SPAD photon detection efficiency simulation modeling method

Abstract

The invention discloses an SPAD photon detection efficiency simulation modeling method. The method comprises the following steps: establishing an SPAD structure model; setting an incident light source; quantum efficiency and avalanche breakdown probabilities under different reverse bias voltages in a depletion region of the SPAD structure model are obtained respectively, and SPAD photon detection efficiency is calculated; and comparing a simulation result with an experiment result, and performing electrical calibration on the SPAD photon detection efficiency parameter model. According to the modeling method disclosed by the invention, the photon detection efficiency of the SPAD under different bias voltages can be obtained, internal physical parameters of the device, such as electric field distribution, breakdown probability and the like, can be obtained along with the variation trend of the bias voltages, a microscopic physical model based on the evolution of the photon detection efficiency is established, and a theoretical support is provided for the design of the high-performance SPAD.

Description

Technical Field

[0001] The present invention belongs to the field of single-photon detector simulation, and in particular relates to a SPAD photon detection efficiency simulation modeling method. Background Art

[0002] Silicon-based optoelectronic devices, with their advantages of low cost, high integration, wide bandwidth, high speed, and strong anti-interference capabilities, have been widely used in consumer electronics, intelligent driving, quantum communications, and other fields. Silicon-based single-photon avalanche diodes (SPADs), solid-state photodetectors, offer higher sensitivity and dynamic range than traditional photomultiplier tubes (PMTs). They can detect and count photons in extremely low-light environments, with low readout noise and power consumption. Consequently, they are specifically targeted for high-precision space missions such as planetary altimeters, satellite laser time transmission, and deep-space lidar. SPADs typically operate in Geiger mode. The carriers generated by photons entering the device are accelerated by the extremely high electric field within the device, undergoing impact ionization and generating a multiplied current. This allows for the detection of signals several orders of magnitude below the noise level, resulting in high photon detection efficiency. However, further optimization of device performance is significantly limited by process technology costs and R&D cycle costs.

[0003] In recent years, many simulation models based on TCAD have been proposed at home and abroad to simulate the response of electrical parameters such as SPAD dark current and breakdown voltage, and to reduce the R&D cost of high-performance devices. TCAD is a numerical simulation tool based on semiconductor physics. It can accurately describe the device response characteristics by coupling the physical equations that control carrier migration, recombination and transport inside the device with the external driving force. However, the carrier multiplication process of SPAD devices has randomness and statistical characteristics. Especially for the simulation of photon detection efficiency, the existing simulation models do not take into account the probability of photon absorption (P) at different positions inside the device. ab ), avalanche breakdown probability (P tr ) and the influence of the difference in electric field distribution on the parameter model, there is a large deviation between the simulation results and the experimental results. Summary of the Invention

[0004] In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is to provide a method for simulating and modeling the SPAD photon detection efficiency.

[0005] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0006] A method for simulating and modeling the SPAD photon detection efficiency includes the following steps:

[0007] S100, establishing a SPAD structure model;

[0008] S200, setting an incident light source in the SPAD structure model, and simulating the photogenerated carrier process and the movement of carriers in silicon;

[0009] S300, setting a reverse bias voltage, extracting the ratio of the anode current to the obtainable photocurrent at each position in the depletion region of the SPAD structure model under the reverse bias voltage, and obtaining the quantum efficiency at each position in the depletion region of the SPAD structure model;

[0010] S400, extracting the avalanche breakdown probability at each position in the depletion region of the SPAD structure model under the same reverse bias voltage;

[0011] S500, calculating the photon detection efficiency of the SPAD based on the quantum efficiency and the breakdown probability;

[0012] S600, changing the reverse bias voltage, repeating steps S300 to S500, and obtaining a simulation result curve of the photon detection efficiency of the SPAD changing with the reverse bias voltage;

[0013] S700: Compare the simulation results with the experimental results and perform electrical calibration on the simulation model.

[0014] Furthermore, the step S100 includes the following sub-steps:

[0015] S110, designing a SPAD structure model according to the shape and size of the SPAD device structure to be simulated;

[0016] S120. Design the doping profile and electric field distribution of the SPAD structure model according to the layout and PDK information;

[0017] S130. Specify a material model related to the quantum efficiency of the optoelectronic device and establish a SPAD structure model.

