A low-gain avalanche photodetector simulation method and system

Abstract

The application discloses a low-gain avalanche detector simulation method and system, the method is: 1) using the device initialization module to set the size of the low-gain avalanche detector and the parameters of each set position; 2) constructing a low-gain avalanche detector model and dividing it into multiple microcells, solving the electric potential in each microcell and obtaining the electric field according to the electric potential gradient; 3) obtaining the generation and propagation of particles in each microcell, and converting the energy deposition generated in each microcell into charge carrier deposition for exciting carriers; 4) according to the electric field and the excited carriers in each microcell, determining the motion trajectory of the carriers and recording the average capture time of the carriers under different irradiation conditions; then estimating the induced current caused by the carriers generated in the low-gain avalanche detector model under laser excitation; 5) after processing the induced current, outputting to an oscilloscope to obtain the simulation results corresponding to different irradiation conditions. The application is closer to the actual test process.

Description

Technical Field

[0001] This invention belongs to the field of semiconductor device simulation, specifically relating to a low-gain avalanche detector simulation method and system. Background Technology

[0002] Matter is composed of elementary particles, and gravity, electromagnetism, the strong force, and the weak force are the four fundamental interactions that describe the interactions between particles. However, the Standard Model remains incomplete and cannot explain mysteries such as the scarcity of antimatter compared to matter. Colliders can be used to study elementary particles and their interactions. New information from the brightness upgrades of large particle colliders may refine the Standard Model and even lead to the discovery of new physics. Brightness is a crucial indicator of collider performance, directly proportional to the number of particle collisions within a given time interval. Higher brightness in collider upgrades means more data and smaller statistical errors. However, at the same time, brightness upgrades lead to extremely high event stacking and ultra-high radiation environments, posing a significant challenge to particle detectors. Using high-resolution time detectors is one way to address the event stacking problem, as it allows for precise determination of particle timing.

[0003] Low-gain avalanche silicon detectors (LGADs) have the potential to become radiation-resistant, high-time-resolution detectors. LGADs can amplify signals by approximately 10 to 100 times while having a relatively small noise amplification factor, improving the detector's signal-to-noise ratio and thus achieving good time resolution. Before irradiation, the time resolution can reach below 30 ps (2.5 × 10⁻⁶). 15 n eq / cm 2 The temporal resolution after irradiation can also reach 40 ps. However, the development of LGAD requires repeated processing, testing, and performance analysis, wasting considerable time and resources. Building an open-source simulation software framework for LGAD can directly obtain device characteristics such as the detector's current-voltage curve (IV curve) by simulating the internal physical processes of carrier generation and recombination in semiconductor detectors, as well as the external electronic readout process. This saves processing and testing steps and yields the required device size, doping, and other parameters.

[0004] Currently, there are relatively few reports on semiconductor device simulation software development in China. Internationally, the mainstream semiconductor simulation software framework includes Allpix. 2 It simulates semiconductor devices by introducing an electric field, simulating the deposition of charge carriers, simulating the propagation of charge carriers according to the standard drift-diffusion model, and digitizing the signal process. It is mainly used to simulate silicon pixel detectors and other semiconductor detectors.

[0005] The existing software framework has not been developed for LGAD simulation; at the same time, the existing software only allows the import of linear electric fields or electric field distribution maps generated by other TCAD software; secondly, the existing software does not include the setting of irradiation conditions, and cannot simulate the performance impact of irradiation on semiconductor devices before and after irradiation. Summary of the Invention

[0006] To address the problems existing in the prior art, the present invention aims to provide a simulation method and system for low-gain avalanche detectors. This invention can autonomously calculate the electric field distribution of the device and adds an irradiation interface to explore the impact of irradiation on the device's performance.

