Verilog-a based modeling method for single photon avalanche diode
By using a Verilog-A-based single-photon avalanche diode modeling method, combined with Monte Carlo simulation and electrical models, the problem that existing models cannot accurately reflect electrical and statistical characteristics in circuit simulation is solved, resulting in a more accurate SPAD model that is suitable for SPAD devices of different sizes and structures.
Patent Information
- Application Number
- CN202610367089.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-24
- Publication Date
- 2026-06-23
AI Technical Summary
Existing simulation models of single-photon avalanche diodes are difficult to accurately reflect electrical and statistical characteristics in circuit simulation environments, resulting in insufficient design verification.
A Verilog-A-based modeling method is adopted, introducing underlying process perturbation factors and combining Monte Carlo simulation to achieve the unification of electrical and statistical models. By calculating the photon detection event time, dark count event occurrence time, and post-pulse trigger time, the avalanche state is dynamically updated, taking into account the effects of temperature and process fluctuations.
It realizes a more accurate SPAD model in circuit simulation, supports high-precision system simulation design, improves the realism and reliability of the model, has good compatibility and scalability, and is suitable for SPAD devices of different sizes and structures.
Smart Images
Figure CN122263771A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of microelectronic optoelectronic devices, specifically relating to a modeling method for single-photon avalanche diodes based on Verilog-A. Background Technology
[0002] Single-photon avalanche diodes (SPADs) are widely used in quantum optics, lidar, and 3D imaging due to their high sensitivity and high temporal resolution. As application requirements evolve, SPADs are showing a trend towards high integration, placing higher demands on their circuit design and system simulation.
[0003] However, most single-photon avalanche diode (SPAD) simulation models only simulate ideal breakdown characteristics, simplifying the electrical behavior of SPADs. They also lack modeling of key statistical characteristics such as photon detection efficiency, dark count, afterpulse, and timing jitter. Traditional models struggle to accurately reflect both electrical and statistical characteristics in circuit simulation environments, leading to insufficient design verification. Therefore, a SPAD model that unifies electrical characteristics and statistical behavior at the circuit simulation level is needed to support high-precision system simulation design. Summary of the Invention
[0004] To address the aforementioned problems in the existing technology, this invention provides a Verilog-A-based method for modeling single-photon avalanche diodes. The technical problem to be solved by this invention is achieved through the following technical solution: This invention provides a Verilog-A-based modeling method for single-photon avalanche diodes, implemented using Verilog-A encoding. The corresponding single-photon avalanche diode model design method includes: Model parameter definition and initialization; among which, the underlying process perturbation factor is introduced during the initialization process, and the model parameters are mapped through the underlying process perturbation factor so that the model meets the requirements of Verilog-A based Monte Carlo simulation; The state of the single-photon avalanche diode is determined. If it is avalanche off, a statistical model calculation is performed. The statistical model calculation includes calculating the photon detection event time, the dark count event time, and the after-pulse trigger time. The system determines whether to activate the avalanche state based on the statistical model calculation results. If the avalanche state is activated, the system performs electrical model calculations. The avalanche state is updated based on the electrical model calculation results and the quenching threshold current based on Gaussian distribution, and each current is output. The electrical model calculations include calculating the leakage current based on area and temperature parameters, the segmented avalanche current, and calculating the junction charge between the SPAD cathode and anode, the parasitic capacitance charge between the SPAD cathode and substrate, and the parasitic capacitance charge between the SPAD anode and substrate based on area and temperature parameters, so as to calculate the corresponding current based on the charge-current relationship.
[0005] In one embodiment of the present invention, the defined model parameters include geometric parameters, electrical parameters, quenching control parameters, junction capacitance-related parameters, temperature and time characteristic parameters, anode-cathode junction temperature characteristic parameters, and other characteristic parameters; wherein... Geometric parameters include: device radius, used to calculate the area of the SPAD; Electrical parameters include: breakdown voltage, junction capacitance temperature coefficient, and reverse saturation current; Quenching control parameters include: mean and standard deviation of quenching current, used to generate a Gaussian-distributed quenching threshold current; Junction capacitance related parameters include: junction capacitance gradient coefficient, cathode-substrate parasitic capacitance, and anode-substrate parasitic capacitance; Temperature and time characteristic parameters include: reference operating temperature and breakdown characteristic thermal voltage; The temperature characteristic parameters of the anode-cathode junction include: zero-bias junction capacitance per unit area, zero-temperature built-in potential, and the temperature coefficient of the built-in potential. Other characteristic parameters include: avalanche resistance in the medium-high overbias region, avalanche resistance in the low overbias region, operating wavelength, and overbias.
