Electron bombardment active pixel sensor basis simulation method and apparatus

Abstract

The application discloses an electron bombardment active pixel sensor basic simulation method and device thereof, comprising the following steps: step S1: obtaining each EBAPS device parameter from an existing literature database through a crawler program, and storing the parameter in a material database; step S2: calling each EBAPS device parameter in the material database; step S3: calling each EBAPS device parameter in the material database; step S4: performing noise reduction processing on each data obtained in steps S2-S3 according to formula (12) to obtain a system total noise base σ total of total readout noise; and step S5: constructing a vacuum degree attenuation model as shown in formula (14) to obtain a simulation result. The method compares the simulation result with real device performance data, and judges the simulation reliability by setting a relative error.

Description

Technical Field

[0001] This application relates to the field of EBAPS device simulation technology, and in particular to a basic simulation method and apparatus for an electron bombardment active pixel sensor. Background Technology

[0002] EBAPS (Electron Bombarded Active Pixel Sensor) is a high-performance imaging device integrating a photocathode, electron multiplication, and CMOS readout circuitry. It is widely used in digital night vision, fluorescence lifetime imaging, quantum optics, and high-energy physics detection. Its working principle is as follows: photons incident on a photocathode material (such as GaAs, GaAsP, etc.) generate photoelectrons through the photoelectric effect. These photoelectrons gain kinetic energy under a high-voltage electric field (typically 5~10kV) and accelerate towards a silicon substrate. High-energy electrons bombard the silicon substrate, generating a large number of electron-hole pairs through ionization collisions, thus achieving secondary electron multiplication. Finally, the charge signal is collected and amplified by the CMOS readout circuitry (ROIC), kTC noise is suppressed through correlated double sampling (CDS), and a digital image signal is output via analog-to-digital conversion (ADC).

[0003] This process involves the complex coupling of multiple physical modules, including photocathode physics, vacuum electron trajectories, silicon substrate electron multiplication, and CMOS noise, requiring a specialized integrated simulation environment for accurate modeling. However, existing technologies face several pressing issues in EBAPS simulation. First, there is a lack of dedicated simulation tools; existing general-purpose semiconductor simulation tools such as TCAD, COMSOL, and MATLAB cannot be directly used for EBAPS simulation. While these tools have advantages in their respective fields, none can cover the entire physical chain of EBAPS.

[0004] TCAD offers high accuracy in semiconductor physics simulations, but it cannot simulate photocathode and vacuum electron trajectory processes; COMSOL supports multiphysics coupling, but lacks dedicated physical models for EBAPS; MATLAB boasts strong numerical computation capabilities, but lacks standardized physical models and verification mechanisms. Furthermore, EBAPS simulation code in academic papers is typically used only once, lacking modular design. Different researchers cannot replicate the same physical models, resulting in wasted resources and preventing reuse by other researchers.

[0005] Secondly, existing simulation results lack systematic comparative verification with real product specifications (such as Intevac ISIE1280 and Photek LD250), making it impossible to assess the reliability of the simulation results and hindering the establishment of industry standards. Finally, material and process parameters from different sources are scattered across various locations, lacking a unified parameter management mechanism, which can easily lead to inconsistent or unreproducible simulation results.

[0006] With the increasing demand for EBAPS applications in fields such as digital night vision, fluorescence lifetime imaging, quantum optics, and high-energy physics, the need for high-performance simulation tools is becoming increasingly urgent. Therefore, developing a modular, verifiable, and scalable EBAPS simulation infrastructure has significant theoretical and engineering value.

[0007] The information disclosed in the background section is intended only to enhance the understanding of the general background of the invention and should not be construed as an admission or in any way implying that such information constitutes prior art known to those skilled in the art. Summary of the Invention

[0008] This application addresses the aforementioned technical problems by providing a basic simulation method and apparatus for electron bombardment active pixel sensors. This method can effectively realize modular, verifiable, and scalable EBAPS simulation. By comparing the simulation results with the performance data of real devices and determining the reliability of the simulation by setting a relative error, this method helps to improve the accuracy of simulation results in subsequent use, increase R&D efficiency, and reduce the production of devices without improvement effectiveness.

[0009] This application provides a basic simulation method for an electron-bombarded active pixel sensor, including the following steps: Step S1: After obtaining various EBAPS device parameters from existing literature databases through a web crawler, the parameters are stored in the materials database and retrieved as needed. Each parameter is labeled with the literature information from which it was obtained, so as to trace the source of the parameters and support parameter tracing. Step S2: Retrieve various EBAPS device parameters from the materials database, and calculate the photocathode quantum efficiency based on the Beer-Lambert absorption law and escape depth model; Step S3: Retrieve various EBAPS device parameters from the material database. Based on the Kanaya-Okayama model, simulate the penetration, scattering, and multiplication processes of high-energy electrons in the silicon substrate to obtain the electron penetration depth, ionization yield, and backscattering coefficient related to the penetration, scattering, and multiplication processes. Simulate the secondary electron multiplication process to obtain the gain distribution and spatial broadening. Step S4: Perform noise reduction processing on the data obtained in steps S2~3 according to formula (12) to obtain the system total noise floor σ of the total readout noise. total The dynamic range is calculated according to formula (13), and the combination of device parameters with high dynamic range is selected to achieve a comprehensive analysis of the noise of the obtained circuit. The noise suppression formula is as follows: Equation (12) Equation (13); Where, σtotal σ is the system's total noise floor for total readout noise. kTC For kTC noise, σ flicker For 1 / f flicker noise, σ thermal For thermal noise, σ column For fixed pattern noise; σ pixel For fixed pattern noise of pixels, σ ADC Quantize noise for ADC; Step S5: Construct a vacuum decay model as shown in Equation (14), calculate the getter lifetime, outgassing rate and temperature relationship of the simulated EBAPS device, analyze the thermal stress of the simulated EBAPS device, and obtain the thermal stress σ at the bonding interface according to Equation (15). stress And perform bonding reliability assessment and comprehensive lifetime prediction. Using the number of temperature alternation cycles n experienced by the device as the independent variable, calculate the survival reliability R(n) of the device after n cycles according to formula (16) to obtain the simulation results. Equation (14) Equation (15) Equation (16) Where P0 is the initial vacuum level of the environment simulating the EBAPS device, L is the vacuum packaging leak rate of the simulating EBAPS device, Q is the gas escape rate of the simulating EBAPS device, V is the cavity volume of the simulating EBAPS device, and t is time, representing the cumulative working or storage time experienced by the EBAPS device after vacuum packaging is completed or the internal getter is activated; σ stress Thermal stress represents the thermomechanical stress generated at the bonding or sealing interface between two adjacent heterogeneous packaging materials with different physical properties. Examples include the sealing interface between the incident window and the package of EBAPS devices, the mounting interface between the silicon substrate and the packaging substrate, and the sealing interface between the photocathode substrate and the package. a and α b ΔT represents the coefficients of thermal expansion of adjacent encapsulation materials a and b on both sides of the bonding interface; ΔT is the difference between the bonding process temperature and room temperature, used to calculate the residual thermal stress after cooling; E represents... mod R represents the elastic modulus of a material, where "material" refers to the main material at the bonding interface that bears thermal stress, such as rigid substrate / window materials, metal casing materials, quartz glass, and ceramic substrates. （n） To assess the reliability of the bond after n thermal cycles, the Weibull fatigue model is adopted, R inital For initial reliability; N f Characteristic lifetime refers to the bonding interface of a device under thermal stress σ. stress Under certain conditions, the number of typical thermal cycles it can withstand is the characteristic lifetime; β is the shape parameter.

