A method for fast calculation of secondary neutron radiation field in wafer proton irradiation process

Abstract

The application discloses a kind of secondary neutron radiation field fast calculation method in wafer proton irradiation process, comprising: step 1, establishing Monte Carlo program source term calculation region, the geometric model of wafer bombarded by proton beam is established using Monte Carlo program, to simulate the irradiation process of proton accelerator;Step 2, using program to establish spherical detector covering wafer, record the energy spectrum, particle number and direction information of secondary neutrons, and use it as the source term of subsequent calculation, carry out next step calculation;Step 3, using neutron division cross section method, according to the existing source term information, the dose influence in space and outside shielding wall is calculated.The application can significantly improve the calculation speed of radiation field by coupling two methods, and the calculation speed of some scenes is improved by more than 100 times;Through the coupling calculation of neutron division cross section method, the use of Monte Carlo database is reduced, the high-difficulty modeling requirement of Monte Carlo method is avoided, and the use threshold is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of semiconductors, and particularly to a method for fast calculation of secondary neutron radiation field in wafer proton irradiation. BACKGROUND

[0002] Wafer proton irradiation is an important process in the field of semiconductor chips. Based on this, an irradiation accelerator is self-developed to irradiate chips, but its radiation impact cannot be ignored. During processing, radiation is generated by the accelerator, which may cause irreversible radiation damage to equipment, personnel, etc. Therefore, the radiation impact needs to be calculated for radiation shielding.

[0003] Radiation shielding calculation is an indispensable part of nuclear technology development, which uses mathematical models to predict and evaluate the protective effect of shielding materials on harmful radiation. Through perfect radiation shielding calculation, basis and optimization scheme can be provided for shielding design, so as to ensure the safe use of nuclear energy technology, reduce the harm of radiation to personnel and environment, and improve the reliability and life of nuclear facilities.

[0004] Currently, the main radiation shielding calculation methods mainly include the following three types: Monte Carlo method, discrete ordinate method and point kernel integration method. These methods have played an important role in the development of nuclear technology, and have provided basis and optimization scheme for shielding design.

[0005] Firstly, the discrete ordinate method is a deterministic method, which uses finite difference approximation to calculate the spatial distribution of neutron or photon flux. In this method, the space is usually divided into many small units, and finite difference approximation is used to calculate the spatial distribution of neutron or photon flux. At the same time, the method also divides the entire energy range of neutron and photon flux to be calculated into multiple energy groups, uses multi-group formula to handle the energy dependence of neutron and photon reaction cross section, and uses Legendre expansion to describe the differential scattering cross section.

[0006] Secondly, the point kernel integration method is a deterministic method, but it has obvious empirical nature. This method discretizes the radioactive source into several point kernels (regarded as point sources), then calculates the dose rate value of each point kernel at the dose point, and finally sums up the dose rate values of all point kernels to obtain the total dose rate at the dose point.

[0007] As for the Monte Carlo method, it is a method based on probability theory, which usually uses random numbers to solve some numerical calculation problems. In shielding calculation, the Monte Carlo method can solve the Boltzmann transport equation into the Fredholm integral equation, which is used to calculate the particle collision probability in the low energy region (<<20MeV) with nuclear data.

[0008] The radiation field calculation of wafer proton irradiation is not only an important way to evaluate the radiation effect of equipment, but also an important guarantee for personnel safety. In the calculation, the secondary particle impact generated by the collision of protons and wafers is usually calculated due to the weak penetration ability of protons, including secondary neutrons and secondary gamma particles, and the dose impact of the particles in space is calculated. In the traditional calculation, the Monte Carlo method is usually used for direct calculation of the shielding calculation of such secondary radiation field, and the Monte Carlo method is limited by its method characteristics and often needs a large amount of time for simulation calculation. The reaction of each particle with the material is estimated and simulated.

