Reconstruction methods for atom probe tomography.

Abstract

Reconstruction method for atom probe tomography. A method (100) for determining the three-dimensional atomic distribution of a sample (201) having a tip during an atom probe tomography process. The method accounts for the fact that the tip is not axisymmetric and does not have a hemispherical apex throughout the evaporation process.

Description

[Technical Field]

[0001] The present invention relates to the field of atom probe tomography, and in particular to determining the three-dimensional atomic distribution of a sample within the field of view of the instrument. [Background technology]

[0002] Atom probe tomography (APT or 3D atom probe) is a nanoscopic material analysis technique that enables three-dimensional atomic-scale imaging and determines the chemical composition of materials with atomic-scale and sub-nanometer spatial resolution. In this technique, a sample is sharpened to a hemispherical shape with a tip radius of less than 50 nm. The sharpened sample is placed in a vacuum chamber and aligned with the center of an ion detector, while a high voltage bias is applied between the tip and the detector. This induces a high electric field (>10 V / nm) at the tip's apex, ionizing atoms at the apex's surface and bringing them close to the evaporation threshold. A laser pulse is often added to trigger the evaporation process by providing additional thermal energy so that the atoms at the apex can overcome the energy barrier to evaporation. The evaporated ions are separated from the tip surface and accelerated toward the detector according to the electric field distribution between the tip and the detector. The impact position on the detector and the time of flight (TOF) are measured. TOF is measured as the time difference between the arrival time (on the detector) and the onset of the voltage or laser pulse that triggers the evaporation process. By analyzing the time-of-flight of the atoms, the mass-to-charge ratio of the sample can be determined. Based on the location where the ions impacted the detector and the evaporation sequence number, a reconstruction algorithm can be designed to convert the raw data into a three-dimensional atomic distribution of the sample. Various approaches for such reconstruction exist, some of which are commercially implemented. Often, a key (simplifying) assumption is made by assuming the tip is axisymmetric and has a hemispherical apex that is linearly approximated to its flight trajectory. For heterogeneous samples and / or laser-based evaporation, the tip shape can differ substantially from such an idealized shape (variable curvature, asymmetric shape), leading to inaccurate reconstruction. Clearly, improved accuracy can only be achieved by employing algorithms that incorporate detailed tip geometry. The most challenging part of reconstruction is figuring out how to accurately and precisely quantitatively describe the tip shape that develops during evaporation.

[0003] A 2019 publication by D. Beinke and G. Schmitz, "Atom Probe Reconstruction With a Locally Varying Emitter Shape," Microscopy and Microanalysis, volume 25, special issue 2, pp. 280–287, discloses an improved method for atom probe tomography. This method allows for variations in tip surface curvature but does not solve the problem of asymmetric tips. A 2020 publication by D. Beinke et al., "Extracting the Shape of Nanometric Field Emitters," Nanoscale, volume 12, issue 4, pp. 2820–2832, proposes a solution for deriving asymmetric tip shapes. While this method has been demonstrated to be capable of estimating evaporated tip shapes through simulations, it has not been studied on actual tip surfaces. Furthermore, this method requires extrapolation of the curvature of undetected regions on the tip surface (i.e., outside the field of view), which can increase error during estimation.

[0004] European Patent Application No. 3537161A1 discloses a method for imaging tip geometry using scanning probe microscopy. Summary of the Invention [Problem to be solved by the invention]

[0005] It is an object of embodiments of the present invention to provide a good method for determining the three-dimensional atomic distribution of a sample during an atom probe tomography process. [Means for solving the problem]

[0006] The above objects are achieved by a method and device according to the present invention.

[0007] In a first aspect, the present invention provides a method for determining the three-dimensional atomic distribution of a tip-shaped sample, and thus a sample having a tip, during an atom probe tomography process. The method comprises: (i) performing an evaporation process comprising evaporating atoms from a sample and projecting the atoms onto a detector where the atoms are detected, the detected atoms including reference atoms and target atoms; (ii) recording a hit map belonging to a given stage of the evaporation process, including the impact position of each detected atom on the detector and the time of flight of each detected atom; (iii) dividing the hit map into zones; (iv) selecting the detected atoms within the zone of the hit map; (v) determining the mass-to-charge ratio of the target atom based on the recorded time-of-flight of the reference atom by comparison with the recorded time-of-flight of the reference atom; (vi) repeating steps (iv) and (v) for all zones of the hit map to construct a mass-to-charge spectrum; (vii) deriving the flight distance of selected atoms of any element at a peak in the mass-to-charge spectrum; (viii) deriving the launch angles of the selected atoms; (ix) estimating an approximate surface geometry of the tip in a first field of view region of the sample based on the derived takeoff angles of the selected atoms; (x) measuring the actual surface geometry of the tip of the sample; (xi) matching the approximate surface geometry to the actual surface geometry; (xii) deriving a size and a position of a first field of view of the detected atoms based on an approximate surface geometry that matches the actual surface geometry; (xiii) recording a hit map belonging to another predetermined stage of the evaporation process, repeating steps (iii) to (xi) and deriving the size and position of a second field of view of the detected atoms based on the approximate surface geometry that matches the actual surface geometry; (xiv) determining a volume enclosed by the first field of view and the second field of view to define a reconstruction volume; (xv) reconstructing a three-dimensional atomic distribution of the detected atoms in a reconstruction volume of the sample.

[0008] An advantage of the method according to an embodiment of the present invention is that the reconstruction process is very accurate: it is not necessary to make the simplifying assumption that the tip is axisymmetric and has a hemispherical apex.

[0009] In a method according to an embodiment of the present invention, the step of recording a hit map belonging to a predetermined stage of the evaporation process may include recording a substantially complete or full hit map of the evaporation process, for example recording a hit map including collisions of all atoms that are evaporated and impinge on a detector during the evaporation process, and extracting from the full hit map a reduced hit map that belongs only to the predetermined stage of the evaporation process.

[0010] In a method according to an embodiment of the present invention, the step of reconstructing the three-dimensional atomic distribution of the detected atoms may include returning the atoms to the surface of the tip, using the percentage of completion to determine the surface geometry and the height of the developing surface on which the atoms must be placed, and using a one-to-one correlation between the locations on the detector and the tip surface to determine the spatial positions of the reconstructed atoms. Using the one-to-one correlation between the locations on the detector and the tip surface may be based on the approximate trajectory during which the launch angle is derived.

