Patent Application
20140149052
The invention relates to the field of material characterization. More particularly, the present invention relates to methods and systems for obtaining information regarding a physical object, e.g. for obtaining tomographic depth information of a sample in an efficient manner.
Advanced electron microscopy involves imaging with resolutions at the Angstrom level, and advanced diffraction methods for determining local structure, local composition and electronic information of materials.
The focus variation method for image reconstruction in high-resolution transmission electron microscopy (HRTEM) has been widely used as a method for the reconstruction of the complex-valued electron wave function at the exit plane of a sample object from a series of transmission electron microscopy (TEM) images obtained at different focal distances. This allows, for example, the reconstruction of a phase image of the wave function in the plane of a graphene layer from experimental EM images. A resolution of 0.5 Angstrom can be achieved with this technique and state-of-the-art TEM technology, which enables the visualization of individual carbon atoms in the graphene layer. Although this method offers important advantages in terms of the reconstruction of the magnitude and phase of an electron wave, i.e. a complex-valued reconstruction based on real-space measurements, it is essentially a two-dimensional reconstruction technique.
TEM allows to detect and to visualize individual atoms, but standard techniques only provide a projected image which may be misleading in some cases. In order to obtain depth information, i.e. information regarding the distance of individual atoms relative a reference imaging plane, imaging along at least three different directions is required. For periodic structures, e.g. bulk material with crystalline structure, such projections along at least three axes may suffice to obtain a three-dimensional representation of the periodic structure. In general however, for example for aperiodic materials, tomography techniques can be used to obtain three-dimensional visualization. In tomography, a large number of images are obtained by passing an electron beam through the sample at different rotation angles around the center of the sample, typically by tilting the sample, e.g. over angles from −80° to 80°. For high resolution TEM applications, the phase-contrast dominates image intensities, therefore the image intensity cannot be considered a monotonic function of object thickness. This may complicate the distinction between lower and higher density inclusions and thus the interpretation of the results. Furthermore, the weak phase object approximation used in these methods require a sufficiently thin object, i.e. a sufficiently short electron path length through the object for all projections, therefore limiting the useable range of rotation around a thin-slice object. This may complicate the tomographic reconstruction, e.g. by limiting resolution.
It is an object of the present invention to provide efficient systems and methods for material characterization. It is an advantage of embodiments according to the present invention that the methods and systems for obtaining information provide a plurality of new applications, such as determination of atomic structure, local composition and local electronic structure of new materials, particularly nano-materials, semiconductors, e.g. the amorphous dielectrics in FET electronics, superconductors, alloys, polymer catalysts, ceramics, small particles, surface layers, multi-layers, composites and proteins. It is an advantage of embodiments according to the present invention that the methods and systems for obtaining information can be used for proteins, even if the protein structure is damaged. For example, it is sufficient that e.g. 10% of the atoms are on their original position, in order to use a method according to an embodiment of the present invention for aligning the reconstructed proteins and determining the position of each of the atoms.
It is an advantage of embodiments according to the present invention that 3-dimensional reconstruction using stereography can be improved.
It is an advantage of embodiments according to the present invention that the thickness of extremely thin specimens, e.g. graphene layers or multi-layers, can be determined, for example a thickness in individual single-atom layers can be determined.
It is an advantage of embodiments according to the present invention that taking into account the propagation behavior of waves with different Fourier components, probing of the geometry of the exit surface and of the mass at atomic scale, can be performed.
The above objective is accomplished by a method and device according to the present invention.
A method for determining information regarding an object comprising particles, the method comprising obtaining a wave function representative of the object detected at a detection surface of a detection system for detecting the wave function, deriving at least two spatial frequencies of the detected wave function and deriving for each of said at least two spatial frequencies at least a phase based on the obtained wave function, and analyzing a functional relationship between the spatial frequency and the phase for said spatial frequencies and deriving therefrom at least one parameter indicative of a property of the object. It is an advantage of embodiments according to the present invention that based on a wave function representative of an object, a plurality of information can be obtained by performing analysis of at least two spatial frequencies of the detected wave function.