[0007] The technical solution of this invention is as follows:

[0008] A simulation method for a low-gain avalanche detector, comprising the following steps:

[0009] 1) Use the device initialization module to set the size of the low-gain avalanche detector, and set the doping concentration, electrode position and size, voltage, particle properties, and laser properties at each set position on the low-gain avalanche detector;

[0010] 2) The device electric field calculation module constructs a low-gain avalanche detector model based on the size of the low-gain avalanche detector, the doping concentration at each set position, and the position size of the electrode; the low-gain avalanche detector model is divided into multiple micro-elements using the finite element method, and the potential in each micro-element is solved using the finite element solver DEVSIM, and the electric field is solved based on the potential gradient.

[0011] 3) The charge carrier deposition module uses Geant4 to obtain the generation and propagation of particles in each micro-element, and converts the energy deposition generated in each micro-element into charge carrier deposition for exciting charge carriers;

[0012] 4) The carrier propagation module determines the trajectory of the carriers and records the average carrier capture time under different irradiation conditions based on the electric field and the carriers excited in each micro-element; then, based on the Shockley-Ramo theorem and the average carrier capture time, it estimates the induced current caused by the carriers generated inside the low-gain avalanche detector model under laser excitation.

[0013] 5) The induced current is processed by simulating the electronic readout circuit of the low-gain avalanche detector using an electronic readout module and then output to an oscilloscope to obtain simulation results corresponding to different irradiation conditions.

[0014] Furthermore, a doping distribution function is constructed to set the doping concentration at each specified location.

[0015] Furthermore, a pair of charge carriers is excited when the energy generated within each microelement is equal to the energy of one bandgap width.

[0016] Furthermore, the charge carriers are generated on the surface of the low-gain avalanche detector model; the charge carrier propagation module uses the discrete random solution of the Langevin equation to determine the random trajectory of the charge carriers.

[0017] Furthermore, the electronic readout module is obtained by using a SPICE netlist to build an analog circuit to simulate the electronic readout circuit of the low-gain avalanche detector.

[0018] A simulation system for a low-gain avalanche detector, characterized in that it includes a device initialization module, a device electric field calculation module, a charge carrier deposition module, a charge carrier propagation module, an irradiation module, and an electronics readout module;

[0019] The device initialization module is used to set the size of the low-gain avalanche detector, and to set the doping concentration, electrode position and size, voltage, particle properties, and laser properties at each set position on the low-gain avalanche detector.

[0020] The device electric field calculation module is used to construct a low-gain avalanche detector model based on the size of the low-gain avalanche detector, the doping concentration at each set position, and the position size of the electrode; the low-gain avalanche detector model is divided into multiple micro-elements using the finite element method, and the potential in each micro-element is solved using the finite element solver DEVSIM, and the electric field is solved based on the potential gradient.

[0021] The charge carrier deposition module is used to obtain the generation and propagation of particles in each micro-element using Geant4, and to convert the energy deposition generated in each micro-element into charge carrier deposition for exciting charge carriers;

[0022] The irradiation module is used to provide different irradiation intensities for the low-gain avalanche detector model;

[0023] The carrier propagation module is used to determine the trajectory of the carriers and record the average carrier capture time under different irradiation conditions based on the electric field and the excited carriers in each micro-element; then, based on the Shockley-Ramo theorem and the average carrier capture time, it estimates the induced current caused by the carriers generated inside the low-gain avalanche detector model under laser excitation.

[0024] The electronic readout module is used to simulate the electronic readout circuit of the low-gain avalanche detector, process the induced current, and output it to an oscilloscope to obtain simulation results corresponding to different irradiation conditions.

[0025] The advantages of this invention are as follows:

[0026] 1. LGAD simulation was achieved for the first time.

[0027] 2. This software framework can autonomously calculate the electric field distribution of devices.

[0028] 3. Adding an irradiation interface can meet the need to explore the impact of irradiation on device performance.

[0029] 4. Using ngspice electronics to simulate electronic readout provides a more realistic test process. Attached Figure Description

[0030] Figure 1 This is a diagram of the open-source software system framework of this invention.

[0031] Figure 2 This is a flowchart illustrating the simulation process of the open-source software system of this invention. Detailed Implementation

[0032] The present invention will now be described in further detail with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0033] The open-source software system in this invention mainly includes the following modules: detector device initialization module, device electric field calculation module, charge carrier deposition module, charge carrier propagation module, irradiation module, and electronics readout module, such as... Figure 1 As shown.