[0011] In a method according to an embodiment of the present invention, the step of dividing the hit map into a plurality of zones may include dividing the hit map into pixels having a suitable shape, for example, but not limited to, a rectangular or square shape.

[0012] In a method according to an embodiment of the present invention, the step of deriving the flight distance of the selected atoms may include assuming that atoms detected within the zone originate from the same point on the sample and have the same flight path.

[0013] In a method according to an embodiment of the present invention, the step of deriving the flight distance and launch angle may be performed by assuming a first flight projection in a high magnetic field gradient region where the tangential direction along the actual flight path of the atom changes significantly from the sample to a predetermined distance, and a second flight projection in a low magnetic field gradient region where the flight path is assumed to be a straight line flight beyond the predetermined distance to the detector.

[0014] In a method according to an embodiment of the present invention, the step of estimating the approximate surface geometry of the tip in the field of view of the sample may include predefining several reference positions at the intersections of the surface of an arbitrary sphere with a line from the origin of the sphere to the detected position, and optimizing the reference positions to new positions that form the field of view. Optimizing the reference positions may include changing either the surface distance or the radius of the sphere by preserving the derived launch angle.

[0015] In a method according to an embodiment of the present invention, the step of measuring the actual surface geometry of the tip of the sample may be performed by using either scanning probe microscopy, transmission electron microscopy, or ptychography.

[0016] In a method according to an embodiment of the present invention, the step of matching the approximate surface geometry to the actual surface geometry may include using an iterative closest point method, in which the approximate surface geometry is pre-aligned to the actual surface geometry and a weighting function is added to scale the size of the surface geometry.

[0017] In a method according to an embodiment of the present invention, matching the approximate surface geometry to the actual surface geometry comprises: creating a surface mesh; - a rough match between the approximate surface geometry and the actual surface geometry to provide an initial guess of the position for alignment; - shifting and scaling the data of the approximate surface geometry based on an initial guess; - precise matching of approximate surface geometry data to actual surface geometry data.

[0018] In a second aspect, the present invention provides a system for determining the three-dimensional atomic distribution of a field of view of a sample during an atom probe tomography process, the system comprising: - means for evaporating atoms from the sample and projecting the atoms onto a detector; a detector for recording a hit map including the collision location and time of flight of each atom; and a controller configured to perform the method of any of the embodiments of the first aspect.

[0019] In a third aspect, the present invention provides a computer program comprising instructions that, when executed by a controller, cause the controller to perform the steps of any of the method embodiments of the first aspect. Nowadays, such computer programs are often provided over the Internet or a company intranet for downloading; therefore, the present invention includes transmitting a computer program according to an embodiment of the present invention over a local or wide area network and / or a data carrier signal carrying the computer program of an embodiment of the third aspect. The controller may be a general-purpose or special-purpose processor, including, for example, one of a microprocessor and an FPGA, and may be for inclusion in a device, for example, a system for determining the three-dimensional atomic distribution of a field of view of a sample during an atom probe tomography process.

[0020] An embodiment of the present invention also provides a computer readable storage medium, such as a magnetic storage device such as a hard disk, a memory key or diskette, or an optical storage device such as a CD-ROM, having stored thereon in machine readable form a computer program of an embodiment of the third aspect.

[0021] Particular and preferred aspects of the invention are set out in the accompanying independent and dependent claims. Features from the dependent claims may be combined with features of the independent claims and with features of other dependent claims as appropriate and not merely as explicitly set out in the claims.

[0022] For purposes of summarizing the invention and the advantages achieved over the prior art, certain objects and advantages of the invention have been described above. Of course, it is to be understood that not necessarily all such objects or advantages may be achieved in accordance with any particular embodiment of the invention. Thus, for example, one skilled in the art will recognize that the invention may be embodied or carried out in a manner that achieves or optimizes one advantage or group of advantages taught herein without necessarily achieving other objects or advantages that may be taught or suggested herein.

[0023] These and other aspects of the invention will be apparent from and elucidated with reference to the embodiment(s) described hereinafter. [Brief explanation of the drawings]

[0024] The invention will now be further described, by way of example, with reference to the accompanying drawings in which:

[0025] [Figure 1] 1 shows a flowchart of an exemplary method for determining a three-dimensional atomic distribution in a sample, according to an embodiment of the present invention. [Figure 2] 1 illustrates a schematic diagram of an example atom probe tomography process, according to an embodiment of the present invention; [Figure 3] 1 illustrates an example of a hitmap as used in an embodiment of the present invention. [Figure 4]10 is a graph showing an example of the number of different types of atoms versus the time of flight of different types of atoms in a selected zone of a hit map, as used in an embodiment of the present invention. [Figure 5] 1 is a graph showing an example of the number of different types of atoms versus the mass-to-charge ratio of the different types of atoms as used in embodiments of the present invention; [Figure 6] 1 shows an example of a partial hit map of reference atom types as used in embodiments of the present invention. [Figure 7] 10A-10C illustrate schematically deriving the launch angle of an atom according to an embodiment of the present invention; [Figure 8] 1A and 1B illustrate schematically estimating approximate surface geometry according to an embodiment of the present invention; [Figure 9] 10 shows an example of measuring actual surface geometry as used in embodiments of the present invention. [Figure 10] 3A-3C illustrate schematically the steps of surface matching between an approximate surface geometry and an actual surface geometry according to an embodiment of the present invention; [Figure 11] 1A and 1B show schematic examples of reconstructions of three-dimensional atomic distributions in a field of view according to embodiments of the present invention;

[0026] The drawings are schematic and non-limiting. In the drawings, the size of some elements may be exaggerated and not drawn to scale for illustrative purposes. The dimensions and relative dimensions do not necessarily correspond to actual reductions to practice of the invention. Any reference signs in the claims should not be construed as limiting their scope. In different drawings, the same reference signs refer to the same or similar elements. DETAILED DESCRIPTION OF THE INVENTION

[0027] The present invention will be described with respect to particular embodiments and with reference to certain drawings but the invention is not limited thereto but only by the claims.

[0028] Terms such as first, second, etc. in this description and claims are used to distinguish between similar elements and are not necessarily used to describe order, whether temporal, spatial, ranking, or in any other way. It is understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operating in orders other than those described or illustrated herein.

