Method for predicting secondary electron emission time based on Monte Carlo

Abstract

The invention provides a method for predicting secondary electron emission time based on Monte Carlo, and the method comprises the following steps: 1, obtaining the fluctuation height and the maximum fluctuation height; 2, determining incident electron characteristics and material types, and setting an initial moment; step 3, simulating an electron scattering and internal secondary electron generation process and calculating a scattering step length; 4, judging whether scattering is in the material or not, if yes, calculating and updating the moment to the step 3, and otherwise, executing the step 5; 5, judging whether the surface potential barrier is traversed or not, and if not, returning to the updating moment to the step 3; otherwise, updating the time to step 6; step 6, judging whether re-incidence occurs or not, if no, updating the moment, and obtaining the secondary electron emission moment; otherwise, calculating the time to the re-incidence point and updating the time, and going to the step 3; and step 7, counting all electron moments to obtain secondary electron emission time. According to the method disclosed by the invention, all durations of electrons from entering the material to generating secondary electrons and completely emitting from the surface are obtained, and the secondary electron emission time characteristic is obtained.

Description

Technical Field

[0001] This invention belongs to the technical field of electronic science and technology, and relates to the secondary electron emission time, specifically to a method for predicting the secondary electron emission time based on Monte Carlo. Background Technology

[0002] Ultra-high-speed data transmission and ultra-high-capacity communication demand higher frequency bands. Due to the increased frequency, the transit order of electrons in the electromagnetic field within microwave components of the same size increases, and the deviation of the electron emission phase further exacerbates the deviation of the electron trajectory. Furthermore, reducing secondary electron emission through surface microstructure design is an effective means of suppressing micro-discharges. This typically involves etching various trap structures on the surface, ranging in size from hundreds of nanometers to hundreds of micrometers. These trap structures inevitably increase the interaction time between electrons and the material. Traditional micro-discharge simulation methods assume that secondary electrons are emitted immediately after an electron collision within the material, excluding the time spent on electron transport, scattering, and emission within the microwave component material. When the time required for an electron to collide with and be emitted from the microwave component surface is comparable to the microwave period, the emission moment of the secondary electron is no longer the collision moment of the incident electron, and the electromagnetic field within the microwave component must be updated accordingly. Summary of the Invention

[0003] In view of the shortcomings of the existing technology, the purpose of this invention is to provide a method for predicting the secondary electron emission time based on Monte Carlo, thereby solving the technical problem that the accuracy of the secondary electron emission time in the existing technology needs to be further improved.

[0004] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: A method for predicting secondary electron emission time based on Monte Carlo methods, the method specifically includes the following steps: Step 1: Characterize and interpolate the surface morphology of the material to be predicted, construct the surface morphology to be analyzed, and obtain the undulation height at any location on the surface of the material to be predicted. and maximum undulation height .

[0005] Step two: Determine the characteristics of the incident electrons and the material type of the material to be predicted, and record the initial moment of the incident electrons. ,set up =0, This is the sequence number of the electron.

[0006] Step 3: Based on the characteristics of the incident electrons and the material type obtained in Step 2, the Monte Carlo method is used to simulate and analyze the scattering process of electrons and the generation process of internal secondary electrons in the material to be predicted, and the scattering step size of the electrons is calculated. .

[0007] Step four, based on the scattering step size obtained in step three. To determine whether an electron is within the material to be predicted, if the electron's position before travel... and electronic position after travel All are within the material to be predicted; the calculation of electron movement within the material to be predicted... arrive travel time Update electronic time , , The sequence number is the number of electron journeys, and Then return to step three for a loop judgment; if electrons reach the surface of the material to be predicted, proceed to step five.

[0008] Step 5: Electrons are scattered across the surface of the material to be predicted. The electron emission probability is calculated based on the electron energy and the material properties of the material. If the electron cannot cross the surface potential barrier of the material, it returns to the material, and the electron time is updated. , Then return to step three and repeat the process; if electrons can cross the surface barrier of the material to be predicted, then electrons can be emitted from the surface, and the potential energy within the material to be predicted is calculated. to surface exit point distance And electrons from the material to be predicted to surface exit point travel time Update electronic time , Then proceed to step six.

