Analysis and calculation method for sub-beam virtual source in multi-beam electron optical system and related device

Abstract

The invention discloses a method for analyzing and calculating a sub-beam virtual source in a multi-beam electron optical system and a related device. The method comprises the following steps: acquiring a transfer mapping relation from an emitting surface to a beam splitting diaphragm plane; obtaining a tangent equation T1 of the off-axis beamlet center electron trajectory R1 on the diaphragm plane and a tangent equation T2 of the paraxial electron trajectory R2 on the diaphragm plane based on the transfer mapping relation; virtual source plane positions of the off-axis beamlets on the meridian plane and the sagittal plane are calculated based on the tangent equation T1 and the tangent equation T2; calculating the Gaussian virtual source position of the off-axis beamlet according to the virtual source plane positions of the off-axis beamlet on the meridian plane and the sagittal plane of the off-axis beamlet; calculating the virtual source size on the meridian plane and sagittal plane corresponding to the off-axis beamlet caused by aberration according to the off-axis beamlet Gaussian virtual source position; and calculating virtual source sizes of the off-axis beamlets on the meridian plane and sagittal plane corresponding to the off-axis beamlets caused by the transverse thermal initial velocity based on the tangent equation T1 and the tangent equation T2.

Description

Technical Field

[0001] This invention relates to the field of electron optical systems, and more specifically to a method and apparatus for analyzing and calculating virtual sources of sub-beams in a multi-beam electron optical system. Background Technology

[0002] Traditional electron beam equipment is limited by the aberrations of electron lenses, using apertures with small diameters, such as tens of micrometers, to restrict the electron beam's angle of attack, ensuring that electrons close to the axis and with a small slope participate in imaging, thus achieving high resolution. However, smaller apertures reduce the amount of light transmitted through the electron beam, resulting in longer imaging or exposure times. In the characterization and observation of biological samples, as well as in micro-nano fabrication and inspection technologies such as electron beam integrated circuit defect detection and electron beam lithography, the amount of light transmitted is the most critical factor limiting electron beam imaging, exposure time, and work efficiency. Multi-beam electron optical systems offer an important solution to the contradiction between high resolution and low light transmitted light. US Patent Application US 20200273667 A1 discloses a multi-beam electron optical system. In this system, a Schottky field emission electron gun emits an initial electron beam, which is then split into sub-beams using an array of beam-splitting apertures. These sub-beams then pass through a subsequent electron optical system and are finally focused onto the sample, forming multiple beam spots, thereby achieving multi-beam scanning imaging. While these sub-bundles increase throughput, they also reduce overall resolution to some extent. For these sub-bundles, regardless of whether they are on-axis or not, their virtual sources are a key parameter for evaluating resolution.

[0003] A virtual source is an imaginary electron source from which all electrons can be considered to originate. Since most electrons are emitted perpendicular to the cathode emitting surface, the location of the virtual source is primarily determined by the perpendicularly emitted electrons. The point where the backward extension of the trajectory of a paraxial electron emitted perpendicular to the emitting surface intersects the principal optical axis is the location of the virtual source. If the transverse thermal velocity at electron emission is disregarded, the virtual source would be a point with no size. In reality, due to the mechanism of thermal field emission, a transverse thermal velocity exists during electron emission, and the virtual source is no longer a point. This transverse thermal velocity causes the backward extension of the electron trajectory to not intersect the axis in the virtual source plane; this off-axis distance is used to assess the size of the virtual source and is also related to the focal length of the electron gun.

[0004] In multi-beam electron optics systems, off-axis sub-beams mostly originate from off-axis emission positions. The electrons in these off-axis sub-beams are no longer paraxial, meaning aberrations must be considered. Furthermore, the optical axes of each sub-beam are no longer the system's principal optical axis, leading to differences in the position and size of the virtual sources in the off-axis sub-beams compared to the central sub-beam. Additionally, space is no longer symmetrical relative to the optical axes of the off-axis sub-beams, implying that each off-axis sub-beam has a virtual source in both the meridional and sagittal planes. Currently, when analyzing the electron optics properties of sub-beams, it is often approximated that the virtual sources of each sub-beam are identical to those of the central sub-beam, without considering the differences between these two planes, which is clearly inconsistent with reality. Traditional trajectory tracing methods, when dealing with large-scale array sub-beams, experience a rapid increase in computational complexity due to the number of sub-beams directly proportional to the computational load. Moreover, these methods can only provide specific solutions for specific systems; as system parameters change, the trajectory tracing process will continue, and no analytical formulas can be provided for studying the underlying mechanisms. Therefore, the analysis and calculation of virtual sources in sub-beams, especially virtual sources in off-axis sub-beams, is one of the urgent and difficult problems to be solved in the research and development of multi-beam electron optical systems. Summary of the Invention