[0029] Furthermore, directional terms such as top, bottom, front, back, leading, trailing, below, and over in this description and claims are used for descriptive purposes with reference to the orientation of the drawings being described and are not necessarily used to describe relative positions. Because components of embodiments of the present invention can be positioned in several different orientations, directional terms are used for illustrative purposes only and are not intended to be limiting in any way, unless otherwise indicated. Accordingly, it should be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the present invention described herein are capable of operation in orientations other than those described or illustrated herein.

[0030] It should be noted that the term "comprising" used in the claims should not be interpreted as being limited to the means listed thereafter, nor does it exclude other elements or steps. Thus, it should be interpreted as specifying the presence of the mentioned features, integers, steps, or components, but not excluding the presence or addition of one or more other features, integers, steps, or components, or groups thereof. Thus, the scope of the expression "a device comprising means A and B" should not be limited to a device consisting only of components A and B. This means that, in the context of the present invention, the only relevant components of the device are A and B.

[0031] References throughout this specification to "one embodiment" or "an embodiment" mean that a particular feature, structure, or characteristic described in connection with that embodiment is included in at least one embodiment of the present invention. Thus, the appearances of the phrases "in one embodiment" or "in an embodiment" in various places throughout this specification do not necessarily all refer to the same embodiment, although they may. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments.

[0032] Similarly, in describing exemplary embodiments of the invention, it should be understood that various features of the invention may be grouped together in a single embodiment, figure, or description to simplify the disclosure and aid in understanding one or more of the various inventive aspects. This method of disclosure, however, is not to be interpreted as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of the invention.

[0033] Furthermore, while some embodiments described herein include some features included in other embodiments but not other features, combinations of features from different embodiments are meant to be within the scope of the present invention and form different embodiments as would be understood by one of ordinary skill in the art. For example, in the following claims, any of the claimed embodiments can be used in any combination.

[0034] It should be noted that the use of a particular term when describing a particular feature or aspect of the invention should not be construed as implying that the term has been redefined herein to be limited to include any particular characteristic of the feature or aspect of the invention with which the term is associated.

[0035] In the description provided herein, numerous specific details are set forth. However, it will be understood that embodiments of the present invention may be practiced without these specific details. In other instances, well-known methods, structures, and techniques have not been shown in detail in order not to obscure an understanding of this description.

[0036] In a first aspect, embodiments of the present invention relate to a method for determining a three-dimensional atomic distribution within a field of view of a sample having a tip during an atom probe tomography (APT) process, the method comprising performing an evaporation process that includes evaporating atoms from the sample and projecting them onto a detector where they are detected.

[0037] The method further includes recording a hit map corresponding to a first predetermined stage of the evaporation process. The hit map includes the impact location of each detected atom on the detector and the time-of-flight of each detected atom, where the time-of-flight of each atom is determined as the travel time between the atom's initial position in the sample and its final position where it impacts the detector. The sample should include at least one known type or material of atom, referred to herein as a reference atom, and one or more unknown types or materials of atom, referred to herein as target atoms. If the sample is made primarily of a first material, such as silicon, and it is desired to know the distribution of a second material in the first material, for example, the distribution of a dopant in a silicon matrix, the reference atoms are silicon atoms and the target atoms are dopant atoms.

[0038] In an embodiment of the present invention, recording a hit map belonging to a first predetermined stage of the evaporation process may be performed by recording the full hit map during the entire evaporation process and extracting from the full hit map a reduced hit map that includes detected atoms that impacted the detector only during the first predetermined stage of the evaporation process. In an alternative embodiment of the present invention, recording a hit map belonging to a first predetermined stage of the evaporation process may be performed by discarding all impacts on the detector outside of the first predetermined stage and storing only data related to the first predetermined stage of the evaporation process (impact locations and time-of-flight of detected atoms). The predetermined stage may be any continuous period of the evaporation process that should include enough detected atoms to analyze the evolution of the tip surface over time.

[0039] The method according to an embodiment of the present invention further comprises dividing the hit map of the first predetermined stage of the evaporation process into a plurality of zones.

[0040] For each zone of the hit map belonging to a given stage, detected atoms are selected. Among these detected atoms, a reference atom is known, and therefore the mass-to-charge ratio of the reference atom is also known (reference mass-to-charge ratio). Based on the recorded time-of-flight of the target atom, its mass-to-charge ratio is identified by comparing the recorded time-of-flight of a reference atom in the sample with a reference mass-to-charge ratio. The selection of detected atoms in the hit map zone and the identification of the mass-to-charge ratio of the target atom are repeated for all zones of the hit map belonging to a given stage of the evaporation process. A mass-to-charge spectrum is constructed from the identified mass-to-charge ratios and lists the number of atoms on the detector detected during a given stage of the evaporation process for each identified mass-to-charge ratio. The mass-to-charge spectrum can be represented as a graph with peaks. The mass-to-charge value with the highest count in a peak represents the mass-to-charge values ​​of all atoms from this peak. The deviation of the mass-to-charge value in a peak indicates the variation in the flight distance of the atom represented by the peak.

[0041] The method according to an embodiment of the present invention further includes deriving flight distances of selected atoms of any element in the peak of the mass-to-charge spectrum, where the flight distance of each atom is specified as the length between the initial position and the final position. The method further includes deriving launch angles of the selected atoms, where the launch angle of each atom is specified as the angle between a line of the apex axis perpendicular to the detector and an extension of the launch direction from the point of the atom's initial position, assumed to be perpendicular to the tip surface.

[0042] The method further includes estimating an approximate surface geometry of the tip in a first field of view of the sample based on the derived departure angle of the selected atom. The method further includes measuring an actual surface geometry of the tip of the sample and matching the approximate surface geometry to the actual surface geometry. The method further includes deriving a size and a position of the first field of view of the detected atom based on the matched approximate surface geometry with the actual surface geometry.