[0009] Step six: After electrons exit the surface of the material to be predicted, determine whether they will re-enter the material. If no re-entry occurs, continue the electron trajectory according to the electron's initial velocity and direction of motion until the electron height reaches the level obtained in step one. At this point, all electrons are emitted, and the point of complete emission is denoted as . ,calculate and Distance between and electronics from arrive travel time , and update electronic time. At this time This is the moment when the electron is completely emitted.

[0010] If electrons are re-injected after emission, the re-injection point is denoted as... , calculate into and Distance between and electron emission points from the surface to re-incidence point travel time Update electronic time , And according to the electron's movement to The state of the point is re-entered into the material to be predicted, and the process returns to step three for repeated judgment.

[0011] Step 7: Using the methods from Steps 1 to 6, count the times when all electrons are completely emitted. According to electronic time The secondary electron emission time under this incident electron state is obtained.

[0012] Compared with the prior art, the present invention has the following technical effects: (I) The method in this invention takes into account both the time consumed by electron scattering in the material to be predicted and the accumulation time of electrons in the morphology during the re-injection process when electrons interact with the morphology. It obtains all the time from the electron entering the material to be predicted to the generation of secondary electrons and their complete emission from the surface, thus supplementing the time characteristics of secondary electron emission.

[0013] (II) The method in this invention provides basic data for the accurate analysis of micro-discharge with surface morphology in the high-frequency band or with morphology for predicting materials, and can identify materials with short time delays, and can be applied to ultrafast detection or ultrafast response. Attached Figure Description

[0014] Figure 1 This is an overall flowchart of the method in this invention.

[0015] Figure 2 The relationship between the secondary electron energy and the secondary electron emission time when 400 eV incident electrons are incident on Cu material in Embodiment 1 of the present invention is shown. The surface of Cu material is a rectangular groove (depth 100 nm, aspect ratio 1, duty cycle 0.5).

[0016] Figure 3 This invention relates to the secondary electron energy and emission time of a Cu material with an incident electron of 400 eV. The surface of the Cu material has three-dimensional square holes (depth 100 nm, hole width 100 nm, square hole period 200 nm).

[0017] The specific content of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Detailed Implementation

[0018] It should be noted that, unless otherwise specified, all the equipment, materials and methods in this invention adopt the equipment, materials and methods commonly known in the art in the prior art. For example, the white light confocal microscope adopts the known white light confocal microscope, the atomic force microscope adopts the known atomic force microscope, the material to be predicted adopts the known material to be predicted, the copper adopts the known copper, the gold adopts the known gold, the silver adopts the known silver, the Monte Carlo method adopts the known Monte Carlo method, and the calculation method for the travel distance or travel time of electrons inside and outside the material to be predicted adopts the calculation method commonly known in the art.

[0019] In this invention, incident electrons refer to all electrons that are directly irradiated onto the surface of the material to be predicted using point irradiation or surface irradiation methods.

[0020] In this invention, "electron" refers to all electrons, including incident electrons, internal secondary electrons, and secondary electrons.

[0021] In this invention, internal secondary electrons refer to new electrons generated after the incident electrons interact with the material to be predicted, but which are not emitted from the surface of the material to be predicted and remain within the material to be predicted.

[0022] In this invention, secondary electrons refer to electrons emitted from the surface of the material to be predicted after the incident electrons interact with the material to be predicted.

[0023] Following the above technical solutions, specific embodiments of the present invention are given below. It should be noted that the present invention is not limited to the following specific embodiments, and all equivalent modifications made on the basis of the technical solutions of the present invention fall within the protection scope of the present invention.

[0024] Example: This embodiment presents a method for predicting secondary electron emission time based on Monte Carlo simulation. In this embodiment, the surface of the material to be predicted is a rectangular groove. The emission time of the secondary electron is calculated as follows: Figure 1 As shown, the method specifically includes the following steps: Step 1: Characterize and interpolate the surface morphology of the material to be predicted, construct the surface morphology to be analyzed, and obtain the undulation height at any location on the surface of the material to be predicted. and maximum undulation height .

