A signal electron current density spatial distribution calculation method and system

Abstract

The application discloses a signal electron current density spatial distribution calculation method and system, signal electron emission sources are divided into a plurality of emission source sub-regions, all signal electrons emitted in each emission source sub-region are divided into a plurality of signal electron beam sub-beams along a polar angle and an azimuth angle, for each signal electron beam sub-beam, only one center reference track needs to be tracked to obtain linear and high-order transmission characteristics of all electrons emitted in the signal electron beam sub-beam at a space arbitrary plane relative to an initial emission plane, and according to electron number conservation and in combination with the transmission characteristics, current density distribution of the signal electrons at the space arbitrary plane can be obtained, the method is not affected by the complexity of a spatial electromagnetic field distribution, and can fully consider initial conditions when the signal electrons are emitted, compared with a traditional track tracking method, the calculation amount of the track is significantly reduced, and the method is favorable for regularity research on a signal electron transmission process.

Description

Technical Field

[0001] This invention relates to the field of electronic optical systems, and more specifically to a method and system for calculating the spatial distribution of signal electron current density. Background Technology

[0002] Defects in semiconductor processing severely restrict the performance of final devices. Failure analysis of electrical and physical defects in chips also plays a guiding role in optimizing semiconductor processing technology. Electron beam semiconductor defect detection equipment based on scanning electron microscopy (SEM) can effectively analyze chip electrical defects such as short circuits and open circuits by changing the energy of the incident electron beam to form a potential contrast image. At the same time, it can also analyze physical defects through morphological images. With the continuous development of semiconductor processing technology, higher requirements are placed on electron beam semiconductor defect detection equipment. On the one hand, a wider range of adjustable incident energy of the electron beam is required to better form a potential contrast image. On the other hand, the electron beam needs to have a larger scanning field of view to improve detection efficiency. To meet the above requirements, US patent document US7759653B2 discloses a SEM system equipped with a swing objective and a repulsive field immersion lens (SORIL). As a core electron optical device in electron beam detection equipment, this system achieves high-resolution large field-of-view scanning by employing two working modes: high scanning speed under a large deflection field of view and high resolution under a small deflection field of view. Furthermore, the incident energy of the electron beam is adjusted by regulating the repulsive field electrode and the sample stage voltage. In this SEM system, signal electrons (e.g., secondary electrons, backscattered electrons) are accelerated to very high energies by the strong electric field at the lens. Therefore, a detector installed inside the lens is required to collect the signal electrons. In addition, the signal electron emission region is also within the influence of a complex electromagnetic field, including an immersion magnetic field, a repulsive field, and a deflection field. For a large deflection field of view, off-axis emission also occurs. Under the combined effect of these conditions, the principal optical axis of the electron beam is neither a straight axis nor free-axis and also exhibits torsion. Traditional analysis methods based on the straight optical axis are difficult to handle this complex situation. The current method for calculating the transmission process of signal electrons mainly uses the trajectory tracking method, which requires calculating a large number of electron trajectories. It is also difficult to calculate the current density distribution of signal electrons at arbitrary planes in the detector plane and transmission space. This is not conducive to the study of the transmission characteristics of signal electrons and the design of signal electron collection systems. Therefore, the study of calculation methods for signal electron transmission characteristics, especially current density distribution, is one of the urgent and difficult problems to be solved in SEM system research. Summary of the Invention

[0003] To address the difficulty in calculating the signal electron beam transmission characteristics in SEM systems, this invention provides a method and system for calculating the spatial distribution of signal electron current density. This invention can effectively calculate the current density distribution and current envelope of signal electrons at any plane in the transmission space, taking into full account the influence of initial emission conditions and various complex electromagnetic fields.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A method for calculating the spatial distribution of signal electron current density includes the following steps:

[0006] Step 1: Assume there is a region called the emission source (102) on the initial emission plane (101). The signal electrons emitted by the emission source with different slopes and energies within a certain solid angle range are called the signal electron beam (103). Divide the emission source into several small regions, each of which is called the emission source sub-region (104). The signal electrons with different slopes emitted in each emission source sub-region are then directed along the polar angle θ and azimuth angle, respectively. The direction is divided into several small regions. The signal electrons contained in each small region are called signal electron beam sub-beams (105). For each signal electron beam sub-beam, a central reference trajectory T1 is tracked. This reference trajectory is called the signal electron beam sub-beam reference trajectory (106). This reference trajectory is emitted from the centroid of its corresponding emission source sub-region. The initial emission parameters of the signal electron beam sub-beam reference trajectory are used as tracking parameters. The transmission characteristics of the signal electron beam sub-beam in any plane in space relative to the initial emission plane are obtained by solving the trajectory equation.

[0007] Step 2: Since the electrons with different slopes and energies emitted near the reference trajectory of the signal electron beam sub-beam on the initial emission plane have their landing point coordinates on the final collection plane (201) concentrated in a sub-beam landing point region (202) near the reference trajectory landing point coordinates, the transformation relationship between the current density function of the signal electron beam sub-beam on the final collection plane and the initial current density distribution on the initial emission plane is established based on the conservation of electron quantity.

