by reconstruction of subvoxel features that are smaller than the electron probe size.

[0313] Fourth, there is provided subvoxel FIB-SEM systems. A subvoxel SEM system described herein is integrated with a focused ion beam, to provide a subvoxel FIB-SEM system configured to image specimens with near-atomic resolution for whole cell imaging.

[0314] Fifth, there is provided subvoxel volume SEM systems. A subvoxel SEM system described herein may be integrated with volume electron microscopy systems. The subvoxel volume SEM systems described herein provide expanded volume SEM technologies, such as serial block face SEM and serial section SEM, and other imaging schema, thereby providing imaging at resolutions higher than the resolution limits of those conventional imaging schema.

[0315] Using SEM systems described herein, resolution of SEM systems is no longer constrained by electron probe size, which has been the fundamental limit since the birth of SEM systems 80 years ago. SEM systems described herein thus provide functional improvements to all existing SEM technologies and associated platforms. Conventional SEM systems do not reach the resolutions described herein. The SEM systems described herein provided super resolution SEM that provides broad impact on life science, materials research, semiconductor manufactory, and other applications.

[0316] Aspects of the disclosure relate to public health, providing an advance in understanding of how cells and tissues function and of what causes diseases. SEM systems described herein transcend the resolution limit of conventional SEM that has persisted for 80 years. The disclosure provides subvoxel FIB-SEM reaching near-atomic resolution for whole cell imaging. In some embodiments, SEM systems described herein may be deployed broadly in the field of electron microscopy, providing discoveries in biology, physiology, pathology, and other fields. In some embodiments the SEM systems described herein provide for discovery of new aspects of structural bases of disease and provide new perspectives on therapeutic development.

[0317] #14520034v4 SEM systems described herein provide for viewing of biomolecules in cells and measuring changes in biomolecule and cell structure, quantity, distribution, and interactions, which is fundamental to understanding biology. In contrast, conventional cryo-electron tomography (cryo-ET) systems may visualize protein molecules at near-atomic resolution within cellular context but is limited to a fraction of whole cell volume.

[0318] Aspects of the disclosure relate to enhanced focused ion beam scanning electron microscopy (FIB-SEM) systems. Enhanced FIB-SEM systems provide powerful biology discovery platforms. For example, enhanced FIB-SEM systems may provide expanded maximum image volume, (for example, expanded by five orders of magnitude) which provides advanced system architecture configured to provide a finest possible isotropic resolution of 4 nm for whole cell imaging. FIB-SEM systems are configured to generate large and detailed brain connectome, and may provide open-access, three-dimensional atlases of whole cells and tissues with 4-nm voxels. Such FIB-SEM systems provide numerous transformational discoveries in life science. However, such 4-nm isotropic resolution may fall short of robust visualization of 3D ultrastructure of sub- 10 nm features. A fundamental barrier of conventional SEM systems is related to conventional SEM system architecture, which may cap SEM system resolution based on a diameter of a scanning electron probe of the SEM system.

[0319] As described above, the SEM systems described herein transcend the conventional SEM system resolution limits that have persisted for 80 years. Furthermore, SEM systems described herein may be combined a focused ion beam (FIB). Such a combined system provides subvoxel FIB-SEM configured to generate near-atomic resolution for whole cell imaging. Conventional systems do not provide near-atomic resolution for whole cell imaging. Accordingly, the SEM systems provided herein bridge fields that are currently not connected: structural biology and cell biology, by providing a probing architecture that is configured to image across scales from protein to organelle to cell, within native tissue environments.

[0320] As described throughout the disclosure, SEM systems described herein may be configured to detect subvoxel features of samples. FIG. 17A shows an exemplary SEM system voxel and subvoxels thereof. FIG. 17A shows a sample comprising a voxel 1750. According to some embodiments, voxel 1750 may have a dimension that is substantially equal to the size of a probe of an SEM system, such as the size of probe 102. Accordingly, voxel 1750 may represent a minimum resolution of a conventional SEM system that is incapable of measuring features smaller than the size of its probe.

[0321] A voxel 1750 and subvoxel features thereof, such as illustrated in FIG. 17A, may be measured by SEM systems described herein. According to some embodiments, voxel 1750

[0322] #14520034v4 comprises a plurality of subvoxels. In the illustrative embodiment of FIG. 17A, voxel 1750 comprises a plurality of eight subvoxels, arranged in a 2x2x2 cube. In other embodiments, voxel 1750 may comprise a lesser or greater number of subvoxels, such as 27 subvoxels arranged in a 3x3x3 cube, 64 subvoxels arranged in a 4x4x4 cube, or subvoxels in other arrangements than cubes, such subvoxels arranged in hexagonal packing schemes or other features arranged in other packing schemes. According to aspects of the disclosure, SEM systems described herein may measure subvoxel features such as the subvoxels 1752a-1752h shown in FIG. 17A even though a probe of the SEM system may be larger than the subvoxels 1752a-1752h.

[0323] The plurality of subvoxels in FIG. 17A includes a first subvoxel 1752a, a second subvoxel 1752b, a third subvoxel 1752c, a fourth subvoxel 1752d, a fifth subvoxel 1752e, a sixth subvoxel 1752f, a seventh subvoxel 1752g, and an eighth subvoxel 1752h. The first subvoxel 1752a is arranged in a front lower right position relative to the view of FIG. 17A and may be referred to as a 00000001 position subvoxel. The second subvoxel 1752b is arranged in a front lower left position and may be referred to as a 00000010 position subvoxel. The third subvoxel 1752c is arranged in a back lower right position and may be referred to as a 00000100 position subvoxel. The fourth subvoxel 1752d is arranged in a back lower left position and may be referred to as a 00001000 position subvoxel. The fifth subvoxel 1752e is arranged in a front upper right position and may be referred to as a 00010000 position subvoxel. The sixth subvoxel 1752f is arranged in a front upper left position and may be referred to as a 00100000 position subvoxel. The seventh subvoxel 1752g is arranged in a back upper right position and may be referred to as a 01000000 position subvoxel. The eighth subvoxel 1752h is arranged in a back upper left position and may be referred to as a 10000000 position subvoxel.