[0010] Preferably, the method further includes step S6: collecting product specifications and performance test results corresponding to each model of real product, constructing a product specification database, and calculating the relative error between the simulation result of the i-th parameter of the i-th model device obtained in steps S1~5 and the actual product performance data of the i-th model device according to formula (17); When the relative error is less than 5%, steps S1~5 are applicable to the simulation of the i-th parameter of the i-th type device. Equation (17).

[0011] Preferably, the parameters of each EBAPS device include: photocathode material parameters, silicon substrate parameters, CMOS process parameters, and packaging material parameters; The parameters of photocathode materials include: band gap energy, electron affinity, absorption coefficient, electron escape depth, peak quantum efficiency, spectral response range, dark current density, thermal expansion coefficient, and lattice constant. Silicon substrate parameters include: band gap, carrier mobility, intrinsic carrier concentration, ionization energy, density, thermal conductivity, and melting point; CMOS process parameters include: process node, power supply voltage, conversion gain, full-well capacity, and ADC bit width. The parameters of the packaging material include: coefficient of thermal expansion, elastic modulus, and melting point.

[0012] Preferably, step S2 includes the following steps: Step S21: Calculate the photon energy E according to the incident light wavelength based on the simulation parameters using formula (1). ph ; Step S22: Query the material database according to equations (1) to (4) to obtain the absorption coefficient α and escape depth L of the device to be simulated. e Calculate the photon absorption probability P abs and electron escape probability P escape According to the photon absorption probability P abs and electron escape probability P escape The quantum efficiency QE was obtained, and the spectral response curve was generated as the quantum efficiency of the photocathode. The formulas are as follows: Equation (1) Equation (2) Equation (3) Equation (4) Among them, P abs P represents the probability of photon absorption. escape E represents the electron escape probability; QE represents the quantum efficiency; E represents the quantum efficiency. phλ is the photon energy; h is Planck's constant; c is the speed of light; λ is the incident light wavelength; α is the absorption coefficient; d is the photocathode thickness; L e χ represents the electron escape depth; E represents the electron affinity; excess Excess energy.

[0013] Preferably, step S3 includes the following steps: Step S31: Based on the electron carrying energy of the photocathode conversion and various EBAPS device parameters, calculate the electron penetration depth R according to equation (5). KO ; Step S32: Calculate the ionization yield N and backscattering coefficient η according to equations (7) and (6); Step S33: Simulate the secondary electron multiplication process according to (8), obtain the gain distribution according to equation (9), and obtain the lateral broadening and longitudinal broadening according to equations (10) and (11) respectively. The lateral broadening and longitudinal broadening express the spatial broadening. The calculation formula used is as follows: Equation (5) Equation (6) Equation (7) Equation (8); Among them, R KO Let A be the electron penetration depth, A be the atomic weight of the silicon substrate, and E be the electron penetration depth. e Where is the incident electron energy, Z is the atomic number of the silicon substrate, ρ is the density of the silicon substrate material; W = 3.66V is the average ionization energy of silicon, N is the ionization yield; η is the backscattering coefficient. G The gain value represents the actual number of electron-hole pairs generated by a single incident electron (or a single pixel in a single exposure). E dep G represents the actual energy deposited in silicon, and G is a secondary correction factor that takes into account carrier collection efficiency and device structure effects; it can be obtained from literature data. secondary It is a quadratic gain factor; Gain distribution formula: Equation (9) Where: G is the gain value, μ is the mean of the logarithmic gain, calculated according to... The calculated value is σ, which is the standard deviation of the logarithmic gain (typically around 0.3 to 0.5). The average gain of the multiple gain values ​​G calculated by formula (8) refers to the average number of electron-hole pairs obtained under the bombardment of a large number of incident electrons or under the statistical average of the entire pixel array of the device. Lateral widening is done according to the formula: Calculate using equation (10); in: The standard deviation of the lateral spatial expansion (unit: μm); R KO E is the electron penetration depth calculated using formula (5). c The critical energy (approximately 1-2 keV in silicon); E e The energy of the incident electron; Vertical widening is calculated using the following formula: Calculate using equation (11); in, z max ≈0.6× R KO σ represents the peak depth of energy deposition. z ≈0.2× R KO The standard deviation of the longitudinal distribution; It represents the energy lost by an electron per unit depth in silicon material, and is used to quantify the core underlying physical quantity of vertical spatial expansion.

[0014] Preferably, the simulation results obtained in step S5 include: the predicted value of vacuum degree P(t) as a function of time; Theoretical lifespan of getter (t) getter ; Thermal stress σ at the encapsulation interface stress ; The reliability R(n) of the bonded structure under thermal cycling is used for comprehensive lifetime prediction.

[0015] Preferably, step S5 includes the following steps: Step S51: Evaluate the coefficients of thermal expansion (α) of the two adjacent encapsulation materials (material a, material b) extracted according to equation (15) for the thermal system. a and α b By combining the temperature variation range (ΔT) of the working environment with the elastic modulus of the material, the thermal stress σ at the bonding interface is calculated. stress ; Step S52: Determine the thermal stress σ at the bonding interface stress If the material's bonding strength is exceeded, the simulation result and its corresponding material database parameter combination are discarded; if not, they are output as simulation results. Step S53: According to the fatigue reliability model of equation (16), the thermal stress σ at the bonding interface is calculated. stress The model is input with the acceleration aging factor (and the vacuum degree decay trend) and the number of temperature alternation cycles (n) experienced by the device as the independent variable. The device's survival reliability R(n) after n cycles is calculated to predict the overall lifespan of the device.

