A fast analysis method of single event upset of SRAM caused by MeV energy region protons

Abstract

The application discloses a quick analysis method for single event upset of SRAM caused by MeV energy area protons, and the method comprises the following steps: establishing a target material geometric model according to a device structure of the SRAM; constructing a material parameter database; adopting a hybrid algorithm combining a continuous energy loss model and a discrete scattering model, iteratively simulating a transport process of protons in the target material geometric model and obtaining total energy deposition of the protons in a sensitive volume on the basis of the material parameter database; comparing the total energy deposition of each proton in the sensitive volume with a preset energy deposition threshold value, and if the total energy deposition exceeds the threshold value, determining that a single event upset event occurs, and counting a total number of events; and obtaining a single event upset cross section on the basis of the total number of events, a total number of incident protons, a total number of bits of the SRAM and a surface area of the target material geometric model.

Description

Technical Field

[0001] This invention belongs to the field of particle physics technology, and in particular relates to a rapid analysis method for single-particle flipping of SRAM caused by protons in the MeV energy region. Background Technology

[0002] The Earth's radiation belts and the surrounding space environment contain a large number of energetic protons, with energies ranging from tens of keV to hundreds of MeV. This energetic proton radiation can cause single-event effects, such as single-event upsets (SEUs), in aerospace electronic devices (e.g., SRAMs), affecting the accurate execution of space missions and even leading to spacecraft malfunctions. With technological advancements, the size of aerospace electronic devices is continuously decreasing, and information storage areas are becoming increasingly compact, further increasing the devices' sensitivity to SEUs. Prolonged exposure to space radiation makes the cumulative effects of SEUs significant enough to have a profound impact on the performance and reliability of aerospace equipment.

[0003] Currently, the most commonly used method for radiation dose calculation and radiation effect assessment by technicians is Monte Carlo (MC) simulation based on large-sample sampling. Its accuracy depends on the number of sampling iterations; generating a sufficiently large number of random samples is a prerequisite for MC calculations. Meanwhile, as the size of electronic device storage structures decreases, the effective sampling probability of radiation tracks further declines. To achieve the expected confidence level in calculating the cross-section of electronic devices experiencing SEUs (Self-Enhancing U-turns) caused by space radiation, the computational burden of traditional MC simulations is constantly increasing.

[0004] Therefore, how to provide an analytical method that can quickly and efficiently calculate the probability of single-particle flipping of SRAM caused by protons in the MeV energy region while ensuring the necessary accuracy is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention proposes a rapid analysis method for single-particle flipping of SRAM caused by protons in the MeV energy region.

[0006] The technical solution of the present invention is as follows:

[0007] A rapid analytical method for single-particle flipping of SRAM caused by protons in the MeV energy range includes the following steps:

[0008] Based on the device structure of SRAM, a geometric model of the target material including the capping layer and the sensitive volume is established;

[0009] Construct a material parameter database containing key performance parameters of target materials corresponding to different material types. The key performance parameters include at least target density, radiation length, and stopping power as a function of energy. The material types include at least the materials corresponding to the capping layer and the sensitive volume.

[0010] A hybrid algorithm combining a continuous energy loss model based on stopping ability and a discrete scattering model based on scattering angle sampling is used to iteratively simulate the transport process of protons in the target geometry model and obtain the total energy deposition in the sensitive volume based on the material parameter database.

[0011] The total energy deposition of each proton in the sensitive volume is compared with a preset energy deposition threshold. If the threshold is exceeded, a single-particle flip event is determined to have occurred, and the total number of events is counted.

[0012] Based on the total number of events, the total number of incident protons, the total number of bits in the SRAM, and the surface area of ​​the target geometry model, the single-particle flip-off cross section is obtained.

[0013] Furthermore, the stopping power among the key performance parameters is constructed using an interpolation function with proton energy as the independent variable.

[0014] Furthermore, the target geometric model is established through the following specific methods: analyzing the structure of the SRAM to construct a target geometric model including the capping layer and the sensitive volume; determining the material composition and geometric dimensions of each layer of the target geometric model based on the structure of the SRAM; creating corresponding cuboid models for each layer based on the determined geometric dimensions; translating and splicing each cuboid model along the incident direction to form a complete target geometric model.

[0015] Furthermore, the expression for the continuous energy loss model based on stopping ability is: In the formula, This represents energy loss per step. To determine the energy of the proton in the current step The ability to query and normalize density from a material parameter database; This is the single-step step size.

