Method for calculating non-ionizing energy loss induced by nuclear reactions in semiconductor materials

Abstract

The present application relates to a kind of non-ionizing energy loss calculation method of nuclear reaction induced in semiconductor material, when simulating the nuclear reaction of radiation particle and semiconductor material using Monte Carlo program, by setting the bias factor b of nuclear reaction cross section, make nuclear reaction cross section increase to actual b times, ensure that sufficient nuclear reaction event number is obtained in very thin semiconductor material target, which can make the non-ionizing energy loss calculated more accurate.The present application can obtain sufficient nuclear reaction event number in shorter simulation time, so that more accurate non-ionizing energy loss induced by nuclear reaction of proton in semiconductor material can be obtained more efficiently.The method can not only be used for the simulation calculation of non-ionizing energy loss induced by nuclear reaction of proton in semiconductor material, but also be suitable for the simulation calculation of non-ionizing energy loss induced by nuclear reaction of neutron, alpha particle or heavy ion in semiconductor material.

Description

Technical Field

[0001] This invention belongs to the field of radiation effects in electronic devices, and specifically relates to a method for calculating non-ionizing energy loss caused by nuclear reactions of protons or other particles in semiconductor materials based on Monte Carlo simulation. Background Technology

[0002] When space radiation particles enter the spacecraft cabin and collide with the lattice atoms inside semiconductor devices, they cause displacement and lattice defects, leading to gradual degradation or even failure of device performance—a phenomenon known as displacement damage. This poses a significant threat to the safe and reliable operation of spacecraft in orbit. Displacement damage in semiconductor devices under irradiation primarily depends on the displacement energy loss deposited within the sensitive volume. Non-ionizing energy loss (NIEL) is a physical quantity describing the energy loss caused by lattice atom displacement due to Coulomb scattering and nuclear reactions as particles pass through a unit length of material. Numerous experimental studies have shown that for most semiconductor devices, the performance changes caused by displacement damage and NIEL exhibit a linear relationship regardless of the type of incident particle. By calculating the NIEL of specific particles with different energies in the device material, the performance changes of the device under different particle irradiations can be evaluated.

[0003] Protons are a major component of the space radiation environment and a primary factor causing displacement damage to semiconductor devices in space. Therefore, the Nitrogen Energy Filtering (NIEL) of protons in semiconductor materials such as silicon, germanium, and gallium is a physical quantity of considerable interest in the field of radiation effects. Typically, the NIEL caused by proton Coulomb scattering is calculated analytically, while the NIEL caused by nuclear reactions is calculated using Monte Carlo simulations. When simulating the interaction between protons and semiconductor materials using Monte Carlo programs such as MCNP and Geant4, a thin-target approximation is generally used for the semiconductor material. This means that, relative to incident protons of different energies, the geometric (cubic prism) thickness of the semiconductor material is 1 / 20–1 / 10 of the proton's range, and the length and width are 10 times the geometric thickness. To minimize energy attenuation during proton passage through the target material, the target material thickness must be as thin as possible; however, to obtain sufficient nuclear reaction events and reduce the statistical error of the final NIEL, the target material thickness cannot be too thin. Considering all factors, the aforementioned thin-target approximation method is generally used for nuclear reaction simulations.

[0004] The thin target approximation method still causes some attenuation of proton energy in the target, which will affect the accuracy of the calculated NIEL of monoenergetic protons. At the same time, for protons with small nuclear reaction cross sections, this thickness setting is still insufficient to simulate enough nuclear reaction events, resulting in low simulation efficiency. Summary of the Invention

[0005] This invention addresses the shortcomings of existing Monte Carlo simulation methods that use thin-target approximation to calculate the non-ionization energy loss induced by nuclear reactions in semiconductor materials, which suffer from insufficient accuracy and simulation efficiency. It provides an improved Monte Carlo simulation method to calculate the non-ionization energy loss induced by nuclear reactions in semiconductor materials, thereby efficiently simulating nuclear reaction events and obtaining more accurate non-ionization energy loss.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A method for calculating non-ionizing energy loss induced by nuclear reactions in semiconductor materials is proposed. This method, when simulating nuclear reactions between radiating particles and semiconductor materials using a Monte Carlo program, increases the nuclear reaction cross-section to b times the actual cross-section by setting a bias factor b. This ensures that a sufficient number of nuclear reaction events are obtained in an extremely thin semiconductor material target, improves simulation efficiency, and makes the calculated non-ionizing energy loss more accurate.

[0008] The nuclear reaction between the radiated particles and the semiconductor material includes: nuclear reactions between protons, neutrons, alpha particles or heavy ions and the semiconductor material.