[0009] On the other hand, the radiation source term generated by irradiation includes secondary neutrons generated from (p, n) reaction, and the yield of this part of neutrons is often low. The efficiency will be further reduced by directly simulating the Monte Carlo method. In addition, when performing shielding calculation, the radiation dose outside the shielding wall needs to be considered, and the Monte Carlo method has the problem of low efficiency for deep penetration problems, and a large amount of time is often needed to simulate the impact of enough scattered and penetrated neutrons on the outside of the shielding wall. Under the superposition of the three influences, the traditional secondary neutron radiation field calculation needs a large amount of computing power and time. Other methods such as discrete ordinate method and point kernel integration method are difficult to directly calculate when calculating the radiation field of secondary neutrons due to their method limitations.

[0010] In summary of the above description, for some scenes that need to quickly evaluate the radiation situation, it is difficult to quickly obtain the neutron radiation field information by using the traditional method. SUMMARY

[0011] The purpose of the application is to provide a secondary neutron radiation field fast calculation method in the process of wafer proton irradiation to solve the above problems existing in the prior art.

[0012] Technical scheme: A secondary neutron radiation field fast calculation method in the process of wafer proton irradiation, comprising:

[0013] Step 1, establishing a Monte Carlo program source term calculation region, using a Monte Carlo program to establish a geometric model of a proton beam bombarding a wafer to simulate the irradiation process of a proton accelerator;

[0014] Step 2, using the program to establish a spherical detector covering the wafer, recording the energy spectrum, particle number and direction information of the secondary neutrons, and taking them as the source term for subsequent calculation, and performing the next step calculation;

[0015] Step 3, using the neutron branching cross-section method to calculate the dose impact in the space and outside the shielding wall according to the existing source term information.

[0016] The coupling of the two methods can significantly improve the calculation speed of the radiation field, and the calculation speed of some scenes is improved by more than 100 times;

[0017] The coupling calculation through the neutron extraction cross section method reduces the use of the Monte Carlo database, avoids the high-difficulty modeling requirement of the Monte Carlo method, and lowers the use threshold;

[0018] The secondary neutron source term caused by wafer proton irradiation is calculated by using the Monte Carlo method, the neutron extraction cross section method is applied to the secondary radiation calculation, and compared with the traditional method, the application scope of the method is wide.

[0019] In a further embodiment, the step 2 further comprises:

[0020] Step 21, the recorded secondary particle information is taken as a theoretical basis for calculating the source term in the next step from the Boltzmann equation, which describes that for a closed surface, the surface equivalent source strength can be:

[0021]

[0022] The calculation is performed;

[0023] In the formula, is the number of particles that can be understood in the scene on the closed surface and the number of particles that are incident and emitted;

[0024] S A (r s , E, Ω) is the set equivalent surface source strength;

[0025] r s , E, Ω respectively the position of a point on the surface source, particle energy, particle motion direction.

[0026] Step 22, the input and emitted particles on the equivalent surface source can be considered as only the inflow part, and the factors considered include:

[0027] 1. According to the method area division principle, the region calculated by the point kernel integration does not generate the source term of the particles;

[0028] 2. The contribution of the backscattered particles from the reflecting surface decreases inversely with the square of the distance, so the particle flow from the Monte Carlo method calculation region to the point kernel integration calculation region is ignored, and the equivalent source strength on this surface is understood as only the number of input particles, and the formula changes to:

[0029]

[0030] Therefore, in the calculation by using the Monte Carlo method, according to the above formula, the number of neutrons, energy, and azimuth angle of the spherical detector need to be recorded when applying the method.

[0031] In a further embodiment, the step 3 further comprises:

[0032] Step 31, read the data calculated by Monte Carlo method to proceed the next radiation field calculation by using the method of neutron leakage cross section, which is one of the point kernel integration methods, and its most important feature is high calculation speed, and its principle can be explained by the following description;

[0033] Step 32, under the shielding of multi-layer heavy material and hydrogen-containing material, the neutron dose equivalent rate of isotropic point source at the dose point can be expressed as

[0034]

[0035] Where S is the neutron source intensity, t i is the shielding thickness of the i-th layer of heavy material, Σ R,i is the leakage cross section of the i-th layer of heavy material relative to the source neutrons;

[0036] is the dose equivalent rate attenuation factor of neutrons in hydrogen-containing medium, whose value is calculated by:

[0037]