[0016] Furthermore, the expression for the discrete scattering model based on scattering angle sampling is: In the formula, The standard deviation of the scattering angle; It is megaelectron volts; Momentum; For particles relative to the speed of light speed; The speed of light; This is the theoretical step size for the current step of the proton; The length of the radiation; The energy of the proton at the current step; a and b are the first and second influencing parameters, respectively; It is a low-energy correction factor;

[0017] Furthermore, the specific method of the hybrid algorithm includes:

[0018] An iterative simulation of the transport process of the incident proton in the target geometry model is performed. In each iteration, the material type and current energy of the target are first determined based on the current position of the proton, and the target density, radiation length and stopping power based on the current energy are obtained from the material parameter database.

[0019] Subsequently, the estimated new energy is calculated based on the preset energy loss ratio, and the theoretical step length corresponding to the decrease of the proton energy from the current value to the new energy is calculated by the integral range formula according to the stopping power value.

[0020] Next, based on the radiation length, theoretical step size and current momentum of the proton, the standard deviation of the scattering angle is calculated through the discrete scattering model, and the scattering angle is obtained by Gaussian sampling. At the same time, the azimuth angle is obtained by random sampling in the range of [0, 2π), thereby determining the normalized motion direction of the proton after scattering.

[0021] Then, the next position of the proton is calculated based on its current position, normalized direction of motion and theoretical step size. The actual step size is determined by judging whether the material types of the current position and the next position are consistent. Then, the single-step energy deposition value of this step is calculated according to the continuous energy loss model. If the trajectory of this step is within the sensitive volume of the target geometry model, the single-step energy deposition value is added to the total deposition energy of the proton.

[0022] Finally, the proton energy and proton position are updated based on the single-step energy deposition value;

[0023] Repeat the above iterative process until the proton energy is exhausted or completely penetrates the target geometry model, and finally output the trajectory of the proton and its total energy deposition in the sensitive volume.

[0024] Furthermore, the specific calculation formula for the single-event flip-off cross section is as follows: In the formula, For energy The number of incident protons, that is, the total number of incident protons; This refers to the number of SEU events counted, i.e., the total number of events. The surface area of ​​the target material's geometric model. This represents the total number of bits in the SRAM.

[0025] Furthermore, the MeV energy region is the energy region where the proton energy is between 0.5 MeV and 1 MeV.

[0026] Furthermore, the SRAM is an ISSI SRAM device manufactured using a 40nm process, with physical planar dimensions of 18.40mm × 12.00mm.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] This invention provides a rapid analysis method for single-particle flipping of SRAM caused by protons in the MeV energy range. This method considers the interaction between the proton and the target material and employs a hybrid algorithm combining a continuous energy loss model based on stopping power and a discrete scattering model based on scattering angle sampling. This enables rapid generation of motion trajectory data and real-time analysis. This solves the problem of high computational cost and complexity caused by the need for large amounts of sampling in traditional Monte Carlo simulation methods, achieving rapid simulation and improving simulation reliability.

[0029] This invention proposes a method to calculate single-step energy deposition by using the particle's range per step and the stopping power of the current step. Employing an discrete stepping method, it calculates energy deposition by adjusting the single-step size and stopping power, resulting in more accurate calculations of proton energy deposition in multilayer targets. This method can rapidly reflect the proton energy loss process, improving the reliability of the calculation results.

[0030] This invention constructs a material parameter database covering key performance characteristics, sets simulation parameters and builds a target geometric model, employs an efficient hybrid algorithm to simulate transport processes and energy deposition, and calculates the flip-off cross-section using a formula based on well-defined statistical events. This invention provides the ability to rapidly calculate the flip-off cross-section, avoiding complex and costly experimental measurements. Furthermore, by selecting representative energy points for calculation, it reduces computational load and time, improving simulation efficiency. This method provides a reliable and rapid theoretical tool for evaluating the radiation sensitivity of devices.

[0031] The method provided by this invention is particularly suitable for the analysis of protons in the 0.5~1 MeV energy range. It not only improves the accuracy and efficiency of flip cross section calculation, but also provides a reliable theoretical basis for subsequent experiments. It helps to verify existing physical models, promotes the design and optimization of new materials, and provides strong support for the radiation-resistant design and reliability assessment of spacecraft electronic devices. Attached Figure Description

[0032] Figure 1 This is a flowchart illustrating the rapid analysis method for single-particle flipping of SRAM caused by protons in the MeV energy region according to the present invention.

