Simulation method for intrinsic detection efficiency of non-uniform superconducting strip photon detector

Abstract

The invention discloses a simulation method for the intrinsic detection efficiency of a non-uniform superconducting strip photon detector, and the method comprises the steps: building a model for simulating the electrical non-uniformity and geometric non-uniformity, representing the non-uniformity and granularity of a superconducting critical temperature used by the electrical non-uniformity, and completing the modeling simulation of a non-uniform SSPD; the method comprises the following steps of: simulating photon incidence by using an initial hot spot, acquiring a forming, growing or fading process of a stop band based on the heterogeneity of a superconducting strip in combination with granularity and spatial distribution, and acquiring first intrinsic detection efficiency; based on the heterogeneity of the superconducting strip, the thermoelectric evolution process of the stopband in the SSPD longitudinal direction is obtained in combination with the finally formed stopband, and the second intrinsic detection efficiency is obtained; the curve corresponding points of the first intrinsic detection efficiency and the second intrinsic detection efficiency are multiplied to serve as the final intrinsic detection efficiency; and improving the performance of the photon detector based on the final intrinsic detection efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of photon detectors, in particular to a simulation method of intrinsic detection efficiency of a non-uniform superconducting strip photon detector. BACKGROUND

[0002] After more than 20 years of development, superconducting strip photon detectors (SSPD) have become a kind of photon detector with excellent comprehensive performance, and have been applied in many fields such as optical imaging and optical quantum information processing. Although the experimental research and application of SSPD have made great progress, the theoretical model and device physics of SSPD still have deficiencies. At present, there is still a lack of simulation platform that can simulate the comprehensive performance of SSPD, especially a lack of effective simulation method of intrinsic detection efficiency (IDE).

[0003] Problems in the field: In the past, researchers have proposed some theories about the IDE of SSPD, but these theories are all focused on the study of uniform SSPD. However, the actual processed SSPD has non-uniformity, including electrical non-uniformity and geometric non-uniformity. The simulation method of IDE of SSPD considering these non-uniformities is not perfect. How to construct a theoretical model and simulation framework containing these non-uniformities to simulate the IDE of non-uniform SSPD is a problem to be solved.

[0004] In addition, the detection process of SSPD after absorbing incident photons includes three sequential stages: first, energy down-conversion; second, formation of a transverse resistive strip; third, longitudinal thermoelectric evolution. The IDE of the first stage is 100%, that is, it must occur. Current research on IDE is limited to the second stage, and the third stage is considered to occur under the premise that the second stage is completed. This conclusion is valid in the case of uniform SSPD; however, in the case of non-uniform SSPD, this conclusion is not valid, that is, the IDE of the third stage must be considered and simulated, and included in the overall IDE. This is the second problem to be solved. SUMMARY

[0005] ​The application provides a simulation method for intrinsic detection efficiency of a non-uniform superconducting strip photon detector. A simulation method for intrinsic detection efficiency of a non-uniform superconducting strip photon detector, the method comprises: A model for simulating electrical and geometric non-uniformity is established, the electrical non-uniformity is represented by non-uniformity of superconducting critical temperature and granularity, and modeling simulation of the non-uniform SSDP is completed; An initial hot spot is used to simulate photon incidence, based on non-uniformity of the superconducting strip, the formation, growth or recession process of the stop band is obtained by combining granularity and spatial distribution, and the first intrinsic detection efficiency is obtained; Based on the non-uniformity of the superconducting strip, the thermal-electric evolution process of the stop band in the longitudinal direction of the SSDP is obtained by combining the finally formed stop band, and the second intrinsic detection efficiency is obtained; The corresponding points of the curves of the first intrinsic detection efficiency and the second intrinsic detection efficiency are multiplied, and the final intrinsic detection efficiency is obtained; Based on the final intrinsic detection efficiency, the performance of the photon detector is improved.

