Method and system for measuring phase of electron wave function based on electronic optical path interference

Abstract

This application provides a method and system for measuring the phase of an electron wavefunction based on electron-optical path interferometry, relating to the fields of electron optics and electron microscopy. The method includes: controlling the propagation paths of the zero-order and first-order diffracted electron beams to achieve spatial overlap and form interference fringes at a preset detection plane; extracting cross-term information generated by the interference of the zero-order and first-order diffracted electron beams by performing spatial frequency domain transformation and filtering on the interference intensity distribution image on the detection plane; and reconstructing the phase distribution of the electron wavefunction based on the cross-term information through inverse transformation. Thus, by using the zero-order and first-order diffracted electron beams generated by the same electron beam diffracted through a carrier grating as self-referenced common-path interference, phase information can be directly extracted through spatial frequency domain filtering. This not only results in a simple system structure and strong resistance to environmental disturbances, but also eliminates the need for iterative phase recovery.

Description

Technical Field

[0001] This application relates to the fields of electron optics and electron microscopy measurement technology, and in particular to a method and system for measuring the phase of an electron wave function based on electron optical path interference. Background Technology

[0002] The free electron wavefunction contains both amplitude information characterized by electron charge density and phase information reflecting the electron propagation path and coherence characteristics. This phase distribution directly determines the interference, diffraction, and coherence behavior of free electrons during propagation, and is a key physical quantity describing the wave properties of electrons. Therefore, accurate measurement and quantitative characterization of the phase information of the free electron wavefunction are of great significance in research fields such as electron microscopy, electron holographic imaging, and electron wavefunction manipulation. However, existing technical solutions still have shortcomings in terms of measurement accuracy, system stability, applicability, and the ability to directly measure the intrinsic phase of the electron wavefunction.

[0003] Therefore, there is an urgent need for a method that has a relatively simple structure, low requirements for the stability of the electron optical system, and can directly and effectively measure the phase distribution of the electron wave function itself. Summary of the Invention

[0004] The purpose of this application is to provide a method and system for measuring the phase of an electronic wave function based on electron-optical path interferometry. It utilizes the zeroth and first-order diffracted electron beams generated by the same electron beam through carrier grating diffraction as self-reference common path interference, and directly extracts phase information through spatial frequency domain filtering. The system has a simple structure, strong resistance to environmental disturbances, and the phase recovery process does not require iteration.

[0005] This application provides a method for measuring the phase of an electronic wavefunction based on electronic optical path interferometry, including: The incident electron beam under test is controlled to transmit through a carrier grating to generate multiple diffracted electron beams, including at least a zero-order diffracted electron beam and a first-order diffracted electron beam. The propagation paths of the zero-order diffracted electron beam and the first-order diffracted electron beam are adjusted so that the zero-order diffracted electron beam and the first-order diffracted electron beam spatially overlap at a preset detection plane and form interference fringes. An interference intensity distribution image on the detection plane is acquired, and the image is subjected to spatial frequency domain transformation and filtering to extract the cross-term information generated by the interference of the zero-order diffracted electron beam and the first-order diffracted electron beam. Based on the cross-term information, an inverse transformation is performed to reconstruct the phase distribution of the electron wave function corresponding to the electron beam under test.

[0006] Optionally, controlling the propagation paths of the zero-order diffracted electron beam and the first-order diffracted electron beam includes: using a first magnetic lens located upstream of the carrier grating to adjust the convergence or divergence state of the incident electron wavefunction when it irradiates the surface of the carrier grating, so as to ensure the wavefront coherence of the diffraction; and using a second magnetic lens located downstream of the carrier grating to adjust the relative position of the focal planes of the zero-order diffracted electron beam and the first-order diffracted electron beam, so that the zero-order diffracted electron beam and the first-order diffracted electron beam intersect and overlap at the detection plane at a preset angle.

[0007] Optionally, the step of extracting the cross-term information generated by the interference of the zero-order diffracted electron beam and the first-order diffracted electron beam by performing spatial frequency domain transformation and filtering on the interference intensity distribution image includes: performing a Fourier transform on the interference intensity distribution image to obtain the spectral distribution of the interference intensity distribution image in the spatial frequency domain; and filtering and selecting the spectral components around the carrier frequency position introduced by the carrier grating in the spatial frequency domain to obtain the cross-term spectrum corresponding to the first-order diffracted electron beam.

[0008] Optionally, the step of performing inverse transform reconstruction based on the cross-term information to obtain the phase distribution of the electron wave function corresponding to the electron beam under test includes: performing an inverse Fourier transform on the filtered selected cross-term spectrum to reconstruct the complex amplitude distribution of the target wave function; taking the phase of the complex amplitude distribution to obtain the phase distribution information of the electron wave function corresponding to the electron beam under test; wherein, the target wave function is the electron wave function carried by the first-order diffracted electron beam after the electron beam under test passes through the carrier grating diffraction.

[0009] Optionally, the method for fabricating the carrier grating structure includes: forming a transmission-type periodic modulation structure with a preset period and duty cycle on a thin film substrate using a focused ion beam etching process or an electron beam lithography process; wherein the thin film substrate is a carbon film or a silicon nitride thin film, and the thin film substrate is transferred and fixed on a support carrier with through holes.