[0033] Figure 2A geometric model diagram of the target material constructed in the simulation provided by this invention;

[0034] Figure 3 The relative deviation diagram of the projected range and lateral straggling of protons in silica materials provided by the present invention;

[0035] Figure 4 The relative deviation diagram of the projected range and lateral strigling of protons in silicon material provided by the present invention;

[0036] Figure 5 A flowchart for calculating proton transport and proton energy deposition in a sensitive volume, provided by the present invention;

[0037] Figure 6 The trajectory distribution diagram of protons in the target material provided by the present invention. Detailed Implementation

[0038] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0039] Example 1:

[0040] This invention provides a rapid analysis method for single-particle flipping of SRAM caused by protons in the MeV energy range, such as... Figure 1 As shown, it includes the following steps:

[0041] Step 1) Device geometry modeling: Based on the SRAM device structure, establish a target geometry model (also known as "device model") that includes the capping layer and sensitive volume.

[0042] Step 2) Material parameter modeling: Construct a material parameter database containing key performance parameters of targets corresponding to different material types. Key performance parameters include at least target density, radiation length, and stopping power as a function of energy. Material types include at least two types: capping material and sensitive volume material.

[0043] Step 3) Rapid simulation of proton transport: A hybrid algorithm combining a continuous energy loss model based on stopping ability and a discrete scattering model based on scattering angle sampling is used. Based on a material parameter database, the transport process of protons in the target geometric model is iteratively simulated and the total energy deposition in the sensitive volume is obtained.

[0044] Step 4) SEU event determination: Compare the total energy deposition of each proton in the sensitive volume with the preset energy deposition threshold. If the threshold is exceeded, a single-particle flip event is determined to have occurred, and the total number of events is counted.

[0045] Step 5) Flip cross section calculation: Based on the total number of events, the total number of incident protons, the total number of bits in the SRAM, and the surface area of ​​the target geometry model, obtain the single-particle flip cross section.

[0046] Furthermore, the stopping power in the key performance parameters is constructed using an interpolation function with proton energy as the independent variable.

[0047] Furthermore, the data source for the interpolation function is selected from the SRIM database.

[0048] Furthermore, the target geometric model is established through the following specific methods: analyzing the structure of the SRAM to construct a target geometric model including the capping layer and the sensitive volume; determining the material composition and geometric dimensions of each layer of the target geometric model based on the structure of the SRAM; creating corresponding cuboid models for each layer based on the determined geometric dimensions; translating and splicing the cuboid models along the incident direction to form a complete target geometric model.

[0049] Furthermore, the expression for the continuous energy loss model based on stopping ability is: In the formula, This represents energy loss per step. To determine the energy of the proton in the current step The ability to query and normalize density from a material parameter database; This is the single-step step size.

[0050] Furthermore, the expression for the discrete scattering model based on scattering angle sampling is as follows: In the formula, The standard deviation of the scattering angle; It is megaelectron volts; Momentum; For particles relative to the speed of light speed; The speed of light; This is the theoretical step size for the current step of the proton; The length of the radiation; The energy of the proton at the current step; a and b are the first and second influencing parameters, respectively; It is a low-energy correction factor;

[0051] The aforementioned first influencing parameter 'a' and second influencing parameter 'b' determine the characteristics of the low-energy correction factor. The optimal combination of influencing parameters can be selected through iterative optimization and cross-validation. For silicon dioxide, a = 0.66 and b = 68; for silicon, a = 0.6 and b = 44. In this invention, the correction normalizes the standard deviation of the scattering angle within the 0.5-1 MeV energy range to a Gaussian distribution. The scattering angle can be sampled from a Gaussian distribution with a mean of 0 and a standard deviation of θ.

[0052] Furthermore, the underlying principle of the hybrid algorithm is as follows:

[0053] In the process of iteratively simulating proton transport, key performance parameters are obtained based on the material parameter database. Then, the position and direction of the proton are determined by the initial energy, initial state of the proton, and the scattering angle obtained by the discrete scattering model based on scattering angle sampling. Finally, the energy loss of the proton is obtained by the continuous energy loss model based on stopping ability, and the energy state is updated. The above position determination and energy update steps are iteratively executed until the preset termination condition is met, so as to generate the trajectory of the proton and the corresponding energy loss distribution.