[0324] One exemplary discussion of unique electron clouds follows. In the exemplary embodiment of a gold cube in epoxy, the high atomic number of the gold material has a feature size of 5 nm, which is smaller than the incoming electron probe size of 10 nm. When the gold cube is arranged in one particular position of the epoxy relative to probe, the sample imparts upon the scattered electrons a distinct pattern in the electron cloud. This distinct pattern of the electron cloud is different from the pattern generated by the sample when the gold cube is located in any other quadrant. As merely one example of differences between the electron data, FIGs. 17C, 18B, 19B, 20B, 21B, 22B, 23B, and 24B (discussed in more detail below) show that a centroid of the electron cloud may be formed in an area opposite the area in which the gold cube is arranged, due to the high reflectivity of gold associated with its high atomic number. This unique centroid may be used by an SEM system to determine that the sample includes a

[0325] #14520034v4 gold feature with a size of 5 nm, and may identify the respective subvoxel in which the gold feature is arranged within the voxel of the sample.

[0326] In various embodiments, probes such as probe 102 may be arranged having different angles relative to the sample. For example, in some embodiments, the probe may be arranged to provide the incoming electron beam substantially perpendicular or perpendicular relative to the sample, (e.g., with 6 = 0), though other angles may be used.

[0327] FIGs. 17B, 18A, 19A, 20A, 21A, 22A, 23 A, and 24A show various exemplary samples for an SEM system. FIGs. 17C, 18B, 19B, 20B, 21B, 22B, 23B, and 24B show various exemplary data of an SEM system for the corresponding samples of FIGs. 17B, 18 A, 19A, 20A, 21 A, 22A, 23 A, and 24A. In the illustrated embodiments, the samples may each correspond to an exemplary 10 nm epoxy block with a 5 nm gold (Au) subvoxel feature arranged at a different position within the epoxy block. By using the different data for each of the different samples, an SEM system may be able to determine subvoxel features of the epoxy block, such as by identifying the size and location of the gold block. FIGs. 17C, 18B, 19B, 20B, 2 IB, 22B, 23B, and 24B may represent data for a hemisphere detection surface. In various embodiments, the electron information, such as the data of FIGs. 17C, 18B, 19B, 20B, 2 IB, 22B, 23B, and 24B (which may be used as training data) may be generated by real-world experimental processes, using Monte Carlo simulations, or by other suitable methods.

[0328] FIG. 17B shows a first exemplary sample 106a for an SEM system 1700a and FIG. 17B shows first exemplary data that may be gathered by the SEM system 1700a for the sample 106a. SEM system 1700a may be the SEM system 100 of FIG. 1 A, and it includes a probe 102 configured to direct incoming probe electrons 108 at a sample 106a, and a detector (not illustrated) configured to detect electrons scattered by the sample 106a, in order to measure sample 106b. Sample 106a represents a voxel (such as voxel 1750) with a subvoxel feature (e.g., the gold block described above) located at the position of the 00000001 position subvoxel, in the front lower right position relative to the view of the illustration (e.g., at the first subvoxel 1752a of FIG. 17A). As shown in FIG. 17B, the probe 102 is the size of the voxel of sample 106a. As shown in FIG. 17C, the SEM system 1700a may obtain electron information 1700b based on detecting electrons scattered by sample 106a. FIG. 17C may represent data with 7373 detected BSE, 7376 total BSE, and 50000 incoming electrons.

[0329] FIG. 18A shows a second exemplary sample 106b for an SEM system 1800a and FIG. 18B shows second exemplary data that may be gathered by the SEM system 1800a for the sample of FIG. 18 A. SEM system 1800a differs from SEM system 1700a in that it is configured to measure sample 106b. Sample 106b represents a voxel (such as voxel 1750) with a subvoxel

[0330] #14520034v4 feature located at the position of the 00000010 position subvoxel, in the front lower left position relative to the view of the illustration (e.g., at the second subvoxel 1752b of FIG. 17A). As shown in FIG. 18A, the probe 102 is the size of the voxel of sample 106b. As shown in FIG. 18B, the SEM system 1800a may obtain electron information 1800b based on detecting electrons scattered by sample 106b. FIG. 18B may represent data with 7262 detected BSE, 7264 total BSE, and 50000 incoming electrons.

[0331] FIG. 19A shows a third exemplary sample 106c for an SEM system 1900a and FIG. 19B shows third exemplary data that may be gathered by the SEM system 1900a for the sample 106c of FIG. 19A. SEM system 1900a differs from SEM system 1700a in that it is configured to measure sample 106c. Sample 106c represents a voxel (such as voxel 1750) with a subvoxel feature located at the position of the 00000100 position subvoxel, in the back lower right position relative to the view of the illustration (e.g., at the third subvoxel 1752c of FIG. 17A). As shown in FIG. 19A, the probe 102 is the size of the voxel of sample 106c. As shown in FIG. 19B, the SEM system 1900a may obtain electron information 1900b based on detecting electrons scattered by sample 106c. FIG. 19B may represent data with 7258 detected BSE, 7259 total BSE, and 50000 incoming electrons.

[0332] FIG. 20 A shows a fourth exemplary sample 106d for an SEM system 2000a and FIG. 20B shows fourth exemplary data that may be gathered by the SEM system 2000a for the sample 106d of FIG. 20 A. SEM system 2000a differs from SEM system 1700a in that it is configured to measure sample 106d. Sample 106d represents a voxel (such as voxel 1750) with a subvoxel feature located at the position of the 00001000 position subvoxel, in the back lower left position relative to the view of the illustration (e.g., at the fourth subvoxel 1752d of FIG. 17A). As shown in FIG. 20A, the probe 102 is the size of the voxel of sample 106d. As shown in FIG. 20B, the SEM system 2000a may obtain electron information 2000b based on detecting electrons scattered by sample 106d. FIG. 20B may represent data with 7402 detected BSE, 7405 total BSE, and 50000 incoming electrons.