[0018] Furthermore, in the step S200, based on the SPAD structure model, the light injection model and the Boltzmann transport model are used to realize the device's photogenerated carriers and carrier transport functions.

[0019] Furthermore, the step S300 includes the following sub-steps:

[0020] S310, applying a reverse bias voltage V to the cathode of the SPAD structure model bias , reverse bias voltage V bias Greater than the breakdown voltage V bd , making the SPAD work in Geiger mode;

[0021] S320, extract the reverse bias voltage V biasAnode current and obtainable photocurrent values ​​under ;

[0022] S330 . Calculate the SPAD quantum efficiency QE based on the ratio of the anode current to the available photocurrent.

[0023] Furthermore, in the step S320, the light generation rate is first solved at the corresponding grid point, and then the photocurrent value is calculated.

[0024] Furthermore, in step S400, the GEIGER single-photon avalanche model is used to simulate the probability of avalanche breakdown after a single electron / hole enters the SPAD multiplication region; the derivative formula of the probability of electron breakdown at any position in the SPAD simulation model is expressed as:

[0025]

[0026] Among them, P e represents the breakdown probability of electrons; P h represents the breakdown probability of holes; α e represents the electron impact ionization coefficient.

[0027] Furthermore, in the step S500, the depletion region volume, coupled quantum efficiency QE and breakdown probability P of the SPAD structure model are calculated. tr , calculate the photon detection efficiency PDE of SPAD at the set wavelength, the formula is as follows:

[0028]

[0029] Among them, V dep represents the volume of the depletion region.

[0030] In the step S700, the simulation model is calibrated by setting the value of the electron impact ionization coefficient in the SPAD structure model.

[0031] The simulation modeling method proposed in the present invention can obtain the photon detection efficiency of SPADs under different bias voltages, and at the same time obtain the internal physical parameters of the SPAD device, such as the changing trends of the electric field distribution and breakdown probability with the bias voltage, to establish a microscopic physical model based on the evolution of the photon detection efficiency, providing theoretical support for the design of high-performance SPADs. The simulation modeling method of the present invention is suitable for simulating the photon detection efficiency of silicon-based single-photon detectors with different pixel unit structures under different wavelengths of light incidence, providing a simulation method and theoretical basis for the optimized design of single-photon detector chips. It is also suitable for extracting relevant optical parameters of other photodetectors and is suitable for use by SPAD device research and development units, scientific research institutes, and space payload units. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0033] Figure 1 Flowchart of an embodiment of the SPAD photon detection efficiency simulation modeling method of the present invention.

[0034] Figure 2 The figure shows the comparison between simulation results and experimental results of the curve of SPAD's photon detection efficiency changing with reverse bias voltage. DETAILED DESCRIPTION

[0035] The following describes the implementation of the present invention through specific examples. The illustrations provided in the following embodiments are only used to schematically illustrate the basic concept of the present invention. The following embodiments and features in the embodiments may be combined with each other unless there is any conflict.

[0036] See also Figure 1 , Figure 1 This is a flow chart of an embodiment of a method for simulating and modeling the SPAD photon detection efficiency of the present invention. The method for simulating and modeling the SPAD photon detection efficiency of this embodiment includes the following steps:

[0037] S100: Establish a SPAD structure model. This step may include the following sub-steps:

[0038] S110 , designing a SPAD structure model according to the shape and size of the SPAD device structure to be simulated.

[0039] S120. Design the doping profile and electric field distribution of the SPAD structure model according to the layout and PDK information.

[0040] S130. Specify a material model related to the quantum efficiency of the optoelectronic device and establish a SPAD structure model.

[0041] The structural model of the SPAD is constructed in the TCAD simulation environment according to the shape and size of the detector structure. Specifically, the SPACE.MULT statement is used to set the grid accuracy during modeling; the device doping profile is formed by calling the ATHENA statement with reference to the actual process steps; the MODEL statement is used to specify material models such as the SRH composite model, the Auger composite model, the carrier concentration and the electric field-related mobility model to construct the SPAD structural model. In this embodiment, the diameter of the SPAD structural model is 100μm, and an avalanche multiplication region is formed by the N+ / P well junction. At the same time, an N well injection is added around the photosensitive area to form a guard ring structure to prevent edge electric field breakdown.