[0006] In one embodiment of the present invention, calculating the photon detection event time, the dark count event occurrence time, and the after-pulse trigger time includes: Calculate the total time jitter; the total time jitter includes Gaussian distributed time jitter components and exponential distributed time jitter components; Calculate the photon detection event time based on the total time jitter; The average dark count rate is selectively calculated using a dual-channel Arrhenius method with over-bias segmentation and temperature threshold switching. The first exponential distribution time interval of dark count events is generated based on the average dark count rate, and the occurrence time of dark count events is calculated based on the first exponential distribution time interval and the total time jitter. The second exponential distribution time interval of the subsequent pulse event is generated using an exponential distribution random number generator, and the subsequent pulse trigger time is calculated based on the second exponential distribution time interval and the total time jitter.
[0007] In one embodiment of the present invention, the leakage current is calculated based on area parameters and temperature parameters, and is expressed as: ; in, Indicates leakage current. Indicates the temperature coefficient. Indicates the current operating temperature. Indicates the reference operating temperature. Indicates the basic leakage current. , Indicates reverse saturation current. Indicates the area ratio coefficient. This represents the area of the SPAD. Indicates the reference area.
[0008] In one embodiment of the present invention, the piecewise avalanche current is calculated as follows: ; in, Indicates avalanche current. Indicates the breakdown characteristic thermal voltage. Indicates an intermediate variable for the exponential term. , This indicates an operation that first calculates the exponent and then finds the extreme value. Indicates over bias voltage. Indicates an avalanche status indicator. A value of 0 indicates that avalanche is disabled. A value of 1 indicates that an avalanche has begun. , Indicates the boundary voltage. This represents the voltage offset parameter in the medium and high voltage range. This represents the avalanche resistance in the low overvoltage region. This represents the avalanche resistance in the medium to high overvoltage region. This represents the reference value for avalanche current. This represents the voltage applied across the SPAD.
[0009] In one embodiment of the present invention, calculating the junction charge of the SPAD cathode-anode based on area and temperature parameters includes: Calculate the junction capacitance of the SPAD cathode-anode based on area and temperature parameters, and calculate the junction charge of the SPAD cathode-anode based on the junction capacitance.
[0010] In one embodiment of the present invention, the junction capacitance of the SPAD cathode-anode based on area and temperature parameters is calculated and expressed as: ; in, This represents the junction capacitance between the cathode and anode of the SPAD. This represents the area of the SPAD. This represents the junction capacitance area factor after temperature compensation. , This represents the zero-bias junction capacitance per unit area. It is the junction capacitance temperature coefficient. Indicates the current operating temperature. Indicates the reference operating temperature. This represents the built-in potential after temperature correction. , This indicates the built-in potential at zero temperature. The temperature coefficient representing the built-in potential. This represents the junction capacitance gradient coefficient; The corresponding calculation of the junction charge between the SPAD cathode and anode is expressed as follows: ; in, This indicates the junction charge between the SPAD cathode and anode. This represents the voltage difference between the anode and the cathode.
[0011] In one embodiment of the present invention, the parasitic capacitance charge of the SPAD cathode-substrate is calculated and expressed as: ; in, This represents the parasitic capacitance charge of the SPAD cathode-substrate. This represents the parasitic capacitance from the cathode to the substrate. This represents the voltage from the cathode to the substrate; The parasitic capacitance charge between the SPAD anode and substrate is calculated and expressed as: ; in, This represents the parasitic capacitance charge between the SPAD anode and the substrate. This represents the parasitic capacitance from the anode to the substrate. This represents the voltage from the anode to the substrate.