[0054] The specific methods of the hybrid algorithm include the following:

[0055] An iterative simulation of the transport process of the incident proton in the target geometry model is performed. In each iteration, the material type and current energy of the target are first determined based on the current position of the proton, and the target density, radiation length and stopping power based on the current energy are obtained from the material parameter database.

[0056] Subsequently, the estimated new energy is calculated based on the preset energy loss ratio, and the theoretical step size corresponding to the decrease of the proton energy from the current value to the new energy is calculated by using the integral range formula based on the stopping power value.

[0057] Next, based on the radiation length, theoretical step size and current momentum of the proton, the standard deviation of the scattering angle is calculated by the discrete scattering model, and the scattering angle is obtained by Gaussian sampling. At the same time, the azimuth angle is obtained by random sampling in the range of [0, 2π), thereby determining the normalized motion direction of the proton after scattering.

[0058] Then, the next position of the proton is calculated based on its current position, normalized direction of motion and theoretical step size. The actual step size is determined by judging whether the material types of the current position and the next position are consistent. Then, the single-step energy deposition value of this step is calculated based on the continuous energy loss model. If the trajectory of this step is within the sensitive volume of the target geometry model, the single-step energy deposition value is added to the total deposition energy of the proton.

[0059] Finally, the proton energy and proton position are updated based on the single-step energy deposition value;

[0060] Repeat the above iterative process until the proton energy is exhausted or completely penetrates the target geometry model, and finally output the trajectory of the proton and its total energy deposition in the sensitive volume.

[0061] Furthermore, the specific steps of the hybrid algorithm are as follows:

[0062] Step 3.1) State and parameter acquisition: Based on the current position P of the proton, determine the material type of the target and the energy E of the current step, and query the corresponding target density from the material parameter database. Radiation length X0 and stopping power ;

[0063] Step 3.2) Energy update and step size calculation: Preset or randomly select the energy loss ratio K, and calculate the estimated energy after a single proton action. , Based on its stopping power, the energy of the proton is calculated to decrease from E to [the point of impact] using the integral range formula. The corresponding theoretical step size R (corresponding to the theoretical step size in the discrete scattering model expression) Furthermore, the integral range formula is: In the formula, This indicates the stopping power based on the current energy E;

[0064] Step 3.3) Scattering direction update: Based on the radiation length X0, theoretical step size R, and momentum p of the energy E corresponding to the current step, the standard deviation of the scattering angle is calculated using a discrete scattering model, and the scattering angle following a Gaussian distribution is obtained by sampling. And the azimuth angle is obtained by random sampling within the range [0, 2π). Combined with scattering angle and azimuth Determine the normalized direction of motion after scattering. ;

[0065] Furthermore, the momentum p corresponding to the energy E of the current step can be obtained by the following method: ,in The proton rest mass energy is 938 MeV / c². It is the speed of light.

[0066] Step 3.4) Position update and energy deposition accumulation calculation, based on the proton's current position P and direction of motion. Using the theoretical step size R, calculate the next position of the proton. , Based on the next position of the proton Based on the relationship between the target material type at the current position P and the actual step size, and according to the continuous energy loss model, the single-step energy loss of the proton in this step is obtained as the single-step energy deposition value. If we move from the current position P of the proton to the next position... If the trajectory of the motion is within the sensitive volume of the target geometry model, then the energy deposition value will be... Total deposition energy added to the proton middle;

[0067] The specific method for obtaining the actual step size is as follows:

[0068] If the next position of the proton If the material type of the target at the current position P is the same, then the theoretical step size is used as the actual step size; if the next position of the proton is... If the material type of the target at the current position P is different from that of the target at the current position P, then the distance from the current position P to the end of the target where the proton is located is used. This represents the actual step size; the distance from the current position P to the end of the target where the proton is located. In the formula This represents the boundary length of the target material along the i-axis. This represents the position coordinates of the proton on the i-axis. This represents the component of the proton motion direction vector along the i-axis, where i represents the x-axis, y-axis, or z-axis, and i is selected based on the direction of the proton ejection from the target.

[0069] Step 3.5) State iteration update, based on single-step energy deposition value To obtain the energy of protons after deducting energy loss. , And update the proton's position to the next position calculated in step 3.4). ;

[0070] Step 3.6) Loop judgment and termination, repeat steps 3.1) to 3.5) to form an iterative loop until the proton energy is exhausted or its position completely penetrates the entire target geometry model;

[0071] Step 3.7) Output the results. After the loop terminates, output the complete simulated motion trajectory of the proton and its total energy deposition in the sensitive volume.