[0038] Where E0 is the source neutron energy, E0 is the lower limit of fast neutron energy, Σ t,H is the total cross section of neutron collision with hydrogen, R is the penetration distance of neutrons in hydrogen medium, K H is the neutron fluence rate to dose equivalent rate conversion coefficient (ICRP Report 74 provides data for calculation);

[0039] Step 33, under the shielding of a shielding body uniformly mixed with hydrogen-containing material and other heavy materials, the neutron dose equivalent rate of an isotropic point source at the dose point is:

[0040]

[0041] Where f H (r) is the dose equivalent rate attenuation factor of fast neutrons in pure hydrogen medium with equivalent bulk density, A i , ρ i , σ R,i are the atomic weight, density and microscopic leakage cross section of the i-th element in the mixture except hydrogen, N A is Avogadro's constant;

[0042] Step 34, for a multi-layer combined shielding and an isotropic neutron point source with an arbitrary energy spectrum S(E0), the neutron dose equivalent rate at the dose point r is:

[0043]

[0044] Where, Σ​R The macroscopic removal cross section of a material in a hydrogenous medium;

[0045] Step 35, in the neutron dose calculation model, the key physical quantity is the removal cross section, which involves the physical process that when fast neutrons travel forward in the shielding material, the energy decreases due to non-elastic collision and "large angle" elastic collision with the atomic nucleus in the shielding material, so that fast neutrons with energy greater than a certain threshold value have been separated from the original energy group before reaching the detection point, so the removal cross section is approximately equal to:

[0046] Σ R = Σ t -f Σ es

[0047] In the formula, Σ R is the macroscopic removal cross section (unit: cm -1 ), Σ t is the total cross section (unit: cm -1 ), Σ es is the elastic scattering cross section (unit: cm-1), and f is a correction factor less than 1, which is the forward scattering part in the elastic scattering angle distribution.

[0048] The removal cross section can be calculated by some empirical expressions that depend on the total cross section Σ, the atomic number Z or the atomic mass number A of the material, etc. The program empirical formula is:

[0049]

[0050] For compounds and mixtures, the removal cross section is calculated by:

[0051]

[0052] In the formula, ρ is the density of the mixture (unit: g·cm -3 ), N A is the Avogadro constant, A i is the atomic weight of the i-th element, f i is the mass percentage of the i-th element, σ Ri is the microscopic removal cross section (b) of the i-th element.

[0053] Step 36, in the final integration, the dose is integrated and calculated, which involves volume integration and energy integration.

[0054] ​Volume integral method: for the radiation source term, the surface or volume thereof is divided into NS source term grids, the geometric center of each grid is taken, the source term intensity on the grid is concentrated on the geometric center, thereby forming a point source set, and based on the calculation model of the gamma and neutron point source, for a certain measuring point, the dose of each point source on the measuring point is accumulated, that is, the fluence rate or dose rate of the source term at the measuring point is obtained; in the application, the neutron irradiation caused by wafer proton irradiation is approximated as an isotropic point source, therefore, the volume of the radiation source in the application can be ignored.

[0055] Energy integration processing: the neutron energy spectrum is discretized into NG energy groups, the fluence rate or dose rate of the source term of each energy group at the measuring point is calculated, the fluence rate and dose rate of the source term at the measuring point are obtained, and the fluence rate is taken as an example and expressed as:

[0056]

[0057] wherein, is the fluence rate of the source term of the jth energy group of the ith point source at the measuring point;

[0058] Step 37: since in wafer proton irradiation, according to the estimation method given in 'Radiation Shielding Specification for Radiotherapy Machine Room Part 5: Proton Accelerator Radiotherapy Machine Room' (GBZT 201.5-2015), when the distance between the point of interest and the beam loss point is much larger than the geometric size of the beam loss point (more than 7 times), the target can be regarded as a point source;

[0059] Therefore, in the application, the volume of the radiation source can be ignored, and the integral relationship is changed to a single energy integration, which is changed to: The calculation of the neutron radiation field is completed.