[0333] FIG. 21 A shows a fifth exemplary sample 106e for an SEM system 2100a and FIG. 21B shows fifth exemplary data that may be gathered by the SEM system 2100a for the sample 106e of FIG. 21 A. SEM system 2100a differs from SEM system 1700a in that it is configured to measure sample 106e. Sample 106e represents a voxel (such as voxel 1750) with a subvoxel feature located at the position of the 0001000 position subvoxel, in the front upper right position relative to the view of the illustration (e.g., at the fifth subvoxel 1752e of FIG. 17A). As shown in FIG. 21 A, the probe 102 is the size of the voxel of sample 106e. As shown in FIG. 21B, the SEM system 2100a may obtain electron information 2100b based on detecting electrons

[0334] #14520034v4 scattered by sample 106e. FIG. 21B may represent data with 6096 detected BSE, 6098 total BSE, and 50000 incoming electrons.

[0335] FIG. 22 A shows a sixth exemplary sample 106f for an SEM system 2200a and FIG. 22B shows sixth exemplary data that may be gathered by the SEM system 2200a for the sample 106f of FIG. 22A. SEM system 2200a differs from SEM system 1700a in that it is configured to measure sample 106f. Sample 106f represents a voxel (such as voxel 1750) with a subvoxel feature located at the position of the 0010000 position subvoxel, in the front upper left position relative to the view of the illustration (e.g., at the sixth subvoxel 1752f of FIG. 17 A). As shown in FIG. 22A, the probe 102 is the size of the voxel of sample 106f. As shown in FIG. 22B, the SEM system 2200a may obtain electron information 2200b based on detecting electrons scattered by sample 106f. FIG. 22B may represent data with 5864 detected BSE, 5867 total BSE, and 50000 incoming electrons.

[0336] FIG. 23A shows a seventh exemplary sample 106g for an SEM system 2300a and FIG. 23B shows seventh exemplary data that may be gathered by the SEM system 2300a for the sample 106g of FIG. 23 A. SEM system 2300a differs from SEM system 1700a in that it is configured to measure sample 106g. Sample 106g represents a voxel (such as voxel 1750) with a subvoxel feature located at the position of the 0100000 position subvoxel, in the back upper right position relative to the view of the illustration (e.g., at the seventh subvoxel 1752g of FIG. 17A). As shown in FIG. 23 A, the probe 102 is the size of the voxel of sample 106g. As shown in FIG. 23B, the SEM system 2300a may obtain electron information 2300b based on detecting electrons scattered by sample 106g. FIG. 23B may represent data with 5919 detected BSE, 5924 total BSE, and 50000 incoming electrons.

[0337] FIG. 24 A shows an eighth exemplary sample 106h for an SEM system 2400a and FIG. 24B shows eight exemplary data that may be gathered by the SEM system 2400a for the sample 106h of FIG. 24A. SEM system 2400a differs from SEM system 1700a in that it is configured to measure sample 106h. Sample 106h represents a voxel (such as voxel 1750) with a subvoxel feature located at the position of the 1000000 position subvoxel, in the back upper left position relative to the view of the illustration (e.g., at the eighth subvoxel 1752h of FIG. 17 A). As shown in FIG. 24A, the probe 102 is the size of the voxel of sample 106h. As shown in FIG. 24B, the SEM system 2400a may obtain electron information 2400b based on detecting electrons scattered by sample 106h. FIG. 24B may represent data with 5970 detected BSE, 5972 total BSE, and 50000 incoming electrons.

[0338] Electron information collected by an SEM system for electrons scattered by a sample may comprise various types of electron information. As shown in FIGs. 17C, 18B, 19B, 20B,

[0339] #14520034v4 21B, 22B, 23B, and 24B, electron information 1700b, 1800b, 1900b, 2000b, 2100b, 2200b, 2300b, and 2400b include various types of electron information.

[0340] Electron information may be collected having multi-dimensional electron profile information. Multi-dimensional electron profile information may in turn be collected at a set of points arranged in multiple spatial dimensions. For example, electron profile information may be multidimensional (e.g., such as two-dimensional) in that it includes both an electron count along a first profile dimension and an electron energy along a second profile dimension.

[0341] Electron profile information may also be collected in multiple spatial dimensions. The multiple spatial dimensions may be for example, on a two-dimensional surface, or on a three- dimensional surface. The surface may comprise a plurality of pixels. Each pixel on a two- dimensional surface may have two spatial coordinates associated with which it is associated. Each pixel on a three-dimensional surface therefore have three spatial coordinates associated with which it is associated.

[0342] Each pixel may collect electron information in two dimensions, e.g., electron count and electron energy, as described above. Therefore, in total, each pixel of a two-dimensional surface may have four pieces of associated information (in each sampling period): two spatial coordinates, electron count, and electron energy. In total, each pixel of a three-dimensional surface may have five pieces of associated information (in each sampling period): three spatial coordinates, electron count, and electron energy.

[0343] At the first row, first column, the electron information shows a first plot of hemisphere detector (which may have a radius of about 800-1200 pm, or a radius of about 1000 pm) counts, with electrons plotted as points, and with a horizontal axis for X position of the hemisphere detector pixel in pm and a vertical axis for Y position of the hemisphere detector pixel in pm. In some embodiments, the center of the sample top surface may correspond to a location at the origin (e.g., X = 0 pm, Y = 0 pm, and Z = 0 pm). The plot at the first row, first column may correspond to a parallel projection of the electron profile (from the hemisphere detector) along the Z axis onto the X-Y plane at Z = 0 pm. At the first row, second column, the electron information shows a second plot at i between 45° and 135° (e.g., a “north” quadrant) with electron counts plotted on the vertical axis, and with a horizontal axis for (p in degrees. At the first row, third column, the electron information shows a third plot with 2D stereographic projection counts, with electrons plotted as points, and with a horizontal axis for X position in pm and a vertical axis for Y position in pm. The third plot at the first row, third column may correspond to a projection of the electron profile from the point X = 0 pm, Y = 0 pm, and Z =

[0344] #14520034v4 1000 pm (1000 pm below the origin) on to the X-Y plane at Z = -1000 pm (the top of the hemisphere detector, 1000 pm above the origin).