[0008] Step 3: Substitute the transmission characteristics calculated in Step 1 into the transformation relationship established in Step 2 and rearrange to obtain the functional relationship between the current density function of the signal electron beam sub-beam in any spatial plane and the coordinates and energy on the initial emission plane. Then, integrate over the region where the current is not zero on the initial emission plane and the initial energy distribution range of the signal electron beam to obtain the current density distribution J formed by the signal electron beam sub-beam at any spatial plane. s The expression;

[0009] Step 4: Calculate the current density distribution J of all signal electron beam sub-beams at any plane in space based on Steps 1 to 3.s The current density distribution of all signal electron beam sub-beams at any plane in space J s By superimposing the data in the laboratory coordinate system, the spatial distribution of the current density J of the signal electron beam is obtained. t ;

[0010] Step 5: Assume the spatial distribution of the signal electron beam's current density at a certain plane in space is J. tp The region containing n% of the total current is defined as the n% current envelope (203), and the area of ​​the n% current envelope is used as a characteristic parameter for evaluating the spatial distribution of current density, and 0≤n≤100;

[0011] Step 6: Select a signal electron beam sub-beam reference trajectory T0 from Step 1, called the signal electron beam center reference trajectory (107). The characteristic of this reference trajectory is that the emission source sub-region (104) to which it belongs contains the centroid of the entire emission source (102), and the reference trajectory is perpendicular to the initial emission plane. The coordinates (x, y) of this reference trajectory in any plane in space are used as the centroid of the n% current envelope in Step 5. Based on the reference trajectory T0 and the n% current envelope, the current density distribution and lateral distribution of the signal electron beam in any plane in space are obtained.

[0012] Furthermore, the initial launch parameters include coordinates (x0, y0), slope (x0', y0'), and energy E0.

[0013] Furthermore, the transmission characteristics in step one include linear characteristics and higher-order characteristics, as shown below:

[0014]

[0015] In the formula, r f Let r be the coordinates of the landing point of the signal electron on the final collection plane and its slope. i Let be the coordinates and slope of the signal electron in the initial plane, and δ be the energy dispersion of the signal electron. For the transfer mapping relationship from the initial launch plane to the final collection plane, then and For transmission characteristics.

[0016] Furthermore, step two specifically involves:

[0017] For each signal electron beam sub-beam, the initial current density distribution when it is emitted from its initial emission plane is represented by f(z0,x0,x0',y0,y0',E0), where z0 represents the z-axis coordinate of the initial emission plane, (x0,y0) are the initial coordinates, (x0',y0') are the initial slope, and E0 is the initial energy.

[0018] Based on the conservation of electron quantity during signal electron transmission, the landing points of signal electrons with different slopes and energies emitted near the reference trajectory T1 of a signal electron beam sub-beam on the initial emission plane are concentrated in a small region dx near the landing point of the signal electron beam sub-beam reference trajectory T1 on the final collection plane. i dy i Within this framework, based on the conservation of electron quantity, a transformation relationship is established between the current density function of the final collection plane and the initial current density distribution of the initial emission plane for the signal electron beam sub-beams:

[0019] f(z0,x0,x′0,y0,y′0,E0)dx′0dy′0dE0=j(z i ,x i ,y i ,x0,y0,E0)dx i dy i dE0

[0020] In the formula, j(z) i ,x i ,y i (x0, y0, E0) represents the signal electron beam sub-beam emitted at point (z0, x0, y0) on the initial emission plane and collected at the final collection plane (z0, x0, y0). i ,x i ,y i The current density function at ().

[0021] Furthermore, step three specifically includes:

[0022] Partial derivatives in transmission characteristics Substituting into the current density function j(z) i ,x i ,y i In the equation (x0, y0, E0), the current density distribution J of the signal electron beam emitted from the source sub-region on the final collection plane is obtained by integrating the region where the current density is not zero on the initial emission plane and the initial energy of the signal electrons. s (z i ,x i ,y i The expression for ) is:

[0023]

[0024] Furthermore, step four specifically involves: calculating the current density distribution J of all signal electron beam sub-beams using steps one through three. s (z i ,x i ,y i After that, the current density distribution J of all signal electron beam sub-beams is calculated.s (z i ,x i ,y i The spatial distribution of the current density of the signal electron beam is obtained by superimposing the data in the laboratory coordinate system. t (z i ,x i ,y i ).

[0025] A system for calculating the spatial distribution of signal electron current density, comprising:

[0026] Transmission characteristic calculation module: used to calculate the transmission characteristics of the signal electron beam sub-beams in any spatial plane relative to the initial emission plane; specifically: assuming there is a region called the emission source (102) on the initial emission plane (101), the signal electrons emitted by the emission source with different slopes and different energies within a certain solid angle range are called the signal electron beam (103), the emission source is divided into several small regions, each called the emission source sub-region (104), and the signal electrons with different slopes emitted in each emission source sub-region are respectively along the polar angle θ and azimuth angle. The direction is divided into several small regions. The signal electrons contained in each small region are called signal electron beam sub-beams (105). For each signal electron beam sub-beam, a central reference trajectory T1 is tracked. This reference trajectory is called the signal electron beam sub-beam reference trajectory (106). This reference trajectory is emitted from the centroid of its corresponding emission source sub-region. The initial emission parameters of the signal electron beam sub-beam reference trajectory are used as tracking parameters. The transmission characteristics of the signal electron beam sub-beam in any plane in space relative to the initial emission plane are obtained by solving the trajectory equation.

[0027] The conversion relationship establishment module is used to establish the conversion relationship between the current density function of the signal electron beam sub-beam in the final collection plane and the initial current density distribution of the initial emission plane. Specifically, since the landing coordinates of electrons with different slopes and energies emitted near the reference trajectory of the signal electron beam sub-beam on the initial emission plane are concentrated in a sub-beam landing region (202) near the reference trajectory landing coordinates, the conversion relationship between the current density function of the signal electron beam sub-beam in the final collection plane and the initial current density distribution of the initial emission plane is established based on the conservation of electron quantity.