[0025] In step one, the undulation height at any location on the surface of the material to be predicted is obtained. h and maximum undulation height The specific method is as follows: The surface height of the material to be predicted is measured using a surface morphology characterization device. The measurement result is a two-dimensional matrix with a fixed width and length, and the value stored in the two-dimensional matrix is ​​the undulation height at that location. And determine the maximum undulation height of the surface. .

[0026] Based on the characterization results of the surface morphology of the material to be predicted, the undulation height at any point on the surface of the material to be predicted within the measurement range is calculated using a first-order linear interpolation method. .

[0027] Surface morphology characterization equipment includes white light confocal microscopy or atomic force microscopy.

[0028] In this embodiment, the first-order linear interpolation method adopts a commonly known method in the art.

[0029] In this embodiment, the surface of the material to be predicted is a rectangular groove that extends infinitely along its length. The platform of the rectangular groove is the top end face of the groove sidewall. A schematic diagram of the structure of the material to be predicted with a rectangular groove surface is shown below. Figure 2 As shown in the lower left corner, the rectangular groove adopts a commonly used rectangular groove in this field. The groove depth is 100nm, the aspect ratio is 1, and the duty cycle is 0.5. Therefore, the groove width is 100nm and the groove wall width is 100nm. .

[0030] In this embodiment, "the rectangular groove extends infinitely in the length direction" means that the length of the rectangular groove is 10 times or more the width of the groove.

[0031] Step two: Determine the characteristics of the incident electrons and the material type of the material to be predicted, and record the initial moment of the incident electrons. ,set up =0, This is the sequence number of the electron.

[0032] In step two, the characteristics of the incident electron include the incident electron energy. Number of incident electrons The incident electron irradiation method and the incident electron angle.

[0033] Number of incident electrons .

[0034] Incident electron irradiation methods include point irradiation or area irradiation.

[0035] The incident electron angle includes the tilt angle. and azimuth 。

[0036] In step two, the material type to be predicted includes copper, gold, or silver.

[0037] In step two, the initial time The initial height fluctuation of the incident electron The moment at which the incident electron contacts the surface of the material to be predicted, or the moment at which the incident electron is in the plane of height.

[0038] First, when the incident electron first reaches the maximum fluctuation height The time at the altitude plane is the initial time. At that time, if When the incident electrons do not come into contact with the surface of the material to be predicted, the calculation of the incident electrons from... The distance from the height plane to the surface in contact with the material to be predicted and corresponding travel time Update electronic time , , The sequence number is the number of electron journeys, and Then proceed to step three; If in When the incident electrons come into contact with the surface of the material to be predicted, then and All are 0.

[0039] Travel time The specific calculation method is as follows: ; In the formula: For incident electrons from The travel time from the height plane to the surface of the material to be predicted, in fs; For incident electrons from The distance from the height plane to the surface of the material to be predicted, in nm; The velocity of electrons outside the material to be predicted is expressed in nm / fs. The sequence number is the number of electron journeys, and .

[0040] Second, the initial moment is the moment when the incident electron contacts the surface of the material to be predicted. Record the initial time. Then proceed to step three.

[0041] In this embodiment, the initial to maximum fluctuation height of the incident electron is considered. The time at the altitude plane is the initial time. .

[0042] In this embodiment, the surface of the material to be predicted is a rectangular groove, and all points on the platform of the rectangular groove have an undulation height of [missing information]. The point; the platform of the rectangular groove is the top end face of the groove sidewall of the rectangular groove.

[0043] In this embodiment, 400eV The incident electron irradiation method is uniform surface irradiation, with an inclination angle of... Azimuth The material type is copper. The method for uniform irradiation of the surface employs methods commonly known in the art.

[0044] Step 3: Based on the characteristics of the incident electrons and the material type obtained in Step 2, the Monte Carlo method is used to simulate and analyze the scattering process of electrons and the generation process of internal secondary electrons in the material to be predicted, and the scattering step size of the electrons is calculated. .

[0045] In step three, if new internal secondary electrons are generated during the scattering process and the generation of internal secondary electrons, the new internal secondary electrons are treated in the same way as the original electrons.

[0046] The scattering step size This refers to the pre-traveling electron position within the material to be predicted. and electronic position after travel The distance between them.