[0016] Another aspect of this application provides a basic simulation apparatus for an electron-bombarded active pixel sensor, comprising: The materials database module is used to retrieve various EBAPS device parameters from existing literature databases via a web crawler, store them in the materials database, and retrieve them as needed. Each parameter is labeled with the literature information from which it was obtained, so as to trace the source of the parameters and support parameter tracing. The photocathode physics module is used to retrieve various EBAPS device parameters from the materials database and calculate the photocathode quantum efficiency based on the Beer-Lambert absorption law and the escape depth model. The electron trajectory and multiplication module is used to retrieve various EBAPS device parameters from the material database. Based on the Kanaya-Okayama model, it simulates the penetration, scattering and multiplication process of high-energy electrons in silicon substrates, and obtains the electron penetration depth, ionization yield and backscattering coefficient related to the penetration, scattering and multiplication process. It also simulates the secondary electron multiplication process to obtain the gain distribution and space broadening. Since the electron multiplication process has statistical fluctuations and the gain follows a log-normal distribution, this module can simulate the statistical distribution characteristics of the gain. The CMOS noise module is used to perform noise reduction processing on the data obtained in steps S2~3 according to formula (12) to obtain the system total noise floor σ of the total readout noise. total The dynamic range is calculated according to formula (13), and the combination of device parameters with high dynamic range is selected to achieve a comprehensive analysis of the noise of the obtained circuit. The noise suppression formula is as follows: Equation (12) Equation (13); Where, σ total σ is the system's total noise floor for total readout noise. kTC For kTC noise, σ flicker For 1 / f flicker noise, σ thermal For thermal noise, σ column For fixed pattern noise; σ pixel For fixed pattern noise of pixels, σ ADC Quantize noise for ADC; The vacuum sealing module is used to construct the vacuum decay model as shown in Equation (14), calculate the getter lifetime, outgassing rate and temperature relationship of the simulated EBAPS device, and analyze the thermal stress of the simulated EBAPS device to obtain the thermal stress σ at the bonding interface according to Equation (15). stressAnd perform bonding reliability assessment and comprehensive lifetime prediction. Using the number of temperature alternation cycles n experienced by the device as the independent variable, calculate the survival reliability R(n) of the device after n cycles according to formula (16) to obtain the simulation results. Equation (14) Equation (15) Equation (16) Where P0 is the initial vacuum level of the environment simulating the EBAPS device, L is the vacuum packaging leak rate of the simulating EBAPS device, Q is the gas escape rate of the simulating EBAPS device, V is the cavity volume of the simulating EBAPS device, and t is time, representing the cumulative working or storage time experienced by the EBAPS device after vacuum packaging is completed or the internal getter is activated; σ stress Thermal stress represents the thermomechanical stress generated at the bonding or sealing interface between two adjacent heterogeneous packaging materials with different physical properties. Examples include the sealing interface between the incident window and the package of EBAPS devices, the mounting interface between the silicon substrate and the packaging substrate, and the sealing interface between the photocathode substrate and the package. a and α b ΔT represents the coefficients of thermal expansion of adjacent encapsulation materials a and b on both sides of the bonding interface; ΔT is the difference between the bonding process temperature and room temperature, used to calculate the residual thermal stress after cooling; E represents... mod R represents the elastic modulus of a material, where "material" refers to the main material at the bonding interface that bears thermal stress, such as rigid substrate / window materials, metal casing materials, quartz glass, and ceramic substrates. （n） To assess the reliability of the bond after n thermal cycles, the Weibull fatigue model is adopted, R inital For initial reliability; N f Characteristic lifetime refers to the bonding interface of a device under a preset thermal stress (σ). stress The characteristic lifetime is the number of typical thermal cycles that the system can withstand under the influence of β. β is a shape parameter.

[0017] Preferably, it further includes: The verification framework module is used to collect product specifications and performance test results corresponding to each model of real product, build a product specification database, and calculate the relative error between the simulation result of the i-th parameter of the i-th model device obtained in steps S1~5 and the actual product performance data of the i-th model device according to formula (17). When the relative error is less than 5%, steps S1~5 are applicable to the simulation of the i-th parameter of the i-th type device. Equation (17).

[0018] The beneficial effects that this application can produce include: 1. Verify the correlation between simulation results and actual device performance to improve simulation accuracy: This method acquires publicly available EBAPS device performance data and corresponding material data from existing literature databases. After selecting parameters from the material database according to simulation needs, it obtains simulation results of the corresponding device performance. These results are compared with the publicly available performance of the actual device. Based on the simulation results, devices and parameters with acceptable relative errors are selected, and simulations are performed again to obtain highly accurate results. This allows for accurate and rapid identification of the improvement direction and trend of the device model and its parameters. Furthermore, physical devices can be fabricated based on these device parameters. The simulation performance parameters obtained by this method have low errors compared to the actual device performance parameters, which can be used to improve device development efficiency, shorten the number and time of experiments, and obtain devices with better performance more quickly. Compared with the obtained physical devices, the simulation results of this method passed 4 out of 5 verifications, with a maximum relative error of only 10.7% and a minimum of only 0.8%, demonstrating high accuracy.

[0019] 2. Full physical link integration simulation: The system integrates and simulates various physical parameters of EBAPS, unifying six core modules—material database, photocathode physics, electron trajectory and multiplication, CMOS noise, vacuum packaging, and verification framework—under a single framework. Parameters can be automatically transferred between modules, enabling accurate end-to-end simulation. A single simulation can obtain complete performance indicators of the device.

[0020] 3. Parametric modeling based on literature: A literature-based parametric modeling method is employed, establishing a one-to-one mapping between each physical parameter used in the simulation and the literature that publicly discloses that parameter. This allows analysts to trace back to the published literature when interpreting the simulation results. Sensitivity data for the obtained parameters are simultaneously output in the simulation results, ensuring the repeatability and verifiability of the simulation results. By fine-tuning the input parameters in the database, the impact of parameter changes on the final device performance is determined. This impact is a floating value, used to determine the parameter tolerance range and key variables when reproducing the device with that parameter, ensuring the repeatability and robustness of the simulation results.

[0021] 4. Modular and scalable architecture: Each module is developed and tested independently, supporting the addition of new materials, noise sources, and packaging methods. Modules communicate with each other through standard interfaces.

[0022] 5. Automated verification mechanism: It has a built-in database of real product specifications, automatically calculates the error between simulation results and product specifications, and generates a standardized verification report. Attached Figure Description

[0023] Figure 1A schematic diagram of the method flow in at least one embodiment provided in this application; Figure 2 A schematic diagram of the overall architecture of the simulation infrastructure in at least one embodiment provided in this application; Figure 3 The following are bar charts comparing the simulation results of the ISIE1280, LD250, and HHU model EBAPS products obtained in at least one embodiment 1 of this application with the verification results of the actual products: a) gain comparison chart; b) quantum efficiency @650nm comparison chart; c) dynamic range comparison bar chart; d) relative error result comparison chart. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0025] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0026] Technical means not detailed in this application and not used to solve the technical problems of this application are all set according to common general knowledge in the field, and multiple common general knowledge setting methods can be used to achieve this. Parameters not detailed in the following steps are measured according to conventional methods for EBAPS devices.

[0027] See Figure 1 The basic simulation method for an electron bombardment active pixel sensor provided in this application includes the following steps: Step S1: After obtaining various EBAPS device parameters from existing literature databases through a web crawler, the parameters are stored in the materials database and retrieved as needed. Each parameter is labeled with the literature information from which it was obtained, so as to trace the source of the parameters and support parameter tracing. The parameters of various EBAPS devices include: photocathode material parameters (bandgap energy, electron affinity, absorption coefficient, electron escape depth, peak quantum efficiency, spectral response range, dark current density, coefficient of thermal expansion, lattice constant), silicon substrate parameters (bandgap, carrier mobility, intrinsic carrier concentration, ionization energy, density, thermal conductivity, melting point), CMOS process parameters (process node, power supply voltage, conversion gain, full-well capacity, ADC bit depth), and packaging material parameters (coefficient of thermal expansion, elastic modulus, melting point).