[0072] Furthermore, the specific formula for calculating the single-particle flip-off cross section is as follows: In the formula, For energy The number of incident protons, that is, the total number of incident protons; The number of SEU events is the total number of single-particle flip events. This represents the surface area of ​​the target's geometric model, which is also the area of ​​the incident particle source in the simulation. This represents the total number of bits in the SRAM.

[0073] Furthermore, the MeV energy region is the energy range of protons between 0.5 MeV and 1 MeV. Protons in this energy region have a high flux during solar proton events and also have a certain flux in the Van Allen radiation belt. They can reach the sensitive volume of SRAM devices and generate significant energy deposition within the sensitive volume of the devices. This is one of the important energy regions that threaten proton single-event effects and is also the energy range that needs to be focused on in order to trigger SRAM single-event flips.

[0074] Furthermore, the SRAM is an ISSI SRAM device manufactured using a 40nm process, with physical planar dimensions of 18.40mm × 12.00mm. The constructed target geometry model, consisting of a capping layer and a sensitive volume, can be used to simulate the energy deposition of protons within the sensitive volume of the SRAM device, and the single-particle flip cross section of the SRAM device can be calculated based on this model.

[0075] This example uses a 0.6 MeV proton incident ISSI SRAM device to rapidly analyze the proton energy deposition and flip-over cross-section in its sensitive volume using the method of this invention. The specific implementation steps are as follows:

[0076] A target geometric model (also called a "target structure model") is constructed through simulation. The structure of the SRAM is analyzed, and a target geometric model including a capping layer and a sensitive volume is built. Both the capping layer and the sensitive volume are cuboid models. Based on the SRAM structure, the material composition and geometric dimensions of each layer of the target geometric model are determined. Based on the determined material composition and geometric dimensions, corresponding cuboid models are created for the capping layer and the sensitive volume. The cuboid models are translated and spliced ​​along the incident direction to form a complete target geometric model. The target geometric model constructed in this embodiment uses silicon dioxide as the capping layer and silicon as the sensitive volume.

[0077] Figure 2 The image shows the target geometry model constructed for this example. In this example, the thickness of the target geometry model is set to 6.31 μm for X (6 μm for the capping layer and 0.31 μm for the sensitive volume), 3.1 μm for Y, and 3.1 μm for Z.

[0078] Specifically, the method for constructing the target geometric model includes: first, establishing a Cartesian xyz coordinate system, and then creating a cover layer model and a sensitive volume model in the coordinate system. The cover layer model has a range of (0, 6) on the X-axis, (-1.55, 1.55) on the Y-axis, and (-1.55, 1.55) on the Z-axis. The sensitive volume model has a range of (6, 6.31) on the X-axis, (-1.55, 1.55) on the Y-axis, and (-1.55, 1.55) on the Z-axis. Then, the created cover layer model and sensitive volume model are combined to form the target geometric model in this example.

[0079] Based on the target structure information, a material parameter database covering density, radiation length, and stopping power is constructed. In this embodiment, the constructed material parameter database is for silicon dioxide and silicon.

[0080] Specifically, this example first finds the density and radiation length of silica and silicon and adds them to the database. Then, it constructs an interpolation function with energy as the independent variable to calculate the stopping power of silica and silicon at different energies. The data source for the interpolation function is selected from the SRIM public database.

[0081] This example employs a hybrid algorithm that combines a continuous energy loss model based on stopping ability with a discrete scattering model based on scattering angle sampling. Based on a material parameter database, iteratively simulates the transport process of protons in the target geometry model and obtains the total energy deposition in the sensitive volume.

[0082] Furthermore, the expression for the continuous energy loss model based on stopping ability is: In the formula, This represents energy loss per step. To determine the energy of the proton in the current step The ability to query and normalize density from a material parameter database; This is the single-step step size.

[0083] Furthermore, the expression for the discrete scattering model based on scattering angle sampling is as follows: In the formula, The standard deviation of the scattering angle; It is megaelectron volts; Momentum; For particles relative to the speed of light speed; The speed of light; This is the theoretical step size for the current step of the proton; The length of the radiation; The energy of the proton at the current step; a and b are the first and second influencing parameters, respectively; It is a low-energy correction factor;

[0084] Specifically, the first influencing parameter 'a' and the second influencing parameter 'b' determine the characteristics of the low-energy correction factor. The optimal combination of influencing parameters can be selected through iterative optimization and cross-validation. For silicon dioxide, a = 0.66 and b = 68; for silicon, a = 0.6 and b = 44.