[0028] Signal electron beam sub-beam current density spatial distribution calculation module: used to calculate the current density distribution formed by the signal electron beam sub-beam at any plane in space. sThe expression is as follows: Specifically, the transmission characteristics calculated by the transmission characteristic calculation module are substituted into the transformation relationship established by the transformation relationship establishment module, and the relationship between the current density function of the signal electron beam sub-beam in any plane of space and the coordinates and energy on the initial emission plane is obtained. Then, the region where the current is not zero on the initial emission plane and the initial energy distribution range of the signal electrons are integrated to obtain the current density distribution J formed by the signal electron beam sub-beam at any plane of space. s The expression;

[0029] Signal electron beam current density spatial distribution calculation module: used to calculate the spatial distribution of the signal electron beam current density. t Specifically: Based on the transmission characteristic calculation module, the transformation relationship establishment module, and the signal electron beam sub-beam current density spatial distribution calculation module, the current density distribution of all signal electron beam sub-beams at any plane in space is calculated. s The current density distribution of all signal electron beam sub-beams at any plane in space J s By superimposing the data in the laboratory coordinate system, the spatial distribution of the current density J of the signal electron beam is obtained. t ;

[0030] Feature parameter setting module: used to set the feature parameters for evaluating the spatial distribution of current density; specifically: assuming the spatial distribution of the signal electron beam's current density at a certain plane in space is J tp The region containing n% of the total current is defined as the n% current envelope (203), and the area of ​​the n% current envelope is used as a characteristic parameter for evaluating the spatial distribution of current density, and 0≤n≤100;

[0031] Distribution Calculation Module: Used to calculate the current density distribution and lateral distribution of the signal electron beam in any plane in space; Specifically: Select a signal electron beam sub-beam reference trajectory T0, called the signal electron beam center reference trajectory (107). The characteristic of this reference trajectory is that its emission source sub-region (104) contains the centroid of the entire emission source (102), and the reference trajectory is perpendicular to the initial emission plane. The coordinates (x, y) of this reference trajectory in any plane in space are used as the centroid of the n% current envelope in step five. The current density distribution and lateral distribution of the signal electron beam in any plane in space are obtained based on the reference trajectory T0 and the n% current envelope.

[0032] Furthermore, the transmission characteristics include linear characteristics and higher-order characteristics, as expressed below:

[0033]

[0034] In the formula, r f Let r be the coordinates of the landing point of the signal electron on the final collection plane and its slope.i Let be the coordinates and slope of the signal electron in the initial plane, and δ be the energy dispersion of the signal electron. For the transfer mapping relationship from the initial launch plane to the final collection plane, then and For transmission characteristics.

[0035] Furthermore, the transformation relationship between the current density function of the final collection plane and the initial current density distribution of the initial emission plane for establishing the signal electron beam sub-beam is specifically as follows:

[0036] For each signal electron beam sub-beam, the initial current density distribution when it is emitted from its initial emission plane is represented by f(z0,x0,x0',y0,y0',E0), where z0 represents the z-axis coordinate of the initial emission plane, (x0,y0) are the initial coordinates, (x0',y0') are the initial slope, and E0 is the initial energy.

[0037] Based on the conservation of electron quantity during signal electron transmission, the landing points of signal electrons with different slopes and energies emitted near the reference trajectory T1 of a signal electron beam sub-beam on the initial emission plane are concentrated in a small region dx near the landing point of the signal electron beam sub-beam reference trajectory T1 on the final collection plane. i dy i Within this framework, based on the conservation of electron quantity, a transformation relationship is established between the current density function of the final collection plane and the initial current density distribution of the initial emission plane for the signal electron beam sub-beams:

[0038] f(z0,x0,x′0,y0,y′0,E0)dx′0dy′0dE0=j(z i ,x i ,y i ,x0,y0,E0)dx i dy i dE0

[0039] In the formula, j(z) i ,x i ,y i (x0, y0, E0) represents the signal electron beam sub-beam emitted at point (z0, x0, y0) on the initial emission plane and collected at the final collection plane (z0, x0, y0). i ,x i ,y i The current density function at ().

[0040] Furthermore, the current density distribution J formed by the calculated signal electron beam sub-beam at any plane in space is... s The expression; specifically:

[0041] Partial derivatives in transmission characteristics Substituting into the current density function j(z) i ,x i ,y i In the equation (x0, y0, E0), the current density distribution J of the signal electron beam emitted from the source sub-region on the final collection plane is obtained by integrating the region where the current density is not zero on the initial emission plane and the initial energy of the signal electrons. s (z i ,x i ,y i The expression for ) is:

[0042]

[0043] Compared with the prior art, the present invention has the following beneficial technical effects:

[0044] The proposed method for calculating the spatial distribution of signal electron current density divides the signal electron emission source into several emission source sub-regions. Within each emission source sub-region, all emitted signal electrons are further divided into several signal electron beam sub-beams along polar and azimuth angles. For each signal electron beam sub-beam, only one central reference trajectory needs to be traced to obtain the linear and higher-order transmission characteristics of all electrons within the sub-beam relative to the initial emission plane at any spatial plane. Based on the conservation of electron quantity and combined with the transmission characteristics, the current density distribution of signal electrons at any spatial plane can be obtained. Furthermore, the method is unaffected by the complexity of the spatial electromagnetic field distribution and can fully consider the initial conditions during signal electron emission. Compared with traditional trajectory tracing methods, this significantly reduces the computational load and is beneficial for studying the laws governing signal electron transmission.

[0045] This invention considers the angular and energy distributions during signal electron emission in the calculation of current density spatial distribution, which is more in line with reality. By defining a current envelope to characterize the current density distribution of the signal electron beam, the evolution of the signal electron beam in space can be obtained by combining the current envelope with the reference trajectory of the signal electron beam center. This provides an effective calculation and analysis method for the calculation and analysis of signal electron transmission characteristics, the optimization design of signal electron collection systems, and the optimization design of other electron optical systems involving the analysis of charged particle beam transmission characteristics. Attached Figure Description

[0046] 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.