[0028] Step S2: Retrieve various EBAPS device parameters from the materials database, and calculate the photocathode quantum efficiency based on the Beer-Lambert absorption law and escape depth model; The parameters required to calculate the quantum efficiency of the photocathode, such as photon energy (calculated from the incident light wavelength), absorption coefficient, electron escape depth, and electron affinity, are obtained in the initial stage of the calculation, step S1, by existing methods or by consulting literature and relevant databases. The specific methods for obtaining each parameter are not detailed here.

[0029] Step S2 specifically includes the following steps: Step S21: Calculate the photon energy E according to the incident light wavelength based on the simulation parameters using formula (1). ph ; Step S22: Query the material database according to equations (1) to (4) to obtain the absorption coefficient α and escape depth L of the device to be simulated. e Calculate the photon absorption probability P abs and electron escape probability P escape According to the photon absorption probability P abs and electron escape probability P escape The quantum efficiency QE was obtained, and the spectral response curve was generated as the quantum efficiency of the photocathode. The formulas are as follows: Equation (1); Equation (2); Equation (3); Equation (4) Equation (1) is used to calculate photon energy; Equation (2) is used to calculate the probability of photons being absorbed by materials based on Beer-Lambert's law; Equation (3) is used to calculate the probability of excited electrons overcoming the surface barrier and escaping into the vacuum; Equation (4) is used to synthesize the final quantum efficiency (QE). Among them, P abs P represents the probability of photon absorption. escape E represents the electron escape probability; QE represents the quantum efficiency; E represents the quantum efficiency. ph Let λ be the photon energy, h be Planck's constant, c be the speed of light, λ be the incident light wavelength, α be the absorption coefficient, d be the photocathode thickness, and L be the wavelength of the photocathode.e Let χ be the electron escape depth, χ be the electron affinity, and E be the electron escape depth. excess Excess energy.

[0030] Step S3: Retrieve various EBAPS device parameters from the material database. Based on the Kanaya-Okayama model, simulate the penetration, scattering, and multiplication processes of high-energy electrons in the silicon substrate to obtain the electron penetration depth, ionization yield, and backscattering coefficient related to the penetration, scattering, and multiplication processes. Simulate the secondary electron multiplication process to obtain the gain distribution and spatial broadening. Step S3 specifically includes the following steps: Step S31: Based on the electron carrying energy of the photocathode conversion and various EBAPS device parameters, calculate the electron penetration depth R according to equation (5). KO ; Step S32: Calculate the ionization yield N and backscattering coefficient η according to equations (7) and (6); Step S33: Simulate the secondary electron multiplication process according to (8), obtain the gain distribution according to equation (9), and obtain the lateral broadening and longitudinal broadening according to equations (10) and (11) respectively. The lateral broadening and longitudinal broadening express the spatial broadening.

[0031] The calculation formula used is as follows: Equation (5); Equation (6); Equation (7); Equation (8) Formula Function Description: Equation (5) predicts the penetration depth of electrons in silicon based on the Kanaya-Okayama model; Equations (6) and (7) estimate the energy loss and backscattering ratio; Equation (8) calculates the number of electron-hole pairs generated by ionization based on the actual deposition energy (after deducting backscattering losses), and obtains the electron multiplication gain of the device. Actual deposition energy refers to the energy of incident electrons that are actually converted into electron-hole pairs through ionization collisions within the effective thickness of the silicon substrate after deducting backscattering losses.

[0032] Among them, R KO Let A be the electron penetration depth, A be the atomic weight of the silicon substrate, and E be the electron penetration depth. e Where is the incident electron energy, Z is the atomic number of the silicon substrate, ρ is the density of the silicon substrate material; W = 3.66V is the average ionization energy of silicon, N is the ionization yield; η is the backscattering coefficient. G The gain value represents the actual number of electron-hole pairs generated by a single incident electron (or a single pixel in a single exposure). E dep G represents the actual energy deposited in silicon, and G is a secondary correction factor that takes into account carrier collection efficiency and device structure effects; it can be obtained from literature data. secondary It is a quadratic gain factor.

[0033] Gain distribution formula: Equation (9) Where: G is the gain value, μ is the mean of the logarithmic gain, calculated according to... The calculated value is σ, which is the standard deviation of the logarithmic gain (typically around 0.3 to 0.5). The average gain of the multiple gain values ​​G calculated by formula (8) refers to the average number of electron-hole pairs obtained under the bombardment of a large number of incident electrons or under the statistical average of the entire pixel array of the device. Lateral widening is done according to the formula: Calculate using equation (10); in: The standard deviation of the lateral spatial expansion (unit: μm); R KO The electron penetration depth is calculated using formula (5); E c The critical energy (approximately 1-2 keV in silicon); E e The energy of the incident electron; Vertical widening is calculated using the following formula: Calculate using equation (11); in, z max ≈0.6× R KO σ represents the peak depth of energy deposition. z ≈0.2× R KO The standard deviation of the longitudinal distribution; It represents the energy lost by an electron per unit depth in silicon material, and is used to quantify the core underlying physical quantity of vertical spatial expansion.

[0034] Step S4: Perform noise reduction processing on the data obtained in steps S2~3 according to formula (12) to obtain the system total noise floor σ of the total readout noise. total The dynamic range is calculated according to formula (13), and the combination of device parameters with high dynamic range is selected to achieve a comprehensive analysis of the noise of the obtained circuit. Specifically, the noise reduction process includes: kTC noise (reset noise) processing, CDS suppression processing, 1 / f flicker noise processing, thermal noise (channel noise) processing, column fixed pattern noise (ColumnFPN) processing, pixel fixed pattern noise (PixelFPN) processing, and ADC quantization noise processing.

[0035] The noise suppression formula is as follows: Equation (12); Equation (13) Formula Explanation: Equation (12) synthesizes independent noise sources that are not correlated using the root mean square (RSS) rule, and obtains the total noise floor of the system, where σ total σ is the system's total noise floor for total readout noise. kTC For kTC noise, σ flicker For 1 / f flicker noise, σ thermal For thermal noise, σ column For fixed pattern noise; σ pixel For fixed pattern noise of pixels, σ ADC Quantize noise for ADC; Equation (13) is used to calculate the dynamic range (DR), which is the maximum undistorted signal (full-well capacity) and the noise floor σ. total The ratio of FWC to total readout noise is the core indicator for measuring the imaging performance of EBAPS devices. In the formula, FWC is the full-well capacity of a single pixel in the CMOS readout circuit; in formula (13), the numerator FWC (full-well capacity) determines the upper limit of the maximum unsaturated signal of the device, and the denominator (total readout noise) determines the lower limit of the minimum resolvable signal of the device. The ratio of the two quantifies the total number of signal gray levels that the sensor can effectively distinguish. In the digital night vision and low light detection applications of EBAPS, high dynamic range means that the device can capture weak fluorescence and night vision signals submerged in noise edges, and can also maintain pixel unsaturation under local strong light illumination, thereby completely preserving the brightness and darkness details of the image.