Deriving at least one parameter indicative of a property of the object may comprise deriving a distance of a particle comprised in the object to a detection surface of the detection system used for detecting the wave function representative of the object. It is an advantage of embodiments according to the present invention that based on a wave function representative of an object, distance information regarding the distance of the object to the detection surface can be obtained. Deriving a distance of the object to a detection surface of the detection system used may comprise taking into account a slope of a relation between the square of the spatial frequency and the phase for different spatial frequencies. The relation may be a linear relation between the square of the spatial frequency and the phase for different spatial frequencies. Deriving at least one parameter indicative of a property of the object may comprise deriving a phase value (φ0). The phase value may be representative of the mass of the object. It is an advantage of embodiments according to the present invention that information regarding the mass of the object can be derived based on the analysis. In some embodiments, e.g. when considering thin objects, besides determining the phase also amplitude may be determined for obtaining information regarding the object, e.g. regarding the atoms involved.
The deriving of a phase value (φ0), for example representative of the mass of the object, may comprise taking into account an extrapolation of the phase to a spatial frequency equal to zero by means of a relation between the square of the spatial frequency and the phase for different spatial frequencies. The relation may be a linear relation between the square of the spatial frequency and the phase for different spatial frequencies.
Obtaining a wave function representative of the object detected at a detection surface of a detection system for detecting the wave function may comprise obtaining an electron wave function representative of an electron beam interacting with the object.
Deriving at least one parameter indicative of a property of the object may comprise deriving an image representation and/or a volumetric image representation of the object.
Analyzing a functional relationship between the spatial frequency and the phase may comprise taking into account a multiplication of a spatial frequency magnitude squared, g2, the mathematical constant π and a wavelength, λ.
The present invention relates to a system for determining information regarding an object, the system comprising an input means for obtaining a wave function representative of the object detected at a detection surface of a detection system for detecting the wave function, a spatial frequency determination means for deriving from the detected wave function at least two spatial frequencies and for deriving for each of said at least two spatial frequencies at least a phase based on the obtained wave function, an analysis means for analyzing a functional relationship between the spatial frequency and the phase and for deriving therefrom at least one parameter indicative of a property of the object, and an output means for outputting the at least one parameter indicative of a property of the object.
The analysis means may be adapted for deriving a distance of the object to a detection surface of the detection system used for detecting the wave function of the object. The analysis means may be adapted for deriving a phase value (φ0). The phase value may be representative of the mass of the object. The analysis means may be adapted for calculating a slope of a linear relation between the square of the spatial frequency and the phase for different spatial frequencies. The analysis means may be adapted for extrapolating the phase to a spatial frequency equal to zero by means of a linear relation between the square of the spatial frequency and the phase for different spatial frequencies. The analysis means also may be adapted for determining amplitude for obtaining information regarding the object, e.g. regarding the atoms involved.
The input means may be adapted for obtaining an electron wave function representative of an electron beam interacting with the object.
The present invention also relates to a computer program product for, when executing on a computing device, carrying out a method as described above.
The present invention also relates to a data carrier comprising a computer program product as described above and to the transmission of such a computer program product over a local or wide area network.
The present invention also relates to an image representation or volumetric image representation obtained by a method as described above.
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.
These and other aspects of the invention will be apparent from and elucidated with reference to the embodiment(s) described hereinafter.
The drawings are only schematic and are non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn on scale for illustrative purposes.
Any reference signs in the claims shall not be construed as limiting the scope.
In the different drawings, the same reference signs refer to the same or analogous elements.
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. The drawings described are only schematic and are non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn on scale for illustrative purposes. The dimensions and the relative dimensions do not correspond to actual reductions to practice of the invention.
Furthermore, the terms first, second and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a sequence, either temporally, spatially, in ranking or in any other manner. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other sequences than described or illustrated herein.
Moreover, the terms top, under and the like in the description and the claims are used for descriptive purposes and not necessarily for describing relative positions. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other orientations than described or illustrated herein.
It is to be noticed that the term “comprising”, used in the claims, should not be interpreted as being restricted to the means listed thereafter; it does not exclude other elements or steps. It is thus to be interpreted as specifying the presence of the stated features, integers, steps or components as referred to, but does not preclude 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 devices consisting only of components A and B. It means that with respect to the present invention, the only relevant components of the device are A and B.
Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment, but 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.
Similarly it should be appreciated that in the description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of 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 this invention.
Furthermore, while some embodiments described herein include some but not other features included in other embodiments, combinations of features of different embodiments are meant to be within the scope of the invention, and form different embodiments, as would be understood by those in the art. For example, in the following claims, any of the claimed embodiments can be used in any combination.
In the description provided herein, numerous specific details are set forth. However, it is understood that embodiments of the 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.
By way of illustration, some features and concepts will be compared and explained based on similarities with astrophysical concepts. It is to be understood that aspects and embodiments of the present invention are not limited thereby and that the comparison is only made for ease of understanding.