[0047] In this embodiment, the Penn dielectric model is used to calculate the inelastic scattering cross section. Inelastic free path The elastic scattering cross section was calculated using the Mott model. and flexible free path Then the mean free path scattering step size Electrons move from within the material to be predicted Scattered to , and The distance between them is .

[0048] Calculate the inelastic scattering probability Elastic scattering probability By generating random numbers uniformly distributed in the range [0,1] ,if If the scattering is inelastic, then the scattering is inelastic; otherwise, it is elastic.

[0049] If inelastic scattering occurs, a new internal secondary electron is generated, and the time of generation of this new secondary electron, i.e., the initial time, is recorded. The values ​​are set to 0. The energies and angles of the scattered electrons and the new inner secondary electrons are processed using the conventional Monte Carlo method, which employs a commonly known processing method in the art. The calculation method for the complete emission time of the new inner secondary electrons is the same as the calculation method for the complete emission time of the incident electrons in this embodiment.

[0050] In this embodiment, the Penn dielectric model is the Penn dielectric model commonly known in the art; the Mott model is the Mott model commonly known in the art.

[0051] Step four, based on the scattering step size obtained in step three. To determine whether an electron is within the material to be predicted, if the electron's position before travel... and electronic position after travel All are within the material to be predicted; the calculation of electron movement within the material to be predicted... arrive travel time Update electronic time , , The sequence number is the number of electron journeys, and Then return to step three for a loop judgment; if electrons reach the surface of the material to be predicted, proceed to step five.

[0052] In step four, the travel time The specific calculation method is as follows: ; In the formula: For electrons to move from within the material to be predicted arrive The travel time of electrons, or the travel time of electrons from the surface of the material to be predicted to their return to the material to be predicted, is expressed in fs. This represents the electron scattering step size, in nm. The electron velocity is the speed of electrons within the material to be predicted, expressed in nm / fs. The sequence number is the number of electron journeys, and .

[0053] In this embodiment, The velocity of electrons within the material to be predicted is the speed at which electrons travel from the material to the target material. arrive The speed of travel or electrons from the material to be predicted to surface exit point The speed of travel.

[0054] Step 5: Electrons are scattered across the surface of the material to be predicted. The probability of electron emission is calculated based on the electron's energy and the material properties of the material. If the electron cannot cross the surface potential barrier of the material, it returns to the material. The travel time of the electron from the surface of the material to its return is calculated. Update electronic time , Then return to step three and repeat the process; if electrons can cross the surface barrier of the material to be predicted, then electrons can be emitted from the surface, and the potential energy within the material to be predicted is calculated. to surface exit point distance And electrons from the material to be predicted to surface exit point travel time Update electronic time , Then proceed to step six.

[0055] In step five, The specific calculation method is as follows: ; In the formula: For electrons to escape from the material to be predicted to surface exit point The travel time, in fs; For the material to be predicted to surface exit point The distance, in nm; The electron velocity is the speed of electrons within the material to be predicted, expressed in nm / fs. The sequence number is the number of electron journeys, and .

[0056] In this embodiment, the concept of surface barrier is the surface barrier commonly known in the art.

[0057] In this embodiment, in step five The calculation method and step four The calculation method is the same.

[0058] Step six: After electrons exit the surface of the material to be predicted, determine whether they will re-enter the material. If no re-entry occurs, continue the electron trajectory according to the electron's initial velocity and direction of motion until the electron height reaches the level obtained in step one. At this point, all electrons are emitted, and the point of complete emission is denoted as . ,calculate and Distance between and electronics from arrive travel time , and update electronic time. At this time This is the moment when the electron is completely emitted.

[0059] If electrons are re-injected after emission, the re-injection point is denoted as... , calculate into and Distance between and electron emission points from the surface to re-incidence point travel time Update electronic time , And according to the movement of electrons to The state of the point is re-entered into the material to be predicted, and the process returns to step three for repeated judgment.

[0060] In step six, The specific calculation method is as follows: ; In the formula: For electrons from arrive The travel time, in fs; for and The distance between them, in nm; The velocity of electrons outside the material to be predicted is expressed in nm / fs. The sequence number is the number of electron journeys, and .