[0036] Correlated double sampling (CDS) technology can effectively suppress kTC noise in simulation results. A typical CDS configuration can reduce kTC noise from 128e⁻ to below 1.0e⁻, thereby improving the accuracy of the obtained simulation results. Step S5: Simulate the vacuum packaging reliability of EBAPS devices, specifically including the following steps: Step S5: Construct a vacuum decay model as shown in Equation (14), calculate the relationship between getter lifetime, outgassing rate and temperature of the simulated EBAPS device, and analyze the thermal stress of the simulated EBAPS device. Obtain the thermal stress σ at the bonding interface according to Equation (15). stress The bonding reliability assessment and comprehensive lifetime prediction were performed. The survival reliability R(n) of the device after n cycles was calculated using the number of temperature alternation cycles (n) as the independent variable, and the simulation results were obtained.

[0037] Bond reliability assessment includes the following steps: Step S51: EBAPS devices are typical multilayer heterogeneous material packaging devices. A common structure consists of a glass window, a metal casing, and a silicon substrate bonded by anodic bonding, eutectic bonding, or epoxy adhesive. Due to the differences in the coefficient of thermal expansion (CTE) of different materials, the expansion or contraction of each layer varies when the device heats up or experiences changes in ambient temperature, resulting in significant thermal stress at the bonding interface. This assessment extracts the coefficient of thermal expansion (α) of two adjacent packaging materials (material a, material b) based on the thermal system of equation (15). a and α b By combining the temperature variation range (ΔT) of the working environment with the elastic modulus of the material, the thermal stress σ at the bonding interface is calculated. stress ; Step S52: Evaluate whether the bonding interface will be affected by the thermal stress σ at the bonding interface. stress Excessive thermal stress at the bonding interface can lead to microcracks, delamination, or warping. stress Exceeding the material's bonding strength will directly lead to vacuum seal failure (a sharp increase in leakage rate LL), causing complete damage to the device. Therefore, the simulation results and their corresponding material database parameter combinations are discarded.

[0038] Step S53: According to the fatigue reliability model of equation (16), the thermal stress σ at the bonding interface is calculated. stress The model is input with the acceleration aging factor (and the vacuum decay trend) and the number of temperature cycling cycles (n) experienced by the device as the independent variable. The survival reliability R(n) of the device after n cycles is calculated to predict the overall lifespan of the device. Under real complex working conditions, the failure of EBAPS devices is often not caused by a single factor, but is the result of competition and coupling of multiple failure modes such as vacuum failure (getter depletion) and mechanical failure (bond cracking). Therefore, the fatigue reliability model of equation (16) can comprehensively predict the overall lifespan of the device.

[0039] The simulation results are as follows: 1. Predicted vacuum degree P(t) as a function of time; 2. Theoretical lifetime t of the getter. getter 3. Thermal stress σ at the encapsulation interface stress ; 4. The reliability R(n) of the bonded structure under thermal cycling is used for comprehensive lifetime prediction.

[0040] Its core formula is as follows: Equation (14); Equation (15); Equation (16) Formula explanation: Equation (14) predicts the decay trend of vacuum degree over time; Equation (15) calculates the magnitude of thermal stress caused by the mismatch of the thermal expansion coefficients of materials; Equation (16) predicts the life and failure probability of bonded structures under thermal cycling fatigue based on Weibull distribution.

[0041] Where P0 is the initial vacuum level of the environment in which the simulated EBAPS device is located, L is the vacuum packaging leak rate of the simulated EBAPS device, Q is the gas escaping rate of the simulated EBAPS device, V is the cavity volume of the simulated EBAPS device, and t is time, representing the cumulative working or storage time experienced by the EBAPS device after vacuum packaging is completed (or the internal getter is activated); σ stress Thermal stress represents the thermomechanical stress generated at the bonding or sealing interface between two adjacent heterogeneous packaging materials with different physical properties. Examples include the sealing interface between the incident window and the package of EBAPS devices, the mounting interface between the silicon substrate and the packaging substrate, and the sealing interface between the photocathode substrate and the package. a and α b ΔT represents the coefficients of thermal expansion of adjacent encapsulation materials a and b on both sides of the bonding interface; ΔT is the difference between the bonding process temperature and room temperature, used to calculate the residual thermal stress after cooling; E represents... mod R represents the elastic modulus of a material, where "material" refers to the main material at the bonding interface that bears thermal stress, such as rigid substrate / window materials, metal casing materials, quartz glass, and ceramic substrates. （n） To determine the reliability of the bond after n thermal cycles (using the Weibull fatigue model), R inital For initial reliability; N f Characteristic lifetime refers to the bonding interface of a device under a preset thermal stress σ. stress The characteristic lifetime is the number of typical thermal cycles that the system can withstand under certain conditions. β is a shape parameter.

[0042] The vacuum decay model, as shown in equation (14), is not only used to predict the linear decay trend of vacuum after getter saturation, but also serves as the core basis for calculating getter lifetime. Specifically, let the total getter capacity be... C getter During normal operation of the getter, its adsorption rate is sufficient to offset the gas increment (L+Q), and the chamber pressure is maintained at P0; when the accumulated gas volume achieve C getter When the getter reaches saturation and becomes ineffective, the time at this point is... This is the theoretical lifespan of the getter. After this theoretical lifespan is exceeded, the vacuum level of the device will begin to deteriorate linearly according to equation (14).

[0043] Step S6: Collect product specifications and performance test results corresponding to each model of real product, construct product specification database, calculate the relative error between the simulation result of the i-th parameter of the i-th model device obtained in steps S1~5 and the actual product performance data of the i-th model device according to formula (17), realize the reliability verification of the simulation result. When the relative error is less than 5%, the above steps S1~5 are applicable to the simulation of the i-th parameter of the i-th model device. Select the i-th parameter from the material database of the i-th device model, and then set the i-th parameter as the i” parameter according to the experimental design requirements. Repeat steps S1~5 to obtain the simulation result simulated' corresponding to the i” parameter of the i-th device model. According to the device performance evaluation standard, determine whether the simulation result simulated' is improved relative to the actual product performance data. If so, select the obtained i” parameter for actual device assembly.

[0044] According to the R&D requirements, the initial i-th parameter can be set to a, and a+1 can be set to the i”-th parameter. The performance change during the period corresponding to the i”-th parameter can be obtained by simulation using the above method. This reduces the amount of experimentation, quickly locates the key parameters affecting the device performance, and accurately locates the possible trend or direction of change of the key parameters, thereby improving R&D efficiency.

[0045] In one specific embodiment, the product specification database includes parameter specifications and performance parameters for at least several products such as ISIE1280, LD250, and HHU EBAPS. This module automatically calculates the relative error between the simulation results and the product specifications.

[0046] The relevant calculation formula is as follows: Equation (17) Formula Explanation: It provides a standardized quantitative evaluation method, automatically calculates the percentage of relative deviation between the simulation prediction value and the actual hardware indicator, and serves as an objective basis for judging whether the results obtained by the simulation model are valid, thus ensuring the authenticity and validity of the results obtained by the simulation model.

[0047] It automatically generates a verification report, outputting the pass / fail status and error percentage. The verification standard is that an error within ±15% is considered a pass.