[0005] To address the problem of difficulty in analyzing and calculating virtual sources of sub-beams in multi-beam electron optical systems, this invention provides a method and related apparatus for analyzing and calculating virtual sources of sub-beams in multi-beam electron optical systems. This invention provides an effective computational analysis tool for the research, design, and development of multi-beam electron optical systems.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: The method for analyzing and calculating the virtual source of the sub-beam in a multi-beam electron optics system includes the following steps: Step 1: Obtain the spatial electric field distribution of the electron gun section in front of the beam splitter in the multi-beam electron optical system. In this spatial electric field distribution region, set the parameter during electron emission as the tracking parameter, track the reference trajectory on the tracking axis, solve the equation of the reference trajectory, and obtain the transfer mapping relationship from the emission surface to the beam splitter plane. Step 2: Based on the transfer mapping relationship, calculate the initial emission position of the off-axis sub-beam center electron trajectory R1 on the initial emission surface according to the position coordinates of the center of the beam splitter aperture. Calculate the slope of the off-axis sub-beam center electron trajectory R1 on the aperture plane based on this initial emission position. Based on the position coordinates and slope of the off-axis sub-beam center electron trajectory R1 on the aperture plane, obtain the tangent equation T1 of the off-axis sub-beam center electron trajectory R1 on the aperture plane. Step 3: Based on an electron near the initial emission position of the central electron, use the transfer mapping relationship to find the position and slope of the paraxial electron trajectory R2 in the aperture plane, and then obtain the tangent equation T2 of the paraxial electron trajectory R2 in the aperture plane. Step 4: Calculate the virtual source plane positions of the off-axis sub-beams in the meridional and sagittal planes based on tangent equations T1 and T2; Step 5: Calculate the Gaussian virtual source position of the off-axis sub-bundle based on its virtual source plane position in the meridional and sagittal planes; Step 6: Calculate the virtual source size on the meridional and sagittal planes corresponding to the off-axis sub-bundle based on the position of the Gaussian virtual source in the off-axis sub-bundle; Step 7: Calculate the virtual source size of the off-axis sub-bundle caused by the transverse thermal initial velocity on its corresponding meridional and sagittal planes based on tangent equations T1 and T2.

[0007] Furthermore, the launching surface in step one is represented as... The beam splitter plane is represented as The transfer mapping relationship from the emitting surface to the beam splitter plane is expressed as follows:

[0008] in, For electrons in the z-plane of the beam splitter a The position coordinates in the x and y directions ( ) and the slopes in the x and y directions ( ), Let z be the position coordinates of the electron in the x and y directions of the emission surface z0. ) and the slopes in the x and y directions ( ), n For the largest order, i , j , l , m Represents the position coordinates of the electron in the x and y directions of the emitting surface z0. and the slopes in the x and y directions powers of, A ijlm , B ijlm , C ijlm , D ijlm To transfer mapping coefficients, used to quantize the emission surface z0 to the beam-splitting stop plane z. a The transfer relationship of electronic trajectory parameters between them.

[0009] Furthermore, in step two, based on the transitive mapping relationship, According to the center of the beam splitter aperture Location The initial emission position of the off-axion beam center electron trajectory R1 on the initial emission surface is calculated; based on this initial emission position... The slope of the off-axion beam center electron trajectory R1 in the aperture plane was calculated. Based on the position coordinates and slope of the off-axis sub-beam center electron trajectory R1 in the aperture plane, the tangent equation T1 of the off-axis sub-beam center electron trajectory R1 in the aperture plane is obtained.

[0010] Furthermore, in step three, based on the initial emission position of the central electron... An electron nearby, the position of which is ,in These are all minute offsets. The position of the paraxial electron trajectory R2 at the aperture plane is determined using the transitive mapping relationship. and slope This leads to the equation T2, the tangent line of the paraxial electron trajectory R2 in the aperture plane.

[0011] Furthermore, in step four, the virtual source plane positions of the off-axis sub-bundle on the meridional and sagittal planes are represented as follows:

[0012] in, z vm Let be the virtual source plane position of the off-axis sub-bundle on its meridional plane. z vs Let be the virtual source plane position of the off-axis sub-bundle on its sagittal plane. z a The position of the beam splitter plane. r 0 represents the off-axis distance from the initial emission position of the electron trajectory at the center of the off-axis sub-beam, i.e. , A 1000 and A 3000 These are the initial coordinates. The relevant first-order and third-order transmission coefficients, C 1000 and C 3000 These are respectively the initial slope The relevant first-order and third-order transmission coefficients.

[0013] Furthermore, in step five, based on the positions of the virtual source planes of the meridional plane and the sagittal plane, there exists a Gaussian virtual source plane between these two virtual source planes. On this Gaussian virtual source plane, the focusing ability is the same on both the meridional and sagittal planes. Based on this condition, the Gaussian virtual source plane is obtained. Substituting this into the tangent equation T1, the position of the Gaussian virtual source of the off-axion bundle in three-dimensional space is obtained:

[0014] in, Let be the position coordinates of the off-axion bundle Gaussian virtual source in three-dimensional space. z a The position of the beam splitter plane. r 0 represents the off-axis distance from the initial emission position of the electron trajectory at the center of the off-axis sub-beam, i.e. , A 1000 and A 3000 These are the initial coordinates. The relevant first-order and third-order transmission coefficients, C 1000 and C 3000 These are respectively the initial slope The relevant first-order and third-order transmission coefficients, The azimuth angle of the center position of the beam stop corresponding to the off-axis sub-beam is, i.e. .

