Improvement of bgr method for predicting proton single event effect cross section and its application

Abstract

This invention discloses an improved BGR method for predicting the proton single-event effect cross section and its application. It involves conducting heavy-ion SEE experiments on electronic devices to determine the heavy-ion SEE cross section curve function; simulating the nuclear reaction of protons with a thin silicon layer, statistically analyzing the energy spectrum of p+Si nuclear reaction products, and calculating the BGR function; and using the improved BGR method to obtain the predicted proton single-event effect cross section. The improved BGR method of this invention imposes corresponding restrictions on the BGR function calculation, considering only recoil nuclei with energies less than ρ. Si t SV L m The situation in (E) altered the trend of the predicted results; the introduction of the nuclear reaction volume thickness parameter t RV， In the calculation of t RV It can be less than t SV It can also be greater than t SV Compared to the original BGR method, the improved BGR method expands the range of prediction results. The final prediction results are consistent with the experimental results in terms of both numerical values ​​and trends, and can effectively predict the proton single-event effect cross section, which is a significant improvement over the original BGR method. The improved BGR method of this invention can also be used to predict the neutron single-event effect cross section.

Description

Technical Field

[0001] This invention belongs to the field of space particle technology, and specifically relates to an improved BGR method for predicting proton single-particle effect cross sections and its application. Background Technology

[0002] Protons are a major component of the space radiation environment, and the single-event effects (SEE) they induce in microelectronic devices are a significant factor contributing to on-orbit malfunctions and even catastrophic consequences in spacecraft. Neutrons are one of the main radiation particles in the atmospheric radiation environment and are a primary cause of SEE in electronic equipment of aircraft, high-reliability industries on Earth, and near-space vehicles, posing corresponding safety risks. Therefore, research on proton and neutron SEE is of paramount importance.

[0003] In related technologies, the single-event effect cross section is defined as:

[0004]

[0005] Where, N SEE The number of single-event effects is M, the number of units contained in the device is Φ, and the incident particle fluence is Φ (in cm⁻¹). -2 Heavy ions induce single-event effects through direct ionization, and linear energy transfer (LET) of heavy ions in silicon is characterized by their ionization ability in silicon. Protons and neutrons generally induce single-event effects indirectly through the ionization of products from nuclear reactions with silicon; their SEE cross-section is generally a function of the incident energy.

[0006] Foreign researchers have established the Burst Generation Rate (BGR) method based on the SEE mechanism of heavy ions, protons, and neutrons. This method can predict the SEE cross sections of protons and neutrons based on the heavy ion SEE cross section.

[0007]

[0008] Where E is the incident particle energy, C is the charge collection efficiency of the sensitive volume (SV), and t SV It is the thickness of SV; BGR(E,E) r ) represents the silicon nucleus number density n Si The energy produced by the reaction with p / n+Si nuclei is greater than E. r The product of the cross-sections of the recoil cores. However, the value of the charge collection efficiency C in this method is ambiguous, resulting in inaccurate predictions and poor performance. Summary of the Invention

[0009] In view of the above-mentioned technical problems existing in the prior art, the purpose of this invention is to provide an improved BGR method for predicting proton single-event effect cross sections with accurate prediction results and good performance, and its application.

[0010] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows: an improved BGR method for predicting proton single-particle effect cross-sections, comprising the following steps:

[0011] (1) Conduct heavy-ion SEE experiments on electronic devices to determine the Wellbull function σ of the heavy-ion SEE cross section of the device. HI (L);

[0012] (2) Simulate the nuclear reaction of protons with thin silicon layers and calculate the energy spectrum and BGR function of the p+Si nuclear reaction products;

[0013] (3) Combining the calculated BGR function and the heavy ion SEE cross section curve, the predicted proton single-particle effect cross section is obtained using the improved BGR method.

[0014] Furthermore, in step (1), a heavy-ion single-event effect experiment is conducted on the electronic device to obtain the heavy-ion SEE cross section at different LET values; the Weibull function σ is obtained by fitting the heavy-ion SEE cross section data of the electronic device. HI (L), where L represents the LET value of the heavy ion.

[0015] Furthermore, in step (1), the Weibull function σ of the heavy ion SEE cross section... HI (L) is:

[0016]

[0017] Where L represents the LET value of heavy ions, σ HI∞ For the saturated cross section, L th Where is the LET threshold of the device, W is the width parameter, and S is the shape factor.

[0018] Furthermore, in step (2), the Geant4 Monte Carlo program for simulating particle-matter interactions is used to simulate the nuclear reaction of a large number of protons with a thin silicon layer.