[0006] The model for simulating electrical and geometric non-uniformity is: In the NbN superconducting SSDP with ideal rectangular geometry, only the influence of electrical non-uniformity is considered, the superconducting critical temperature has a spatial distribution , the mean value is , and the mean square deviation is The definition of electrical non-uniformity is ; The physical quantity for measuring electrical non-uniformity is granularity, which is defined as: the SSDP is considered uniform below this scale, and the characteristic length starts to change above this scale; the granularity is determined by the polydomain size of NbN.

[0007] Geometric non-uniformity refers to the non-uniformity of film thickness, for a superconducting film with non-uniform thickness, it is assumed that the thickness has a spatial distribution , the distribution function is Gaussian, the mean value is , and the mean square deviation is The definition of geometric non-uniformity is .

[0008] The process of obtaining the formation, growth, or regression of the blocking band by combining particle size and spatial distribution, and obtaining the first intrinsic detection efficiency, is as follows: the first intrinsic detection efficiency is obtained by the Monte Carlo method based on the formation, growth, or regression of the blocking band.

[0009] The formation of the stopband exhibits two evolutionary patterns: 1) the stopband does not grow and disappears after a period of time; 2) the stopband disappears rapidly; in both cases, photon loss occurs.

[0010] The combination of the final formed stopband to obtain the thermoelectric evolution process of the stopband in the longitudinal direction of the SSPD, and the resulting second intrinsic detection efficiency is: When the bias current is close to or below the threshold current that allows the thermoelectric evolution to be completed in the stopband The presence of time inhomogeneities leads to photon loss, affecting the thermoelectric evolution stage. - The curve broadens and takes an "S" shape, allowing the second intrinsic detection efficiency to be obtained using the Monte Carlo method.

[0011] The beneficial effects of the technical solution provided by this invention are: 1. This invention provides a more realistic simulation method for the intrinsic detection efficiency of SSPDs. Specifically, it provides a simulation method for the non-uniformity of superconducting strips; an IDE simulation method for the formation process of the transverse stopband in non-uniform superconducting strips; and an IDE simulation method for the longitudinal thermoelectric evolution process of non-uniform superconducting strips. These simulation methods provide a basis and platform for the simulation design of SSPDs, which is helpful for the research and development of SSPDs. 2. The simulation method provided by this invention comprehensively considers the electrical and geometric non-uniformity in non-uniform SSPDs, and more accurately describes the dynamic formation mechanism of the transverse stopband and the longitudinal thermoelectric coupling evolution process. This allows the simulation model to more accurately reflect the microscopic physical processes of hotspot formation, expansion, and signal generation in actual devices, thus providing a reliable theoretical tool and quantitative basis for optimizing the geometry, material formulation, and electrode design of superconducting strips. Based on this, it can specifically guide the synergistic optimization of key performance indicators such as intrinsic detection efficiency and dark count rate of photon detectors, and promote the design and manufacturing of high-performance, high-reliability SSPD devices. Attached Figure Description

[0012] Figure 1 A flowchart illustrating a simulation method for the intrinsic detection efficiency of a non-uniform superconducting strip photon detector; Figure 2 A schematic diagram of the Monte Carlo sampling results; Where (a)-(d) represent the non-uniformity respectively 1%, 5%, 10%, 15% of Monte Carlo samples Statistical histograms of the values; (e)-(h) correspond to respectively Simulation regions at 1%, 5%, 10%, and 15% Spatial distribution map.

[0013] Figure 3 A schematic diagram of the spatial distribution of the normalized superconducting order parameter and the current density streamlines under steady state; Among them, electrical non-uniformity is 5%, with particle sizes of (a) (b) (c) (d) A schematic diagram.

[0014] Figure 4 A schematic diagram illustrating the relationship between the detection threshold current and the lateral position of the incident photon; Wherein, the width of SSPD is (a) (b) The photon wavelengths are 1310, 1550, and 2000 nm (from bottom to top).

[0015] Figure 5 Width SSPD schematic diagram; Among them, the incident photons with wavelengths of 1310, 1550, and 2000 nm had Fano fluctuation intensities of respectively. (Thin solid line) and (Thick solid line) - Schematic diagram of the curve.