[0042] S200: Setting an incident light source in the SPAD structure model to implement the device's photogenerated carrier and carrier transport functions and simulate the movement of photogenerated carriers in silicon. In this step, based on the SPAD structure model, the light injection model and the Boltzmann Transport Model (BTM) model are used to implement the device's photogenerated carrier and carrier transport functions.

[0043] Specifically, the BEAM statement is used to set the light source position and incident angle parameters to achieve collimated light injection into the structure. The light source position is determined by setting parameters such as X.ORIGIN and Y.ORIGIN, and the beam propagation direction and incident range relative to the X-axis are specified by setting parameters such as ANGLE, MIN.WINDOW, and MAX.WINDOW. In the device simulation module, the beam is automatically split into a series of rays within the specified incident range based on the device geometry. After light injection, the BTM model is used to simulate the movement of photogenerated carriers in silicon, considering that the energy of the initial carriers is related to the wavelength and that the carrier motion path is affected by the local electric field.

[0044] In this embodiment, a light source with a wavelength of 850 nm is set to be incident vertically on the SPAD device, and the incident range of the light beam is slightly larger than the diameter of the SPAD simulation model to prevent edge effects.

[0045] S300: Set the reverse bias voltage, extract the anode current and available photocurrent at each position in the depletion region of the SPAD structure model, calculate the ratio of the two, and obtain the SPAD quantum efficiency QE. This step includes the following sub-steps:

[0046] S310, applying a reverse bias voltage V to the cathode of the SPAD structure model bias , reverse bias voltage V bias Need to be greater than the breakdown voltage V bd , making the SPAD work in Geiger mode. At this time, the sensitivity of the SPAD will increase dramatically, and a multiplication region with an extremely high electric field will be generated inside it. After the photogenerated carriers enter the multiplication region, they are accelerated by the electric field and cascade collisions occur, resulting in an avalanche current.

[0047] In this embodiment, a reverse bias voltage V is applied to the photodiode region. bias , reverse bias voltage V bias A high electric field is generated in the depletion region. When the electric field reaches 10 5 When the value is around V / cm, the number of photogenerated carriers increases rapidly, generating an avalanche current.

[0048] S320: Extract the anode current and available photocurrent value under the reverse bias voltage. In this step, first solve the light generation rate at the corresponding grid point, and then calculate the photocurrent value. The formula for calculating the light generation rate G is as follows:

[0049]

[0050] Where η0 is the internal quantum efficiency, which represents the number of carrier pairs generated by each photon; P is the ray intensity factor, which includes damage caused by reflection, transmission, and material absorption along the light path; y is the relative distance of the ray; h is Planck's constant; λ is the wavelength of light; c is the speed of light; α is the absorption coefficient; and k is the imaginary part of the refractive index of light.

[0051] S330 , calculating the SPAD quantum efficiency value QE based on the ratio of the anode current to the available photocurrent.

[0052] In this embodiment, the SOLVE statement is used to simulate the IV characteristics of the SPAD and obtain the curve of the anode current changing with the reverse bias voltage. The current increases with the increase of the reverse bias voltage. When the reverse bias voltage is about 110V, an extremely high electric field is formed in the multiplication region. The generated electron-hole pairs enter the multiplication region and are accelerated by the electric field, resulting in a cascade collision, generating about 10 -4 Avalanche current. Use the EXTRACT statement to extract the anode current and available photocurrent. By calculating the ratio of the cathode current to the available photocurrent, the device quantum efficiency (QE) at the reverse bias voltage is obtained.

[0053] S400, extract the avalanche breakdown probability P at each position in the depletion region of the SPAD structure model under the same reverse bias voltage tr .