[0047] Figure 1 This is a schematic diagram showing how a signal electron emission source is divided into several small regions.

[0048] Figure 2 This is a diagram illustrating the sub-beam division and transmission principle of the signal electron beam.

[0049] Figure 3 This is a schematic diagram of the signal electron collection device in the SEM system calculated in the embodiments of the present invention.

[0050] Figure 4 This is a schematic diagram of the energy distribution of signal electrons in an embodiment of the present invention.

[0051] Figure 5 This is the reference trajectory of the center of the signal electron beam in this embodiment of the invention.

[0052] Figure 6 This is the calculated result of the current density distribution of signal electrons in the final collection plane in the embodiment of the present invention.

[0053] Figure 7 This refers to the change in the 80% current envelope space of the signal electrons calculated in the embodiments of the present invention. Detailed Implementation

[0054] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0055] 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.

[0056] 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.

[0057] Example 1

[0058] The first step involves emitting signal electrons from a source 102 on the initial emission plane 101. All signal electrons emitted from points within this source with different inclinations form a hemispherical region in space. All signal electrons within this hemispherical region are called the signal electron beam 103. The signal electron beam has a certain angular distribution along the polar angle direction and a certain energy distribution. Since the transmission characteristics of signal electrons at different positions and emission polar angles vary significantly, the source 102 is first divided into several small regions, each called a source sub-region 104. Within each source sub-region, signal electrons with different inclinations are further divided along the polar angle (θ) and azimuth angle (φ) directions into several smaller regions. The signal electrons contained within each smaller region are called signal electron beam sub-beams 105. For each signal electron beam sub-beam, a central reference trajectory T1 emitted from the centroid of the emission source sub-region 104 is traced. This trajectory is called the signal electron beam sub-beam reference trajectory 106. The initial coordinates (x0, y0), slope (x0', y0'), and energy E0 of its emission are used as tracking quantities. By solving the trajectory equation, the transmission characteristics of the signal electron beam sub-beam in any plane in space relative to the initial emission plane can be obtained, as shown in Equation (1).

[0059]

[0060] In the formula, r f Let r be the coordinates and slope of the point where the signal electron lands on the final collection plane 201. i Let be the coordinates and slope of the signal electron in the initial plane, and δ be the energy dispersion of the signal electron. This represents the transfer mapping from the initial launch plane to the final collection plane. and The transmission characteristics include linear transmission characteristics and higher-order transmission characteristics. When the signal electron beam sub-beams are divided sufficiently, the transmission characteristics of all signal electrons emitted within the signal electron beam sub-beams with different slopes and energies can be characterized by the transmission characteristics calculated from the signal electron beam sub-beam reference trajectory T1, and the influence of higher-order transmission characteristics can be ignored.

[0061] The second step considers that the signal electrons have angular and energy distributions during emission. Therefore, for each signal electron sub-beam, its initial current density distribution on the initial emission plane can be expressed as a function f(z0,x0,x0',y0,y0',E0) that includes the initial angular and energy distributions. According to the conservation of the number of electrons during transmission, the landing coordinates of signal electrons with different slopes and energies emitted near the reference trajectory T1 of the signal electron sub-beam center on the initial emission plane are concentrated in a sub-beam landing region 202 near the landing coordinates of the reference trajectory T1. Therefore, based on the conservation of the number of electrons, the transformation relationship between the current density function of the final collection plane and the initial current density distribution of the initial emission plane can be established, as shown in equation (2):

[0062] f(z0,x0,x′0,y0,y′0,E0)dx′0dy′0dE0=j(z i ,x i ,y i ,x0,y0,E0)dx i dy i dE0 (2)

[0063] In the formula, j(z) i ,x i ,y i (x0, y0, E0) represents the signal electron beam sub-beam emitted at point (z0, x0, y0) on the initial emission plane and collected at the final collection plane (z0, x0, y0). i ,x i ,y i The current density function at ().

[0064] The third step is to apply the partial derivative relationship in the transmission characteristics calculated in the first step, based on the transformation relationship established in the second step. Substituting into equation (2) and rearranging, we can obtain the final current density function j(z) on the collecting plane. i ,x i ,y i The relationship between the initial coordinates (x0, y0, E0) and energy is expressed as a function. Then, by integrating over the region where the current is not zero on the initial emission plane and the initial energy distribution range of the signal electrons, the current density distribution J formed by the sub-beams of the signal electron beam at the final collection plane can be obtained. s The expression for is shown in equation (3):

[0065]

[0066] The fourth step is to calculate the current density distribution J of all signal electron beam sub-beams using the method described in the third step. sThen, by superimposing them in the laboratory coordinate system, the overall current density distribution J formed by the signal electron beam at any plane in space can be obtained. t .

[0067] Fifth step, based on the overall current density distribution J calculated in step four. t Therefore, characteristic parameters need to be selected as indicators to evaluate the spatial distribution of the overall current density of the signal electron beam. Since the lateral distribution of the signal electron beam is crucial for electron collection, the region containing n% of the total current is first defined as the n% current envelope 203, where n is a positive real number and 0 ≤ n ≤ 100. Then, the area of ​​the n% current envelope is used as a characteristic parameter to evaluate the spatial distribution of the current density. For example, the areas of the 85%, 90%, and 95% current envelopes can be selected as characteristic parameters, representing the areas containing 85%, 90%, and 95% of the total current, respectively.