[0016] Figure 6 Width SSPD schematic diagram; Wherein, the bias currents are respectively (Following the directions of the black arrows), the Fano fluctuation intensity is... Inner quantum efficiency and photon wavelength - Schematic diagram of the curve.

[0017] Figure 7 Width Particle size The SSPD, with incident photons at a wavelength of 1550 nm, respectively in ; ; (From left to right, according to the arrow direction) Simulation results in three cases - Schematic diagram of the curve; Figure 8 Width Particle size Inhomogeneity , A schematic diagram of the non-uniform SSPD with an incident photon wavelength of 1310 nm. Among them, (a) is - (b) is a schematic diagram of the curve. - Schematic diagram of curve simulation; the dashed line in the figure corresponds to the case of uniform SSPD.

[0018] Figure 9 Width Particle size Inhomogeneity , A schematic diagram of the non-uniform SSPD with an incident photon wavelength of 1000 nm.

[0019] Among them, (a) is - (b) is a schematic diagram of the curve. - Schematic diagram of curves; (c) represents the total. - Schematic diagram of the curve. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below.

[0021] Example 1 See Figure 1 This invention provides a simulation method for the intrinsic detection efficiency of a non-uniform superconducting strip photon detector. The overall scheme of this method includes: (1) a simulation method for the non-uniformity of the superconducting strip; (2) an IDE simulation method for the second stage of photodetection of the non-uniform superconducting strip, namely the formation process of the transverse stopband; and (3) an IDE simulation method for the third stage of the non-uniform superconducting strip, namely the longitudinal thermoelectric evolution process, as detailed below: 101: Establish a model to simulate electrical and geometric inhomogeneities, where electrical inhomogeneities are represented by the inhomogeneity of the superconducting critical temperature and the particle size, and complete the modeling and simulation of the inhomogeneous SSPD. 102: Using the initial hot spot to simulate photon incidence, based on the non-uniformity of the superconducting strip, and combining the particle size and spatial distribution, the formation, growth or decay process of the stopband is obtained, and the first intrinsic detection efficiency, i.e., IDE1, is obtained. 103: Based on the non-uniformity of superconducting strips, the thermoelectric evolution process of the stopband in the longitudinal direction of the SSPD is obtained by combining the final formed stopband, and the second intrinsic detection efficiency, i.e., IDE2, is obtained. 104: Multiply the corresponding points of the curves for the first intrinsic detection efficiency and the second intrinsic detection efficiency to obtain the final intrinsic detection efficiency, i.e., IDE; 105: Improve the performance of photon detectors based on the final intrinsic detection efficiency.

[0022] In summary, the embodiments of the present invention, through the above steps 101-105, can specifically guide the synergistic optimization of key performance indicators of photon detectors such as intrinsic detection efficiency and dark count rate, thereby promoting the design and manufacturing of high-performance, high-reliability SSPD devices.

[0023] Example 2 The design principles in Example 1 will be further explained below with reference to the simulation process. See the description below for details: 201: Simulation method for non-uniformity of superconducting strips; Both theory and experiments demonstrate that the superconducting critical temperature of dirty superconducting materials exhibits spatial inhomogeneity under steady-state conditions. Since the superconducting critical temperature directly affects almost all electrical properties of the superconductor, this spatial inhomogeneity is termed electrical inhomogeneity. Furthermore, during the fabrication of superconducting thin films by magnetron sputtering, thickness inhomogeneity also exists at various points; in this paper, geometric inhomogeneity refers to the inhomogeneity of the film thickness.

[0024] In a NbN (niobium nitride) superconducting SSPD with an ideal rectangular geometry, considering only the effects of electrical inhomogeneity, it is assumed that the superconducting critical temperature has a spatial distribution. The mean is The mean squared error is The definition of electrical non-uniformity is... Another physical quantity for measuring electrical inhomogeneity is granularity. , is defined as: the feature length of SSPD that is considered uniform below this scale, but begins to change above this scale. It is mainly determined by the size of the polydomains of NbN.