[0060] Beneficial effects: the application discloses a secondary neutron radiation field fast calculation method in a wafer proton irradiation process, the application can significantly improve the calculation speed of the radiation field by coupling two methods, and the calculation speed is improved by more than 100 times in some scenarios;

[0061] Through the coupling calculation of the neutron separation cross section method, the use of the Monte Carlo database is reduced, the high-difficulty modeling requirement of the Monte Carlo method is avoided, and the use threshold is reduced;

[0062] The secondary neutron source term caused by wafer proton irradiation is calculated by using the Monte Carlo method, the neutron separation cross section method is applied to the secondary radiation calculation, and compared with the traditional method, the application has a wide application range. BRIEF DESCRIPTION OF DRAWINGS

[0063] Figure 1 It is a schematic diagram for calculating the secondary neutron yield by using the Monte Carlo method.​

[0064] Figure 2 Geometric diagram of the calculation model.

[0065] Figure 3 Dose distribution map of the secondary neutron radiation field calculated by the present application.

[0066] Figure 4 Dose distribution map of the secondary neutron radiation field calculated by the prior art.

[0067] The reference signs are:

[0068] A, wafer; B, concrete wall; C, irradiation room. DETAILED DESCRIPTION

[0069] The present application relates to a method for rapidly calculating the secondary neutron radiation field in the process of wafer proton irradiation, which will be explained in detail through specific embodiments.

[0070] In wafer proton irradiation, due to the weak penetration ability of protons, the radiation dose of neutrons and photons generated by nuclear reactions is often considered when performing environmental evaluation, but the traditional method has difficulties in calculating the secondary radiation field.

[0071] In order to solve the above-mentioned difficulties, the present application proposes a method for efficiently calculating the secondary neutron radiation field caused in wafer proton irradiation, which overcomes the deficiencies of traditional radiation field calculation methods in calculation efficiency and accuracy.

[0072] In order to rapidly evaluate the influence of radiation on instruments and personnel, the method combines the Monte Carlo method with the neutron division cross-section method.

[0073] The specific embodiments and cases adopted by the present application to solve the above-mentioned technical problems are as follows:

[0074] (1) Establish the calculation part of the Monte Carlo model.

[0075] Place the wafer horizontally at the geometric center of the space, and use a spherical detector to completely wrap the wafer chip. During simulation calculation, the proton beam directly hits the wafer from the vertical direction, and the entire secondary neutron number calculation model is in a vacuum region to reduce the scattering, attenuation and other material effects of protons in the air.

[0076] (2) Record the secondary neutrons

[0077] The spherical detector around the wafer adopts a dot matrix structure, which is composed of multiple small detectors. Each small detector independently records the number, energy and direction of neutrons entering the small detector, and outputs.

[0078] (3) Establish the calculation part of the division cross-section method model

[0079] In the present application, the main radiation field calculation is calculated by the outscattering cross section method, which is a high-efficiency radiation calculation method. In the calculation, first, a geometric model is established, a three-dimensional rectangular coordinate system is developed by using a programming language FORTRAN, and a geometric model in an actual wafer irradiation space, such as a wall, a pipeline, etc., is established according to an algorithm.

[0080] (4) Calculation of outscattering cross section

[0081] In the present application, the most important outscattering cross section is an important parameter for describing the neutron reaction process in the outscattering cross section method, and the accuracy directly affects the calculation accuracy of the outscattering cross section method. In the present application, the outscattering cross section is preliminarily calculated by an empirical formula and iteratively calculated by using a Monte Carlo method.

[0082] (5) Calculation of secondary neutron radiation field

[0083] After the calculation of the secondary neutron yield in the early stage is completed, all data are imported into the calculation of the outscattering cross section method, the dose of the radiation field in the region is calculated according to the outscattering cross section of the existing model, the number of neutrons, etc., calculated by the Monte Carlo method, and a reference for the radiation influence on personnel and equipment is provided.

[0084] The present application will be further described below in combination with specific implementation cases.