[0068] Step 6: Based on the aforementioned method for calculating the spatial distribution of current density, a reference trajectory T0 107 for the signal electron beam sub-beam is selected from Step 1. The emission source sub-region 104 to which this reference trajectory belongs contains the centroid of the entire emission source 102, and the reference trajectory T0 is perpendicular to the initial emission plane. The coordinates (x, y) of the reference trajectory T0 at any plane in space are used as the centroid of the n% current envelope in Step 5. Therefore, based on the reference trajectory T0 and the n% current envelope, the current density distribution and lateral distribution of the signal electron beam at any plane in space can be obtained, i.e., the evolution of the signal electron beam current in space. Based on this, the design of the signal electron collection system in the SEM system can be guided.

[0069] In one example, the calculated SEM system includes: a magnetic lens 301, an electric lens 302, a sample stage 303, an electrostatic deflector 304, an in-lens ring detector 305, primary electrons 306, and signal electrons 307. The magnetic lens 301 generates an immersion magnetic field. The sample stage 303 holds the sample being observed and places it within the immersion magnetic field, which focuses the primary electrons 306 onto the sample surface. The electric lens 302 controls the landing energy of the primary electrons 306 on the sample stage. The electrostatic deflector 304 generates a deflection signal to deflect the primary electrons on the sample surface, achieving a large field of view. After the primary electrons 306 illuminate the sample surface, they generate signal electrons 307. These signal electrons 307 are collected by the detector 305 and converted into image signals under the action of the electromagnetic lens and deflector.

[0070] Example 2

[0071] In this embodiment, when the signal electron 307 is a secondary electron (SE), its emission angle distribution is a cosine distribution, and its energy distribution is as follows: Figure 3As shown, the energy peak of the secondary electrons is around 5 eV, and the energy distribution range is within 50 eV. The emission source is a circular region. In this example, the emission polar angle θ of the signal electron beam sub-beam reference trajectory is set to 6° increments from 0° to 36°, and the azimuth angle Φ is set to 10° increments from 0° to 350°. The central energy of its energy distribution is 5 eV, and the energy range is 5 eV ± 5 eV. Assume the initial current density spatial distribution at emission is as follows:

[0072]

[0073]

[0074] Where σ = r / 1.177, r is the radius of the emission source, which is 50 nm in this example, E SE The energy of the second electron is eV. m The most probable energy of a secondary electron is eV in this example. m =5eV. According to the above calculation method, in this example, since the emission source is small enough, there is no need to divide the emission source region into sub-regions. Therefore, it is only necessary to divide the signal electron beam sub-beams in the polar angle and azimuth angle directions. When the signal electron beam sub-beams are sufficiently small, only the first-order transmission characteristics need to be considered. According to the aforementioned calculation method, the reference trajectory T0 of the signal electron beam sub-beam tracked by the secondary electrons along a path perpendicular to the initial emission plane can be obtained. Figure 5 ), detector planar current density distribution ( Figure 6 a) Spatial evolution of current density distribution (90% current envelope), Figure 7 ).

[0075] Example 3

[0076] In this embodiment, when the signal electron 307 is a backscattered electron (BSE), its emission angle distribution is a cosine distribution, and its energy distribution is as follows: Figure 3 As shown, the peak energy position is related to the incident primary electron energy, increasing with the increase of the incident primary electron energy. In this example, the emission polar angle θ of the signal electron beam sub-beam reference trajectory is set to 6° intervals from 0° to 30°, the azimuth angle Φ is set to 10° intervals from 0° to 350°, the incident primary electron 406 energy is 1keV, the center energy of the backscattered electron energy distribution is 950eV, the energy range is 950eV±50eV, and the emission source is a circular region. Assume the initial current density spatial distribution at emission is as follows:

[0077]

[0078]

[0079] Where σ = r / 1.177, r is the radius of the emission region, which is 50 nm in this example, E BSE For the backscattered electron energy, E PE Given the electron energy, based on the calculation method described above, in this example, since the emission source is small enough, there is no need to divide the emission source region into sub-regions. Therefore, it is only necessary to divide the signal electron beam sub-beams in the polar angle and azimuth angle directions. When the signal electron beam sub-beams are sufficiently small, only the first-order transmission characteristics need to be considered. According to the aforementioned calculation method, the reference trajectory T0 of the signal electron beam sub-beam tracked by the backscattered electrons along a path perpendicular to the initial emission plane can be obtained. Figure 5 ), detector planar current density distribution ( Figure 6 b) Spatial evolution of current density distribution (90% current envelope) Figure 7 ).

[0080] Example 4

[0081] A system for calculating the spatial distribution of signal electron current density, comprising:

[0082] Transmission characteristic calculation module: used to calculate the transmission characteristics of the signal electron beam sub-beams in any spatial plane relative to the initial emission plane; specifically: assuming there is a region called the emission source 102 on the initial emission plane 101, and all signal electrons with different slopes and energies emitted by this emission source within a certain solid angle range are called the signal electron beam 103, the emission source is divided into several small regions, each called the emission source sub-region 104, and the signal electrons with different slopes emitted in each emission source sub-region are calculated along the polar angle θ and azimuth angle respectively. The direction is divided into several small regions. The signal electrons contained in each small region are called signal electron beam sub-beams 105. For each signal electron beam sub-beam, a central reference trajectory T1 is tracked. This reference trajectory is called the signal electron beam sub-beam reference trajectory 106. This reference trajectory is emitted from the centroid of its corresponding emission source sub-region. The initial emission parameters of the signal electron beam sub-beam reference trajectory are used as tracking quantities. The transmission characteristics of the signal electron beam sub-beam in any plane in space relative to the initial emission plane are obtained by solving the trajectory equation.