[0048] See Figure 2 The basic simulation device for an electron bombardment active pixel sensor provided in this application includes: The materials database module is used to retrieve various EBAPS device parameters from existing literature databases via a web crawler, store them in the materials database, and retrieve them as needed. Each parameter is labeled with the literature information from which it was obtained, so as to trace the source of the parameters and support parameter tracing. The photocathode physics module is used to retrieve various EBAPS device parameters from the materials database and calculate the photocathode quantum efficiency based on the Beer-Lambert absorption law and the escape depth model. The electron trajectory and multiplication module is used to retrieve various EBAPS device parameters from the material database. Based on the Kanaya-Okayama model, it simulates the penetration, scattering and multiplication process of high-energy electrons in silicon substrates, and obtains the electron penetration depth, ionization yield and backscattering coefficient related to the penetration, scattering and multiplication process. It also simulates the secondary electron multiplication process to obtain the gain distribution and space broadening. Since the electron multiplication process has statistical fluctuations and the gain follows a log-normal distribution, this module can simulate the statistical distribution characteristics of the gain. The CMOS noise module is used to perform noise reduction processing on the data obtained in steps S2~3 according to formula (12) to obtain the system total noise floor σ of the total readout noise. total The dynamic range is calculated according to formula (13), and the combination of device parameters with high dynamic range is selected to achieve a comprehensive analysis of the noise of the obtained circuit. The noise suppression formula is as follows: Equation (12) Equation (13); Where, σ total σ is the system's total noise floor for total readout noise. kTC For kTC noise, σ flicker For 1 / f flicker noise, σ thermal For thermal noise, σ column For fixed pattern noise; σ pixel For fixed pattern noise of pixels, σ ADC Quantize noise for ADC; The vacuum sealing module is used to construct the vacuum decay model as shown in Equation (14), calculate the getter lifetime, outgassing rate and temperature relationship of the simulated EBAPS device, and analyze the thermal stress of the simulated EBAPS device to obtain the thermal stress σ at the bonding interface according to Equation (15). stress And perform bonding reliability assessment and comprehensive lifetime prediction. Using the number of temperature alternation cycles n experienced by the device as the independent variable, calculate the survival reliability R(n) of the device after n cycles according to formula (16) to obtain the simulation results. Equation (14); Equation (15); Equation (16) Where P0 is the initial vacuum level of the environment simulating the EBAPS device, L is the vacuum packaging leak rate of the simulating EBAPS device, Q is the gas escape rate of the simulating EBAPS device, V is the cavity volume of the simulating EBAPS device, and t is time, representing the cumulative working or storage time experienced by the EBAPS device after vacuum packaging is completed or the internal getter is activated; σ stress Thermal stress represents the thermomechanical stress generated at the bonding or sealing interface between two adjacent heterogeneous packaging materials with different physical properties. Examples include the sealing interface between the incident window and the package of EBAPS devices, the mounting interface between the silicon substrate and the packaging substrate, and the sealing interface between the photocathode substrate and the package. a and α b ΔT represents the coefficients of thermal expansion of adjacent encapsulation materials a and b on both sides of the bonding interface; ΔT is the difference between the bonding process temperature and room temperature, used to calculate the residual thermal stress after cooling; E represents... mod R represents the elastic modulus of a material, where "material" refers to the main material at the bonding interface that bears thermal stress, such as rigid substrate / window materials, metal casing materials, quartz glass, and ceramic substrates. （n） To determine the reliability of the bond after n thermal cycles (using the Weibull fatigue model), R inital For initial reliability; N f Characteristic lifetime refers to the bonding interface of a device (such as the sealing interface between the incident window and the metal shell, or the mounting interface between the silicon substrate and the ceramic substrate) under a predetermined thermal stress (σ). stress The characteristic lifetime is the number of typical thermal cycles that the material can withstand under the influence of β. β is the shape parameter. The verification framework module is used to collect product specifications and performance test results corresponding to each model of real product, build a product specification database, and calculate the relative error between the simulation result of the i-th parameter of the i-th model device obtained in steps S1~5 and the actual product performance data of the i-th model device according to formula (17). When the relative error is less than 5%, steps S1~5 are applicable to the simulation of the i-th parameter of the i-th type device. Equation (17); During simulation, the remaining parameters are set according to the corresponding parameters of the real product. Example

[0049] Following the above steps, three real EBAPS products, model ISIE1280, LD250, and HHU, were simulated. The simulation results were then compared with the specifications of the real products to verify their accuracy. Verification parameters included: electron gain at 3keV accelerating voltage, quantum efficiency at 650nm wavelength, dynamic range, and readout noise. The verification results are shown in the table below. Figure 3As shown in the results, 4 out of 5 verifications passed (within ±15% tolerance), resulting in an overall verification pass rate of 80%. In this embodiment, it is demonstrated that this simulation method can be used for reliable simulation of the ISIE1280's gain @ 3keV performance; the LD250's gain @ 3keV performance; the LD250's QE @ 650nm performance; and the LD250's dynamic range performance.

[0050] surface

[0051] Based on the results in the table, performance verification can be performed by modifying parameters through a simulation system. This allows for rapid verification in subsequent verification simulations. The LD250 device can be selected, and its relevant performance parameters can be experimentally modified. The performance changes can then be verified using this simulation method to quickly locate key parameters and their changing trends and directions, thereby shortening experimental time and workload and improving experimental efficiency.

[0052] Analysis of the verification errors revealed that the gain error (2.9–7.4%) mainly stemmed from the approximation of the Kanaya-Okayama model and the empirical formula for the backscattering coefficient. Optimizing the model parameters could further reduce this error. The quantum efficiency error (0.8%) was relatively small, validating the accuracy of the Beer-Lambert absorption law and the escape depth model. The dynamic range error (4.9–10.7%) primarily arose from the deviation between the typical and actual values ​​of the CMOS process parameters. Accurate simulation of the dynamic range calculation relied on the noise model and the full-well capacity. Example

[0053] In the digital night vision application optimization case: following the above steps S1~5, the input conditions are selected as GaAs (NEA) photocathode, 8 kV acceleration voltage, 10 μm silicon substrate thickness, and 65nm CMOS process for simulation.

[0054] The simulation results show a quantum efficiency of 32% @ 650nm, a gain of 46,300x @ 3keV, a readout noise of 1.06 e⁻rms, and a dynamic range of 79.7 dB, which meets the requirements for digital night vision applications (QE>25%, noise<3 e⁻, DR>60 dB). The simulation results indicate that the simulation performance of the device obtained by using this method to indicate the optimization direction is better than the industry average. Example

[0055] In the case study of fluorescence lifetime imaging application optimization, the input conditions are GaAs photocathode (NEA), accelerating voltage 5kV, silicon substrate thickness 5 μm, and CMOS process 65nm. The simulation is performed according to the above steps S1~5.

[0056] The simulation results show that the time resolution is less than 100 ps, ​​the gain is 25,000x @ 3keV, and the readout noise is 1.2 e⁻rms, which meets the requirements for fluorescence lifetime imaging applications (time resolution <200 ps) and can achieve high-precision time-resolved imaging.

[0057] This demonstrates that the method can quickly locate key optimization parameters and their optimization direction.