[0009] Furthermore, the method for calculating the non-ionizing energy loss caused by nuclear reactions in semiconductor materials, as described above, taking the calculation of the non-ionizing energy loss caused by proton nuclear reactions in semiconductor materials as an example, specifically includes the following steps:

[0010] (1) In the Monte Carlo program, the geometric thickness h of the semiconductor material is set according to the incident proton energy E to ensure that the energy loss of the proton is minimal relative to E;

[0011] (2) Set the bias factor b of the nuclear reaction cross section to increase the nuclear reaction cross section to b times the actual value;

[0012] (3) The nuclear reaction event between protons and semiconductor materials was simulated using the Monte Carlo program. In the first round of simulation, the number of incident protons N was set to a number that could be simulated in a short time. The number of protons N that underwent the nuclear reaction was observed. r According to the proportion of protons that undergo nuclear reactions To adjust the nuclear reaction cross-section bias factor b, so that most of the incident protons can undergo nuclear reactions in the target;

[0013] (4) After adjusting the bias factor b of the nuclear reaction cross section, the incident proton number N is set to a large number to ensure that the number of simulated nuclear reaction events is sufficient to make the statistically calculated proton non-ionization energy loss relatively accurate. Monte Carlo simulation of the nuclear reaction between protons and semiconductor materials is performed, and the atomic number Z of each nuclear reaction product generated in the target is recorded. i Mass number A i and energy Ei The subscript i represents the i-th nuclear reaction product;

[0014] (5) Calculate the non-ionization energy loss caused by proton nuclear reactions in semiconductor materials using the following formula.

[0015]

[0016] Where NIEL is the non-ionization energy loss, ρ is the density of the semiconductor material, and Q is the energy loss. i The energy E of nuclear reaction products in semiconductor materials i The percentage used for non-ionization energy loss.

[0017] Furthermore, as a specific implementation, in step (1), the geometric thickness h can be set to less than one-thousandth of the range of a proton with energy E in the semiconductor material; the length and width of the semiconductor material target can be set to 10 times the thickness.

[0018] Specifically, the geometric thickness h can be set to less than or equal to 1 μm.

[0019] Furthermore, as a specific implementation, in step (2), the bias factor b should be set to meet the following conditions: bias is applied only to nuclear interactions and not to other interactions; bias is applied only to incident protons and not to secondary particles generated by the nuclear reaction between protons and semiconductor materials; bias is applied only to the first nuclear reaction of incident protons and not to incident protons after elastic scattering.

[0020] Furthermore, as a specific implementation method, in step (3), when adjusting the nuclear reaction cross section bias factor b, it should be ensured that not all incident protons undergo nuclear reaction.

[0021] Specifically, the bias factor b can be set to greater than or equal to 10. 5 .

[0022] Furthermore, as a specific implementation method, in step (4), the number of incident protons N can be set to be greater than or equal to 10. 6 .

[0023] Furthermore, as a specific implementation method, in step (5), Q i It can be calculated using the Lindhard separation function or a modified Lindhard separation function.

[0024] The beneficial effects of this invention are as follows: This invention ingeniously employs a nuclear reaction cross-section bias method to perform Monte Carlo simulations of nuclear reaction events between protons and semiconductor materials. The target can be set to be extremely thin, and a large bias factor is set to ensure a sufficient number of nuclear reaction events, effectively improving simulation efficiency. A sufficient number of nuclear reaction events can be obtained in a shorter simulation time. Simultaneously, the thin target setting makes the obtained non-ionization energy loss of protons more accurate, thus enabling more efficient and accurate acquisition of the non-ionization energy loss caused by nuclear reactions of protons in semiconductor materials. This method can not only be used to simulate the non-ionization energy loss caused by nuclear reactions of protons in semiconductor materials, but is also applicable to the simulation of the non-ionization energy loss caused by nuclear reactions of neutrons, alpha particles, and heavy ions in semiconductor materials. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating the method for calculating non-ionization energy loss caused by proton nuclear reactions in semiconductor materials in a specific embodiment of the present invention.

[0026] Figure 2 This is a schematic diagram of the non-ionization energy loss caused by the nuclear reaction of protons in silicon in the 10-1000MeV energy range in a specific embodiment of the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0028] This invention proposes to employ a nuclear reaction cross-section bias method to simulate the nuclear reaction between radiated particles and semiconductor materials, thereby calculating the non-ionizing energy loss induced by the nuclear reaction of radiated particles in the semiconductor material. When simulating the nuclear reaction between radiated particles and semiconductor materials using a Monte Carlo program, this method increases the nuclear reaction cross-section to a factor of b, ensuring a sufficient number of nuclear reaction events in an extremely thin semiconductor target, thus improving simulation efficiency and resulting in more accurate calculations of the non-ionizing energy loss. The nuclear reaction between radiated particles and semiconductor materials includes the nuclear reaction between protons, neutrons, alpha particles, or heavy ions and the semiconductor material.