[0010] Optionally, the transfer and fixation process of the thin film substrate includes: after depositing the thin film substrate on the substrate surface, peeling the thin film substrate off the substrate surface by means of liquid surface tension; using a support grid with aperture to retrieve and attach the thin film substrate from the liquid surface, and after drying, forming a stable self-supporting structure for electron transmission.

[0011] This application also provides an electronic wavefunction phase measurement system based on electronic optical path interferometry, comprising: The vacuum electronic optical path module includes a multi-stage magnetic lens for adjusting the propagation state of the electron beam; a carrier grating structure disposed at the sample plane position between the multi-stage magnetic lenses; an electron detection module disposed downstream of the multi-stage magnetic lenses for recording the interference intensity distribution image; and a data processing unit for performing the spatial frequency domain transformation, filtering processing, and phase inverse transformation reconstruction calculation.

[0012] This application also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the steps of the electron wave function phase measurement method based on electron-optical path interferometry as described above.

[0013] The electron wavefunction phase measurement method and system based on electron-optical path interferometry provided in this application firstly controls the incident electron beam to be measured to pass through a carrier grating to generate multiple diffracted electron beams, including at least a zero-order diffracted electron beam and a first-order diffracted electron beam. Then, the propagation paths of the zero-order and first-order diffracted electron beams are adjusted so that they spatially overlap at a preset detection plane and form interference fringes. An interference intensity distribution image on the detection plane is acquired, and the image is subjected to spatial frequency domain transformation and filtering to extract the cross-term information generated by the interference of the zero-order and first-order diffracted electron beams. Finally, an inverse transformation is performed based on the cross-term information to reconstruct the phase distribution of the electron wavefunction corresponding to the electron beam under test. Thus, by using the zero-order and first-order diffracted electron beams generated by the same electron beam diffracted through a carrier grating as self-referenced common-path interference, phase information can be directly extracted through spatial frequency domain filtering. This not only results in a simple system structure and strong resistance to environmental disturbances, but also eliminates the need for iterative phase recovery. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is the electronic interference optical path diagram provided in this application; Figure 2 This is a flowchart illustrating the electronic wave function phase measurement method based on electronic optical path interferometry provided in this application; Figure 3 This is a schematic diagram of the phase recovery process of the electronic wave function provided in this application; Figure 4 This is a schematic diagram of the fabrication process of the carrier grating provided in this application. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0017] The terms "first," "second," etc., used in the specification and claims of this application are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such use of data can be interchanged where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first," "second," etc., are generally of the same class and the number of objects is not limited; for example, a first object can be one or more. Furthermore, "and / or" in the specification and claims indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship. All actions involving the acquisition of signal information or data in this application are performed in accordance with the relevant data protection laws and policies of the country where the application is located and with authorization from the relevant system owner.

[0018] In related technologies, free electron phase measurement mainly relies on interferometric measurement techniques and phase retrieval methods based on propagation inversion. Electron holographic imaging technology introduces a reference electron wave, which interferes with the electron wave being measured, thereby encoding phase information into the interference fringes, and then extracting the phase through numerical reconstruction. Propagation inversion methods typically rely on multiple intensity distributions under different propagation conditions, combined with iterative algorithms to indirectly recover the electron phase.

[0019] Iterative phase retrieval methods, exemplified by the Gerchberg-Saxton algorithm, work by repeatedly propagating the electron wavefunction between multiple planes with known intensity distributions and alternately applying amplitude constraints to each plane, thereby gradually approximating the phase distribution that satisfies the experimental intensity conditions. This method does not require a reference interference wave and has relatively low requirements for the experimental system structure, but it is highly dependent on the accuracy of the propagation distance and geometric parameters. In practical electron microscopy systems, the propagation distance is often difficult to calibrate with high precision, thus affecting the accuracy of phase retrieval. Furthermore, this method is a nonlinear iterative algorithm, which is sensitive to initial phase conditions and experimental noise, easily gets trapped in local extrema, and suffers from slow convergence, insufficient stability, and uncertainties in the reconstructed results.

[0020] Analytical phase inversion methods, exemplified by the intensity transport equation algorithm, establish the relationship between intensity gradient and phase gradient by measuring the change in electron intensity along the propagation direction, and reconstruct the electron phase by solving partial differential equations. This method does not require large-scale iterative calculations and has a relatively simple mathematical form. However, this method is highly restrictive to experimental conditions, relying on the paraxial approximation and weak phase modulation assumptions, thus limiting its applicability under complex wavefront conditions with rapid phase changes or large phase gradients. Furthermore, because this method primarily relies on small changes in intensity along the propagation direction to invert the phase, it is sensitive to experimental noise, and high spatial frequency phase information is easily smoothed or lost during propagation, thus limiting the spatial resolution and accuracy of phase reconstruction.