[0034] In the detector device initialization module, the x, y, and z dimensions of the low-gain avalanche detector, as well as parameters such as doping concentration, electrode position and size, voltage, particle properties, and laser properties at each designated location of the low-gain avalanche detector, are set. A doping distribution function is constructed to set the doping concentration at each designated location. The initialization parameter set for the irradiation module is the irradiation intensity, which is correlated with the carrier trapping time based on experimental experience, thus affecting the induced current. Laser properties influence carrier generation, while particle properties are determined by the detector's doping type. The generated carriers, under the influence of an external electric field, are used to calculate the magnitude of the induced current.

[0035] In the device electric field calculation module, the finite element method is used. The low-gain avalanche detector is divided into micro-elements using the DEVSIM finite element solver, approximating a uniform potential within each micro-element for solution. The specific process of calculating the potential using DEVSIM is as follows:

[0036] ① Construct a device model and divide it into meshes. Divide the device into many micro-elements. Set the model according to the parameters set in the device initialization module. Set the device material, doping type and doping concentration at different micro-elements.

[0037] ② Initial solutions and physical boundary conditions are set by establishing three different models—node model, boundary model, and circuit element model—and assembling different sets of equations for initial solution. Boundary conditions for the initial solution are defined by defining parameters at the boundaries. Nodes are introduced to the boundaries to establish sets of equations at those nodes. Boundary continuity is achieved during equation assembly, and convergence is achieved using matrix assembly.

[0038] ③ Solve the finite element equations to obtain the electric potential at each location.

[0039] Under the influence of irradiation, deep-level defects are generated inside the detector, affecting the internal electric field and carrier drift. DevSIM is used to simulate the introduction of these deep-level defects within the device, calculating the electric field distribution under irradiation. A complete simulation is performed for each irradiation intensity, comparing the performance of the low-gain avalanche detector under different irradiation intensities, and summarizing the impact of irradiation intensity on the detector device.

[0040] In the charge carrier deposition module, an interface with Geant4 is constructed to obtain the generation and propagation of particles in each micro-element. The energy deposition generated within each micro-element is converted into charge carrier deposition to excite charge carriers. This invention simplifies this process, assuming that for every unit of energy absorbed by the detector device across the bandgap, an electron-hole pair (i.e., charge carrier) is generated. Geant4 (GEometry ANd Tracking) is a Monte Carlo application software package developed by CERN for simulating the physical processes of particle transport in matter. The particles generated within the micro-element are the particles to be measured by the detector; irradiation does not generate new particles, and irradiation only affects deep-level defects.

[0041] In the carrier propagation module, by simplifying the physical process, it is assumed that carriers are generated on the surface of a low-gain avalanche detector model. The discrete random solution of the Langevin equation is used to determine the random trajectory of the carriers. Under increased irradiation, the irradiation dose affects the type and number of deep-level defects formed in the band gap. These deep-level defects can trap electrons or holes (collectively called carriers), thus affecting carrier propagation and reducing charge collection efficiency, which in turn affects the average carrier trapping time. Therefore, the effect of irradiation dose on carrier propagation in the detector is transformed into an effect on the average carrier trapping time. Based on the Shockley-Ramo theorem, the average carrier trapping time is taken into account to estimate the magnitude of the induced current caused by carriers generated inside the detector under laser excitation.

[0042] The electronics readout module integrates the open-source circuit simulation program ngspice. Based on the resistors, capacitors, inductors, and power supplies in the readout electronics path during actual testing, a simulated circuit is built using SPICE netlists. This simulates the process of signals passing through the front-end amplifier and being imaged on the oscilloscope in the actual circuit, making the simulation more closely resemble the actual testing process. Compared to abstracting the actual readout electronics module into a transfer function, this method does not rely on actual experimental test results. The doping parameters of the devices are optimized based on the simulation results, such as doping location, doping thickness, doping concentration, and the functional representation of doping.