[0025] For superconducting thin films with non-uniform thickness, it is assumed that the thickness has a spatial distribution. Its distribution function is Gaussian, and its mean is The mean squared error is The definition of geometric non-uniformity is... .

[0026] 202: IDE simulation method for the formation process of transverse stopband in non-uniform superconducting strip optical detection; Simulation Method Overview: Based on step 201, non-uniformity is introduced into the time-dependent Ginzburg-Landau (TDGL) equations to simulate the steady state of the SSPD under a fixed bias current, simulate the threshold probe current, and simulate IDE1. Following the above steps, the specific simulation method is as follows: Based on step 201, electrical inhomogeneity is added: the spatial distribution of the superconducting critical temperature is introduced into the time-dependent Ginzburg-Landau equation to simulate the effect of electrical inhomogeneity on temperature, superconducting order parameter and potential.

[0027] Based on step 201, geometric inhomogeneity is added: by normalizing the geometric parameters, the TDGL (Time-dependent Ginzburg-Landau) equation for thickness inhomogeneity is established to simulate the effect of thickness variation on superconducting properties.

[0028] Steady-state simulation: Before photon incidence, the steady-state of the superconducting magnetic field depletion device (SSPD) needs to be determined. Numerical solutions are used to ensure all physical quantities reach a steady state. By solving for the steady-state distribution of the SSPD under bias current, the spatial distribution of the superconducting order parameter and current density can be obtained. In actual simulations, the time required for each physical quantity to reach steady state varies for different non-uniform SSPD samples; therefore, a sufficiently long time period needs to be selected. This ensures that the SSPD can reach a steady state under all circumstances.

[0029] Due to the introduction of electrical non-uniformity, the critical current of the SSPD... Will be lower For different inhomogeneities and particle sizes, The degree of reduction varies. Detection threshold current simulation: By scanning the bias current, the detection threshold current under different incident photon positions and energies is determined, and its relationship with photon wavelength and SSPD width is analyzed. Intrinsic detection efficiency simulation: Combining Fano fluctuations, the variation curve of IDE with bias current is simulated, and its "S"-shaped characteristics and consistency with experiments are analyzed. Through the processing in step 202, the formation, growth, or decay process of the stopband is obtained, and IDE1 is obtained using the Monte Carlo method.

[0030] 203: IDE simulation method for longitudinal thermoelectric evolution process of non-uniform superconducting strip optical detection; Once the initial stopband in step 202 is fully formed, the stopband will undergo a thermoelectric evolution stage, which is mainly the process of longitudinal resistance growth and contraction of the SSPD.

[0031] When the SSPD is operating normally, after the initial stopband forms, the resulting Joule heating disrupts the superconducting state near the stopband, causing the stopband to grow rapidly in the longitudinal direction of the SSPD. The SSPD's resistance will quickly reach the kΩ level, generating a relatively steep voltage rise pulse. Subsequently, a large amount of current is diverted to the external circuit, and the Joule heating generated in the SSPD balances with the substrate's heat dissipation, halting stopband growth. As the current further diverts to the external circuit, the Joule heating generated in the SSPD becomes insufficient to balance the substrate's heat dissipation, causing the stopband to shrink and eventually disappear, completing one thermoelectric cycle.

[0032] When the bias current of the SSPD is low, the initial stopband formation may exhibit the following two evolution scenarios: (1) the stopband does not grow and disappears after a period of time; (2) the stopband disappears rapidly. In scenario (1), the Joule heat generated after the initial stopband formation is just enough to balance the heat dissipation of the substrate. In scenario (2), the Joule heat generated after the initial stopband formation is insufficient to balance the heat dissipation of the substrate. In both of these scenarios, the stopband cannot complete a normal thermoelectric evolution process, which will result in no obvious voltage pulse formation at the load, i.e., photon loss occurs.

[0033] When the bias current is close to or below the threshold current that allows the thermoelectric evolution to be completed in the stopband At that time, due to the existence of inhomogeneities leading to photon loss, the thermoelectric evolution stage... - The curve will also broaden and take on an "S" shape. IDE2 is obtained using the Monte Carlo method.