[0043] The method then further includes recording a hit map belonging to a second predetermined stage of the evaporation process. Similar to recording a hit map belonging to the first predetermined stage of the evaporation process, recording a hit map belonging to the second predetermined stage of the evaporation process may involve recording a complete hit map during the complete evaporation process (the same complete hit map used to record the hit map belonging to the first predetermined stage of the evaporation process) and extracting from the complete hit map a reduced hit map that includes detected atoms that impacted the detector only during the second predetermined stage of the evaporation process. In an alternative embodiment of the present invention, recording a hit map belonging to the second predetermined stage of the evaporation process may be performed by discarding all impacts on the detector outside the second predetermined stage and storing only data related to the second predetermined stage of the evaporation process (impact locations and times of flight of detected atoms). The second predetermined stage may be any continuous period of the evaporation process that includes enough detected atoms to analyze the evolution of the tip surface over time.

[0044] Hereinafter, similar steps performed on the first predetermined stage of data are performed on a second predetermined stage of data, including identifying the mass-to-charge ratios of those detected atoms in the second predetermined stage and deriving the flight distances and departure angles of selected peaks in the calibrated mass-to-charge ratio spectrum.

[0045] The size and position of the second field of view of the detected atoms can be derived based on an approximate surface geometry that matches the actual surface geometry.

[0046] The method therefore further includes determining a volume enclosed by the first field of view and the second field of view to define a reconstruction volume. Finally, the method includes reconstructing a three-dimensional atomic distribution of the sample in the reconstruction volume.

[0047] By way of example, and not limitation, further standard and optional features of exemplary embodiments according to the present invention will now be described with reference to the drawings.

[0048] FIG. 1 illustrates a method 100 for determining a three-dimensional atomic distribution of a sample according to an embodiment of the present invention. The method 100 includes performing an evaporation process, which includes evaporating atoms from the sample and projecting them onto a detector 205 where they are detected. An example of the evaporation process 200 is illustrated (not to scale) in FIG. 2. The evaporation process 200 includes obtaining a sample 201 mounted on a sample holder 202 and placing the sample 201 in a chamber, such as a vacuum chamber 203. The sample 201 is sharpened so that it has a sufficiently sharp tip 204, for example, the tip has a radius of less than 50 nm. The tip 204 has a point C1 at the top surface location of its apex. The tip 204 can be symmetric or asymmetric at any time before, during, or after the evaporation process.

[0049] The vacuum chamber 203 further includes a position-sensitive detector 205, e.g., an ion detector, capable of measuring the two-dimensional position of an impinging particle on the sensor surface. The ion detector 205 has a geometric shape with a center point C2 at its center. The ion detector 205 may have, for example, a circular shape, a rectangular shape, or any other suitable geometric shape. The ion detector 205 has a detection efficiency of at least 50%, e.g., 50% to 70%, meaning that only 50% to 70% of the ions reaching the detector are recorded. The sample 201 is positioned within the vacuum chamber 203 so that the apex C1 and the center point C2 are separated by a distance D. The apex C1 and the center point C2 are aligned so that they are located on a line passing through the apex C1, which is substantially perpendicular to the tip 204, and the center point C2, which is substantially perpendicular to the detector 205. Under ideal conditions, the deviation in the positions of C1 and C2 should be very small, e.g., less than a few micrometers, preferably less than a few tenths of a micrometer. However, in practical cases deviations of a few millimeters are possible.

[0050] Performing the evaporation process involves applying a voltage bias between the sample and the detector 205 close to the threshold for breaking atomic bonds, and optionally, a superimposed laser pulse train impinging on the sample. In one example shown in FIG. 2, a voltage bias 206 is applied between the sample holder 202 and the detector 205. The sample holder 202 is made, for example, of a tungsten wire attached to a conductive holder, which has a lower electrical resistance than the supported tungsten wire and the tip. The applied voltage bias 206 can be, for example, 2 to 10 kV. The voltage bias generates an electric field between the sample and the detector, for example, with a strength of 10 V / nm or greater. A laser pulse train 207 impinging on the tip 204 of the sample 201 can be introduced as a supplement to thermal energy to help atoms at the apex of the sample 201 overcome the energy barrier to evaporation. The laser pulses of the laser pulse train 207 can have a pulse frequency of, for example, 1 to 300 kHz or greater. The wavelength of the laser pulses in the laser pulse train 207 generated by the laser source can be between 300 nm and 12,000 nm, for example, 1,030 nm for an IR laser, 515 nm for a green laser, or 343 nm for a UV laser or other laser source of a different wavelength. The strength of the electric field induced by the voltage bias 206 must be sufficiently close to the threshold for breaking the atomic bonds of the atoms in the sample 201. Therefore, when a laser pulse in the laser pulse train 207 of sufficiently high intensity is superimposed on the voltage bias 206, the atomic bonds of the atoms in the sample 201 are broken, and atoms from the sample 201 are evaporated.

[0051] During the evaporation of atoms from the sample 201, the atoms are ionized to become ionized atoms, which are separated from the tip 204 and accelerated toward the detector 205 according to the electric field distribution between the tip 204 and the detector 205. For example, during application of the voltage bias 206, one laser pulse of the laser pulse train 207 can evaporate one atom in the sample 201, or one laser pulse of the laser pulse train 207 can evaporate multiple atoms in the sample 201, or multiple laser pulses in the laser pulse train 207 can evaporate one atom in the sample 201. To avoid two signals simultaneously impinging on the detector 205 from the same pulse and wasting too much time on the experiment, it is preferable that the evaporation flux be adjusted to a condition where multiple laser pulses evaporate one single atom.

[0052] In the absence of application of voltage bias 206, the laser pulses of laser pulse train 207 alone will not evaporate atoms in sample 201. In the absence of laser pulses of laser pulse train 207, application of voltage bias 206 alone will not result in evaporation of atoms in sample 201.

[0053] The sample 201 to be analyzed contains atoms of a known reference atom type and atoms of one or more unknown target atom types. The APT user typically has prior knowledge of the major elements of the measured sample, hence the reference atom type. The reference atom type 210 has a first atomic population in the sample 201. The target atom type 211 has a second atomic population in the sample 201.

[0054] The evaporated atom may impact the ion detector 205, e.g., the evaporated atom may have its impact point, e.g., first impact point 208, on the ion detector 205. If the impact point of the evaporated atom is on the ion detector 205, e.g., first impact point 208, the atom is said to be in the field of view. Alternatively, the evaporated atom may not impact the ion detector 205, e.g., the evaporated atom may have its impact point, e.g., second impact point 209, that is off the ion detector 205. If the impact point of the evaporated atom is off the ion detector 205, e.g., second impact point 209, the atom is said to be out of the field of view.