[0054] In this step, the GEIGER single-photon avalanche model can be used to simulate the probability of avalanche breakdown of a single electron after entering the SPAD multiplication region. The formula for the probability of electron breakdown at any position in the SPAD simulation model is expressed as:

[0055]

[0056] Among them, P e represents the breakdown probability of electrons; P h represents the breakdown probability of holes; α e represents the electron impact ionization coefficient.

[0057] In this embodiment, the GEIGER single-photon avalanche model is called. For photogenerated carriers generated in the device multiplication region, the absorption probability is 1, and the delay distribution depends on the carrier transport time. For photogenerated carriers generated in the neutral region of the device, the drift diffusion model is used to calculate their probability distribution and time delay distribution. The PROBE statement is called to extract the probability P of a single electron entering the SPAD multiplication region and undergoing avalanche breakdown at each position in the SPAD depletion region under the same bias voltage. tr .

[0058] S500, calculate the SPAD photon detection efficiency based on the quantum efficiency and breakdown probability. In this step, the quantum efficiency QE and the breakdown probability P are calculated based on the depletion region volume of the SPAD structure model. tr Integrate and calculate the photon detection efficiency (PDE) of the SPAD at the set light source wavelength. The formula is as follows:

[0059]

[0060] Among them, V dep represents the volume of the depletion region.

[0061] In this embodiment, the depletion region volume V of the SPAD structure model is obtained by setting the TONYPLOT display parameters. dep , for the entire depletion region volume, the integral of the quantum efficiency and breakdown probability is calculated to obtain the photon detection efficiency value PDE under the reverse bias voltage.

[0062] S600 , changing the reverse bias voltage, repeating steps S300 to S500 , and obtaining a curve of the SPAD photon detection efficiency varying with the reverse bias voltage.

[0063] S700, compare the SPAD photon detection efficiency simulation results and experimental test results, perform electrical calibration on the SPAD photon detection efficiency parameter model, and reduce the error of the simulation results to within a predetermined range. In this embodiment, an 850nm pulsed laser is used as a controlled light source, and a universal counter (SR400) is used to monitor the output of the SPAD device to obtain the experimental test results of PDE; by adjusting the electron impact ionization coefficient α e The model is calibrated using the value of .

[0064] See also Figure 2 , which are the simulation results and experimental test results of the PDE curve with reverse bias voltage after calibration. Among them, the solid line is the curve of PDE with reverse bias voltage obtained by experimental test, and the dotted line is the curve of PDE with reverse bias voltage obtained by simulation. Figure 2It can be seen that the simulation results are consistent with the experimental test results, proving the correctness of the simulation method and physical model used. This SPAD photon detection efficiency parameter model can be used to simulate the photon detection efficiency of silicon-based single-photon detectors. This embodiment can obtain the photon detection efficiency of SPADs under different reverse bias voltages, supplementing and improving the simulation modeling method of SPAD key parameters, and providing a reference for optical parameter simulation modeling of other photodetectors with statistical properties.

[0065] This embodiment provides a simulation modeling method for the photon detection efficiency (PDE) of a silicon-based single-photon detector (SSPD) under different bias voltages. Using TCAD simulation technology, based on a device structure model, the material model, light injection model, carrier transport model, and multiplication model are invoked to extract the device anode current and available photocurrent under reverse bias voltage. The device quantum efficiency is then determined based on the ratio of the two. The breakdown probability at each location within the depletion region of the device structure model under the same bias voltage is also extracted. The PDE is calculated by coupling the quantum efficiency and breakdown probability. The model is then electrically calibrated based on experimental results under a wide range of bias voltages. Results demonstrate that the method of this embodiment can accurately obtain the PDE and intuitively demonstrate the impact of factors such as the internal electric field distribution and carrier lifetime on the PDE. This method provides ideas and methods for optimizing device design in practical application scenarios, effectively guiding device performance improvement. This method can also serve as a reference for modeling and simulating key parameters of photodetectors with different processes and structures.