[0034] 204: If we simultaneously consider the photon losses during the initial stopband formation stage and the stopband thermoelectric evolution stage, assuming these two stages are independent, then the internal quantum efficiency of the overall process can be expressed as the product of the internal quantum efficiencies of these two stages, i.e. ; 205: Improve the performance of photon detectors based on the final intrinsic detection efficiency.

[0035] In summary, the embodiments of the present invention, through the above steps 201-205, can specifically guide the synergistic optimization of key performance indicators of photon detectors such as intrinsic detection efficiency and dark count rate, thereby promoting the design and manufacturing of high-performance, high-reliability SSPD devices.

[0036] Example 3 The following section describes the specific calculation formulas and simulation process. Figures 2-9The solutions in Examples 1 and 2 will be further described below: 301: Constructing a simulation module for the inhomogeneity of superconducting strips; Superconducting band gap parameters obtained from scanning tunneling spectroscopy (STS) measurements The spatial distribution of the superconducting bandgap was analyzed, and the average value of the superconducting bandgap parameter was extracted. and standard deviation , The range is between 4% and 6%. (Assuming...) The spatial distribution follows a normal distribution. According to the BCS (Bardeen–Cooper–Schrieffer) theory, in In this case, ,in It is the Boltzmann constant, therefore It also follows a normal distribution. According to mathematical relationships, we have... Therefore, there is Therefore, it can be based on Numerical estimation The value is also between 4% and 6%.

[0037] According to estimates The size ranges from a few nanometers to tens of nanometers, which is typical for polycrystalline domains in NbN. Simulations scanned different particle sizes. (Specific numerical range is 3.75 to 30 nm), and select The main simulation results are presented here. The average zero-temperature Ginzburg-Landau length of the non-uniform nanowire.

[0038] For superconducting thin films with non-uniform thickness, it is assumed that the thickness has a spatial distribution. Its distribution function is Gaussian, and its mean is The mean squared error is The definition of geometric non-uniformity is... . The specific value depends on the fabrication process of the superconducting thin film, and is generally estimated to be around 5%. In actual simulations, a value is selected... There are four scenarios: 1%, 5%, 10%, and 15%.

[0039] 302: Simulation module for the formation process of transverse stopband in non-uniform superconducting strip optical detection; Incorporating electrical inhomogeneity: Under conditions of electrical inhomogeneity, temperature T, superconducting order parameter Δ, and electric potential... Satisfy the following equation:

[0040]

[0041]

[0042] in, , , , These are the electron diffusion coefficient, normal state resistivity, electron heat capacity, electron-phonon inelastic scattering coefficient, reduced Planck constant, Ginzburg-Landau coherence length, and current density on the strip.

[0043] Incorporating geometric inhomogeneities: To handle inhomogeneities in the thickness direction, the TDGL equations for thickness variations are required. This involves introducing a normalized geometric parameter. ,because It follows a Gaussian distribution. It also follows a Gaussian distribution with a mean of 1 and a standard deviation of . Under the above assumptions, the geometrically inhomogeneous TDGL equation is:

[0044] To study the effect of geometric non-uniformity separately, electrical non-uniformity is neglected in the above equations; that is, the critical temperature of SSPD is used as the reference. Treat as a constant ,correspond The critical temperature at which the equation is calculated. In actual simulations, the normalized form of the equation is:

[0045] In the formula This represents the normalized superconducting order parameter.

[0046] SSPD Steady-State Simulation: In actual simulations, the time it takes for each physical quantity to reach steady state varies for different non-uniform SSPD samples. Therefore, a sufficiently long time period needs to be selected. This ensures that the SSPD reaches a steady state under all conditions. Let the non-uniformity be... 5%, with particle sizes of The spatial distribution of steady-state normalized superconducting order parameters and current density streamlines obtained from the simulation are shown. Due to the introduction of electrical inhomogeneities, the critical current of the SSPD is... Will be lower For different inhomogeneities and particle sizes, The degree of reduction varies. The normalized critical current is obtained through simulation. and The relationship. The simulation method is as follows: for each given electrical inhomogeneity and grain size, the length of the SSPD is set to be sufficiently long: Solve the steady-state equation above (i.e.: From 0 to scanning ,when Less than the critical value When the iteration results converge to .when Rise to a certain critical value When the superfluid velocity exceeds the critical value At this point, the superconductor will return to its normal state, and solving the Ginzburg-Landau equation will not reach a steady state. Furthermore, as the iteration continues, The amplitude of the oscillation increases, and the following will occur. The situation.