[0029] Since protons are a major component of the space radiation environment and a primary factor causing displacement damage to semiconductor devices in space, the nuclear reaction cross-section bias method of this invention will be specifically described below using protons as an example. Those skilled in the art will understand that this method is also applicable to the simulation calculation of non-ionizing energy loss induced by nuclear reactions in semiconductor materials involving neutrons, alpha particles, and heavy ions.

[0030] like Figure 1 As shown, a method for calculating the non-ionizing energy loss (NIEL) induced by proton nuclear reactions in semiconductor materials is presented, with the following specific steps:

[0031] 1. Set the geometric thickness h of the semiconductor material according to the incident proton energy E to ensure that the energy loss of the proton in it is minimal relative to E. For example, h can be set to one-thousandth or even smaller of the range of a proton with energy E in the semiconductor material. The target length and width can be set to 10 times the thickness.

[0032] 2. In the Monte Carlo program, a bias factor *b* is set for the nuclear reaction cross-section, increasing it to *b* times the actual cross-section. This compensates for the drawback of a thin target and a low number of nuclear reaction events. Simultaneously, when setting *b*, the following conditions should be met: bias is applied only to nuclear interactions, not to other interactions such as electromagnetic interactions; bias is applied only to the incident protons, not to secondary particles generated by the nuclear reaction between protons and semiconductor materials; bias is applied only to the first nuclear reaction of the incident protons, not to the incident protons after elastic scattering.

[0033] 3. Develop a Monte Carlo simulation program to simulate nuclear reaction events between protons and semiconductor materials. In the first simulation, set the number of incident protons N to a number that can be simulated in a short time, and observe the number of protons N that undergo nuclear reaction. r According to the proportion of protons that undergo nuclear reactions The bias factor b of the nuclear reaction cross section is adjusted so that a significant portion of the incident protons can undergo nuclear reactions in the target, but not all of the incident protons will undergo nuclear reactions.

[0034] 4. After adjusting the bias factor b of the nuclear reaction cross section, the incident proton number N is set to a large number to ensure that the number of simulated nuclear reaction events is sufficient to make the statistical proton NIEL relatively accurate. Then, a Monte Carlo simulation is performed on the nuclear reaction between protons and semiconductor materials, and the atomic number Z of each nuclear reaction product produced within the target is recorded. i Mass number A i and energy E i , where the subscript i represents the i-th nuclear reaction product.

[0035] 5. The non-ionization energy loss caused by proton nuclear reactions in semiconductor materials is

[0036]

[0037] Where ρ is the density of the semiconductor material, Q i The energy E of nuclear reaction products in semiconductor materials i The percentage used for non-ionizing energy loss. Q iIt can be calculated using the Lindhard separation function or a modified Lindhard separation function.

[0038] Example

[0039] The following example, using the calculation of NIELs induced by proton nuclear reactions in silicon within the 10-1000 MeV energy range using the Geant4 program, illustrates the implementation process of this invention. A Geant4 program was developed, selecting incident proton energies of 10, 14, 20, 25, 30, 40, 50, 60, 70, 80, 90, 100, 150, 200, 230, 300, 500, 800, and 1000 MeV. The silicon target thickness was set to 1 μm, and the length and width of the silicon target were each set to 10 μm. The number of incident protons was set to 10. 6 The bias factor of the nuclear reaction cross section was set to 10. 5 Monte Carlo simulations showed that the number of nuclear reaction events occurring in a silicon target with protons of these energies was approximately 2.38 × 10⁻⁶. 5 Up to 5.12×10 5 In between, sufficient statistics on nuclear reaction events can be obtained, thus enabling a relatively accurate calculation of proton non-ionization energy loss. One simulation round is performed for each energy level, for a total of 19 rounds. Without using parallel simulation, the total simulation time is only about 4 hours, demonstrating high simulation efficiency.

[0040] In Monte Carlo simulations, the atomic number Z of each nuclear reaction product is... i Mass number A i and energy E i Record it down, and calculate the NIEL induced by the nuclear reaction of protons in silicon according to equation (1), where Q i The calculations were performed using the Robinson-modified Lindhard function, i.e., according to equations (2)-(5), where Z and A are the atomic number and mass number of silicon, respectively. The final calculated NIEL (Neural Energy Emission Rate) for proton nuclear reactions in silicon within the 10-1000 MeV energy range is shown below. Figure 2 As shown.