[0345] While the exemplary detector may have a size of about 1000 pm as discussed above, detectors in various embodiments may have other dimensions. For example, detectors may have a size ranging from about a few millimeters to several centimeters. Detectors may be sized based on sample size or based on a desired sample space size.

[0346] At the second row, first column, the electron information shows a second plot at ip between 135° and -135° (e.g., a “west” quadrant) with electron counts plotted on the vertical axis, and with a horizontal axis for (p in degrees. At the second row, second column, the electron information shows a second plot at ip between -180° and 180° (e.g., a sum of all four quadrants) with electron counts plotted on the vertical axis, and with a horizontal axis for (p in degrees. At the second row, third column, the electron information shows a second plot at ip between -45° and 45° (e.g., a “east” quadrant) with electron counts plotted on the vertical axis, and with a horizontal axis for (p in degrees.

[0347] At the third row, first column, the electron information shows a seventh plot with 2D flattened detector counts, with electrons plotted as points, and with a horizontal axis for ip in degrees and a vertical axis for (p in degrees. At the third row, second column, the electron information shows a second plot at ip between -135° and -45° (e.g., a “south” quadrant) with electron counts plotted on the vertical axis, and with a horizontal axis for (p in degrees. At the third row, third column, the electron information shows a ninth plot with 2D energy profile, with energy in kV on the vertical axis, and with horizonal axes for ip and (p in degrees.

[0348] According to various embodiments, electron information such as electron information 1700b, 1800b, 1900b, 2000b, 2100b, 2200b, 2300b, and 2400b (or other electron information) may be used to determine subvoxel information of the samples 106a-106h. For example, an SEM system may process the electron information and determine that the electron information corresponds to a subvoxel feature being arranged at a particular location within a voxel. As can be observed from the electron information 1700b, 1800b, 1900b, 2000b, 2100b, 2200b, 2300b, and 2400b, the electron scattered by the various samples 106a-106h are encoded different information depending on the different subvoxel features of the sample (for example, a differing position of a gold block in the epoxy block). E.g., locations of electron counts can be observed to vary throughout electron information 1700b, 1800b, 1900b, 2000b, 2100b, 2200b, 2300b, and 2400b, with different regions having greater densities for different samples, with angular plots having different shapes and peaks at different locations, and with electron energy varying by sample. SEM systems described herein may exploit the different information encoded in the

[0349] #14520034v4 electrons for different samples in order to determine subvoxel features of the samples. In some embodiments, SEM systems may identify subvoxel features only using angular (or positional) electron information, without using electron energy information, thereby reducing detector complexity as the detector does not need to measure electron energy.

[0350] FIG. 16 shows an exemplary process flow 1600 of a method of determining subvoxel information for use with a scanning electron microscopy (SEM) system. Process flow 1600 includes act 1602, act 1604, and act 1606. At act 1602, the process flow 1600 may include obtaining an energy of incoming probe electrons and a direction of the incoming probe electrons. At act 1604, the process flow 1600 may obtaining a two-dimensional energy profile map of detected electrons. At act 1606, the process flow 1600 may include determining subvoxel information of a sample using the energy of incoming probe electrons, the direction of the incoming probe electrons, and the two-dimensional energy profile map of the detected electrons.

[0351] III. Statistical Models

[0352] An SEM system may process the electron information as training data for generating a trained statistical model, as described throughout the disclosure. In some embodiments, SEM systems may include a model. The model may be configured to receive, as input, detected electron information based on electron scattered by a sample, and provide, as output, color information or subvoxel information of the sample. In some embodiments, the model may comprise a statistical model trained on training data for known or annotated color information or subvoxel information.

[0353] Models described herein may be trained using supervised machine learning. Supervised machine learning may include providing labeled training data to a classifier and penalizing or rewarding the classifier depending on whether the classifier correctly classifies the training data. For example, training a classifier to classify images of objects labeled as red, blue, or green may include rewarding the classifier for correctly classifying a green-labeled image of grass as green, and penalizing the classifier for incorrectly classifying a red-labeled image of a firetruck as blue. Thus, the classifier may properly classify future image inputs and infer whether to classify the images as red, blue or green. Accordingly input data may comprise labels indicating that the data is known to have similar characteristics, and / or different characteristics, in order to emphasize and / or de-emphasize the similar and / or different characteristics during training. During training of a model, weights and / or biases of the model may be adjusted to emphasize

[0354] #14520034v4 recognition of the particular characteristics of the training data. Supervised learning techniques may be useful for sorting new data into known categories, as in the image example.

[0355] Models described herein may also be trained using unsupervised machine leaning. Unsupervised machine learning may include providing unlabeled training data to an encoder which the encoder may sort into self-similar groups. For example, the same images provided to the classifier above may be provided to an encoder, which may map the images into a continuous space. In this example, the encoder may form clusters of similar images based on various perceived characteristics of the images, such as the color of the object in each image. However, unlike training the classifier, the encoder may take into account other characteristics of the input data, such as the shape of the objects in the images, and the encoder is not penalized for doing so in the manner described for the classifier. Accordingly, such encoders may be configured to group future inputs based on characteristics encountered during training. In some embodiments, models described herein may be trained using machine learning techniques that combine aspects of unsupervised and supervised machine learning.

[0356] In one such embodiment, a trained statistical model such as a neural network, or other appropriate statistical model, may be trained to output color information or subvoxel information using the electron information described herein as input to the trained statistical model. In one embodiment, the electron information, such as some or all of the electron information from the plots described with respect to FIGs. 2A, 2B, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17C, 18B, 19B, 20B, 2 IB, 22B, 23B, and 24B (or other electron information), along with information identifying known color information or subvoxel information of samples as input as training data into a statistical model in a machine learning module. Once these inputs have been received, the machine learning module may generate a trained statistical model using the training data. The resulting output from the machine learning module may correspond to a color information or subvoxel information model, which is a trained statistical model of color information or subvoxel information as a function of some or all of the types of electron information described with respect to FIGs. 2A, 2B, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17C, 18B, 19B, 20B, 21B, 22B, 23B, and 24B. The trained statistical model may also be stored in an appropriate non-transitory computer readable medium for subsequent use as detailed further below.