[0083] The transmission characteristics include linear characteristics and higher-order characteristics, as shown below:

[0084]

[0085] In the formula, r f Let r be the coordinates of the landing point of the signal electron on the final collection plane and its slope. i Let be the coordinates and slope of the signal electron in the initial plane, and δ be the energy dispersion of the signal electron. For the transfer mapping relationship from the initial launch plane to the final collection plane, then and For transmission characteristics.

[0086] The conversion relationship establishment module is used to establish the conversion relationship between the current density function of the signal electron beam sub-beam in the final collection plane and the initial current density distribution of the initial emission plane. Specifically, since the landing point coordinates of electrons with different slopes and energies emitted near the reference trajectory of the signal electron beam sub-beam on the initial emission plane are concentrated in a sub-beam landing point region 202 near the reference trajectory landing point coordinates on the final collection plane 201, the conversion relationship between the current density function of the signal electron beam sub-beam in the final collection plane and the initial current density distribution of the initial emission plane is established based on the conservation of electron quantity.

[0087] For each signal electron beam sub-beam, the initial current density distribution when it is emitted from its initial emission plane is represented by f(z0,x0,x0',y0,y0',E0), where z0 represents the z-axis coordinate of the initial emission plane, (x0,y0) are the initial coordinates, (x0',y0') are the initial slope, and E0 is the initial energy.

[0088] Based on the conservation of electron quantity during signal electron transmission, the landing points of signal electrons with different slopes and energies emitted near the reference trajectory T1 of a signal electron beam sub-beam on the initial emission plane are concentrated in a small region dx near the landing point of the signal electron beam sub-beam reference trajectory T1 on the final collection plane. i dy i Within this framework, based on the conservation of electron quantity, a transformation relationship is established between the current density function of the final collection plane and the initial current density distribution of the initial emission plane for the signal electron beam sub-beams:

[0089] f(z0,x0,x′0,y0,y′0,E0)dx′0dy′0dE0=j(z i ,x i ,y i ,x0,y0,E0)dx i dy i dE0

[0090] In the formula, j(z) i ,x i ,y i (x0, y0, E0) represents the signal electron beam sub-beam emitted at point (z0, x0, y0) on the initial emission plane and collected at the final collection plane (z0, x0, y0). i ,x i ,y i The current density function at ().

[0091] Signal electron beam sub-beam current density spatial distribution calculation module: used to calculate the current density distribution formed by the signal electron beam sub-beam at any plane in space. s The expression is as follows: Specifically, the transmission characteristics calculated by the transmission characteristic calculation module are substituted into the transformation relationship established by the transformation relationship establishment module, and the relationship between the current density function of the signal electron beam sub-beam in any plane of space and the coordinates and energy on the initial emission plane is obtained. Then, the region where the current is not zero on the initial emission plane and the initial energy distribution range of the signal electrons are integrated to obtain the current density distribution J formed by the signal electron beam sub-beam at any plane of space. s The expression;

[0092] Partial derivatives in transmission characteristics Substituting into the current density function j(z) i ,x i ,y i In the equation (x0, y0, E0), the current density distribution J of the signal electron beam emitted from the source sub-region on the final collection plane is obtained by integrating the region where the current density is not zero on the initial emission plane and the initial energy of the signal electrons. s (z i ,x i ,y i The expression for ) is:

[0093]

[0094] Signal electron beam current density spatial distribution calculation module: used to calculate the spatial distribution of the signal electron beam current density. t Specifically: Based on the transmission characteristic calculation module, the transformation relationship establishment module, and the signal electron beam sub-beam current density spatial distribution calculation module, the current density distribution of all signal electron beam sub-beams at any plane in space is calculated. s The current density distribution of all signal electron beam sub-beams at any plane in space J s By superimposing the data in the laboratory coordinate system, the spatial distribution of the current density J of the signal electron beam is obtained. t .

[0095] Feature parameter setting module: used to set the feature parameters for evaluating the spatial distribution of current density; specifically: assuming the spatial distribution of the signal electron beam's current density at a certain plane in space is J tp The region containing n% of the total current is defined as the n% current envelope 203, and the area of ​​the n% current envelope is used as a characteristic parameter for evaluating the spatial distribution of current density, and 0≤n≤100.

[0096] Distribution Calculation Module: Used to calculate the current density distribution and lateral distribution of the signal electron beam in any plane in space; specifically: a signal electron beam sub-beam reference trajectory T0 is selected, called the signal electron beam center reference trajectory 107. The characteristic of this reference trajectory is that its corresponding emission source sub-region 104 contains the centroid of the entire emission source 102, and the reference trajectory is perpendicular to the initial emission plane. The coordinates (x, y) of this reference trajectory in any plane in space are used as the centroid of the n% current envelope in step five. Based on the reference trajectory T0 and the n% current envelope, the current density distribution and lateral distribution of the signal electron beam in any plane in space are obtained.