[0019] Furthermore, in step (2), when N in When a proton with energy E is incident on a thin silicon layer of thickness H, the energy spectrum of the p+Si nuclear reaction products is:

[0020]

[0021] Among them, E r The energy of the recoil nucleus is ΔN, where ΔN is the energy at... The number of recoil nuclei within a small interval, n si H represents the silicon nucleus number density, and H represents the thickness of the thin silicon layer.

[0022] Further, in step (2), the BGR function is:

[0023]

[0024] Where, n si E r The definition is given in equation (4), BGR(E,E) r ) represents the silicon nucleus number density n si The energy produced by the reaction with p+Si nuclei is greater than E. r The product of the cross sections of the recoil nuclei; when calculating the BGR function, the case where most of the energy of the recoil nuclei is deposited outside the sensitive volume should not be considered; a restriction is added to the calculation of the BGR function, only considering recoil nuclei energies less than ρ Si t SV L m In case (E), where L m (E) is the maximum LET value of the recoil nucleus produced by the reaction of a proton with energy E with a silicon nucleus.

[0025] Furthermore, the proton SEE cross section contributed by the recoil nucleus across the entire energy range is:

[0026]

[0027] Among them, t RV The thickness of the nuclear reaction volume (RV) is n. si E r The definition is given in equation (4).

[0028] Furthermore, in step (3), the predicted single-particle effect cross section σ(E) of the proton is:

[0029]

[0030] Among them, t RV E represents the assumed nuclear reaction volume thickness. r The definition is given in equation (4), BGR(E,E) r The definition of ) is given in equation (5); where L and E are... r The relation is:

[0031] E r =t SV ρ Si L (8)

[0032] Where, ρ Si t is the density of silicon. SVL is the thickness of the sensitive volume of the device, defined in equation (3).

[0033] This invention provides an improved application of the BGR method for predicting proton single-event effect cross sections, which can also be used to predict neutron single-event effect cross sections.

[0034] The beneficial effects of the technical solution of this invention are as follows: an improved BGR method for predicting the proton single-event effect cross section and its application; conducting heavy-ion SEE experiments on electronic devices to determine the heavy-ion SEE cross section of the device and fitting a heavy-ion SEE cross section curve function; simulating the nuclear reaction of protons with thin silicon layers, statistically analyzing the energy spectrum of p+Si nuclear reaction products, and calculating the BGR function; combining the calculated BGR function and the heavy-ion SEE cross section curve, and based on the derived relationship between the proton and heavy-ion SEE cross sections, obtaining the proton single-event effect cross section. The improved BGR method of this invention imposes corresponding restrictions on the calculation of the BGR function, considering only recoil nuclei with energies less than ρ. Si t SV L m In case (E), the trend of the predicted results can be altered; the nuclear reaction volume thickness parameter t is introduced. RV In the calculation of t RV It can be less than t SV It can also be greater than t SV Compared to the original BGR method, the improved BGR method expands the range of prediction results. The final prediction results are consistent with the experimental results in terms of both numerical values ​​and trends, and can effectively predict the proton single-event effect cross section, which is a significant improvement over the original BGR method. The improved BGR method of this invention can also be used to predict the neutron single-event effect cross section. Attached Figure Description

[0035] Figure 1 This is a flowchart of the improved BGR method for predicting proton single-particle effect cross sections according to Embodiment 1 of the present invention;

[0036] Figure 2 This invention relates to an improved BGR method for predicting proton single-event effect cross-sections in Embodiment 2 of the present invention, which predicts the proton SEU cross-sections of four SRAM devices at t SV The BGR function when the value is 0.3μm;

[0037] Figure 3 This invention relates to an improved BGR method for predicting proton single-event effect cross-sections in Embodiment 2 of the present invention, which predicts the proton SEU cross-sections of four SRAM devices at t SV The BGR function when the value is 0.5μm;

[0038] Figure 4This is a comparison between the prediction of the proton SEU cross section of SRAM A device using the improved BGR method for predicting the proton single-particle effect cross section in Embodiment 2 of the present invention, experimental results, and the original BGR method;

[0039] Figure 5 This is a comparison of the predicted proton SEU cross section of SRAM B device using the improved BGR method for predicting proton single-particle effect cross section according to Embodiment 2 of the present invention, with experimental results and the original BGR method;

[0040] Figure 6 This is a comparison of the predicted proton SEU cross section of SRAM C device using the improved BGR method for predicting proton single-event effect cross section according to Embodiment 2 of the present invention, with experimental results and the original BGR method;