[0012] In one embodiment of the present invention, updating the avalanche state based on the calculation results of the electrical model and the quenching threshold current based on a Gaussian distribution includes: The avalanche state is updated based on the avalanche current calculated from the electrical model. The update process includes: comparing the magnitude of the avalanche current with the quenching threshold current; if the avalanche current is less than the quenching threshold current, the avalanche is quenched, the state of the single-photon avalanche diode is updated to avalanche off, and the quenching threshold current is updated; otherwise, the state of the single-photon avalanche diode is maintained as avalanche on. The quenching threshold current follows a Gaussian distribution.
[0013] The beneficial effects of this invention are: This invention proposes a Verilog-A-based modeling method for single-photon avalanche diodes (SPADs). It simultaneously implements both electrical and statistical models of the SPAD using Verilog-A. The electrical model simulates the SPAD's electrical characteristics by dynamically calculating piecewise avalanche current, leakage current, and charge storage, while also considering the influence of temperature on various parameters. The statistical model includes photon detection event time, dark count event occurrence time, and post-pulse trigger time, comprehensively reflecting the device's operating characteristics. This integrated modeling of the SPAD's electrical and statistical characteristics makes the model more accurate in circuit simulations. During initialization, this invention introduces a low-level process disturbance factor, causing the model parameters to exhibit a statistical distribution across different simulation runs. This reflects the impact of manufacturing process fluctuations on the SPAD's breakdown voltage, leakage current, and avalanche behavior, improving the model's realism and reliability in circuit-level Monte Carlo simulations. Furthermore, this invention introduces a Gaussian-distributed quenching threshold current and dynamic current criterion, enabling automatic triggering and natural quenching of the avalanche process, accurately reflecting the SPAD's operating cycle and reset behavior. This invention is implemented in Verilog-A and supports mainstream circuit simulators such as SPICE and Spectre. It has good compatibility and scalability. Through parameterized definition, the model can be quickly adjusted according to SPAD devices of different sizes and structures to achieve system-level co-simulation.
[0014] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description
[0015] Figure 1 This is a flowchart illustrating a Verilog-A-based single-photon avalanche diode modeling method provided in an embodiment of the present invention. Detailed Implementation
[0016] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.
[0017] Please see Figure 1 This invention provides a Verilog-A-based modeling method for single-photon avalanche diodes, implemented using Verilog-A encoding. The corresponding single-photon avalanche diode model design method includes: S10, Model parameter definition and initialization; wherein, the underlying process disturbance factor is introduced during the initialization process, and the model parameters are mapped through the underlying process disturbance factor so that the model meets the requirements of Monte Carlo simulation based on Verilog-A.
[0018] Based on the physical and electrical behavior of the device, the embodiments of this invention define model parameters including geometric parameters, electrical parameters, quenching control parameters, junction capacitance-related parameters, temperature and time characteristic parameters, anode-cathode junction temperature characteristic parameters, and other characteristic parameters. Geometric parameters include: device radius, used to calculate the SPAD area; electrical parameters include: breakdown voltage, junction capacitance temperature coefficient, and reverse saturation current; quenching control parameters include: mean and standard deviation of quenching current, used to generate a Gaussian-distributed quenching threshold current; junction capacitance-related parameters include: junction capacitance gradient coefficient, cathode-substrate parasitic capacitance, and anode-substrate parasitic capacitance; temperature and time characteristic parameters include: reference operating temperature and breakdown characteristic thermal voltage; anode-cathode junction temperature characteristic parameters include: zero-bias junction capacitance per unit area, zero-temperature built-in potential, and the temperature coefficient of the built-in potential; other characteristic parameters include: avalanche resistance in the medium-high overbias region, avalanche resistance in the low overbias region, operating wavelength, and overbias voltage. The defined model parameters can be obtained directly through TCAD Sentaurus simulation software or experiments. The model parameters in this invention are derived from the physical structure of the device and experimental measurements. They can be extracted directly through TCAD Sentaurus simulation software or experiments, which can ensure the transferability and reliability of the model.
[0019] The core interface structure of the device is defined by module spad(a, k, trigger): bidirectional ports a (anode), k (cathode), and trigger (trigger signal) constitute the external connection point; electrical node type declaration and ground establish the electrical reference system; branches define the main avalanche path, junction capacitance, cathode-substrate, and anode-substrate.