[0357] It should be understood that the trained statistical models disclosed herein may be generated using any appropriate statistical model. For example, a machine learning module may correspond to any appropriate fitting method capable of generating the desired trained statistical models. It should also be understood that the above methods may be combined with any

[0358] #14520034v4 appropriate type of fitting approximation to provide a desired combination of model accuracy versus computational expense.

[0359] In general, a statistical model comprises a functional component designed and / or trained to analyze new inputs based on probabilistic patterns observed in prior training inputs. In this sense, statistical models differ from “rule-based” models, which typically apply hard-coded deterministic rules to map from inputs having particular characteristics to particular outputs. By contrast, a statistical model may operate to determine a particular output for an input with particular characteristics by considering how often (e.g., with what probability) training inputs with those same characteristics (or similar characteristics) were associated with that particular output in the statistical model’s training data. To supply the probabilistic data that allows a statistical model to extrapolate from the tendency of particular input characteristics to be associated with particular outputs in past examples, statistical models are typically trained (or “built”) on large training corpuses with great numbers of example inputs. Typically, the example inputs may be labeled with the known outputs with which they should be associated, usually by a human labeler with expert knowledge of the domain. Characteristics of interest (known as “features”) are identified (“extracted”) from the inputs, and the statistical model learns the probabilities with which different features are associated with different outputs, based on how often training inputs with those features are associated with those outputs. When the same features are extracted from a new input (e.g., an input that has not been labeled with a known output by a human), the statistical model can then use the learned probabilities for the extracted features (as learned from the training data) to determine which output is most likely correct for the new input. Illustrative implementations of a fact extraction component using one or more statistical models are described further below.

[0360] IV. Definitions

[0361] An illustrative implementation of a computer system 1400 that may be used in connection with any of the embodiments of the disclosure provided herein is shown in FIG. 14. The computer system 1400 may include one or more processors 1410 and one or more articles of manufacture that comprise non-transitory computer-readable storage media (e.g., memory 1420 and one or more non-volatile storage media 1430). The processor 1410 may control writing data to and reading data from the memory 1420 and the non-volatile storage device 1430 in any suitable manner. To perform any of the functionality described herein, the processor 1410 may execute one or more processor-executable instructions stored in one or more non-transitory computer-readable storage media (e.g., the memory 1420), which may serve as non-transitory

[0362] #14520034v4 computer-readable storage media storing processor-executable instructions for execution by the processor 1410.

[0363] The terms “program” or “software” are used herein in a generic sense to refer to any type of computer code or set of processor-executable instructions that can be employed to program a computer or other processor to implement various aspects of embodiments as discussed above. Additionally, it should be appreciated that according to one aspect, one or more computer programs that when executed perform methods of the disclosure provided herein need not reside on a single computer or processor but may be distributed in a modular fashion among different computers or processors to implement various aspects of the disclosure provided herein.

[0364] Processor-executable instructions may be in many forms, such as program modules, executed by one or more computers or other devices. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Typically, the functionality of the program modules may be combined or distributed as desired in various embodiments.

[0365] Also, data structures may be stored in one or more non-transitory computer-readable storage media in any suitable form. For simplicity of illustration, data structures may be shown to have fields that are related through location in the data structure. Such relationships may likewise be achieved by assigning storage for the fields with locations in a non-transitory computer-readable medium that convey relationship between the fields. However, any suitable mechanism may be used to establish relationships among information in fields of a data structure, including through the use of pointers, tags or other mechanisms that establish relationships among data elements.

[0366] Also, various inventive concepts may be embodied as one or more processes, of which examples (for example, FIGs. 1C and 16) are provided. The acts performed as part of each process may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments.

[0367] Various aspects of the embodiments described above may be used alone, in combination, or in a variety of arrangements not specifically discussed in the embodiments described in the foregoing and is therefore not limited in its application to the details and arrangement of components set forth in the foregoing description or illustrated in the drawings. For example, aspects described in one embodiment may be combined in any manner with aspects described in other embodiments.

[0368] #14520034v4 All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and / or ordinary meanings of the defined terms.

[0369] The indefinite articles “a” and “an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean “at least one.”

[0370] The phrase “and / or,” as used herein in the specification and in the claims, should be understood to mean “either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Multiple elements listed with “and / or” should be construed in the same fashion, i.e., “one or more” of the elements so conjoined. Other elements may optionally be present other than the elements specifically identified by the “and / or” clause, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, a reference to “A and / or B,” when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc.

[0371] As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and / or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc.

[0372] Use of ordinal terms such as “first,” “second,” “third,” etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely

[0373] #14520034v4 as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements.

[0374] In the claims, as well as in the specification above, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” “composed of,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of’ and “consisting essentially of’ shall be closed or semi-closed transitional phrases, respectively.

[0375] The terms “approximately,” “about,” and “substantially” may be used to mean within ±20% of a target value in some embodiments, within ±10% of a target value in some embodiments, within ±5% of a target value in some embodiments, within ±2% of a target value in some embodiments. The terms “approximately,” “about,” and “substantially” may include the target value.

[0376] Having thus described several aspects of at least one embodiment, it is to be appreciated that various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be part of this disclosure and are intended to be within the spirit and scope of the principles described herein. Accordingly, the foregoing description and drawings are by way of example only.

[0377] #14520034v4

Claims

CLAIMSWhat is claimed is:

1. A color scanning electron microscopy (SEM) system, comprising: a probe configured to direct incoming probe electrons at a sample; a detector configured to detect electrons scattered by the sample; and at least one processor configured to determine a material of the sample based on the detected electrons scattered by the sample.

2. The SEM system of claim 1, wherein the at least one processor is further configured to generate a color SEM image of the sample based on the detected electrons scattered by the sample.

3. The SEM system of claim 2, wherein generating the color SEM image of the sample comprises determining at least one color in the color SEM image based on the determined material of the sample.

4. The SEM system of claim 1, wherein detecting the electrons scattered by the sample comprises detecting an electron profile dimension of the electrons scattered by the sample with respect to a spatial dimension.