[0055] The method 100 further includes recording 102 a hit map belonging to a first predetermined stage of the evaporation process, e.g., a hit map belonging to the last predetermined number of seconds of the evaporation process, e.g., the last 180 seconds, or a hit map belonging to the last predetermined number of atoms detected by the detector 205, e.g., the last 100,000 atoms. The hit map includes the impact location of each detected atom on the detector 205 and the associated time-of-flight of each detected atom. The time-of-flight of each evaporated atom is determined as the travel time between when the ionized atom is separated from the tip 204 (the atom's initial position on the tip) and when the ionized atom impacts the ion detector 205 (its final position on the detector), e.g., due to a pulse in the laser pulse train 207. A continuous period of the evaporation process is defined as a predetermined stage within which atoms 103 are sufficiently detected for analysis, as illustrated in the hit map shown at 300 in FIG. 3 .

[0056] In an embodiment of the present invention, recording a hit map 300 belonging to a predetermined stage of the evaporation process may include recording a full hit map of the evaporation process, including the impact location of each detected atom on the detector during the evaporation process and the associated flight time for each detected atom, and extracting a reduced hit map from the full hit map, including only the impact locations and associated flight times of atoms that impacted the detector and that belong to the predetermined stage of the evaporation process.

[0057] The method further includes dividing the hit map 300 into a plurality of zones, each corresponding to a predetermined stage of the evaporation process. The hit map 300 may be divided into a regular array of zones 301, 302, each having predetermined dimensions, e.g., rectangular zones ranging from 0.2 cm x 0.2 cm to 0.5 cm x 0.5 cm. However, this is not intended to limit the scope of the present invention. The hit map 300 may be divided into a regular or irregular array of zones 301. The zones 301 may or may not all have the same dimensions. The zones may have a rectangular or square shape, or any other suitable geometric structure. After dividing the hit map 300 into zones 301, each zone is analyzed separately from the other zones.

[0058] The evaporated atoms are sequentially detected on the detector 205, and atoms belonging to a predetermined stage of the evaporation process that impinge on the detector in a particular zone 301 are selected 103 to derive a surface geometry corresponding to the selected atoms. By way of example only, and although the invention is not limited thereto, the last 100,000 detected atoms may be selected 103 to derive a surface of a first field of view that belongs to a first predetermined stage, e.g., the surface after the evaporation process.

[0059] The time-of-flight is recorded in the hit map 300 for each detected atom at a given stage of the evaporation process, allowing the number of atoms detected in the zone 302 having the same time-of-flight or the same time-of-flight within a given error range to be counted. Figure 4 shows an exemplary graph 400 of different time-of-flights of atoms detected in the first zone 302 of the hit map 300. The time-of-flight is plotted on the horizontal axis (in nanoseconds) versus the number of impact points on the vertical axis (logarithmic scale). The statistical results show several peaks in the time-of-flight bins. Every time-of-flight bin corresponds to a specific type of atom detected. The number of impact points of different types of atoms corresponds to the presence of several atoms of the different types of atoms in the sample 201. Typically, a sample has a reference atom type with a substantially higher number of atoms than the number of atoms of the target atom type. Thus, for example, in an example where the time-of-flight is shown to be approximately 450 ns, it can be estimated that the highest peak 403 belongs to the reference atom type 210 in the sample 201. Other peaks, such as the second highest peak 404 in the example shown with a time of flight around 320 ns, belong to the target atom type 211 in the sample 201 .

[0060] The method 100 may include: determining a time-of-flight interval based on the recorded time-of-flight of the atom;

number

number

number

[0061] The target time of flight tof2 of the target atom type 211 in the sample 201 and the reference time of flight tof1 of the reference atom type 210 in the sample 201 are described by the first and second equations as follows:

number

number

number

number

[0062] The third formula is the target atom type 211 in the sample 201.

number

number

[0063] The same formula may be applied to obtain the mass-to-charge ratios of atoms of other peaks in the time-of-flight graph 400 from the selected first zone 302 of the hit map 300 .

[0064] The same algorithm is continually applied to other zones in hit map 300 until all zones have been analyzed. The calibrated mass-to-charge ratios of all selected atoms belonging to a first predetermined stage of the evaporation process, e.g., the last 100,000 detected atoms, can be plotted on the horizontal axis of a calibrated mass-to-charge spectrograph 500, as shown in FIG. 5, for all zones in hit map 300, with the vertical axis (logarithmic scale) being a function of the number of atoms of each of the different types of atoms in sample 201. In FIG. 5, the highest peak 503 corresponds to the highest peak 403 in FIG. 4, which corresponds to reference atom type 210, and the second highest peak 504 corresponds to the second highest peak 404 in FIG. 4, which corresponds to target atom type 211.

[0065] The method 100 further includes deriving 105 the distance of flight of selected atoms of any element in the peaks of the mass-to-charge spectrum 500. In a calibrated mass spectrum, in FIG. 5, the m / n ratio with the highest count in a peak represents the mass-to-charge ratio of all atoms from this peak. Deviations in the m / n ratios in a peak indicate variations in the time of flight. Thus, a user can range over any one of the peaks and calculate the time of flight of atoms in this peak using the following formula (corresponding to the second formula): m / n=2eV.(tof / L) 2 where e represents the element charge, V represents the applied voltage, L represents the flight distance from the ejection position to the collision point on the detector, and to represents the corresponding flight time. For example, peak 503, which has a representative m / n value of 28.1, may be selected and the flight distance of each atom in the peak may be calculated.

[0066] Furthermore, in combination with the hit map 300, the calibrated mass-to-charge graph 500 of FIG. 5 can be used to extract a partial hit map of any type of atom in the sample 201, i.e., a partial hit map of atoms of one peak in the mass-to-charge spectrograph 500, for example, the partial hit map 600 of FIG. 6 of the highest peak 503 of the reference atom type 211.

[0067] The method 100 further includes deriving 106 a launch angle for the selected atom. Because the size of the APT tip is at least five orders of magnitude smaller than the flight distance, as previously described, it can be assumed that all evaporated atoms launch from the same point. FIG. 7 shows the actual flight path 701 of an atom launching from the origin a of the launch angle θ and arriving at the detector at the impact location b. The derived flight distance L is insufficient to accurately depict the actual trajectory of the atom, which means that it is difficult to derive the correct launch angle θ.