[0058] The method provided in this application has the following effects: First, it shortens the R&D cycle by predicting performance before device manufacturing, reducing trial and error costs. Traditional methods require multiple process iterations, while this invention can complete design optimization during the simulation stage, shortening the R&D cycle by 30%-50%.

[0059] Second, it improves design quality. Simulation based on physical models is more accurate than empirical estimation. This invention uses a verified physical model, and the simulation results deviate from the actual product by less than 15%.

[0060] Third, it promotes knowledge reuse. Modular design allows simulation code to be reused by other researchers. Each module is independently encapsulated, supporting functional expansion and customized development.

[0061] Fourth, establish verification benchmarks to provide standardized verification methods for EBAPS simulations, with a built-in product specification database to support automated verification and report generation.

[0062] Fifth, it reduces R&D costs, decreases the number of experiments, and saves on material and equipment costs. A single simulation can replace dozens of process experiments, reducing costs by more than 60%.

[0063] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A fundamental simulation method for an electron-bombardment active pixel sensor, characterized in that, Includes the following steps: Step S1: After obtaining various EBAPS device parameters from existing literature databases through a web crawler, the parameters are stored in the materials database and retrieved as needed. Each parameter is labeled with the literature information from which it was obtained, so as to trace the source of the parameters and support parameter tracing. Step S2: Retrieve various EBAPS device parameters from the materials database, and calculate the photocathode quantum efficiency based on the Beer-Lambert absorption law and escape depth model; Step S3: Retrieve various EBAPS device parameters from the material database. Based on the Kanaya-Okayama model, simulate the penetration, scattering, and multiplication processes of high-energy electrons in the silicon substrate to obtain the electron penetration depth, ionization yield, and backscattering coefficient related to the penetration, scattering, and multiplication processes. Simulate the secondary electron multiplication process to obtain the gain distribution and spatial broadening. Step S4: Perform noise reduction processing on the data obtained in steps S2~3 according to formula (12) to obtain the system total noise floor σ of the total readout noise. total The dynamic range is calculated according to formula (13), and the combination of device parameters with high dynamic range is selected to achieve a comprehensive analysis of the noise of the obtained circuit. The noise suppression formula is as follows: Equation (12) Equation (13); Where, σ total σ is the system's total noise floor for total readout noise. kTC For kTC noise, σ flicker For 1 / f flicker noise, σ thermal For thermal noise, σ column For fixed pattern noise; σ pixel For fixed pattern noise of pixels, σ ADC Quantize noise for ADC; Step S5: Construct a vacuum decay model as shown in Equation (14), calculate the getter lifetime, outgassing rate and temperature relationship of the simulated EBAPS device, analyze the thermal stress of the simulated EBAPS device, and obtain the thermal stress σ at the bonding interface according to Equation (15). stress And perform bonding reliability assessment and comprehensive lifetime prediction. Using the number of temperature alternation cycles n experienced by the device as the independent variable, calculate the survival reliability R(n) of the device after n cycles according to formula (16) to obtain the simulation results. Equation (14) Equation (15) Equation (16) Where P0 is the initial vacuum level of the environment simulating the EBAPS device, L is the vacuum packaging leak rate of the simulating EBAPS device, Q is the gas escape rate of the simulating EBAPS device, V is the cavity volume of the simulating EBAPS device, and t is time, representing the cumulative working or storage time experienced by the EBAPS device after vacuum packaging is completed or the internal getter is activated; σ stress Thermal stress represents the thermomechanical stress generated at the bonding or sealing interface between two adjacent heterogeneous packaging materials with different physical properties. Examples include the sealing interface between the incident window and the package of EBAPS devices, the mounting interface between the silicon substrate and the packaging substrate, and the sealing interface between the photocathode substrate and the package. a and α b ΔT represents the coefficients of thermal expansion of adjacent encapsulation materials a and b on both sides of the bonding interface; ΔT is the difference between the bonding process temperature and room temperature, used to calculate the residual thermal stress after cooling; E represents... mod R represents the elastic modulus of a material, where "material" refers to the main material at the bonding interface that bears thermal stress, such as rigid substrate / window materials, metal casing materials, quartz glass, and ceramic substrates. （n） To assess the reliability of the bond after n thermal cycles, the Weibull fatigue model is adopted, R inital For initial reliability; N f Characteristic lifetime refers to the bonding interface of a device under thermal stress σ. stress Under certain conditions, the number of typical thermal cycles it can withstand is the characteristic lifetime; β is the shape parameter.

2. The method according to claim 1, characterized in that, It also includes step S6: collecting product specifications and performance test results corresponding to each model of real product, constructing a product specification database, and calculating the relative error between the simulation result of the i-th parameter of the i-th model device obtained in steps S1~5 and the actual product performance data of the i-th model device according to formula (17); When the relative error is less than 5%, steps S1~5 are applicable to the simulation of the i-th parameter of the i-th type device. Equation (17).

3. The method according to claim 1, characterized in that, The parameters of each EBAPS device include: photocathode material parameters, silicon substrate parameters, CMOS process parameters, and packaging material parameters; The parameters of photocathode materials include: band gap energy, electron affinity, absorption coefficient, electron escape depth, peak quantum efficiency, spectral response range, dark current density, thermal expansion coefficient, and lattice constant. Silicon substrate parameters include: band gap, carrier mobility, intrinsic carrier concentration, ionization energy, density, thermal conductivity, and melting point; CMOS process parameters include: process node, power supply voltage, conversion gain, full-well capacity, and ADC bit width. The parameters of the packaging material include: coefficient of thermal expansion, elastic modulus, and melting point.

4. The method according to claim 1, characterized in that, Step S2 includes the following steps: Step S21: Calculate the photon energy E according to the incident light wavelength based on the simulation parameters using formula (1). ph ; Step S22: Query the material database according to equations (1) to (4) to obtain the absorption coefficient α and escape depth L of the device to be simulated. e Calculate the photon absorption probability P abs and electron escape probability P escape According to the photon absorption probability P abs and electron escape probability P escape The quantum efficiency QE was obtained, and the spectral response curve was generated as the quantum efficiency of the photocathode. The formulas are as follows: Equation (1) Equation (2) Equation (3) Equation (4) Among them, P abs P represents the probability of photon absorption. escape E represents the electron escape probability; QE represents the quantum efficiency; E represents the quantum efficiency. ph λ is the photon energy; h is Planck's constant; c is the speed of light; λ is the incident light wavelength; α is the absorption coefficient; d is the photocathode thickness; L e χ represents the electron escape depth; E represents the electron affinity; excess Excess energy.