[0015] Furthermore, in step six, the obtained coordinates z of the off-axis sub-bundle Gaussian virtual source plane are... v Substituting the tangent equation T1 for the off-axis electron trajectory R1 and the tangent equation T2 for the paraxial electron trajectory R2, we obtain the tangent equations T1 and T2 in the Gaussian imaginary source plane z. v The virtual source dimensions on the meridional plane, caused by aberrations, are located at positions on the meridional and sagittal planes respectively. The tangent equations T2 and T1 on the meridional plane are given by the Gaussian virtual source plane z. v The distance at which the virtual source on the sagittal plane is given by the tangent equations T2 and T1 on the sagittal plane at the distance from the Gaussian virtual source plane z. v The distance at point A is calculated using the following formula:

[0016] in, These represent the virtual source sizes in the meridional and sagittal planes, respectively, caused by aberrations. R Let be the radius of the beam splitter.

[0017] Furthermore, in step seven, based on tangent equations T1 and T2, the focal lengths of the off-axis sub-bundle on the meridional and sagittal planes are:

[0018] in, The focal length on the meridian plane. Let be the focal length on the sagittal plane; Furthermore, the virtual sources caused by the transverse thermal initial velocity have the following virtual source sizes on the meridional and sagittal planes:

[0019] in, These represent the virtual source sizes on the meridional and sagittal planes, respectively, caused by the initial transverse thermal velocity. e The amount of electron charge. k Boltzmann's constant, T The cathode emission temperature, U ext This is the extraction electrode voltage.

[0020] A system for analyzing and calculating virtual sources of sub-beams in a multi-beam electron optics system, including: The first module is used to obtain the spatial electric field distribution of the electron gun part in front of the beam splitter in a multi-beam electron optical system. In this spatial electric field distribution region, the parameter of electron emission is set as the tracking parameter, the reference trajectory on the tracking axis is used, the equation of the reference trajectory is solved, and the transfer mapping relationship from the emission surface to the beam splitter plane is obtained. The second module: Based on the transfer mapping relationship, the initial emission position of the off-axis sub-beam center electron trajectory R1 on the initial emission surface is calculated according to the position coordinates of the center of the beam splitter aperture. Based on the initial emission position, the slope of the off-axis sub-beam center electron trajectory R1 on the aperture plane is calculated. Based on the position coordinates and slope of the off-axis sub-beam center electron trajectory R1 on the aperture plane, the tangent equation T1 of the off-axis sub-beam center electron trajectory R1 on the aperture plane is obtained. The third module: Based on an electron near the initial emission position of the central electron, the position and slope of the paraxial electron trajectory R2 at the aperture plane are obtained by using the transfer mapping relationship, and then the tangent equation T2 of the paraxial electron trajectory R2 at the aperture plane is obtained. Module 4: Calculate the virtual source plane positions of the off-axis sub-beams in the meridional and sagittal planes based on tangent equations T1 and T2; Module 5: Calculate the Gaussian virtual source position of the off-axis sub-bundle based on its virtual source plane position in the meridional and sagittal planes; Module 6: Calculate the virtual source size on the meridional and sagittal planes corresponding to the off-axis sub-bundle based on the position of the Gaussian virtual source in the off-axis sub-bundle; Module 7: Calculate the virtual source size of the off-axis sub-bundle caused by the transverse thermal initial velocity on its corresponding meridional and sagittal planes based on tangent equations T1 and T2.

[0021] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of an analysis and calculation method for sub-beam virtual sources in a multi-beam electron optical system.

[0022] Compared with the prior art, the present invention has the following beneficial technical effects: 1. This invention successfully solves the technical challenge of analyzing and calculating virtual sources in sub-beams, especially off-axis sub-beams, in multi-beam systems, and establishes a complete theoretical calculation system. The formulas for calculating the position and size of virtual sources in sub-beams derived from this theoretical framework provide a clear mathematical expression for subsequent theoretical research on the characteristics of virtual sources.