[0020] The initialization process at the beginning of the simulation includes: calculation of geometric parameters and reference area; calculation of actual breakdown voltage after temperature compensation; initialization of the photon detection probability model, using a double Gaussian distribution varying with wavelength; clearing the statistical event counter; initialization of the dark count rate model, generating the average time interval through polynomial and exponential distributions; setting the afterpulse probability and average time interval; setting the time jitter distribution parameters, including Gaussian and exponential mixtures; initialization of the random number seed, generating independent random sources for each event; calculation of leakage current and temperature correction; initialization of avalanche state, aval=0, i.e., avalanche shutdown; generation of the quenching threshold current from a normal distribution; calculation of the area and temperature correction of the breakdown resistance in the low over-bias region; etc.
[0021] To characterize the impact of manufacturing process variations on the electrical behavior of SPADs, a low-level process perturbation factor is introduced. (Dimensionless, calibrated by percentage) It is used to drive the random offset of key parameters of multiple compact models and completes parameter mapping in the initialization phase, ultimately realizing Monte Carlo simulation based on Verilog-A.
[0022] To ensure input validity, the underlying process disturbance factor is first limited: ; in, This represents the minimum possible value of the underlying perturbation parameter. This represents the maximum possible value of the underlying perturbation parameters. This indicates the maximum value selection operation. This indicates the minimum value selection operation. That is: ; Define the set of model parameters to be perturbed: ; in, , Indicates reverse saturation current. This is the avalanche resistor in the medium to high overbias region.
[0023] Considering the limitations of Verilog-A in simulating low-level model parameters, a discrete calibration point lookup table (LUT) and interpolation method are used to... Convert to model parameters .
[0024] Let the discrete disturbance axis be: ; And establish a model parameter lookup table: ; in, Indicates the first One underlying process disturbance factor This indicates the total number of model parameters.
[0025] when Precisely falls on a certain discrete point At that time, directly retrieve the table value: ; when When interpolating, define the interpolation weights: ; Interpolation is then performed on each model parameter. To improve accuracy and numerical stability, different interpolation domains can be used for different parameters: For approximately linearly varying parameters (e.g.) , Linear interpolation is used: ; ; For nonlinear changing parameters (e.g.) Logarithmic field interpolation is used:
[0026]
[0027] Finally, the parameter set obtained by mapping The simulation was obtained from TCAD Sentaurus to enable the model to perform Monte Carlo simulations based on Verilog-A.
[0028] The theoretical part of the Verilog-A single-photon avalanche diode model in this embodiment of the invention includes: statistical and electrical parts.
[0029] S20. Determine the state of the single-photon avalanche diode. If it is avalanche off, perform statistical model calculations. The statistical model calculations include calculating the photon detection event time, the dark count event occurrence time, and the after-pulse trigger time.
[0030] The statistically related part involves calculating the photon detection event time, the dark count event occurrence time, and the after-pulse trigger time. In this embodiment of the invention, calculating the photon detection event time, the dark count event occurrence time, and the after-pulse trigger time includes: calculating the total time jitter; the total time jitter includes a Gaussian distributed time jitter component and an exponential distributed time jitter component; calculating the photon detection event time based on the total time jitter; selectively calculating the average dark count rate using a dual-channel Arrhenius method with over-bias segmentation and temperature threshold switching; generating a first exponentially distributed time interval for dark count events based on the average dark count rate; calculating the dark count event occurrence time based on the first exponentially distributed time interval and the total time jitter; generating a second exponentially distributed time interval for after-pulse events using an exponentially distributed random number generator; and calculating the after-pulse trigger time based on the second exponentially distributed time interval and the total time jitter. More specifically: Total time jitter It is obtained by adding the Gaussian and exponential components: ; in, This represents the time jitter component of the Gaussian distribution. This represents the time jitter component of the exponential distribution.
[0031] Photon Detection Power (PDP) Model: ; in, Represents the normalization coefficient. Indicates the wavelength of the incident light. , They represent wavelengths respectively. , Intensity parameters of the Gaussian distribution of the photon detection probability. , They represent wavelengths respectively. , The width parameter of the Gaussian distribution of photon detection efficiency.