[0061] In step six, The specific calculation method is as follows: ; In the formula: The point where electrons exit from the surface to re-incidence point The travel time, in fs; for and The distance between them, in nm; The velocity of electrons outside the material to be predicted is expressed in nm / fs. The sequence number is the number of electron journeys, and .

[0062] In this embodiment, v r The electron's velocity outside the material to be predicted is either the velocity of the electron after it exits the surface of the material or the velocity of the electron before it is re-entered after exiting the surface of the material.

[0063] In this embodiment, the surface emission point Q i Corresponding undulation height h Less than or equal to h max ;Full exit point R i Corresponding undulation height h equal h max .

[0064] In steps four through six, electronic timing The specific calculation method is as follows: , , , or ; In the formula: For the first The electron in the first electron Electronic time after the next movement; For the first The electron in the first electron Electronic time after the next movement; For the sequence number of electrons; The sequence number is the number of electron journeys, and ; For incident electrons from The travel time from the height plane to the surface of the material to be predicted, in fs; For electrons to move from within the material to be predicted arrive The travel time, in fs; For electrons to escape from the material to be predicted to surface exit point The travel time, in fs; For electrons from arrive The travel time, in fs; The point where electrons exit from the surface to re-incidence point The travel time is expressed in fs.

[0065] In this embodiment, if the first As the secondary electron travels, the electron's position before travel is... and electronic position after travel All electrons either remain within the material to be predicted, or after traveling, the electron reaches the surface of the material but fails to cross the surface potential barrier and returns to the material. In this case, the electron's travel time is... If the first During the secondary electron's journey, after exiting the predicted material surface, the electron undergoes re-intrusion. The point at which the electron re-intrudes from the predicted material surface is... .

[0066] Step 7: Using the methods from Steps 1 to 6, count the times when all electrons are completely emitted. According to electronic time The secondary electron emission time under this incident electron state is obtained.

[0067] Figure 2 The method described in this embodiment is presented to predict the relationship between the secondary electron energy and the secondary electron emission time when an incident electron with an energy of 400 eV is incident on Cu material. The surface of Cu material is a rectangular groove (depth 100 nm, aspect ratio 1, duty cycle 0.5). It can be seen that the emission time of a very small number of secondary electrons can reach up to 1500 fs. This is mainly due to the long-term movement of electrons in the infinite extension direction of the rectangular groove (i.e., the groove length direction). Part of the secondary electron emission time is concentrated around 100 fs. This part is the secondary electron generated when the incident electron irradiates the rectangular groove. Another part is concentrated below 1 fs. This part is the secondary electron emission time when the incident electron irradiates the platform of the rectangular groove. Since it does not cross the groove depth, the time is relatively short.

[0068] Example 2: This embodiment presents a method for predicting secondary electron emission time based on Monte Carlo simulation. The method in this embodiment is basically the same as that in Embodiment 1, except that in step one, the surface of the material to be predicted has three-dimensional square holes. A schematic diagram of the structure of the material to be predicted with three-dimensional square holes is shown below. Figure 3As shown in the lower left corner, the hole depth is 100nm, the hole width is 100nm, and the square hole period is 200nm.

[0069] In this embodiment, the platform of the material to be predicted, whose surface is a three-dimensional square hole, refers to the top end face of the sidewall of the hole, i.e., all the undulations with a height of... The plane containing the point.

[0070] In this embodiment, the period of the square hole refers to the total width of the platform between two adjacent square holes and the total width of one square hole.

[0071] In this embodiment, the relationship between the secondary electron energy and the secondary electron emission time when 400 eV incident electrons are incident on the Cu material is as follows: Figure 3 As shown in the figure, the secondary electron emission time of the material to be predicted, whose surface has three-dimensional square holes, also consists of two parts. Figure 3 The denser region in the upper middle part is mainly composed of secondary electrons emitted after the incident electrons enter the three-dimensional square hole. Since the secondary electron suppression energy of the three-dimensional square hole is stronger than that of the rectangular slot, relatively few electrons can be emitted from the depth of the hole. The emission time of the secondary electrons is mainly concentrated in the upper layer from tens to hundreds of fs. Figure 3 The relatively concentrated electron distribution at the lower center is the secondary electron emission time when the incident electron irradiates the platform. It is equivalent to the secondary electron emission time when the surface of the material to be predicted is planar, which is usually less than 1 fs.