[0023] 2. The proposed method for calculating sub-beam virtual sources in multi-beam electro-optical systems achieves a systematic analysis of the positions and dimensions of all sub-beam virtual sources through a single reference trajectory tracking strategy. Compared to traditional trajectory tracking methods, this method avoids repetitive trajectory calculations for beam-splitter apertures at different off-axis distances, fundamentally reducing the computational load. This significant improvement in computational efficiency provides an efficient analytical tool for in-depth exploration of the distribution patterns of sub-beam virtual sources in multi-beam systems and for subsequent design optimization of multi-beam sources. Attached Figure Description

[0024] The accompanying drawings are provided to further understand the invention and constitute a part of this invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0025] Figure 1 This is a schematic diagram of a typical Schottky emission source in a multi-beam electron optics system; Figure 2 This is a schematic diagram illustrating the principle of calculating the virtual source position of the off-axis sub-bundle in one embodiment of the present invention; Figure 3 This is a schematic diagram of the array-type beam splitter distribution in one embodiment of the present invention; Figure 4 In one embodiment of this invention, the trajectory tracking method calculates the relationship between the initial emission position of the electron and the position and slope of the electron in the aperture plane; Figure 5 In one embodiment of the present invention, the electron beam trajectory of an off-axis beam splitter is projected onto the meridional plane based on the tangent of the position of the beam splitter plane. Figure 6 In one embodiment of the present invention, the electron beam trajectory of an off-axis beam splitter is projected onto the sagittal plane based on the tangent of the position of the beam splitter plane. Figure 7 This is an example of the relationship between the position of the off-axis sub-beam virtual source plane and the off-axis distance of its corresponding beam-splitting aperture in one embodiment of the present invention; Figure 8 This is the distribution of Gaussian virtual source positions in each sub-bundle in an example of the present invention; Figure 9 In one embodiment of the present invention, the Gaussian virtual source positions of each sub-bundle are... xy Distribution on a plane; Figure 10This is an example of the relationship between the size of the off-axis sub-beam virtual source and the off-axis distance of its corresponding beam-splitting aperture in one embodiment of the present invention. Detailed Implementation

[0026] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0027] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0028] Example 1 This invention provides a method for analyzing and calculating virtual sources of sub-beams in a multi-beam electron optical system, comprising the following steps: The first step involves numerically calculating the spatial electric field distribution of the electron gun section in front of the beam splitter in a multi-beam electron optical system using the finite element method. For this region, parameters related to electron emission, such as position and slope, are set as tracking parameters, and a reference trajectory on the tracking axis is established. The trajectory equation is then solved using differential-algebraic methods to obtain the electric field distribution from the emission surface. To the beam splitter plane Transitive mapping relationship: (1) in, For electrons in the z-plane of the beam splitter a The position coordinates in the x and y directions ( ) and the slopes in the x and y directions ( ), Let z be the position coordinates of the electron in the x and y directions of the emission surface z0. ) and the slopes in the x and y directions ( ), n For the largest order, i ,j , l , m Represents the position coordinates of the electron in the x and y directions of the emitting surface z0. and the slopes in the x and y directions powers of, A ijlm , B ijlm , C ijlm , D ijlm To transfer mapping coefficients, used to quantize the emission surface z0 to the beam-splitting stop plane z. a The transitive relationship of electron trajectory parameters (position, slope) between different electrons. For example, if the order n=1, then: (2) The second step, based on the transfer mapping relationship from the first step, involves determining the location of the beam splitter aperture center. The initial emission position of the off-axion beam center electron trajectory R1 at the initial emission surface was calculated. Based on the initial launch position The slope of the off-axion beam center electron trajectory R1 in the aperture plane was calculated. Based on the position coordinates (i.e., the position coordinates of the center electron trajectory R1 of the off-axle sub-beam) in the aperture plane and the slope, the tangent equation T1 of the center electron trajectory R1 of the off-axle sub-beam in the aperture plane is obtained.

[0029] The third step is based on the initial emission position of the electrons at the center of the off-axion beam. An electron nearby, the position of which is ,in These are all minute offsets. The position of the paraxial electron trajectory R2 at the aperture plane is determined using the transfer mapping relationship. and slope This leads to the equation T2, the tangent line of the paraxial electron trajectory R2 in the aperture plane.

[0030] The fourth step is to calculate the virtual source plane positions of the off-axis sub-bundle in the meridional and sagittal planes. The virtual source position in the meridional plane is the intersection of the tangent equations T1 and T2 obtained in steps two and three, respectively, on the meridional plane. Similarly, the virtual source position in the sagittal plane is the intersection of the tangent equations T1 and T2 obtained in steps two and three, respectively, on the sagittal plane. Here, only the initial offset is considered. The linear term. The positions of the virtual source planes of the off-axis sub-bundle in the meridional and sagittal planes are obtained as follows: (3) in, z vmLet be the virtual source plane position of the off-axis sub-bundle on its meridional plane. z vs Let be the virtual source plane position of the off-axis sub-bundle on its sagittal plane. z a The position of the beam splitter plane. r 0 represents the off-axis distance from the initial emission position of the electron trajectory at the center of the off-axis sub-beam, i.e. , A 1000 and A 3000 These are the initial coordinates. The relevant first-order and third-order transmission coefficients, C 1000 and C 3000 These are respectively the initial slope The relevant first-order and third-order transmission coefficients.