[0021] Multi-beam electron interferometry typically involves splitting the electron wavefunction into a target wave and a reference wave, causing them to interfere on the probe plane, and then using the phase difference information carried in the interference fringes to achieve phase recovery. In this method, the object of measurement is usually the phase modulation introduced by the sample onto the electron wavefunction, rather than the phase distribution of the electron wavefunction itself. Furthermore, introducing a reference wave often leads to a complex experimental system structure, greater difficulty in debugging, and limitations in measurement efficiency.

[0022] To address the aforementioned technical problems in related technologies, embodiments of this application provide a method for measuring the phase of an electronic wavefunction based on electronic-optical path interferometry, such as... Figure 1 As shown, it mainly consists of three parts: ① vacuum electron optical path, ② carrier grating structure, and ③ electron detection module. The wave function to be measured is the phase of the first-order electron diffraction function. The functions of each part are described below.

[0023] (1) Vacuum electronic optical path section The first part is the vacuum electronic optical path module, which is used to precisely control the propagation state of the electron beam and its focusing conditions before and after the carrier grating. This module mainly consists of multi-stage magnetic lenses. By independently adjusting the current of the magnetic lens coils, flexible control of the electron beam's convergence, divergence, and focal plane position can be achieved.

[0024] The first-stage magnetic lens is used to adjust the propagation state of the incident electron beam at the carrier grating plane. By changing the excitation current of the magnetic lens, the electron beam can be focused, collimated, or slightly divergent on the surface of the carrier grating, thereby ensuring that the electron wave function has suitable spatial coherence and wavefront quality at the grating, providing stable incident conditions for subsequent diffraction and interference processes.

[0025] After passing through a carrier grating, the electron beam is split into zero-order diffraction and multiple higher-order diffraction components. A second-order magnetic lens is used to control the propagation of electrons of different diffraction orders after passing through the carrier grating. Its function is to change the focal plane position of the zero-order and first-order diffraction electrons, causing them to spatially overlap and interfere at the electron detection plane. By appropriately adjusting the focal length of this magnetic lens, off-axis interference fringes with spatial carrier characteristics can be formed on the detection plane.

[0026] The zeroth-order diffracted electrons serve as the reference electron wave, while the first-order diffracted electrons carry information about the electron wave function modulated by a carrier grating. The interference intensity distribution between the two contains the phase information of the original electron wave function. By performing frequency domain analysis and filtering on the interference pattern, the phase characteristics of the original electron wave function can be recovered.

[0027] (2) Carrier grating structure The second part is the carrier grating structure, used to periodically modulate the incident electron wavefunction and generate multiple diffraction orders. The carrier grating is fabricated on a thin-film substrate using methods such as focused ion beam etching (FIB) and electron beam lithography (EBL), enabling precise control of the grating structure parameters. The thin film material is either carbon or silicon nitride, which allows for low-loss electron transmission while maintaining structural integrity. The period of the carrier grating is typically selected from 100 to 500 nm. This period range introduces an appropriate spatial carrier frequency in the electron propagation direction, effectively separating the zeroth-order diffraction from the first-order diffraction in the frequency domain. On the one hand, this design enables small-angle diffraction, ensuring that diffracted electrons can be effectively collected by subsequent magnetic lenses; on the other hand, the larger grating period significantly reduces the requirements for nanoscale fabrication precision.

[0028] The carrier grating is placed at the sample surface position in the electron optical path, that is, at the center region of the electron beam focusing plane adjusted by the first-stage magnetic lens, so as to ensure that the incident electron wave function has good coherence conditions at the grating, thereby improving the diffraction efficiency.

[0029] (3) Electronic detection module The third part is the electron detection module, which is used to record and analyze the interference results formed by the zeroth-order diffracted electrons and the first-order diffracted electrons. This module is usually composed of an electron detector or imaging system, which can acquire high signal-to-noise ratio electron intensity distribution images on the detection plane.

[0030] Under suitable magnetic lens adjustment conditions, zero-order diffracted electrons and first-order diffracted electrons undergo off-axis interference in the detection plane, forming an interference fringe structure with a defined spatial carrier. After the electron detection module acquires this interference pattern, subsequent data processing steps (including Fourier transform, frequency domain filtering, and inverse transform) can be used to separate and reconstruct the cross-term information related to the first-order diffraction.

[0031] Through the above detection and reconstruction process, the complex amplitude distribution corresponding to the original electronic wave function can be obtained, thereby realizing the measurement of the phase of the electronic wave function.

[0032] The method for measuring the phase of the electronic wave function based on electronic optical path interference provided in this application will be described in detail below with reference to the accompanying drawings, through specific embodiments and application scenarios.

[0033] like Figure 2 As shown in the embodiment of this application, an electronic wavefunction phase measurement method based on electronic optical path interferometry is provided. This method may include the following steps 201 to 204: Step 201: Control the incident electron beam to be tested to transmit through a carrier grating to generate multiple diffracted electron beams, including at least a zero-order diffracted electron beam and a first-order diffracted electron beam.

[0034] For example, the aforementioned incident electron beam is a free electron beam, which can be emitted by an electron gun and formed after acceleration and preliminary focusing. The aforementioned carrier grating is a transmission grating with a periodic structure, used to periodically modulate the incident electron wave function and generate multiple diffraction orders.