Where in embodiments of the present invention reference is made to “Hubble plots”, reference is made to a graph of phase speed values corresponding to a spatial frequency magnitude as function of phases corresponding to said spatial frequency magnitudes.
Where is embodiments of the present invention reference is made to a phase speed, reference is made to a multiplication of a spatial frequency magnitude squared, g2, the mathematical constant π and a wavelength, λ.
The present invention relates to methods and systems for obtaining information regarding an object comprising particles. Such information is for example spatial information regarding relative position or small scale structure, e.g. a three-dimensional representation of an object. The information may for example be a volumetric image with resolution smaller than 10 μm/pixel, e.g. smaller than 10 nm/pixel, or smaller than 0.1 nm/pixel, for example 0.05 nm/pixel. Such information may be for example properties regarding particles, e.g. particle mass or internal structure information. The object may for example be a material specimen, e.g. a graphene layer, a protein or a dielectric for use in an electronic component, such as a field effect transistor (FET). The particles advantageously are objects that can be regarding as point objects such as for example atoms. The particles advantageously may be of atomsize. The particles may have a size in the order of Angström.
In a first aspect, the present invention relates to a method for obtaining information regarding an object. The method is especially suitable for obtaining three-dimensional spatial information regarding objects comprising particles that can be considered point objects. By way of illustration, embodiments of the present invention not being limited thereto, an exemplary method 100 is shown in
The exemplary method 100 furthermore comprises deriving 120 at least two spatial frequencies g of the detected wave function and deriving 130 for each of said at least two spatial frequencies at least a phase φ based on the obtained wave function. Said spatial frequencies and phases may for example be obtained by performing a spatial domain to spatial frequency domain transform, e.g. a discrete Fourier transform, or a Fast Fourier Transform (FFT), on the wave function, i.e. the array of numeric values. Advantageously, any method providing the pure spatial frequencies may be used. By spatial frequency g the magnitude of a spatial frequency vector may be intended. Therefore, for each spatial frequency g, a set of complex-valued components can be obtained, i.e. a G-band, each such component associated with a spatial frequency vector having said spatial frequency magnitude g. By way of illustration, embodiments of the present invention not being limited thereto, an example of a decomposition of an exit wave into several different spatial frequencies (g) is illustrated in
Furthermore, a plurality of derived phases φ for each spatial frequency g may be obtained by calculating the phase, i.e. the argument, of a plurality of complex-valued components associated with said spatial frequency g.
The method 100 furthermore comprises analyzing 140 the spatial frequency as function of the phase and deriving 150 therefrom at least one parameter indicative of a property of the object. In embodiments according to the present invention, such a property of the object may comprise a distance 141 of a particle in the object to the detection surface of the detection system used for detecting the wave function of the object. Also, in embodiments according to the present invention, such a property of the object may comprise a phase value (φ0) 142. In some embodiments, the phase value may be representative of the mass of a particle in the object. In some embodiments, also amplitude may be used for obtaining information regarding the particles involved.
In some embodiments of the present invention, analyzing 140 the relation between spatial frequency and phase may involve the application of a model, for example a linear regression model, wherein the model assumes a linear relation, e.g. φ−φ0=πλg2(f−f0). The factor πλg2, wherein λ is the wavelength of the wave represented by the wave function, is further referred to as the phase speed, in reference to velocity in an analogous cosmology model elucidated below. In this relation, f represents a focal distance and f0 a distance of a particle in the object to the focus. Furthermore, the phase value φ0 can, in some embodiments, be considered to be proportional to the mass of said particle. It will be seen that for the present example of a linear regression model of phase speed in function of phase will yield a slope coefficient (i.e. a coefficient equal to 1/(f−f0)), a distance of a particle in the object to the detection surface of the detection system used for detecting the wave function of the object could be derived. Said linear regression model furthermore yields an intercept coefficient, (i.e. a coefficient equal to φ0) e.g. a linear extrapolation of phase to phase speed equal to zero, i.e. an extrapolation of phase to spatial frequency equal to zero, representative of the mass of a particle in the object. Obviously, slope and intercept coefficients of a linear regression model of phase in function of phase speed allow calculation of the same properties.
In embodiments of the present invention, analyzing 140 the relation between spatial frequency and phase may furthermore involve a corrective step to adjust phase values by addition or subtraction of integer multiples of π, i.e. when deriving 120 of spatial frequencies and deriving 130 of phases associated with said spatial frequencies is inherently insensitive to phase shifts over multiples of π, e.g. a discrete 2D Fourier analysis. Such a correction is illustrated in
Methods according to embodiments of the present invention, may be suitable for implementation in a processing system as hardware or as software, such as in a programmable logic controller or a computer system. In other words, they may be computer implementable.