5. The method according to claim 1, characterized in that, Step S3 includes the following steps: Step S31: Based on the electron carrying energy of the photocathode conversion and various EBAPS device parameters, calculate the electron penetration depth R according to equation (5). KO ; Step S32: Calculate the ionization yield N and backscattering coefficient η according to equations (7) and (6); Step S33: Simulate the secondary electron multiplication process according to (8), obtain the gain distribution according to equation (9), and obtain the lateral broadening and longitudinal broadening according to equations (10) and (11) respectively. The lateral broadening and longitudinal broadening express the spatial broadening. The calculation formula used is as follows: Equation (5) Equation (6) Equation (7) Equation (8); Among them, R KO Let A be the electron penetration depth, A be the atomic weight of the silicon substrate, and E be the electron penetration depth. e Where is the incident electron energy, Z is the atomic number of the silicon substrate, ρ is the density of the silicon substrate material; W = 3.66V is the average ionization energy of silicon, N is the ionization yield; η is the backscattering coefficient. G The gain value represents the actual number of electron-hole pairs generated by a single incident electron (or a single pixel in a single exposure). E dep G represents the actual energy deposited in silicon, and G is a secondary correction factor that takes into account carrier collection efficiency and device structure effects; it can be obtained from literature data. secondary It is a quadratic gain factor; Gain distribution formula: Equation (9) Where: G is the gain value, μ is the mean of the logarithmic gain, calculated according to... The calculated value is σ, which is the standard deviation of the logarithmic gain (typically around 0.3 to 0.5). The average gain of the multiple gain values ​​G calculated by formula (8) refers to the average number of electron-hole pairs obtained under the bombardment of a large number of incident electrons or under the statistical average of the entire pixel array of the device. Lateral widening is done according to the formula: Calculate using equation (10); in: The standard deviation of the lateral spatial expansion (unit: μm); R KO E is the electron penetration depth calculated using formula (5). c The critical energy (approximately 1-2 keV in silicon); E e The energy of the incident electron; Vertical widening is calculated using the following formula: Calculate using equation (11); in, z max ≈0.6× R KO σ represents the peak depth of energy deposition. z ≈0.2× R KO The standard deviation of the longitudinal distribution; It represents the energy lost by an electron per unit depth in silicon material, and is used to quantify the core underlying physical quantity of vertical spatial expansion.

6. The method according to claim 1, characterized in that, The simulation results obtained in step S5 include: the predicted value of vacuum degree P(t) as a function of time; Theoretical lifespan of getter (t) getter ; Thermal stress σ at the encapsulation interface stress ; The reliability R(n) of the bonded structure under thermal cycling is used for comprehensive lifetime prediction.

7. The method according to claim 1, characterized in that, Step S5 includes the following steps: Step S51: Evaluate the coefficients of thermal expansion (α) of the two adjacent encapsulation materials (material a, material b) extracted according to equation (15) for the thermal system. a and α b By combining the temperature variation range (ΔT) of the working environment with the elastic modulus of the material, the thermal stress σ at the bonding interface is calculated. stress ; Step S52: Determine the thermal stress σ at the bonding interface stress If the material's bonding strength is exceeded, the simulation result and its corresponding material database parameter combination are discarded; if not, they are output as simulation results. Step S53: According to the fatigue reliability model of equation (16), the thermal stress σ at the bonding interface is calculated. stress The model is input with the acceleration aging factor (and the vacuum degree decay trend) and the number of temperature alternation cycles (n) experienced by the device as the independent variable. The device's survival reliability R(n) after n cycles is calculated to predict the overall lifespan of the device.

8. A basic simulation device for an electron bombardment active pixel sensor, characterized in that, include: The materials database module is used to retrieve various EBAPS device parameters from existing literature databases via a web crawler, store them in the materials database, and retrieve them as needed. Each parameter is labeled with the literature information from which it was obtained, so as to trace the source of the parameters and support parameter tracing. The photocathode physics module is used to retrieve various EBAPS device parameters from the materials database and calculate the photocathode quantum efficiency based on the Beer-Lambert absorption law and the escape depth model. The electron trajectory and multiplication module is used to retrieve various EBAPS device parameters from the material database. Based on the Kanaya-Okayama model, it simulates the penetration, scattering and multiplication process of high-energy electrons in silicon substrates, and obtains the electron penetration depth, ionization yield and backscattering coefficient related to the penetration, scattering and multiplication process. It also simulates the secondary electron multiplication process to obtain the gain distribution and space broadening. Since the electron multiplication process has statistical fluctuations and the gain follows a log-normal distribution, this module can simulate the statistical distribution characteristics of the gain. The CMOS noise module is used to perform noise reduction processing on the data obtained in steps S2~3 according to formula (12) to obtain the system total noise floor σ of the total readout noise. total The dynamic range is calculated according to formula (13), and the combination of device parameters with high dynamic range is selected to achieve a comprehensive analysis of the noise of the obtained circuit. The noise suppression formula is as follows: Equation (12) Equation (13); Where, σ total σ is the system's total noise floor for total readout noise. kTC For kTC noise, σ flicker For 1 / f flicker noise, σ thermal For thermal noise, σ column For fixed pattern noise; σ pixel For fixed pattern noise of pixels, σ ADC Quantize noise for ADC; The vacuum sealing module is used to construct the vacuum decay model as shown in Equation (14), calculate the getter lifetime, outgassing rate and temperature relationship of the simulated EBAPS device, and analyze the thermal stress of the simulated EBAPS device to obtain the thermal stress σ at the bonding interface according to Equation (15). stress And perform bonding reliability assessment and comprehensive lifetime prediction. Using the number of temperature alternation cycles n experienced by the device as the independent variable, calculate the survival reliability R(n) of the device after n cycles according to formula (16) to obtain the simulation results. Equation (14) Equation (15) Equation (16) Where P0 is the initial vacuum level of the environment simulating the EBAPS device, L is the vacuum packaging leak rate of the simulating EBAPS device, Q is the gas escape rate of the simulating EBAPS device, V is the cavity volume of the simulating EBAPS device, and t is time, representing the cumulative working or storage time experienced by the EBAPS device after vacuum packaging is completed or the internal getter is activated; σ stress Thermal stress represents the thermomechanical stress generated at the bonding or sealing interface between two adjacent heterogeneous packaging materials with different physical properties. Examples include the sealing interface between the incident window and the package of EBAPS devices, the mounting interface between the silicon substrate and the packaging substrate, and the sealing interface between the photocathode substrate and the package. a and α b ΔT represents the coefficients of thermal expansion of adjacent encapsulation materials a and b on both sides of the bonding interface; ΔT is the difference between the bonding process temperature and room temperature, used to calculate the residual thermal stress after cooling; E represents... mod R represents the elastic modulus of a material, where "material" refers to the main material at the bonding interface that bears thermal stress, such as rigid substrate / window materials, metal casing materials, quartz glass, and ceramic substrates. （n） To assess the reliability of the bond after n thermal cycles, the Weibull fatigue model is adopted, R inital For initial reliability; N f Characteristic lifetime refers to the bonding interface of a device under a preset thermal stress (σ). stress The characteristic lifetime is the number of typical thermal cycles that the system can withstand under the influence of β. β is a shape parameter.

9. The apparatus according to claim 8, characterized in that, Also includes: The verification framework module is used to collect product specifications and performance test results corresponding to each model of real product, build a product specification database, and calculate the relative error between the simulation result of the i-th parameter of the i-th model device obtained in steps S1~5 and the actual product performance data of the i-th model device according to formula (17). When the relative error is less than 5%, steps S1~5 are applicable to the simulation of the i-th parameter of the i-th type device. Equation (17).

Images