[0047] Simulation of threshold current detection: First, based on the TDGL (Time-dependent Ginzburg-Landau equations) coupled heat conduction model, under the initial conditions of bias current and ambient temperature, the coupled equations are numerically solved to bring the superconducting SSPD system to a stable initial state, and the spatial distribution of its superconducting order parameter, temperature field and electric potential are obtained.

[0048] After the system reaches steady state, an event of photon absorption is simulated. This event is achieved by injecting a localized thermal perturbation at a specific location in the SSPD. The spatial distribution of this perturbation is typically described by a Gaussian function, with its amplitude proportional to the incident photon energy and its size related to the photon's absorption volume. This perturbation instantaneously creates a high-temperature region locally, significantly suppressing or even completely destroying the superconducting order parameter in that region, thereby initializing a "stopped band".

[0049] After introducing photon perturbations, the coupled time-domain solution of the TDGL equation and the thermal equation is restarted to simulate the dynamic evolution of the system on a timescale of picoseconds to nanoseconds. During this process, the spatiotemporal changes of the superconducting order parameter, total resistance, and voltage across the entire SSPD are closely monitored to track the formation, growth, or decay of the stopband.

[0050] When the peak value of the voltage pulse reaches the threshold, the photon event is considered to have been successfully detected. For a given SSPD sample and photon incident conditions, the magnitude of the bias current is systematically changed using a step-scan method, and the above process is repeated to find the minimum current value that can trigger successful detection, i.e., the detection threshold current.

[0051] Intrinsic detection efficiency simulation: First, based on the TDGL coupled thermal conduction model, under set initial conditions such as bias current and ambient temperature, the coupled equations are numerically solved to bring the SSPD system to a stable initial state, obtaining its superconducting order parameter, temperature field, and potential spatial distribution. After the system reaches steady state, a photon absorption event is simulated. This event is achieved by injecting a local thermal energy perturbation at a specific location in the SSPD. The temperature rise ΔT of the hotspot follows a Gaussian distribution, thus simulating Fano energy fluctuations. This perturbation instantaneously forms a high-temperature region locally, significantly suppressing or even completely destroying the superconducting order parameter in that region, thereby initializing a "stopped band". After introducing the photon perturbation, the coupled time-domain solution of the TDGL equations and thermal equations is restarted to simulate the dynamic evolution of the system on a picosecond to nanosecond timescale. During this process, the spatiotemporal changes of the superconducting order parameter, total resistance, and voltage across the entire SSPD are closely monitored to track the formation, growth, or decay of the stopped band.

[0052] When the voltage pulse peak reaches the threshold, the photon event is considered successfully detected. The Monte Carlo method is used to repeatedly simulate the absorption of 1000 photons, and the number of photons N detected is recorded. detect The result is IDE=Ndetect / 1000.

[0053] 303: Simulation module for longitudinal thermoelectric evolution process of non-uniform superconducting strip optical detection IDE.

[0054] The temperature of the SSPD after considering coupling with external circuitry. Current It can be described by a one-dimensional thermoelectric model:

[0055]

[0056] in, The heat capacity of the SSPD consists of two parts: electronic and phonon heat capacities. , It is the thermal conductivity of SSPD. It is the heat exchange coefficient between the SSPD and the substrate. It is the resistivity of the SSPD in its normal state (i.e., the stopband in steps 202 and 302). It is the substrate temperature. It is the load capacitor. It is the kinetic energy inductor of the SSPD. This is the resistance of the SSPD. When the SSPD is in its normal operating state, the electronic heat capacity... thermal conductivity ,in, It is the Lorentz number; when the SSPD is in the superconducting state, ,in, It is Boltzmann's constant. , From the relation Decide, .