It is to be noticed that nearly all tomographic methods, such as filtered back projection, SIRT, wave tomography, single particle Cryo, etc.) make use of a large number of projections along different directions. Often full rotation of the object is imaged. One technique that can be used when depth information is required for distinguished objects is the use of stereo vision or stereopairs. The method as described in embodiments above, allows viewing all atoms in 2D, in some embodiments with a precision up to 1 picometer and with a depth resolution of 1 Angström. Nevertheless, when a given atom hides an atom in the viewing direction, the hided atom cannot be seen. According to some embodiments of the present invention, the method and system are adapted for viewing under small angle, i.e. up to a few degrees by applying two stereopairs. A system may for example be provided with a controller adapted for controlling viewing under a small angle. Viewing under small angle thus may allow viewing hidden atoms, with the same precision as the non-hidden atoms. It is an advantage of embodiments of the present invention that the big-bang method thus allows viewing all atoms in 3D using only two stereopairs.
The latter also is experimentally advantageous as one of the largest restrictions in electron tomography is the unaccuracy and the inertia of the mechanical tilters. As a tilt of few degrees can be obtained by electronically tilting the electron beam, the restrictions occurring in the prior art systems could be overcome, as tilting over small angles is, in combination with the method as described above, sufficient for obtaining detailed information regarding all atoms. Although electronically tilting of the imaging beam may have some effects on the imaging quality, advanced aberration corrections for electron microscopes can compensate at least partially for this.
The method and use of the system are especially advantageous for studying proteins as the procedure for obtaining an image wherein hidden information can be viewed can be shortened as only a small tilting is required which can be performed through electronically tilting. The latter results in the advantage that the imaging time can be small and therefore less radiation damage is introduced.
In a second aspect, the present invention relates to a system for determining information regarding an object. By way of illustration, embodiments of the present invention not being limited thereto, an exemplary system 200 is shown in
The system 200 comprises an input means 210 for obtaining a wave function representative of the object detected at a detection surface of a detection system for detecting the wave function. In embodiments of the present invention, such input means 210 may be adapted for obtaining an electron wave function representative of an electron beam interacting with the object. The input means may comprise an electronic storage device, such as a random-access memory chip, for storing a numerical array of values related to wave measurements, such as electron beam intensity measurements obtained from a physical array of detective elements on a detector surface, e.g. a charge-coupled device (CCD), the electron beam having interacted with, i.e. being diffracted by, the object while traveling from an electron beam generator through a guidance system. The input means may in fact comprise a transmission electron microscopy (TEM) apparatus with a detector surface, an electron beam generator, typically comprising a high-voltage supply and an electron gun, and a beam guidance and collimation system, typically comprising electrostatic and electromagnetic “lenses”, or means for receiving detection information from such an apparatus, such as a signal transmission line connection, a radio-frequent communication module and/or a reader for magnetic storage media.
The input means may furthermore comprise a processor for processing data, such as for example a numerical array of values. The processor thus may be adapted for calculating a phase and amplitude representation from beam intensity measurements. The input means may comprise means for transmitting the wave function information to the frequency determination means 220. There typically may be a data communication line from the input means to the frequency determination means 220.
The system 200 also comprises a spatial frequency determination means 220 for deriving from the detected wave function at least two spatial frequencies and for deriving for each of said at least two spatial frequencies at least a phase based on the obtained wave function. Such frequency determination means 220 may comprise a processor, for example a processor executing a Fourier transform on the detected wave function. The frequency determination means may be adapted for receiving said detected wave function from the input means 210 and for transmitting spatial frequency and phase information to the analysis means 230, e.g. by means of electric or optical signal transmission, radio-frequent communication or by interaction with a physical data carrier, such as magnetic data storage media.
Furthermore, the system 200 comprises an analysis means 230 for analyzing the spatial frequency as function of the phase and for deriving therefrom at least one parameter indicative of a property of the object. Such analysis means may comprise a processor programmed for executing methods as disclosed by embodiments of the present invention. The analysis means may be adapted for receiving spatial frequency and phase information from the means for spatial frequency determination 220.