[0068] Therefore, the objective of an embodiment of the present invention is to derive an estimated launch angle α of the estimated flight path 702 (dashed line) of an atom evaporated from the sample 201. As previously mentioned, the initial position of the evaporated atom is assumed to be point a on the tip 204, and the final position of the atom is assumed to be point b on the detector 205. In ideal conditions, point a lies on a straight line passing through the center point C2 of the detector 205 and is substantially perpendicular to or orthogonal to the detector surface. In the practical case of this example, based on the assumption that atoms on the surface of the tip fly straight to the detector, point a is defined on the detector 205 on a straight line passing through the position C3 with the shortest flight distance, as shown in the partial hit map 600. The deviation of the position of the ideal point C2 compared to point C3 is very small, e.g., less than a few millimeters.

[0069] Calculating the electric field from electrostatic simulations reveals that the electric field varies strongly near the apex of the tip 204, and after a given distance, the field fluctuations decrease. Deriving the flight distance and launch angle 106 involves calculating the flight distance and launch angle d from the sample. field This can be done by assuming a first flight projection in a high magnetic field gradient region where the tangential direction along the atom's actual flight path changes significantly, and a second flight projection in a low magnetic field gradient region where the flight path is assumed to be a straight line flight over a predetermined distance to the detector (205).

[0070] This is illustrated in Figure 7. The tangential direction along the actual flight path 701 is determined by a defined predetermined distance d field The first flight projection in the high magnetic field gradient region within the trajectory changes significantly, and the path beyond that is assumed to be a straight line flight toward the detector. With this assumption, the actual trajectory 701 can be simply fitted by two straight lines 703, 705 that form the estimated flight path 702, and the transition point P is the distance from the launch position a to the d field where the sum of the two straight lines is equal to the actual flight distance previously derived for the atom. The resulting angle α between the apex axis and the direction to the transition point can then be used as an approximation of the actual launch angle θ. The distance d fieldis a constant value that is applied to derive the launch angles of all atoms.

[0071] The method 100 further includes estimating 107 an approximate surface geometry of the tip 204 in the first field of view of the sample 201 based on the derived take-off angles of the selected atoms, as shown in Figure 8. For estimating 107, it is necessary to find the ideal take-off positions on the tip surface for all detected atoms.

[0072] Initially, the apex axis is aligned so that a line passing through point C1 at the apex position of the tip and substantially perpendicular, or preferably perpendicular, to the tip surface passes through point C3 on the detector 205 with the shortest flight distance and is substantially perpendicular, or preferably perpendicular, to the detector surface. FIG. 8 shows atoms launching from an actual point AP on the surface of tip 204 with an actual flight path 701 and an actual takeoff angle θ. The initial direction of the atoms is perpendicular to the tip surface, and the atoms land on the detector 205 at an impact location 208. The tip 204 can be approximated by an actual sphere 801 (e.g., shown by a solid line) having an actual radius AR and an actual origin AO, which passes through the apex C1 of the tip 204. The actual takeoff angle θ lies between a line perpendicular to the tip 204 and passing through the actual point AP and the actual origin AO, and a line passing through the apex C1, substantially perpendicular to the tip 204, and point C3 with the shortest flight distance and substantially perpendicular to the ion detector 205.

[0073] Estimating 107 begins by assuming a first reference sphere 802 (e.g., shown by a dashed line in FIG. 8 ) having a first reference radius FR and a first reference origin FO on the apex axis, where the first reference sphere 802 passes through the apex C1 of the tip 204. The location of the first reference origin FO is defined on the apex axis having a distance equal to the sum of the shortest flight distance and the first reference radius FR. The first reference point FP is located at the intersection of the first reference sphere 802 and a line from the first reference origin FO to the impact point 208 on the detector 205, with a linear angle γ between the line and the apex axis.

[0074] Since the actual launch angle θ is approximated by the angle α derived from the flight distance, if the launch angle α derived from the flight distance is greater than the linear angle γ, the first reference radius FR of the first reference sphere 802 is scaled in a scaling process to a second reference radius SR (e.g., indicated by a dotted line) of a second reference sphere 804 that also passes through the vertex C1 of the tip 204 and has a second reference origin SO on the tip axis. The second reference point SP is defined as the intersection point between the line of the linear flight path 803 and the second reference sphere. Assume a curved flight path 805 from the second reference point SP to the impact point 208. During scaling, the end of the sphere remains aligned with point C1 by shifting the origin FO to SO and moving the reference point FP to SP along the tip axis, causing the launch angle to increase from γ to γ'. The scaling process continues until the launch angle γ' matches the previously derived launch angle α.

[0075] If the scaling process continues and leads to one or more further reference points at the end of the scaling process, the positions of the reference points, for example, the first reference point FP or the second reference point SP or the further reference points, are considered as possible ejection positions of atoms on the tip surface. The estimation 107 process and scaling process are performed for all evaporated atoms. Finally, the distribution of the reference points forms an approximate surface geometry.

[0076] The method 100 further includes measuring 108 the actual surface geometry of the tip 204 of the sample 201. The measurement may be performed, for example, by atomic force microscopy (AFM), scanning probe microscopy, transmission electron microscopy (TEM), ptychography, or any other suitable measurement technique. An example of the three-dimensional surface of a tip measured using AFM is shown in FIG. 9.