5. The SEM system of claim 4, wherein the spatial dimension comprises angle.

6. The SEM system of claim 5, wherein the electron profile dimension comprises electron count.

7. The SEM system of claim 6, wherein determining the material of the sample based on the detected electrons scattered by the sample comprises generating an electron distribution for the sample, the electron distribution representing electron count with respect to angle.

8. The SEM system of claim 7, wherein determining the material of the sample based on the detected electrons scattered by the sample further comprises: comparing the electron distribution for the sample to respective electron distributions for a plurality of materials; and#14520034v4selecting the material of the sample from the plurality of materials based on a result of the comparing.

9. The SEM system of claim 8, wherein: comparing the electron distribution for the sample to the respective electron distributions for the plurality of materials comprises inputting the electron distribution for the sample into a rules-based model; and selecting the material of the sample from the plurality of materials based on the result of the comparing comprises selecting the material based on an output of the rules-based model.

10. The SEM system of claim 8, wherein: comparing the electron distribution for the sample to the respective electron distributions for the plurality of materials comprises inputting the electron distribution for the sample into a trained statistical model; and selecting the material of the sample from the plurality of materials based on the result of the comparing comprises selecting the material based on an output of the trained statistical model.

11. The SEM system of claim 5, wherein: the electron profile dimension comprises electron energy; and determining the material of the sample based on the detected electrons scattered by the sample comprises generating an electron distribution for the sample, the electron distribution representing electron energy with respect to angle.

12. The SEM system of claim 1, wherein the detector comprises a three-dimensional detection surface.

13. The SEM system of claim 1, wherein the at least one processor is further configured to generate a three-dimensional color SEM image of the sample based on the detected electrons scattered by the sample.

14. The SEM system of claim 1, wherein the SEM system is a focused ion beam scanning electron microscopy (FIB-SEM) system comprising a focused ion beam (FIB) emitter configured to direct a FIB at the sample to separate layers of the sample.#14520034v415. The SEM system of claim 14, wherein the FIB-SEM system is further configured to: for a first layer of the sample having a sample layer thickness, detect electrons scattered by the sample; using the FIB, separate the first layer of the sample from a second layer of the sample; for the second layer of the sample, detect electrons scattered by the sample; and generate a three-dimensional color SEM image of the sample based on the detected electrons scattered by the sample, the three-dimensional color SEM image having a thickness greater than the sample layer thickness.

16. The SEM system of claim 1, wherein the at least one processor further configured to: determine a two-dimensional energy profile map of the detected electrons; and determine the material of the sample based on the two-dimensional energy profile map.

17. The SEM system of claim 16, wherein the two-dimensional energy profile map of the detected electrons comprises: a map having at least two spatial dimensions; and for a plurality of points in the map, a two-dimensional energy profile comprising: an electron count along a first profile dimension; and an electron energy along a second profile dimension.

18. The SEM system of claim 1, wherein determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function and a second parameter affecting a mode of the function; comparing the determined first parameter and the determined second parameter to, for two or more known materials, a known one of the first parameter of the function and a known one of the second parameter of the function; and determining the material of the sample based on the comparing.

19. The SEM system of claim 1, wherein determining the material of the sample based on the detected electrons scattered by the sample comprises:#14520034v4determining an electron angular distribution of the detected electrons scattered by the sample; fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function, a second parameter affecting a mode of the function, and a third parameter affecting a width of the function; comparing the determined first parameter, the determined second parameter, and the determined third parameter to, for two or more known materials, a known one of the first parameter of the function, a known one of the second parameter of the function, and a known one of the third parameter of the function; and determining the material of the sample based on the comparing.

20. The SEM system of claim 19, wherein fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function, a second parameter affecting a mode of the function, and a third parameter affecting a width of the function comprises: fitting the electron angular distribution to a Power Sine function by determining a first parameter ho defining an amplitude of the function, a second parameter (p defining a mode of the function, and a third parameter p defining a width of the function.

21. The SEM system of claim 1, wherein determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; determining a ratio between electron count at a first angle and electron count at a second angle; comparing the determined ratio to, for two or more known materials, a known one of the first ratio between electron count at the first angle and electron count at the second angle; and determining the material of the sample based on the comparing.

22. The SEM system of claim 21, wherein: the first angle is between 15 and 45° and the second angle is between 45 and 85°.

23. The SEM system of any of claims 18-22, wherein determining an electron angular distribution of the electrons scattered by the sample comprises:#14520034v4determining the electron angular distribution without electrons having energies less than a threshold energy, wherein the threshold energy is 0.05 keV or greater.

24. The SEM system of claim 23, wherein: the threshold energy is 50% of the energy of the incoming probe electrons or greater.

25. The SEM system of any of claims 18-22, wherein determining an electron angular distribution of the electrons scattered by the sample comprises: determining the electron angular distribution without electrons having energies less than a lower threshold energy and without electrons having energies greater than an upper threshold energy, wherein the lower threshold energy is 0.05 keV or greater; and wherein the upper threshold energy is 100% of an energy of the incoming probe electrons or lower.

26. The SEM system of claim 25, wherein: the upper threshold energy is 95% of the energy of the incoming probe electrons or lower.

27. The SEM system of any of claims 18-22, wherein determining an electron angular distribution of the electrons scattered by the sample comprises: determining the electron angular distribution without electrons having energies less than a lower threshold energy and without electrons having energies greater than an upper threshold energy, wherein the lower threshold energy is 90% of the energy of the incoming probe electrons or greater; and wherein the upper threshold energy is 100% of an energy of the incoming probe electrons or lower.

28. A method of performing color scanning electron microscopy (SEM), comprising: directing incoming probe electrons at a sample; detecting electrons scattered by the sample; and#14520034v4determining a material of the sample based on the detected electrons scattered by the sample.

29. The method of claim 28, further comprising generating a color SEM image of the sample based on the detected electrons scattered by the sample.

30. The method of claim 29, wherein generating the color SEM image of the sample comprises determining at least one color in the color SEM image based on the determined material of the sample.

31. The method of claim 29, wherein detecting the electrons scattered by the sample comprises detecting an electron profile dimension of the electrons scattered by the sample with respect to a spatial dimension.