[0085] Figure 3 This is a relative deviation diagram of the projected range and lateral straggling of protons in silica materials provided by the present invention; Figure 4 This is a relative deviation diagram of the projected range and lateral strigling of protons in silicon material provided by the present invention.

[0086] Furthermore, specific methods for hybrid algorithms include:

[0087] In the process of iteratively simulating proton transport, key performance parameters are obtained from the material parameter database based on the initial energy and initial position of the proton. Then, the single-step size of the proton is calculated, and the scattering angle obtained by the discrete scattering model based on scattering angle sampling is used to determine the proton position and scattering direction. Finally, the proton energy loss is obtained by the continuous energy loss model based on stopping ability, and the energy state is updated. The above position determination and energy update steps are iteratively executed until the preset termination condition is met, so as to generate the trajectory of the proton and the corresponding energy loss distribution.

[0088] The specific steps of the hybrid algorithm in this example are as follows:

[0089] Step 3.1) State and parameter acquisition: Based on the proton's current energy E and its current position P, determine the target material type and query the corresponding target density from the material parameter database. Radiation length X0 and stopping power ;

[0090] Specifically, in this example, the initial energy of the proton is set to 0.6 MeV, which is used as the energy for the first step of the proton's motion. The initial position (0, y, z) is a randomly selected position from the radiation surface (the radiation surface is on the YZ plane with X=0 in the XYZ coordinate system, and the size of the radiation surface is 3.1 μm × 3.1 μm), which is used as the position for the current step. The proton is set to be incident perpendicularly along the positive x-axis. At this time, the current position of the proton is (0, y, z), located at the boundary of the silicon dioxide material. Then, based on the material parameter database, the silicon dioxide density, the radiation length of silicon dioxide, and the stopping power of the proton with an energy of 0.6 MeV in the silicon dioxide material are selected. If the current position of the proton is (6, y, z), located at the boundary of the silicon material, then based on the material parameter database, the silicon density, the radiation length of silicon, and the stopping power of the proton with the energy reaching the current position in the silicon material are selected.

[0091] Step 3.2) Energy update and step size calculation: Preset energy loss ratio K, calculate the estimated energy after a single proton action. , Based on its stopping power, the energy of the proton is calculated to decrease from E to [the point of impact] using the integral range formula. The corresponding theoretical step size R; further, the integral range formula is: In the formula, This indicates the stopping power based on the current energy E;

[0092] Specifically, if a preset proton energy loss ratio of 0.05 is selected, the estimated new energy of the proton after the first interaction is: =0.6MeV−0.6MeV×0.05=0.57MeV. Using the energy of the current step (initial energy 0.6MeV), the new energy (0.57MeV), the silicon dioxide density, and the stopping power of the proton in its first step, the proton's single-step step length R is calculated using the integral range formula. If the proton moves to the sensitive volume (silicon material), then using the energy of the current step, the estimated new energy, the silicon density, and the stopping power, the proton's single-step step length R is calculated using the integral range formula.

[0093] Step 3.3) Scattering direction update: Based on the radiation length X0, theoretical step size R, and momentum p of the energy E corresponding to the current step, the standard deviation of the scattering angle is calculated using a discrete scattering model, and the scattering angle following a Gaussian distribution is obtained by sampling. And the azimuth angle is obtained by random sampling within the range [0, 2π). Combined with scattering angle and azimuth Determine the normalized direction of motion after scattering. ;

[0094] Specifically, based on the energy of the current step (0.6 MeV) of the proton's first motion, the calculated theoretical step size R, and the radiation length X0, the standard deviation of the scattering angle after this interaction is calculated using a discrete scattering model, and the scattering angle is sampled. Simultaneously, the azimuth angle is obtained by random sampling from the interval [0, 2π]. This allows us to determine the direction of motion of the protons after scattering. After that, for each step of the proton's motion, the standard deviation of the scattering angle is calculated based on the energy of the current step, the theoretical step size, and the radiation length. The scattering angle is sampled, and the scattering direction is determined based on the azimuth angle and the scattering angle.

[0095] Furthermore, the momentum p corresponding to the energy E of the current step can be obtained by the following method: ,in The proton rest mass energy is 938 MeV / c². It is the speed of light.