[0041] Figure 7 This is a comparison between the prediction of the proton SEU cross section of SRAM D devices using the improved BGR method for predicting proton single-event effect cross section according to Embodiment 2 of the present invention, experimental results, and the original BGR method. Detailed Implementation

[0042] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0043] Example 1

[0044] See attached document Figure 1 Embodiment 1 of the present invention provides an improved BGR method for predicting proton single-particle effect cross sections, comprising the following steps:

[0045] (1) Conduct heavy-ion SEE experiments on electronic devices to determine the heavy-ion SEE cross section of the devices and fit the Weibull function σ of the heavy-ion SEE cross section. HI (L);

[0046] (2) Simulate the nuclear reaction of protons with thin silicon layers and calculate the energy spectrum and BGR function of the p+Si nuclear reaction products;

[0047] (3) Combining the calculated BGR function and the heavy ion SEE cross section curve, the predicted single-particle effect cross section of the proton is obtained using the improved BGR method.

[0048] Preferably, in step (1), a heavy-ion single-event effect experiment is conducted on the electronic device to obtain the heavy-ion SEE cross section at different LET values; the Weibull function σ is obtained by fitting the heavy-ion SEE cross section data of the electronic device. HI (L), where L represents the LET value of the heavy ion.

[0049] Preferably, in step (1), the Weibull function of the heavy ion SEE cross section is:

[0050]

[0051] Where L represents LET, σ HI∞ For the saturated cross section, L th Where is the LET threshold of the device, W is the width parameter, and S is the shape factor.

[0052] Preferably, in step (2), the Geant4 Monte Carlo program for simulating particle-matter interactions is used to simulate the nuclear reaction of a large number of protons with a thin silicon layer.

[0053] Preferably, in step (2), when N in When a proton with energy E is incident on a thin silicon layer of thickness H, the energy spectrum of the p+Si nuclear reaction products is:

[0054]

[0055] Among them, E r The energy of the recoil nucleus is ΔN, where ΔN is the energy at... The number of recoil nuclei within a small interval, n si H represents the silicon nucleus number density, and H represents the thickness of the thin silicon layer.

[0056] Preferably, in step (2), the BGR function is:

[0057]

[0058] Where, n si E r The definition is given in equation (4), BGR(E,E) r ) represents the silicon nucleus number density n si The energy produced by the reaction with p+Si nuclei is greater than E. r The product of the cross sections of the recoil nuclei; when calculating the BGR function, the case where most of the energy of the recoil nuclei is deposited outside the sensitive volume should not be considered; a restriction is added to the calculation of the BGR function, only considering recoil nuclei energies less than ρ Si t SV L m In case (E), where L m (E) is the maximum LET value of the recoil nucleus produced by the reaction of a proton with energy E with a silicon nucleus.

[0059] This invention assumes that a thickness of t exists within the electronic device. RV The reaction volume (RV) is defined as follows: all proton SEE events are achieved by recoil nuclei generated by nuclear reactions within RV. It is also assumed that the recoil nuclei deposit all their energy within the sensitive volume SV, therefore a single recoil nucleus with energy E... r The energy of the recoil nucleus deposited within the SV is related to a LET value. The energy of heavy ions perpendicularly incident on SV is the same for deposition.

[0060] When a proton with energy E and flux Φ irradiates a device with area A and containing M units, the energy generated by the reaction in the RV core is... The number of recoil nuclei within the small interval is The recoil core can be considered as having a LET value of L. e Injection volume is For a heavy ion vertical incidence device, according to formula (1), the SEE cross section contributed by the recoil nuclei is... It can be seen that the proton SEE cross section contributed by the recoil nucleus across the entire energy range is:

[0061]

[0062] Among them, t RV The thickness of the nuclear reaction volume (RV) is n. si E r The definition is given in equation (4).

[0063] Preferably, in step (3), the predicted proton single-particle effect cross section σ(E) obtained according to equation (6) is:

[0064]

[0065] Among them, t RV E represents the assumed nuclear reaction volume thickness. r The definition is given in equation (4), BGR(E,E) r The definition is given in equation (5).

[0066] Preferably, L and E r The relation is:

[0067] E r =t SV ρ Si L (8)

[0068] Where, ρ Si t is the density of silicon. SV L is the thickness of the sensitive volume of the device, defined in equation (3).

[0069] This invention provides an improved application of the BGR method for predicting proton single-event effect cross sections, and can also be used to predict neutron single-event effect cross sections.

[0070] Example 2

[0071] The improved BGR method of Embodiment 1 of this invention is used to predict the proton single-event effect cross section of four SRAM devices.