Claims

1. A method of predicting secondary electron emission time based on Monte Carlo, characterized in that, The method specifically comprises the following steps: Step one, characterizing and interpolating the surface morphology of the material to be predicted, constructing the surface morphology to be analyzed, obtaining the fluctuation height of any position of the surface of the material to be predicted and the maximum fluctuation height ; Step two, determine the characteristics of the incident electron and the material type of the material to be predicted, and record the initial time of the incident electron , set = 0, is the serial number of the electron; Step three, according to the characteristics of the incident electrons obtained in step two and the material type, simulating and analyzing the scattering process and internal secondary electron generation process of the electrons in the material to be predicted by using a Monte Carlo method, and calculating the scattering step length of the electrons ; Step four, based on the scattering step size obtained in step three. To determine whether an electron is within the material to be predicted, if the electron's position before travel... and electronic position after travel All are within the material to be predicted; the calculation of electron movement within the material to be predicted... arrive travel time Update electronic time , Then return to step three for a loop check; if electrons reach the surface of the material to be predicted, proceed to step five. Step five, electron scatters through the surface of the material to be predicted, according to the energy of the electron and the material properties of the material to be predicted, the exit probability of the electron is calculated, if the electron cannot cross the surface potential barrier of the material to be predicted, the electron returns to the material to be predicted, and the electron time is updated , , then return to step three and cycle; if the electron can cross the surface potential barrier of the material to be predicted, the electron can exit from the surface, calculate the distance of the electron in the material to be predicted to the surface exit point , and the travel time of the electron from the material to be predicted to the surface exit point , , , , , then go to step six; Step six, after the electron is emitted from the surface of the material to be predicted, it is determined whether the electron will be incident on the material to be predicted again. If the electron does not re-enter, the electron trajectory is advanced according to the velocity and direction of motion of the electron at the time of emission until the electron reaches the height obtained in step one At this time, the electron is completely emitted, and the point of complete emission is recorded as The distance between and is calculated and the travel time of the electron from to is calculated , and the electron time is updated The electron time at this time is the electron time at which the electron is completely emitted. If the electron re-enters after the ejection, the re-entering point is recorded as , the distance between the entering point and the re-entering point is calculated , the travel time of the electron from the surface ejection point to the re-entering point is calculated , the electron time is updated , , and the electron enters the material to be predicted again according to the state of the electron moving to the point , and returns to step three for a cycle of judgment. Step seven, using the method of step one to step six, count all the electron time of electron completely out , according to the electron time get the secondary electron emission time under the incident electron state.

2. The method of claim 1, wherein the Monte Carlo based prediction of the time of secondary electron emission is based on a time of flight of the primary electron. In step one, the specific method for obtaining the fluctuation height of any position on the surface of the material to be predicted is as follows: using a surface morphology characterization device to measure the surface height of the material to be predicted, the measurement result is a two-dimensional matrix with fixed width and length, the storage value in the two-dimensional matrix is the fluctuation height of the position point, and the maximum fluctuation height of the surface is determined. h The specific method for obtaining the fluctuation height of any position on the surface of the material to be predicted is as follows: using a surface morphology characterization device to measure the surface height of the material to be predicted, the measurement result is a two-dimensional matrix with fixed width and length, the storage value in the two-dimensional matrix is the fluctuation height of the position point, and the maximum fluctuation height of the surface is determined. The specific method for obtaining the fluctuation height of any position on the surface of the material to be predicted is as follows: using a surface morphology characterization device to measure the surface height of the material to be predicted, the measurement result​​ According to the characterization result of the surface morphology of the material to be predicted, the fluctuation height of any point of the surface of the material to be predicted in the measurement range is calculated by using a first-order linear interpolation method .

3. The method of claim 2, wherein the Monte Carlo based prediction of the time of secondary electron emission is based on a time of flight of the primary electron. The surface morphology characterization device comprises a white light confocal microscope or an atomic force microscope.