[0057] In order to simulate this stage - The curves, using the Monte Carlo method, sample 1000 critical temperatures for a given inhomogeneity and particle size. ,thickness ,width A sample represents 1000 photon incident positions on a non-uniform SSPD. For a specific bias current, the thermoelectric evolution of these 1000 samples is calculated using the thermoelectric equation. IDE2 calculates the ratio of the number of samples that can complete the thermoelectric evolution normally to the total number of samples.

[0058] Unless otherwise specified, the model numbers of the various devices in this embodiment of the invention are not limited, and any device that can perform the above functions is acceptable.

[0059] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0060] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. 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 simulation method for the intrinsic detection efficiency of a non-uniform superconducting strip photon detector, characterized in that, The method includes: A model simulating electrical and geometric inhomogeneities was established. The electrical inhomogeneity was represented by the inhomogeneity of the superconducting critical temperature and the particle size. The modeling and simulation of the inhomogeneous SSPD were completed. Using initial hotspots to simulate photon incidence, based on the non-uniformity of superconducting strips, and combining particle size and spatial distribution, the formation, growth or decay process of the stopband is obtained, and the first intrinsic detection efficiency is obtained. Based on the non-uniformity of superconducting strips, the thermoelectric evolution process of the stopband in the longitudinal direction of the SSPD is obtained by combining the final formed stopband, and the second intrinsic detection efficiency is obtained. The corresponding points of the curves for the first intrinsic detection efficiency and the second intrinsic detection efficiency are multiplied together to obtain the final intrinsic detection efficiency. The performance of the photon detector is improved based on the final intrinsic detection efficiency.

2. The simulation method for the intrinsic detection efficiency of a non-uniform superconducting strip photon detector according to claim 1, characterized in that, The model for simulating electrical and geometric inhomogeneities is as follows: In NbN superconducting SSPDs with ideal rectangular geometry, considering only the effects of electrical inhomogeneities, the superconducting critical temperature exhibits a spatial distribution. The mean is The mean squared error is The definition of electrical non-uniformity ; Another physical quantity for measuring electrical inhomogeneity is particle size. , defined as: the characteristic length of SSPD that is considered uniform below this scale, but begins to change above this scale; the grain size is determined by the polydomain size of NbN; The thickness inhomogeneity of a thin film is called geometric inhomogeneity. For a superconducting thin film with inhomogeneous thickness, the thickness has a spatial distribution. Its distribution function is Gaussian, and its mean is The mean squared error is The definition of geometric non-uniformity is .

3. The simulation method for the intrinsic detection efficiency of a non-uniform superconducting strip photon detector according to claim 1, characterized in that, The process of obtaining the formation, growth, or regression of the blocking band by combining particle size and spatial distribution is used to obtain the first intrinsic detection efficiency: the first intrinsic detection efficiency is obtained by Monte Carlo method based on the formation, growth, or regression process of the blocking band.

4. The simulation method for the intrinsic detection efficiency of a non-uniform superconducting strip photon detector according to claim 1, characterized in that, After the stopband is formed, it may exhibit the following two evolutionary scenarios: 1) The stopband does not grow and disappears after a period of time; 2) The stopband disappears rapidly; in both of these cases, photon loss occurs.

5. The simulation method for the intrinsic detection efficiency of a non-uniform superconducting strip photon detector according to claim 1, characterized in that, The combined process, which ultimately forms a stopband, is used to obtain the thermoelectric evolution of the stopband in the longitudinal direction of the SSPD, and the second intrinsic detection efficiency is obtained as follows: When the bias current is close to or below the threshold current that allows the thermoelectric evolution to be completed in the stopband The presence of time inhomogeneities leads to photon loss during the thermoelectric evolution stage. - The curve broadens and takes an "S" shape, allowing the second intrinsic detection efficiency to be obtained using the Monte Carlo method.

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