[0085] Traditional single radiation calculation methods, such as the Monte Carlo method, the discrete ordinate method, and the point kernel integration method, have different applicability in radiation source terms, particles, and geometric environments. The Monte Carlo method, as a common radiation simulation means, has the greatest advantage in handling complex geometric problems, such as irregular geometric shapes or irregular radioactive source terms. However, the biggest problem in using the Monte Carlo method to calculate radiation is that the method requires a large amount of simulation time to obtain reliable results. Especially when the shielding body is thick or the space is large, the Monte Carlo method needs a large amount of time to reduce the error. This makes the method not suitable for some radiation scenes that need to be calculated quickly. The discrete ordinate method has a unique advantage in calculating deep penetration problems, but according to the use of many researchers, the calculation result error of the discrete ordinate method depends on its parameters, and the ray effect of the method affects the calculation accuracy. The point kernel integration is a traditional radiation dose level calculation means and is widely used in radiation calculation process. As a deterministic method, the method can quickly calculate the radiation field, but because the method uses many empirical parameters, the accuracy of the method is difficult to effectively guarantee in some complex use scenarios, such as complex geometric models or complex radioactive source terms.

[0086] The application provides a secondary neutron radiation field fast calculation method in a wafer proton irradiation process, and is used for solving the above problems and comprises the following steps:

[0087] Step 1, establishing a Monte Carlo program source item calculation region, a geometric model of a wafer bombarded by a proton beam is established by using a Monte Carlo program to simulate a proton accelerator irradiation process;

[0088] Step 2, a spherical detector is used to coat the wafer, the energy spectrum, the particle number and the direction information of the secondary neutrons are recorded, and the secondary neutrons are used as source items for subsequent calculation, and the next step is calculated;

[0089] Step 3, the dose influence in the space and outside the shielding wall is calculated by using a neutron division cross section method according to the existing source item information.

[0090] The application can significantly improve the calculation speed of the radiation field by coupling two methods, and the calculation speed of some scenes is improved by more than 100 times;

[0091] By coupling calculation of the neutron division cross section method, the use of the Monte Carlo database is reduced, the high-difficulty modeling requirement of the Monte Carlo method is avoided, and the use threshold is reduced;

[0092] The secondary neutron source item caused by wafer proton irradiation is calculated by using the Monte Carlo method, the neutron division cross section method is applied to the secondary radiation calculation, and compared with the traditional method, the application has a wide application range.

[0093] The step 2 further comprises the following steps.

[0094] Step 21, the recorded secondary particle information is used as a theoretical basis for source item calculation in the next step, which is derived from a Boltzmann equation, and the equation describes that for a closed surface, the surface equivalent source strength can be calculated by:

[0095]

[0096] The calculation is performed.

[0097] In the formula, is the number of particles entering and exiting the closed surface in the scene;

[0098] S A (r s ,E,Ω) is a set equivalent surface source strength;

[0099] r s ,E,Ω are respectively a position of a point on the surface source, a particle energy and a particle motion direction.

[0100] Step 22, the input and exiting particles on the equivalent surface source can be regarded as only the inflow part, and the factors to be considered include:

[0101] 1、According to the method area division principle, the region calculated by point kernel integration does not generate particle source term;

[0102] 2、The contribution of backscattered particles from the reflecting surface decreases inversely with the square of the distance, so the particle flux of the region calculated by point kernel integration is negligible compared to the Monte Carlo method, and the equivalent source strength on this surface is understood to be only the number of input particles, and the formula changes to:

[0103]

[0104] Therefore, in the Monte Carlo method calculation, according to the above formula, the number of neutrons, energy, and azimuth angle of the spherical detector need to be recorded when applying this method.

[0105] The step 3 further includes:

[0106] Step 31, read the Monte Carlo method calculation data for the next radiation field calculation using the neutron division cross section method, which is one of the point kernel integration methods, and its most important feature is high calculation speed, and its method principle can be explained by the following description:

[0107] Step 32, under the shielding of multiple heavy materials and hydrogen-containing materials, the neutron dose equivalent rate of an isotropic point source at a dose point can be expressed as

[0108]

[0109] In the formula, S is the neutron source strength, t i is the shielding thickness of the i-th layer of heavy material, Σ R,i is the division cross section of the i-th layer of heavy material relative to the source neutrons;

[0110] is the dose equivalent rate attenuation factor of neutrons in hydrogen-containing media, which is calculated by:

[0111]

[0112] In the formula, E0 is the source neutron energy, E0 is the lower limit of fast neutron energy, Σ t,H is the total cross section of neutron and hydrogen collision, R is the penetration distance of neutron in hydrogen medium, K H is the neutron fluence rate to dose equivalent rate conversion coefficient (ICRP Report 74 provides data for calculation);

[0113] Step 33, under the shielding of a shielding body uniformly mixed with hydrogen-containing materials and other heavy materials, the neutron dose equivalent rate of an isotropic point source at a dose point is:

[0114] ​

[0115] where f H (r) is the fast neutron dose equivalent rate attenuation factor in a pure hydrogen medium of equivalent macroscopic density, A i , p i , σ R , i are the atomic weight, density and microscopic cross section of the i-th element in the mixture except hydrogen, N A is the Avogadro constant;

[0116] Step 34, for a multi-layer combined shield and an isotropic neutron point source with arbitrary energy spectrum S(E0), the neutron dose equivalent rate at the dose point r is:

[0117]

[0118] where ∑ R is the macroscopic cross section (unit cm R -1) of the material except hydrogen in the hydrogen-containing medium;

[0119] Step 35, in the neutron dose calculation model, the key physical quantity is the macroscopic cross section, which involves the physical process that when a fast neutron travels forward in the shielding material, its energy decreases due to non-elastic collision and "large-angle" elastic collision with the atomic nucleus in the shielding material, so that the fast neutron with energy greater than a certain threshold value has been separated from the original energy group before reaching the detection point, so the macroscopic cross section is approximately equal to:

[0120] ∑ t =∑ es

[0121] where ∑ R is the macroscopic cross section (unit cm -1 -1), ∑ t is the total cross section (unit cm -1 -1), ∑ es is the elastic scattering cross section (unit cm-1), and f is a correction factor less than 1, which is the fraction of forward scattering in the elastic scattering angular distribution;

[0122] The macroscopic cross section can be calculated by some empirical expressions that depend on the total cross section ∑, the atomic number Z or the atomic mass number A of the material, etc. The program empirical formula is:

[0123]

[0124] For compounds and mixtures, the macroscopic cross section is calculated by:

[0125] ​

[0126] wherein, p is the density of the mixture (unit g·cm -3 ), N A is the Avogadro constant, A i is the atomic weight of the i-th element, f i is the mass percentage of the i-th element, σ Ri is the microscopic cross section of the i-th element (b);

[0127] Step 36, in the final integration, the dose is integrated, which involves volume integration and energy integration;

[0128] Volume integration method: for the radiation source term, its surface or volume is divided into NS source term grids, the geometric center of each grid is taken, and the source term intensity on the grid is concentrated on the geometric center, thereby forming a point source set, and based on the calculation model of gamma and neutron point sources, for a certain measuring point, the dose of each point source on the measuring point is accumulated, that is, the fluence rate or dose rate of the source term at the measuring point is obtained; in the present application, the neutron irradiation caused by wafer proton irradiation is approximately isotropic point source, therefore, the volume of the radiation source in the present application can be ignored.

[0129] Energy integration processing: the neutron energy spectrum is discretized into NG energy groups, and the fluence rate or dose rate of the source term of each energy group at the measuring point is calculated, thereby obtaining the fluence rate and dose rate of the source term at the measuring point, and the fluence rate For example, it is expressed as:

[0130]

[0131] wherein, is the fluence rate of the j-th energy group of the i-th point source at the measuring point;

[0132] Step 37, in wafer proton irradiation, according to the estimation method given in “Radiation Shielding Specification for Radiotherapy Machine Room Part 5: Proton Accelerator Radiotherapy Machine Room” (GBZT 201.5-2015), when the distance between the point of interest and the beam loss point is much larger than the geometric size of the beam loss point (more than 7 times), the target can be regarded as a point source;

[0133] Therefore, in the present application, the volume of the radiation source can be ignored, and the integral relationship is changed to a single energy integration, which is changed to: The calculation of the neutron radiation field is completed.