[0035] Specifically, a carrier grating is placed at the sample surface position in the electron optical path, that is, at the center region of the electron beam focusing plane adjusted by the first-order magnetic lens, thereby ensuring that the incident electron wavefunction has good coherence conditions at the grating, thus improving diffraction efficiency. When the incident electron beam passes through the carrier grating, it is split into a zero-order diffracted electron beam and multiple higher-order diffracted electron beams. Among them, the zero-order diffracted electron beam serves as a self-referenced reference wave, and the first-order diffracted electron beam serves as the object beam carrying phase information.

[0036] For example, the structural period of the carrier grating ranges from 100 nanometers to 500 nanometers. This period range allows for the introduction of an appropriate spatial carrier frequency in the electron propagation direction, enabling effective separation of zero-order and first-order diffraction in the frequency domain. On the one hand, this design enables small-angle diffraction, ensuring that diffracted electrons can be effectively collected by subsequent magnetic lenses; on the other hand, the larger grating period also significantly reduces the requirements for nanoscale fabrication precision.

[0037] It should be noted that the magnetic lens is mainly used to adjust the propagation mode of the electron beam before and after the carrier grating. On the one hand, by adjusting the magnetic lens located before the carrier grating, the incident electrons are made to form a suitable focusing or diverging state at the grating plane, thereby ensuring that the electron wavefunction has good spatial coherence at the grating. On the other hand, by adjusting the magnetic lens behind the carrier grating, the propagation path and focal plane position of the zeroth-order diffracted electrons and the first-order diffracted electrons can be changed, so that electrons of different diffraction orders spatially overlap at the detector plane and form stable interference fringes. Since the adjustment of the magnetic lens is achieved entirely by current control, without the need for mechanical moving components, it has the advantages of fast response, good repeatability, and high stability. By reasonably setting the parameters of the magnetic lens, the propagation characteristics of the electron beam can be finely controlled over a wide operating range.

[0038] Step 202: Adjust the propagation paths of the zero-order diffraction electron beam and the first-order diffraction electron beam so that the zero-order diffraction electron beam and the first-order diffraction electron beam spatially overlap at a preset detection plane and form interference fringes.

[0039] For example, the above-described control process is achieved through a multi-stage magnetic lens disposed in the electronic optical path. Specifically, step 202 above, the step of controlling the propagation paths of the zeroth-order diffracted electron beam and the first-order diffracted electron beam, may further include steps 202a1 and 202a2: Step 202a1: Using a first magnetic lens located upstream of the carrier grating, adjust the convergence or divergence state of the incident electron wave function when it irradiates the surface of the carrier grating to ensure the wavefront coherence of the diffraction.

[0040] Step 202a2: Using the second magnetic lens located downstream of the carrier grating, adjust the relative position of the focal planes of the zero-order diffraction electron beam and the first-order diffraction electron beam so that the zero-order diffraction electron beam and the first-order diffraction electron beam intersect and overlap at the detection plane at a preset angle.

[0041] For example, such as Figure 1 As shown, the electronic optical path includes a first magnetic lens located upstream of the carrier grating and a second magnetic lens located downstream of the carrier grating.

[0042] By using a first magnetic lens located upstream of the carrier grating, the convergence or divergence state of the incident electron wave function when it illuminates the surface of the carrier grating is adjusted to ensure the coherence of the wavefront formed by diffraction. By changing the excitation current of the first magnetic lens, the electron beam can be made to form a focused, collimated, or slightly divergent wavefront on the surface of the carrier grating, thereby providing stable incident conditions for subsequent diffraction and interference processes.

[0043] By using a second magnetic lens located downstream of the carrier grating, the zeroth-order diffracted electron beam and the first-order diffracted electron beam are made to intersect and overlap at a predetermined angle on the detection plane. By appropriately adjusting the focal length of the magnetic lens, off-axis interference fringes with spatial carrier characteristics can be formed on the detection plane.

[0044] Since the zeroth-order and first-order diffracted electron beams originate from the same incident electron wavefunction, their spatial and temporal coherence is naturally matched. Furthermore, they share the majority of their propagation paths, and the phase noise introduced by mechanical drift and magnetic lens jitter in the system is highly correlated with their effects, effectively canceling them out during interferometric measurements.

[0045] Step 203: Acquire the interference intensity distribution image on the detection plane, and extract the cross-term information generated by the interference of the zero-order diffracted electron beam and the first-order diffracted electron beam by performing spatial frequency domain transformation and filtering on the interference intensity distribution image.

[0046] For example, the aforementioned interference intensity distribution image is acquired by an electron detection module at the detection plane. The electron detection module typically consists of an electron detector or imaging system, capable of acquiring a high signal-to-noise ratio electron intensity distribution image on the detection plane.

[0047] Specifically, step 203 above, which involves spatial frequency domain transformation and filtering of the interference intensity distribution image, may include steps 203a and 203b: Step 203a: Perform a Fourier transform on the interference intensity distribution image to obtain the spectral distribution of the interference intensity distribution image in the spatial frequency domain.

[0048] Step 203b: In the spatial frequency domain, the spectral components around the carrier frequency position introduced by the carrier grating are filtered and selected to obtain the cross-term spectrum corresponding to the first-order diffracted electron beam.