[0096] Step 3.4) Position update and energy deposition accumulation calculation, based on the proton's current position P and direction of motion. Using the theoretical step size R, calculate the next position of the proton. , Based on the next position of the proton Based on the relationship between the target material type and the current position P, the actual step size is obtained, and according to the continuous energy loss model, the single-step energy loss of the proton in this step is obtained as the single-step energy deposition value. If we move from the current position P of the proton to the next position... If the trajectory of the motion is within the sensitive volume of the target geometry model, then the energy deposition value will be... Total deposition energy added to the proton middle;

[0097] The specific method for obtaining the actual step size is as follows:

[0098] If the next position of the proton If the material type of the target at the current position P is the same, then the theoretical step size is used as the actual step size; if the next position of the proton is... If the material type of the target at the current position P is different from that of the target at the current position P, then the distance from the current position P to the end of the target where the proton is located is used. This represents the actual step size; the distance from the current position P to the end of the target where the proton is located. In the formula This represents the boundary length of the target material along the i-axis. This represents the position coordinates of the proton on the i-axis. This represents the component of the proton motion direction vector along the i-axis, where i represents the x-axis, y-axis, or z-axis, and i is selected based on the direction of the proton ejection from the target.

[0099] Specifically, if the next position of the proton is the same as the material type of the target at the current position, then the theoretical step size is used as the actual step size; if the next position of the proton is different from the material type of the target at the current position, for example, the next position of the proton is in silicon, while the current position is in silicon dioxide, and the proton exits the capping layer along the x-axis, then the actual step size is the distance from the current position to the end of the capping layer of the target geometry model, and the actual step size is (6- ) / 6 represents the position of the cover layer on the x-axis. This represents the position coordinates of the proton on the x-axis. This represents the component of the proton's motion direction vector along the x-axis.

[0100] Step 3.5) State iteration update, based on single-step energy deposition value To obtain the energy corresponding to the next position of the proton. , And update the proton's position to the next position calculated in step 3.4). ;

[0101] Step 3.6) Loop judgment and termination, repeat steps 3.1) to 3.5) to form an iterative loop until the proton energy is exhausted or its position completely penetrates the entire target geometry model;

[0102] Step 3.7) Output the results. After the loop terminates, output the complete simulated motion trajectory of the proton and the total energy deposition accumulated in the sensitive volume.

[0103] Please see Figure 5 This is a flowchart of the calculation of proton transport and proton energy deposition in a sensitive volume provided by the present invention.

[0104] Step 4) The method for counting the total number of events includes: During the proton transport simulation, calculating the total energy deposition value generated by each proton within the sensitive volume (SV). After the proton transport ends, logically comparing the cumulative energy deposition of the proton within the sensitive volume with a preset critical energy threshold. Once the cumulative energy deposition exceeds the threshold, it is recorded as a valid flip event. The above steps are repeated to cover a preset number of proton samples, and finally, the total number of single-particle flip events under the current radiation environment is calculated.

[0105] Specifically, in this example, 100,000 protons are set, and the preset energy deposition threshold is 21.6 keV. If the total energy deposition value of a single proton in the sensitive volume exceeds the preset energy deposition threshold, it is recorded as a valid flip event. The total number of single-particle flip events that occur among 100,000 protons is counted.

[0106] Furthermore, the specific formula for calculating the single-particle flip-off cross section is as follows: In the formula, For energy The number of incident protons, that is, the total number of protons incident with the initial incident energy; The number of SEU events is the total number of single-particle flip events. This represents the surface area of ​​the target's geometric model, which is also the area of ​​the incident particle source in the simulation. This represents the total number of bits in the SRAM.

[0107] Figure 6 This is a trajectory distribution diagram of protons in the target material provided by the present invention.

[0108] In this example, taking a proton with an energy of 0.6 MeV as an example, the projected range and lateral straggling parameters of the proton in silicon and silica materials were calculated using the discrete scattering model method of this invention. The calculation results (see Table 1) were compared with data in the SRIM database, and the relative deviation was small. Simultaneously, the flipping cross section of the proton under the target geometry model of SRAM was calculated and compared with existing literature data. Experimental results show that the method of this invention significantly shortens the calculation time of the flipping cross section while keeping the error within 5%, achieving fast and high-precision simulation calculation of the proton flipping cross section.