[0032] The photon detection probability model is used to determine whether a photon detection event has been triggered. For example, if a photon detection event is triggered in response to an external trigger signal, the rising edge of the trigger signal is detected, and processing begins when the trigger voltage exceeds a threshold. The current photon detection event time is then calculated. ; in, This indicates the ideal trigger time for photon detection.
[0033] For dark counting events, a spontaneous avalanche caused by random thermal noise is simulated through a timed event. The dark counting time is triggered when the timer reaches a preset time. If the device is not currently in an avalanche state, aval=1 to initiate the avalanche. Average dark counting rate. With temperature and over bias voltage Since there is a significant correlation, this embodiment of the invention uses a dual-channel Arrhenius form with over-bias segmentation and temperature threshold switching to improve the dark counting model, and selectively calculates the average dark counting rate based on the set temperature and over-bias.
[0034] Set the over-bias segment boundary as ,but: ; in, Indicates the first The average dark count rate corresponding to each over-biased interval.
[0035] Within each overbias segment, a temperature threshold is introduced. Used to describe the switch between shallow-level dominance and deep-level dominance: ; in, Indicates the first The temperature threshold corresponding to each over-biased range Indicates the first The fitting coefficient factor for each overbiased interval where the temperature is less than the threshold. Indicates the first The activation energy corresponding to the temperature below the threshold in each overbiased range. Indicates the first The fitting coefficient factor corresponding to the temperature greater than the threshold in each overbiased range. Indicates the first The activation energy corresponding to the temperature above the threshold in each overbiased range. This represents the Boltzmann constant. Convert the average dark count rate to the average dark count interval: ; Subsequently, based on the average dark count interval The first exponential distribution time interval for generating dark count events Then calculate the time of the next dark counting event: ; in, This is the absolute time since the last dark counting event.
[0036] For afterpulse events, the re-triggering process caused by the recombination release of trapped charges is modeled. This is achieved using uniformly distributed random numbers and a set afterpulse probability. A comparison is made to determine whether an afterpulse event has occurred. A second exponentially distributed time interval for the next afterpulse event is generated using an exponentially distributed random number generator. Then, the next pulse trigger time is calculated: ; in, This is the absolute time since the last pulse event.
[0037] After any of the above-mentioned photon detection event, dark counting event, or afterpulse event occurs, the avalan state changes from aval = 0 to aval = 1, that is, the avalan state changes from avalanche off to avalanche on.
[0038] S30. Determine whether to activate the avalanche state based on the statistical model calculation results. If the avalanche is activated, perform the electrical model calculation, update the avalanche state based on the electrical model calculation results and the quenching threshold current based on Gaussian distribution, and output each current. The electrical model calculation includes calculating the leakage current based on area parameters and temperature parameters, the segmented avalanche current, and calculating the junction charge of SPAD cathode-anode, the parasitic capacitance charge of SPAD cathode-substrate, and the parasitic capacitance charge of SPAD anode-substrate based on area parameters and temperature parameters, so as to calculate the corresponding current according to the charge-current relationship.
[0039] When aval = 1, the SPAD enters the breakdown conduction state and performs electrical model calculations. The electrical-related parts involve calculating leakage current and segmented avalanche current based on area and temperature parameters, and calculating the junction charge between the SPAD cathode and anode, the parasitic capacitance charge between the SPAD cathode and substrate, and the parasitic capacitance charge between the SPAD anode and substrate based on area and temperature parameters, in order to calculate the corresponding current according to the charge-current relationship. Specifically: The temperature dependence model of breakdown voltage reflects the characteristic that the breakdown voltage changes with temperature. The model in this invention uses a linear temperature compensation model to approximate this relationship: ; in, VBTC represents the calculated breakdown voltage, where VBTC represents the temperature coefficient of the breakdown voltage. Indicates the current operating temperature. Indicates the reference operating temperature. Indicates reference operating temperature The breakdown voltage below.
[0040] The total static DC branch current of the SPAD consists of the superposition of leakage current and avalanche current:
[0041] in, This represents the total static DC branch current of the SPAD. Indicates avalanche current. The leakage current is represented by a segmented avalanche current in this invention, and the leakage current is calculated based on area parameters and temperature parameters.