[0031] The fifth step is to determine the position of the Gaussian virtual source plane. Based on the positions of the virtual source planes on the meridional and sagittal planes, there exists a Gaussian virtual source plane between these two virtual source planes. On this Gaussian virtual source plane, the focusing power is the same on both the meridional and sagittal planes. Based on this condition, the Gaussian virtual source plane can be obtained. Substituting this into the tangent equation T1, the position of the Gaussian virtual source of the off-axion bundle in three-dimensional space is obtained: (4) in, Let be the position coordinates of the off-axion bundle Gaussian virtual source in three-dimensional space. z a The position of the beam splitter plane. r 0 represents the off-axis distance from the initial emission position of the electron trajectory at the center of the off-axis sub-beam, i.e. , A 1000 and A 3000 These are the initial coordinates. The relevant first-order and third-order transmission coefficients, C 1000 and C 3000 These are respectively the initial slope The relevant first-order and third-order transmission coefficients, The azimuth angle of the center position of the beam stop corresponding to the off-axis sub-beam is, i.e. .

[0032] Step 6: Calculate the virtual source size caused by aberrations. Then, calculate the obtained off-axis sub-bundle Gaussian virtual source plane coordinates z... vSubstituting the tangent equation T1 for the off-axis electron trajectory R1 and the tangent equation T2 for the paraxial electron trajectory R2, we obtain the tangent equations T1 and T2 in the Gaussian imaginary source plane z. v The virtual sources on the meridional and sagittal planes, respectively, are located thereon. The virtual source dimensions on the meridional plane, caused by aberrations, are given by the tangent equations T2 and T1 on the meridional plane at the Gaussian virtual source plane z. v The distance at which the virtual source on the sagittal plane is given by the tangent equations T2 and T1 on the sagittal plane at the distance from the Gaussian virtual source plane z. v The distance at point A is calculated using the following formula: (5) in, These represent the virtual source sizes in the meridional and sagittal planes, respectively, caused by aberrations. R Let be the radius of the beam splitter.

[0033] Step 7: Calculate the virtual source size caused by the transverse thermal initial velocity. Based on tangent equations T1 and T2, the focal lengths of the off-axis sub-beams in the meridional and sagittal planes are: (6) in, The focal length on the meridian plane. Let be the focal length on the sagittal plane.

[0034] Furthermore, the virtual sources caused by the transverse thermal initial velocity have the following virtual source sizes on the meridional and sagittal planes: (7) in, Let be the virtual sources caused by the transverse thermal initial velocity in the meridional and sagittal planes, respectively, and let e be the electron charge. k Boltzmann's constant, T The cathode emission temperature, U ext This is the extraction electrode voltage.

[0035] To more accurately analyze the electron optical properties of sub-beams in multi-beam electron optical systems, this invention provides a method and, along with formulas for calculating the size and position of the virtual sources of the sub-beams in such systems. Furthermore, this invention considers the influence of system aberrations on the off-axis virtual sources of the sub-beams and takes into account the properties of the meridional and sagittal planes, thus better reflecting physical reality.

[0036] Example 2 The method for calculating the virtual source position and size of a sub-beam in a multi-beam electron optical system of the present invention is designed for a typical Schottky emission source in a real-world multi-beam system, consisting of a spearhead 100, a suppressor 101, and an extractor 102, such as... Figure 1As shown, its array-type beam-splitting aperture plane 103 is located in the field-free space behind the extraction electrode 102, and the entire system is rotationally symmetric with respect to the principal optical axis 104. The initial electron beam is emitted from the tip of the gun, reaches the aperture plane, and is then split into individual sub-beams.

[0037] In this embodiment, Figure 1 In the electron gun system shown, the voltage of the suppression electrode 101 is -300V, the voltage of the extraction electrode 102 is 5000V, and the radius of the planar region of the cathode emitting surface 106 is... h 250nm, radius of curvature r The aperture is 500 nm, while the remaining dimensions are typical of a Schottky emission gun structure. The cathode emitting surface has 106 coordinates. The array-type beam splitter plane 103 is =7.6mm. For example... Figure 2 As shown, the beam splitter 400 is an array of 21×21 orthogonally arranged apertures, with each aperture having a radius of 20μm and a spacing of 55μm.