[0049] For example, under suitable magnetic lens adjustment conditions, the zeroth-order diffracted electron beam and the first-order diffracted electron beam undergo off-axis interference in the detector plane, forming an interference fringe structure with a defined spatial carrier. After performing a Fourier transform on this interference fringe image, it will exhibit a central zeroth-order peak and symmetrically distributed first-order cross-term spectral components in the spatial frequency domain. The zeroth-order diffracted electron beam serves as a self-referenced reference wave, and the first-order diffracted electron beam serves as the object beam carrying phase information.

[0050] Specifically, step 203b above may also include the following steps 203b1 and 203b2: Step 203b1: Perform an inverse Fourier transform on the selected cross-term spectrum after filtering to reconstruct the complex amplitude distribution of the target wave function.

[0051] Step 203b2: Take the phase of the complex amplitude distribution to obtain the phase distribution information of the electron wave function corresponding to the electron beam under test.

[0052] The target wavefunction is the electron wavefunction carried by the first-order diffracted electron beam after the electron beam under test passes through the carrier grating.

[0053] For example, the introduction of a carrier grating shifts the target wavefunction in the frequency domain, and the cross term corresponding to the first-order diffraction is moved to the vicinity of the carrier frequency position determined by the carrier grating, thereby achieving effective separation from the intensity autocorrelation term located at the center of the spectrum in the frequency domain. Therefore, by filtering the spectral region around the carrier frequency position in the spatial frequency domain, the spectrum of the cross term corresponding to the first-order diffraction can be selected.

[0054] For example, such as Figure 3 The diagram shown illustrates the process for recovering the phase of the electron wavefunction, with the target wavefunction (first-order diffraction) as shown. ) and reference light (zero-order diffraction, The spatial distribution (interference intensity) of the interference light intensity obtained after interference is as follows: .according to Figure 1 The results of electron spatial optical path diffraction are shown. The signal received by the electron detector is the Fourier transform of the interference intensity: ; in, I : Represents the spatial distribution of interference intensity formed after the zeroth-order diffracted electron beam (reference light) and the first-order diffracted electron beam (target wave function) interfere with each other on the detection plane. A : Represents the amplitude distribution of the target wave function. The intensity distribution corresponding to the target wave function itself. : Represents the target wave function, that is, the complex amplitude distribution carried by the first-order diffracted electron beam after the electron beam under test is diffracted by the carrier grating. : Represents the complex conjugate of the target wave function. : Represents the spatial frequency vector introduced by the carrier grating. Its magnitude is related to the grating period, and its direction is perpendicular to the grating scribe line direction. : indicates that it is located in the spatial frequency domain place The function characterizes the translation effect of the carrier grating on the spectrum of the target wave function. : indicates the Fourier transform operation, which transforms the real space distribution to the spatial frequency domain (k-space).

[0055] For example, the introduction of a carrier grating shifts the Fourier spectrum of the target wavefunction in the frequency domain, and the cross terms corresponding to the first-order diffraction are shifted to... The location is nearby, thus achieving effective separation from the intensity autocorrelation term located at the center of the spectrum in the frequency domain. Therefore, by performing operations in k-space (i.e., the aforementioned spatial frequency domain)... Filtering the spectral region near the carrier frequency position (i.e., the spectral components introduced by the carrier grating) allows us to select the cross-term spectrum corresponding to the first-order diffraction, yielding the Fourier transform result of the target wavefunction. Subsequently, performing an inverse Fourier transform on the filtered spectrum reconstructs the complex amplitude distribution of the target wavefunction. Further taking the phase of the obtained complex amplitude yields the phase distribution information of the target wavefunction. This can be specifically expressed by the following formula: ; Step 204: Perform inverse transformation and reconstruction based on the cross-term information to obtain the phase distribution of the electron wave function corresponding to the electron beam under test.

[0056] For example, the phase distribution of the original electronic wave function can be directly recovered from the interference intensity distribution image through the above steps without iterative calculation or setting initial values.

[0057] It should be noted that the method provided in this application embodiment can be used to measure the intrinsic phase distribution formed by the free electron wave function during propagation or the additional phase distribution introduced by external field modulation, and is applicable to research fields such as electron microscopy, electron holographic imaging and electron wave function modulation.

[0058] Optionally, in this embodiment of the application, the method for fabricating the above-mentioned carrier grating structure may include the following step 205: Step 205: On the thin film substrate, a transmission-type periodic modulation structure with a preset period and duty cycle is formed by using focused ion beam etching or electron beam lithography.

[0059] The thin film substrate is a carbon film or a silicon nitride film, and the thin film substrate is transferred and fixed on a support carrier with through holes; the structural period of the carrier grating structure ranges from 100 nanometers to 500 nanometers.

[0060] Specifically, in step 205 above, the process of transferring and fixing the thin film substrate may further include the following steps 205a1 and 205a2: Step 205a1: After depositing the thin film substrate on the substrate surface, the thin film substrate is peeled off from the substrate surface by means of liquid surface tension.