[0042] This invention calculates the leakage current based on area and temperature parameters, as follows: ; in, Indicates leakage current. Indicates the temperature coefficient. Indicates the current operating temperature. Indicates the reference operating temperature. Indicates the basic leakage current. , Indicates reverse saturation current. Indicates the area ratio coefficient. The area of the SPAD is calculated from the device radius. This represents the reference area. It is evident that the leakage current calculation is based on the superposition of area and temperature effects.
[0043] The present invention calculates the segmented avalanche current as follows: ; in, Indicates avalanche current. Indicates the breakdown characteristic thermal voltage. Indicates an intermediate variable for the exponential term. , This indicates an operation that first calculates the exponent and then finds the extreme value. Indicates over bias voltage. Indicates an avalanche status indicator. A value of 0 indicates that avalanche is disabled. A value of 1 indicates that an avalanche has begun. , Indicates the boundary voltage. This represents the voltage offset parameter in the medium and high voltage range. This represents the avalanche resistance in the low overvoltage region. This represents the avalanche resistance in the medium to high overvoltage region. This represents the reference value for avalanche current. This represents the voltage applied across the SPAD.
[0044] This invention provides an embodiment for calculating the junction charge of a SPAD cathode-anode based on area and temperature parameters, including: calculating the junction capacitance of the SPAD cathode-anode based on area and temperature parameters, and calculating the junction charge of the SPAD cathode-anode based on the junction capacitance. Specifically: This invention calculates the junction capacitance of the SPAD cathode-anode based on area and temperature parameters, as shown in the following embodiment: ; in, This represents the junction capacitance between the cathode and anode of the SPAD. This represents the area of the SPAD. This represents the junction capacitance area factor after temperature compensation. , This represents the zero-bias junction capacitance per unit area. It is the junction capacitance temperature coefficient. Indicates the current operating temperature. Indicates the reference operating temperature. This represents the built-in potential after temperature correction. , This indicates the built-in potential at zero temperature. The temperature coefficient representing the built-in potential. This represents the junction capacitance gradient coefficient; it can be seen that the junction capacitance model of the SPAD cathode-anode is constructed from area parameters and temperature correction parameters.
[0045] The corresponding calculation of the junction charge between the SPAD cathode and anode is expressed as follows: ; in, This indicates the junction charge between the SPAD cathode and anode. This represents the voltage difference between the anode and the cathode.
[0046] The parasitic capacitance charge of the SPAD cathode-substrate in this embodiment of the invention is calculated as follows: ; in, This represents the parasitic capacitance charge of the SPAD cathode-substrate. The parasitic capacitance from the cathode to the substrate was extracted in S10 using TCAD Sentaurus simulation software. This represents the voltage from the cathode to the substrate; The parasitic capacitance charge between the SPAD anode and substrate is calculated and expressed as: ; in, This represents the parasitic capacitance charge between the SPAD anode and the substrate. The parasitic capacitance from the anode to the substrate is represented and extracted in S10 using TCAD Sentaurus simulation software. This represents the voltage from the anode to the substrate.
[0047] In this SPAD model, the dynamic current calculation of each branch follows the charge-current relationship: ; in, The values are calculated from the charges of each branch. include , , The current is distributed to each branch based on its charge, including the main path current (anode-cathode), cathode-substrate, and anode-substrate parasitic currents. The model continuously updates these currents during the transient solution process, resulting in dynamic behavior.
[0048] This invention, in its embodiment, updates the avalanche state based on the calculation results of an electrical model and a quenching threshold current based on a Gaussian distribution. The update process includes: updating the avalanche state based on the avalanche current calculated from the electrical model results; the update process includes: comparing the avalanche current... With quenching threshold current The size, if the avalanche current Current less than the quenching threshold If the avalanche quenching occurs, the state of the single-photon avalanche diode is updated to avalanche off, at which point aval is set to 0, and the quenching threshold current is updated. Otherwise, the state of the single-photon avalanche diode is maintained as avalanche on, i.e., aval = 1; where the quenching threshold current is... A modeling method for single-photon avalanche diodes that follow a Gaussian distribution based on Verilog-A.