[0038] In this embodiment, the center coordinates 302 of a beam splitter aperture are (110μm, 0, 7.6mm). The virtual source is then calculated using a trajectory tracing method. First, the center electron trajectory 200 of the off-axis sub-beam defined by the aperture is confirmed using a test firing method. That is, different initial emission positions are selected on the initial emission plane 106 so that the position of its trajectory on the aperture plane is the aforementioned center coordinates. Figure 4 Given an initial position, 200 electron trajectories are calculated at intervals of 1 nm, showing their positions and slopes on the aperture plane. The initial emission position 301 of the central electron trajectory R1(200) is (44.8 nm, 0, 0), and its slope on the aperture plane is 0.0144. A large number of points 303 are selected near this initial position for trajectory tracing, yielding the positions 304 and slopes of these trajectories on the aperture plane. This leads to the tangent equation T2(203) for these electron trajectories R2(202). Extending this equation in the opposite direction, the plane intersecting the tangent T1(201) is the virtual source plane 204, and the intersection point is the virtual source position 300. In this example, the initial positions are selected as follows: centered on the emission position 301, with radii of 1, 2, and 3 nm, each circle has 30 points evenly distributed according to the angle, resulting in a total of 90 trajectories. For more accurate calculations, the more trajectories selected, the better. Due to the asymmetry, the virtual source positions of the meridional plane and the sagittal plane are different, such as Figure 5 As shown, by projecting the trajectory tangent onto the sagittal plane and the meridional plane respectively, the positions of the virtual source planes on the meridional plane and the sagittal plane can be obtained as follows: =-31.55μm, =-31.41μm. Furthermore, for an N×N array of orthogonally arranged beam dividers, to calculate the virtual sources of all off-axis sub-beams, due to symmetry, at least 90 / 8*N needs to be calculated. 2 A trajectory.

[0039] In this embodiment, the electric field distribution of the Schottky emission source is solved using the finite element method. Then, a reference trajectory on an axis is traced using the differential algebra method. This reference trajectory coincides with the main optical axis 104 of the system. Using the initial position and slope at electron emission as tracing parameters, the transfer mapping relationship from the emission plane 106 to the array-type beam-splitter plane 103 can be obtained. Due to rotational symmetry, based on this transfer mapping relationship, for the beam-splitter located at (110 μm, 0, 7.6 mm), the emission position of the center electron trajectory 200 of its sub-beam and its slope on the beam-splitter plane can be obtained by the following equation: (8) In this embodiment, A 1000 =2440, A 3000 =7.841E15m -2 , C 1000 =3.198E5m -1 , C 3000 =1.026E18m -3 The initial position is obtained as x 0 = 44.79 nm. Furthermore, according to formula (2), the virtual source planes of this off-axis sub-beam in the meridional and sagittal planes are respectively... =-31.56μm, =-31.42μm. The above result is consistent with the trajectory tracking result, but the computational complexity is significantly reduced, requiring only the calculation of one reference trajectory. Furthermore, for different beam-splitting stops, only equation (8) needs to be solved repeatedly, without the need to calculate other trajectories.

[0040] In this embodiment, based on the transfer mapping relationship obtained in step one, equation (8) is solved to obtain the initial position. Based on formulas (3) and (4), the relationship between the virtual source plane position of the off-axis sub-beam (including the meridional virtual source position, the sagittal virtual source position, and the Gaussian virtual source position) and its corresponding off-axis distance from the beam-splitting aperture can be obtained. Figure 7 Based on formula (4), the relationship between the position of the off-axis sub-beam Gaussian virtual source and the position of the beam splitter aperture can be calculated. Figure 8 , Figure 9 Based on formulas (5)-(7), the relationship between the size of the off-axis sub-beam virtual source (including the effects of aberrations and transverse thermal initial velocity) and the off-axis distance of the beam splitter aperture can be obtained. Figure 10 In particular, Figure 3 The positions of the Gaussian virtual sources of the off-axis sub-beams corresponding to the upper right aperture 401 and the lower right aperture 402 are respectively Figure 9 The bottom left corner position is 501 and the top left corner position is 502.

[0041] Example 3 The first module is used to obtain the spatial electric field distribution of the electron gun part in front of the beam splitter in a multi-beam electron optical system. In this spatial electric field distribution region, the parameter of electron emission is set as the tracking parameter, the reference trajectory on the tracking axis is used, the equation of the reference trajectory is solved, and the transfer mapping relationship from the emission surface to the beam splitter plane is obtained. The second module: Based on the transfer mapping relationship, the initial emission position of the off-axis sub-beam center electron trajectory R1 on the initial emission surface is calculated according to the position coordinates of the center of the beam splitter aperture. Based on the initial emission position, the slope of the off-axis sub-beam center electron trajectory R1 on the aperture plane is calculated. Based on the position coordinates and slope of the off-axis sub-beam center electron trajectory R1 on the aperture plane, the tangent equation T1 of the off-axis sub-beam center electron trajectory R1 on the aperture plane is obtained. The third module: Based on an electron near the initial emission position of the central electron, the position and slope of the paraxial electron trajectory R2 at the aperture plane are obtained by using the transfer mapping relationship, and then the tangent equation T2 of the paraxial electron trajectory R2 at the aperture plane is obtained. Module 4: Calculate the virtual source plane positions of the off-axis sub-beams in the meridional and sagittal planes based on tangent equations T1 and T2; Module 5: Calculate the Gaussian virtual source position of the off-axis sub-bundle based on its virtual source plane position in the meridional and sagittal planes; Module 6: Calculate the virtual source size on the meridional and sagittal planes corresponding to the off-axis sub-bundle based on the position of the Gaussian virtual source in the off-axis sub-bundle; Module 7: Calculate the virtual source size of the off-axis sub-bundle caused by the transverse thermal initial velocity on its corresponding meridional and sagittal planes based on tangent equations T1 and T2.