[0109] Table 1

[0110]

[0111] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A rapid analytical method for single-particle flipping of SRAM caused by protons in the MeV energy range, characterized in that, Includes the following steps: Based on the device structure of SRAM, a geometric model of the target material including the capping layer and the sensitive volume is established; Construct a material parameter database containing key performance parameters of target materials corresponding to different material types. The key performance parameters include at least target density, radiation length, and stopping power as a function of energy. The material types include at least the materials corresponding to the capping layer and the sensitive volume. A hybrid algorithm combining a continuous energy loss model based on stopping ability and a discrete scattering model based on scattering angle sampling is used to iteratively simulate the transport process of protons in the target geometry model and obtain the total energy deposition in the sensitive volume based on the material parameter database. The total energy deposition of each proton in the sensitive volume is compared with a preset energy deposition threshold. If the threshold is exceeded, a single-particle flip event is determined to have occurred, and the total number of events is counted. Based on the total number of events, the total number of incident protons, the total number of bits in the SRAM, and the surface area of ​​the target geometric model, the single-particle flip-off cross section is obtained; The expression for the continuous energy loss model based on stopping ability is: In the formula, This represents energy loss per step. To determine the energy of the proton in the current step The ability to query and normalize density from a material parameter database; The step size is a single step. The expression for the discrete scattering model based on scattering angle sampling is: In the formula, The standard deviation of the scattering angle; It is megaelectron volts; Momentum; For particles relative to the speed of light speed; The speed of light; This is the theoretical step size for the current step of the proton; The length of the radiation; The energy of the proton at the current step; a and b are the first and second influencing parameters, respectively; It is a low-energy correction factor; The specific methods of the hybrid algorithm include: An iterative simulation of the transport process of the incident proton in the target geometry model is performed. In each iteration, the material type and current energy of the target are first determined based on the current position of the proton, and the target density, radiation length and stopping power based on the current energy are obtained from the material parameter database. Subsequently, the estimated new energy is calculated based on the preset energy loss ratio, and the theoretical step length corresponding to the decrease of the proton energy from the current value to the new energy is calculated by the integral range formula according to the stopping power value. Next, based on the radiation length, theoretical step size and current momentum of the proton, the standard deviation of the scattering angle is calculated through the discrete scattering model, and the scattering angle is obtained by Gaussian sampling. At the same time, the azimuth angle is obtained by random sampling in the range of [0, 2π), thereby determining the normalized motion direction of the proton after scattering. Then, the next position of the proton is calculated based on its current position, normalized direction of motion and theoretical step size. The actual step size is determined by judging whether the material types of the current position and the next position are consistent. Then, the single-step energy deposition value of this step is calculated according to the continuous energy loss model. If the trajectory of this step is within the sensitive volume of the target geometry model, the single-step energy deposition value is added to the total deposition energy of the proton. Finally, the proton energy and proton position are updated based on the single-step energy deposition value; Repeat the above iterative process until the protons are exhausted or completely penetrate the target geometry, ultimately outputting the proton's trajectory and its total energy deposition in the sensitive volume; the integral range formula is: In the formula, This indicates the ability to stop based on the current energy E.

2. The rapid analysis method for single-event flips in SRAM caused by protons in the MeV energy range according to claim 1, characterized in that, The stopping power among the key performance parameters is constructed using an interpolation function with proton energy as the independent variable.

3. The rapid analysis method for single-event flips in SRAM caused by protons in the MeV energy range according to claim 1, characterized in that, The target geometric model is established through the following specific methods: analyzing the structure of the SRAM to construct a target geometric model including the capping layer and the sensitive volume; determining the material composition and geometric dimensions of each layer of the target geometric model based on the structure of the SRAM; creating corresponding cuboid models for each layer based on the determined geometric dimensions; translating and splicing the cuboid models along the incident direction to form a complete target geometric model.

4. The rapid analysis method for single-event flips in SRAM caused by protons in the MeV energy range according to claim 1, characterized in that, The specific formula for calculating the single-event flip-off cross section is as follows: In the formula, For energy The number of incident protons, that is, the total number of incident protons; This refers to the number of SEU events counted, i.e., the total number of events. The surface area of ​​the target material's geometric model. This represents the total number of bits in the SRAM.

5. The rapid analysis method for single-event flips in SRAM caused by protons in the MeV energy range according to claim 1, characterized in that, The MeV energy region refers to the energy region where the proton energy is between 0.5 MeV and 1 MeV.

6. The rapid analysis method for single-event flips in SRAM caused by protons in the MeV energy range according to claim 1, characterized in that, The SRAM is an ISSI SRAM device manufactured using a 40nm process, with physical planar dimensions of 18.40mm × 12.00mm.

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