[0072] The basic parameters of the four SRAM devices and the Weibull fitting parameters of the heavy ion particle upset (SEU) cross section are shown in Table 1.

[0073] Table 1. Basic parameters of four SRAM devices and Weibull fitting parameters of their heavy-ion SEU cross sections.

[0074]

[0075] Where σ HI∞ The unit is cm 2 / bit, L th The unit for W is MeV·cm 2 / mg

[0076] In this embodiment of the invention, t SV The values ​​are 0.3μm and 0.5μm, and the BGR function is obtained using the above formula. (See appendix.) Figure 2 , 3 This indicates that the BGR function of the method in the embodiments of the present invention is related to t. SV The value of t is related to the value of t. SV The BGR function curve changes depending on the value of .

[0077] Embodiments of the present invention at different t SV The values ​​of C and t were used to predict the proton SEU cross-section of four devices and to compare them with existing methods. SV The predictions and experimental results were compared for different values.

[0078] See attached document Figures 4-7 The proton SEU cross-section data predicted by the method in this embodiment of the invention are in good agreement with the experimental results, demonstrating good prediction performance. In contrast, the proton SEU cross-section predicted by the original BGR method shows a significant difference in trend from the experiment, especially at high energies where the trend is opposite to the actual experimental trend, and also exhibits large numerical discrepancies, resulting in poor prediction performance. Therefore, the improved BGR method represents a significant improvement over the original BGR method in both the predicted numerical values ​​and the trend analysis.

[0079] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention is also intended to include these modifications and variations.

Claims

1. An improved method for predicting the BGR method for proton single-event effect cross-sections, characterized in that, Includes the following steps: (1) Conduct heavy-ion SEE experiments on electronic devices to determine the Wellbull function of the heavy-ion SEE cross section of the devices. ; (2) Simulate the nuclear reaction between protons and thin silicon layers, and calculate the energy spectrum and BGR function of the p+Si nuclear reaction products; when calculating the BGR function, the case where most of the energy of the recoil nuclei is deposited outside the sensitive volume should not be considered; therefore, a restriction is added to the calculation of the BGR function, and only the recoil nuclei energy E is considered. r Less than In the case of, t is the density of silicon. SV It is the thickness of the sensitive volume of the device. It is the maximum LET value of the recoil nucleus produced by the reaction of a proton with energy E with a silicon nucleus; (3) Combining the calculated BGR function and the Wellbull function of the heavy ion SEE cross section Using the improved BGR method, the predicted proton single-event effect cross section was obtained. for: Among them, t RV For the thickness of the nuclear reaction volume, Silicon nucleus number density The energy produced by the reaction with p+Si nuclei is greater than E. r The product of the cross sections of the recoil core, E r ν is the energy of the recoil nucleus, and L is the LET value of the heavy ion.

2. An improved method for predicting the BGR method for proton single-particle effect cross-sections according to claim 1, characterized in that, In step (1), heavy ion single-event effect experiments are conducted on electronic devices to obtain heavy ion SEE cross sections at different LET values. The Weibull function is obtained by fitting heavy-ion SEE cross-sectional data of electronic devices. , where L represents the LET value of heavy ions.

3. An improved method for predicting the BGR method for proton single-particle effect cross-sections according to claim 1, characterized in that, In step (1), the Weibull function of the heavy ion SEE cross section for: (3) Where L represents the LET value of heavy ions. For the saturated cross section, L th Where is the LET threshold of the device, W is the width parameter, and S is the shape factor.

4. An improved method for predicting the BGR method for proton single-event effect cross-sections according to claim 1, characterized in that, In step (2), when N in When a proton with energy E is incident on a thin silicon layer of thickness H, the energy spectrum of the p+Si nuclear reaction products is: (4) Among them, E r For the energy of the recoil nucleus, For energy in The number of recoil nuclei within a small interval, n si H represents the silicon nucleus number density, and H represents the thickness of the thin silicon layer.

5. An improved method for predicting the BGR method for proton single-particle effect cross-sections according to claim 4, characterized in that, In step (2), the BGR function is: (5) Where, n si E r The definition is given in equation (4); Silicon nucleus number density The energy produced by the reaction with p+Si nuclei is greater than E. r The product of the cross sections of the recoil core.

6. An improved method for predicting the BGR method for proton single-event effect cross-sections according to claim 1, characterized in that, L and E r The relation is: (8) in, t is the density of silicon. SV It is the thickness of the sensitive volume of the device, and L is the LET value of heavy ions.

7. The application of the improved BGR method for predicting proton single-particle effect cross sections according to any one of claims 1 to 6, characterized in that, It is also used to predict the cross section of neutron single-event effects.

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