[0066] Since further optimization of SPAD performance is limited by the time cost and process technology of research and development, simulation technology is needed to save time and economic costs and effectively improve device performance. The simulation modeling method proposed in this embodiment can be used to obtain the photon detection efficiency of SPAD under different bias voltages, and at the same time obtain the changing trends of the internal physical parameters of the device, such as the electric field distribution and breakdown probability with the bias voltage, and establish a microscopic physical model based on the evolution of the photon detection efficiency, providing theoretical support for the design of high-performance SPAD. The simulation modeling method of this embodiment is suitable for simulating the photon detection efficiency of silicon-based single-photon detectors with different pixel unit structures under different wavelengths of light incidence, providing a simulation method and theoretical basis for the optimization design of single-photon detector chips, and is also suitable for the extraction of related optical parameters of other photodetectors, and is suitable for use by SPAD device research and development units, scientific research institutes and space payload units.

[0067] The above embodiments merely represent preferred embodiments of the present invention. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art would be able to make various modifications and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the patent for this invention shall be determined by the appended claims.

Claims

1. A method for simulating and modeling the SPAD photon detection efficiency, characterized in that: The following steps are involved: S100, establishing a SPAD structure model; S200, setting an incident light source in the SPAD structure model, and simulating the photogenerated carrier process and the movement of carriers in silicon; S300, setting a reverse bias voltage, extracting the ratio of the anode current to the obtainable photocurrent at each position in the depletion region of the SPAD structure model under the reverse bias voltage, and obtaining the quantum efficiency at each position in the depletion region of the SPAD structure model; S400, extracting the avalanche breakdown probability at each position in the depletion region of the SPAD structure model under the same reverse bias voltage; S500, calculating the photon detection efficiency of the SPAD based on the quantum efficiency and the breakdown probability; S600, changing the reverse bias voltage, repeating steps S300 to S500, and obtaining a simulation result curve of the photon detection efficiency of the SPAD changing with the reverse bias voltage; S700: Compare the simulation results with the experimental results and perform electrical calibration on the simulation model.

2. The SPAD photon detection efficiency simulation modeling method according to claim 1, wherein: The step S100 includes the following sub-steps: S110, designing a SPAD structure model according to the shape and size of the SPAD device structure to be simulated; S120. Design the doping profile and electric field distribution of the SPAD structure model according to the layout and PDK information; S130. Specify a material model related to the quantum efficiency of the optoelectronic device and establish a SPAD structure model.

3. The SPAD photon detection efficiency simulation modeling method according to claim 1, wherein: In the step S200, based on the SPAD structure model, the light injection model and the Boltzmann transport model are used to realize the device's photogenerated carriers and carrier transport functions.

4. The SPAD photon detection efficiency simulation modeling method according to claim 1, wherein: The step S300 includes the following sub-steps: S310, applying a reverse bias voltage V to the cathode of the SPAD structure model bias , reverse bias voltage V bias Greater than the breakdown voltage V bd , making the SPAD work in Geiger mode; S320, extract the reverse bias voltage V bias Anode current and obtainable photocurrent values ​​under ; S330 . Calculate the SPAD quantum efficiency QE based on the ratio of the anode current to the available photocurrent.

5. The SPAD photon detection efficiency simulation modeling method according to claim 4, wherein: In the step S320, the light generation rate is first solved at the corresponding grid point, and then the photocurrent value is calculated.

6. The SPAD photon detection efficiency simulation modeling method according to claim 1, wherein: In the step S400, the GEIGER single-photon avalanche model is used to simulate the probability of avalanche breakdown after a single electron / hole enters the SPAD multiplication region; the derivative formula of the probability of electron breakdown at any position in the SPAD structure model is expressed as: Among them, P e represents the breakdown probability of electrons; P h represents the breakdown probability of holes; α e represents the electron impact ionization coefficient.

7. The SPAD photon detection efficiency simulation modeling method according to claim 1, wherein: In the step S500, the depletion region volume, coupled quantum efficiency QE and breakdown probability P of the SPAD structure model are calculated. tr , calculate the photon detection efficiency PDE of SPAD at the set wavelength, the formula is as follows: Among them, V dep represents the volume of the depletion region.

8. The SPAD photon detection efficiency simulation modeling method according to claim 1, wherein: In the step S700, the simulation model is calibrated by setting the value of the electron impact ionization coefficient in the SPAD structure model.

Images