4. The method of claim 1, wherein the Monte Carlo based prediction of the time of secondary electron emission is based on a time of flight of the primary electron. In step two, the characteristics of the incident electrons include incident electron energy , incident electron number , incident electron irradiation mode and incident electron angle; The number of incident electrons ; The incident electron irradiation mode comprises point irradiation or surface irradiation. The incident electron angle includes a tilt angle and an azimuth angle ; In step two, the material type of the material to be predicted comprises copper, gold or silver.

5. The method of claim 1, wherein the Monte Carlo based prediction of the time of secondary electron emission is based on a time of flight of the primary electron. In step two, the initial moment at which the incident electron first reaches the maximum height of the undulation at which the height plane is reached, or at which the incident electron touches the surface of the material to be predicted; First, when the incident electron first reaches the maximum fluctuation height of the height plane where it is located at the initial time , if the incident electron is not in contact with the surface of the material to be predicted at , the distance from the height plane where the incident electron is located to the surface of the material to be predicted in contact is calculated , and the corresponding travel time , the electron time , , is updated to the sequence number of the number of electron travels, and ; Then step three is entered. If the incident electron contacts the surface of the material to be predicted at time t, then and are both 0; The travel time The specific calculation method is: ； In the formula: For incident electrons from The travel time from the height plane to the surface of the material to be predicted, in fs; For incident electrons from The distance from the height plane to the surface of the material to be predicted, in nm; v0 is the speed of the electron outside the material to be predicted, in nm / fs; is a sequence number for the number of times of electronic travel, and ; Second, when the time at which the incident electron contacts the surface of the material to be predicted is taken as the initial time The initial time is recorded and step three is entered.

6. The method of claim 1, wherein the Monte Carlo based prediction of the time of secondary electron emission is based on a time of flight of the primary electron. In step three, if new internal secondary electrons are generated in the scattering process and the internal secondary electron generation process, the new internal secondary electrons and the original electrons are processed in the same way. The scattering step size Refers to the distance between the pre-electron position And post-electron position Inside the material to be predicted.

7. The method of claim 1, wherein the Monte Carlo based prediction of the time of secondary electron emission is based on a time of flight of the primary electron. In step four, the travel time The specific calculation method is: ； In the formula: the travel time of an electron within the material to be predicted from to in fs; for the scattering step of the electrons, in nm; is the electron travel speed in the material to be predicted, in nm / fs; is the sequence number of the number of electronic travels, and .

8. The method of claim 1, wherein the Monte Carlo based prediction of the time of secondary electron emission is based on a time of flight of the primary electron. In step five, the The specific calculation method is: ； In the formula: the travel time of an electron from within the material to be predicted to the exit point on the surface in fs; the distance from the surface exit point to the surface exit point in nm; is the electron travel speed in the material to be predicted, in nm / fs; is the sequence number of the number of electronic travels, and .

9. The method of claim 1, wherein the Monte Carlo based prediction of the time of secondary electron emission is based on a time of flight of the primary electron. In step six, the The specific calculation method is: ； In the formula: travel time of the electrons from to in fs; is and the distance between and, in nm; v0 is the speed of the electron outside the material to be predicted, in nm / fs; is a sequence number for the number of times of electronic travel, and ; In step six, the The specific calculation method is: ； In the formula: travel time of the electron from the surface exit point to the re-entry point in fs; is and the distance between and, in nm; v0 is the speed of the electron outside the material to be predicted, in nm / fs; is the sequence number of the number of electronic travels, and .

10. The method of claim 1, wherein the Monte Carlo based prediction of secondary electron emission time is based on a time of flight of the primary electron beam. In steps four to six, the electronic time point The specific calculation method is: , , , or ; In the formula: In the formula: the first electron at the first time after the first electron has traveled a first distance; and the second electron at the second time after the second electron has traveled a second distance; and the first electron at the first time after the first electron the first the first the first Sequence number for the electron; is a sequence number for the number of times of electronic travel, and ; For incident electrons from The travel time from the height plane to the surface of the material to be predicted, in fs; the travel time of an electron within the material to be predicted from to in fs; the travel time of an electron from within the material to be predicted to the exit point on the surface in fs; travel time of the electrons from to in fs; travel time of the electron from the surface exit point to the re-entry point in fs.

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