[0097] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0098] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0099] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0100] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0101] 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 calculating the spatial distribution of signal electron current density, characterized in that, Includes the following steps: Step 1: Assume there is a region called the emission source (102) on the initial emission plane (101). The signal electrons emitted by the emission source with different slopes and energies within a certain solid angle range are called the signal electron beam (103). Divide the emission source into several small regions, each of which is called the emission source sub-region (104). The signal electrons with different slopes emitted in each emission source sub-region are then directed along the polar angle θ and azimuth angle, respectively. The direction is divided into several small regions. The signal electrons contained in each small region are called signal electron beam sub-beams (105). For each signal electron beam sub-beam, a central reference trajectory T1 is tracked. This reference trajectory is called the signal electron beam sub-beam reference trajectory (106). This reference trajectory is emitted from the centroid of its corresponding emission source sub-region. The initial emission parameters of the signal electron beam sub-beam reference trajectory are used as tracking parameters. The transmission characteristics of the signal electron beam sub-beam in any plane in space relative to the initial emission plane are obtained by solving the trajectory equation. Step 2: Since the electrons with different slopes and energies emitted near the reference trajectory of the signal electron beam sub-beam on the initial emission plane have their landing point coordinates on the final collection plane (201) concentrated in a sub-beam landing point region (202) near the reference trajectory landing point coordinates, the transformation relationship between the current density function of the signal electron beam sub-beam on the final collection plane and the initial current density distribution on the initial emission plane is established based on the conservation of electron quantity. Step three: the transmission characteristics calculated in step one are brought into the conversion relationship established in step two and the function relationship of the current density function of the signal electron beam sub-beam in the space arbitrary plane and the coordinate and energy on the initial emission plane is obtained, then the region where the current is not zero on the initial emission plane and the initial energy distribution range of the signal electron beam are integrated to obtain the current density distribution J formed by the signal electron beam sub-beam at the space arbitrary plane s ; Step four: Calculate the current density distribution J of all signal electron beam sub-beams at any plane in space according to steps one to three s , the current density distribution J of all signal electron beam sub-beams at any plane in space s , the current density distribution J of all signal electron beam sub-beams at any plane in space t ; Step 5: Assume the spatial distribution of the signal electron beam's current density at a certain plane in space is J. tp The region containing n% of the total current is defined as the n% current envelope (203), and the area of ​​the n% current envelope is used as a characteristic parameter for evaluating the spatial distribution of current density, and 0≤n≤100; Step 6: Select a signal electron beam sub-beam reference trajectory T0 from Step 1, called the signal electron beam center reference trajectory (107). The characteristic of this reference trajectory is that the emission source sub-region (104) to which it belongs contains the centroid of the entire emission source (102), and the reference trajectory is perpendicular to the initial emission plane. The coordinates (x, y) of this reference trajectory in any plane in space are used as the centroid of the n% current envelope in Step 5. Based on the reference trajectory T0 and the n% current envelope, the current density distribution and lateral distribution of the signal electron beam in any plane in space are obtained.

2. The method for calculating the spatial distribution of signal electron current density according to claim 1, characterized in that, The initial launch parameters include coordinates (x0, y0), slope (x0', y0'), and energy E0.

3. The method for calculating the spatial distribution of signal electron current density according to claim 1, characterized in that, The transmission characteristics in step one include linear characteristics and higher-order characteristics, as shown below: In the formula, r f Let r be the coordinates of the landing point of the signal electron on the final collection plane and its slope. i Let be the coordinates and slope of the signal electron in the initial plane, and δ be the energy dispersion of the signal electron. For the transfer mapping relationship from the initial launch plane to the final collection plane, then and For transmission characteristics.

4. The method for calculating the spatial distribution of signal electron current density according to claim 3, characterized in that, Step two specifically involves: For each signal electron beam sub-beam, the initial current density distribution when it is emitted from its initial emission plane is represented by f(z0,x0,x0',y0,y0',E0), where z0 represents the z-axis coordinate of the initial emission plane, (x0,y0) are the initial coordinates, (x0',y0') are the initial slope, and E0 is the initial energy. Based on the conservation of electron quantity during signal electron transmission, the landing points of signal electrons with different slopes and energies emitted near the reference trajectory T1 of a signal electron beam sub-beam on the initial emission plane are concentrated in a small region dx near the landing point of the signal electron beam sub-beam reference trajectory T1 on the final collection plane. i dy i Within this framework, based on the conservation of electron quantity, a transformation relationship is established between the current density function of the final collection plane and the initial current density distribution of the initial emission plane for the signal electron beam sub-beams: f(z0,x0,x′0,y0,y′0,E0)dx′0dy′0dE0=j(z i ,x i ,y i ,x0,y0,E0)dx i dy i dE0 In the formula, j(z) i ,x i ,y i (x0, y0, E0) represents the signal electron beam sub-beam emitted at point (z0, x0, y0) on the initial emission plane and collected at the final collection plane (z0, x0, y0). i ,x i ,y i The current density function at ().

5. The method for calculating the spatial distribution of signal electron current density according to claim 4, characterized in that, Step three specifically involves: Partial derivatives in transmission characteristics Substituting into the current density function j(z) i ,x i ,y i In the equation (x0, y0, E0), the current density distribution J of the signal electron beam emitted from the source sub-region on the final collection plane is obtained by integrating the region where the current density is not zero on the initial emission plane and the initial energy of the signal electrons. s (z i ,x i ,y i The expression for ) is:

6. The method for calculating the spatial distribution of signal electron current density according to claim 5, characterized in that, Step four specifically involves: calculating the current density distribution J of all signal electron beam sub-beams using steps one through three. s (z i ,x i ,y i After that, the current density distribution J of all signal electron beam sub-beams is calculated. s (z i ,x i ,y i The spatial distribution of the current density of the signal electron beam is obtained by superimposing the data in the laboratory coordinate system. t (z i ,x i ,y i ).