[0043] Although specific embodiments of the invention have been disclosed for illustrative purposes to aid in understanding and implementing the invention, those skilled in the art will understand that various substitutions, variations, and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, the invention should not be limited to the content disclosed in the preferred embodiments, and the scope of protection claimed by the invention is defined by the claims.

Claims

1. A simulation method for a low-gain avalanche detector, comprising the following steps: 1) Use the device initialization module to set the size of the low-gain avalanche detector, and set the doping concentration, electrode position and size, voltage, particle properties, and laser properties at each set position on the low-gain avalanche detector; 2) The device electric field calculation module constructs a low-gain avalanche detector model based on the size of the low-gain avalanche detector, the doping concentration at each set position, and the position size of the electrode; the low-gain avalanche detector model is divided into multiple micro-elements using the finite element method, and the potential in each micro-element is solved using the finite element solver, and the electric field is solved based on the potential gradient. 3) The charge carrier deposition module obtains the generation and propagation of particles in each micro-element, and converts the energy deposition generated in each micro-element into charge carrier deposition, which is used to excite the charge carriers; 4) The carrier propagation module determines the trajectory of the carriers and records the average capture time of the carriers under different irradiation conditions based on the electric field and the carriers excited in each micro-element. Then, based on the Shockley-Lamo theorem and the average capture time of the carriers, it estimates the induced current caused by the carriers generated inside the low-gain avalanche detector model under laser excitation. The carriers are generated on the surface of the low-gain avalanche detector model. The carrier propagation module uses the discrete random solution of the Langevin equation to determine the random trajectory of the carriers. 5) The electronic readout module simulates the electronic readout circuit of the low-gain avalanche detector to process the induced current and obtain simulation results corresponding to different irradiation conditions.

2. The method according to claim 1, characterized in that, Construct a doping distribution function to set the doping concentration at each specified location.

3. The method according to claim 1, characterized in that, When the energy generated within each microelement is equal to the energy of one bandgap width, a pair of charge carriers is excited.

4. The method according to claim 1, characterized in that, The electronic readout module is obtained by simulating the electronic readout circuit of the low-gain avalanche detector using an analog circuit.

5. A simulation system for low-gain avalanche detectors, characterized in that, It includes a device initialization module, a device electric field calculation module, a charge carrier deposition module, a charge carrier propagation module, an irradiation module, and an electronics readout module; The device initialization module is used to set the size of the low-gain avalanche detector, and to set the doping concentration, electrode position and size, voltage, particle properties, and laser properties at each set position on the low-gain avalanche detector. The device electric field calculation module is used to construct a low-gain avalanche detector model based on the size of the low-gain avalanche detector, the doping concentration at each set position, and the position size of the electrode; the low-gain avalanche detector model is divided into multiple micro-elements using the finite element method, and the potential in each micro-element is solved using the finite element solver, and the electric field is solved based on the potential gradient. The charge carrier deposition module is used to obtain the generation and propagation of particles in each micro-element, and to convert the energy deposition generated in each micro-element into charge carrier deposition for exciting charge carriers; The irradiation module is used to provide different irradiation intensities for the low-gain avalanche detector model; The carrier propagation module is used to determine the trajectory of the carriers and record the average capture time of the carriers under different irradiation conditions based on the electric field and the carriers excited in each micro-element; then, based on the Shockley-Lamo theorem and the average capture time of the carriers, it estimates the induced current caused by the carriers generated inside the low-gain avalanche detector model under laser excitation; wherein the carriers are generated on the surface of the low-gain avalanche detector model; the carrier propagation module uses the discrete random solution of the Langevin equation to determine the random trajectory of the carriers; The electronic readout module is used to simulate the electronic readout circuit of the low-gain avalanche detector to process the induced current and obtain simulation results corresponding to different irradiation conditions.

6. The system according to claim 5, characterized in that, When the energy generated within each microelement is equal to the energy of one bandgap width, a pair of charge carriers is excited.

7. The system according to claim 5, characterized in that, The electronic readout module is obtained by simulating the electronic readout circuit of the low-gain avalanche detector using an analog circuit.

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