[0041]

[0042]

[0043]

[0044]

[0045] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. Thus, the invention also intends to include such variations and adaptations if they fall within the scope of the claims and their equivalents.

[0046] The above embodiments are merely illustrative examples of the present invention. The present invention may also be implemented in other specific ways or forms without departing from its spirit or essential characteristics. Therefore, the described embodiments should be considered illustrative rather than limiting in any respect. The scope of protection of the present invention should be defined by the claims, and any variations equivalent to the intent and scope of the claims should also be included within the scope of the present invention.

Claims

1. A method for calculating non-ionizing energy loss caused by nuclear reactions in semiconductor materials, characterized in that: This method, when simulating the nuclear reaction between radiated particles and semiconductor materials using a Monte Carlo program, increases the nuclear reaction cross-section to a factor of b, ensuring a sufficient number of nuclear reaction events in an extremely thin semiconductor target. This improves simulation efficiency and makes the calculated non-ionizing energy loss more accurate. The calculation of the non-ionizing energy loss caused by proton nuclear reactions in semiconductor materials includes the following steps: (1) In the Monte Carlo program, the geometric thickness h of the semiconductor material is set according to the incident proton energy E to ensure that the energy loss of the proton is minimal relative to E; (2) Set the bias factor b of the nuclear reaction cross section to increase the nuclear reaction cross section to b times the actual value; (3) The nuclear reaction event between protons and semiconductor materials was simulated using the Monte Carlo program. In the first round of simulation, the number of incident protons N was set to a number that could be simulated in a short time. The number of protons N that underwent the nuclear reaction was observed. r According to the proportion of protons that undergo nuclear reactions To adjust the nuclear reaction cross-section bias factor b, so that most of the incident protons can undergo nuclear reactions in the target; (4) After adjusting the bias factor b of the nuclear reaction cross section, the incident proton number N is set to a large number to ensure that the number of simulated nuclear reaction events is sufficient to make the statistically calculated proton non-ionization energy loss relatively accurate. Monte Carlo simulation of the nuclear reaction between protons and semiconductor materials is performed, and the atomic number Z of each nuclear reaction product generated in the target is recorded. i Mass number A i and energy E i The subscript i represents the i-th nuclear reaction product; (5) Calculate the non-ionization energy loss caused by proton nuclear reactions in semiconductor materials using the following formula. Where NIEL is the non-ionization energy loss, ρ is the density of the semiconductor material, and Q is the energy loss. i The energy E of nuclear reaction products in semiconductor materials i The percentage used for non-ionization energy loss.

2. The method for calculating non-ionizing energy loss caused by nuclear reactions in semiconductor materials as described in claim 1, characterized in that, The nuclear reaction between the radiated particles and the semiconductor material includes: nuclear reactions between protons, neutrons, alpha particles or heavy ions and the semiconductor material.

3. The method for calculating non-ionizing energy loss caused by nuclear reactions in semiconductor materials as described in claim 1, characterized in that, In step (1), the geometric thickness h is set to be less than one-thousandth of the range of a proton with energy E in the semiconductor material.

4. The method for calculating non-ionizing energy loss caused by nuclear reactions in semiconductor materials as described in claim 1, characterized in that, In step (2), the bias factor b should be set to meet the following conditions: bias is applied only to nuclear interactions and not to other interactions; bias is applied only to incident protons and not to secondary particles generated by the nuclear reaction between protons and semiconductor materials; bias is applied only to the first nuclear reaction of incident protons and not to incident protons after elastic scattering.

5. The method for calculating non-ionizing energy loss caused by nuclear reactions in semiconductor materials as described in claim 1, characterized in that, In step (3), when adjusting the nuclear reaction cross section bias factor b, it should be ensured that not all incident protons undergo nuclear reaction.

6. The method for calculating non-ionizing energy loss induced by nuclear reactions in semiconductor materials as described in claim 5, characterized in that, The bias factor b is set to greater than or equal to 10. 5 .

7. The method for calculating non-ionizing energy loss induced by nuclear reactions in semiconductor materials as described in claim 1, characterized in that, In step (4), the number of incident protons N is set to be greater than or equal to 10. 6 .

8. The method for calculating non-ionizing energy loss induced by nuclear reactions in semiconductor materials as described in claim 1, characterized in that, In step (5), Q i The calculation is performed using the Lindhard separation function or a modified Lindhard separation function.

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