In embodiments of the present invention, the analysis means 230 may be adapted for deriving a distance of the object to a detection surface of the detection system used for detecting the wave function of the object. In embodiments of the present invention, the analysis means 230 may be adapted for deriving a phase value (φ0). Such a phase value may, depending on the object, be representative of the mass of the object. For example, the analysis means 230 may comprise a processor for executing a method for calculating a linear regression between the square of spatial frequency and the phase obtained from the spatial frequency determination means 220. The analysis means also may, in addition, be adapted for deriving amplitude which may provide information of the particles involved.
Furthermore, the system 200 comprises an output means 240 for outputting the at least one parameter indicative of a property of the object. The output means 240 may for example comprise a display device, such as a computer monitor, a writing device for storing information on magnetic storage media and/or a printer device. The output means may comprise a processor for transforming the at least one parameter indicative of a property of the object into a suitable presentation. The output provided by the output means 240 may be static in nature, or a dynamic presentation adjustable by means of input from a user. The output means may be adapted for receiving information regarding the at least one parameter indicative of a property of the object from the analysis means 230.
The system 200, or parts thereof, may comprise or consist of a processing system which includes at least one programmable processor coupled to a memory subsystem that includes at least one form of memory, e.g., RAM, ROM, and so forth. A storage subsystem may be included that has at least one disk drive and/or CD-ROM drive and/or DVD drive. In some implementations, a display system, a keyboard, and a 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 also may be included. More elements such as network connections, interfaces to various devices, and so forth, may be included. The various elements of the processing system may be coupled in various ways, including via a bus subsystem.
In a third aspect, the present invention also relates to computer implemented processing systems adapted for performing the different method steps of method embodiments as described above. The different steps may be implemented in a processing system as hardware or as software. Such processing system may for example be comprised in a system according to embodiments of the present invention. The memory of the memory subsystem of such processing system may at some time hold part or all of a set of instructions that when executed on the processing system implement the step(s) of the method embodiments of the present invention. Thus, while a processing system as such is prior art, a system that includes the instructions to implement aspects of the present invention is not prior art. The present invention also includes a computer program product which provides the functionality of any of the methods according to the present invention when executed on a computing device. Further, the present invention includes a data carrier such as for example a CD-ROM, a DVD-ROM or a diskette which stores the computer product in a machine readable form and which executes at least one of the methods of the invention when executed on a computing device. Nowadays, such software is often offered on the Internet or a company Intranet for download, hence the present invention includes transmitting the computer product according to the present invention over a local or wide area network.
Advantages obtained using methods and systems according to embodiments of the present invention can be understood from the following considerations, although embodiments of the presented invention are not to be considered as limited by such theoretical considerations or mathematical formalisms.
The principles of the present invention may be explained by referring to
An analogy with the Big-Bang theory may be considered. The Big-Bang concept was developed in response to the observation of Edwin Hubble that the speed of a stellar system v, measureable by Doppler shift, is proportional to its distance D, i.e. v=H0D. H0 thereby is the Hubble's constant. This gave rise to the theory that all such stellar systems are fragments originating from a central explosion site, and allowed to calculate the elapsed time since such an explosion. Similarities between the Big Bang concept and embodiments of the present invention whereby the propagation of waves influenced by atoms is studied, are shown in
By way of illustration, embodiments of the present invention not being limited thereto, an example of information obtained using a method according to an embodiment of the present invention is further described below with reference to
By way of illustration, embodiments of the present invention not being limited thereto, the method is illustrated for a Buckled Hexagonal Graphene Structure (BHGS). The structure can be observed in a single sheet area. The tilting of the graphene sheet can be determined. It can be seen that the tilting information may be smeared out in a single atom column by thermal vibration.
a and
From the experiments, it can be seen that thermal vibration may play an important role. It can be noticed that bi-atoms are bound more strongly which makes the layer stiffer and the thermal displacement smaller. It also can be noticed that two atoms focus better than one. This makes the exit wave more sharply peaked and thus results in better depth precision. The columns of type no. 3 are more randomly distributed which is due to the fact that they are more loosely bound and can vibrate thermally more along the vertical axis so that the statistical precision is worse and larger than the systematic effect of the tilt. The tilt effect thus may be smeared out by thermal vibration. An example illustrating this effect is shown in
In the present example, a buckled hexagonal sheet can be seen, e.g. in
| Number | Date | Country | Kind |
|---|---|---|---|
| 1109014.9 | May 2011 | GB | national |
| Filing Document | Filing Date | Country | Kind | 371c Date |
|---|---|---|---|---|
| PCT/EP2012/059914 | 5/25/2012 | WO | 00 | 2/5/2014 |