[0061] Step 205a2: Using a support grid with aperture, the thin film substrate is retrieved from the liquid surface and attached to it. After drying, a stable self-supporting structure for electron transmission is formed. For example, such as Figure 4The diagram illustrates the fabrication process of a carrier grating. First, a carbon film is grown on a substrate using sputtering deposition or thermal evaporation to obtain a thin film structure with uniform thickness and a continuous surface. The selected substrate can be a silicon wafer or other flat substrate. By adjusting the deposition rate and deposition time, the thickness of the carbon film can be precisely controlled within 30 nm. After the carbon film deposition is complete, the chip is held using a special fixture, and the side with the carbon film is slowly brought into contact with a liquid surface. Utilizing the surface tension of the liquid, the carbon film is gradually peeled off from the substrate surface and released onto the liquid surface.

[0062] Subsequently, a thin copper mesh was used as a support to retrieve the carbon film floating on the liquid surface, allowing it to spread evenly and adhere to the mesh aperture area. The copper mesh not only provides the necessary mechanical support for the ultrathin carbon film but also facilitates its installation and positioning in electron microscopes or subsequent processing systems. After retrieval, the sample was subjected to natural drying or low-temperature drying to further enhance the adhesion stability between the carbon film and the copper mesh.

[0063] Finally, the carbon film sample transferred to the copper grid is placed in a focused ion beam system, and the carbon film surface is precisely etched to form a carrier grating structure within a predetermined area. By adjusting the accelerating voltage, beam current intensity, and scanning parameters of the ion beam, a grating structure with controllable period and duty cycle can be obtained, thereby achieving effective modulation of the electron wave function. This fabrication process is simple, highly repeatable, and suitable for the batch fabrication of carrier gratings with different period parameters.

[0064] Compared with the technical solutions in related technologies, the electron wave function phase measurement method based on electron-optical path interference provided in this application has the following advantages: (1) The overall framework structure is simple and does not require the introduction of additional multi-beam electronic control modules. The electronic phase measurement scheme proposed in this patent is based on a single-beam electronic optical path structure combining carrier grating and magnetic lens control. It extracts the phase information of the electronic wavefunction by interfering with the zero-order and first-order diffraction generated by the same electron beam during propagation. Compared with existing phase measurement methods that rely on multi-beam electron splitting, compound interferometer arms, or complex double-slit electronic structures, this scheme eliminates the need for an additional multi-beam electronic control module in the electronic optical path, and also eliminates the need for independent path adjustment and synchronization control of different electron beams.

[0065] Since the zeroth-order and first-order diffracted electrons originate from the same incident electron wavefunction, their spatial and temporal coherence is good, thus significantly reducing system complexity and assembly difficulty. The overall optical path structure is compact with few modules, making it easy to integrate into existing electron microscopes or free electron experimental platforms, and it has good engineering feasibility and promotional value.

[0066] (2) The measurement process does not depend on the mechanical accuracy of the system. This patent's phase measurement method uses zero-order diffracted electrons as the reference wave and first-order diffracted electrons as the object beam carrying phase information. Both propagate and interfere within the same electronic optical path. Since the reference wave and object beam share most of their propagation path, the phase noise introduced by mechanical drift and magnetic lens jitter is highly correlated with each other and can be effectively canceled out during interferometric measurement. Therefore, this method does not require extremely high precision in the magnetic lens current or sample stage, avoiding the stringent dependence on system stability found in traditional electron holography or multi-beam interferometry schemes. In practical applications, even with certain instabilities, stable and repeatable phase recovery results can still be obtained.

[0067] (3) The phase recovery process is highly robust and has a wide range of applications. This patent employs a phase retrieval strategy combining off-axis interferometry based on carrier modulation and frequency domain filtering. By separating the zero-order term and the first-order cross term in the spatial frequency domain, it effectively suppresses the influence of background intensity terms and conjugate interference terms on phase reconstruction. This phase retrieval process exhibits high tolerance to noise, contrast variations, and local intensity inhomogeneities, and can operate stably over a wide range of experimental conditions. Unlike previous GS and TS algorithms, the method proposed in this patent starts from the interferometric results, eliminating the need to set initial values ​​and iteration step sizes. Furthermore, this method is independent of the specific shape of the measured electron wavefunction and demonstrates good adaptability to different sample thicknesses, phase modulation intensities, and electron energy conditions. It can be widely applied in electron phase imaging, electron wavefront modulation, and related basic research and application scenarios. The calculation method is simple, and the retrieval results are accurate and reliable.

[0068] The electron wavefunction phase measurement method based on electron-optical path interferometry provided in this application first controls the incident electron beam to be measured to pass through a carrier grating to generate multiple diffracted electron beams, including at least a zero-order diffracted electron beam and a first-order diffracted electron beam. Then, the propagation paths of the zero-order and first-order diffracted electron beams are adjusted so that they spatially overlap at a preset detection plane and form interference fringes. An interference intensity distribution image on the detection plane is acquired, and the image is subjected to spatial frequency domain transformation and filtering to extract the cross-term information generated by the interference of the zero-order and first-order diffracted electron beams. Finally, an inverse transformation is performed based on the cross-term information to reconstruct the phase distribution of the electron wavefunction corresponding to the electron beam under test. Thus, by using the zero-order and first-order diffracted electron beams generated by the same electron beam diffracted through a carrier grating as self-referenced common-path interference, phase information can be directly extracted through spatial frequency domain filtering. This method not only has a simple system structure and strong resistance to environmental disturbances, but also eliminates the need for iterative phase recovery.