[0134] Embodiment

[0135] I. Technical problems to be solved:

[0136] In a certain scenario of irradiation, in order to evaluate the dose influence of neutrons generated by 9 MeV proton bombardment on wafers on instrument equipment and staff outside the irradiation hall, it is necessary to quickly calculate the neutron radiation field in the process.

[0137] Secondly, the open source Monte Carlo program GEANT4 (Geometry ANd Tracking 4) developed by CERN (European Organization for Nuclear Research) and the neutron radiation field split cross section calculation program NRFC (Neutron Radiation Field Calculation Program) independently developed are used.

[0138] The calculation platform is AMD Ryzen 97945HX.

[0139] Thirdly, results

[0140] According to the flow in the application, the dose results are calculated step by step. The results show that, under the same calculation scenario, the traditional Monte Carlo calculation method needs more than 20 hours to calculate the complete results in the multi-thread parallel case (30 threads), which is far from the planned rapid calculation requirement. In contrast, under the same calculation condition (30 threads), the radiation field calculation results can be obtained in only 10 minutes by using the calculation method in the application, which greatly improves the calculation speed. On the other hand, the deviation of the calculation method in the application is controlled to be less than 30%, which is slightly larger than the traditional method, which is conservative in the field of radiation protection and is more acceptable.

[0141] Working principle: Establish the source term calculation region of the Monte Carlo program, use the Monte Carlo program to establish the geometric model of the proton beam bombarding the wafer to simulate the proton accelerator irradiation process; use the program to establish a spherical detector covering the wafer, record the energy spectrum, particle number and direction information of the secondary neutrons, and use them as the source term for the next calculation, and then perform the next calculation; use the neutron split cross section method to calculate the dose influence in the space and outside the shielding wall according to the existing source term information.

[0142] The preferred specific embodiments of the application are described in detail above in combination with the drawings, but the application is not limited to the specific details in the above specific embodiments, and various equivalent transformations can be made to the technical solutions of the application within the technical concept of the application, and these equivalent transformations all belong to the protection scope of the application.

Claims

1. A method for fast calculation of secondary neutron radiation field in wafer proton irradiation process, comprising: Step 1, establishing a Monte Carlo program source term calculation region, using a Monte Carlo program to establish a geometric model of a proton beam bombarding a wafer to simulate a proton accelerator irradiation process; Step 2, using the program to establish a spherical detector covering the wafer, recording the energy spectrum, particle number and direction information of the secondary neutrons, and taking them as the source term for subsequent calculation, and performing the next step of calculation; Step 3, using the neutron division cross section method to calculate the dose influence in the space and outside the shielding wall according to the existing source term information; The step 3 further comprises: Step 31, using the neutron division cross section method to read the data calculated by the Monte Carlo method for the next step of radiation field calculation; Step 32, under the shielding of a combination of multiple heavy materials and hydrogen-containing materials, the neutron dose equivalent rate of an isotropic point source at a dose point can be expressed as ； wherein S is the neutron source strength, t i is the first i is the shielding thickness of the layer of heavy material, Σ R,i is the first i is the removal cross section of the layer of heavy material relative to the source neutrons; Dose equivalent rate reduction factor for neutrons in hydrogenous media, whose value is given by: computing; wherein E 0 is the source neutron energy, E 0 is the lower limit of fast neutron energy, Σ t,H is the total cross section for neutron-hydrogen collisions, R is the neutron penetration distance in a hydrogen medium, K H is the neutron fluence-to-dose-equivalent conversion coefficient; Step 33, under the shielding of a shielding body uniformly mixed with hydrogen-containing materials and other heavy materials, the neutron dose equivalent rate of an isotropic point source at a dose point is: ； In the formula, f H (r) is the dose-equivalence attenuation factor for fast neutrons in pure hydrogen media of equivalent volume density. A i , The step 2 further comprises: i , Boltzmann R,i The first, excluding hydrogen, of the mixed weight i Atomic weight, density, and microscopic separation cross-section of the elements. N A It is Avogadro's constant; Step 34, for a multi-layer combined shielding and isotropic neutron point source with arbitrary energy spectrum S ( E 0) at the dose point r is: ； wherein ,∑ R is the out-scattering cross section of the material in the hydrogenous medium other than hydrogen.