[0077] The method further includes matching 109 the approximate surface geometry to the actual surface geometry of the tip 204 of the sample 201. Matching can be performed by a rough surface matching process followed by a non-standard iterative closest point (ICP) method in the sequence of steps shown in FIG. 10 . The ICP method can be replaced by any other suitable method. In this case, matching is performed on a first group of scattered points representing the approximate surface geometry derived from the APT data in estimation step 107, and a second group of points representing the actual surface geometry from step 108, as measured, for example, by AFM. Matching 109 begins with creating a surface mesh 1001. Then, a rough surface matching 1002 matches the created 1001 smoothed and meshed surface of the first and second groups of scattered points. Matching 1002 provides an initial guess of where the first point group should be shifted, i.e., to initial alignment, so that the first point group matches the actual surface of the second point group, and a size to which the first point group should be scaled so that the first point group matches the actual surface of the second point group. Matching 109 further includes shifting and scaling 1003 the first point group based on the initial guess in 1002. The scaling is performed using a weighting function. The shifted and scaled data of the first point group has a first centroid, and the second point group has a second centroid. ICP includes iteratively aligning the first centroid to the second centroid or the second centroid to the first centroid. Furthermore, ICP includes iteratively fine-matching 1004 the two point groups, e.g., fine-matching the approximate surface geometry data to the actual surface geometry data, until a minimum distance between the two point groups is found. Generally, or in ICP, it is allowed to rotate the data points in all directions. However, according to an embodiment of the present invention, the derived tip shape and the SPM measured tip apex axis are aligned in the same direction as the laser coming from, so rotation can be negated. A weighting function is added to scale the size of the surface geometry.The updated first and second point groups are recorded after each iteration, and the points in the second point group that are closest to or opposite each point in the first point group are identified. The ICP method requires a level of precision in both the first and second point groups. Here, the first point group is assumed to match the second point group, but vice versa is also possible. The matched area of ​​the two data groups defines a first field of view 110, which belongs to a first predetermined stage of the evaporation process, e.g., the last 100,000 detected atoms.

[0078] To determine the reconstructed volume 111, a hit map belonging to a second predetermined stage of the evaporation process is required 102, e.g., recorded as such or extracted from the complete hit map as described above for recording a hit map belonging to a first predetermined stage of the evaporation process. Accordingly, other detected atoms are selected 103 belonging to the second predetermined stage of the evaporation process to define a second FOV region. By way of example only, and the invention is not limited thereto, the surface of the first FOV region may be the surface at the end of the evaporation process, and the surface of the second FOV region may be the surface at the beginning of the evaporation process. To define the surface of the second FOV region, another group of detected atoms, e.g., the first 100,000 detected atoms, is selected 102, and steps 103-110 of method 100 are repeated. Further details are omitted here; please refer to the above description regarding determining the first field of view region.

[0079] The area enclosed by the two determined FOV regions, e.g., the first and second FOV regions, then determines the volume to be reconstructed, also referred to as the reconstruction volume 111. The number of detected atoms corresponding to the surface of the second FOV region and the number of detected atoms corresponding to the surface of the first FOV region may or may not be the same.

[0080] The method 100 further includes reconstructing 112 a three-dimensional atomic distribution in the field of view of the tip 204 of the sample 201. Reconstructing 112 is performed over a reconstruction volume, which ideally should have the exact same shape and volume as the enclosed region of the FOV surface in 111. Reconstructing 112 may include returning the atoms detected on the detector 205 to their initial positions on the tip 204 of the sample 201. This is done by using the completion percentage to determine the surface geometry and reconstruction height of the developing surface where the atoms must be placed, and using a one-to-one correlation between the location on the detector and the tip surface to determine the spatial location of each reconstructed atom, e.g., the launch position on the tip surface of each detected atom. The completion percentage is a percentage of the reconstructed volume relative to the total volume of the field of view and is introduced to evaluate the completion of the reconstruction utilized in time to define the reconstruction height of the tip surface where the queried atom will be placed. The developing surface geometry of the intermediate surface can be linearly interpolated between the first and second FOV regions, or alternatively, method steps 102-110 can be repeated for different stages of the evaporation process. According to the estimated flight path, also called the trajectory, the detector surface during which the launch angle is derived can be divided into several zones, and each zone on the detector can be registered with a corresponding surface on the tip surface. Because the trajectory is independent of atomic mass and atomic charge state, this one-to-one correlation persists for all distinct elements of the detected atoms. Therefore, the spatial location of the launch position can also be defined.

[0081] An example of a reconstructed volume 1100 is shown in FIG. 11. The reconstructed volume 1100 is bounded by a first field of view 1101 and a second field of view 1102. The first field of view 1101 may be the field of view at a first time point where the APT process ends, corresponding to a reconstruction completion percentage of 0 percent, for example. The second field of view 1102 is the field of view at a second time point where the APT process begins, corresponding to a reconstruction completion percentage of 100 percent. The final stage of the evaporation process begins with the reconstruction from the surface of the final FOV by reversing the order of evaporation 1103, i.e., the last detected atom is reconstructed first, so the reconstruction completion is set to 0 percent. The total reconstructed volume includes the volume of detected and missing atoms, which depends on the detection efficiency of the detector 205. Because the detection efficiency and pulse frequency of the laser are known parameters, the reconstructed volume between pulses can be calculated according to the required pulses between detected atoms. This allows the percentage of completion in time to be calculated while reconstructing each atom. Therefore, the reconstructed height and developing surface geometry for the corresponding pulse when each atom is detected can be derived. For example, the reconstructed height and intermediate surface 1104 are derived, where an atom erupts from position 1105 and reaches position 1106 on the detector. Based on the trajectory 1107 of the atom on the extracted surface 1104, the detector surface is divided into multiple zones, and each zone, e.g., zone 1108 on the detector, can be registered to zone 1109 on the tip surface. Therefore, the erupted position 1105 of the detected atom at position 1106 can be reconstructed.

[0082] In a further aspect, the present invention also relates to a processing system adapted to perform the different method steps of the above-described method embodiments. The different steps may be implemented as hardware or software within the processing system. Such a processing system may include at least one programmable processor coupled to a memory subsystem including at least one form of memory, e.g., RAM, ROM, etc. A storage subsystem having at least one disk drive and / or CD-ROM drive and / or DVD drive may be included. In some implementations, a display system, keyboard, and pointing device may be included as part of a user interface subsystem to provide for a user to manually input information. Ports for inputting and outputting data may also be included. More elements may be included, such as network connections, interfaces to various devices, etc. The various elements of the processing system may be coupled in various ways, including via a bus subsystem. The memory of the memory subsystem may at some point hold some or all of a set of instructions that, when executed on the processing system, implement the steps of the method embodiments of the present invention. Thus, while the processing system itself is prior art, a system including instructions for implementing aspects of the present invention is not prior art.