[0042] Example 4 This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the analysis and calculation method for sub-beam virtual sources in the multi-beam electron optical system.

[0043] Example 5 This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the analysis and calculation method for the sub-beam virtual source in the multi-beam electron optical system.

[0044] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit its scope of protection. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading the present invention, they can still make various changes, modifications or equivalent substitutions to the specific implementation of the invention, but these changes, modifications or equivalent substitutions are all within the scope of protection of the pending claims of the invention.

Claims

1. A method for analyzing and calculating virtual sources of sub-beams in a multi-beam electron optical system, characterized in that, Includes the following steps: Step 1: Obtain the spatial electric field distribution of the electron gun section in front of the beam splitter in the multi-beam electron optical system. In this spatial electric field distribution region, set the parameter during electron emission as the tracking parameter, track the reference trajectory on the tracking axis, solve the equation of the reference trajectory, and obtain the transfer mapping relationship from the emission surface to the beam splitter plane. Step 2: Based on the transfer mapping relationship, calculate the initial emission position of the off-axis sub-beam center electron trajectory R1 on the initial emission surface according to the position coordinates of the center of the beam splitter aperture. Calculate the slope of the off-axis sub-beam center electron trajectory R1 on the aperture plane based on this initial emission position. Based on the position coordinates and slope of the off-axis sub-beam center electron trajectory R1 on the aperture plane, obtain the tangent equation T1 of the off-axis sub-beam center electron trajectory R1 on the aperture plane. Step 3: Based on an electron near the initial emission position of the central electron, use the transfer mapping relationship to find the position and slope of the paraxial electron trajectory R2 in the aperture plane, and then obtain the tangent equation T2 of the paraxial electron trajectory R2 in the aperture plane. Step 4: Calculate the virtual source plane positions of the off-axis sub-beams in the meridional and sagittal planes based on tangent equations T1 and T2; Step 5: Calculate the Gaussian virtual source position of the off-axis sub-bundle based on its virtual source plane position in the meridional and sagittal planes; Step 6: Calculate the virtual source size on the meridional and sagittal planes corresponding to the off-axis sub-bundle based on the position of the Gaussian virtual source in the off-axis sub-bundle; Step 7: Calculate the virtual source size of the off-axis sub-bundle caused by the transverse thermal initial velocity on its corresponding meridional and sagittal planes based on tangent equations T1 and T2.

2. The method for analyzing and calculating the virtual source of the sub-beam in a multi-beam electron optical system according to claim 1, characterized in that, The launching surface in step one is represented as The beam splitter plane is represented as The transfer mapping relationship from the emitting surface to the beam splitter plane is expressed as follows: in, For electrons in the z-plane of the beam splitter a The position coordinates in the x and y directions ( ) and the slopes in the x and y directions ( ), Let z be the position coordinates of the electron in the x and y directions of the emission surface z0. ) and the slopes in the x and y directions ( ), n For the largest order, i , j , l , m Represents the position coordinates of the electron in the x and y directions of the emitting surface z0. and the slopes in the x and y directions powers of, A ijlm , B ijlm , C ijlm , D ijlm To transfer mapping coefficients, used to quantize the emission surface z0 to the beam-splitting stop plane z. a The transmission relationship of electronic trajectory parameters between them.

3. The method for analyzing and calculating the virtual source of the sub-beam in a multi-beam electron optical system according to claim 2, characterized in that, In step two, based on the transitive mapping relationship, According to the center of the beam splitter aperture Location The initial emission position of the off-axion beam center electron trajectory R1 on the initial emission surface is calculated; based on this initial emission position... The slope of the off-axion beam center electron trajectory R1 in the aperture plane was calculated. Based on the position coordinates and slope of the off-axis sub-beam center electron trajectory R1 in the aperture plane, the tangent equation T1 of the off-axis sub-beam center electron trajectory R1 in the aperture plane is obtained.

4. The method for analyzing and calculating the virtual source of the sub-beam in a multi-beam electron optical system according to claim 2, characterized in that, In step three, based on the initial emission position of the central electron... An electron in the vicinity, the position of which is ,in These are all minute offsets. The position of the paraxial electron trajectory R2 at the aperture plane is determined using the transitive mapping relationship. and slope This leads to the equation T2, the tangent line of the paraxial electron trajectory R2 in the aperture plane.

5. The method for analyzing and calculating the virtual source of the sub-beam in a multi-beam electron optical system according to claim 2, characterized in that, In step four, the virtual source plane positions of the off-axis sub-bundle on the meridional and sagittal planes are represented as follows: in, z vm Let be the virtual source plane position of the off-axis sub-bundle on its meridional plane. z vs Let be the virtual source plane position of the off-axis sub-bundle on its sagittal plane. z a The position of the beam splitter plane. r 0 represents the off-axis distance from the initial emission position of the electron trajectory at the center of the off-axis sub-beam, i.e. , A 1000 and A 3000 These are the initial coordinates. The relevant first-order and third-order transmission coefficients, C 1000 and C 3000 These are respectively the initial slope The relevant first-order and third-order transmission coefficients.