[0069] It should be noted that the electron wave function phase measurement method based on electron-optical path interferometry provided in this application embodiment can be executed by an electron wave function phase measurement system based on electron-optical path interferometry, or by a control module within that system for executing the electron wave function phase measurement method based on electron-optical path interferometry. This application embodiment uses the execution of the electron wave function phase measurement method based on electron-optical path interferometry by an electron wave function phase measurement system as an example to illustrate the electron wave function phase measurement system based on electron-optical path interferometry provided in this application embodiment.

[0070] It should be noted that, in the embodiments of this application, the electronic wave function phase measurement methods based on electron-optical path interferometry shown in the accompanying drawings are all illustrated by way of example with reference to one of the accompanying drawings in the embodiments of this application. In specific implementation, the electronic wave function phase measurement methods based on electron-optical path interferometry shown in the accompanying drawings of the above methods can also be implemented in conjunction with any other accompanying drawings that can be combined with the above embodiments, which will not be elaborated here.

[0071] The electron wave function phase measurement system based on electron-optical path interferometry provided in this application is described below. The electron wave function phase measurement method based on electron-optical path interferometry described below can be referred to in correspondence with the electron wave function phase measurement method described above.

[0072] This application embodiment also provides an electronic wave function phase measurement system based on electronic interferometry. This system is used to perform the aforementioned electronic wave function phase measurement method based on electronic optical path interferometry. The system includes: a vacuum electronic optical path module containing multi-stage magnetic lenses for adjusting the propagation state of the electron beam; a carrier grating structure disposed at the sample plane position between the multi-stage magnetic lenses; an electron detection module disposed downstream of the multi-stage magnetic lenses for recording interference intensity distribution images; and a data processing unit for performing the spatial frequency domain transformation, filtering processing, and phase inverse transformation reconstruction calculations.

[0073] The electron wavefunction phase measurement system based on electron-optical path interferometry provided in this application first controls the incident electron beam to be measured to pass through a carrier grating to generate multiple diffracted electron beams, including at least a zero-order diffracted electron beam and a first-order diffracted electron beam. Then, the propagation paths of the zero-order and first-order diffracted electron beams are adjusted so that they spatially overlap at a preset detection plane and form interference fringes. An interference intensity distribution image on the detection plane is acquired, and the image is subjected to spatial frequency domain transformation and filtering to extract the cross-term information generated by the interference of the zero-order and first-order diffracted electron beams. Finally, an inverse transformation is performed based on the cross-term information to reconstruct the phase distribution of the electron wavefunction corresponding to the measured electron beam. Thus, by using the zero-order and first-order diffracted electron beams generated by the same electron beam diffracted through a carrier grating as self-referenced common-path interference, phase information can be directly extracted through spatial frequency domain filtering. This not only results in a simple system structure and strong resistance to environmental disturbances, but also eliminates the need for iterative phase recovery.

[0074] On the other hand, this application also provides a computer program product, which includes a computer program stored on a computer-readable storage medium. The computer program includes program instructions, and when the program instructions are executed by the computer, the computer is able to execute the electron wave function phase measurement method based on electron-optical path interference provided by the above methods. The method includes: first, controlling the incident electron beam to be measured to transmit a carrier grating to generate multiple diffracted electron beams, including at least a zero-order diffracted electron beam and a first-order diffracted electron beam; then, adjusting the propagation paths of the zero-order diffracted electron beam and the first-order diffracted electron beam so that the zero-order diffracted electron beam and the first-order diffracted electron beam spatially overlap at a preset detection plane and form interference fringes; acquiring an interference intensity distribution image on the detection plane, and extracting the cross-term information generated by the interference of the zero-order diffracted electron beam and the first-order diffracted electron beam by performing spatial frequency domain transformation and filtering on the interference intensity distribution image; finally, performing an inverse transformation reconstruction based on the cross-term information to obtain the phase distribution of the electron wave function corresponding to the electron beam to be measured. Thus, by using the zeroth and first-order diffracted electron beams generated by the same electron beam through carrier grating diffraction as self-reference common-path interference, phase information can be directly extracted through spatial frequency domain filtering. This not only results in a simple system structure and strong resistance to environmental disturbances, but also eliminates the need for iteration in the phase recovery process.