[0083] A particular embodiment of the present invention relates to a system for determining a three-dimensional atomic distribution in a field of view of a sample 201 during an atom probe tomography process 200, comprising means 206, 207 for evaporating atoms from the sample 201 and projecting them onto a detector 205, the detector 205 adapted to record a hit map including the impact location and time of flight of each atom, and a controller configured to implement a method of an embodiment of the first aspect of the present invention. The system is configured to automatically perform the steps of the method. Such an automatic task may be performed after a user commands the system to do so, for example by clicking a graphically displayed button.

[0084] The present invention also includes a computer program product that provides the functionality of any of the method embodiments according to the present invention when executed on a computing device. Furthermore, embodiments of the present invention include a data carrier, such as an optical or solid-state storage medium, a CD-ROM, a DVD-ROM, or a diskette, that stores the computer product in machine-readable form and that performs at least one of the methods according to the present invention when executed on a computing device. Nowadays, such software is often provided for downloading over the Internet or a company intranet; therefore, the present invention also includes transmitting a computer product according to the present invention over a local or wide area network.

[0085] While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive. The foregoing description sets forth several embodiments of the invention in detail. However, no matter how detailed the foregoing is, it will be understood that the invention can be practiced in many ways. The invention is not limited to the disclosed embodiments. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims.

Claims

1. A method (100) for determining a three-dimensional atomic distribution of a sample (201) having a tip during an atom probe tomography process, comprising: (i) performing an evaporation process comprising evaporating (101) atoms from the sample (201) and projecting the atoms onto a detector (205) where the atoms are detected, the detected atoms comprising reference atoms and target atoms; (ii) recording (102) a hit map (300) belonging to a given stage of the evaporation process, comprising the impact position of each detected atom on the detector (205) and the time of flight of each detected atom; (iii) dividing the hit map (300) into a plurality of zones; (iv) selecting (103) the detected atoms within a zone of the hit map (300); (v) determining the mass-to-charge ratio of the target atom based on the recorded time-of-flight of the reference atom by comparison with the recorded time-of-flight of the reference atom (104); (vi) repeating steps (iv) and (v) for all zones of the hit map to construct a mass-to-charge spectrum (500); (vii) deriving (105) the flight distance of a selected atom of any element at a peak in the mass-to-charge spectrum; (viii) deriving a launch angle (α) of the selected atom (106); (ix) estimating (107) an approximate surface geometry of the tip in a first field of view of the sample based on the derived takeoff angles of the selected atoms; (x) measuring (108) the actual surface geometry of the tip of the sample; (xi) matching the approximate surface geometry to the actual surface geometry (109); (xii) deriving (110) a size and a position of a first field of view of the detected atoms based on the approximate surface geometry that matches the actual surface geometry; (xiii) recording a hit map belonging to another predetermined stage of the evaporation process, repeating steps (iii) to (xi) and deriving the size and position of a second field of view of the detected atoms based on the approximate surface geometry matching the actual surface geometry (110); (xiv) determining (111) a volume enclosed by the first field of view and the second field of view to define a reconstruction volume; (xv) reconstructing (112) the three-dimensional atomic distribution of detected atoms in the reconstruction volume of the sample.

2. 2. The method of claim 1, wherein the step of recording a hit map of the evaporation process comprises recording a complete hit map of the evaporation process and extracting from the complete hit map a reduced hit map that only belongs to the predetermined stage of the evaporation process.

3. 3. The method of claim 1, wherein the step of reconstructing the three-dimensional atomic distribution of detected atoms comprises returning atoms to the surface of the tip, using a percentage of completion to determine the surface geometry and the height of a developing surface on which the atoms must be placed, and using a one-to-one correlation between locations on the detector and the tip surface to determine the spatial positions of the atoms to be reconstructed.

4. 4. The method of claim 3, wherein using a one-to-one correlation between the location on the detector and the tip surface is based on an approximate trajectory during derivation of a takeoff angle.

5. 3. The method (100) of claim 1 or 2, wherein dividing the hit map into a plurality of zones comprises dividing the hit map by pixels in a suitable shape.

6. 3. The method (100) of claim 1 or 2, wherein the step (105) of deriving the flight distance of the selected atom comprises assuming that the atoms detected within a zone originate from the same point on the sample and have the same flight path.

7. The steps (105 and 106) of deriving the flight distance and the launch angle are performed at a predetermined distance (d ｆｉｅｌｄ 3. The method (100) of claim 1 or 2, wherein the method is performed by assuming a first flight projection in a high magnetic field gradient region where the tangential direction along the actual flight path of the atom changes significantly, over the predetermined distance to the detector (205), and a second flight projection in a low magnetic field gradient region where the flight path is assumed to be a straight line of flight, over the predetermined distance to the detector (205).

8. 3. The method according to claim 1, wherein the step of estimating the approximate surface geometry of the tip in a field of view of the sample comprises predefining several reference positions at intersections of the surface of an arbitrary sphere with a line from the origin of the sphere to the detected position, and optimizing these reference positions to a new position that forms the field of view.

9. 9. The method of claim 8, wherein optimizing the reference position comprises changing either a surface distance or a radius of the sphere by maintaining the derived launch angle.

10. 3. The method (100) of claim 1 or 2, wherein measuring (108) the actual surface geometry of the tip of the sample is performed by using any of scanning probe microscopy, transmission electron microscopy, or ptychography.

11. 3. The method (100) of claim 1 or 2, wherein the step (109) of matching the approximate surface geometry to the actual surface geometry comprises using an iterative closest point (ICP) method, in which the approximate surface geometry is pre-aligned to the actual surface geometry and a weighting function is added to scale the size of the surface geometry.

12. The step (109) of matching the approximate surface geometry to the actual surface geometry comprises: - creating a surface mesh (1001); - a rough matching (1002) of the approximate surface geometry with the actual surface geometry to provide an initial guess of the position for alignment; - shifting and scaling (1003) the data of the approximate surface geometry based on the initial guess; - a fine matching (1004) of the data of the approximate surface geometry to the data of the actual surface geometry.

13. 1. A system for determining a three-dimensional atomic distribution in a field of view of a sample during an atom probe tomography process, comprising: - means for evaporating atoms from the sample and projecting said atoms onto a detector; a detector for recording a hit map containing the collision location and time of flight of each atom; A controller configured to perform the method of any one of claims 1 to 12.

14. A computer program comprising instructions that, when said program is executed by a controller, cause said controller to perform the steps of the method of claim 1.

15. A computer-readable storage medium storing the computer program according to claim 14.

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