7. A system for calculating the spatial distribution of signal electron current density, characterized in that, include: Transmission characteristic calculation module: used to calculate the transmission characteristics of the signal electron beam sub-beams in any spatial plane relative to the initial emission plane; specifically: assuming there is a region called the emission source (102) on the initial emission plane (101), the signal electrons emitted by the emission source with different slopes and different energies within a certain solid angle range are called the signal electron beam (103), the emission source is divided into several small regions, each called the emission source sub-region (104), and the signal electrons with different slopes emitted in each emission source sub-region are respectively along the polar angle θ and azimuth angle. The direction is divided into several small regions. The signal electrons contained in each small region are called signal electron beam sub-beams (105). For each signal electron beam sub-beam, a central reference trajectory T1 is tracked. This reference trajectory is called the signal electron beam sub-beam reference trajectory (106). This reference trajectory is emitted from the centroid of its corresponding emission source sub-region. The initial emission parameters of the signal electron beam sub-beam reference trajectory are used as tracking parameters. The transmission characteristics of the signal electron beam sub-beam in any plane in space relative to the initial emission plane are obtained by solving the trajectory equation. The conversion relationship establishment module is used to establish the conversion relationship between the current density function of the signal electron beam sub-beam in the final collection plane and the initial current density distribution of the initial emission plane. Specifically, since the landing coordinates of electrons with different slopes and energies emitted near the reference trajectory of the signal electron beam sub-beam on the initial emission plane are concentrated in a sub-beam landing region (202) near the reference trajectory landing coordinates, the conversion relationship between the current density function of the signal electron beam sub-beam in the final collection plane and the initial current density distribution of the initial emission plane is established based on the conservation of electron quantity. Signal electron beam sub-beam current density spatial distribution calculation module: used to calculate the current density distribution formed by the signal electron beam sub-beam at any plane in space. s The expression is as follows: Specifically, the transmission characteristics calculated by the transmission characteristic calculation module are substituted into the transformation relationship established by the transformation relationship establishment module, and the relationship between the current density function of the signal electron beam sub-beam in any plane in space and the coordinates and energy on the initial emission plane is obtained. Then, the region where the current is not zero on the initial emission plane and the initial energy distribution range of the signal electron beam sub-beam are integrated to obtain the current density distribution J formed by the signal electron beam sub-beam at any plane in space. s The expression; Signal electron beam current density spatial distribution calculation module: used to calculate the spatial distribution of the signal electron beam current density. t Specifically: Based on the transmission characteristic calculation module, the transformation relationship establishment module, and the signal electron beam sub-beam current density spatial distribution calculation module, the current density distribution of all signal electron beam sub-beams at any plane in space is calculated. s The current density distribution of all signal electron beam sub-beams at any plane in space J s By superimposing the data in the laboratory coordinate system, the spatial distribution of the current density J of the signal electron beam is obtained. t ; Feature parameter setting module: used to set the feature parameters for evaluating the spatial distribution of current density; specifically: assuming the spatial distribution of the signal electron beam's current density at a certain plane in space is J tp The region containing n% of the total current is defined as the n% current envelope (203), and the area of ​​the n% current envelope is used as a characteristic parameter for evaluating the spatial distribution of current density, and 0≤n≤100; Distribution Calculation Module: Used to calculate the current density distribution and lateral distribution of the signal electron beam in any plane in space; Specifically: Select a signal electron beam sub-beam reference trajectory T0, called the signal electron beam center reference trajectory (107). The characteristic of this reference trajectory is that its emission source sub-region (104) contains the centroid of the entire emission source (102), and the reference trajectory is perpendicular to the initial emission plane. The coordinates (x, y) of this reference trajectory in any plane in space are used as the centroid of the n% current envelope in step five. The current density distribution and lateral distribution of the signal electron beam in any plane in space are obtained based on the reference trajectory T0 and the n% current envelope.

8. The signal electron current density spatial distribution calculation system according to claim 7, characterized in that, The transmission characteristics include linear characteristics and higher-order characteristics, as shown below: In the formula, r f Let r be the coordinates of the landing point of the signal electron on the final collection plane and its slope. i Let be the coordinates and slope of the signal electron in the initial plane, and δ be the energy dispersion of the signal electron. For the transfer mapping relationship from the initial launch plane to the final collection plane, then and For transmission characteristics.

9. The signal electron current density spatial distribution calculation system according to claim 8, characterized in that, The transformation relationship between the current density function of the final collection plane and the initial current density distribution of the initial emission plane for establishing the signal electron beam sub-beam is specifically as follows: For each signal electron beam sub-beam, the initial current density distribution when it is emitted from its initial emission plane is represented by f(z0,x0,x0',y0,y0',E0), where z0 represents the z-axis coordinate of the initial emission plane, (x0,y0) are the initial coordinates, (x0',y0') are the initial slope, and E0 is the initial energy. Based on the conservation of electron quantity during signal electron transmission, the landing points of signal electrons with different slopes and energies emitted near the reference trajectory T1 of a signal electron beam sub-beam on the initial emission plane are concentrated in a small region dx near the landing point of the signal electron beam sub-beam reference trajectory T1 on the final collection plane. i dy i Within this framework, based on the conservation of electron quantity, a transformation relationship is established between the current density function of the final collection plane and the initial current density distribution of the initial emission plane for the signal electron beam sub-beams: f(z0,x0,x′0,y0,y′0,E0)dx′0dy′0dE0=j(z i ,x i ,y i ,x0,y0,E0)dx i dy i dE0 In the formula, j(z) i ,x i ,y i (x0, y0, E0) represents the signal electron beam sub-beam emitted at point (z0, x0, y0) on the initial emission plane and collected at the final collection plane (z0, x0, y0). i ,x i ,y i The current density function at ().

10. The signal electron current density spatial distribution calculation system according to claim 9, characterized in that, The current density distribution J formed by the calculated signal electron beam sub-beam at any plane in space s The expression; specifically: Partial derivatives in transmission characteristics Substituting into the current density function j(z) i ,x i ,y i In the equation (x0, y0, E0), the current density distribution J of the signal electron beam emitted from the source sub-region on the final collection plane is obtained by integrating the region where the current density is not zero on the initial emission plane and the initial energy of the signal electrons. s (z i ,x i ,y i The expression for ) is:

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