6. The method for analyzing and calculating the virtual source of the sub-beam in a multi-beam electron optical system according to claim 2, characterized in that, In step five, based on the positions of the virtual source planes on the meridional and sagittal planes, a Gaussian virtual source plane exists between these two virtual source planes. On this Gaussian virtual source plane, the focusing power is the same on both the meridional and sagittal planes. Based on this condition, the Gaussian virtual source plane is obtained. Substituting this into the tangent equation T1, the position of the Gaussian virtual source of the off-axion bundle in three-dimensional space is obtained: in, Let be the position coordinates of the off-axion bundle Gaussian virtual source in three-dimensional space. z a The position of the beam splitter plane. r 0 represents the off-axis distance from the initial emission position of the electron trajectory at the center of the off-axis sub-beam, i.e. , A 1000 and A 3000 These are the initial coordinates. The relevant first-order and third-order transmission coefficients, C 1000 and C 3000 These are respectively the initial slope The relevant first-order and third-order transmission coefficients, The azimuth angle of the center position of the beam stop corresponding to the off-axis sub-beam is, i.e. .

7. The method for analyzing and calculating the virtual source of the sub-beam in a multi-beam electron optical system according to claim 6, characterized in that, In step six, the obtained coordinates z of the off-axis sub-bundle Gaussian virtual source plane are... v Substituting the tangent equation T1 for the off-axis electron trajectory R1 and the tangent equation T2 for the paraxial electron trajectory R2, we obtain the tangent equations T1 and T2 in the Gaussian imaginary source plane z. v The virtual source dimensions on the meridional plane, caused by aberrations, are located at the positions on the meridional plane and the sagittal plane, respectively. The tangent equations T2 and T1 on the meridional plane are then applied to the Gaussian virtual source plane z. v The distance at which the virtual source on the sagittal plane is given by the tangent equations T2 and T1 on the sagittal plane at the distance in the Gaussian virtual source plane z. v The distance at point A is calculated using the following formula: in, These represent the virtual source sizes in the meridional and sagittal planes, respectively, caused by aberrations. R Let be the radius of the beam splitter.

8. The method for analyzing and calculating the virtual source of the sub-beam in a multi-beam electron optical system according to claim 6, characterized in that, In step seven, based on tangent equations T1 and T2, the focal lengths of the off-axis sub-beams on the meridional and sagittal planes are: in, The focal length on the meridian plane. Let be the focal length on the sagittal plane; Furthermore, the virtual sources caused by the transverse thermal initial velocity have the following virtual source sizes on the meridional and sagittal planes: in, These represent the virtual source sizes on the meridional and sagittal planes, respectively, caused by the initial transverse thermal velocity. e The amount of electron charge. k Boltzmann's constant, T The cathode emission temperature, U ext This is the extraction electrode voltage.

9. A system for analyzing and calculating virtual sources of sub-beams in a multi-beam electron optical system, characterized in that, include: The first module is used to obtain the spatial electric field distribution of the electron gun part in front of the beam splitter in a multi-beam electron optical system. In this spatial electric field distribution region, the parameter of electron emission is set as the tracking parameter, the reference trajectory on the tracking axis is used, the equation of the reference trajectory is solved, and the transfer mapping relationship from the emission surface to the beam splitter plane is obtained. The second module: Based on the transfer mapping relationship, the initial emission position of the off-axis sub-beam center electron trajectory R1 on the initial emission surface is calculated according to the position coordinates of the center of the beam splitter aperture. Based on the initial emission position, the slope of the off-axis sub-beam center electron trajectory R1 on the aperture plane is calculated. Based on the position coordinates and slope of the off-axis sub-beam center electron trajectory R1 on the aperture plane, the tangent equation T1 of the off-axis sub-beam center electron trajectory R1 on the aperture plane is obtained. The third module: Based on an electron near the initial emission position of the central electron, the position and slope of the paraxial electron trajectory R2 at the aperture plane are obtained by using the transfer mapping relationship, and then the tangent equation T2 of the paraxial electron trajectory R2 at the aperture plane is obtained. Module 4: Calculate the virtual source plane positions of the off-axis sub-beams in the meridional and sagittal planes based on tangent equations T1 and T2; Module 5: Calculate the Gaussian virtual source position of the off-axis sub-bundle based on its virtual source plane position in the meridional and sagittal planes; Module 6: Calculate the virtual source size on the meridional and sagittal planes corresponding to the off-axis sub-bundle based on the position of the Gaussian virtual source in the off-axis sub-bundle; Module 7: Calculate the virtual source size of the off-axis sub-bundle caused by the transverse thermal initial velocity on its corresponding meridional and sagittal planes based on tangent equations T1 and T2.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the analysis and calculation method for the sub-beam virtual source in the multi-beam electron optical system as described in any one of claims 1 to 8.

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