[0075] In another aspect, this application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, performs the aforementioned methods for measuring the phase of the electron wave function based on electron-optical path interference. The method includes: first, controlling the incident electron beam to be measured to transmit through a carrier grating to generate multiple diffracted electron beams, including at least a zero-order diffracted electron beam and a first-order diffracted electron beam; then, adjusting the propagation paths of the zero-order diffracted electron beam and the first-order diffracted electron beam to spatially overlap at a preset detection plane and form interference fringes; acquiring an interference intensity distribution image on the detection plane, and extracting cross-term information generated by the interference of the zero-order diffracted electron beam and the first-order diffracted electron beam by performing spatial frequency domain transformation and filtering on the interference intensity distribution image; finally, performing an inverse transformation and reconstruction based on the cross-term information to obtain the phase distribution of the electron wave function corresponding to the electron beam to be measured. Thus, by using the zeroth and first-order diffracted electron beams generated by the same electron beam through carrier grating diffraction as self-reference common-path interference, phase information can be directly extracted through spatial frequency domain filtering. This not only results in a simple system structure and strong resistance to environmental disturbances, but also eliminates the need for iteration in the phase recovery process.

[0076] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0077] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0078] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for measuring the phase of an electron wavefunction based on electron-optical path interferometry, characterized in that, include: The incident electron beam to be tested is controlled to transmit through a carrier grating to generate multiple diffracted electron beams, including at least a zero-order diffracted electron beam and a first-order diffracted electron beam. The propagation paths of the zero-order diffraction electron beam and the first-order diffraction electron beam are adjusted so that the zero-order diffraction electron beam and the first-order diffraction electron beam spatially overlap at a preset detection plane and form interference fringes. An image of the interference intensity distribution on the detection plane is acquired, and the cross-term information generated by the interference of the zero-order diffracted electron beam and the first-order diffracted electron beam is extracted by performing spatial frequency domain transformation and filtering on the image of the interference intensity distribution. Based on the cross-term information, an inverse transform reconstruction is performed to obtain the phase distribution of the electron wave function corresponding to the electron beam under test.

2. The method according to claim 1, characterized in that, Controlling the propagation paths of the zeroth-order diffracted electron beam and the first-order diffracted electron beam includes: By using a first magnetic lens located upstream of the carrier grating, the convergence or divergence state of the incident electron wave function when it irradiates the surface of the carrier grating is adjusted to ensure the wavefront coherence of the diffraction. Using a second magnetic lens located downstream of the carrier grating, the relative positions of the focal planes of the zero-order diffraction electron beam and the first-order diffraction electron beam are adjusted so that the zero-order diffraction electron beam and the first-order diffraction electron beam intersect and overlap at the detection plane at a preset angle.

3. The method according to claim 1, characterized in that, The step of extracting the cross-term information generated by the interference of the zero-order diffracted electron beam and the first-order diffracted electron beam by performing spatial frequency domain transformation and filtering on the interference intensity distribution image includes: Perform a Fourier transform on the interference intensity distribution image to obtain the spectral distribution of the interference intensity distribution image in the spatial frequency domain; In the spatial frequency domain, the spectral components around the carrier frequency position introduced by the carrier grating are filtered and selected to obtain the cross-term spectrum corresponding to the first-order diffracted electron beam.

4. The method according to claim 3, characterized in that, The inverse transform reconstruction based on the cross-term information to obtain the phase distribution of the electron wavefunction corresponding to the electron beam under test includes: The inverse Fourier transform of the selected cross-term spectrum after filtering is performed to reconstruct the complex amplitude distribution of the target wave function; By taking the phase of the complex amplitude distribution, the phase distribution information of the electron wave function corresponding to the electron beam under test is obtained; The target wavefunction is the electron wavefunction carried by the first-order diffracted electron beam after the electron beam under test passes through the carrier grating.

5. The method according to claim 1, characterized in that, The method for fabricating the carrier grating structure includes: On a thin film substrate, a transmission-type periodic modulation structure with a preset period and duty cycle is formed by using focused ion beam etching or electron beam lithography. The thin film substrate is a carbon film or a silicon nitride film, and the thin film substrate is transferred and fixed on a support carrier with through holes.

6. The method according to claim 5, characterized in that, The transfer and fixation process of the thin film substrate includes: After the thin film substrate is deposited on the substrate surface, the thin film substrate is peeled off from the substrate surface by means of the surface tension of the liquid. The thin film substrate is retrieved from the liquid surface and attached using a support grid with aperture, and then dried to form a stable self-supporting structure for electron transmission.

7. The method according to claim 1, characterized in that, The structural period of the carrier grating structure ranges from 100 nanometers to 500 nanometers.

8. The method according to claim 1, characterized in that, The zeroth-order diffracted electron beam serves as a self-referenced reference wave, and the first-order diffracted electron beam serves as the object beam carrying phase information.

9. The method according to claim 1, characterized in that, The method is used to measure the intrinsic phase distribution of a free electron wavefunction during propagation or the additional phase distribution introduced by external field modulation.

10. A phase measurement system for electronic wavefunctions based on electronic interferometry, characterized in that, The system employing the electron wavefunction phase measurement method based on electron-optical path interferometry as described in any one of claims 1 to 9 comprises: The vacuum electronic optical path module includes a multi-stage magnetic lens for adjusting the propagation state of the electron beam; A carrier grating structure is positioned on the sample plane between the multi-stage magnetic lenses; An electronic detection module, located downstream of the multi-stage magnetic lens, is used to record the interference intensity distribution image; The data processing unit is used to perform the spatial frequency domain transformation, filtering, and phase inverse transformation reconstruction calculations.

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