2. The method of claim 1, wherein the method further comprises: determining the secondary neutron fluence rate at the wafer surface based on the secondary neutron fluence rate at the wafer surface and the wafer surface area. The calculation is performed; Step 21, the recorded secondary particle information is used as the theoretical basis for calculating the source term in the next step The step 2 further comprises: Equation, in which the surface equivalent source strength for a closed surface is described by: ； Step 22, the input and emitted particles on the equivalent surface source can be considered as only the inflow part, and the factors considered include: wherein , is the number of particles that are incident on and emergent from the closed curved surface in the scene; for a set equivalent plane source intensity; respectively, the position of a certain point on the surface source, the particle energy, and the particle motion direction.

3. The method of claim 1, wherein the method further comprises: calculating the secondary neutron fluence rate at the wafer surface using the following equation: ###0002### where: φ is the secondary neutron fluence rate at the wafer surface; E is the neutron energy; and φ0 is the primary neutron fluence rate at the wafer surface.

1. According to the method area division principle, the region calculated by the point kernel integration does not generate a source term of particles; 2. The contribution of backscattered particles from the reflection surface decreases inversely with the square of the distance, so the particle flow from the point kernel integration calculation region to the Monte Carlo method calculation region is ignored, and the equivalent source strength on this curved surface is understood as only the number of input particles, and the formula changes to: Therefore, in the Monte Carlo method calculation, according to the above formula, the number of neutrons, energy, and azimuth angle of the spherical detector need to be recorded. The step 3 further comprises: ； Step 35, in the neutron dose calculation model, the key physical quantity is the division cross section, which is approximately equal to:

4. The method of claim 1, wherein the method further comprises: calculating the secondary neutron fluence rate at the wafer surface using the following equation: ###0002### where: φ is the secondary neutron fluence rate at the wafer surface; E is the neutron energy; and φ0 is the primary neutron fluence rate at the wafer surface. For compounds and mixtures, the division cross section is obtained by: The step 3 further comprises: ； where Σ R is the macroscopic removal cross section, Σ t is the total cross section, Σ es is the elastic scattering cross section, f is a correction factor less than 1, being the fraction of the elastic scattering angular distribution that scatters forward; The partial cross section is calculated by an empirical expression depending on the total cross section Σ, the atomic number or the atomic mass number of the material Z A The program empirical formula is:​ ； Step 36, in the final integration, the dose is integrated and calculated, which involves volume integration and energy integration; computing; wherein NS is the mixture density, N A is the Avogadro constant, A i is the atomic weight of the i element, f i is the mass percentage of the i element, NG Ri is the microscopic cross section of the i element.

5. The method of claim 1, wherein the method further comprises: calculating the secondary neutron fluence rate at the wafer surface using the following equation: ###0002### where: φ is the secondary neutron fluence rate at the wafer surface; E is the neutron energy; and φ0 is the primary neutron fluence rate at the wafer surface. The step 3 further comprises: Step 37, when the distance between the point of interest and the beam loss point is much larger than the geometric size of the beam loss point, the target is regarded as a point source; Volume integral method: for the radiation source term, divide its surface or volume into ​ source term grids, take the geometric center of each grid, concentrate the source term intensity on the grid on the geometric center, thereby forming a point source set, and based on the calculation model for gamma and neutron point sources, for a certain measuring point, add up the dose of each point source on it, that is, the fluence rate or dose rate of the source term at the measuring point is obtained; Treatment of energy integration: Discretize the neutron energy spectrum into ​ groups, calculate the fluence rate or dose rate at the measuring point for each energy group respectively, and obtain the fluence rate and dose rate of the source term at the measuring point. Take the fluence rate as an example, and express it as: ​ ​ ； in, ​ ij It is the first i The first point source j Flux rate of the source term of an energy group at the measurement point.

6. The method for rapid calculation of secondary neutron radiation field during wafer proton irradiation according to claim 1, characterized in that: ​ ​ Therefore, the volume of the source is ignored, and the integral relation becomes a single energy integral, which is changed to: , which completes the calculation of the neutron radiation field.

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