[0049] In summary, the Verilog-A-based single-photon avalanche diode (SPAD) modeling method proposed in this invention simultaneously implements both electrical and statistical models of the SPAD using Verilog-A. The electrical model simulates the SPAD's electrical characteristics by dynamically calculating piecewise avalanche current, leakage current, and charge storage, while also considering the influence of temperature on various parameters. The statistical model includes photon detection event time, dark count event occurrence time, and post-pulse trigger time, comprehensively reflecting the device's operating characteristics. This integrated modeling of the SPAD's electrical and statistical characteristics makes the model more accurate in circuit simulations. During the initialization process, a low-level process disturbance factor is introduced, causing the model parameters to exhibit a statistical distribution in different simulation runs. This reflects the impact of manufacturing process fluctuations on the SPAD's breakdown voltage, leakage current, and avalanche behavior, improving the model's realism and reliability in circuit-level Monte Carlo simulations. Furthermore, this invention introduces a Gaussian-distributed quenching threshold current and dynamic current criterion, enabling automatic triggering and natural quenching of the avalanche process, accurately reflecting the SPAD's operating cycle and reset behavior. This invention is implemented in Verilog-A and supports mainstream circuit simulators such as SPICE and Spectre. It has good compatibility and scalability. Through parameterized definition, the model can be quickly adjusted according to SPAD devices of different sizes and structures to achieve system-level co-simulation.
[0050] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.
[0051] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art, by reviewing the specification and accompanying drawings, will understand and implement other variations of the disclosed embodiments in carrying out the claimed invention. In the specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. While certain measures are described in different embodiments, this does not mean that these measures cannot be combined to produce good results.
[0052] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.
Claims
1. A design method for a single-photon avalanche diode model based on Verilog-A, characterized in that, Based on Verilog-A encoding, the corresponding design methods for single-photon avalanche diode models include: Model parameter definition and initialization; among which, the underlying process perturbation factor is introduced during the initialization process, and the model parameters are mapped through the underlying process perturbation factor so that the model meets the requirements of Verilog-A based Monte Carlo simulation; The state of the single-photon avalanche diode is determined. If it is avalanche off, a statistical model calculation is performed. The statistical model calculation includes calculating the photon detection event time, the dark count event time, and the after-pulse trigger time. The system determines whether to activate the avalanche state based on the statistical model calculation results. If the avalanche state is activated, the system performs electrical model calculations. The avalanche state is updated based on the electrical model calculation results and the quenching threshold current based on Gaussian distribution, and each current is output. The electrical model calculations include calculating the leakage current based on area and temperature parameters, the segmented avalanche current, and calculating the junction charge between the SPAD cathode and anode, the parasitic capacitance charge between the SPAD cathode and substrate, and the parasitic capacitance charge between the SPAD anode and substrate based on area and temperature parameters, so as to calculate the corresponding current based on the charge-current relationship.
2. The method for modeling single-photon avalanche diodes based on Verilog-A according to claim 1, characterized in that, The defined model parameters include geometric parameters, electrical parameters, quenching control parameters, junction capacitance-related parameters, temperature and time characteristic parameters, anode-cathode junction temperature characteristic parameters, and other characteristic parameters; among them, Geometric parameters include: device radius, used to calculate the area of the SPAD; Electrical parameters include: breakdown voltage, junction capacitance temperature coefficient, and reverse saturation current; Quenching control parameters include: mean and standard deviation of quenching current, used to generate a Gaussian-distributed quenching threshold current; Junction capacitance related parameters include: junction capacitance gradient coefficient, cathode-substrate parasitic capacitance, and anode-substrate parasitic capacitance; Temperature and time characteristic parameters include: reference operating temperature and breakdown characteristic thermal voltage; The temperature characteristic parameters of the anode-cathode junction include: zero-bias junction capacitance per unit area, zero-temperature built-in potential, and the temperature coefficient of the built-in potential. Other characteristic parameters include: avalanche resistance in the medium-high overbias region, avalanche resistance in the low overbias region, operating wavelength, and overbias.