32. The method of claim 31, wherein the spatial dimension comprises angle.

33. The method of claim 32, wherein the electron profile dimension comprises electron count.

34. The method of claim 33, wherein determining the material of the sample based on the detected electrons scattered by the sample comprises generating an electron distribution for the sample, the electron distribution representing electron count with respect to angle.

35. The method of claim 34, wherein determining the material of the sample based on the detected electrons scattered by the sample further comprises: comparing the electron distribution for the sample to respective electron distributions for a plurality of materials; and selecting the material of the sample from the plurality of materials based on a result of the comparing.

36. The method of claim 35, wherein: comparing the electron distribution for the sample to the respective electron distributions for the plurality of materials comprises inputting the electron distribution for the sample into a rules-based model; and#14520034v4selecting the material of the sample from the plurality of materials based on the result of the comparing comprises selecting the material based on an output of the rules-based model.

37. The method of claim 35, wherein: comparing the electron distribution for the sample to the respective electron distributions for the plurality of materials comprises inputting the electron distribution for the sample into a trained statistical model; and selecting the material of the sample from the plurality of materials based on the result of the comparing comprises selecting the material based on an output of the trained statistical model.

38. The method of claim 32, wherein: the electron profile dimension comprises electron energy; and determining the material of the sample based on the detected electrons scattered by the sample comprises generating an electron distribution for the sample, the electron distribution representing electron energy with respect to angle.

39. The method of claim 28, wherein detecting the electrons scattered by the sample comprises detecting the electrons using a three-dimensional detection surface.

40. The method of claim 28, further comprising generating a three-dimensional color SEM image of the sample based on the detected electrons scattered by the sample.

41. The method of claim 28, further comprising directing a focused ion beam (FIB) at the sample to separate layers of the sample.

42. The method of claim 41, further comprising: for a first layer of the sample having a sample layer thickness, detecting electrons scattered by the sample; using the FIB, separating the first layer of the sample from a second layer of the sample; for the second layer of the sample, detecting electrons scattered by the sample; and generating a three-dimensional color SEM image of the sample based on the detected electrons scattered by the sample, the three-dimensional color SEM image having a thickness greater than the sample layer thickness.#14520034v443. The method of claim 28, further comprising: determining a two-dimensional energy profile map of the detected electrons; and determining the material of the sample based on the two-dimensional energy profile map.

44. The method of claim 43, wherein the two-dimensional energy profile map of the detected electrons comprises: a map having at least two spatial dimensions; and for a plurality of points in the map, a two-dimensional energy profile comprising: an electron count along a first profile dimension; and an electron energy along a second profile dimension.

45. The method of claim 28, wherein determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function and a second parameter affecting a mode of the function; comparing the determined first parameter and the determined second parameter to, for two or more known materials, a known one of the first parameter of the function and a known one of the second parameter of the function; and determining the material of the sample based on the comparing.

46. The method of claim 28, wherein determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function, a second parameter affecting a mode of the function, and a third parameter affecting a width of the function; comparing the determined first parameter, the determined second parameter, and the determined third parameter to, for two or more known materials, a known one of the first parameter of the function, a known one of the second parameter of the function, and a known one of the third parameter of the function; and#14520034v4determining the material of the sample based on the comparing.

47. The method of claim 46, wherein fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function, a second parameter affecting a mode of the function, and a third parameter affecting a width of the function comprises: fitting the electron angular distribution to a Power Sine function by determining a first parameter ho defining an amplitude of the function, a second parameter (p defining a mode of the function, and a third parameter p defining a width of the function.

48. The method of claim 28, wherein determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; determining a ratio between electron count at a first angle and electron count at a second angle; comparing the determined ratio to, for two or more known materials, a known one of the first ratio between electron count at the first angle and electron count at the second angle; and determining the material of the sample based on the comparing.

49. The method of claim 48, wherein: the first angle is between 15 and 45° and the second angle is between 45 and 85°.

50. The method of claim 45-49, wherein determining an electron angular distribution of the electrons scattered by the sample comprises: determining the electron angular distribution without electrons having energies less than a threshold energy, wherein the threshold energy is 0.05 keV or greater.

51. The method of claim 50, wherein: the threshold energy is 50% of the energy of the incoming probe electrons or greater.

52. The method of any of claims 45-49, wherein determining an electron angular distribution of the electrons scattered by the sample comprises:#14520034v4determining the electron angular distribution without electrons having energies less than a lower threshold energy and without electrons having energies greater than an upper threshold energy, wherein the lower threshold energy is 0.05 keV or greater; and wherein the upper threshold energy is 100% of an energy of the incoming probe electrons or lower.

53. The method of claim 52, wherein: the upper threshold energy is 95% of the energy of the incoming probe electrons or lower.

54. The method of any of claims 45-49, wherein determining an electron angular distribution of the electrons scattered by the sample comprises: determining the electron angular distribution without electrons having energies less than a lower threshold energy and without electrons having energies greater than an upper threshold energy, wherein the lower threshold energy is 90% of the energy of the incoming probe electrons or greater; and wherein the upper threshold energy is 100% of an energy of the incoming probe electrons or lower.

55. At least one non-transitory computer-readable storage medium having instructions encoded thereon that, when executed by at least one processor, cause the at least one processor to perform a method of performing color scanning electron microscopy (SEM), comprising: directing incoming probe electrons at a sample; detecting electrons scattered by the sample; and determining a material of the sample based on the detected electrons scattered by the sample.

56. The at least one non-transitory computer-readable storage medium of claim 55, wherein the method further comprises generating a color SEM image of the sample based on the detected electrons scattered by the sample.#14520034v457. The at least one non-transitory computer-readable storage medium of claim 56, wherein generating the color SEM image of the sample comprises determining at least one color in the color SEM image based on the determined material of the sample.

58. The at least one non-transitory computer-readable storage medium of claim 55, wherein detecting the electrons scattered by the sample comprises detecting an electron profile dimension of the electrons scattered by the sample with respect to a spatial dimension.

59. The at least one non-transitory computer-readable storage medium of claim 58, wherein the spatial dimension comprises angle.

60. The at least one non-transitory computer-readable storage medium of claim 59, wherein the electron profile dimension comprises electron count.

61. The at least one non-transitory computer-readable storage medium of claim 60, wherein determining the material of the sample based on the detected electrons scattered by the sample comprises generating an electron distribution for the sample, the electron distribution representing electron count with respect to angle.

62. The at least one non-transitory computer-readable storage medium of claim 61, wherein determining the material of the sample based on the detected electrons scattered by the sample further comprises: comparing the electron distribution for the sample to respective electron distributions for a plurality of materials; and selecting the material of the sample from the plurality of materials based on a result of the comparing.

63. The at least one non-transitory computer-readable storage medium of claim 62, wherein: comparing the electron distribution for the sample to the respective electron distributions for the plurality of materials comprises inputting the electron distribution for the sample into a rules-based model; and selecting the material of the sample from the plurality of materials based on the result of the comparing comprises selecting the material based on an output of the rules-based model.#14520034v464. The at least one non-transitory computer-readable storage medium of claim 62, wherein: comparing the electron distribution for the sample to the respective electron distributions for the plurality of materials comprises inputting the electron distribution for the sample into a trained statistical model; and selecting the material of the sample from the plurality of materials based on the result of the comparing comprises selecting the material based on an output of the trained statistical model.

65. The at least one non-transitory computer-readable storage medium of claim 59, wherein: the electron profile dimension comprises electron energy; and determining the material of the sample based on the detected electrons scattered by the sample comprises generating an electron distribution for the sample, the electron distribution representing electron energy with respect to angle.

66. The at least one non-transitory computer-readable storage medium of claim 55, wherein detecting the electrons scattered by the sample comprises detecting the electrons using a three- dimensional detection surface.

67. The at least one non-transitory computer-readable storage medium of claim 55, wherein the method further comprises generating a three-dimensional color SEM image of the sample based on the detected electrons scattered by the sample.

68. The at least one non-transitory computer-readable storage medium of claim 55, wherein the method further comprises directing a focused ion beam (FIB) at the sample to separate layers of the sample.

69. The at least one non-transitory computer-readable storage medium of claim 68, wherein the method further comprises: for a first layer of the sample having a sample layer thickness, detecting electrons scattered by the sample; using the FIB, separating the first layer of the sample from a second layer of the sample; for the second layer of the sample, detecting electrons scattered by the sample; and#14520034v4generating a three-dimensional color SEM image of the sample based on the detected electrons scattered by the sample, the three-dimensional color SEM image having a thickness greater than the sample layer thickness.

70. The at least one non-transitory computer-readable storage medium of claim 55, wherein the method further comprises: determining a two-dimensional energy profile map of the detected electrons; and determining the material of the sample based on the two-dimensional energy profile map.

71. The at least one non-transitory computer-readable storage medium of claim 70, wherein the two-dimensional energy profile map of the detected electrons comprises: a map having at least two spatial dimensions; and for a plurality of points in the map, a two-dimensional energy profile comprising: an electron count along a first profile dimension; and an electron energy along a second profile dimension.

72. The at least one non-transitory computer-readable storage medium of claim 55, wherein determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function and a second parameter affecting a mode of the function; comparing the determined first parameter and the determined second parameter to, for two or more known materials, a known one of the first parameter of the function and a known one of the second parameter of the function; and determining the material of the sample based on the comparing.

73. The at least one non-transitory computer-readable storage medium of claim 55, wherein determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample;#14520034v4fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function, a second parameter affecting a mode of the function, and a third parameter affecting a width of the function; comparing the determined first parameter, the determined second parameter, and the determined third parameter to, for two or more known materials, a known one of the first parameter of the function, a known one of the second parameter of the function, and a known one of the third parameter of the function; and determining the material of the sample based on the comparing.

74. The at least one non-transitory computer-readable storage medium of claim 73, wherein fitting the electron angular distribution to a function by determining a first parameter affecting an amplitude of the function, a second parameter affecting a mode of the function, and a third parameter affecting a width of the function comprises: fitting the electron angular distribution to a Power Sine function by determining a first parameter ho defining an amplitude of the function, a second parameter (p defining a mode of the function, and a third parameter p defining a width of the function.

75. The at least one non-transitory computer-readable storage medium of claim 55, wherein determining the material of the sample based on the detected electrons scattered by the sample comprises: determining an electron angular distribution of the detected electrons scattered by the sample; determining a ratio between electron count at a first angle and electron count at a second angle; comparing the determined ratio to, for two or more known materials, a known one of the first ratio between electron count at the first angle and electron count at the second angle; and determining the material of the sample based on the comparing.

76. The at least one non-transitory computer-readable storage medium of claim 75, wherein: the first angle is between 15 and 45° and the second angle is between 45 and 85°.

77. The at least one non-transitory computer-readable storage medium of claim 72-76, wherein determining an electron angular distribution of the electrons scattered by the sample comprises:#14520034v4determining the electron angular distribution without electrons having energies less than a threshold energy, wherein the threshold energy is 0.05 keV or greater.

78. The at least one non-transitory computer-readable storage medium of claim 77, wherein: the threshold energy is 50% of the energy of the incoming probe electrons or greater.

79. The at least one non-transitory computer-readable storage medium of any of claims 72-76, wherein determining an electron angular distribution of the electrons scattered by the sample comprises: determining the electron angular distribution without electrons having energies less than a lower threshold energy and without electrons having energies greater than an upper threshold energy, wherein the lower threshold energy is 0.05 keV or greater; and wherein the upper threshold energy is 100% of an energy of the incoming probe electrons or lower.

80. The at least one non-transitory computer-readable storage medium of claim 79, wherein: the upper threshold energy is 95% of the energy of the incoming probe electrons or lower.

81. The at least one non-transitory computer-readable storage medium of any of claims 72-76, wherein determining an electron angular distribution of the electrons scattered by the sample comprises: determining the electron angular distribution without electrons having energies less than a lower threshold energy and without electrons having energies greater than an upper threshold energy, wherein the lower threshold energy is 90% of the energy of the incoming probe electrons or greater; and wherein the upper threshold energy is 100% of an energy of the incoming probe electrons or lower.#14520034v4

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