3. The method for modeling single-photon avalanche diodes based on Verilog-A according to claim 1, characterized in that, Calculate the photon detection event time, the dark count event occurrence time, and the after-pulse trigger time, including: Calculate the total time jitter; the total time jitter includes Gaussian distributed time jitter components and exponential distributed time jitter components; Calculate the photon detection event time based on the total time jitter; The average dark count rate is selectively calculated using a dual-channel Arrhenius method with over-bias segmentation and temperature threshold switching. The first exponential distribution time interval of dark count events is generated based on the average dark count rate, and the occurrence time of dark count events is calculated based on the first exponential distribution time interval and the total time jitter. The second exponential distribution time interval of the subsequent pulse event is generated using an exponential distribution random number generator, and the subsequent pulse trigger time is calculated based on the second exponential distribution time interval and the total time jitter.
4. The method for modeling single-photon avalanche diodes based on Verilog-A according to claim 1, characterized in that, The leakage current, calculated based on area and temperature parameters, is expressed as: ； in, Indicates leakage current. Indicates the temperature coefficient. Indicates the current operating temperature. Indicates the reference operating temperature. Indicates the basic leakage current. , Indicates reverse saturation current. Indicates the area ratio coefficient. This represents the area of the SPAD. Indicates the reference area.
5. The method for modeling single-photon avalanche diodes based on Verilog-A according to claim 1, characterized in that, The piecewise avalanche current is calculated as follows: ； in, Indicates avalanche current. Indicates the breakdown characteristic thermal voltage. Indicates an intermediate variable for the exponential term. , This indicates an operation that first calculates the exponent and then finds the extreme value. Indicates over bias voltage. Indicates an avalanche status indicator. A value of 0 indicates that avalanche is disabled. A value of 1 indicates that an avalanche has begun. , Indicates the boundary voltage. This represents the voltage offset parameter in the medium and high voltage range. This represents the avalanche resistance in the low overvoltage region. This represents the avalanche resistance in the medium to high overvoltage region. This represents the reference value for avalanche current. This represents the voltage applied across the SPAD.
6. The method for modeling single-photon avalanche diodes based on Verilog-A according to claim 1, characterized in that, Calculation of the junction charge of the SPAD cathode-anode based on area and temperature parameters includes: Calculate the junction capacitance of the SPAD cathode-anode based on area and temperature parameters, and calculate the junction charge of the SPAD cathode-anode based on the junction capacitance.
7. The Verilog-A-based single-photon avalanche diode modeling method according to claim 6, characterized in that, The junction capacitance of the SPAD cathode-anode, calculated based on area and temperature parameters, is expressed as: ； in, This represents the junction capacitance between the cathode and anode of the SPAD. This represents the area of the SPAD. This represents the junction capacitance area factor after temperature compensation. , This represents the zero-bias junction capacitance per unit area. It is the junction capacitance temperature coefficient. Indicates the current operating temperature. Indicates the reference operating temperature. This represents the built-in potential after temperature correction. , This indicates the built-in potential at zero temperature. The temperature coefficient representing the built-in potential. This represents the junction capacitance gradient coefficient; The corresponding calculation of the junction charge between the SPAD cathode and anode is expressed as follows: ； in, This indicates the junction charge between the SPAD cathode and anode. This represents the voltage difference between the anode and the cathode.
8. The method for modeling single-photon avalanche diodes based on Verilog-A according to claim 1, characterized in that, The parasitic capacitance charge of the SPAD cathode-substrate is calculated and expressed as: ； in, This represents the parasitic capacitance charge of the SPAD cathode-substrate. This represents the parasitic capacitance from the cathode to the substrate. This represents the voltage from the cathode to the substrate; The parasitic capacitance charge between the SPAD anode and substrate is calculated and expressed as: ； in, This represents the parasitic capacitance charge between the SPAD anode and the substrate. This represents the parasitic capacitance from the anode to the substrate. This represents the voltage from the anode to the substrate.
9. The method for modeling single-photon avalanche diodes based on Verilog-A according to claim 1, characterized in that, The avalanche state is updated based on the calculation results of the electrical model and the quenching threshold current based on Gaussian distribution, including: The avalanche state is updated based on the avalanche current calculated from the electrical model. The update process includes: comparing the magnitude of the avalanche current with the quenching threshold current; if the avalanche current is less than the quenching threshold current, the avalanche is quenched, the state of the single-photon avalanche diode is updated to avalanche off, and the quenching threshold current is updated; otherwise, the state of the single-photon avalanche diode is maintained as avalanche on. The quenching threshold current follows a Gaussian distribution.